building scientific apparatus

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BUILDING

SCIENTIFIC

APPARATUS

Fourth Edition

Unrivalled in its coverage and unique in its hands-on

approach, this guide to the design and construction of

scientiﬁc apparatus is essential reading for all scientists and

students in the physical, chemical, and biological sciences

and engineering.

Covering the physical principles governing the opera-

tion of the mechanical, optical and electronic parts of an

instrument, the fourth edition contains new sections on

detectors, low-temperature measurements, high-pressure

apparatus, and updated engineering speciﬁcations. There

are over 400 ﬁgures and tables to permit speciﬁcation of

the components of apparatus, many new to this edition.

Data on the properties of materials and components used

by manufacturers are included. Mechanical, optical, and

electronic construction techniques carried out in the labo-

ratory, as well as those let out to specialized shops, are also

described. Step-by-step instruction, supported by many

detailed ﬁgures, is given for laboratory skills such as sol-

dering electrical components, glassblowing, brazing,

and polishing.

john h. moore is Professor Emeritus at the University of

Maryland. He is a Fellow of the American Physical Society and

the American Association for the Advancement of Science.

His research has included plasma chemistry, high-energy electron

scattering, and the design and fabrication of instruments for use in

the laboratory and on spacecraft.

christopher c. davis is Professor of Electrical and Com-

puter Engineering at the University of Maryland. He is a Fellow of

the Institute of Physics, and a Fellow of the Institute of Electrical and

Electronics Engineers. Currently his research deals with free space

optical and directional RF communication systems, plasmonics,

near-ﬁeld scanning optical microscopy, chemical and biological

sensors, interferometry, optical systems, bioelectromagnetics, and

RF dosimetry.

michael a. coplan is Professor and Director of the Chem-

ical Physics Program at the University of Maryland. He is a Fellow of

the American Physical Society and has research programs in space

science, electron scattering, and neutron detection.

sandra c. greer is Professor Emerita of Chemistry and Bio-

chemistry and Professor of Chemical and Biomolecular Engineer-

ing at the University of Maryland and is now Provost and Dean of

the Faculty at Mills College in Oakland, California. She is a Fel-

low of the American Physical Society and the American Associ-

ation for the Advancement of Science, and recipient of the

American Chemical Society Francis P. Garvan–John M. Olin

Medal.

Building Scientiﬁc Apparatus covers a wide range of topics

critical to the construction, use, and understanding of sci-

entiﬁc equipment. It serves as a reference to a wealth of

technical information, but is also written in a familiar style

that makes it accessible as an introductory text. This new

edition includes updates throughout, and will continue to

serve as a bookshelf standard in laboratories around the

world. I never like to be too far from this book!

Jason Hafner, Rice University, Houston, Texas

For many years, Building Scientiﬁc Apparatus has been the

ﬁrst book I reach for to remind myself of an experimental

technique, or to start learning a new one. And it has been

one of the ﬁrst references I’ve recommended to new stu-

dents. With valuable additions (e.g. tolerances table for

machining, formula for aspheric lenses, expanded infor-

mation on detector signal-to-noise ratios, solid-state

detectors...) and updated lists of suppliers, the newest

addition will be a welcome replacement for our lab’s

well-thumbed previous editions of BSA.

Brian King, McMaster University, Canada

I like this book a lot. It is comprehensive in its coverage of

a wide range of topics that an experimentalist in the phys-

ical sciences may encounter. It usefully extends the scope

of previous editions and highlights new technical develop-

ments and ways to apply them. The authors share a rich

pool of knowledge and practical expertise and they have

produced a unique and authoritative guide to the building

of scientiﬁc apparatus. The book provides lucid descrip-

tions of underlying physical principles. It is also full of

hands-on advice to enable the reader to put these principles

into practice. The style of the book is very user-friendly

and the text is skillfully illustrated and informed by numer-

ous ﬁgures. The book is a mine of useful information

ranging from tables of the properties of materials to lists

of manufacturers and suppliers. This book would be an

invaluable resource in any laboratory in the physical sci-

ences and beyond.

George King, University of Manchester

The construction of novel equipment is often a prerequi-

site for cutting-edge scientiﬁc research. Jack Moore and

his coauthors have made this task easier and more efﬁ-

cient by co ncentrating several careers’ worth of equip-

ment-building experience into a singl e volume – a

thoroughly revised and updated edition of a 25-year-old

classic. Covering areas ranging from glassblowing to

electron optics and from temperature controllers to

lasers, the invaluable information in this book is destined

to save years of collective frustration for students and

scientists. It is a ‘‘must-have’’ on the sh elf of every

research lab.

Nicholas Spencer, Eidgeno

ssische Technische

Hochschule, Zu

rich.

This book is a unique resource for the beginning experi-

menter, and remains valuable throughout a scientist’s

career. Professional engineers I know also own and enjoy

using the book.

Eric Zimmerman, University of Colorado at Boulder,

Colorado

BUILDING

SCIENTIFIC

APPARATUS

Fourth Edition

John H. Moore F Christopher C. Davis F Michael A. Coplan,

with

a chapter by Sandra C. Greer

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,

São Paulo, Delhi, Dubai, Tokyo

Cambridge University Press

The Edinburgh Building, Cambridge CB2 8RU, UK

First published in print format

ISBN-13 978-0-521-87858-6

ISBN-13 978-0-511-58009-3

2009

Information on this title: www.cambrid

e.or

/9780521878586

This publication is in copyright. Subject to statutory exception and to the

provision of relevant collective licensing agreements, no reproduction of any part

may take place without the written permission of Cambridge University Press.

Cambridge University Press has no responsibility for the persistence or accuracy

of urls for external or third-party internet websites referred to in this publication,

and does not guarantee that any content on such websites is, or will remain,

accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

eBook

(

EBL

)

Hardback

To our families

CONTENTS

Preface xiii

MECHANICAL DESIGN AND

FABRICATION

1.1 Tools and Shop Processes 2

1.1.1 Hand Tools 2

1.1.2 Machines for Making Holes 2

1.1.3 The Lathe 4

1.1.4 Milling Machines 7

1.1.5 Electrical Discharge Machining (EDM) 9

1.1.6 Grinders 9

1.1.7 Tools for Working Sheet Metal 10

1.1.8 Casting 10

1.1.9 Tolerance and Surface Quality for Shop Processes 12

1.2 Properties of Materials 12

1.2.1 Parameters to Specify Properties of Materials 13

1.2.2 Heat Treating and Cold Working 14

1.2.3 Effect of Stress Concentration 16

1.3 Materials 18

1.3.1 Iron and Steel 18

1.3.2 Nickel Alloys 20

1.3.3 Copper and Copper Alloys 21

1.3.4 Aluminum Alloys 22

1.3.5 Other Metals 22

1.3.6 Plastics 23

1.3.7 Glasses and Ceramics 24

1.4 Joining Materials 25

1.4.1 Threaded Fasteners 25

1.4.2 Rivets 28

1.4.3 Pins 29

1.4.4 Retaining Rings 29

1.4.5 Soldering 30

1.4.6 Brazing 31

1.4.7 Welding 33

1.4.8 Adhesives 34

1.4.9 Design of Joints 34

1.4.10 Joints in Piping and Pressure Vessels 37

1.5 Mechanical Drawing 39

1.5.1 Drawing Tools 39

1.5.2 Basic Principles of Mechanical Drawing 40

1.5.3 Dimensions 44

1.5.4 Tolerances 46

1.5.5 From Design to Working Drawings 48

1.6 Physical Principles of Mechanical Design 49

1.6.1 Bending of a Beam or Shaft 50

1.6.2 Twisting of a Shaft 52

1.6.3 Internal Pressure 52

1.6.4 Vibration of Beams and Shafts 54

1.6.5 Shaft Whirl and Vibration 55

1.7 Constrained Motion 57

1.7.1 Kinematic Design 57

1.7.2 Plain Bearings 59

1.7.3 Ball Bearings 60

1.7.4 Linear-Motion Bearings 61

1.7.5 Springs 62

1.7.6 Flexures 63

Cited References 66

General References 66

Chapter 1 Appendix 68

vii

WORKING WITH GLASS 76

2.1 Properties of Glasses 76

2.1.1 Chemical Composition and Chemical Properties of Some

Laboratory Glasses 76

2.1.2 Thermal Properties of Laboratory Glasses 77

2.1.3 Optical Properties of Laboratory Glassware 78

2.1.4 Mechanical Properties of Glass 78

2.2 Laboratory Components Available in

Glass

2.2.1 Tubing and Rod 78

2.2.2 Demountable Joints 79

2.2.3 Valves and Stopcocks 80

2.2.4 Graded Glass Seals and Glass-to-Metal Seals 81

2.3 Laboratory Glassblowing Skills 81

2.3.1 The Glassblower’s Tools 81

2.3.2 Cutting Glass Tubing 82

2.3.3 Pulling Points 83

2.3.4 Sealing Off a Tube: The Test-Tube End 84

2.3.5 Making a T-Seal 85

2.3.6 Making a Straight Seal 87

2.3.7 Making a Ring Seal 87

2.3.8 Bending Glass Tubing 88

2.3.9 Annealing 88

2.3.10 Sealing Glass to Metal 89

2.3.11 Grinding and Drilling Glass 91

Cited References 92

General References 92

VACUUM TECHNOLOGY 93

3.1 Gases 93

3.1.1 The Nature of the Residual Gases in a Vacuum

System 93

3.1.2 Gas Kinetic Theory 93

3.1.3 Surface Collisions 95

3.1.4 Bulk Behavior versus Molecular Behavior 95

3.2 Gas Flow 95

3.2.1 Parameters for Specifying Gas Flow 95

3.2.2 Network Equations 96

3.2.3 The Master Equation 96

3.2.4 Conductance Formulae 97

3.2.5 Pumpdown Time 98

3.2.6 Outgassing 98

3.3 Pressure and Flow Measurement 98

3.3.1 Mechanical Gauges 98

3.3.2 Thermal-Conductivity Gauges 100

3.3.3 Viscous-Drag Gauges 101

3.3.4 Ionization Gauges 101

3.3.5 Mass Spectrometers 103

3.3.6 Flowmeters 103

3.4 Vacuum Pumps 104

3.4.1 Mechanical Pumps 105

3.4.2 Vapor Diffusion Pumps 109

3.4.3 Entrainment Pumps 112

3.5 Vacuum Hardware 115

3.5.1 Materials 115

3.5.2 Demountable Vacuum Connections 118

3.5.3 Valves 120

3.5.4 Mechanical Motion in the Vacuum System 123

3.5.5 Traps and Bafﬂes 124

3.5.6 Molecular Beams and Gas Jets 127

3.5.7 Electronics and Electricity in Vacuo 130

3.6 Vacuum-System Design and

Construction

131

3.6.1 Some Typical Vacuum Systems 132

3.6.2 Differential Pumping 138

3.6.3 The Construction of Metal Vacuum Apparatus 139

3.6.4 Surface Preparation 142

3.6.5 Leak Detection 143

3.6.6 Ultrahigh Vacuum 144

Cited References 145

General References 145

OPTICAL SYSTEMS 147

4.1 Optical Terminology 147

4.2 Characterization and Analysis of Optical

Systems

150

4.2.1 Simple Reﬂection and Refraction Analysis 150

4.2.2 Paraxial-Ray Analysis 151

4.2.3 Nonimaging Light Collectors 162

4.2.4 Imaging Systems 162

4.2.5 Exact Ray Tracing and Aberrations 166

4.2.6 The Use of Impedances in Optics 174

4.2.7 Gaussian Beams 179

viii CONTENTS

4.3 Optical Components 182

4.3.1 Mirrors 182

4.3.2 Windows 187

4.3.3 Lenses and Lens Systems 187

4.3.4 Prisms 196

4.3.5 Diffraction Gratings 201

4.3.6 Polarizers 204

4.3.7 Optical Isolators 211

4.3.8 Filters 212

4.3.9 Fiber Optics 217

4.3.10 Precision Mechanical Movement Systems 219

4.3.11 Devices for Positional and Orientational Adjustment

of Optical Components 222

4.3.12 Optical Tables and Vibration Isolation 229

4.3.13 Alignment of Optical Systems 229

4.3.14 Mounting Optical Components 230

4.3.15 Cleaning Optical Components 232

4.4 Optical Materials 236

4.4.1 Materials for Windows, Lenses, and Prisms 236

4.4.2 Materials for Mirrors and Diffraction Gratings 245

4.5 Optical Sources 247

4.5.1 Coherence 248

4.5.2 Radiometry: Units and Deﬁnitions 248

4.5.3 Photometry 249

4.5.4 Line Sources 250

4.5.5 Continuum Sources 252

4.6 Lasers 261

4.6.1 General Principles of Laser Operation 267

4.6.2 General Features of Laser Design 268

4.6.3 Speciﬁc Laser Systems 270

4.6.4 Laser Radiation 283

4.6.5 Coupling Light from a Source to an Aperture 284

4.6.6 Optical Modulators 287

4.6.7 How to Work Safely with Light Sources 289

4.7 Optical Dispersing Instruments 291

4.7.1 Comparison of Prism and Grating Spectrometers 293

4.7.2 Design of Spectrometers and Spectrographs 295

4.7.3 Calibration of Spectrometers and Spectrographs 299

4.7.4 Fabry–Perot Interferometers and Etalons 299

4.7.5 Design Considerations for Fabry–Perot Systems 308

4.7.6 Double-Beam Interferometers 309

Endnotes 314

Cited References 314

General References 318

CHARGED-PARTICLE OPTICS 324

5.1 Basic Concepts of Charged-Particle

Optics

324

5.1.1 Brightness 324

5.1.2 Snell’s Law 325

5.1.3 The Helmholtz–Lagrange Law 325

5.1.4 Vignetting 326

5.2 Electrostatic Lenses 327

5.2.1 Geometrical Optics of Thick

Lenses 327

5.2.2 Cylinder Lenses 329

5.2.3 Aperture Lenses 331

5.2.4 Matrix Methods 332

5.2.5 Aberrations 333

5.2.6 Lens Design Example 336

5.2.7 Computer Simulations 338

5.3 Charged-Particle Sources 338

5.3.1 Electron Guns 338

5.3.2 Electron-Gun Design

Example 341

5.3.3 Ion Sources 343

5.4 Energy Analyzers 345

5.4.1 Parallel-Plate Analyzers 346

5.4.2 Cylindrical Analyzers 347

5.4.3 Spherical Analyzers 348

5.4.4 Preretardation 350

5.4.5 The Energy-Add Lens 350

5.4.6 Fringing-Field Correction 352

5.4.7 Magnetic Energy Analyzers 353

5.5 Mass Analyzers 354

5.5.1 Magnetic Sector Mass

Analyzers 354

5.5.2 Wien Filter 354

5.5.3 Dynamic Mass Spectrometers 355

5.6 Electron- and Ion-Beam Devices:

Construction

355

5.6.1 Vacuum Requirements 355

5.6.2 Materials 356

5.6.3 Lens and Lens-Mount Design 357

5.6.4 Charged-Particle Detection 358

5.6.5 Magnetic-Field Control 358

Cited References 360

CONTENTS ix

ELECTRONICS 362

6.1 Preliminaries 362

6.1.1 Circuit Theory 362

6.1.2 Circuit Analysis 365

6.1.3 High-Pass and Low-Pass Circuits 369

6.1.4 Resonant Circuits 372

6.1.5 The Laplace-Transform Method 374

6.1.6 RLC Circuits 377

6.1.7 Transient Response of Resonant Circuits 378

6.1.8 Transformers and Mutual Inductance 379

6.1.9 Compensation 380

6.1.10 Filters 380

6.1.11 Computer-Aided Circuit Analysis 381

6.2 Passive Components 382

6.2.1 Fixed Resistors and Capacitors 383

6.2.2 Variable Resistors 384

6.2.3 Transmission Lines

6.2.4 Coaxial Connectors

6.2.5 Relays

6.3 Active Components 402

6.3.1 Diodes 403

6.3.2 Transistors 406

6.3.3 Silicon-Controlled Rectiﬁers 419

6.3.4 Unijunction Transistors 420

6.3.5 Thyratrons 421

6.4 Ampliﬁers and Pulse Electronics 421

6.4.1 Deﬁnition of Terms 421

6.4.2 General Transistor-Ampliﬁer Operating

Principles 424

6.4.3 Operational-Ampliﬁer Circuit Analysis 428

6.4.4 Instrumentation and Isolation Ampliﬁers 432

6.4.5 Stability and Oscillators 434

6.4.6 Detecting and Processing Pulses 435

6.5 Power Supplies 441

6.5.1 Power-Supply Speciﬁcations 442

6.5.2 Regulator Circuits and Programmable Power

Supplies 443

6.5.3 Bridges 445

6.6 Digital Electronics 447

6.6.1 Binary Counting 447

6.6.2 Elementary Functions 447

6.6.3 Boolean Algebra 448

6.6.4 Arithmetic Units 448

6.6.5 Data Units 448

6.6.6 Dynamic Systems 450

6.6.7 Digital-to-Analog Conversion 453

6.6.8 Memories 458

6.6.9 Logic and Function 460

6.6.10 Implementing Logic Functions 464

6.7 Data Acquisition 467

6.7.1 Data Rates 467

6.7.2 Voltage Levels and Timing 469

6.7.3 Format 469

6.7.4 System Overhead 470

6.7.5 Analog Input Signals 472

6.7.6 Multiple Signal Sources: Data Loggers 474

6.7.7 Standardized Data-Acquisition Systems 474

6.7.8 Control Systems 479

6.7.9 Personal Computer (PC) Control of Experiments 482

6.8 Extraction of Signal from Noise 491

6.8.1 Signal-to-Noise Ratio 491

6.8.2 Optimizing the Signal-to-Noise Ratio 492

6.8.3 The Lock-In Ampliﬁer and Gated Integrator or

Boxcar 493

6.8.4 Signal Averaging 494

6.8.5 Waveform Recovery 495

6.8.6 Coincidence and Time-Correlation Techniques 496

6.9 Grounds and Grounding 500

6.9.1 Electrical Grounds and Safety 500

6.9.2 Electrical Pickup: Capacitive Effects 503

6.9.3 Electrical Pickup: Inductive Effects 504

6.9.4 Electromagnetic Interference and r.f.i 505

6.9.5 Power-Line-Coupled Noise 505

6.9.6 Ground Loops 506

6.10 Hardware and Construction 508

6.10.1 Circuit Diagrams 508

6.10.2 Component Selection and Construction Techniques 508

6.10.3 Printed Circuit Boards 513

6.10.4 Wire Wrapä Boards 523

6.10.5 Wires and Cables 524

6.10.6 Connectors 528

6.11 Troubleshooting

6.11.1 General Procedures

6.11.2 Identifying Parts 535

Cited References 537

General References 538

Chapter 6 Appendix 541

x CONTENTS

388

399

401

533

DETECTORS 547

7.1 Optical Detectors 547

7.2 Noise in Optical Detection Process 548

7.2.1 Shot Noise 548

7.2.2 Johnson Noise 549

7.2.3 Generation-Recombination (gr) Noise 549

7.2.4 1/f Noise 549

7.3 Figures of Merit for Detectors 550

7.3.1 Noise-Equivalent Power 550

7.3.2 Detectivity 550

7.3.3 Responsivity 551

7.3.4 Quantum Efﬁciency 552

7.3.5 Frequency Response and Time Constant 553

7.3.6 Signal-to-Noise Ratio 553

7.4 Photoemissive Detectors 554

7.4.1 Vacuum Photodiodes 554

7.4.2 Photomultipliers 555

7.4.3 Photocathode and Dynode Materials 556

7.4.4 Practical Operating Considerations for Photomultiplier

Tubes 561

7.5 Photoconductive Detectors 566

7.6 Photovoltaic Detectors

(Photodiodes)

572

7.6.1 Avalanche Photodiodes 574

7.6.2 Geiger Mode Avalanche Photodetectors 577

7.7 Detector Arrays 578

7.7.1 Reticons 578

7.7.2 Quadrant Detectors 578

7.7.3 Lateral Effect Photodetectors 578

7.7.4 Imaging Arrays 580

7.7.5 Image Intensiﬁers 581

7.8 Signal-to-Noise Ratio Calculations 582

7.8.1 Photomultipliers 582

7.8.2 Direct Detection with p–i–n Photodiodes 582

7.8.3 Direct Detection with APDs 584

7.8.4 Photon Counting 585

7.9 Particle and Ionizing Radiation

Detectors

585

7.9.1 Solid-State Detectors 589

7.9.2 Scintillation Counters 591

7.9.3 X-Ray Detectors 591

7.10 Thermal Detectors 591

7.10.1 Thermopiles 593

7.10.2 Pyroelectric Detectors 593

7.10.3 Bolometers 594

7.10.4 The Golay Cell 595

7.11 Electronics to be Used With Detectors 596

7.12 Detector Calibration 597

Endnotes 597

Cited References 597

General References 599

MEASUREMENT AND CONTROL OF

TEMPERATURE

600

8.1 The Measurement of Temperature 600

8.1.1 Expansion Thermometers 601

8.1.2 Thermocouples 602

8.1.3 Resistance Thermometers 605

8.1.4 Semiconductor Thermometers 609

8.1.5 Temperatures Very Low: Cryogenic

Thermometry 610

8.1.6 Temperatures Very High 611

8.1.7 New, Evolving, and Specialized Thermometry 612

8.1.8 Comparison of Main Categories of

Thermometers 612

8.1.9 Thermometer Calibration 612

8.2 The Control of Temperature 613

8.2.1 Temperature Control at Fixed Temperatures 613

8.2.2 Temperature Control at Variable Temperatures 613

Cited References 621

General References 623

Index 625

CONTENTS xi

PREFACE

Building Scientiﬁc Apparatus provides an overview of the

physical principles that one must grasp to make useful and

creative decisions in the design of scientiﬁc apparatus. We

also describe skills, such as mechanical drawing, circuit

analysis, and optical ray-tracing and matrix methods

that are required to design an instrument. A large part

of the text is devoted to components. For each class of

components – electrical, optical, thermal and so on – the

parameters used by manufacturers to specify their products

are deﬁned. Useful materials and components such as

infrared detectors, metal alloys, optical materials, and

operational ampliﬁers are discussed, and examples and

performance speciﬁcations are given. Of course, having

designed an apparatus and chosen the necessary compo-

nents, one must build it. We deal in considerable detail

with basic laboratory skills: soldering electrical compo-

nents, glassblowing, brazing, polishing, and so on.

Described in lesser detail are operations such as lathe turn-

ing, milling, casting, laser cutting, and printed-circuit pro-

duction, which one might let out to an outside shop.

Understanding the capabilities and limitations of shop pro-

cesses is necessary to fully exploit them in designing and

building an instrument. Overall, we recognize that there

are many engineering and technical texts that cover every

aspect of instrument design; our goal in Building Scientiﬁc

Apparatus has been to winnow the available information

down to the essentials required for practical work by the

designer and builder of scientiﬁc instruments.

In the 25 years since Building Scientiﬁc Apparatus ﬁrst

appeared, there have been profound changes in the way in

which unique apparatus is assembled, as well as in the

scientists who require unique apparatus. Twenty-ﬁve years

ago the technology discussed in the ﬁrst edition – optics,

electronics, charged-particle beams, and vacuum systems –

was generally the purview of engineers. Today sophisti-

cated apparatus is conceived of and built by chemists,

physicists, and biologists, as well as medical and social

scientists. In the past, microprocessors were a component

that needed to be programmed and wired into an apparatus.

Now computer controls are an integral part of devices such

as power supplies, pressure gauges, and machine tools.

Similarly, lasers were once assembled in the lab from indi-

vidual optical components; today a complete laser is itself

a component, less expensive than the elements from which

it is assembled. The fourth edition of Building Scientiﬁc

Apparatus recognizes this evolution in the complexity of

available components and the concomitant implications

for the instrument designer.

We acknowledge the importance that the World Wide

Web has acquired as a resource for research. Throughout

the text we mention particular suppliers of materials and

components. There are certainly many that have escaped

our attention. The suppliers of equipment, devices, com-

ponents, and materials along with speciﬁcations, availabil-

ity, and cost can be readily located using a suitable search

engine.

This book was written with the goal of contributing to

the quality and functionality of apparatus designed and

built for research in disciplines from the engineering and

physical sciences to the life sciences. We welcome com-

ments; many suggestions from the past have been incorpo-

rated in the current text.

xiii

MECHANICAL DESIGN AND FABRICATION

Every scientiﬁc apparatus requires a mechanical structure,

even a device that is fundamentally electronic or optical in

nature. The design of this structure determines to a large

extent the usefulness of the apparatus. It follows that a

successful scientist must acquire many of the skills of

the mechanical engineer in order to proceed rapidly with

an experimental investigation.

The designer of research apparatus must strike a balance

between the makeshift and the permanent. Too little initial

consideration of the expected performance of a machine

may frustrate all attempts to get data. Too much time spent

planning can also be an error, since the performance of a

research apparatus is not entirely predictable. A new

machine must be built and operated before all the short-

comings in its design are apparent.

The function of a machine should be speciﬁed in some

detail before design work begins. One must be realistic in

specifying the job of a particular device. The introduction

of too much ﬂexibility can hamper a machine in the per-

formance of its primary function. On the other hand, it may

be useful to allow space in an initial design for anticipated

modiﬁcations. Problems of assembly and disassembly

should be considered at the outset, since research equip-

ment rarely functions properly at ﬁrst and often must be

taken apart and reassembled repeatedly.

Make a habit of studying the design and operation of

machines. Learn to visualize in three dimensions the size

and positions of the parts of an instrument in relation to

one another.

Before beginning a design, learn what has been done

before. It is a good idea to build and maintain a library

of commercial catalogs in order to be familiar with what is

available from outside sources. Too many scientiﬁc

designers waste time and money on the reinvention of

the wheel and the screw. Use nonstandard parts only when

their advantages justify the great cost of one-off con-

struction in comparison with mass production. Consider

modiﬁcations of a design that will permit the use of stand-

ardized parts. An evening spent leaﬁng through the catalog

of one of the major tool and hardware suppliers can be

remarkably educational – catalogs from McMaster-Carr

or W. M. Berg, for example, each list over 200 000 stand-

ard fasteners, bearings, gears, mechanical and electrical

parts, tools etc.

Become aware of the available range of commercial

services. In most big cities, specialty job shops perform

such operations as casting, plating, and heat-treating inex-

pensively. In many cases it is cheaper to have others pro-

vide these services rather than attempt them oneself. Some

of the thousands of suppliers of useful services, as well as

manufacturers of useful materials, are noted throughout

the text.

In the following sections we discuss the properties of

materials and the means of joining materials to create a

machine. The physical principles of mechanical design are

presented. These deal primarily with controlling the

motion of one part of a machine with respect to another,

both where motion is desirable and where it is not. There

are also sections on machine tools and on mechanical

drawing. The former is mainly intended to provide enough

information to enable the scientist to make intelligent use

of the services of a machine shop. The latter is presented in

sufﬁcient detail to allow effective communication with

people in the shop.

CHAPTER

1.1 TOOLS AND SHOP PROCESSES

A scientist must be able to make proper use of hand tools to

assemble and modify research apparatus. A successful

experimentalist should be able to perform elementary

operations safely with a drill press, lathe, and milling

machine in order to make or modify simple components.

Even when a scientist works with instruments that are

fabricated and maintained by research technicians and

machinists, an elementary knowledge of machine-tool

operations will allow the design of apparatus that can

be constructed with efﬁciency and at reasonable cost.

The following is intended to familiarize the reader with

the capabilities of various tools. Skill with machine tools

is best acquired under the supervision of a competent

machinist.

1.1.1 Hand Tools

A selection of hand tools for the laboratory is given in

Table 1.1. A research scientist in physics or chemistry will

hav

e use for most of these tools, and if possible should

have the entire set in the lab. The tool set outlined in Table

1.1 is not too expensive for any scientist to have on hand.

laboratory scientist should adopt a craftsman-like atti-

tude toward tools. Far less time is required to ﬁnd and use

the proper tool for a job than will be required to repair the

damage resulting from using the wrong one.

1.1.2 Machines for Making Holes

Holes up to about 25 mm (1 in.) diameter are made using

a twist drill (Figure 1.1) in a drill press. A boring

bar

Table 1.1 Tool Set for Laboratory Use

Screwdrivers:

No. 1, 2, and 3 drivers for slotted-head screws

No. 1, 2, and 3 Phillips screwdrivers

Allen (hex) drivers for socket-head screws, both a

fractional set (1/16–1/4 in.) and a metric set (1.5–10 mm)

Nut drivers for hex-head screws and nuts, both fractional

(1/8–1/2 in.) and metric (4–11 mm)

Set of jeweller’s screwdrivers

Wrenches:

Combination box and open-end wrenches, both a

fractional set (3/8–1 in.) and a metric set (10–19 mm)

3/8 in. square-drive ratcheting socket driver with both

fractional (3/8–7/8 in.) and metric (10–19 mm) socket sets

Adjustable wrenches (small, medium, and large)

Pipe wrench

Pliers:

Slip-joint pliers

Channel-locking pliers

Large and small needle-nose pliers

Large and small diagonal cutters

Small ﬂush cutters

Hemostats

Hammers:

Small and medium ball-peen hammers

Soft-faced hammer with plastic or rubber inserts

Files:

Second-cut, ﬂat, half-round, and round ﬁles with handles

Smooth-cut, ﬂat, half-round, and round ﬁles with handles

Six-piece Swiss-Pattern ﬁle set

Miscellaneous:

Dial caliper or micrometer

Forceps

Sheet-metal shears

Hacksaw

Tubing cutter

Center punch

Scriber

Small machinist’s square

Steel scale

Divider

Tapered hand reamer

Tap wrench with:

4-40 to 1/4-20 UNC and 3 3 0.6 to 12 3 1.75 metric

tap sets

1/8 to 1/2 NPT or 6 mm to 15 mm BPST (metric) pipe

thread tap sets

Electric hand drill motor or small drill press

Drills, 1/16–1/2 in. in 1/32 in. increments, in drill index

Drills, Nos. 1–60, in drill index

Small bench vise

2 MECHANICAL DESIGN AND FABRICATION

(Figure 1.1) is used in a lathe or vertical milling machine to

bore out a drilled hole to make a large hole. Of course,

a hole can be drilled with a twist drill in a handheld

drill motor; this method, although convenient, is not very

accurate and should only be employed when it is not pos-

sible to mount the work on the drill press table.

Twist drills are available in fractional inch sizes and

metric sizes as well as in number and letter series of sizes

at intervals of only a few thousandths of an inch. Sizes

designated by common fractions are available in 1/64 in.

increments in diameters from 1/64 to 1 3/4 in., in 1/32 in.

increments in diameters from 1 3/4 to 2 1/4 in., and in

1/16 in. increments in diameters from 2 1/4 to 3 1/2 in;

metric sizes are available in 0.05 mm increments in diam-

eters from 1.00 mm to 2.50 mm, in 0.10 mm increments

from 2.50 mm to 10.00 mm, and in 0.50 mm increments

from 10.00 mm to 17.50 mm. Number drill sizes are given

in Appendix 1.1. The included angle at the point of a drill

118°. A designer should always choose a hole size that

can be drilled with a standard-size drill, and the shape of the

bottom of a blind hole should be taken to be that left by a

standard drill unless another shape is absolutely necessary.

If many holes of the same size are to be drilled, it may be

worthwhile to alter the drill point to provide the best per-

formance in the material that is being drilled. In very hard

materials the included angle of the point should be increased

to as much as 140°. For soft materials such as plastic or ﬁber

it should be decreased to about 90°. Many shops maintain a

set of drills with points specially ground for drilling in brass.

The included angle of such a drill is 118°, but the cutting

edge is ground so that its face is parallel to the axis of the

drill in order to prevent the drill from digging in.

A drilled hole can be located to within about 0.3 mm

(0.01 in.) by scribing two intersecting lines and making a

punch mark at the intersection. The indentation made by

the punch holds the drill point in place until the cutting

edges ﬁrst engage the material to be drilled. With care,

locational accuracy of 0.03 mm (.001 in.) can be achieved

in a milling machine or jig borer. Locational error is pri-

marily a result of the drill’s ﬂexing as it ﬁrst enters the

material being drilled. This causes the point of the drill to

wander off the center of rotation of the machine driving the

drill; the hole should be started with a center drill (Figure

1.1) that is short and stiff. Once the hole is started, drilling

completed with the chosen twist drill.

A drill tends to produce a hole that is out-of-round and

oversize by as much as 0.2 mm (.005 in.). Also, a drill

point tends to deviate from a straight line as it moves

through the material being drilled. This run-out can

amount to 0.2 mm (.008 in.) for a 6 mm (1/4 in.) drill

making a 25 mm (1 in.) deep hole; more for a smaller

diameter drill. It is particularly difﬁcult to make a round

hole when drilling material that is so thin that the drill

point breaks out on the under side before the shoulder

Figure 1.1 Tools for making and shaping holes.

TOOLS AND SHOP PROCESSES 3

enters the upper side. Clamping the work to a backup block

of similar material alleviates the problem. When roundness

and diameter tolerances are important, it is good practice

to drill a hole slightly undersize and ﬁnish up with the

correct size drill; better yet, the undersized hole can be

accurately sized using a reamer.

Before drilling in a drill press, the location of the hole

should be center-punched and the work should be securely

clamped to the drill-press table. The drill should enter

perpendicular to the work surface. When drilling curved

or canted surfaces, it is best to mill a ﬂat, perpendicular to

the hole axis at the location of the hole.

The speed at which the drill turns is determined by the

maximum allowable surface speed at the outer edge of the bit

as well as the rate at which the drill is fed into the work. The

rate at which a tool cuts is typically speciﬁed as meters per

minute (m/min) or surface feet per minute (sfpm). Suggested

tool speeds are given in Table 1.2. A drill (or any cutting

tool)

should be cooled and lubricated by ﬂooding with solu-

ble cutting oil, kerosene, or other cutting ﬂuid. Brass or

aluminum can be drilled without cutting oil if necessary.

A drilled hole that must be round and straight to close tol-

erances is drilled slightly undersize and then reamed using a

tool such as is shown in Figure 1.1.Reamerswitharound

ank are meant to be grasped in the collet chuck of a mill-

ing machine; the reamer inserted after the drill is removed

from the chuck without moving the work-piece on the bed of

the milling machine. A reamer with a square shank is to be

grasped in a tap handle for use by hand. A hand reamer has a

slight initial taper to facilitate starting the cut. The diameter

tolerance on a reamed hole can be 0.03 mm (.001 in.) or

better. The chamfer (taper) tolerance can be kept to 0.0002

millimeter per millimeter (or 8 microinch per inch) or better.

Tapered drill and reamer sets are available for preparing the

tapered holes for standard taper pins used to secure one part

to another with great and repeatable precision.

A drilled hole can be threaded with a tap (shown in

Figure 1.1). Cutting threads with a tap is usually carried

out

by hand. A tap has a square shank that is clamped in a

tap handle. The tap is inserted in the hole and slowly turned,

cutting as it goes. The tool should be lubricated and should

be backed at least part way out of the hole after each full

turn of cutting in order to clear metal chips from the tool.

Taps are chamfered (tapered) on the end so that the ﬁrst few

teeth do not cut full depth. This makes for smoother cutting

and better alignment. For more precise tapping the tap can

be placed in a drill press with the work-piece held under-

neath. The drill chuck can be rotated by hand to start the tap

off correctly, parallel to the hole. Some drill presses come

with a foot-operated reversing mechanism so that with the

drill operating at a slow speed the correct action of tap–

reverse-tap can be carried out. The chamfer on a tap extends

for nearly 10 teeth in a taper tap, 3 to 5 teeth on a plug tap,

and 1 to 2 teeth on a bottom tap. The ﬁrst two are intended

for threading through a hole, the latter for ﬁnishing the

threads in a blind hole. The hole to be threaded is drilled

with a tap drill with a diameter speciﬁed to allow the tap to

cut threads to about 75% of full depth. Appendix 1.1 gives

p drill sizes for American National and metric threads.

The head of a bolt can be recessed by enlarging the entra-

nce of the bolt hole with a counterbore (shown in Figure 1.1).

keyway slot can be added to a drilled hole or a drilled

hole can be made square or hexagonal by shaping the hole

with a broach (Figure 1.1). A broach is a cutting tool with a

series

of teeth of the desired shape, each successive cutting

edge slightly larger than the one preceding. The broach can

be driven through the hole by a hand-driven or hydraulic

press. In some broaching machines the tool is pulled

through the work. A broach can, at some expense, be

ground to a nonstandard shape. The expense is probably

only justiﬁed if many holes are to be broached.

1.1.3 The Lathe

A lathe (Figure 1.2) is used to produce a surface of revo-

lution such as a cylindrical or conical surface. The work to

Table 1.2 Tool Speeds for High-speed Steel Tools

(Speeds can be increased 2 3 with carbide-tipped tools)

Material m/min (sfpm)

Drill Lathe Mill

Aluminum 60 (200) 100 (300) 120 (400)

Brass 60 (200) 50 (150) 60 (200)

Cast iron 30 (100) 15 (50) 15 (50)

Carbon steel 25 (80) 30 (100) 20 (60)

Stainless steel 10 (30) 30 (100) 20 (60)

Copper 60 (200) 100 (300) 30 (100)

Plastics 30 (100) 60 (200) 60 (200)

4 MECHANICAL DESIGN AND FABRICATION

be turned is grasped by a chuck that is rotated by the driv-

ing mechanism within the lathe headstock. Long pieces are

supported at the free end by a center mounted in the tail-

stock. A cutting tool held atop the lathe carriage is brought

against the work as it turns. As shown in Figure 1.2, the

tool

holder is clamped to the compound rest mounted to a

rotatable table atop the cross-feed that in turn rests on the

carriage. The carriage can be moved parallel to the axis of

rotation along slides or ways on the lathe bed. A cylindri-

cal surface is produced by moving the carriage up or down

the ways, as in the ﬁrst cut illustrated in Figure 1.3. Driving

the

cross-feed produces a face perpendicular to the axis of

rotation; driving the tool with the compound-rest screw

produces a conical surface.

Most lathes have a lead screw along the side of the lathe

bed. This screw is driven in synchronization with the rotat-

ing chuck by the motor drive of the lathe. A groove running

the length of the lead screw can be engaged by a clutch in

the carriage apron to provide power to drive either the

carriage or the cross-feed in order to produce a long uni-

form cut. When cutting threads the lead screw can be

engaged by a split nut in the apron to provide uniform

motion of the carriage.

A variety of attachments are available for securing work

to the spindle in the headstock. Most convenient is the

three-jaw chuck. All three jaws are moved inward and

outward by a single control so that a cylinder placed in

the chuck is automatically centered. A four-jaw chuck with

independently controlled jaws is used to grasp a work-

piece that is not cylindrical or to hold a cylindrical piece

off center. Large irregular work can be bolted to a face

plate that is attached to the lathe spindle. Small round

pieces can be grasped in a collet chuck. A collet is a slotted

tube with an inner diameter of the same size as the work

and a slightly tapered outer surface. The work is clamped

Figure 1.2 A lathe.

Figure 1.3 Cuts made on a lathe.

TOOLS AND SHOP PROCESSES 5

in the collet by a mechanism that draws the collet into a

sleeve mounted in the lathe spindle.

The cutting tool largely determines the quality of work

produced in a lathe. The efﬁciency of the tool bit used in a

lathe depends upon the shape of the cutting edge and the

placement of the tool with respect to the work-piece. A

cutting tool must be shaped to provide a good compromise

between sharpness and strength. The sharpness of the cut-

ting edge is determined by the rake angles indicated in

Figure 1.4. The indicated r

elief angles are required to pre-

vent the noncutting edges and surfaces of the tool from

interfering with the work. Placement of the tool in relation

to the work-piece is illustrated in Figure 1.5.

the past, a machinist was obliged to grind tool steel

stock to the required shape to made a tool bit. Now vir-

tually all work is done with prepared tool bits. These may

be simply ground-to-shape tool bits. Especially sharp,

robust tools are available with sintered tungsten carbide

(so-called ‘‘carbide’’) or diamond tips. Many tools are

made with replaceable carbide inserts. The insert, which

is clamped to the end of the tool, is triangular or square to

provide three or four cutting edges by rotating the insert in

its holder. Examples are illustrated in Figure 1.6.

in drilling, the cutting speed for turning in a lathe

depends upon the material being machined. Cutting speeds

for high-speed steel tools are given in Table 1.2. Modern

carbide-

and ceramic-tipped cutters are much faster than

tool-steel bits; they also produce a cleaner, more precise cut.

Typically, a cut should be 0.1 to 0.3 mm (.003–.010 in.)

deep, although much deeper cuts are permissible for rough

work if the lathe and work-piece can withstand the stress.

Holes in the center of a work-piece may be drilled by

placing a twist drill in the tailstock and driving the drill

into the rotating work with the hand-wheel drive of the

tailstock. The hole should ﬁrst be located with a center

drill (Figure 1.1), or the drill point will wander off center.

Figure 1.4 Tool angles for a right-cutting round-nose tool.

A right-cutting tool has its cutting edge on the right when

viewed from the point end.

Figure 1.5 Placement of tool with respect to the work in a

lathe.

Figure 1.6 (a) Single-point carbide-tipped lathe tool.

(b) Lathe tool with replaceable carbide insert. The insert has

three cutting points.

6 MECHANICAL DESIGN AND FABRICATION

A drill, a lathe tool, or a milling cutter is usually bathed

with a cutting ﬂuid to cool the tool and to produce a

smooth cut. Cutting ﬂuids include soluble oils, mineral

oils, and base oils. Soluble oils form emulsions when

mixed with water and are used for cutting both ferrous

and nonferrous metals, when cooling is most important.

Mineral oils are petroleum products including parafﬁn oils

and kerosene. They are typically used for light, high-speed

cutting. Base oils are inorganic or fatty oils with or without

sulfur-containing additives. Base oils are called for when

making heavy cuts in ferrous materials.

Tolerances of 0.1 mm (.004 in.) can be maintained with

ease when machining parts in a lathe. Diameters accurate

to 60.01 mm (6.0004 in.) can be obtained by a skilled

operator at the expense of considerable time. Any modern

lathe will maintain a straightness tolerance of 0.4 mm/m

(0.005 in/ft) provided the work-piece is stiff enough not to

spring away from the cutting tool.

1.1.4 Milling Machines

Milling, as a machine-tool operation, is the converse of

lathe turning. In milling the work-piece is brought into

contact with a rotating cutter. Typical milling cutters are

illustrated in Figure 1.7.Aplain

milling cutter has teeth

only on the periphery and is used for milling ﬂat surfaces.

A side milling cutter has cutting edges on the periphery

and either one or both ends so that it can be used to mill a

channel or groove. An end mill is rotated about its long

axis and has cutters on both the end and sides. There are

also a number of specially shaped cutters for milling dove-

tail slots, T-slots, and Woodruff key-slots. A ﬂy cutter is

another useful milling tool. It consists of a cylinder with a

single, movable cutting edge and is used for cutting round

holes and milling large ﬂat surfaces. Radial saws are also

used in milling machines for cutting narrow grooves and

for parting off. Ordinary milling cutters are made of tough,

hard steel known as high-speed steel. Other alloys are used

as well, frequently with coatings of titanium nitride (TiN)

or titanium carbonitride (TiCN) for a harder surface and

improved lubricity. Both carbide-tipped cutters and tools

with replaceable carbide inserts are available. Solid car-

bide end mills can be had for about twice the cost of high-

speed steel mills.

There are two basic types of milling machine. The plain

miller has a horizontal shaft, or arbor, on which a cutter is

mounted. The work is attached to a movable bed below the

cutter. The plain miller is typically used to produce a ﬂat

surface or a groove or channel. It is not much used in the

fabrication of instrument components. The vertical mill

has a vertical spindle located over the bed. Milling cutters

can be mounted to an arbor in the spindle of the vertical

Figure 1.7 Milling cutters.

TOOLS AND SHOP PROCESSES 7

mill, or a collet chuck for grasping an end mill can replace

the arbor. Motion of the mill bed in three dimensions is

controlled by hand-wheels. Big machines may have

power-driven beds. An essential accessory for a vertical

mill is a rotating table so that the work-piece can be rotated

under the cutter for cutting circular grooves and for milling

a radius at the intersection of two surfaces.

The two possible cutting operations are illustrated in

Figure 1.7. Climb

milling, in which the cutting edge enters

the work from above, has the advantage of producing a

cleaner cut. Also, climb milling tends to hold the work ﬂat

and deposits chips behind the direction of the cut. There is

however a danger of pulling the work into the cutter and

damaging both the work and the tool. Up milling is pre-

ferred when the work cannot be securely mounted and

when using older, less rigid machines. Cutter speeds are

given in Table 1.2.

Dimensional

accuracy of 60.1 mm (6.004 in.) is easily

achieved in a milling operation; ﬂatness and squareness of

much higher precision are easily maintained. Both the mill

operator and the designer specifying a milled surface

should be aware that milled parts tend to curl after they

are unclamped from the mill bed. This problem is partic-

ularly acute with thin pieces of metal. It can be alleviated

somewhat if cuts are taken alternately on one side and then

the other, ﬁnishing up with a light cut on each side.

The vertical milling machine is the workhorse of the

model shop where instruments are fabricated. A scientist

contemplating the design of a new instrument should

become familiar with the milling machine’s capability and,

if possible, gain at least rudimentary skill in its operation.

Two electronic innovations have signiﬁcantly increased

the utility and ease of operation of the milling machine: the

electronic digital position readout and computer control of

the motion of the mill arbor and the mill bed.

All machine tools suffer from backlash in the mechan-

ical controls. In a milling machine the position of the mill

bed is read off vernier scales on the hand-wheels that

drive the screws that position the bed. In additi on to the

inconveniencecausedbythissort of readout, the operator

must realize that reversing the direction of rotat ion of the

hand-wheel does not instant ly reverse the direction of

travel of the bed, owing to inevitable c learances between

the threads of the drive screw and the nut that it engages.

This backlash must be accounted for in even the roughest

work. The problem is entirely obviated by the ﬁtting of

electronic position s ensors on the bed that read out in

inches or millim eters on displays mounted to t he

machine. This simple innovation signiﬁcantly incre ases

the speed of operation for a skilled operat or, while at the

same time reducing the number of errors. These displays

invariably improve the quality of work of a relatively

unskilled operator.

Even modest shops now use milling machines in which

the bed and arbor are driven by electric motors under com-

puter control – CNC (computer numerical control) machi-

nes. Most modern machinists, working from mechanical

drawings provided by the designer, can efﬁciently program

these machines. The time required is frequently offset by

time saved by the machine operating under computer con-

trol, so in many instances it is quite reasonable to use a

CNC machine for one-off production. This is particularly

true when a complex sequence of bed and arbor motions

is required to turn out a part. Conversely, when a CNC

machine is available, the designer can contemplate many

more complex shapes in a design than would be econo-

mically feasible to produce with manually controlled

machines. An additional advantage for the instrument

designer is that complex parts can initially be turned out

in an inexpensive material, such as polyethylene, to check

shape and ﬁt before the ﬁnal part is machined from some

expensive material.

The ultimate application of computer-controlled machi-

nes is for them to be operated directly by programs pro-

duced by the software the designer employs in the process

of preparing the engineering drawings. This is the integra-

tion of computer-aided design (CAD) with computer-aided

manufacturing (CAM) in a so-called CAD/CAM system.

At present, however, this mode of fabrication is not usually

practical for the scientist-designer. The time involved in

learning to use sophisticated CAD/CAM software, as well

as its cost, cannot be justiﬁed. In addition, few model shops

have machines that can be operated by the output of high-

level CAD programs.

Mills and lathes are both relatively powerful machines.

One cannot expect the machine to stop should rotating

parts of the machine get caught on loose clothing, such

as a shirt cuff or necktie, or, worse, on a limb or digit.

Initial operation of these machines should be under the

guidance of a competent instructor. One must always be

8 MECHANICAL DESIGN AND FABRICATION

certain that the machine is in proper operating condition

and that the work in the machine is securely clamped to the

bed (of the milling machine) or by the jaws (of the lathe

chuck); a loose work-piece can become a projectile. Metal

chips may come ﬂying off the cutting tool; eye protection

is mandatory.

1.1.5 Electrical Discharge Machining

(EDM)

A spark between an electrode and a work-piece will

remove material from the work as a consequence of highly

localized heating and various electron- and ion-impact

phenomena. As improbable as it may seem, the process

of spark erosion has been developed into an efﬁcient and

very precise method for machining virtually any material

that conducts electricity. In electrical discharge machining

(EDM), the electrode and the work-piece are immersed in

a dielectric oil or de-ionized water, a pulsed electrical

potential is applied between the electrode and the work,

and the two are brought into close proximity until sparking

occurs. The dielectric ﬂuid is continuously circulated to

remove debris and to cool the work. The position of the

work-piece is controlled by a computer servo that main-

tains the required gap and moves the work-piece into the

electrode to obtain the desired cut.

There are two types of electrical discharge machines:

the plunge or die-sinking EDM and the wire EDM. The

plunge EDM is used to make a hole or a well. The elec-

trode is the male counterpart to the female concavity pro-

duced in the work. The electrode is machined from

graphite, tungsten, or copper. Making the electrode in the

required shape is a signiﬁcant portion of the entire cost of

the process. The electrode for wire EDM is typically a

vertically traveling copper or copper-alloy wire 0.05 to

0.4 mm (.002 to .012 in.) in diameter. The wire is eroded

as cutting progresses. It comes off a spool to be fed through

the work and is discarded after a single pass. With

two-dimensional horizontal (XY) control of the work-

piece, a cutting action analogous to that of a bandsaw is

obtained. XYZ-control permits the worktable to be tilted

up to 20° so that conical surfaces can be generated.

In an EDM process, the cavity or kerf is always larger

than the electrode. This overcut is highly predictable and

may be as small as 0.03 mm (.001 in.) for wire EDM. As a

consequence, an accuracy of 60.03 mm (6.001 in.) is

routine and an accuracy of 6.003 mm (6.0001 in.) is

possible. Furthermore, EDM produces a very high-quality

ﬁnish; a surface roughness less than 0.0003 mm (12 micro-

inches) RMS (root mean squared) is routinely obtained.

Part of the reason for the great accuracy obtained in

EDM is that there is no force applied to the work and hence

no possibility of the work-piece being deﬂected from the

cutting tool. There is no work-hardening and no residual

stress in the material being cut. The efﬁcacy of EDM is

independent of the hardness of the material of the work.

Tool steel, conductive ceramics such as graphite and car-

bide, and refractory metals such as tungsten are cut with

the same ease as soft aluminum. A particular advantage is

that the material can be heat treated before fabrication

since very little heat is generated in the cutting operation.

A precision CNC electrical discharge machine may cost

in excess of $100 000. As a consequence these machines

are seldom found in the typical university model shop; the

EDM machine has become, however, the workhorse of the

tool-and-die industry. Owing to the cost of the machines

and the fact that, once programmed, they can run virtually

24 hours a day, job shops are usually anxious to have out-

side work to keep the machines running full time and

usually welcome scientists with one-off jobs.

1.1.6 Grinders

Grinders are used for the most accurate work and to pro-

duce the smoothest surface attainable in most machine

shops. A grinding machine is similar to a plain milling

machine except that a grinding wheel rather than a milling

cutter is mounted on the rotating arbor. In most machines

the work is clamped magnetically to the table and the table

is raised until the work touches the grinding wheel. The

table is automatically moved back and forth under the

wheel at a fairly rapid rate. Many lathes incorporate, as

an accessory, a grinder that can be mounted to the com-

pound rest in place of the tool holder, so that cylindrical

and conical surfaces can be ﬁnished by grinding.

Even the hardest steel can be ground, but grinding is

seldom used to remove more than a small fraction of a

millimeter (a few thousandths of an inch) of metal. For

complicated pieces to be made of hardened bronze or steel,

it is advantageous to soften the stock material by annealing,

TOOLS AND SHOP PROCESSES 9

machine it slightly oversize with ordinary cutting tools,

re-harden the material, and then grind the critical surfaces.

A ﬂatness tolerance of 60.003 mm (6.0001 in.) can be

maintained in grinding operations. The average variation

of a ground surface should not exceed 0.001 mm (50

microinches); a surface roughness less than 0.0003 mm

(10 microinches) RMS is possible.

Safety is a primary concern in any grinding operation.

Grinding wheels are typically held together with an inor-

ganic ceramic cement. They are brittle and can fail cata-

strophically. Signiﬁcant forces come into play when

grinding: the centrifugal force on the spinning wheel; the

force generated between the wheel and the work; and espe-

cially the shock produced when the wheel ﬁrst contacts the

work. A guard should enclose the wheel. The exposed por-

tion of the wheel should be no more than necessary to carry

out the operation at hand. The bearings and pilot shaft

supporting the wheel must be in good condition; check

for balance before spinning up; unbalanced forces can be

destructive. The ﬂanges clamping the grinding wheel to the

drive shaft must be correct for the wheel in use. Wheel

speed should not exceed that speciﬁed for the wheel. The

wheel speed is usually speciﬁed as meters per minute (m/

min) or surface feet per minute (sfpm), thus requiring the

operator to calculate the rotational speed required to attain

a speciﬁed linear speed at the outer circumference of the

wheel. In general, the surface speed at the outer edge of an

inorganic-bonded wheel should not exceed about 2000 m/

min (6000 sfpm). In a dry grinding operation an exhaust

system should be in place to carry away the considerable

dust and metal residue that is generated. ANSI standards

for safe grinding operations are given in condensed form in

Machinery’s Handbook Pocket Companion.

1.1.7 Tools for Working Sheet Metal

Most machine shops are equipped with the tools necessary

for making panels, brackets, and rectangular and cylindrical

boxes of sheet metal. The basic sheet-metal processes are

illustrated in Figure 1.8.

Sheet

metal is cut in a guillotine shear. Shears are

designed for making long straight cuts or for cutting out

inside corners. A typical shear can make a cut a meter

in length in sheet metal of up to 1.5 mm (1/16 in.) in

thickness.

A sheet-metal brake is used to bend sheet stock. A typ-

ical instrument-shop brake can accommodate sheet stock

at least a meter wide and up to 1.5 mm (1/16 in.) thick. The

minimum bend radius is equal to the thickness of the sheet

metal. Dimensional tolerances of 1 mm (.04 in.) can be

maintained.

Sheet can be formed into a simple curved surface on a

sheet-metal roll. The roll consists of three long parallel

rollers, one above and two below. Sheet is passed between

the upper roller and the two lower rollers. The upper roller

is driven. The distance between the upper roller and the

lower rollers is adjustable and determines the radius of the

curve that is formed.

Holes can be punched in sheet metal. A sheet-metal

punch consists of a punch, a guide bushing, and a die.

The punch is the male part. The cross section of the punch

determines the shape and size of the hole. The punch is a

close ﬁt into the die, so that sheet metal placed between the

two is sheared by the edge of the punch as it is driven into

the die. Round and square punches are available in standard

sizes. A punch-and-die set to make a nonstandard hole

can be fabricated, but the cost may be justiﬁed only if a

large number of identical holes are required. On the other

hand, a very precisely shaped hole can be made in a punch-

and-die operation since the tools can be made with great

precision.

Sheet metal can be embossed with a stamp and die,

similar to a punch and die except that the die is somewhat

larger than the stamp, so that the metal is formed into the

die rather than sheared off at the edge.

Sheet metal can be formed into surfaces that are ﬁgures

of revolution by spinning. The desired shape is ﬁrst turned

in hard wood in a lathe. A circular sheet-metal blank is

then clamped against the wooden form by a rubber-faced

rotating center mounted in the lathe tailstock. Then as

the wooden form is rotated the sheet metal is gradually

formed over the surface of the wood by pressing against

the sheet with a blunt wooden or brass tool. Spinning

requires few special tools and is economical for one-off

production.

1.1.8 Casting

Sand casting is the most common process used for the

production of a small number of cast parts. Although

10 MECHANICAL DESIGN AND FABRICATION

few instrument shops are equipped to do casting, most

competent machinists can make the required wooden pat-

terns that can then be sent to a foundry for casting in iron,

brass, or aluminum alloy. There are both mechanical and

economical advantages to producing some complicated

parts by casting rather than by building them up from

machined pieces. Very complicated shapes can be pro-

duced economically because the patternmaker works in

wood rather than metal. Castings can be made very rigid

by the inclusion of appropriate gussets and ﬂanges that can

only be produced and attached with difﬁculty in built-up

work. Most parts on an instrument require only a few

accurately located surfaces. In this case the part can be

cast and then only critical surfaces machined.

A designer must understand the sand-casting process in

order to design parts that can be produced by this method.

A sand-casting mold is usually made in two parts, as

shown in Figure 1.9. The lower mold box, called the drag,

ﬁlled with sand, and the wooden pattern is pressed into

the sand. The sand is leveled and dusted with dry parting

sand. Then the upper box, or cope, is positioned over the

lower and packed with sand. The two boxes are separated,

the pattern is removed, and a ﬁlling hole, or sprue, is cut in

the upper mold. A deep hole can be cast by placing a sand

core in the impression, as shown in Figure 1.9(c). Note that

the

pattern has lugs, called core prints, which create a

depression to support the core. The two halves of the mold

are then clamped together and ﬁlled with molten metal.

It is obvious that a part to be cast must include no

involuted surfaces above or below the parting plane, so

that the pattern can be withdrawn from the mold without

damaging the impression. It is also good practice to taper

all protrusions that are perpendicular to the parting plane

to facilitate withdrawal of the pattern from the mold. A

Figure 1.8 Sheet-metal shop processes.

TOOLS AND SHOP PROCESSES 11

taper or draft of 1–2° is adequate. Surfaces to be machined

should be raised to allow for the removal of metal. That

is the purpose of the boss shown in Figure 1.9(d). When

possible,

all parts of the casting should be of the same

thickness to avoid stresses that may build up as the

molten metal solidiﬁes. All corners and edges should be

radiused. With care, a tolerance of 1 mm (.03 in.) can be

maintained.

1.1.9 Tolerance and Surface Quality for

Shop Processes

The designer must decide on the precision and accuracy

required in making each part of an apparatus. Also a deci-

sion must be made about the quality of the surfaces of each

part to assure proper ﬁt and function. It follows that the

capabilities of the various shop processes must be taken into

consideration, as well as the cost of production, to meet

desired tolerances and surface quality (note Figure 1.45).

Prec

ision and accuracy are speciﬁed as the toler-

ance (+/) on each dimension of a part. The surface

roughness is speciﬁed as the RMS (Route Mean Squar ed)

variation in the height of a surface.

Figure 1.10 gives an approximate indication of the tol-

erance

normally obtainable for the shop processes dis-

cussed in this section. Figure 1.11 speciﬁes the surface

quality

normally obtained in various shop process as well

in industrial processes used in the manufacturer of materi-

als from which parts are machined. An important point to

be made here is that it is often possible to use materials as

they come from the supplier without further machining of

the surfaces. It should be noted as well that obtainable

tolerances and surface quality depend upon the size of the

part being made. A tolerance of 60.05mm (6.002 in.)

is easily obtained in a milling operation on a part that is

only a few centimeters across. In a part that is 100 times

larger, a tolerance of 60.5 mm (6.02 in.) is the best that

can be obtained in a milling operation without the expen-

diture of considerable effort.

1.2 PROPERTIES OF MATERIALS

The materials employed in the construction of an appara-

tus – metals, plastics, glass, ceramic, ev en wood – are char-

acterized by their strength, ﬂexibility, hardness, toughness,

Figure 1.9 Sand casting: (a) the pattern and core;

(b) making an impression in the lower mold box; (c) inserting

the sand core in the impression; (d) the ﬁnished casting.

Figure 1.10 Tolerance that can be reasonably maintained

in shop processes for a work-piece dimension of 1 to 10 cm.

(Adapted from ASME, ANSI Std. B4.1-1967)

12 MECHANICAL DESIGN AND FABRICATION

machinability, electrical and thermal conductivity, and so

on. In order to wisely choose a material for a part of an

apparatus, it is essential to understand the ways in which

these properties are speciﬁed, how these properties can be

modiﬁed by heating and working, and how to design to

best exploit these properties.

1.2.1 Parameters to Specify Properties of

Materials

The strength and elasticity of metal are best understood in

terms of a stress–strain curve such as is shown in Figure

1.12. Str

ess is the force applied to the material per unit of

cross-sectional area [MN m

2

, psi (pounds per square

inch)]. This may be a stretching, compressing, shearing,

or twisting force. Direct strain is the change in length per

unit length that occurs in response to an in-line stress

[strain is unitless (cm/cm, in/in) or expressible as a per-

cent]. Shear strain is the sideward displacement per unit

length in response to a transverse stress (again without

units). A torsional stress induces a shear strain. Most met-

als deform in a similar way under compression or elonga-

tion. When a stress is applied to a metal, the initial strain

is elastic and the metal will return to its original dimen-

sions if the stress is removed. Beyond a certain stress how-

ever, plastic strain occurs and the metal is permanently

deformed.

The tensile strength or ultimate strength of a metal is the

stress applied at the maximum of the stress–strain curve.

The metal is very much deformed at this point, so that in

most cases it is impractical to work at such a high load.

A more important parameter for design work is the yield

strength. This is the stress required to produce a stated,

small, plastic strain in the metal – usually 0.2% permanent

deformation. For some materials the elastic limit is speciﬁed.

This is the maximum stress that the material can withstand

without permanent deformation.

The slope of the straight-line portion of the stress–strain

curve is a measure of the stiffness of the material; this is the

modulus of elasticity, E, sometimes referred to as ‘‘Young’s

modulus.’’ It is worthwhile to note that E is about the same

Figure 1.11 Surface quality as RMS variation in surface

height for various machining and production processes.

(Adapted from ASME, ANSI Std. B46.1-1961)

Figure 1.12 Stress–strain curve for a metal.

PROPERTIES OF MATERIALS 13

for all grades of steel (about 210 GN/m

or 30 3 10

psi)

and about the same for all aluminum alloys (about 70

GN/m

or 10 3 10

psi), regardless of the strength or hard-

ness of the alloy. The effect of elastic deformation is

speciﬁed by Poisson’s ratio, l, the ratio of transverse con-

traction per unit dimension of a bar of unit cross-section to

its elongation per unit length, when subjected to a tensile

stress. For most metals, l ¼ 0.3. A modulus of elasticity in

shear or shear modulus, G, is similarly deﬁned for a tor-

sional stress. The shear modulus is typically about one

third of Young’s modulus for a metal.

The hardness of a material is a measure of its resistance

to indentation and is usually determined from the force

required to drive a standard indenter into the surface of

the material or from the depth of penetr ation of an inden-

ter under a standa rdized f orce . The common hardness

scales used for metals are the Brinell hardnes s number

(BHN), the Vickers scale (VHN), and the Rockwell C

scale. Type 304 stai nless steel is about 150 B HN, 160

Vickers , or 0 Rockwell C. A ﬁle is 600 BHN, 650 Vic kers,

or 6 0 Rockwell C. The Shore hardness scale is deter-

mined by the heigh t o f rebo und o f a ste el b all dro ppe d

from a speciﬁed distance above the surface of a material

under tes t. Mineralogi sts and c eramic enginee rs use the

Mohs hardness scale. It is based upon standard materials,

each of which will scratch all materials below it on the

scale. Knoop hardness is used as a measure for very brit-

tle materials or thin sheets, where only a microindenta-

tion with a pyramidal diamond point can be made.

Figure 1.13 shows the approximate relation of the various

rdness sca les .

A designer must consider the machinability of a mate-

rial before specifying its use in the fabrication of a part that

must be lathe-turned or milled. In general, the harder and

stronger a material, the more difﬁcult it is to machine. On

the other hand, soft metals, such as copper and some nearly

pure aluminum alloys, are also difﬁcult to machine

because the metal tends to adhere to the cutting tool and

produce a ragged cut. Some metals are alloyed with other

elements to improve their machinability. Free-machining

steels and brass contain a small percentage of lead or sul-

fur. These additives do not usually affect the mechanical

properties of the metal, but since they have a relatively

high vapor pressure, their out-gassing at high temperature

can pose a problem in some applications.

1.2.2 Heat Treating and Cold Working

The properties of many metals a nd metal al loys ca n be

considerably changed by heat treating or cold working to

modify the chemical or mechanical nature of the granular

structure of the metal.

The e ffect of heat treatment

depends u pon the te mpe rat ure to which th e m ate ria l is

heated relative to the temperatures at which phase tran-

sitions occur in the metal, and the rate at which the metal

is cooled. If the metal is heated above a transition temper-

ature and quickly cooled or quenched, the chemical and

physical structure of the high-temperature phase may be

frozen in, or a transition to a new metastable phase may

occur. Que nching is acc omplished by plunging the heated

part into w ater or o il. This proc es s is usually ca rried out to

harden the metal. Hardened metals can be softened by

annealing, wherein the metal is h eated above the transi-

tion temperature and then slowly cooled. It is frequently

desirable to a nneal hardened metals before machining

and re-harden after working, although hardening and

annealing can result in distortion, owing to differences

in density of the high and low temperature phases. Temper-

ing is an intermediate heat treatment wherein previously

hardened metal is reheated to a temperature below the tran-

sition point in order to relieve stresses and then cooled at a

rate that preserves the desired properties of the hardened

material.

Repeated plastic d eformation w ill reduce the size of

the grai ns or crystallites within the metal. This is cold

working that accompanies bending, rolling, drawing, ham-

mering, and, to a lesser extent, cutting operations. Not

all metals beneﬁt from cold working, but for some the

strength is greatly increased. Because of the annealing

effect, the strength and hardness derived from cold work-

ing begin to disappear as a metal is heated. This occurs

above 250 °C for steel and above 125 °C for aluminum. In

rolling or spinning operations, some metals will work-

harden to such an extent that the material must be periodi-

cally annealed during fabrication to retain its workability.

Cold working reduces the toughness of metal. The surface

of a metal part can be work-hardened, without modifying

the internal structure, by peening or shot blasting and by

some rolling operations. The strength of metal stock may

depend upon the method of manufacture. For example,

14 MECHANICAL DESIGN AND FABRICATION

sheet metal and metal wire are usually much stronger than

the bulk metal because of the work hardening produced by

rolling or drawing.

The surface of a metal part may be chemically modiﬁed

and then heat-treated to increase its hardness while retain-

ing the toughness of the bulk of the material beneath. This

process is called case hardening. The many methods of

case hardening are usually named for the chemical that

is added to the surface. Carburizing (C), cyaniding (C

and N), and nitriding (N) are common processes for case-

hardening steel. Of these, carburizing of low-carbon steel is

most conveniently performed in the lab or shop. The part to

be hardened is packed in bone charcoal or Kasenit in an

open metal box and heated in a furnace to 900 °C (salmon-

red heat). The time in the furnace, from 15 minutes to

several hours, determines the depth of the case. Steel will

absorb carbon by this process to a maximum depth of about

0.4 mm (0.015 in.) The part is removed from the furnace

Figure 1.13 Approximate relation of Brinell (BHN), Rockwell (R

), Vickers

(VHN), Shore, and Mohs hardness scales.

PROPERTIES OF MATERIALS 15

and promptly quenched in water. The quenching hardens

the case, but the core remains tough and ductile.

1.2.3 Effect of Stress Concentration

In choosing a material for a particular job, one must con-

sider not only the stress the part is expected to bear, but

also the way in which the stress is distributed. Careless

design can lead to failure in very strong materials under

relatively light loads if the stress of the load is concentrated

in a small volume.

An abrupt change in the cross-section of a loaded beam

or shaft produces a concentration of stresses, as shown in

Figures 1.14(a) and 1.15(a). For the element in tension

[Figure 1.14(a)] the lines indicate the direction of tensile

force;

this is a so-called ‘‘force ﬂow depiction.’’ For an

element under torsional stress, Figure 1.15(a), the lines

indicate

the cross-section of concentric cylindrical shells

each under the same torque. Stress increases when the force

ﬂow lines or equitorque surfaces become sharply curved

and crowded together . Stress concentrations are located at

steps, grooves, keyways, holes, dents, and scratches. Failure

occurs as a result of shear forces in the region of highest

stress concentration. Anyone who has ever broken a bolt is

familiar with this effect; a bolt invariably fails at the step

where the head joins the shaft. The effects of stress concen-

tration may be especially important in fatigue failure result-

ing from cyclic applications of stress.

Stress is often concentrated in the area of the smallest

radius of curvature of a part, as suggested in Figures

1.14(a) and 1.15(a). This observation explains the manner

which a crack propagates once a part has begun to fail:

the radius of curvature is small at the end of a crack, thus

stress is concentrated at the tip of the crack and further

failure ensues. Increasing the radius of curvature of a stress

riser can mitigate stress concentration. It is often more

practical to introduce features that move the force ﬂow

lines away from the stress riser when it is not possible to

modify the offending aspect. Examples are given in Fig-

ures

1.14 and 1.15.

Threaded

parts are often a problem. The ‘‘V’’ bottom of

the thread groove is an insipient stress riser. As suggested

in Figure 1.16, reducing the diameter of the adjoining

unthreaded

portion of a shaft has the effect of moving

the equitorque surfaces away from the threads.

There are a number of means of detecting stress in a

part. One of the most useful is the photoelastic method.

this technique a transparent plastic model is stressed in the

same way as the element of interest without necessarily

duplicating the magnitude of the stress. The model is illu-

minated with polarized, monochromatic light and viewed

through a polarizer. As shown in Figure 1.17, the stress

distrib

ution appears as fringes in the image; closely spaced

fringes characterize stress concentrations. Most glassblow-

ing shops are equipped with a polarizing device of this type

for detecting residual stresses in worked glass (see Figure

2.16, next chapter).

Figure 1.14 Force ﬂow lines in a beam under

stress: (a) A notch in a beam under tension

concentrates stress in the vicinity of the notch.

(b) and (c) suggest means to mitigate the stress

concentration.

16 MECHANICAL DESIGN AND FABRICATION

In a similar fashion, fabricated parts can be nondestruc-

tively tested by means of holography. A hologram of the

object is made; then the part is stressed and a second holo-

gram is made. The two holograms are then superposed and

placed in the holographic projector. The resulting three-

dimensional image consists of patterns of fringes that are

densest in the areas of greatest distortion in the stressed

object. Holographic nondestructive testing (HNDT) is car-

ried out as a commercial service.

Figure 1.15 A shaft under torsional stress. Lines

indicate concentric equitorque surfaces: (a) A step in

a shaft under a torsional load concentrates stress in

the vicinity of the step. (b) and (c) suggest means to

mitigate the stress concentration.

Figure 1.16 Threads on a shaft may

produce a concentration of stress.

Reducing the diameter of the adjoining

shaft moves the equitorque surfaces

away from the threads.

Figure 1.17 Stress distribution in a transparent plastic

model as observed when the part is illuminated with

polarized light and observed with a crossed polarizer.

PROPERTIES OF MATERIALS 17

A particularly simple and inexpensive means of locating

stress concentrations in a working part has been developed

by Magnaﬂux. The part to be tested is sprayed with a

substance that forms a hard, brittle layer over the surface.

The part is returned to service for a time, and any ﬂexing of

the part causes the surface coating to crack. The part is

then removed and dipped in a dye that permeates the

cracks to reveal the areas where the strain under load

was greatest.

1.3 MATERIALS

We shall discuss in a qualitative manner the properties of

useful metals, plastics and ceramics. Quantitative data are

gathered together in Table 1.3.

1.3.1 Iron and Steel

For instrument work, iron is used primarily as a casting

material. The advantages of cast iron are hardness and a

high degree of internal damping. Cast iron is harder than

most steels and is used for sliding parts, where resistance

to wear is important. The damping capacity of iron, that is,

the ability to dissipate the energy of vibration, is about 10

times that of steel and for this reason the frame of a del-

icate instrument is often made of cast iron.

Cast iron contains a few % carbon. The carbon is in a

free state in gray cast iron, while it is chemically incorpo-

rated into the structure of white cast iron. Gray iron is

inexpensive and easy to machine. Class-30 gray iron has

a Brinell hardness of about 200 BHN. It is, however, rather

brittle and is only about half as strong as steel. White iron

is stronger and harder than gray iron, and thus it is very

wear-resistant. White iron is difﬁcult to machine and is

usually shaped by grinding. The machinability and ductil-

ity of cast irons can be considerably improved by various

heat treatments.

Steel is an iron alloy. There are more than 10 000 differ-

ent types of steel. Steels are classed as cast or wrought

steels depending on the method of manufacture. Wrought

steels are produced by rolling and are almost the only kind

used for one-off machine work. Steels are also classiﬁed as

either carbon steels or alloy steels. Carbon steels are

speciﬁed by a four-digit number. Plain carbon steels are

speciﬁed as 10xx, where xx is a two-digit number that

indicates the carbon content in hundredths of %. In general

the strength and hardness of carbon steel increases with

carbon content, but these properties also depend upon the

nature of the heat treatment and cold working that the

metal has received. Alloy steels containing elements in

addition to carbon have special properties especially useful

for the manufacture of tools and dies. These include, for

example, manganese steels (designated 13xx for tool steel

with 1.8% Mn), nickel alloy steel (23xx, 3.5% Ni; 25xx,

5% Ni), molybdenum steel (40xx, 0.20 % Mo), and so on.

Steels with a carbon content in the 0.10–0.50% range

are referred to as low- and medium-carbon steels or mild

steels. These steels are supplied rolled or drawn and are

most suitable for machine work.

High-carbon steels are difﬁcult to machine and weld,

although their machinability is improved if they are ﬁrst

annealed by heating to 750 °C (orange heat) and cooling

slowly in air. They may be returned to their hard state by

reheating to 750 °C and quenching in water; however, this

process inevitably produces some distortion.

The most common alloy steels are the types known as

stainless steels. The main constituents of stainless steels

are iron, chromium, and nickel. They are classiﬁed as fer-

ritic, martensitic, or austenitic, depending on the nickel

content. The high-nickel austenitic alloys comprise the

200 and 300 series of stainless steels. 300-series stainless

steels are most useful for instrument construction because

of their superior toughness, ductility, and corrosion resist-

ance. The austenitic stainless steels are sensitive to heat

treatment and cold working, although the heat-treatment

processes are rather more complicated than for plain car-

bon steels. For example, quenching from 1000 °C leaves

these steels soft. Cold working, however, can more than

double the strength of the annealed alloy. The heat asso-

ciated with welding of austenitic stainless steels can result

in carbide pr ecipitation at the grain boundaries in the vicinity

of a weld, leaving the weld subject to attack by corrosive

agents. The carbides can be returned to solution by annealing

the steel after welding. There are also some special stainless

steels that do not suffer from carbide precipitation. In general,

stainless steels are more expensi v e than plain carbon steels,

but their superior qualities often of fset the extra cost.

Type 303 is the most machinable of the 300-series

alloys. Type 316 has the greatest resistance to heat and

18 MECHANICAL DESIGN AND FABRICATION

Table 1.3 Properties of Research Materials

Material Density

(kg m

3

)

Yield

Strength

(MN m

2

)

Tensile

Strength

(MN m

2

)

Modulus

of Elasticity

(GN m

2

)

Shear

Modulus

(GN m

2

)

Hardness

Coefﬁcient

of Thermal

Expansion

(10

6

1

)

Comments

Ferrous Metals

Cast gray

iron (ASTM 30)

6990 170 210 90 36 200 BHN 11

1015 steel (hot-ﬁnished) 7850 190 340 200 76 100 BHN 15 Low carbon (0.15% C)

1030 steel (hot-ﬁnished) 7850 250 470 200 76 137 BHN 15 Medium carbon

(0.30% C)

1050 steel (hot-ﬁnished) 7850 340 620 200 76 180 BHN 15 High carbon

(0.50% C)

Type 304 stainless

steel (annealed)

7910 240 590 190 69 150 BHN 17 Austenitic

Type 304 stainless

steel (cold-worked)

7910 520 760 190 69 240 BHN 17 Austenitic

Type 316 stainless

steel (cold-worked)

7910 410 620 190 69 190 BHN 16 Austenitic

Nickel Alloys

Monel 400: 25 °C 8820 170 480 110 BHN 14 Slightly magnetic

500 °C 150 310 180 16

Monel 500: 25 °C 8460 280–1000 600–1200 14 Nonmagnetic

500 °C 620 65 180 140 BHN 16

Inconel 600: 25 °C 8400 250 620 210 12 Strong, resists

high-temperature

oxidation

650 °C 180 450 140 120 BHN 16

Invar (0–100 °C) 8130 160 480 140 140 BHN 1.3 small temperature

coefﬁcient

Aluminum Alloys

1100-0 2760 30 90 70 30 23 BHN 23 99% Al

2024-T4 2710 320 470 70 30 120 BHN 23 3.8% Cu, 1.2% Mg,

0.3% Mn

2024-T4 (200 °C) 2710 80 120

6061-T6 2760 280 310 70 30 95 BHN 23 0.15% Cu, 0.8% Mg,

0.4% Si

7075-T6 2790 500 570 70 30 150 BHN 23 5.1% Zn, 2.1% Mg,

1.2% Cu

Copper Alloys

Yellow brass (annealed) 8460 410 510 100 40 20 65% Cu, 35% Zn

Yellow brass

(cold-worked)

8460 410 510 100 40 150 BHN 20 65% Cu, 35% Zn

Cartridge brass (1/2 hard) 8510 360 480 110 40 145 BHN 20 70% Cu, 30% Zn

Beryllium copper

(precipitation-hardened)

8210 960 1200 130 48 380 BHN 17 98% Cu, 2% Be

MATERIALS 19

corrosion. All of these alloys are fairly nonmagnetic; types

304 and 316 are the least magnetic. Machining and cold

working tends to increase the magnetism of these alloys.

Residual magnetism can be relieved by heating to 1100 °C

[safely above the temperature range (450–900°) where

carbide precipitation occurs] and quenching in water. Thin

pieces that might distort excessively may be quenched in

an air blast.

1.3.2 Nickel Alloys

Nickel alloys are typically tough and strong, and resistant to

corrosion and oxidation. The machining characteristics of

the wrought alloys are similar to those of steel, and they are

readily brazed and welded. Nickel alloys mostly do not go

by a standard speciﬁcation like steel, but rather are referred

to by trade names. These names often allude to an alloy or

Table 1.3. (contd.)

Material Density

(kg m

3

)

Yield

Strength

(MN m

2

)

Tensile

Strength

(MN m

2

)

Modulus

of Elasticity

(GN m

2

)

Shear

Modulus

(GN m

2

)

Hardness

Coefﬁcient

of Thermal

Expansion

(10

6

1

)

Comments

Unalloyed Metals

Copper 8930 70 220 110 45 44 BHN 17

Molybdenum 10200 560 650 320 120 190 VHN 5.4 Refractory, nonmagnetic

Tantalum 16590 330 460 180 70 80 VHN 6.5 Refractory, somewhat

ductile

Tungsten 19270 1520 1520 410 150 350 VHN 5 Refractory, very dense

Plastics

Phenolics 1350 50 7 125 R

81 Bakelite, Formica

Polyethylene (low density) 910 10 0.2 10 R

180

Polyethylene (high density) 940 30 0.8 40 R

216

Polyamide 1110 80 2.8 118 R

90 Nylon

Polymethylmethacrylate 1190 50 2.9 90 R

72 Lucite, Plexiglas

Polytetraﬂuoroethylene 2130 20 0.4 60 R

99 Teﬂon

Polychlorotriﬂuoroethylene 2100 40 1.7 110 R

70 Kel-F

Poly(amide-imide) 1440 150 5.8 80 R

28 Torlon < 200 °C

to 220 °C

Polyimide 1440 80 2.6 45 R

54 Vespel 270 °Cto

290 °C

Polycarbonate 1190 60 2.3 70 R

70 Lexan

Ceramics

Alumina (polycrystalline) 3900 240 330 9 Mohs 8 99% alumina

Macor 2520 30 60 25 400 VHN 13 Corning machinable

ceramic

Steatite 3590 60 100 10.6

Wood

Douglas ﬁr (air-dried) 300 65,3

10 6,35

Typical of softwoods

Oregon white

oak (air-dried)

700 70,6

16 5,55

Typical of hardwoods

BHN ¼ Brinell hardness number; R ¼ Rockwell hardness; VHN ¼ Vickers hardness.

Parallel to ﬁber, across ﬁber.

20 MECHANICAL DESIGN AND FABRICATION

class of alloys that have been designed to optimize a partic-

ular property. Nickel alloys are expensive compared to alloy

steels, but not so much so that they shouldn’t be used when

an instrument can exploit their special properties.

The Monel alloys are nickel–copper alloys whose prop-

erties make them a better choice than austenitic stainless

steels in some applications. The most familiar is Monel

400. It is resistant to attack by both acids and bases and

is sufﬁciently ductile for parts to be fabricated by spin-

ning and stamping. Monel 404 is similar, but it is quite

nonmagnetic, and its magnetic properties are not affected

by cold working. Monel 500 is similarly nonmagnetic and

retains most of its strength up to 500 °C.

Inconel alloys are notable for their strength at high tem-

peratures. The Inconel 600 series of alloys retain their

strength to 700 °C and are very resistant to oxidation at

high temperatures. Inconel 600 is nonmagnetic. The Inconel

700 series are so-called ‘‘superalloys’’ with tensile strengths

on the order of 1000 MN m

2

(150 000 psi). They are used

in highly-stressed parts that will maintain their strength to

1000 °C. They must be heat-treated to obtain the maximum

high-temperature strength. The Inconel 700 alloys, espe-

cially Inconel 702 and Inconel X-750, are nonmagnetic.

The Hastelloy alloys, of which Hastelloy B is most com-

mon, contain primarily nickel and molybdenum and are nearly

as strong as the Inconel 700 alloys and somewhat more duc-

tile. These alloys are notable for their resistance to corrosion.

In certain instances the dimensions of a component of an

instrument must be very stable in the face of variations of

temperature. Iron–nickel alloys containing about 36%

nickel have been found to meet this requirement. Invar

(Carpenter Technology Corp.) is one such alloy. This

material has a coefﬁcient of expansion of 1.3 3 10

6

1

in the range 0 to 100 °C and about twice this at temper-

atures up to 200 °C. Better yet, the alloy Super-Invar (from

Eagle Alloys or High Temp Metals) has a coefﬁcient of

0.3 3 10

6

1

in the range 0 to 100 °C. By comparison,

the coefﬁcient of expansion of stainless steel is about

1.5 3 10

5

1

. One disadvantage of Invar in certain

applications is that it is magnetic below 277 °C.

After being machined, Invar may require stress relieving

to achieve maximum stability. Rosebury

suggests the fol-

lowing heat treatment: heat to about 350 °C for one hour

and allow to cool in air; heat to a temperature slightly above

the operating temperature and cool slowly to a temperature

below the operating temperature; repeat step 2. To achieve

the minimum coefﬁcient of thermal expansion for Super-

Invar, Eagle Alloys recommendthefollowingheat treatment:

hold at 830 °C for 10 minutes, quench rapidly in water or

with an air blast; hold at 315 °C for 60 minutes and then air

cool; hold at 100 °C for 24 hours and then air cool.

Kovar is an iron–nickel–cobalt alloy designed for mak-

ing metal-to-glass seals. Its thermal expansion character-

istics match that of several hard glasses including Corning

7052 and 7056. Unfortunately, Kovar is magnetic and

easily oxidized.

1.3.3 Copper and Copper Alloys

Copper is a soft, malleable metal. Of all metals (short of the

noble metals) it is the best electrical and thermal conductor.

For instrument applications, oxygen-free high-conductivity

(OFHC) copper is preferred because of its high purity and

excellent conductivity and because it is not subject to hydro-

gen embrittlement (see p. 33). Ordinary copper becomes

brittle and porous when exposed to hydrogen at elevated

temperatures such as may occur in welding or brazing.

Alloys of copper are classiﬁed as either brasses or

bronzes. Brass is basically an alloy of copper and zinc.

Generally, brass is much easier to machine than steel but

not quite so strong, and its electrical and thermal coefﬁ-

cients are about half those of pure copper. Its properties

vary considerably with the proportions of copper to zinc,

and also with the addition of small amounts of other ele-

ments. Soldering or brazing readily joins brass parts. Brass

is expensive, but, because it is easy to work, it is well

suited to instrument construction, where the cost of fabri-

cation far outweighs the cost of materials.

For general machine work, yellow brass (35% Zn) is most

suitable. Free-machining brass is similar except that it con-

tains 0.5–3% lead. Cartridge brass (30% Zn) is very ductile

and is suitable for the manufacture of parts by drawing and

spinning, and for rivets. It work-hardens during cold form-

ing and may require periodic annealing to 600 °C. Stresses

that have built up in a cold-formed part during manufacture

can be relieved by heating to 250 °C for an hour.

The name bronze originally meant an alloy of copper

and tin, but the term now also refers to alloys of copper

and many other elements, such as aluminum, silicon,

beryllium, or phosphorus. Bronzes, generally harder and

MATERIALS 21

stronger than brasses, often are of special value to the

designer of scientiﬁc apparatus. Beryllium copper or

beryllium bronze is a versatile material whose properties

can be considerably modiﬁed by heat treatment. In its soft

form it has excellent formability and resistance to fatigue

failure. Careful heat treating will produce a material that

is harder and stronger than most steels. It is useful for the

manufacture of springs and parts that must be corrosion-

resistant. Also it is nearly impossible to strike a spark on

beryllium bronze; this makes it useful for parts to be used

in an explosive atmosphere. Beryllium bronze hand tools

are available for use around explosive materials. Phosphor

bronze cannot be heat-treated, but it is very formable and

has great resistance to fatigue. It is used for bellows and

springs. Aluminum bronze is highly resistant to corrosion

and is strong and tough. It is used in marine applications.

Bronze stock can be manufactured by sintering. Compact-

ing and heating a bronze powder at a temperature below

the melting point produces sintered bronze. It is quite

porous in this form and can be used as a ﬁlter or can be

impregnated with lubricant for use as a bearing.

1.3.4 Aluminum Alloys

Aluminum alloys are valued for their light weight, good

electrical and thermal properties, and excellent machina-

bility. Aluminum is about one third as dense as steel. Its

electrical conductivity is 60% that of copper, but it is a

better conductor per unit weight.

Aluminum is resistant to most corrosive agents except

strong alkalis, owing to an oxide ﬁlm that forms over the

surface. This layer is hard and tenacious, and forms nearly

instantaneously on a freshly exposed surface. Because the

oxide layer is an insulator, electrical connections to alumi-

num parts are problematic. In some applications aluminum

parts can accumulate a surface charge. This problem can

be overcome by copper- or gold-plating critical surfaces.

The oxide layer makes plating difﬁcult, but reliable plating

can be carried out by specialty plating shops. Aluminum

parts cannot be easily soldered or brazed (see, however,

Handy & Harman AL802 ﬂux-cored aluminum solder).

Heliarc or TIG (tungsten inert gas) welding is quite practical

with aluminum (see, for example, the plethora of welded-

aluminum-frame bicycles on the market). Welds in alumi-

num tend to be porous, and welding weakens the metal in

the vicinity of the weld because of the rapid conduction of

heat into the surrounding metal during the operation.

Aluminum stock is produced in cast or wrought form.

Wrought aluminum, produced by rolling, is used for most

machine work. A four-digit number that indicates the com-

position of the alloy, followed by a sufﬁx, beginning with T

or H that speciﬁes the state of heat treatment or work hard-

ness, speciﬁes aluminum alloys. The heat-treatment scale

extends from T0 through T10. T0 indicates that the mate-

rial is dead soft, and T10 that it is fully tempered. The

1000-series alloys are more than 99% aluminum. The

2000-series alloys are aluminum alloyed with copper.

The 6000-series alloys contain magnesium and silicon.

The 7000-series are alloys with zinc. Readily available

stock includes 1100-T0, a soft, formable alloy that is

nearly pure aluminum and is used for extrusions. 2024-

T4 or -T6 is as strong as annealed mild steel and is used

for general machine work. 6061-T6 is not quite so strong

as 2024-T4, but is more easily cold-worked. Its machina-

bility is excellent. The strongest readily available alumi-

num alloy is 7075-T6. It is easily machined; its corrosion

resistance, however, is inferior to that of other alloys.

Aluminum is available as plate, bar, and round and

square tube stock. Aluminum jig plate is useful for instru-

ment construction. This is rolled plate that has been ﬂy-cut

by the manufacturer to a high degree of ﬂatness.

Aluminum may be anodized to give it a pleasing appear-

ance and to improve corrosion resistance. Anodizing of

aluminum is carried out inexpensively by most commer-

cial plating services. A number of proprietary formulas,

such as Birchwood-Casey AlumaBlack, are available to

blacken aluminum to reduce its reﬂectivity. Beware, how-

ever, of difﬁculties in making a reliable electrical connec-

tion to an anodized aluminum surface.

1.3.5 Other Metals

Magnesium alloys are useful because their density i s only

0.23 times that of steel. Magnesium is very stiff per unit

weight, and is completely nonmagnetic. It is very easy

to machine, although there is a ﬁre hazard. Magnesium

chips can be ignit ed, but not the bulk material. The

strength of magnesium alloys is considerably reduced

above 100 °C. The cost of these alloys is at least 10 times

that of steel.

22 MECHANICAL DESIGN AND FABRICATION

Titanium is about half as dense as steel, while titanium

alloys are stronger than steel. Titanium is very resistant

to corrosion and completely nonmagnetic. It is readily

machined, if one proceeds slowly with sharp carbide-

tipped cutters, and can be welded under an inert gas atmos-

phere. Titanium and titanium alloys (99%) are useful for

extreme-temperature service, since they maintain their

mechanical properties from –250 °C to well above 400 °C.

A titanium–manganese alloy (Ti-8Mn; 6.5–9% Mn) retains

a tensile strength greater than 100 000 psi to temperatures

in excess of 400 °C. Its strength and hardness (up to 36 R

)

can be varied considerably by heat treatment. Titanium–

aluminum–vanadium alloy (Ti-6Al-4V; 5.5–6.7% Al; 3.5–

4.5% V) is a similarly strong, versatile material. These

alloys are more easily machined than unalloyed titanium.

Titanium fasteners are available.

Molybdenum is a refractory metal. It exhibits a very low,

uniform, surface potential and is used for fabricating elec-

trodes and electron-optical elements. Molybdenum is brittle

and must be machined slowly using very sharp tools.

Molybdenum is produced from a melt or from a sintered

powder. The sintered stock is very difﬁcult to machine.

Tungsten is the most dense of the readily available ele-

ments. Its density is 2.5 times that of steel. Compact coun-

terweights in scientiﬁc mechanisms are often made of

this material. Tungsten is also used for extreme high-

temperature service, such as torch nozzles and plasma

electrodes. Suppliers of refractory metals such as tungsten

and molybdenum include A. D. Mackay and Philips Elmet.

1.3.6 Plastics

Plastics are classiﬁed as either thermoplastic or thermoset-

ting. Within limits, thermoplastics can be softened by heat-

ing and will return to their original state upon cooling.

Thermosetting plastics undergo a chemical change when

heated during manufacture, and they cannot be re-softened.

Phenol-formaldehyde plastics, or phenolics, are the

most widely used thermosetting plastics. Phenolics are

hard, light in weight, and resistant to heat and chemical

attack. They make excellent electrical insulators. Phe-

nolics are usually molded to shape in manufacture and

typically incorporate a paper or cloth ﬁller. Thus rein-

forced, the phenolic plastics are easily sawn and drilled.

Bakelite is a linen-reinforced phenolic plastic.

Representative thermoplastics include polyethylene,

nylon, Delrin, Plexiglas, Teﬂon, and Kel-F.

Polyethylene is inexpensive, machinable, and very

resistant to attack by most chemicals. It is soft and not

very strong. Its physical properties vary with the molecular

weight and the extent of chain branching within the poly-

mer. It is produced in high-density and low-density forms

that are whitish and translucent, respectively. It is also

manufactured in a blackened form that is not degraded

by ultraviolet radiation, as is the white form. Polyethylene

softens at 90 °C and melts near 110 °C. It can be welded

with a hot wire or a stream of hot air from a heat gun. It can

be cast, although it shrinks a great deal upon solidifying.

Care must be exercised when heating polyethylene

because it will burn. Polyethylene is an excellent electrical

insulator, with a dielectric strength of 40 000 V/mm [1000

V/mil (0.001 in.)].

Nylon, a polyamide, is strong, tough, and very resistant

to fatigue failure. It retains its mechanical strength up to

about 120 °C. It does not cold-ﬂow, and is self-lubricating

and thus is useful for all types of bearing surfaces. Nylon is

available as rod and sheet in both a white and a black form.

Nylon balls and gears are also readily available. There

is no ﬁre hazard with nylon, since it is self-extinguishing.

It is hygroscopic, and its volume increases and strength

decreases somewhat when moisture is absorbed.

Delrin is a polyacetal resin with properties similar to

hard grades of nylon in most respects, except that it is

not hygroscopic.

All plastics are electrical insulators, although the hygro-

scopic ones are liable to surface leakage currents. DuPont

produces a polyamide ﬁlm known as Kapton that is

widely used as an electrical insulator. This material has a

high dielectric strength in thin ﬁlms. It is strong and

tough, resists chemicals and radiation, and is a better ther-

mal conductor than most plastics. It is used in sheets as an

insulator between layers of windings in magnets. Kapton-

insulated wire is available. DuPont also supplies bulk

polyamide in standard shapes under the trade-name Vespel.

This material is relatively hard, strong, and machinable.

It is probably the best plastic material for use in vacuum

because of its low vapor pressure and its high-temperature

stability. Amoco produces a line of engineering plastics

under the name Torlon that are based upon poly(amide-

imide) copolymer. These thermoplastics are very strong

MATERIALS 23

and can be used up to 250 °C. Torlon is also an excellent

choice when plastics must be used in vacuum.

Plexiglas, Lucite, and Perspex are all trade names for

polymethylmethacrylate (PMMA). These materials, also

known as acrylic plastics, are strong, hard, and transparent.

Because they are machinable, heat-formable, and shatter-

resistant, polymethylmethacrylates are used in many appli-

cations as replacements for glass.

Thermoforming of acrylic sheet into curved surfaces is a

fairly simple operation. Begin with a wooden or metal

pattern of the desired shape. Rest the sheet on top of the

pattern, warm the plastic to about 130 °C, and permit grav-

ity to pull the softened sheet down over the form. The

forming may be done in an oven, or the plastic may be

heated with infrared lamps or with hot air from a heat gun.

It is necessary to apply the heat slowly and uniformly.

Polymethylmethacrylate dissolves in a number of

organic solvents. Parts can be cemented by soaking the

edges to be joined in acetone or methylene chloride for

about a minute and then clamping the softened edges

together until the solvent has evaporated.

General Electric manufactures a polycarbonate plastic

known as Lexan. It is transparent and machinable, it has

excellent vacuum properties, and is so tough as to be nearly

unbreakable. It is the preferred plastic replacement for

window glass. Lexan is one of the most useful plastics

for instrument construction.

Teﬂon is a ﬂuorocarbon polymer. It is only slightly

stronger and harder than polyethylene, but it is useful at

sustained temperatures as high as 250 °C and as low as

–200 °C. Teﬂon is resistant to all chemicals, and nothing

will stick to it. In most applications it is not as good as

nylon as a bearing surface, since it tends to cold-ﬂow away

from the area where pressure is applied. A thin ﬁlm of

Teﬂon, such as is found on modern cookware, provides

dry lubrication and prevents dust and moisture adhesion.

Specialty shops that serve the food industry can apply

these ﬁlms. Teﬂon is about ten times as expensive as nylon.

Kel-F is a ﬂuorochlorocarbon polymer. Its chemical

resistance is similar to Teﬂon, but it is much stronger

and harder. Like Teﬂon, Kel-F does not absorb water.

A number of rubber-like polymeric materials, known as

elastomers, ﬁnd application in scientiﬁc apparatus. Materials

of interest include Buna-N, Viton-A, and RTV. Buna-N is a

synthetic rubber. It can be used at sustained temperatures up

to 80 °C without suffering permanent deformation under

compression. It is available as sheet or in block form. It is

useful as a gasket material and for vibration isolation. Viton-

A is a ﬂuorocarbon elastomer similar in appearance and

mechanical properties to Buna-N. Useful up to 250 °C, it

tends to take a set at higher temperatures. Unlike Buna-N,

Viton-A shows no tendency to absorb water or cleaning

solvents. RTV, a self-curing silicone rubber produced by

General Electric, comes in a semiliquid form and cures to

a rubber by reaction with moisture in the air. It is useful as a

sealant, a potting compound for electronic apparatus, and an

adhesive. It can be cast in a plastic mold.

1.3.7 Glasses and Ceramics

Borosilicate glasses such as Corning Pyrex 7740 or Kimble

KG-33 are used extensively in the lab. These glasses are

strong, hard, and chemically inert, and they retain these

properties to 500 °C. As will be discussed in the succeed-

ing chapter, they are conveniently worked with a natural-

gas–oxygen ﬂame.

Quartz or fused silica has a number of unique properties.

It has the smallest known coefﬁcient of thermal expansion

of any pure material: 1 3 10

6

1

. By comparison, the

thermal expansion coefﬁcient of the borosilicate glasses

is 3 3 10

6

1

, and that of steel is 15 3 10

6

1

. Quartz

can be drawn into long, thin ﬁbers. The internal damping in

these ﬁbers is very low, and their stress–strain relation for

twisting is linear to the breaking point. Springs of quartz

ﬁbers provide the best possible realization of Hooke’s law.

Torsion springs and coil springs made of a quartz ﬁber are

used in delicate laboratory balances. Quartz retains its

excellent mechanical properties up to 800 °C. It softens at

1500 °C and hence can only be worked with a hydrogen–

oxygen ﬂame.

Alumina (Al

) is the most durable and heat-resistant of

the readily available ceramics. Only diamond, borazon, and

a fe w exotic metal carbides are harder. The compressive

strength of alumina exceeds 2000 MN/m

(300 000 psi),

although its tensile strength and shear strength are some what

less than those of steel. Alumina is brittle and, because of its

hardness, it ordinarily is shaped or cut by grinding with a

diamond-grit wheel. Alumina rod, tube, thermocouple wells,

and electrical insulators are av ailable. These shapes are pro-

duced by molding a slurry of alumina powder and various

24 MECHANICAL DESIGN AND FABRICATION

binders to the desired shape and then ﬁring at high temper-

ature to produce the hard ceramic. One particularly useful

product is alumina rod that has been centerless-ground to a

roundness tolerance of better than 60.03 mm (6.001 in.)

and a straightness of 2 mm/m (1/32 in./ft.) (see for e xample,

McDanel Refractory Porcelain Co.). A transparent form of

alumina is sapphire, which is a clear , hard material very

valuable in optical applications (see Chapter 4). Polycrystal-

line,

as well as single-crystal, (sapphire) balls are av ailable

that have been ground to a roundness tolerance of 60.001

mm (6.00003 in.) (Industrial Tectonics, Inc.). They are sur-

prisingly inexpensi v e: balls of 3 to 12 mm (0.125 to 0.500

in.) diameter cost only a few dollars. These balls are used as

electrical insulators and bearings, and in valves and ﬂow-

meters. Alumina circuit board substrate is available as plate

0.3to1.5mm(.010to.060in.)thickand15cm(6in.)

square. Owing to the scale of the circuit board industry,

the facilities for custom fabrication by laser cutting of alu-

mina plate are widely available and inexpensiv e.

Corning produces a machinable glass ceramic known as

Macor, and Aremco produces machinable ceramics called

Aremcolox. These materials are not nearly so strong or

hard as alumina, but can be machined to intricate shapes

that ﬁnd wide application in instrument work. They can be

drilled and tapped and can be turned and milled with

conventional high-speed steel tools. They resist chipping

and are insensitive to thermal shock. Machinable ceramics

have a dielectric strength of 40 000–80 000 V/mm [1000–

2000 V/mil (.001 in.)].

Aluminum silicate, or lava, is another useful, machinable

ceramic. Blocks of grade A lava are available in the unﬁred

condition. This material is readily machined into intricate

shapes that are subsequently ﬁred at 1050 °Cinairforhalf

an hour. The ﬁred ceramic should be cooled at about 150 K/

hour to prevent cracking. It grows about 2% upon ﬁring.

The development of so-called technical ceramics has

burgeoned over the past two decades. A remarkable range

of pure oxide ceramics as well as composite materials are

available with mechanical, electrical, magnetic, and ther-

mal properties to ﬁt all sorts of special applications. The

ultra-low thermal expansion glass ceramic, Zerodur, pro-

duced by Schott Glass, is an example that has found use in

the construction of highly stable mechanical elements

and mirrors. A glass ceramic consists of a crystalline phase

dispersed in a glass phase. The quartz-like crystalline

phase in Zerodur has a negative thermal coefﬁcient, while

the glassy phase has a positive coefﬁcient. In the appro-

priate proportion a material with a thermal expansion

coefﬁcient of the order of 10

8

/K is obtained.

1.4 JOINING MATERIALS

Soldering, brazing, welding, or ri veting may permanently

join the parts of an apparatus, or demountable fasteners

such as screws, rivets, pins, or retaining rings may join them.

1.4.1 Threaded Fasteners

Threaded fasteners are used to join parts that must be

frequently disassembled. A thread on the outside of a cyl-

inder, such as the thread on a bolt, is referred to as an

external or male thread. The thread in a nut or a tapped

hole is referred to as an internal or female thread. The

terminology used to specify a screw thread is illustrated

in Figure 1.18. The pitc

h is the distance between succes-

sive crests of the thread, equivalent to the axial distance

traveled in one turn of a screw. The pitch of metric threads

is speciﬁed in millimeters. In English units the pitch is

speciﬁed as the number of turns or threads per inch (tpi).

The major diameter is the largest diameter of either

an external or an internal thread. The minor diameter is

the smallest diameter. In the United States, Canada, and

the United Kingdom, the American Standard speciﬁes the

form of a thread. SI metric threads conform to ISO and

DIN standards. Both the crest and root of these threads are

ﬂat, as shown in Figure 1.18, or slightly rounded. The

American

Standard and SI thread angle is always 60°.

Figure 1.18 Screw-thread terminology.

JOINING MATERIALS 25

Two American Standard thread series are commonly

used for instrument work. The coarse-thread series, des-

ignated UNC for Uniﬁed National Coarse, is for general

use. Coarse threads provide maximum strength. The ﬁne-

thread series, designated UNF, is for use on parts subject to

shock or vibration, since a tightened ﬁne-thread nut and

bolt are less likely to shake loose than a coarse-thread nut

and bolt. The UNF thread is also used where ﬁne adjust-

ment is necessary. The pitch of standard metric fasteners is

intermediate between UNC and UNF-series threads. There

is no interchangeability between American Standard and

metric threaded fasteners. An obsolete thread type for

small screws that can show up in some older equipment

is the BA (British Association) thread type, which was

very close to a metric thread.

TheﬁtofAmericanStandardthreadedfastenersis

speciﬁed by toler ances designat ed as 1A, 2A, 3A, and

5A for external threads and 1B, 2B, 3B, and 5B for in-

ternal threads. The ﬁt of 2A and 2B threads is ade quate

for most applications, and such threads are usuall y pro-

vided if a tolerance is not speciﬁed. Many types of

machine scr ews are only available with 2A threads. The

2A and 2B ﬁts allow sufﬁcient clearance for plating. 1A

and 1 B ﬁts leave sufﬁcient clearance that dirty and

scratched parts can be easily assembled. 3A and 3B ﬁts

are for very precise work. 5A and 5B are interference ﬁts,

such as are used on studs tha t are to b e installed semi-

permanently. The metric tolerance class 6g is approxi-

mately equivalent to American Standard tolerance class

2A. Class 4g 6g is a more precise thread approximately

equivalent to class 3A.

A left-hand thread may be speciﬁed to assure unique-

ness or when it is thought that a disturbing rotation or

vibration would tend to loosen a right-hand threaded fas-

tener. Circumferential notches between the ﬂats or an

arrow on the face indicating the direction to be turned to

tighten the nut identify a left-hand thread nut.

In the American Standard, a gauge number speciﬁes

major diameters less than 1/4 inch. The relation between

gauge number, n, and diameter, d, in inches, is given by

d ¼ð0:013n þ0:060Þ in:

The speciﬁcation of threaded parts on a mechanical

drawing is illustrated by the following examples:

(1) An externally threaded part with a nominal major

diameter of 3/8 in., a coarse thread of 16 threads per inch,

and a 2A tolerance is

3=816 UNC2A

(2) An internally threaded part with a nominal major

diameter of 5/8 in., a ﬁne thread of 18 tpi, and a 2B toler-

ance is designated

5=818 UNF2B

(3) An American Standard, 8 gauge (0.164 in. diameter)

coarse thread (32 tpi) is designated

832 UNC

(4) A metric thread with a nominal major diameter of

5 mm and a pitch of 0.8 mm is designated

M5 X 0:8

The letters LH following these designations speciﬁes a

left-hand thread.

Speciﬁcations for UNC and UNF thread forms are given

in Appendix 1.2 and for metric threads in Appendix 1.3.

The

indicated tap drill size speciﬁes the diameter of the

hole to be drilled before cutting threads with a tap. For

metric threads, the tap drill size is the diameter of the

corresponding screw in millimeters minus the pitch in

millimeters.

The common forms of machine screws are illustrated in

Figure 1.19.

x-head cap screws are ordinarily available in sizes

larger than 1/4 in. They have a large bearing surface and

thus cause less damage to the surface under the head than

other types of screws. A large torque can be applied to a

hex-head screw, since it is tightened with a wrench.

Slotted-head screws and Phillips screws are driven with a

screwdriver. They are available with round, ﬂat,andﬁllister

heads. The ﬂat head is countersunk so that the top of the

head is ﬂush. Fillister screws are preferred to round-head

screws, since the square shoulders of the head provide better

support for the blade of a screwdriver.

Socket-head cap screws with a hexagonal recess are

preferred for instrument work. These are also known as

26 MECHANICAL DESIGN AND FABRICATION

Allen screws. L-shaped, straight, and ball-pointed hex driv-

ers are available that permit Allen screws to be installed in

locations inaccessible to a wrench or screwdriver. An

Allen screw can only be driven by a wrench of the correct

size, so the socket does not wear as fast as the slot in a

slotted-head screw. Socket-head screws have a relatively

small bearing surface under the head and should be used

with a washer where possible.

Setscrews are used to ﬁx one part in relation to another.

They are often used to secure a hub to a shaft. In this

application it is wise to put a ﬂat on the shaft where the

setscrew is to bear; otherwise the screw may mar the shaft,

making it impossible for it to be withdrawn from the hub.

Setscrews should not be used to lock a hub to a hollow

shaft, since the force exerted by the screw will deform the

shaft. In general, setscrews are suitable only for the trans-

mission of small torque, and their use should be avoided if

possible.

Machine screws shorter than 5 cm (2 in.) are threaded

their entire length. Longer screws are only threaded for

part of their length. Screws are usually only available with

class 2A coarse or ﬁne threads.

The type of head on a screw is usually designated by an

abbreviation such as ‘‘HEX HD CP SCR’’ or ‘‘FILL HD

MACH SCR.’’ For example, a socket-head screw 1 1/2 in.

long with an 8–32 thread is designated

832 UNC 1 1=2 SOC HD CAP SCR

The torque T required to produce a tension load F in a

bolt of diameter D is

T ¼ CDF,

where the coefﬁcient C depends upon the state of lubrica-

tion of the threads. In general, C may be taken as 0.2. If

the threads are oiled or coated with molybdenum disulﬁde,

a value of 0.15 may be more accurate. If the threads are

very clean, C may be as large as 0.4. The tension load on

the bolt is equal to the compressive force exerted by the

underside of the bolt head.

Steel bolts meeting SAE speciﬁcations are identiﬁed by

markings on the head:

The strength of the bolt increases with the SAE grade

number. Most common steel bolts are SAE grade 2. In sizes

up to 1 in., these bolts have a yield strength of 30 000 to

50 000 psi. The yield strength of SAE grade 5 bolts exceeds

90 000 psi while that of grade 8 bolts exceeds 130 000 psi.

When a bolt is to be tightened to a speciﬁed torque, the

threads should be ﬁrst seated by an initial tightening. It

should then be loosened and retightened to the computed

torque with a torque wrench. The torque corresponding

to the yield strength should not be exceeded during this

operation.

To obtain maximum load-carrying strength, a steel bolt

engaging an internal thread in a steel part should enter the

thread to a distance equal to at least one bolt diameter . For a

steel bolt entering an internal thread in brass or aluminum, the

length of engagement should be closer to two bolt diameters.

Machine screws are readily available in a remarkable

range of materials and ﬁnishes. Run-of-the-mill steel

screws are often zinc plated, but nickel- and chrome-plated

screws are available for enhanced corrosion resistance and

better appearance. In addition to steel screws, major

suppliers provide screws and nuts in types 304 and 316

stainless steel, Monel, brass, silicon bronze, 2024-T4 alu-

minum, titanium, Nylon, Teﬂon, and ﬁberglass-reinforced

Figure 1.19 Machine screws: hex head; round head

(slotted); ﬂat head (Phillips); ﬁllister head; socket head.

JOINING MATERIALS 27

plastic. The choice of the material for a threaded fastener

depends on the desired strength in the joint to be made, the

materials to be joined, and the environment of the ﬁnished

assembly. The possibility of corrosion weakening a joint or

preventing disassembly is often a major factor. Galvanic

action between the materials of the fastener and the joined

assembly is the culprit here. The material of the fastener

and of the metals being joined should be close to one

another in the galvanic series. Metal screws are to be

avoided when joining metals far apart in the galvanic ser-

ies; brazing is preferable in this situation.

As a threaded assembly is tightened, the interlocking

threaded surfaces are held together by the stress created

by elastic deformation of the fastener and the clamped

parts. Shock, vibration, and thermal cycling can relieve

this tension and the assembly becomes loose. All manner

of schemes have been developed to keep threaded parts

locked together. For instrument assembly, lockwashers

often sufﬁce. These come in two forms: the spring lock-

washer and the serrated washer. The former is simply a

washer in the form of a single-turn spring that is placed

under the head of a bolt or under a nut before it is screwed

onto the bolt. The washer is ﬂattened as the assembly is

tightened. The spring force creates friction to resist the bolt

turning. A toothed or serrated washer simultaneously

engaging the surface of the joined part and the underside

of a bolt or nut similarly resists a bolt’s turning loose. As

an aside it is usually noted that a lockwasher should not be

used along with a ﬂat washer since the lockwasher will

engage the ﬂat washer on one side, but the other side of the

ﬂat washer will slip. Self-locking screws are made with a

nylon insert in the threads. The nylon deforms as the screw

is installed to take up the clearance between the mating

threaded surfaces. Nuts with nylon inserts, so-called ‘‘air-

craft nuts,’’ are readily available and quite effective in

resisting loosening under vibration. A simple means of

securing a nut and bolt assembly is to install a second

nut, the locknut, after the ﬁrst nut is tightened. With the

ﬁrst nut held securely with a wrench to prevent its turning,

the locknut is tightened down on the ﬁrst. The effect is to

create opposing tension in the bolt that takes up clearance in

the threads and increases friction between the mating sur-

faces. A threaded assembly can also be secured with adhe-

sive applied to the threads to take up clearances and stick

the surfaces together. Specialized adhesives for this purpose

(Loctite) are available in a range of strengths for both

removable and permanent installations.

Excessive wear may result when a steel bolt is screwed

into a threaded (tapped) hole in a soft material such as

plastic o r aluminum. Threaded inserts (Heli-Coils) can

be installed in the softer material to alleviate this prob-

lem. These inserts are tightly wound helices of stainless

steel or phosphor bronze wire with a diamond-shaped cross

section. The insert is placed in a tapped oversize hole and

the mating bolt is screwed into the insert. Special taps are

required to prepare a hole for the insert, and a special tool

is required to drive the insert into the hole.

1.4.2 Rivets

Rivets are used to join sheet-metal or sheet-plastic parts.

They are frequently used when some degree of ﬂexibility is

desired in a joint, as when joining the ends of a belt to give

a continuous loop. Common rivet shapes are shown in

Figure 1.20. Rivets are made of soft copper, aluminum,

carbon

steel, and stainless steel, as well as plastic. As for

threaded fasteners, the strength required in a joint and the

possibility of corrosion are considered in choosing the

material for a rivet. To join two pieces, a hole, slightly

larger than the body of the rivet, is drilled or punched in

each piece. The holes are aligned and the rivet is inserted.

The length of the rivet should be such that it protrudes a

distance equal to one to one and half times its diameter.

The head of the rivet is backed-up with a heavy tool while

the plain end of the rivet is ‘‘upset’’ by hammering to

draw the two pieces together. The hammering action

swells the body of the rivet to ﬁll the hole. Vise-like hand

tools with appropriate die sets are available for setting

rivets in a one-handed operation.

Blind rivets or ‘‘pop’’ rivets, illustrated in Figure 1.20 ,

e use ful in t he lab. These can be installed without ac cess

to the back side of the joint. An inexpensive blind r ivet

tool is required. The tool grasps a mandrel that passes

through t he center of the rivet, the rivet is i nserted into

the hole, and the rivet tool pulls the mandrel back until it

breaks. The head of the mandrel rolls the stem of the rivet

over to form a head. Some pop rivets are designed so that

the remaining broken portion of the mandrel seals the

center hole of the rivet. The installation of pop rivets in

carefully positioned, reamed holes is an excellent means

28 MECHANICAL DESIGN AND FABRICATION

of aligning two thin pieces with respect to one another.

Poprivetedjointscanberegardedassemipermanent.

The rivet is easily removed by drilling into its center with

an oversize drill until the head separates from the body.

With care, the drill will never touch the parts joined by

the rivet.

1.4.3 Pins

Pins such as are shown in Figure 1.21 are used to precisely

locate one part with respect to another or to ﬁx a point of

rotation. To install a pin, the two pieces to be joined are

clamped together and the hole for the pin is drilled and

then reamed to size simultaneously in both pieces.

Straight pins are made of steel that has been ground to a

diameter tolerance of 60.003 mm ( 6.0001 in.). They

require a hole that has been reamed to a close tolerance;

straight pins are to be pressed into place. If a straight pin is

to serve as a pivot or if it is to locate a part that is to be

removable, the hole in the movable part is reamed slightly

oversize.

A roll pin has the advantage of ease of installation and

removal and does not require a precision-reamed hole. The

spring action of the wall of the pin holds it in place.

Taper pins are installed in holes that are shaped with a

special reamer. The American taper is 0.250 in. per ft. The

metric taper is 1:50. Plain taper pins are driven into place.

Taper pins with the small end threaded are drawn into

place with a nut that then secures the installed pin.

A shoulder screw is effectively a straight pin with a

shoulder to provide location and a threaded end below

for attachment. Shoulder screws are used as pivots. These

screws are hardened, and the shoulder is ground to a diam-

eter tolerance of 60.0001 in.

1.4.4 Retaining Rings

A retaining ring (Figure 1.22) serves as a removable shoul-

der to position an assembly of parts on a shaft or in a hole.

An axially assembled external retaining ring is expanded

slightly with a special pair of pliers, then slipped over the

end of a shaft and allowed to spring shut in a groove on the

shaft. An axially assembled internal ring is compressed,

inserted in a hole and permitted to spring open into a

groove. A radially assembled external retaining ring is

Figure 1.21 Pins and shoulder screws.

Figure 1.20 Rivets and riveted joints.

JOINING MATERIALS 29

forced onto a shaft from the side. It springs open as it slides

over the diameter and then closes around the shaft. Some

retaining rings have a beveled edge, as shown in the ﬁgure.

Spring action of the ring on the edge of its groove produces

an axial load to take up unwanted clearances between

assembled parts. This scheme is frequently used to take

up the end-play in a ball bearing. A bowed retaining ring

provides another solution to end-play take-up. The variety

and range of sizes of retaining rings are truly remarkable.

The Truarc Division of Waldes Kohinoor is a major sup-

plier of retaining rings.

1.4.5 Soldering

In soldering, as well as brazing, two metal surfaces are

joined by an alloy that is applied in the molten state to

the joint. The melting point of the alloy is below that of the

metal of the parts to be joined (the so-called base metal).

Soldering and brazing differ in the composition of the fusi-

ble alloy. Solder is a tin alloy that melts at a relatively low

temperature – in the 200–300 °C range. Brazing was orig-

inally done with a copper alloy that melts at about 900 °C.

There are now many different brazing alloys with working

temperatures from 400 °C to more than 2000 °C. Today the

term ‘‘brazing’’ usually implies ‘‘silver brazing’’ with silver-

containing alloys that ﬂow in the 450–800 ° C range.

The molten soldering or brazing alloy must wet the

surfaces of the metal parts being joined. When the alloy

wets the surfaces of closely spaced parts, capillary action

draws the alloy into the joint to provide the largest possible

contact area and correspondingly the strongest possible

joint. A dirty or oxidized metal surface will not be wetted.

A chemically-active ﬂux is applied as the base metal is

heated to remove oxides and protect the surface thus

cleansed. The ﬂux employed is, to a certain extent, speciﬁc

to the base metal and the alloy as well as the temperature

required for melting the solder or braze alloy.

For routine soldering of copper or brass parts, 50–50

tin–lead solder (50% tin, 50% lead) has traditionally been

the alloy of choice. Lead-containing solder is no longer

used for piping in contact with potable water. Tin–lead

solder has being replaced by 95–5 tin–antimony for joining

copper to copper. The 96–4 tin–silver eutectic (96.5% tin,

3.5% silver) has melting and ﬂow properties similar to

tin–lead solder and, with the use of the proper ﬂux, will

wet copper, brass, steel, and stainless steel. 60–40 tin–lead

solder is used to join electronic components. Soldered

joints are appropriate when great strength and cleanliness

are not required and when it is most convenient to work at

Figure 1.22 Retaining rings and retaining ring installations.

30 MECHANICAL DESIGN AND FABRICATION

low temperatures. The tensile strength of a copper sleeve

joint with tin–lead solder is about 40 MN/m

(6000 psi).

The shear strength is about 35 MN/m

(5000 psi). The

strength of a tin–lead joint is considerably reduced at tem-

peratures above 100 °C.

Steel and stainless steel, as well as brass and copper, can

be soldered with tin–silver alloy solders. The 96–4 tin–

silver eutectic alloy is almost universally applicable in the

laboratory for low-temperature soldering. It melts at 221 °C

and can produce a joint with a tensile strength of 100 MN/

(15 000 psi) and a shear strength of 75 MN/m

(11 000

psi). The manufacturers of soldering and brazing alloys

(including Engelhard, Handy & Harman/Lucas–Milhaupt,

Harris Products, Wesgo Metals, CWB Ltd.) provide tin–

silver alloy solders in wire form, in wire with a rosin ﬂux

core for electronic applications, and as a paste or slurry of

alloy powder in a liquid ﬂux. The last is simply painted on

the surface where desired and heated indirectly. The

absence of ﬂux on adjoining areas keeps solder from ﬂow-

ing where it is not wanted.

Soldering alloys containing lead, zinc, antimony, or cad-

mium should be avoided. These components are volatile.

Zinc is sufﬁciently volatile at room temperature to be a

signiﬁcant contaminate in high-vacuum applications. Cad-

mium vapor at soldering temperatures is a serious health

hazard.

The ﬁrst step in soldering a joint is to clean the surfaces

to be joined with ﬁne emery paper or steel wool. The sur-

faces are then covered with soldering ﬂux, assembled,

and heated. A gap of 0.1–0.2 mm (.003–.006 in.) is desir-

able between surfaces to be soldered. In some cases it may

be necessary to insert a piece of brass shim stock to main-

tain this clearance. When heated, the ﬂux removes oxides to

cleanse the surfaces so the molten solder will wet them. Sal

ammoniac (NH

Cl) ﬂux, available from hardware suppli-

ers, is used for lead–tin solders. The suppliers of lead-free

solders provide proprietary ﬂuxes. A natural-gas–air ﬂame

or propane–air ﬂame is most convenient. The assembly may

also be heated on an electric or gas hot plate. Flame heating

should be done indirectly if possible. Play the ﬂame on the

metal near the joint, particularly on the heavier of the two

pieces. Periodically test the temperature of the two pieces

by touching each with the solder. When each piece is hot

enough to melt the solder, remove the ﬂame and apply

solder to the joint. The solder should ﬂow by capillary

action into and through the joint. Sufﬁcient solder should

be applied to ﬁll the joint and produce a meniscus or ﬁllet of

solder at the juncture of the two parts (Figure 1.23). The

ﬁ

llet radius should be 1/16–1/8 in. Residual ﬂux must be

removed. This is why it is important that the joint is ﬁlled

with molten solder. Flux trapped in the joint will lead to

hidden corrosion. Inorganic ﬂux can be dissolved in hot

water. Organic ﬂuxes will require an organic solvent.

1.4.6 Brazing

A brazed joint is strong and leak tight. The brazing process

is amenable to the laboratory and the simplest shop. A

brazed assembly can offer real advantages to the designer

of an apparatus. Surprisingly often, a complex part can be

inexpensively made by brazing together an assembly of

standard off-the-shelf parts. Brazing offers a relatively

easy means of joining materials with very different proper-

ties: a hard metal can be joined to a ﬂexible metal stem;

a metal with desirable electrical and thermal properties

can be incorporated in an assembly made of a metal with

entirely different properties; a strong metal-to-ceramic

brazed joint is possible.

There a re hundreds of brazing alloys.

The choice of an

alloy depends upon t he metals to be joined and the appli-

cation of the brazed part. The strength of the alloy in a

joint is seldom an issue in a properly designed joint. I n

some instances the joint strength will exceed that of the

base metal. The wetting and ﬂow characteristics of the

molten brazing alloy are often of primary importance. Of

course the working temperature of the brazing alloy must

be l ess than the melting poi nt of the base metal, some-

times, much less, to avoid an undesirable phase transition

in the base metal.

Alloys are characterized by a solidus, the temperature

at which, upon heating, liquid mixed with solid ﬁrst

Figure 1.23 A soldered joint.

JOINING MATERIALS 31

appears, and a liquidus, the temperature at which the alloy

becomes completely liquid. The difference between the

two temperatures is the melting range. In brazing a joint,

an alloy with a narrow melting range (0–20 °C) becomes

ﬂuid quickly and will tend to ﬂow into the narrowest gap.

For a joint with relatively large gap (greater than about 0.1

mm), a large melting range is desired so that upon heating,

the alloy remains in the melting range and ﬂows sluggishly

to ﬁll the joint. A eutectic alloy melts at a single temper-

ature; there is no melting range.

For routine brazing of steel parts, borate-ﬂux-coated,

brass brazing rod is available from hardware suppliers as

well as specialized suppliers of brazing and welding mate-

rials. The tensile strength of joints made with brass brazing

alloy can be of the order of 50 000 psi. An oxyacetylene

torch is required for brass brazing alloys.

Silver brazing alloys are preferred for most laboratory

work. Silver alloys are lower-melting than brass alloys and

can be used on brass as well as steel parts. The tensile

strength, as well as the shear strength, of silver-brazed

joints is in the 200–350 MN m

2

(30 000–50 000 psi)

range, depending upon the alloy and the joint design.

The alloy of approximately 60% silver, 30% copper, and

10% tin is generally applicable. It melts at 600 °C (solidus)

and ﬂows at 720 °C (liquidus), and can be worked with the

same gas-oxygen torch used for laboratory glassblowing.

A ﬂuoride ﬂux is required. Parts made of copper, brass,

steel, stainless steel, and even refractory metals can be

joined with this brazing alloy.

When volatile metals cannot be tolerated, the silver–

copper eutectic (72% Ag, 28% Cu) makes a suitable braz-

ing alloy for copper, stainless steel, Kovar, and many

refractory metals. This alloy melts at 780 °C. For torch

brazing, an oxyacetylene ﬂame is required. The addition

of indium produces a lower-melting alloy with much the

same properties as the silver–copper eutectic. Incusil-15

(62% Ag, 24% Cu, 15% In, Wesgo), for example, has a

solidus of 630 °C and a liquidus of 705 °C. Silver-bearing

brazing alloys containing cadmium or other volatile metals

should be avoided. Cadmium vapor is toxic. Volatile com-

ponents (i.e., zinc) of a brazing alloy can cause signiﬁcant

contamination in a high-vacuum system.

The manufacturers (including Handy & Harman/Lucas–

Milhaupt, Engelhard, Harris Products, Wesgo, Aufhauser,

CWB Ltd.) provide alloys for a remarkable range of

applications along with the ﬂuxes appropriate for each

alloy–base metal combination. Brazing alloys are offered

in rod or wire form, as either ﬂux-coated or ﬂux-cored rod,

and as a paste incorporating powdered alloy and ﬂux.

Torch brazing is the simplest and most convenient braz-

ing operation. An oxyacetylene torch is required for brass

brazing alloys. A natural-gas–oxygen ﬂame can be used

for lower-melting alloys. The ﬂame must be nonoxidizing.

The ﬂame should be adjusted to provide a well-deﬁned,

blue, inner cone 8–10 mm long. The oxyacetylene ﬂame

should have a greenish feather at the tip of the inner cone.

A ﬁreproof working surface is also required. Most ﬂuxes

contain sodium, which emits yellow light when heated. A

pair of didymium eyeglasses, such as are used in glass-

blowing, will ﬁlter out the sodium yellow lines and make

the work much more visible while brazing. Parts to be

brazed should, if possible, be designed to be self-locating.

A clearance between parts of 0.03–0.1 mm (.001–.003 in.)

will assure maximum strength in the ﬁnished joint. Surfa-

ces to be wetted by the brazing alloy must be clean.

The brazing process is not unlike the soldering process

described above. Coat the joint surfaces with ﬂux and

assemble the parts. Clamp if necessary: parts move as a

consequence of differential expansion as they are heated;

the blast of gas from a torch can misalign an assembly.

Preheat the base metals in the area of the joint nearly to

the melting temperature of the brazing alloy. The ﬂux

should melt from its crystalline form to a glassy ﬂuid as

the brazing temperature is approached. Continue heating

while testing both pieces to be joined by touching the base

metal with the brazing rod. The rod should melt in contact

with both pieces. Do not apply the ﬂame directly to the

brazing rod. When the brazing alloy ﬂows, continue to heat

the entire area of the joint. There are two dangers: insufﬁ-

cient heat and too localized heating. The molten alloy ﬂows

toward the hottest area of the joint; a void may be left in a

cool area to weaken the joint. Intense localized heating will

consume ﬂux and leave the base metal exposed to oxidation

that will prevent further wetting by the molten alloy, once

again leaving a weak place in the joint. Overheating also

mars the ﬁnish of the metal. In general, make sure there is

adequate ﬂux and that the quantity of alloy is sufﬁcient to ﬁll

the joint and leave a ﬁllet at the juncture of the parts being

joined. It is sometimes convenient to preplace snippets of

brazing wire in or near the joint before heating, rather than

32 MECHANICAL DESIGN AND FABRICATION

applying the alloy after the work is heated. Alloy/ﬂux pastes

provide another effective means for assuring that the alloy is

effectively introduced in a joint. Finally it is essential that

corrosive ﬂux residues be removed from the ﬁnished joint.

One of the easiest approaches is to quench the brazed part in

water before it is completely cool. The thermal shock frac-

tures the glassy residue which then dissolves in the hot

water. Be careful here: the thermal shock may also distort

thin sections in the part being brazed. A wire brush and

emery cloth may be used to ﬁnish the job. A rinse in an

acid solution may be necessary if the part has been over-

heated to the extent that the base metal has been oxidized.

Many metals, as well as brazing ﬂuxes and alloys, con-

tain toxic components that are volatile at brazing temper-

atures. Brazing should be carried out in a well-ventilated

hood. Cadmium-containing brazing alloys should not be

used in the laboratory. One should be aware that many

standard parts are plated with cadmium or zinc. The

plating must be removed before heating to brazing

temperatures.

Copper, Kovar, Monel, nickel, steel, and stainless steel

can be brazed without ﬂux if the metal is heated in a hydro-

gen atmosphere in a furnace. The hydrogen serves as a ﬂux

by reducing surface oxides to produce a clean surface that

will be wetted by the molten brazing alloy. Alloys contain-

ing chromium must be brazed in dry hydrogen. The surface

oxide of chromium found on stainless steel is reduced by

dry hydrogen at temperatures above 1050 °C. Furnace

brazing provides for more uniform heating of the work

so there is usually less distortion than in torch brazing.

The work is also stress-relieved to some extent. Hydro-

gen-brazed parts come out clean and bright. Although it

is possible to carry out hydrogen brazing in the lab, the job

is better let out to a specialty shop. Commercial heat-treat-

ing shops operate dissociated-ammonia tunnel kilns. The

work travels slowly through the kiln on a car. Ammonia

introduced in the middle of the furnace dissociates to

hydrogen and nitrogen to provide the ﬂux.

Parts to be hydrogen-brazed should be chemically clean.

Avoid ﬁngerprints, since inorganic salts from the skin are

not affected by hydrogen and will remain as stains on the

ﬁnished work. Assemble the parts and place snippets of

ﬁller-metal wire at the junction of the parts to be brazed.

For parts that are not securely self-aligned it may be worth-

while to pin the joints to maintain precise alignment. A

rough calculation of the volume to be ﬁlled will determine

the amount of wire to be used. When the ﬁller metal melts,

it is drawn into the nearby joint by capillary action. If the

joints to be brazed are not visible from outside the furnace,

place a piece of brazing metal on top of the work where it

can be observed by the operator, in order to determine

when the brazing temperature has been reached. If the

walls of the brazing apparatus are opaque, a thermocouple

will be required for this purpose.

The ﬁller metal used in hydrogen brazing should melt at

a temperature higher than that required for the hydrogen to

effectively clean the surface of the base metal. OFHC

(oxygen-free high-conductivity) copper has a melting

point of 1083 °C and is an excellent ﬁller metal for brazing

steel, stainless steel, Kovar, and nickel. If low-melting

alloys, such as the silver–copper eutectic, are used, a small

amount of ﬂux is required. Brazing alloys that contain

volatile metals should never be used for hydrogen brazing.

It is unwise to braze parts of ordinary electrolytic copper or

to use ordinary copper as a ﬁller in a hydrogen atmosphere.

Oxides in the metal are reduced to water that is trapped

within the crystalline structure of the metal. This water can

cause out-gassing problems in vacuum applications, and, if

the copper is heated, the expanding water vapor will pro-

duce internal cracks (hydrogen embrittlement). For instru-

ment work, OFHC copper should be used for all copper

parts that are to be brazed.

A brazed joint between ceramic pieces or between metal

and ceramic is entirely possible although the operation

must be carried out in a vacuum furnace or in a furnace

under an inert atmosphere. Appropriate ﬁller metal–ﬂux

pastes are used (for example, Lucanex from Lucas–

Milhaupt). One must take into account the difference in

thermal expansion of the parts to be joined. Refractory

metals, such as molybdenum, tantalum, or tungsten, have

coefﬁcients of thermal expansion close to those of most

ceramics. Ferrous and cuprous alloys can be brazed to

ceramic materials if the metal part is thin in the region

of the joint to allow for some give in the metal part as it

cools down from the brazing temperature.

1.4.7 Welding

In welding, parts are fused together by heating above the

melting temperature of the base metal. Sometimes a ﬁller

JOINING MATERIALS 33

metal of the same type as the base metal is used. Fusion

temperatures are attained with a torch, with an electric arc,

or by ohmic heating at a point of electrical contact. For

most instrument work the preferred method is arc welding

under an argon atmosphere using a nonconsumable elec-

trode. This method is referred to as tungsten-inert-gas

(TIG) welding or heliarc welding. All metals can be

welded, although refractory metals must be welded under

an atmosphere that is completely free of oxygen. Arc weld-

ing requires special skills and equipment, but most instru-

ment shops are prepared to do TIG welding of steel,

stainless steel, and aluminum on a routine basis.

The effect of the high temperatures involved must be

considered when specifying a welded joint. Some distor-

tion of welded parts is inevitable. Provision should be

made for remachining critical surfaces after welding.

The state of heat treatment of the base metal is affected

by welding. Hardened steels will be softened in the vicinity

of a weld. Stainless steels may corrode because of carbide

precipitation at a welded joint.

Spot welding or resistance welding is a good technique

for joining metal sheets or wires in the lab. The joint is

heated by the brief passage of a large electric current

through a spot contact between the pieces to be joined.

Steel, nickel, and Kovar, as well as refractory metals such

as tungsten and molybdenum, can be spot-welded. Copper

and the precious metals are not easily spot-welded because

their electrical resistance is so low that very little power

can be dissipated at the point of contact. Small spot-

welding units with hand-held electrodes are available

from commercial sources (Ewald Instruments, Miyachi

Unitek, PUK).

1.4.8 Adhesives

Epoxy resins are the most universally applicable adhesives

for the laboratory. They are available in a variety of

strengths and hardnesses. Epoxies that are either thermally

or electrically conducting are also available. Epoxy adhe-

sives consist of a resin and a hardener that are mixed just

prior to use. The mixing proportions and curing schedule

must be controlled to achieve the desired properties. A

variety of epoxy adhesives is available prepackaged in

small quantities in the correct proportions. Epoxies will

adhere to metals, glass, and some plastics. Hard, smooth

surfaces should be roughened prior to the application of

the adhesive. Sandblasting is a convenient method. Parts of

a surface that are not to receive the adhesive can be masked

with tape during this operation. To obtain maximum

strength in an epoxied joint, the gap ﬁlled by the epoxy

should be 0.05–0.2 mm (.002–.006 in.) wide. To maintain

this gap between ﬂat smooth surfaces, shims can be

inserted to hold them apart.

Self-curing silicone rubber such as General Electric

RTV (Room Temperature Vulcanizing) can be used as an

adhesive. RTV is chemically stable and will stick to most

surfaces. The cured rubber is not mechanically strong; this

can be an advantage when making a joint that may occa-

sionally have to be broken.

Cyanoacrylate contact adhesives, so-called ‘‘super

glues,’’ have found wide use in instrument construction.

Eastman 910 and Techni-Tool Permabond are representa-

tive of this type of adhesive. These adhesives are mono-

mers that polymerize rapidly when pressed into a thin ﬁlm

between two surfaces. They will adhere to most materials,

including metal, rubber, and nylon. Cyanoacrylate adhe-

sives are not void-ﬁlling and only work to bond surfaces

where contours are well matched. An adhesive ﬁlm of about

0.03 mm (0.001 in.) gives best results. A ﬁrm set is achieved

in about a minute, and maximum strength is usually reached

within a day. When joining metals and plastics, a shear

strength in excess of 7 MN/m

(1000 psi) is possible.

Ceramic cements are available for a remarkable range of

applications (Sauereisen, Dylon). These are inorganic mate-

rials (silica, zirconia, graphite) in powder, paste, or liquid

form that are used to join ceramics, graphite, and metals.

Some are intended to make electrically insulating coatings;

others may be used for casting small ceramic parts. The

tensile strength of these materials is generally not great,

but the materials are serviceable up to 1100 °C and higher

(much higher in the case of graphite cements).

1.4.9 Design of Joints

The design of the joints between parts of a machine deserves

special attention. Experience indicates that failure of an

assembly frequently occurs at or near a joint. A well-

designed joint must suit the designer’s purposes while at

the same time assuring that there will not be an undesirable

concentration of stress in the vicinity of the joint.

34 MECHANICAL DESIGN AND FABRICATION

The basic idea is to design the joint so that the assembly

allows for a smooth ﬂow of tensile, bending, and torsional

forces through the joint. One may not intend to stress an

assembly to the point that noticeable distortion occurs, but

imagine that one has done just that: does the strain appear

as a smooth bend or ﬂex or does the strained part have a

‘‘kink’’ in the vicinity of a joint?

There are two types of joints, the butt joint and the

overlap joint, as shown in Figure 1.24 . A butt joint permits

parts

to be joined without an increase in thickness. The

same advantage is realized with a hybrid butt/overlap joint,

at the expense of additional machining and ﬁtting. The

woodworker’s or shipwright’s scarf joint is an example

of a butt/overlap joint.

A joint should be as strong as the parts leading up to the

joint in order to avoid an un desirable stress concentration.

It follows that a butt joint is only amenable to welding.

The contact area in a butt joint is usually too small for a

brazed or soldered joint to provide the strength o f the

adjoining parts. For thin parts butted together, a full-

penetration weld should be speciﬁed. (Imagine two thin

pieces of steel butt-welded with only pa rtial weld pene-

tration. If the assembly were ﬂexed it would hinge and

kink at the weld.)

An overlap joint can be soldered, brazed, or glued, pro-

vided the contact area is sufﬁcient to attain the desired

strength. The stronger the material being joined, the longer

must be the overlap so that the joint strength is commen-

surate with the strength of the material.

The butt/overlap joint is amenable to joining with braze,

solder, glue, or rivets. The advantage of a constant cross-

section is lost if the joint is bolted, unless the material

being joined is sufﬁciently thick that a recessed-head

design is possible.

The designer must decide how permanent a joint is to

be. A brazed, soldered, or welded joint is ordinarily quite

permanent. Reheating, however, can easily disassemble a

soldered electrical connection. Similarly, wires and thin

metal parts that have been lightly spot-welded together

can be broken apart at the weld without damaging the

components. Spot-welding is a useful means for making

electrical connections between refractory-metal parts and

between parts to be used in a high-temperature environ-

ment. A glued joint may be permanent, but, if a soft adhe-

sive such as self-curing silicone is used, the joint can be

disassembled, although not conveniently. A riveted joint

can be disassembled if required and, of course, a bolted

joint can be assembled and disassembled repeatedly. A

force ﬁt permits parts to be assembled in precise alignment

and without fasteners. A force ﬁt usually involves inserting

a round piece into a round hole. The inner piece is

made larger than the hole so that the parts interfere upon

assembly. The parts are permanently or semipermanently

assembled depending on the extent of interference. The

parts must be made with great precision to achieve the

desired result. Mechanical design and drafting books

provide tables of ﬁts. A ‘‘light force ﬁt’’ of parts that can

be disassembled with a press or pin driver requires an

interference of approximately 0.01 to 0.03 mm (.0005 to

.001 in.) in parts up to 5 cm (2 in.) in diameter. Interference

two to three times greater requires a heavy press or heating

to expand the outer part (or cooling to contract the inner

part) to be assembled. Immersion of a part into liquid

nitrogen before it is placed into a hole can lead to a very

strong force ﬁt. Heavy force ﬁts or ‘‘shrink ﬁts’’ are effec-

tively permanent.

It is sometimes desirable to allow for some ‘‘give’’ in a

joint. For example, there is much to be said in favor of

rivets being used to join soft materials such as plastics or

fabric. A riveted lap joint in this case will allow for some

movement between the parts when a stress is applied. This

Figure 1.24 Joints.

JOINING MATERIALS 35

helps relieve stress concentration at the location of the

rivets. As another example, consider a situation where it

is anticipated that joined parts will change their relative

position or shape in response to a sudden temperature

change or differential. A springy fastener such as a bowed

retaining ring may be called for.

As a general rule, a joint should be designed so that the

pieces being joined are of roughly equal strength at the

point where they are joined, as suggested in Figure 1.25.

or parts of the same material, this implies that the parts

have the same cross-section at the joint or the same thick-

ness if the parts are of the same width. This is important in

the design of welded and brazed joints for reasons of both

manufacturer and application. Welding (as well as brazing)

parts of different thicknesses risks a weak joint because of

the differential in the rate of heat loss through the parts

being joined. The thinner part is overheated or the thicker

part does not achieve the temperature needed for fusion to

the proper depth (or, in the case of brazing, to be properly

wetted). The resulting state of heat treatment may be dif-

ferent on one side from the other. This will create a stress

riser since one side may be more ﬂexible than the other. In

general, the dimension of weld penetration should be the

same as the thickness of the parts near the joint. When a

thick piece of metal must be welded to a thin piece, it is

common practice to cut a groove in the thick piece, near

the joint, to limit the rate of heat loss into the heavier piece,

to effectively equalize the dimensions of the weld and the

parts at the location of the weld, and to avoid a concen-

tration of stress at the joint [Figure 1.25(b)]. This situation

arises

when welding a thin tube into a heavy ﬂange (Sec-

tion

3.6.3 and Figure 3.39).

ints with discrete fasteners such as bolts or rivets have

unique problems. Flexing of the assembled parts may lead

to a stress concentration at the corners of the head of the bolt

or rivet, as suggested in Figure 1.25(d). The designer must

lso allow adequate clearance for manufacture and assem-

bly. A tapped hole must leave the machinist clear access

with a drill and tap. For assembly there must be sufﬁcient

clearance to insert a bolt or screw, as well as space for the

wrench or screwdriver used to tighten the fastener. A rivet

hole requires access for a drill and reamer as well as clear-

ance for the tools employed to set the rivet. A threaded hole

that does not pass clear through a part, that is, a ‘‘blind

hole,’’ is sometimes necessary but should be avoided if

possible. A blind hole is difﬁcult to keep clean and free of

debris that will bind the threaded parts when they are being

assembled. There is also the possibility of damage should a

bolt longer than speciﬁed be driven into the bottom of a

blind hole. (The author once spent two weeks looking for

a vacuum leak through a crack at the bottom of a blind hole

created by an overlong bolt’s being driven into the bottom.)

The strength of a brazed or soldered overlap joint

depends upon the length of the lap and the shear strength

of the ﬁller metal. An oft-cited rule of thumb for a brazed

joint suggests that the length of the lap should be at least

three times the thickness of the thinner of two pieces being

joined. More precisely, The Brazing Book,

[also published

Figure 1.25 A joint should be designed so that the joined

parts are equally strong at the joint.

36 MECHANICAL DESIGN AND FABRICATION

online by Handy and Harman (www.handyharmancanada.

com)], speciﬁes the length of overlap in a brazed joint as

‘ ¼

where S

is the tensile strength of the weaker of the two

parts being joined, t is the thickness of that part, S

is the

shear strength of the ﬁller metal, and K is a ‘‘joint integrity

factor’’ to account for how effectively the ﬁller metal has

penetrated the joint and wetted the surfaces being joined (a

value of about 0.8 is typical). Note that the overlap must

increase when joining high-strength materials.

The space between brazed and soldered parts has a sig-

niﬁcant effect upon the strength of the joint. A brazed joint

between parts spaced 0.03 to 0.10 mm (.001 to .003 in.)

apart can be stronger than the base metal. The clearance

between ‘‘slip-ﬁtted’’ machined parts is usually adequate,

although, for parts of materials of very different coefﬁ-

cients of thermal expansion, one must consider the clear-

ance at the brazing temperature. Shims may be necessary

to keep polished surfaces apart. A blind joint is undesir-

able. The ﬁller metal entering a joint must displace the

ﬂux. Residual ﬂux trapped in a joint will lead to corrosion.

Additionally, visual inspection is required to assure that

the ﬁller metal has ﬂowed completely through a joint.

If a blind joint is unavoidable, vent holes should be pro-

vided for ﬂux escape and inspection into the deepest part

of the joint.

In general, parts to be joined should be designed to be

self-aligning when clamped together. If this is not possible,

or if very precise alignment is required, parts can be pinned

together. The parts are assembled and clamped in the

proper position, small holes are drilled and reamed, and

pins inserted to maintain alignment while the joints are

brazed, welded, or glued.

Special consideration must be given to a joint between

parts made of dissimilar metals. Two important issues are

the differential in the rates of thermal expansion of the

joined parts and electrical currents produced at the point

of contact. Welds between dissimilar metals may crack as

the parts cool or develop cracks when exposed to large

temperature swings. Brazed joints between dissimilar met-

als may be more tolerant of changes in temperature, but

electrolytic corrosion can be a problem. If a brazed joint is

contemplated, a brazing alloy more noble than the base

metals should be used. If electrolytic effects are a problem,

one solution may be to interpose an insulating layer

between the parts being joined. A layer of paint will sufﬁce

provided that the parts are secured in such a way that

relative movement between the parts does not abrade the

insulating layer. In a wet environment, avoid threaded con-

nections between dissimilar metals; corrosion will occur at

the threads where they are hidden from inspection.

1.4.10 Joints in Piping and Pressure

Vessels

Safety is the primary consideration in specifying or design-

ing a joint in a pressurized conduit or vessel. At high

pressures a sudden failure in a joint threatens life and limb.

At lower pressures a ruptured joint can result in expensive

damage if not personal injury. Of course, having consid-

ered safety in the design of a joint, the next requirement is

that the joint not leak. Short of personal injury, there is

perhaps no worse lab disaster than to spring a water leak

late Friday after everyone has gone home for the weekend.

It is generally desirable that a pressure vessel be built up

of cylindrical sections: the design and analysis of a cylindri-

cal vessel is easiest and most reliable (see Section 1.6.3);

joints

between concentric cylindrical sections are most easily

manufactured and assembled. Joints in the side of a cylin-

drical section are to be avoided: the design of such a joint is

difﬁ cult at best, the joint is a stress riser , and the fabrication

is inevitably difﬁ cult and expensiv e. In any event, a joint in a

pressure vessel must be as strong as the joined parts.

A joint in a pressure vessel may be demountable or

permanent depending on the particular requirements. A

demountable joint requires a compressible element of

rubber or metal – a gasket – that is trapped between more

robust surfaces at the joint. This element is elastically

deformed to provide the force required for sealing.

A permanent, leak-proof joint can be welded, brazed, sol-

dered, or glued depending on the pressure in the ﬂuid being

contained. A pipe-threaded joint may be demountable, but

often inconveniently so.

Pipes and pipe ﬁttings are threaded together. Pipe threads

are tapered so that a seal is formed when an externally

threaded pipe is screwed into an internally threaded ﬁtting.

The American Standard Pipe Thread, designated NPT for

National Pipe Thread, has a taper of 1 in 16. The diameter of

JOINING MATERIALS 37

a pipe thread is speciﬁed by stating the nominal internal

diameter of a pipe that will accept that thread on its outside.

For example, a pipe with a nominal internal diameter of

1/4 in. and a standard thread of 18 tpi is designated

1=418 NPT

or simply

1=4NPT:

The American Standard Pipe Thread speciﬁcations are

listed in Appendix 1.4.

Britain and Europe the usual tapered pipe thread

speciﬁcation is the British Standard Pipe Thread Tapered

(BSPT, BS EN 10226 equivalent to ISO 7). The taper is 1

in 16 and the size is given as the nominal bore of a pipe

with an external thread. The speciﬁcations for the British

Standard Pipe Thread Tapered are given in Appendix 1.5.

One

should take care not to confuse tapered pipe threads

(ISO 7) with the British Standard Pipe thread Parallel (ISO

228). The latter are not intended to make a leak-tight joint.

Demountable pressure ﬁttings are illustrated in

Figure 1.26. These include joints where the tubing itself

sﬂaredorswagedtomakeoneelementofthejoint,

joints where the seal is effected by a rubber O-ring or

soft metal gasket, and ultrahigh-pressure joints, in which

a c onical surface machined on the end of thick-wall tub-

ing is driven against a conical receptacle by a threaded

assembly (a so-called ‘‘coned-and-threaded’’ joint). The

last are commonly found in the laboratory as connections

to gas cylinders an d pressure regulators. T he conﬁgura-

tion of cone and thread are speciﬁc to each gas. These

connections have been stand ardiz ed by the Compressed

Gas Association and are identiﬁed by a ‘‘CGA’’ number.

The mechanical conﬁgurations of thirty three CGA ﬁt-

tings are given in Ap pend ix 1.6. Note that some of these

ﬁ

ttings have a left-hand thread to prevent mixing of ﬁt-

tings for incompati ble gases. For all mechanical ﬁttings it

is important to foll ow the manufacturer’s instructions for

assembly (this is especially important for the assembly of

ﬂare and swage ﬁttings, where precise deformation of the

tubing is essential to a leak-proof seal). Pay attention a s

well to the manufacturer’s speciﬁcation of pressure lim-

its, bearing in mind that the pressure limitation for each

type of connection is likely todecreasewithanincrease

in the diameter of the tubing.

The commercial market offers a remarkable number of

inexpensive assemblies that employ standard demountable

joints. These include tees, crosses, Ys, reducers, valves, and

pumps in sizes from a few millimeters to at least 20 cm in

Figure 1.26 Demountable joints for

tubing: (a) a ﬂare ﬁtting, (b) an ‘‘O’’-ring

gasketed joint (Swagelok

VCO),

(d) a ‘‘coned-and-threaded’’

ultrahigh-pressure connection.

38 MECHANICAL DESIGN AND FABRICATION

brass, steel, and stainless steel. These assemblies may be

intended for the dairy, automotive, or hydraulic equipment

industries, but can serve well in the lab. An entire apparatus

can be assembled from readily available standard assem-

blies at signiﬁcant savings in money and time. An hour’s

research on the web can save reinventing the wheel.

Permanent joints in piping and pressure vessels are

typically soldered or brazed cylindrical overlap joints, or

welded cylindrical butt joints.

Roughly speaking and assuming the ratio of diameter (D)

to wall thickness (t) does not exceed about 10, a joint sol-

dered with soft lead–tin solder can be used up to 1 MPa (150

psi) and tin–silver solder to perhaps 3 MPa; brazed joints

are acceptable to at least 10 MPa and welded joints to 100

MPa (assuming an appropriately certiﬁed welding techni-

cian). Above 100 MPa and up to 1 GPa, a system should be

built up of specialty ultrahigh-pressure assemblies employ-

ing coned-and-threaded ultrahigh-pressure ﬁttings. For

brazed or soldered, thin-wall vessels (D/t > 10), one must

be careful that hoop stress (Section 1.6.3) under pressure

es not exceed the shear strength of the ﬁller metal.

Brazing or soldering joints in cylindrical sections is

most practical in the lab. Joint design is illustrated in

Figure 1.27. The simple overlap joint requires no machin-

ing

provided one ﬁnds stock tubing that nests. The butt/

overlap joint makes for a constant wall thickness. The

socket joint is used to install a ﬁtting on a length of tubing

(see Figure 1.26). Manufacturers of demountable ﬁttings

provide

ﬁttings with sockets sized for tubing of standard

diameters. The Brazing Book gives the length of overlap

for a brazed tubular joint as:

‘ ¼

tðD tÞ

ð1:1Þ

where S

is the tensile strength of the weaker of the two

tubes being joined, t is the thickness of that tube, S

is the

shear strength of the ﬁller metal, and K is the joint integrity

factor (see above).

1.5 MECHANICAL DRAWING

Mechanical drawing is the language of the instrument

designer. Initial ideas for a design are expressed in terms

of simple, full-scale drawings that develop in complexity

and detail as the design matures. The construction of an

apparatus is realized through communications to shop per-

sonnel in the form of working drawings of each part of the

device. Successful design and construction relies on the

designer’s command of the language of mechanical draw-

ing. Even in the event that a scientist does both the design

and machine work, the completed instrument will beneﬁt

from the preparation of carefully executed mechanical

drawings.

1.5.1 Drawing Tools

Earlier editions of Building Scientiﬁc Apparatus provided a

list of the draftsman’s tools – pencils, triangles, T-square,

and so on – along with instructions in their use. The

Figure 1.27 Brazed joints in tubing: (a)

an overlap joint, (b) a socket joint, (c) a

butt/overlap joint.

MECHANICAL DRAWING 39

traditional instruments are still appropriate for the prepara-

tion of one or two drawings, but, more and more, computer-

aided design (CAD) programs have replaced them. For the

scientist for whom instrument design is a small, occasional

activity in the pursuit of broader scientiﬁc goals, a CAD

program offers relatively simple, but important, advan-

tages. Lines can be positioned precisely on a drawing and

the line weight is consistently and accurately controlled.

Scaling is done precisely so that dimensions can be deter-

mined directly from the drawing. Deletions are done at the

stroke of a key – a signiﬁcant time-saver compared to the

difﬁcult process of erasing pencil lines. Shapes can be dupli-

cated and tracings can be made with ease. Files can be saved

in an orderly fashion and easily retrieved for modiﬁcation

and updating. Lettering, once the laborious trademark of

good mechanical drawing, is done at the keyboard.

In truth, CAD programs offer much more than can be

effectively employed by the scientist–draftsman. With the

remarkable power of modern CAD programs, ‘‘modeling’’

has evolved as a new method of design. The traditional

draftsman–designer developed the plan of an instrument

in two-dimensional orthographic projections. With a

powerful CAD program it is possible to model an object

in a three-dimensional representation and extract the

required two-dimensional projections after the fact. This

approach has considerable appeal since the ﬁt between

parts can be seen graphically and interferences easily

avoided, however, from the point of view of this book, it

is hard to justify the time and effort required to learn to use

a three-dimensional CAD program, as well as the cost of

many of these programs. Another apparent advantage of

computer-assisted design with powerful drafting programs

is that the program can produce computer ﬁles that will

drive the lathes and milling machines in the shop, thus

obviating the need for drawings on paper, however, the

integration of computer-aided design and computer-aided

machining (CAD/CAM) is rarely practical for small model

shops building one-off instruments. The preparation of

two-dimensional orthographic working drawings is, at

least for the present, an essential step in building an instru-

ment. The designer of scientiﬁc apparatus must learn the

language of mechanical drawing.

The most modest drafting software (as opposed to ‘‘draw-

ing’’ software) will ordinarily serve the requirements of the

builder of scientiﬁc apparatus – Claris Cad, MiniCAD,

Graphite, or Vector Works for Mac and AutoCAD-LT or

ProEngineer for PC are examples of entirely satisfactory

programs. If a three-dimensional modeling program is

available, one quickly discovers that the two-dimensional

routines at the front end of these programs will fulﬁll most

needs. It follows that only modest computing power will be

required.

A drafting program incorporates hund reds or even

thousands of commands. The user must become conver-

sant with a signiﬁcant subset of these commands to

make progress without frequent reference to a manual.

Many successful designers make a practice of learning

at least one new command during every session at the

computer.

In contrast to the modest CPU requirements for com-

puter drafting, it is advantageous to have the largest pos-

sible monitor – a 21in. monitor is none too large. The

conception of an instrument in the drawing phase is deﬁ-

nitely enhanced if an entire, full-scale, drawing can be

viewed at once.

A printer or a plotter is an essential element of a CAD

system since one ordinarily must send paper copies of

working drawings to the shop. Although reduced-scale

drawings are appropriate for large industrial projects, the

instructions for the fabrication of the parts of an instrument

are best communicated in full-scale drawings. The letter-

size format of an ofﬁce laser printer is usually too small for

mechanical drawings. Investment in a large-format laser or

ink-jet printer or a pen plotter is frequently worthwhile.

Ink-jet printers accepting paper a meter wide are now

available. The large-format, E-size, pen plotter is the

drafting-room standard.

1.5.2 Basic Principles of Mechanical

Drawing

If mechanical drawing is the designer’s language, then

the line is the alphabet of this language. Some of the

basic lines used in pencil drawing are illustrated in the plane

view shown in Figure 1.28. Three line widths are employed:

ick lines for visible outlines, short breaks, and cutting

planes (explained below); medium lines for hidden outlines;

thin lines for center, extension, dimension, and long break

lines. A CAD program typically chooses a line width of 0.5

mm for thick lines, 0.3 mm for medium lines, and 0.2 mm

40 MECHANICAL DESIGN AND FABRICATION

for thin lines. If only two line weights are available, medium

lines are shown thin. For pencil-and-paper work, H-grade

lead is used for heavy lines and lettering, 2H for medium

and light lines, 4H for layout.

The shape of an object is described by orthographic

projection. This is the view that one obtains when an object

is far from the eye so that there is no apparent perspective.

There are six principal views of an object, as illustrated in

Figure 1.29. As indicated in the illustration, not all views

are

required to completely describe an object. The drafts-

man should present only those views that are necessary for

a complete description.

In America the relative position of the views i n ortho-

graphic projection must be as shown in Figure 1.29.Thus

e view seen from the right side of an object is placed

to the right of the front view; the view seen fr om the top

is placed above the front view. This is the so-called

third-angle projection. Of course, for clarity or conven-

ience, the draftsman is i nitially free to choose any side

of the o bjec t a s t he ‘‘front.’’ In Europe and Asia the ﬁrst-

angle projection is empl oyed (Figure 1.30). In this

projection

the view shown to the left of the front view

Figure 1.28 Lines used in mechanical drawing exempliﬁed

in a CAD drawing of a side view of the object at the top.

Figure 1.29 The six principal views of the bracket shown on the left. This is a third-angle

projection. This is the preferred projection in the New World. The views not required to

describe the bracket in this particular case have been crossed out.

MECHANICAL DRAWING 41

represents what would be seen i f the object in front view

wer e r olled to the left; the view shown above the front

view represents what would be seen were the object in

front view rolled 90° upwards. Of course it is very impor-

tant that anyone who views a drawing understands the

convention being used. Fi gure 1.31 shows orthographic

projecti

ons of a ‘‘tapered stopper’’ that can be unambig-

uously identiﬁed as either a ﬁrst-angle projection (on

the left) or a third-angle projection (on the right). These

‘‘pictograms’’ are recommended f or use a s symbols on

drawings to conﬁrm the projection intended by the drafts-

man. In this text, the third-angle projection is employed

throughout.

In some cases an auxiliary view will simplify a presen-

tation. For example, a view no rma l to an inclined surface

may be easie r to draw a nd more informative than one

of the six principal views. Such a case is illustrated in

Figure 1.32 . The relationship of the auxiliary view to the

Figure 1.30 A ﬁrst-angle projection of the bracket

shown in Figure 1.29. This is the projection preferred

Europe and Asia.

Figure 1.31 One or the other of these pictograms can be

placed on a drawing to distinguish a ‘‘third-angle

projection’’ from a ‘‘ﬁrst-angle projection.’’

Figure 1.32 Effective use of an auxiliary view.

Figure 1.33 Full section along the indicated plane.

42 MECHANICAL DESIGN AND FABRICATION

front v iew must be as shown. That is, the auxiliary view

of an inclined surface must be placed in the direction of

the normal to the s urfa ce. No te t he extens ion of th e cen ter

line from the auxiliary view to the front view to show the

direction of the auxiliary view.

Often the internal structure of an object cannot be

clearly indicated with hiddenedgesindicatedbydashed

lines. In this case it is u seful to show t he view that would

be seen if the object were cut open. Such a view is called

a section. An example of a full section is shown in

Figure 1.33.Thecutting

plane in the section is repre-

sented by cross-hatching with ﬁne lines to suggest a

saw cut. The cross-hatch lines should always be at an

oblique angle to the heavy lines that indicate the outline

of the section. If the cutting plane extends through more

than one part of an assembly, the cross-hatch lines on two

adjacent parts should be in dist inctly different directions.

The cutting plane in a view perpendicular to the section

is shown by a heavy section line of alternating long

and two short dashes. Arrows on the section line indi cate

the direction of sight from which the section is viewed.

Sections may be identiﬁed with letters at each end of the

cutting-plane line.

It is often useful to have the cutting plane change direc-

tions so that it passes through several features. Angled

surfaces are then revolved into a common plane and offset

surfaces are projected onto a common plane to give an

aligned section, as illustrated in Figures 1.34 and 1.35,

ther than a true projection of the cutt ing plane.

Other convenient sectioning techniques include the half

section of a symmetrical object, as shown in Figure 1.36,

and

the revolved section of a long bar or spoke, as shown in

Figure 1.37.

Man

y details, such as screw threads, rivets, springs, and

welds, are so tedious to draw, and appear so often, that they

are designated by symbols rather than faithful representa-

tions. Symbols for threads are illustrated in Figure 1.38.

Figure 1.34 An aligned view.

Figure 1.35 An aligned section.

MECHANICAL DRAWING 43

Drawings of parts too long to be conveniently ﬁtted on a

piece of drawing paper can be represented as though a

piece from the middle of the part had been broken out

and the two ends moved together. Three conventional

breaks are illustrated in Figure 1.39.

Mechanical

drawings include dimensions, tolerances,

and special descriptions and instructions in written form.

Lettering on mechanical drawings employs only uppercase

letters in a sans serif font. Letters about 6 mm (1/4 in.) high

are usually appropriate.

1.5.3 Dimensions

After the shape of an object is described by an ortho-

graphic projection, dimensions and notes on the drawing

specify its size. The dimensions to be speciﬁed depend

upon the function of the object and upon the machine

operations to be performed by the workman when fabricat-

ing the object.

Eitheradimensionoranotespeciﬁesdistanceona

drawing. A dimension indicates the distance between

points, edges, or surfaces (Figure 1.40). A no

te is a writ-

ten instruction that gives information on the size and

shape of a part (Figure 1.41). If SI units are intended,

the

linear unit of distance is the millimeter. In the New

World t he customary unit i n engineeri ng drawing is the

decimal inch. The c hoice of unit is stated in a note:

UNLESS OTHERWISE SPECIFIED, ALL DIMENSIONS

ARE IN MILLIMETERS (or IN INCHES , as applicable).

Apart from this note, the units of a dimension are not

ordinarily speciﬁed on a drawing. Contrary to usual

Figure 1.36 A half section.

Figure 1.37 A revolved section.

Figure 1.38 Thread symbols.

Figure 1.39 Breaks.

44 MECHANICAL DESIGN AND FABRICATION

scientiﬁc practice, when dimensions are in inches, a dec-

imal dimension less than unity is written without a zero

preceding the decimal point: .256 rather than 0.256.Onthe

other hand, when specifying millimeter dimensions, a zero

precedes the decimal for a dimension less than one milli-

meter: 0.8 rather than .8.

Dimensions may be given in series or parallel

(Figure 1.42). If a combination of these two methods is

used,

care must be taken to ensure that the size of the

object is not over-determined. An example of an over-

dimensioned drawing is given in Figure 1.43. Dimensions

should

not be duplicated, and a drawing should include no

more dimensions than are required. When several features

of a drawing are obviously identical, it is only necessary to

dimension one of them.

Dimensions are often speciﬁed with respect to a datum.

This is a single feature whose location is assumed to be

exact. When choosing a datum, consider the functional

importance of locating other features of an object relative

to the datum, as well as the ease with which the workman

can locate the datum itself. (In Figure 1.46, the center of

the

.427R circular section serves as a datum point.)

Figure 1.40 Dimensions.

Figure 1.42 Dimensions: (a) series dimensions;

(b) parallel dimensions.

Figure 1.41 A note.

MECHANICAL DRAWING 45

If possible, all dimensions should be placed outside

the view with extension lines leading out from the view.

As shown in Figure 1.42, the shorter dimensions are nearer

the object line. Dimension lines never cross extension

lines. Extension lines may cross extension lines if

necessary. Dimensions within the view are permissible to

eliminate long extension lines and if the dimension does

not obscure some detail of the view. The dimension closest

to the outside of a view should be about 12 mm (1/2 in.)

from the edge. Successive dimensions should be placed

at 9 to 12 mm (3/8 to 1/2 in.) intervals. Dimension values

should be staggered, as in Figure 1.44, rather than stacked

ver

tically or horizontally. Dimension values are oriented so

that they can be read from the bottom or the right side of

the drawing. Notice that the extension lines do not touch

the outline of the view, but rather stop about a millimeter

(1/16 in.) short.

Giving the diameter or radius, and dimensions to

locate the center of the radius of curvature, can specify a

round hole or circular part. As in Figure 1.43 and elsewhere,

e centerlines are extended to become extension lines.

Notes are used to specify the size of standard parts and

parts too small to be dimensioned. Notes are also used to

specify a feature that is derived from a standard operation

such as drilling, reaming, tapping, or spotfacing. Notes

such as ‘‘TAP 10-32 UNF, .75 DEEP’’ or ‘‘1/2 DRILL,

SPOTFACE .75D 3 .10 DEEP,’’ that refer to a speciﬁc

feature, are accompanied by a leader emanating from the

beginning or end of the note and terminating in an arrow-

head that indicates the location of the feature (Figure 1.41).

General

notes, such as ‘‘REMOVE BURRS’’ or ‘‘ALL

FILLETS 1/4 R,’’ that refer to the whole drawing, do not

require a leader.

Many abbreviations are used in writing dimensions and

notes. Common abbreviations used on mechanical draw-

ings are given in Table 1.4.

1.5.4 Tolerances

One of the most important parts of design work is the

selection of manufacturing tolerances so that a designed

part fulﬁlls its function and yet can be fabricated with a

minimum of effort. The designer must car efull y and

thoughtfully specify the function of each part of an appa-

ratus in order to arrive at realistic tole rances on each

dimension of a drawing. It is important to appreciate

the c apabilities of the machines that will be used in

manufacture, and t he time and effort required to maintain

a given tolerance. As indicated in Figure 1. 45 ,thecost

production is approximately inversely related to the

tolerances.

Usually only one or two tolerance speciﬁcations will

apply to most of the dimensions on a drawing. It is then

convenient to encode the tolerance speciﬁcation in the

dimension rather than afﬁx a tolerance to each dimension.

In instrument design most dimensions are written as

Figure 1.43 An overdimensioned drawing. One

of the dimensions is superﬂuous.

Figure 1.44 Placement of dimensions and dimen-

sion values.

46 MECHANICAL DESIGN AND FABRICATION

decimals. The number of decimal places of the dimension

can then indicate the tolerance on a dimension. Dimen-

sions expressed to two decimal places have one tolerance

speciﬁcation, to three decimal places another, and so on.

The speciﬁcations are given in a note. An example of this

system is given in Figure 1.46.

Fractions

may be used in the American system to give

the size of some features derived from standardized oper-

ations, such as drilling or threading; similarly a whole

number millimeter speciﬁcation may be used in the Euro-

pean system. A tolerance speciﬁcation is unnecessary in

these cases, since both the designer and workman should

know what precision could be expected.

There are two methods of expressly stating the

tolerance on a dimension. The allowable variation, plus

and minus, may be stated after the dimension. Alterna-

tively, the limits of the dimension can be stated without

giving a tolerance at all. Examples of these two methods

are given in Figure 1.47. The trend is toward limit dimen-

sioning.

Table 1.4 Abbreviations Used on Mechanical Drawings

Word Abbr. Word Abbr. Word Abbr.

Bearing BRG Fillister FIL Right hand RH

Bolt circle BC Grind GRD Rivet(ed) RIV

Bracket BRKT Groove GRV Round RD

Broach(ed) BRO Ground GRD Root mean square RMS

Bushing BUSH Head HD Screw SCR

Cap screw CAP SCR Inside diameter ID Socket SOC

Center line CL Key K Space(d) SP

Chamfer CHAM Keyway KWY Spot face(d) SF

Circle CIR Left hand LH Square SQ

Circumference CIRC Long LG Stainless STN

Concentric CONC Maximum MAX Steel STL

Counterbore CBORE Minimum MIN Straight STR

Counterdrill CDRILL Not to scale NTS Surface SUR

Countersink CSK Number NO Taper(ed) TPR

Cross section XSECT Opposite OPP Thread(ed) THD

Diameter DIA, D, Ø Outside diameter OD Tolerance TOL

Drawing DWG Pipe thread PT T

ypical TYP

Drill(ed) DR Press PRS Vacuum VAC

Each EA Punch PCH Washer WASH

Equal(ly) EQ Radius R With W/

Fillet FIL Reference line REF Without W/O

Figure 1.45 Approximate relation between tolerance and

the cost of production.

MECHANICAL DRAWING 47

When the absolute size of two mati ng parts is not

important, but the clearance between them is critical,

specify the desired ﬁt. Fits are classiﬁed as sli ding ﬁts,

clearance locational ﬁts, transition ﬁts, interference ﬁts,

and force ﬁts. The uses of the various classes of ﬁts and

tables of the tolerances required to give such ﬁts are given

in standard texts on mechanical drawing.

Beware of an unde sirable accumulation of tolerances.

In series dimens ioning, th e tolerance on the distance

between two points separated by two or more dimensions

is equal to the sum of the tolerances for each of the

intervening dimensions. In Figure 1.42(a) the toler ance

the lateral location of the hole with respect to the right

side of the object is given by the sum of two tolerances.

For parallel dimensions, the location o f each feature

relative to the datum depends on only one tolerance;

however, the d ifference in t he distance between two loca-

tions depends upon two tolerances. In Figure 1.42(b),the

tolerance

on the distance between the two holes is given

by the sum of the tolerances on th e dimens ions that

locate the holes.

As much as possible, dimensions and tolerances should

be chosen so that materials can be used in their stock sizes

and shapes. Do not call for unnecessary ﬁnishing. For

example, the area around a hole in a casting or other rough

piece of metal can be spotfaced to provide a bearing sur-

face for a bolt if the quality of the rest of the surface is not

critical.

The dimensions and tolerances on a ﬁnished drawing

should be carefully checked. Imagine yourself as the

machinist who must use the drawing to make a part.

Proceed mentally through each step of the fabrication

to see that all necessary dimensions appear on the draw-

ing and that the speciﬁed dimensions are easy to use.

Also satisfy yourself t hat all desired tolerances are

within the capabilities of the anticipated machine-tool

operations.

1.5.5 From Design to Working Drawings

The ﬁrst step in designing an instrument is to draw the

entire assembly. Start with rough sketches in pencil and

Figure 1.46 A decimal system for the speciﬁcation of tolerances.

48 MECHANICAL DESIGN AND FABRICATION

paper before turning to the computer. Then, with the CAD

program, draw the outline of the most important parts

of the instrument. Work to full scale if possible. Add sub-

sidiary parts after the conﬁguration of the essential ele-

ments has been established. Most dimensions, tolerances,

and ﬁne details can be omitted at this point.

Pay attention to the manner in which pieces ﬁt together.

Will the apparatus be convenient to assemble and disas-

semble? Is there sufﬁcient clearance to insert bolts, pins,

and other fasteners? Are some parts much stronger or

weaker than required? Does a strong part depend upon a

weak one for location or support? Are all shapes as simple

as possible? Are standard shapes of materials and standard

bolts, couplings, bearings, and shafts used wherever pos-

sible?

Time spent at the drawing board mentally assembling

and disasse mbling a device will save hours of frustration

in the laboratory. Careful consideration of production

techniques c an save hundr eds of dollars in the shop.

With the initial orthographic drawing of the apparatus in

hand, it is wise to discuss it with the people who will do

the work.

After the design has reached its ﬁnal form, the designer

must make a working drawing of each piece of the appa-

ratus. A working drawing is a fully dimensioned and tol-

eranced drawing to be used in the shop. Work to scale if

possible. The CAD program is especially useful at this

point. A new layer can be superimposed on the assembly

drawing and the outline of a single part transferred to the

new layer without fear of error. Alternatively the outline

of an individual part can be copied and transferred to a

new ﬁle. The draftsman should develop a systematic way

of naming drawings so they can be stored and easily

retrieved.

The critical test of a set of working drawings is their

usefulness. All necessary communication between scien-

tist and machinist should appear on the drawings. The

machinist should not require oral instructions, and should

not be required to make decisions affecting the perform-

ance of an instrument.

In the above discussion we have assumed that the sci-

entiﬁc designer has the services of a model shop. This is

the case in industrial laboratories and in many university

laboratories. The designer should follow the same proce-

dure when he fabricates his own apparatus. All questions

of sizes, tolerances, and ﬁts must be answered before con-

struction. When a scientist attempts to make these deci-

sions as he proceeds with construction, the results are

invariably poor.

1.6 PHYSICAL PRINCIPLES OF

MECHANICAL DESIGN

No material is perfectly ri gid. W hen any member of a

machine is subjected to a force, no matter how small, it

will bend or twist to s ome extent. Even in the absence of

an external load, a mechanical element bends under its

own weight (so-called ‘‘body forces’’). A machine ele-

ment subj ect ed to a force that varies in time will vibrate.

A designer must appreciate the extent of deﬂection of

mechanical parts under load. The forces applied to or

contained by an a pparatus must be anticipated in specify-

ingthematerialanddimensionsofeachelement.The

Figure 1.47 Two methods of stating the tolerance

on a dimension: (a) as the allowable variation on a

dimension; (b) in terms of the allowable limits of

the dimension.

PHYSICAL PRINCIPLES 49

hallmark of a well-designed machine is that every el e-

ment bears the same level of stress and that stress does not

threaten the function of the machine or the capabilities of

the materials of whi ch the machine is constructed or the

fasteners that hold the parts together.

1.6.1 Bending of a Beam or Shaft

When a beam bends, one side of the beam experiences a

tensile load and the other a compressive load. Consider a

point in the ﬂexed beam in Figure 1.48. The stress at this

point

depends upon its distance, c, from the centroid of the

beam in the direction of the applied force. The centroid is

the center of gravity of the cross section of the beam [see

Figure 1.48(b)]. The stress is given by:

s ¼

ð1:2Þ

where M is the bending moment at the point of interest

and I is the centroidal moment of inertia of the section of

the beam containing the point of interest. Cl early the

stress in a ﬂexed beam i s greatest at the oute r surface of

the beam.

The centroidal moment of inertia of the section (more

correctly known as the second moment of the area of

the cross-section) is the integral of the square of the dis-

tance from the centroid multiplied by the differential

area at that distance. The integral is taken along a line

through the centroid and parallel to the applied force.

ForarectangularsectionofheightH and width B,such

as that shown in Figure 1.48 (b ), the centro idal moment of

inert

ia is:

I ¼

B=2

B=2

H=2

H=2

dhdb ¼

ð1:3Þ

The centroidal moments of inertia of some common sym-

metrical sections are given in Figure 1.49.

The bending

moment is proportional to the curvature

produced by the applied force:

M ¼ EI

ð1:4Þ

where y is the deﬂection produced by the force and E is the

modulus of elasticity of the material of which the beam is

composed. For the example given in Figure 1.48, assuming

the

weight of the shaft can be ignored, the bending moment

is simply:

M ¼FðL  xÞð1:5Þ

where L is the length of the beam. The bending

moments for this and other simple systems are given in

Figure 1.50.

The

deﬂection of a stressed beam at a point a distance x

from a supported end of the beam depends upon the mod-

ulus of elasticity of the material, the centroidal moment of

the section of the beam, and the nature of the support. We

consider the case where the beam is rigidly ﬁxed to its

support(s) (as in Figure 1.48) and the case where the beam

supported at each end by a simple fulcrum. Expressions

Figure 1.48 A ﬂexed beam: (a) the beam bending under a load; (b) a cross section sowing

the centroid; (c) the distribution of shear forces along the long axis of the beam.

50 MECHANICAL DESIGN AND FABRICATION

for the deﬂection of both point-loaded and uniformly

loaded beams are given in Figure 1.50.

sufﬁciently large bending moment will result in

the permanent deformation of a beam. This is the yield

point. A conservative relation between t he bending

moment at the yield point, M

, and the yield strength of

the material, s

, is given by M

¼ s

I/c

max

. [For the rec-

tangular sect ion beam supported at one end ( Fi gu re 1 . 48),

max

¼ H/2 and M

¼ s

/6.] To determine the max-

imum allowable load on a beam or shaft one simply sets

equal to the expression fo r the maximum value of the

bending moment on the beam and solves f or the force.

Figure 1.49 Centroidal moments of inertia.

Figure 1.50 Bending formulae: M ¼ bending moment;

E ¼ modulus of elasticity; I ¼ centroidal moment of inertia;

w ¼ weight per unit length.

PHYSICAL PRINCIPLES 51

(For the re ctangular section beam supported at one end,

¼ s

/6L.) In reality the yield strength of a beam in

bending is grea ter than for a beam i n tension, since the

inner ﬁbers of the m aterial must be loaded to their yield

point to a cons iderable depth before the be am is perm a-

nently deforme d.

Even in the absence of applied forces, the e lements of

a machine bend under their own weight or if the machine

is otherwise accelerated or decelerated. An important

conclusion of the discussion above is that this effect is

reduced if the size of the machine is reduced; a mechan-

ical structure becomes stiffer as it is scaled down in size.

Consider a horizontal b eam of rectangular cross-section

cantilevered from a wall. From Figure 1.50, setting x ¼

the weight of the beam causes a deﬂection at the

free end:

max

8EI

ð1:6Þ

where w is weight per unit length of the beam. Taking

w ¼ qBH,whereq is the weight density of the material of

the beam, and substituting for I gives:

max

3qL

2EH

ð1:7Þ

If the dimensions of the beam are scaled down by a

factor f:

max

3qð1LÞ

2Eð1HÞ

¼ f

3qL

2EH

ð1:8Þ

The deﬂection decreases as the square of the scale factor;

the relative deﬂection,

max

decreases linearly with the

scale factor.

It should be noted that all of the preceding discussion

assumes the tensile strength of a material to be the same as

the compressive strength. For materials such as cast iron

where this is not true, the bending equations are much

more complicated. The foregoing also ignores shear

stresses in a loaded beam. For very short beams, shear

stresses become important and the shear strength of the

material must be considered.

1.6.2 Twisting of a Shaft

The stress at a point in a hollow round shaft subjected to a

torsional load is:

s ¼

, J ¼

 D



ð1:9Þ

where c is the distance of the point of interest from the

center of the shaft and T is the appl ied torque. J is

the centroidal polar moment o f inertia of the section of

the shaft, and D

,andD

are t he outer and inner diameters

of the shaft.

The total angle of twist in a shaft of length L is:

h ¼

57LT

deg ð1:10Þ

where G is the modulus of elasticity in shear, or shear

modulus, of the material of the shaft. For metals, the shear

modulus is about 1/3 the elastic modulus.

1.6.3 Internal Pressure

In the scientiﬁc lit erature, ‘‘high pressure’’ implies pres-

sures in excess of 1 GPa (15000 0 psi). Beyond 1 GPa

most ﬂuids condense to s olid phases. At pressures in

excess of 1 GPa, remarkable pressur e-induc ed chemi cal

changes are observed. Not coincidently, 1 GPa corre-

sponds approximately to the yield strength of the stron-

gest materials. We shall not discuss here the special

technologies, notably the diamond anvil, that are requir ed

above 1 GPa.

To an engineer, 0.1 to 1 GPa is ‘‘ultrahigh pressure.’’ In

spite of what this term might i mply, familiar technologies

are appropriate. Ultrahigh pre ssur e t ub ing and tube ﬁt-

tings, demountable joints, valves, and piston pumps are

commercially available (forexample,HighPressure

Equipment Company, PO Box 8248, Erie, PA 16505,

USA). As noted previously, scientiﬁc app ar atus to be

operated i n this pressure range should be built up entirely

of commercial components with coned and threaded

joints; joints brazed or welded in the lab or the local shop

are n ot safe or reliable at pressures above 0.1 GPa.

Indeed, consideratio ns of b oth safety and economics

52 MECHANICAL DESIGN AND FABRICATION

favor the use of commerc ial c omp onents when building

apparatus to operate at elevated pressures.

A pressure vessel should incorporate only cylindrical

sections if at all possible. The design and analysis of a

cylinder under internal press is easiest and most reliable.

Joints between cylindrical sections are most easily manu-

factured and assembled (see Section 1.4.10). Of course the

stress

exerted by an internal pressure is easily calculated

for vessels with other simple geometric shapes (spheres,

cones); their manufacture, however, can be daunting. In

any event, it is recommended that one design for at least

ﬁve times the anticipated pressure, unless a professional

engineer is consulted.

The maximum stress on a cylinder under internal pres-

sure is a tensile stress tangent to the inner surface of the

cylinder. For a cylinder with i nner and outer radii, R

and

, respectively, under pressure P, the maximum value of

this tangential stress, the so-called ‘‘hoop stress,’’ is:

PðR

þ R

 R

ð1:11Þ

Shearing forces are most often responsible for rupture in

ductile materials. The maximum shear stress is at the inner

surface where:

sheer

 R

ð1:12Þ

For a thin-wall cylinder the expression for the hoop

stress reduces to:

¼ P

ð1:13Þ

where R is the inner radius and t the wall thickness, and it is

assumed t < 0.1R. The longitudinal (axial) stress and the

shear stress in this approximation are then just half the

hoop stress.

Expansion of a vessel under internal pressure may be an

issue in some instances. In the thin-wall approximation the

hoop strain is:

e ¼

2Et

ð2  lÞð1:14Þ

where E is the modulus of elasticity and l is Poisson’s ratio

for the material of which the cylinder is made. Recalling

that strain is the increase in length per unit length, the

dilation, or radial growth of a cylinder under internal

pressure is:

d ¼

2Et

ð2  lÞð1:15Þ

The longitudinal strain is:

e ¼

2Et

ð1  2lÞð1:16Þ

The end closure of a cylindrical vessel may be spherical,

torospherical (elliptical in cross-section) or ﬂat. The ﬁrst

two are certainly more robust than a ﬂat plate closure, but

the manufacture will be difﬁcult and expensive. The stress

in a ﬂat end plate depends upon how securely the end plate

is attached to the cylindrical vessel. If there is the possi-

bility of movement between the end plate and the cylinder

to which it is attached, such as for a removable, gasketed-

and-bolted, endplate, the maximum stress occurs at the

center of the plate where, for a plate of thickness d and

radius R:

s ¼



ð1 þ lÞP ð1:17Þ

The deﬂection under pressure at the center of the plate is:

d ¼

3PR

ð5 þ lÞð1  lÞ

16Ed

ð1:18Þ

For a permanently afﬁxed ﬂat closure, such as an end

plate welded to a cylindrical vessel, the maximum stress is

at the edge where the radial stress is:



P ð1:19Þ

and the tangential stress is:



ð1 þ lÞP ð1:20Þ

PHYSICAL PRINCIPLES 53

Deﬂection under pressure at the center of a permanently

ﬁxed end plate is:

d ¼

3PR

ð1  l

16Ed

ð1:21Þ

Design for external pressure is discussed in Section

3.6.2 in the context of vacuum chambers.

1.6.4 Vibration of Beams and Shafts

In many instruments, vibration of a supporting beam or

shaft c an adversely affect operati on. The designer must

pay spe cial attention t o the natur al frequencies of vibra-

tion of the parts of an instrument. A periodic d isturbance

with a frequency near that of one of the natural fre-

quencies will induce a large and possibly destructive

vibration. For the purpose of illustration, the response

of an oscillator to the frequency of a driving force is

shown in Figure 1.51.

here a re two wa ys for the designer t o prevent destruc-

tive vibratio ns. The critica l element can be designed so

that its natural frequency of vibration is far removed from

the frequency of a disturbing force, or the disturbing force

can be in hi bited in the vicinity o f th e natural frequency o f

the critical element. The latter scheme is called damping.

Very low-frequency vibrations can be damped by a

hydraulic or friction shock absorber such as is employed

on automobile suspensions. High frequencies can be

damped by coup ling the objectionable source of vibration

to its surroun ding s th rough a member that has a very low

natural frequency of vibration. Mounts made of rubber or

cork are very effecti v e for absorbing high-frequency vibra-

tions and sudden shocks, since these materials possess a low

modulus of elasticity.

The fundamental frequency of vibration (in Hz) of a

shaft or beam with one or more concentrated masses

attached is given by:

qAY

dx þ +

ð1:22Þ

where:

I ¼ centroidal moment of inertia of the shaft,

M ¼ M(x) ¼ maximum bending moment at x, i.e., the

amplitude of the bending moment induced by the forces on

the shaft at x,

a ¼ inertial acceleration experienced by the shaft and its

weights (for a nonrotating shaft, a ¼ g),

E ¼ modulus of elasticity of shaft material,

q ¼ weight density of the shaft [(q /g) is the mass

density],

A ¼ cross-sectional area of the shaft,

L ¼ length of the shaft

Y ¼y(x) ¼ maximum deﬂection of the shaft at x, i.e., the

amplitude of vibration at x,

¼ force exerted by the ith mass (for a nonrotating

shaft, this is the weight of the ith mass),

¼ maximum deﬂection at the location of the ith

mass.

Figure 1.51 Response of a machine element to a

periodically varying force. Y# is the amplitude of

vibration of the element and f

is its natural frequency

of vibration. Y and f are the amplitude and frequency of

the driver.

54 MECHANICAL DESIGN AND FABRICATION

For a system similar to one of the static deﬂection

cases treated in Figure 1.50, one need only substitute the

appropriate

expressions for the bending moment and

deﬂections and solve the resulting equation to determine

the natural frequency. Consider for example a beam of

negligible mass that is rigidly supported at one end and

supports a mass of weight W at its free end. This is the case

illustrated at the top of Figure 1.50. The natural frequency

vibration is:

L  xðÞ

W

6EI

3Lx

 x



x¼L



3gEI



1=2

Hz: ð1:23Þ

In general, the shape of the deﬂection curve is not known.

However, the assumption of some reasonable deﬂection

curve usually will provide a useful result. In most cases

one can assume a sine curve for a shaft supported (but

not clamped) at both ends, or a parabola for a shaft sup-

ported at only one end. More precise approaches to com-

plex systems are given in many engineering texts on

vibration.

Consider once again the beam of negligible mass, rig-

idly supported at one end, with a weight W at the free end.

A parabolic deﬂection curve with the correct limit proper-

ties is given by:

y ¼

L  xðÞ

ð1:24Þ

where y

is the maximum deﬂection of the free end. The

bending moment is then:

M ¼ EI

¼EI



: ð1:25Þ

Substituting in the equation for the natural frequency

gives:

2EI y



W y

ðÞ

gEI



Hz ð1:26Þ

in reasonable agreement with the exact solution derived

above.

For the special case of a heavy shaft or beam with a

centrally placed load, a correct solution can be derived

by assuming the shaft to be weightless and adding half

the weight of the shaft to the concentrated load.

1.6.5 Shaft Whirl and Vibration

A shaft and rotor can never be perfectly balanced, and the

axis of rotation can never be exactly located by the shaft

bearings. As a shaft rotates, centrifugal force on the unbal-

anced mass deﬂects the shaft and causes it to whirl around

its axis of rotation. This whirling motion appears as a vibra-

tion to a stationary observer, and can be treated as such.

There is a critical speed at which the whirl becomes violent.

In this unstable condition, the shaft or its bearings are likely

to be damaged and intense vibration will be transmitted

through the bearing mount to other parts of the machine.

This critical condition occurs when the shaft speed (in rps)

equals the natural frequency (in Hz) of the stationary shaft

and rotor assembly. It follows that the mathematical deriva-

tions of natural frequencies of assemblies of beams and

weights can be applied to the calculation of critical speeds

for shafts and rotors. The actual centrifugal loads on the

rotating shaft need not be determined. This is because the

load F always appears as the ratio F/a and:

¼ m ð1:27Þ

where W is the weight of the element that is ex erting the load.

The critical speed for a rotor-shaft assembly depends

upon how rigidly the shaft bearings support the shaft.

Two extreme cases are considered: a thin bearing, such

PHYSICAL PRINCIPLES 55

as a ball bearing, for which the angle of the shaft passing

through the bearing is not ﬁxed; and a thick bearing, such

as a plain sleeve bearing, that rigidly maintains the angular

alignment of the shaft. The critical speed for a rotor on a

weightless shaft supported on thin bearings is:

¼ 0:276

gEIL



1=2

rps ð1:28Þ

where W is the weight of the rotor, I is the centroidal

moment of inertia of the shaft, E the modulus of elasticity

of the shaft material, L the length of the shaft between the

bearings, and a and b are the distances from the rotor to the

bearings. If the ends of the shaft are rigidly supported in

long bearings the critical speed is:

¼ 0:276

gEIL



1=2

rps ð1:29Þ

Notice that the critical speed can be increased by placing

the rotor near one end of the shaft so that a or b is small.

In this case the rotor acts as a gyro tending to stiffen the shaft.

For an unloaded shaft on thin bearings the critical

speed is:

¼ 1:57

EIg

qAL



1=2

rps ð1:30Þ

and for an unloaded shaft on long bearings:

¼ 3:53

EIg

qAL



1=2

rps ð1:31Þ

where q is the weight density of the shaft material. The

units of the individual quantities appearing in brackets in

the four equations above must be such that overall the

quantity in brackets has units of s

. For the particular case

of a solid, round, steel shaft the critical speeds are:

The special case of a centrally placed rotor on a heavy

shaft can be treated by adding half the weight of the shaft

to the rotor and taking the shaft to be weightless. The

critical speed for a shaft carrying several rotors can be

approximated by:

þ +



1=2

ð1:33Þ

where n

is the critical speed of the shaft alone and n

the critical speed for the ith rot or alone on a weightless shaft.

The designer must manipulate the dimensions and mate-

rial of a shaft and rotor, and the location of the rotor, so that

its critical speed does not coincide with the design speed of

an assembly. It is usually sufﬁcient for these two speeds to

differ by a factor of

ﬃﬃﬃ

. The most desirable situation is for

the critical speed to exceed the design speed. If this is not

possible, the drive motor for the rotating assembly should be

so powerful that the shaft accelerates very rapidly through

the region of the critical speed. The drive motor will require

an excess of power because considerable power is dissipated

to vibration at the critical speed.

The formulae above give the lowest frequency of vibra-

tion and the lowest critical speed for a shaft and rotor

assembly. A shaft with a number of weights has as many

different fundamental modes of vibration as it has weights.

In addition, vibration will occur at harmonics of the fun-

damentals.

For rotational speeds far away from a critical speed, a

rotating assembly can be considered to be rigid. Neverthe-

less, imbalance can lead to inertial (centrifugal) forces that

may damage the shaft or its bearings. If the unbalanced

mass lies within a plane perpendicular to the axis of

¼ 80 000

rps ½thin bearings; D ¼ diameter ð in:Þ; L ¼ length ðin:Þ

¼ 3 150

rps ½thin bearings; D ¼ diameter ðmmÞ; L ¼ length ðmmÞ

¼ 180 000

rps ½long bearings; D ¼ diameter ðin: Þ; L ¼ length ðin:Þ

¼ 7 100

rps ½long bearings; D ¼ diameter ðmmÞ; L ¼ length ðmmÞ ð1:32Þ

56 MECHANICAL DESIGN AND FABRICATION

rotation, as for the case of a thin rotor on a shaft, the rotor

can be statically balanced. The condition for static balance

is that the axis of rotation passes through the center of

gravity. In practice this can be accomplished by placing

the shaft with its rotor across a pair of knife-edge rails.

The shaft will roll or rock until coming to rest with the

unbalanced inertial force pointed radially downwards.

Weight is then added or removed along the vertical radius

until balance is achieved.

If there are unbalanced masses acting at different points

along the axis, then dynamic balancing is required. The

conditions for dynamic balance are that the axis of rotation

passes through the center of gravity and that the axis of

rotation coincides with a principal axis of the inertial force.

Dynamic balancing is difﬁcult without specialized equip-

ment. Balancing is done inexpensively and accurately as a

commercial service.

1.7 CONSTRAINED MOTION

In addition to a rigid support structure, most machines

include some moving parts. The motion of these parts must

usually be constrained in some fashion to obtain the

required function. Most often the desired motion is trans-

lation in a plane or along a line, or rotation about one or

more axes. The design of the constraining mechanism for a

moving part must meet dimensional, strength, and wear-

resistance speciﬁcations.

To achieve constrained motion the designer may either

create a support structure for the moving part that will give

the desired alignment, or make use of a standard, commer-

cially available machine element. In the former case, it is

necessary to understand the principles and limitations of

geometric design. In the latter, the designer must be famil-

iar with the range and precision of commercial bearings,

shafts, sliders, and so on. The economics of the choice

should not be ignored.

1.7.1 Kinematic Design

A rigid body has six independent degrees of freedom of

motion. These are usually taken to be the translational

motions along three or tho gona l axes through the center

of gravity and the rotational motions about these axes.

Any motion can be described as a linear combination of

these six motions. Similarly, six coordinates deﬁne the

position of a body: three p ositi on coordina tes and th ree

angle coordinates. Motion is constrained and the number

of degrees of freedom is reduced if one o f these coordi-

nates is ﬁxed or if some linear combination of these

coordinates is ﬁxed. For example, a rigid object will be

constrained to move in a plane if one of its position coor-

dinates is ﬁxed. Kinematic design for constrained motion

consists of ﬁxing a point on a body for each degree of

freedom to be constrained.

In general, one degree of freedom can be removed by

constraining a point on a body to remain in contact with a

reference surface. The following examples illustrate this

principle of kinematic design:

(1) Consider a sphere constrained to maintain point con-

tact with each of two reference planes: a ball resting in

a V-groove. The ball is free to rotate about any axis,

but it can only translate along a line parallel to the

intersection of the planes. The ball has lost two

degrees of freedom.

(2) A three-legged ‘‘milking stool’’ that is constrained to

maintain three points of contact with a plane surface

has only three degrees of freedom: translation in two

directions parallel to the plane and rotation about an

axis perpendicular to the plane.

(3) A body in contact at three points with a cylindrical

surface has three degrees of freedom: translation in

the direction of the cylinder axis, revolution about the

cylinder axis, and rotation about an axis perpendicular

to the plane deﬁned by the three points of contact.

The object of kinematic design is to permit motion to be

constraine d wit hout d ep end ing up on pr ec ision of ma nu -

facture. A co mpl icatio n exists if two contact point s are

degenerate in the sense that the function of the two points

can be served b y a si ngle point of co nt ac t. Conside r a

four-legged table vis-a

-vis a three-legged table. One of

the four legs provides a degenera te point of contact with

the ﬂoor. The fourth leg may provide some much-needed

stability, but it also introduces uncertainty in the location

of the table t op unless all four legs are of precisely the

same length. Of course, the sort of c onsid erat ion s that

lead to the production of four-legged tables often dictates

CONSTRAINED MOTION 57

a semikinematic or degenerate kinematic design for other

devic es as well.

Kinematic designs are illustrated in Figures 1.52–1.54.

e ball feet on the carriage shown in Figure 1.52

provide ﬁve points of c ontact b etween the carriage and

its

base. Thus the carriage is only free to slide in one

direction. One problem with this design is that it is difﬁ-

cult to mill a V-groove with smooth surfac es. The s urface

quality o f t he g roove can be improved by lapping with

carborundum, u sing a V-shaped brass lap that ﬁts in the

gro ove.

An improved version of the design in Figure 1.52 is

sho

wn in Figure 1.53. A pair of steel rods replaces the

-groove, and balls replace the feet of the carriage. This

design is both more precise and more economical than the

previous one. Stainless-steel shafting, hardened and cen-

terless-ground to a diameter tolerance of 60.001 mm

(6.00005 in.), is available at a cost of a few euros a foot.

Stainless-steel balls with a roundness tolerance of 60.001

mm are also inexpensive. The channel that contains the

rods must be milled, but the surface quality in this channel

is not critical. In a milling operation, the sides of the

Figure 1.52 Kinematic design that constrains a

carriage to move in a straight line.

Figure 1.53 An improved version of the design

shown in Figure 1.52.

Figure 1.54 Kinematic design that permits an

accurately located part to be removed and replaced

in the same position.

58 MECHANICAL DESIGN AND FABRICATION

channel can easily be kept straight and parallel to within

0.01 mm/m (.0001 in./ft.).

The three grooves in the platform shown in Figure 1.54

allow precise relocation of a three-legged table after it has

been

removed. The ball feet of the table make six points of

contact with the platform, so that there are no degrees of

freedom.

In applying the principles of kinematic design it must be

borne in mind that all materials are more or less elastic.

Deformation or deﬂection of the elements of a kinematic

structure under load leads to a deviation from true kinematic

behavior. In the absence of careful analysis of such effects, it

is often possible to obtain higher precision location or move-

ment, as well as greater stability, through the use of standard,

nonkinematic elements such as bearings and ball sliders.

Smith and Chetwynd discuss the analysis and exploitation

of elastic deformation on kinematic designs in their excel-

lent book on the design of precision mechanism.

1.7.2 Plain Bearings

A bearing is a stationary element that locates and carries

the load of a moving part. Bearings can be divided into two

categories depending upon whether there is sliding or

rolling contact between the moving and stationary parts.

Sliding-contact bearings are called plain bearings. Rolling

bearings will be discussed in the next section.

Plain bearings may be designed to carry a radial load,

an axial load, or both. Different types are illustrated in

Figure 1.55. A radial bearing consists of a cylindrical shaft

or journal rotating

or sliding within a shell, which is the

bearing proper. The entire assembly is referred to as a

journal bearing. An axial bearing consists of a ﬂat bearing

surface, like a washer, against which the end of the shaft

rests. These are called thrust bearings. A journal bearing

may incorporate a ﬂanged journal, in which case it will

support a radial load as well as an axial load.

A journal is usually hardened steel or stainless steel.

Precision-ground shafts and shafts with precision-ground

journals are available in diameters from 1 to 25 mm (1/32

to 1 in.). Bearing shells of bronze or oil-impregnated

bronze are available to ﬁt. Nylon bearings for light loads

and oil-free applications are also available. Commercial

shafting and bearings are manufactured to provide a clear-

ance of 0.005–0.02 mm (.0002–.0010 in.).

Many different methods of lubrication can be employed

instead of oil impregnation. The inner surface of the bear-

ing can be grooved, and oil or grease can be forced into the

groove through a hole in the shell. If oil is objectionable, a

groove on the inner surface of the bearing can be packed

with molybdenum disulﬁde or other dry lubricant.

A plain bearing is installed by pressing it into a hole in

the supporting structure. An interference of about 0.03 mm

(.001 in.) is desirable for bearings up to an inch in diam-

eter. That is, the outer diameter of the bearing shell should

be about 0.03 mm (.001 in.) larger than the hole into which

it is pressed. If the interference is too great, the inner

diameter of the bearing may be signiﬁcantly reduced.

A variety of bearing housings and pillow blocks (Figure

1.56) are available. These mountings are bored to accept

standard

bearings and in many instances the bearing is

premounted. These mounts replace precision-bored bear-

ing mounts.

Figure 1.55 Plain bearings: (a) a journal bearing; (b) a

thrust bearing; (c) a ﬂanged jour nal bearing.

Figure 1.56 (a) A bearing housing; (b) a bearing mounted

in a pillow block.

CONSTRAINED MOTION 59

It is usually necessary to provide axial location for a

shaft in a journal bearing. This can be accomplished with

a retaining ring in a groove on the shaft (Section 1.4.4) or a

collar secured by a setscrew.

Plain bearings run smoothly and quietly, and have a high

load-carrying ability. Properly installed and lubricated,

they have a very long life. Because of the close clearances

between parts, they are not easily fouled by dirt in their

environment. Plain bearings are limited to relatively low-

speed operation. Speeds in excess of a few hundred rpm

are not practical without forced lubrication. The primary

disadvantage of plain bearings is their high starting fric-

tion, although, when properly installed and lubricated,

their running friction can be very low.

1.7.3 Ball Bearings

The rolling element in a rolling contact bearing may be a

ball, cylinder, or cone. Ball bearings are used for light

loads and high speeds. Roller bearings employing cylin-

drical or conical rollers are suitable for very heavy loads,

but are not often used for instrument work. We shall dis-

cuss only ball bearings.

As with plain bearings, there are both radial and thrust

ball bearings (Figure 1.57). A radial

ball bearing consists

of an inner and an outer race with a row of balls between.

The grooves in each race have a radius slightly larger than

the radius of the balls so that there is only point contact

between the balls and the race. The balls are separated by a

retainer that prevents the balls from rubbing against one

another and keeps them uniformly spaced around the bear-

ing. A radial ball bearing can tolerate a substantial thrust

load, but for pure axial loads a thrust bearing should be

used. A thrust bearing is similar to an axial bearing except

that it has upper and lower races rather than inner and outer.

Ball bearings are made of steel or stainless steel. They are

graded 1, 3, 5, 7, or 9 dependingon manufacturing tolerances.

Grades7and9havegroundracesandaremadetotheclosest

tolerances. They cost little more than lower-grade ones and

should be speciﬁed for instrument applications.

Proper installation is required to obtain good perform-

ance from a ball bearing. The rotating race should be given

a ﬁrm interference ﬁt, and the stationary race given a light

‘‘push ﬁt’’ to permit some rotational creep. This slight

movement of the stationary race helps prevent the maxi-

mum load from always bearing on the same spot.

Press ﬁtting changes the internal clearances in a bearing.

Bearing manufacturers specify the amount of interference

that should be used. As shown in Figure 1.58, the press

arbor

used to drive a bearing onto a shaft or into a housing

should be designed so that the thrust is not transmitted

through the balls. Never hammer a bearing into place.

Figure 1.57 Ball bearings: (a) a radial ball bearing;

(b) a thrust ball bearing.

Figure 1.58 Installation of a bearing. The press

arbor should bear on the race that is being ﬁtted.

60 MECHANICAL DESIGN AND FABRICATION

The surface quality and diameter tolerance of the shaft

that is to be ﬁtted into a bearing, or the hole that is to house

a bearing, must be of the same quality as the bearing. For

high-quality bearings the mounting surfaces should be

ground. Centerless-ground precision shafting is available

to ﬁt all standard bearings. Bearing mounts and pillow

blocks with premounted bearings are similarly available

to eliminate the need for precision machine work when

installing ball bearings.

Ball bearings are designed with both radial and axial

clearances. This play is intended to allow for axial misalign-

ment and for dimensional changes that occur upon installa-

tion or because of thermal stresses. For the best locational

precision and to obtain smooth, vibration-free operation, a

ball bearing should be pr eloaded to remove most of this play.

A preloading force that displaces one race axially with

respect to the other will remove both radial and axial play

by causing the balls to roll up the sides of their groov es. The

use of a shim to take up the play in a bearing is illustrated in

Figure 1.59. For light-duty applications, the end play can

also

be taken up by installing a spring washer (Section

7.5) instead of a shim. W ith proper installation, a ball

bearing

will locate a revolving axis to within a few thou-

sandths of a millimeter (ten-thousandths of an inch).

Bearings must be protected from effects that damage the

race surface on which the balls roll. Ball bearings are most

likely to fail because of occasional large static loads that

produce an indentation in the race. Such a dent is called a

brinell. Dynamic loads are distributed around the race and

are less likely to cause damage; however, a hard vibration

can cause brinelling in the form of a series of dents or

waves on the surface of a race. Of course, a bearing is also

damaged by the introduction of foreign matter that abrades

or corrodes the bearing surfaces.

Bearings should be lubricated with petroleum oils or

greases. For high speeds and light loads the lightest, ﬁnest

grades of machine oil can be used. Ball bearings require

very little oil. Lubrication is sufﬁcient if there is enough oil

to produce an observable meniscus at the point where each

ball contacts a race.

Cleanliness is important. In a dirty environment, bear-

ings with built-in side shields should be used. It is probably

wise to use enclosed bearings in all instrument applications

to keep the bearings clean and to prevent oil from contam-

inating the environment.

The chief advantages of ball bearings are their low starting

friction and very low running friction. They are well suited to

high-speed, low-load operation. Relativ e to plain bearings,

ball bearings are noisy and occupy a large volume. The cost

of quality ball bearings is so small that economic consider-

ations are usually not important in choosing between rolling

bearings and plain bearings for an instrument.

1.7.4 Linear-Motion Bearings

A linear-motion bearing may be of either the sliding or

rolling type. A plain journal bearing can be used to locate

a shaft that is to move axially. A V-shaped or dovetail

groove sliding over a mating rail can serve as a bearing

between a heavily loaded, slowly moving carriage and a

stationary platform. This is the type of bearing used

between the carriage and the bed of a lathe.

Linear ball bearings are commercially available. In a

bearing for use with an axially moving shaft, the balls that

carry the load between the outer race and the shaft move in

grooves that run parallel to the axis of the shaft. The balls

are recirculated through a return track when they roll to the

end of a groove. Linear-motion ball bearings will locate a

shaft to within 60.005 mm (6.0002 in.) of a reference

axis. Their cost is comparable to conventional rotating ball

bearings. Complete roller-slide assemblies are also avail-

able. These employ balls rolling in V-grooves. Roller slides

will maintain straight-line motion to within 0.002 mm per

centimeter (.0002 in. per inch) of travel.

Figure 1.59 Installation of a shim to remove end play in a

shaft mounted on ball bearings.

CONSTRAINED MOTION 61

1.7.5 Springs

In many instances it is desirable for a motion to be con-

strained by a ﬂexible element such as a spring. Springs are

used to hold two parts in contact when zero clearance is

required, to absorb shock loads, to damp vibrations, and to

measure forces.

A spring is characterized by the ratio of the magnitude

of applied force to the resulting deﬂection, d. This is the

spring rate:

k ¼

ð1:34Þ

As is the case for any ﬂexible system, an assembly con-

sisting of a spring and attached load has a natural fre-

quency of vibration:



1=2

Hz ð1 :35Þ

where m includes the mass of both the spring and any load

that is afﬁxed to it. Since m ¼ W/g ¼ F/a,wehave,upon

substituting for the spring rate in this equation



1=2

Hz, ð1:36Þ

where d

is the static deﬂection produced by the weight of

the spring plus the attached load.

In most applications it is desirable to choose a spring

that will not resonate with any other part of the apparatus

into which it is installed. If the spring is expected to damp a

vibratory motion, its natural frequency should differ from

that of the disturbance by more than an order of magnitude.

A spring will exert an uneven force wh en it is subjected

to a p eri odic ally varying load whose frequency is close to

the natural frequency of the spring. When the vibration

of the spring is in phase with the load, the reactive force

of the spring will be less than its static force for any given

deﬂection. When the spring is out of phase with the load,

it will exert a greater force than expected. This phenomenon

is called surge. Surge can be reduced or eliminated by using

two springs with different natural frequencies. In the case

of helical springs, they can be placed one inside the other.

In instrument work, helical springs are most often used.

Helical torsion, extension, and compression springs are

illustrated in Figure 1.60. The number of coils in a helical

spring

must be sufﬁcient to ensure that the spring wire

remains within its elastic limit when the spring is at max-

imum deﬂection. The number of coils in a compression

spring also determines the minimum length that is realized

when successive coils come into contact. A long compres-

sion spring may buckle under stress. This tendency is dis-

couraged if the ends of the spring are square. It can be

prevented by placing a rod through the center or by instal-

ling the spring in a hole. In general, a compression spring

must be supported by some means if its length exceeds its

diameter by more than a factor of ﬁve.

The spring rate of a helical spring made of round wire is:

k ¼

ð1:37Þ

where G is the shear modulus of the spring material (about

1/3 of the elastic modulus), t the diameter of the wire, N the

number of coils, and D the mean diameter (the average of

the inner and outer diameters) of the spring. The natural

frequencies for free vibrations are:

4pND



1=2

Hz ð1:38Þ

where q is the weight density of the spring wire and n is an

integer. For steel wire:

14000nt

Hz ðD and t in inchesÞ

550nt

Hz ðD and t in millimetersÞð1:39Þ

A variety of steels and bronzes are used for spring

manufacture. High-carbon steel wire works well. If

Figure 1.60 Springs: (a) helical torsion spring; (b) helical

extension spring; (c) helical compression spring.

62 MECHANICAL DESIGN AND FABRICATION

necessary the spring can be wound in the annealed state

and hardened after forming. Music wire, or piano wire, is

one of the best materials for one-off construction of

small springs. It is available in diameters of 0.1 to 3

mm (.004 to .103 in.). This wire is very strong and hard

because of the drawing process used in its production,

and doe s not ne ed to be hardene d after fo rming.

Type-302 stainless-s teel wi re is u seful for springs that

are subject to a corrosive environment. Springs of ber-

ylli um–copper wire are especially useful in applications

where spring deﬂection is used to gauge a force, since this

material maintains a linear stress–strain relation almost

to the point of permanent deformation. As mentioned

earlier, quartz ﬁber torsion springs can also be used in these

applications.

Winding wire on a mandrel as it is rotated in a lathe

conveniently forms helical coil springs. The wire must be

kept under tension as it is pulled onto the mandrel. When

the tension is released, the formed spring will expand so

the mandrel must be somewhat smaller than the desired

inner diameter of the ﬁnished spring. The production of a

small number of springs of a given size and spring rate is

probably best carried out by cut-and-try.

Commercially manufactured springs are readily avail-

able. They are convenient to use because the supplier

speciﬁes such properties as the spring rate and free length.

There are hundreds of possible spring conﬁgurations;

however, disk springs are the only form that we shall men-

tion other than coil springs. A disk spring, also known as a

Belleville spring washer, is a cone-shaped disk with a hole

in the center [Figure 1.61(a)]. When loaded, the cone

ﬂattens.

This is a very stiff spring that can absorb a large

amount of energy per unit length. Stacking disk springs as

in Figure 1.61(b) can create a s pring of any desired travel.

heymustbealignedbyarodpassingthroughtheir

centers or else by stacking them in a hole slightly larger

than the outer diameter of the disks. If the disks are

stacked in parallel as shown in Figure 1.61(c), they will

pro

vide a great deal of damping owing to friction b etween

the faces of the disks.

1.7.6 Flexures

Flexures are beams made of a ﬂexible spring material,

such as beryllium–copper or spring steel, that are

intended to provide a small, controlled, displacement

along or about a known axis. They are basically ﬂexible

hinges. A clock pendulum is often suspended from a ﬂex-

ure. Owing to their uncomplicated nature and ease of

manufactur e they are particularly attractive for the pro-

vision of controlled motion in small devices. They have

the advantages of requiring no lubrication and having no

hysteresis since there is no friction and there are no clear-

ances. It is often possible to create a ﬂexure by machining

a thin section in a single monolithic mechanism rat her

than forming and mounting a separa te ﬂexible element

to the machine. This is not only e conomical, but avoids

problems with alignment between the mechanism and the

ﬂexible hinge, as well as movement about the fastener that

joins the hinge to the machine. A ﬂexure is typically a

simple homogeneous shape so the force–displacement rela-

tion can be accurately calculated from elementary physical

principles (described in Section 1.6.1). W ith careful design,

linear force–displacement relation can be achieved for

small displacements.

Figure 1.62 illustrates, at least conceptually, two basic

motions

obtainable with a ﬂexible beam. In both cases the

ﬂexible element is rigidly mounted to a stationary base at

one end and to a moveable platform at the free end. In

Figure 1.62(a) a force applied to the platf orm produces a

rot

ation of the platform. For small displacements the

angle of rotation is proportional to the applied force. I n

Figure 1.62(b) a bracket is attached to the

platform so that

the force can be applied along a line normal to the center

of the ﬂexure. The ﬂexed spring bends near its ends and

assumes a n ‘‘S’’ shape with a straight section in the

Figure 1.61 Belleville spring washers; (a) a disk spring;

(b) disk springs stacked on a shaft; (c) disk springs stacked

in parallel.

CONSTRAINED MOTION 63

middle. The ben ding moment, being a function of the

curvature of the beam, is zero at the midpoint in line with

the applied force and the platform undergoes a linear

displacement (d) that, for small displacem ents, is propor-

tional to the force (F):

d ¼

12EI

ð1:40Þ

where I is the centroidal moment of inertia of the spring

section and E the modulus of elasticity of the spring mate-

rial. The spring constant, or stiffness,isF/d.

In pr act ice neither of the arr ange ments in Figure 1.62

is satisfactory since any misalignment of the applied

force

leads to pitching or twisting of the platform. A

practical d esign for a linea r translation platform i s illus-

trated in Figure 1.63. The wide springs illustrated offer

res

istance to twisting and provide a wider platform f or the

attachment of other components of the apparatus. Using

two springs in a parallelogram arrangement offers resist-

ance to pitching. In many applications of this design, the

force is applied directly to th e platform; however, max-

imum resist ance to pitching is gained if a bracket is

attached, as in Figu re 1.62 (b) so that the force act s

rough the midpoint of the springs. With two springs,

the stiffness of the mechanism is doubled and the dis-

placement for a given f orce is halved. The parall elogram

arrangement results in a slightly curved path of the plat-

form; the platform moves downward with increasing dis-

placement. This err or in the linear motion has been

analyzed in detail by Jones

and must b e accounted for

in precision applications.

The vertical displacement error in the design in Figure

63 is corrected in the compound ﬂexure design shown

in Figure 1.64. Here t he platform in the simple ﬂexure

become

s the base f or a second ﬂexure. The downward

displacement of the intermediate platform is exactly

compensatedbyanupwarddisplacementofthelower

platform. The driving force is appl ied to the lower plat-

form. The overall stiffness is half that of the si mple ﬂex -

ure in Figure 1.63. It is worth noting that the compound

esign also compensates for temperature effects on the

lengths of the springs.

A leaf spring with clamped ends moving in antiparallel

directions bends into an ‘‘S’’ shape as noted above. Nearly

all the ﬂexion occurs near the clamped ends with the center

section remaining straight as if it were rigid. This ﬂexion

Figure 1.62 A platform mounted to a ﬂexure attached to a

solid base: (a) a transverse force applied at the end of the

ﬂexure produces a rotation of the platform; (b) a force

applied normal to the center of the ﬂexure produces a linear

translation of the platform.

Figure 1.63 A practical design for a linear

translation platform mounted on leaf springs. The

inset illustrates the vertical error in the linear motion.

64 MECHANICAL DESIGN AND FABRICATION

near the clamped end of a spring is quite similar to what

would occur when a bending moment is applied to a

cantilever that is notched near its ﬁxed end, as shown in

Figure 1.65(a). This is a notch

hinge. A beam with a notch

hinge at each end can simulate a leaf spring ﬁxed at one

end to a base and at the other end to a transversely moving

platform. The obvious extension of this idea is a ﬂexure in

which the base, platform, and spring are all machined from

a single piece of material. Figure 1.65(b) shows the mono-

lithic

notch-hinge analogy to the basic linear-motion ﬂex-

ure illustrated in Figure 1.62(b) . The force–displacement

relation

for the notch hinge has been derived analytically

by Paros and Weisbord

and by ﬁnite element methods

by Smith, Chetwynd, and Bowen.

The latter analysis

gives:

d ¼

3FKRL

EBt

ð1:41Þ

for the basic linear-motion ﬂexure illustrated in

Figure 1.65(b),whereR i

s the radius of each of the notches,

t is the width of the web at each notch, B is the width of the

beam (as in Figure 1.48), and the factor K ac

counts for the

effective length of the ﬂexible part of the web. K varies from

about 0.2 for a relatively thin, ﬂexible web, where t is much

less than R, to about 0.7 for a relatively stiff spring, with t

comparable to R.

Flexures provide for relatively small displacements,

especially ﬂexures employing notch hinges. Linear

force–displacement response, free of hysteresis, requires

that the elastic limit of the spring material not be exceeded.

For the linear-motion notch-hinge ﬂexure in Figure 1.65(b),

maximum

displacement, in the model of Smith, et al.,

approximated by:

max

¼ 4K



max



L ð1:42Þ

where s

max

is the maximum tolerable stress in the material

of the spring. For design purposes, s

max

can be taken to be

the yield strength of the material, or, conservatively, some

fraction thereof. The ratio of the yield strength to the mod-

ulus of elasticity (E) for mild steel, stainless steel, or tem-

pered aluminum alloy is about 0.003 and for hard plastics

such as polyamide (Nylon) or polyimide (Vespel) the ratio

is about 0.03. In a simple notch-hinge linear-motion

ﬂexure, the ratio (R/t) is typically about 5; this gives a

maximum displacement of no more than about 0.01L for

a simple metal ﬂexure and 0.1L for a plastic ﬂexure.

As s ugg ested by the cont our of the notch hinges shown

in Figure 1.65, fabri cation of a monolithic ﬂexure

requi

res only milling a nd bori ng operations. The preci-

sion of the motion, as well as the stiffness, of a monolithic

ﬂexure is determined primarily by the precision in the

location of the centers of t he holes that create a notch.

The relative ease of manufacture of precise monolithic

ﬂexures allows for q uite complex designs. An elegant,

Figure 1.64 A compound ﬂexure design to correct for the

error shown in Figure 1.63.

Figure 1.65 Monolithic ﬂexures analogous to those shown

in Figure 1.62.

CONSTRAINED MOTION 65

stable, and precise, double-c om pound, recti linear sprin g

is shown in Figure 1.66.

There are many variations on the basic notch spring. On

a beam, a closely spaced pair of notches at right angles

provides for two degrees of freedom. Notch springs

machined into thin metal stock can serve the function of

a Belleville spring to absorb shock or take up end-play in a

mechanism or to limit motion to a single plane. Examples

are shown in Figure 1.67. In these ﬂexures the material in

the

notch is stressed in torsion.

Cited References

1. R. P. Pohandish (Ed.), Machinery’s Handbook

Pocket Companion, Industrial Press Inc., New York, 2000.

2. ASM Handbook Volume 04: Heat Treating, ASM

International, Ohio, 1991.

3. J. W. Dally and W. F. Riley, Experimental Stress Analysis,

McGraw-Hill, New York, 1965, pp. 165–221.

4. F. Rosebury, Handbook of Electron Tube and Vacuum

Techniques, Addison-Wesley, Reading, MA, 1965.

5. A comprehensive list of brazing alloys has been compiled

by W. H. Kohl, in Handbook of Vacuum Physics, Vol. 3,

Technology, A. H. Beck (Ed.), Pergamon Press, Elmsford,

NY, 1964; Materials and Techniques for Electron Tubes,

Reinhold, N, 1959. See also reference 6.

6. The Brazing Book, Lucas-Milhaupt/Handy & Harman of

Canada, Cudahy, WI, USA.

7. R. J. Roark, Formulas for Stress and Strain, 4th edn.,

McGraw-Hill, New York, 1965.

8. C. Mathews, A. S. M. E. Engineer’s Data Book, 2nd edn.,

ASME Press, NY, 2001, pp. 75, 188–189.

9. D. E. Newland, Mechanical Vibration Analysis and

Computation, Longman Scientiﬁc & Technical/John Wiley

& Sons, Inc., New York, 1989; S. S. Rao, Mechanical

Vibrations, 2nd edn., Addison-Wesley, Reading, MA, 1990;

W. Weaver, Jr., S. P. Timoshenko, and D. H. Young,

Vibration Problems in Engineering, 5th edn., John

Wiley & Sons, Inc., New York, 1990.

10. A useful review of kinematic design is given by J. E. Furse,

J. Phys. E., 14, 264, 1981.

11. S. T. Smith and D. G. Chetwynd, Foundations of

Ultraprecision Mechanism Design, Gordan and Breach

Science Publishers, Philadelphia, 1992.

12. R. V. Jones, J. Sci. Instr ., 28, 38, 1951; J. Sci. Instr ., 33,

11, 1956.

13. J. M. Paros and L. Weisbord, Machine Design, 151, 25 Nov.

1965.

14. S. T. Smith, D. G. Chetwynd, and D. K. Bowen, J. Phys.

E: Sci. Instrum., 20, 977, 1987.

General References

Design of Moving and Rotating

Machinery

R. M. Phelan, Dynamics of Machinery, McGraw-Hill, New York,

1967.

Figure 1.66 Monolithic, double-compound, rectilinear

spring (reference 14).

Figure 1.67 Monolithic ﬂexures in a thin material.

66 MECHANICAL DESIGN AND FABRICATION

Vibration Analysis

D. E. Newland, Mechanical Vibration Analysis and Computation,

5th edn., Longman Scientiﬁc & Technical, Essex, England and

John Wiley & Sons, New York, 1989.

S. S. Rao, Mechanical Vibrations, 2nd edn., Addison-Wesley,

Reading, MA, 1990.

W. Weaver, Jr., S. P. Timoshenko, and D. H. Young,

Vibration Problems in Engineering, John Wiley & Sons,

New York, 1990.

Mechanical Design Texts

A. D. Deutschman, W. J. Michels, and C. E. Wilson, Machine

Design, Macmillan, New York, 1975.

V. M. Faires, Design of Machine Elements, 4th edn., Macmillan,

New York, 1965.

R. E. Parr, Principles of Mechanical Design , McGraw-Hill,

New York, 1970.

R. M. Phelan, Fundamentals of Mechanical Design, 3rd edn.,

McGraw-Hill, New York, 1970.

S. T. Smith and D. G. Chetwynd, Foundations of Ultraprecision

Mechanism Design, Gordan and Breach Science Publishers,

Philadelphia, 1992.

Mechanical-Drawing Texts

T. E. French and C . J. Vierck, Engineering Drawing and

Graphic Technology,11thedn.,McGraw-Hill,NewYork,

1972; (entitled A Manual of Enginee ring Drawing in its ﬁrst

10 editions).

F. E. Ciesecke, A. Mitchell, H. C. Spencer, and I. L. Hill,

Technical Drawing, 5th edn., Macmillan, New York, 1967.

Mechanical Engineering Handbooks

R. Timings, Mechanical Engineer’s Pocket Book, 3rd edn.,

Newnes/Elsevier, Oxford, 2006.

R. P. Pohandish (Ed.), Machinery’s Handbook Pocket Companion,

Industrial Press Inc., New York, 2000.

C. Mathews, A. S. M. E. Engineer’s Data Book, 2nd edn., ASME

Press, NY, 2001.

Properties of Materials

A. J. Moses, The Practicing Scientist’s Handbook, Van Nostrand

Reinhold, New York, 1978; F. Rosebury, Handbook of Electron

Tube and Vacuum Techniques, Addison-Wesley, Reading,

MA, 1965.

Goodfellow Catalog, Berwyn, PA and, Goodfellow

Cambridge Limited, Cambridge, web catalog http://

www.goodfellow.com.

Brazing

The Brazing Book, Lucas-Milhaupt/Handy & Harman

of Canada, Cudahy, WI and online at http://www.

handyharmancanada.com

REFERENCES 67

Appendix 1.1 Number drills with inch and metric

equivalents and tap sizes for approximately 75% thread

depth.

SIZE No

or Letter

inches mm Tap Size

American

National

Tap Size ISO

Metric Coarse

Thread Series

80 .0135 0.34

79 .0145 0.37

78 .0160 0.41

77 .0180 0.46

76 .0200 0.51

75 .0210 0.53

74 .0225 0.57

73 .0240 0.61

72 .0250 0.64

71 .0260 0.66

70 .0280 0.71

69 .0292 0.74

0.75 M1

68 .0310 0.79

67 .0320 0.81

66 .0330 0.84

65 .0350 0.89

64 .0360 0.91

63 .0370 0.94

0.95 M1.2

62 .0380 0.97

61 .0390 0.99

60 .0400 1.02

59 .0410 1.04

58 .0420 1.07

57 .0430 1.09

1.15 M1.4

56 .0465 1.18

3/64 0-80

1.30 M1.6

55 .0520 1.32

54 .0550 1.40

1.50 M1.8

53 .0595 1.51 1-64

52 .0635 1.61

1.65 M2

51 .0670 1.70

50 .0700 1.78 2-56

1.8 M2.2

49 .0730 1.85

48 .0760 1.93

47 .0785 1.99 3-48

68 MECHANICAL DESIGN AND FABRICATION

Appendix 1.1. (contd.)

SIZE No

or Letter

inches mm Tap Size

American

National

Tap Size ISO

Metric Coarse

Thread Series

46 .0810 2.06

45 .0820 2.08

2.10 M2.5

44 .0860 2.18

43 .0890 2.26 4-40

42 .0935 2.37

41 .0960 2.44

40 .0980 2.49

39 .0995 2.53

2.55 M3

38 .1015 2.58 5-40

37 .1040 2.64

36 .1065 2.71 6-32

35 .1100 2.79

34 .1110 2.82

33 .1130 2.87

32 .1160 2.95 M3.5

31 .1200 3.05

30 .1285 3.26

3.40 M4

29 .1360 3.45 8-32

28 .1405 3.57

27 .1440 3.66

26 .1470 3.73

25 .1495 3.80 10-24 M4.5

24 .1520 3.86

23 .1540 3.91

22 .1570 3.99

21 .1590 4.04 10-32

20 .1610 4.09

19 .1660 4.22

4.30 M5

18 .1695 4.31

17 .1730 4.39

16 .1770 4.50 12-24

15 .1800 4.57

14 .1820 4.62

13 .1850 4.70

12 .1890 4.80

11 .1910 4.85

10 .1935 4.91

9 .1960 4.98

8 .1990 5.05

APPENDIX 69

Appendix 1.1. (contd.)

SIZE No

or Letter

inches mm Tap Size

American

National

Tap Size ISO

Metric Coarse

Thread Series

5.10 M6

7 .2010 5.11 1/4-20

6 .2040 5.18

5 .2055 5.22

4 .2090 5.31

3 .2130 5.41 1/4-28

2 .2210 5.61

1 .2280 5.79

A .234 5.94

B .238 6.05

6.10 M7

C .242 6.15

D .246 6.25

E .250 6.35

F .257 6.53 5/16-18

G .261 6.63

H .266 6.76

6.90 M8

I .272 6.91

J .277 7.04

K .281 7.14

L .290 7.37

M .295 7.49

N .302 7.67

7.90 M9

5/16 3/8-16

O .316 8.03

P .323 8.20

Q .332 8.43

8.60 M10

R .339 8.61

S .348 8.84

T .358 9.09

U .368 9.35 7/16-14

V .377 9.58

9.60 M11

W .386 9.80

X .397 10.08

Y .404 10.26

10.40 M12

Z .413 10.49

27/64 1/2-13

29/64 1/2-20

.480 12.20 M14

70 MECHANICAL DESIGN AND FABRICATION

Appendix 1.3 ISO (Metric) Coarse Threads.

Size

M(mm)

Pitch

(mm)

Tap Drill

(mm)

Size

M(mm)

Pitch

(mm)

Tap Drill

(mm)

M1 0.25 0.75 M3.5 0.6 2.90

M1.2 0.25 0.95 4 0.7 3.30

M1.4 0.30 1.10 5 0.8 4.20

M1.6 0.35 1.25 6 1 5.00

M1.8 0.35 1.45 8 1.25 6.80

M2 0.4 1.60 10 1.5 8.50

M2.2 0.45 1.75 12 1.75 10.50

M2.5 0.45 2.05 14 2 12.00

M3 0.5 2.50 16 2 14.00

M3.5 0.6 2.90 18 2.5 15.50

Appendix 1.2 American Standard Threads. Uniﬁed National Coarse (UNC) and

Uniﬁed National Fine (UNF) threads with tap drill and clearance drill sizes.

The tap drill size is for approximately 75% thread depth. A range of

clearance hole drills is given depending upon whether a close ﬁt

or a free ﬁt is desired.

(Number and letter drill diameters are given in Appendix 1.1.)

Size

(Nominal

Diameter,

Inches)

UNC UNF Clearance

Hole Drill

Close-Free

Threads

per Inch

Tap Drill

Size

Threads

per Inch

Tap Drill

Size

0 (0.060) 80 3/64 52–50

1 (0.073) 64 53 72 53 48–46

2 (0.086) 56 50 64 50 43–41

3 (0.099) 48 47 56 45 37–33

4 (0.112) 40 43 48 42 32–30

5 (0.125) 40 38 44 37 30–29

6 (0.138) 32 36 40 33 27–25

8 (0.164) 32 29 36 29 18–16

10 (0.190) 24 25 32 21 9–7

12 (0.216) 24 16 28 14 2–1

1/4 20 7 28 3 F–H

5/16 18 F 24 I P–Q

3/8 16 5/16 24 Q W–X

7/16 14 U 20 25/64 29/64–15–32

1/2 13 27/64 20 29/64 33/64–17/32

Note: ASA B1.1-1989.

APPENDIX 71

Appendix 1.5 British Standard Pipe Thread Tapered.

(BSPT, BS EN 10226 equivalent to ISO 7)

Nominal

Bore Size

of Pipe

(in.)

Nominal

Bore Size of

Pipe

(mm)

Pipe

(mm)

Threads

per

Inch

Pitch

(mm)

Length of

Engagement

by Hand

(mm)

Effective

Thread

Length

(mm)

1/8 6 10.2 28 0.907 4.0 6.5

1/4 8 13.5 19 1.337 5.0 8.7

3/8 10 17.5 19 1.337 6.4 10.1

1/2 15 21.3 14 1.814 8.2 13.2

3/4 20 26.9 14 1.814 9.5 14.5

1 25 33.7 11 2.309 10.4 16.8

11/4 32 42.4 11 2.309 12.7 19.1

11/2 40 48.3 11 2.309 12.7 19.1

Nominal bore sizes in inches and mm are equivalents not conversions

Appendix 1.4 American Standard Taper Pipe Threads.

Nominal Bore

Size of Pipe

(in.)

Actual O.D.

of Pipe

(in.)

Threads

per Inch

Length of

Engagement

by Hand

(in.)

Length of

Effective

Thread

(in.)

1/8 0.405 27 0.180 0.260

1/4 0.540 18 0.200 0.401

3/8 0.675 18 0.240 0.408

1/2 0.840 14 0.320 0.534

3/4 1.050 14 0.340 0.546

1 1.315 11 1/2 0.400 0.682

11/4 1.660 11 1/2 0.420 0.707

11/2 1.900 11 1/2 0.420 0.724

2 2.375 11 1/2 0.436 0.756

21/2 2.875 8 0.682 1.136

3 3.500 8 0.766 1.200

Note: ASA B2.1-1989.

72 MECHANICAL DESIGN AND FABRICATION

Appendix 1.6 CGA connections for high-pressure gas cylinders.

CGA 110

.3125-32UNEF-2B-RH-INT

CGA 165

.4375-20UNF-2A-RH-EXT (1⁄4" SAE Flare)

CGA 180

.625-18UNF-2A-RH-EXT

CGA 240

.375-18NGT-RH-INT

CGA 280

.745-14NGO-RH-EXT

CGA 290

.745-14NGO-LH-EXT

CGA 295

.750-16UNF-2A-RH-EXT (1⁄2" SAE Flare)

CGA 296

.803-14UNS-2B-RH-INT

CGA 320

.825-14NGO-RH-EXT (Flat Nipple)

CGA 326

.825-14NGO-RH-EXT (Small Round Nipple)

CGA 330

.825-14NGO-LH-EXT (Flat Nipple)

CGA 346

.825-14NGO-RH-EXT (Large Round Nipple)

CGA 347

.825-14NGO-RH-EXT (Long Round Nipple)

CGA 350

.825-14NGO-LH-EXT (Round Nipple)

CGA 170

.5625-18UNF-2A-RH-EXT

Washer or O-Ring

may be used

APPENDIX 73

CGA 500

.885-14NGO-RH-INT (Bullet Nipple)

CGA 510

.885-14NGO-LH-INT (Bullet Nipple)

CGA 540

.903-14NGO-RH-EXT

CGA 555

.903-14NGO-LH-EXT

CGA 580

.965-14NGO-RH-INT

CGA 590

.965-14NGO-LH-INT

CGA 660

1.030-14NGO-RH-EXT (Face Washer)

CGA 670

1.030-14NGO-LH-EXT (Face Washer)

CGA 677

1.030-14NGO-LH-EXT (Round Nipple)

CGA 678

1.030-14NGO-LH-EXT (Recessed Washer)

CGA 679

1.030-14NGO-LH-EXT (Tipped Nipple)

CGA 680

1.045-14NGO-RH-INT

CGA 695

1.045-14NGO-LH-INT

CGA 701

1.103-14NGO-RH-EXT

CGA 440

.875-14UNF-2A-RH-EXT (5⁄8" SAE Flare)

Appendix 1.6 (contd.)

74 MECHANICAL DESIGN AND FABRICATION

CGA 702

1.125-14NGO-RH-INT

CGA 703

1.125-14NGO-LH-INT

CGA 705

1.125-14UNS-2A-RH-EXT

Appendix 1.6 (contd.)

APPENDIX 75

WORKING WITH GLASS

Glass has been called the miraculous material. The ubiq-

uity of glass in the modern laboratory certainly conﬁrms

this. Because glass is chemically inert, most containers are

made of it. Glass is transparent to many forms of radiation,

and its transmission properties can be varied by controlling

its composition; all sorts of windows and lenses are made

of glass. Because glass can be polished to a high degree

and is dimensionally stable, most mirrors are supported on

glass surfaces. Glass is strong and stiff, and is often used as

a structural material. Considering its mechanical rigidity

and density, it is a reasonably good thermal insulator. It is

an excellent electrical insulator. Perhaps the greatest virtue

of this material is that many glasses are inexpensive and

can be cut and shaped in the laboratory with inexpensive

tools.

Fifty years ago, most glass laboratory apparatus was

produced by the scientist or technician in situ by blowing

molten glass or by grinding, cutting, and polishing hard

glass. Today the glass industry has grown to such an extent

that nearly all components of a glass apparatus are available

from commercial sources at low cost. These include all sorts

of containers, chemical labware, vacuum-system compo-

nents, mirrors, windows, and lenses. It is often only neces-

sary for laboratory scientists to acquaint themselves with the

range of components available and to acquire the skills

needed to assemble an apparatus from these components.

2.1 PROPERTIES OF GLASSES

The chemical composition of glass is inﬁnitely variable,

and so therefore are the thermal, electrical, mechanical,

and chemical properties of glass. Furthermore, glass is a

ﬂuid that retains a memory of its past history. It is possible,

however, to review the general properties of glass and to

specify the properties of glasses of a particular composi-

tion and method of manufacture.

2.1.1 Chemical Composition and Chemical

Properties of Some Laboratory

Glasses

The chief constituent of any commercial glass is silica

(SiO

). All laboratory ware is at least 3/4 silica, with other

oxides added to obtain certain thermal properties or chem-

ical resistance.

The least expensive and, until the last quarter century,

the most common glass used for laboratory ware is known

as soda-lime glass or soft glass. This glass contains 70–

80% silica, 5–10% soda (Na

O), 5–10% potash (K

O), and

10% lime (CaO). A particular advantage of this glass is

that it can be softened in a natural-gas–air ﬂame.

Borosilicate glass has supplanted soda-lime glass for the

manufacture of labware. In this glass the alkali found in

soft glass is replaced by B

and alumina (Al

). Boro-

silicate glass is superior to soda-lime glass in its resistance

to chemical attack and thermal or mechanical shock. It

softens at a higher temperature than soft glass, however,

and is more difﬁcult to work. Borosilicate glasses of many

different compositions are manufactured for various labo-

ratory applications, but far and away the most common

laboratory glass is the borosilicate glass designated by

Corning as Pyrex 7740 and by Kimble as Kimax KG-33.

The composition is: SiO

, 80.5%; B

, 12.9%; Na

CHAPTER

3.8%; Al

, 2.2%; K

O, 0.4%. Borosilicate glass tubing

and rod, as well as a wide range of components, are avail-

able from many suppliers, including Corning Glass Works,

Kimble-Kontes, Wilmad-Labglass, ChemGlass, and Ace

Glass.

Glassware of extremely good chemical resistance is pro-

duced from borosilicate glass by thermal and chemical

processing: a heat treatment causes the glass to separate

into two phases – one high in silica and the other rich in

alkali and boric oxides. This second phase is leached out

with acid, and the remaining phase is heated to give a clear

consolidated glass that is nearly pure silica. This glass is

known as 96% silica glass and is designated by Corning as

Vycor No. 7900.

Glass composed only of silica is known as vitreous or

fused silica or simply as ‘‘quartz.’’ Because of its refrac-

tory properties and chemical durability, this material

would be the most desirable glass were it not for the high

cost of making it and the extremely high temperatures

required to work it. On the other hand, the relative cost

of quartz is decreasing to the extent that the market for

96% silica glass is rapidly disappearing.

Most laboratory glasses are transparent to visible light,

making visual distinction between the various glass com-

positions impossible. For this reason it is important to label

glass materials before storing and to avoid mixing different

kinds of glass. When necessary it is possible to distinguish

different glasses from one another by differences in ther-

mal or optical properties. The gas–air ﬂame of a Bunsen

burner will soften soda-lime glass, but not borosilicate

glass. A natural-gas–oxygen ﬂame is required to soften

borosilicate glass, but this ﬂame will not affect fused silica.

Fused silica must be raised to a white heat in an oxyhy-

drogen ﬂame before it will soften. Glasses of different

composition cannot generally be successfully fused

together because of differences in the amount of expansion

and contraction on heating and cooling. An unknown piece

of glass may be compared with a known piece by placing

the two side by side with their ends coincident. The two

ends are softened together in a ﬂame and pressed together

with tweezers. Then the fused ends are reheated and drawn

out into a long ﬁber about 0.5 mm in diameter and permit-

ted to cool. If the ﬁber remains straight, the two pieces

have the same coefﬁcient of expansion. If the ﬁber curves,

the two pieces are of different composition.

A measurement of the refractive index is usually a sen-

sitive and reliable test of glass composition. A piece of

glass placed in a liquid of exactly the same refractive index

will become invisible. For example, a test solution for

Pyrex 7740 can be made of 16 parts by volume of methanol

in 84 parts benzene. This test solution should be kept in a

tightly covered container so that its composition does not

change as a result of evaporation.

As can be judged from the extreme chemical environ-

ments to which glasses are routinely subjected, glass is

indeed resistant to chemical action. However, one need

only observe windows clouded by the action of rainfall

in a polluted atmosphere or glassware permanently stained

by laboratory chemicals to conﬁrm that glass is not entirely

impervious to chemical attack. Glass is attacked most

readily by alkaline solutions, and all types are affected

about equally. Water has an effect. The soft glasses are

most susceptible, borosilicate glass is only slightly

affected, and 96% silica hardly at all, since most of its

soluble components were leached out in manufacture.

Acids attack glass more readily than water, although,

again, borosilicate glass is more resistant to acids than soda

glass, and 96% silica is more resistant yet.

2.1.2 Thermal Properties of

Laboratory Glasses

One of t he most important pro perties of glass is its very

low coefﬁcient of therm al expansi on. It is this property

thatpermitsglasstobeformedathightemperaturesina

molten state and then cooled without changing shape or

breaki ng. The coe fﬁcient s of linear expansion of several

types of glass are given in Table 2.1. As can be seen from

ese data, borosilicate glass is much more resistant to

thermal shock than soft glass. Fused s ilica is so stable that

a white-hot piece can be immersed in liquid air without

fracturing.

Glass does not have a melting point. Instead, the work-

ing properties of a glass are speciﬁed by particular points

on its viscosity–temperature curve. The softening point is

approximately the temperature at which a glass can be

observed to ﬂow under its own weight. The annealing

point is the temperature at which internal stresses can be

relieved (annealed) in a few minutes. The strain point is

the temperature below which glass can be quickly cooled

PROPERTIES OF GLASSES 77

without introducing additional stress. The working point is

the temperature at which the glass is formed by a skilled

glassblower.

The speciﬁc heat of glass is about 0.8 J g

1

, and the

thermal conductivity of glass is about 0.008 J cm sec

1

2

1

. For reference, this thermal conductivity is

about an order of magnitude less than that of graphite,

two orders less than that of metal, and about an order of

magnitude greater than that of wood.

2.1.3 Optical Properties of Laboratory

Glassware

In many experiments light must be transmitted through the

wall of a glass container. The transmission as a function of

wavelength depends upon the composition of the glass.

The composition of the soda-lime glasses varies consider-

ably, and the optical properties of each piece should be

determined by spectroscopic analysis before it is used in

an experiment requiring light transmission. Spectrophoto-

metric curves for some lab glasses of well-deﬁned compo-

sition are given in Figure 2.1. As can be seen, fused silica is

transparent

over the widest wavelength range.

2.1.4 Mechanical Properties of Glass

The tensile, compressive, and shear strength of a piece of

glass depends upon its shape and history and upon the time

over which it is loaded. Glass appears to be much stronger

in compression than tension. This is in part due to the fact

that a glass surface can be made very smooth in order

to uniformly distribute a compressive load. Values of

400–1200 MN/m

(60 000–180 000 psi) are quoted for

the compression strength. (1 psi (pound per square inch) ¼

6895 N/m

Glass is nearly perfectly elastic. When it breaks it does

so without plastic deformation. Springs made of glass or

quartz ﬁbers behave almost ideally. The modulus of

elasticity of glass is high and, of course, depends upon

composition. Young’s modulus (the modulus of elasticity)

for Pyrex 7740 is 63 GN m

2

(9.1 3 10

psi) at 0 °C and

65 GN m

2

(9.4 3 10

psi) at 100 °C. For fused silica the

corresponding values are 72 GN m

2

(10.5 3 10

psi) and

74 GN m

2

(10.7 3 10

psi).

Glass ﬁbers are very strong. A quartz ﬁber 0.3 mm (.01 in.)

in diameterhas a tensile strength of 0.3 GN m

2

(50 000 psi);

a ﬁber 0.03 mm (.001 in.) in diameter a strength of at least

1.3 GN m

2

(200 000 psi); and a ﬁber 0.003 mm (.0001 in.)

in diameter a strength in excess of 7 GN m

2

(1 000 000 psi).

2.2 LABORATORY COMPONENTS

AVAILABLE IN GLASS

The list of laboratory apparatus components produced com-

mercially in glass is nearly endless. The laboratory scientist

should make a careful survey of lab suppliers’ literature

before embarking on the design and construction of a glass

apparatus. Very often a complex device can be assembled

in the lab entirely from inexpensive components without

requiring the services of a skilled glassblower. Some of

the most frequently used glass components are described

below.

2.2.1 Tubing and Rod

Most laboratory supply houses carry a wide range of tub-

ing and rod of Pyrex 7740 or Kimax KG-33 in 1 m lengths

at a cost of only a few euros per kilogram. Outer diameters

Table 2.1 Thermal properties of glass

Glass Linear Expansion

Coefﬁcient (cm

1

)

Strain Point

(°C)

Annealing Point

(°C)

Softening Point

(°C)

Working Point

(°C)

Soda-lime (typical) 8–10 3 10

6

500 550 700 1000

Pyrex 7740 (borosilicate) 3.3 3 10

6

510 555 820 1250

Vycor 7900 (96% silica) 0.75 3 10

6

890 1020 1500 —

Fused Silica 0.55 3 10

6

950 1100 1600 —

78 WORKING WITH GLASS

between 3 and 178 mm are readily available. The standard

wall thickness ranges from 0.5 mm for the smallest tubing

to 3.5 mm for the largest. Heavy-wall tubing with wall

thickness ranging from 2 to 10 mm is also available. In

addition, heavy-wall tubing of very small bore diameter

(0.5–4 mm), known as capillary tubing, is available.

Finally, solid rod of 3 to 30 mm diameter is a standard

item.

2.2.2 Demountable Joints

Laboratory apparatus can be quickly assembled if compo-

nents are connected with joints of the type illustrated in

Figure 2.2.

gas- or liquid-tight seal between two close-ﬁtting

pieces of glass can be achieved if the mating surfaces are

lightly coated with a viscous lubricant before assembly. A

number of low-vapor-pressure lubricants such as Apiezon

vacuum grease or Dow-Corning silicone vacuum grease

are especially formulated for this purpose. The taper joint

and the ball-and-socket joint in Figure 2.2(a) and (b) are

assembled

in this manner. The mating surfaces must ﬁt

together very well. In general this requires that they be

Figure 2.2 Demountable joints: (a) standard-taper joint;

(b) ball-and-socket joint; (c) O-ring joint; (d) a quick-connect

joint. (a), (b), and (c) are used for attaching glass compo-

nents to one another; (d) is used for joining a glass tube to a

metal component.

Figure 2.1 Optical-transmission curves for Pyrex 7740, Vycor 7900 (96% silica), and

fused silica.

LABORATORY COMPONENTS IN GLASS 79

lapped together. This is accomplished by coating the sur-

faces with a ﬁne abrasive such as Carborundum in water,

ﬁtting the pieces together, and rotating one with respect to

the other. The rotation should not be continuous, but rather

after half a turn or so the pieces should be pulled apart and

then assembled again so as to redistribute the abrasive.

Fortunately, taper and ball-and-socket joints with ground

mating surfaces are now commercially produced in stand-

ard sizes with sufﬁcient precision that lapping and grinding

in the lab is seldom necessary.

The standard taper (indicated

) for ground joints is

1:10. Standard-taper joints on tubing with outer diameters

between 8 and 50 mm are available. These joints are iden-

tiﬁed by ﬁgures that indicate the diameter of the large end

of the taper and the length of the ground zone in milli-

meters. For example,

10/30 indicates a ground zone

10 mm in diameter at the large end and 30 mm in length.

Standard-taper ground joints are available in borosilicate

glass, quartz, and type-303 stainless steel. These compo-

nents are interchangeable, and thus it is often convenient

to make a transition from glass to quartz or from glass to

metal with a taper joint.

Ball-and-socket ground joints do not seal as reliably as

taper joints; however, their design p erm its misalignment

and even some slight motion between joined parts. This

type of joint must be secured with a suitable clamp. Ball-

and-socket joints are designated by a two-number code

(i.e., 28/15). The ﬁrst number gives the diameter of the

ball in millimeters, the second number the inner diameter

of the tubing to which the ball and socket are attached.

Ball-and-socket joints of standard sizes are commer-

cially available in borosilicate glass, quartz, and stainless

steel.

The O-ring joint illustrated in Figure 2.2(c) is rapidly

replacing

the ground joint as a means of making demount-

able joints in glass vacuum apparatus. These joints require

no grease. Furthermore, the mating pieces are sexless,

since each member of the joint is grooved to a depth of

less than half the thickness of the O-ring. To date, these

joints are only available in borosilicate glass.

Quick-connects of the type shown in Figure 2.2(d) are

also

sealed with an O-ring. They are suited to joining either

glass or metal tubing to a metal container. Quick-connects

are often used to join glass ion-gauge tubes to metal vac-

uum apparatus.

2.2.3 Valves and Stopcocks

A glass stopcock of one of the types illustrated in Figures

2.3(a)–(c) has traditionally been used for control ling ﬂuid

ﬂo

w in glass apparat us. These c onsist of a hollow tapered

body and a plug with a hole bored through that can be

aligned by rotation with inlet and outlet ports in the body.

The simplest and least expensive version uses a glass plug

with a ground surface that mates with a ground surface on

the interior o f the stopcock body. The surf ace of the plug

must be lightly lubricated with stopcock grease to ensure

a good seal a nd f ree do m of r ota tio n. A stopcock of th is

typemaybeusedtocontrolliquidﬂoworgasﬂowat

pressures down to a few millitorr. For use at pressur es

above 1 atm the end of the plug may be ﬁtted with a

spring-loaded clip or collar to prevent i ts being blown

out. Stopcocks of this type are now available with a

Teﬂon plug. These are well suited for use with liquids.

Figure 2.3 Stopcocks and valves for controlling ﬂuid ﬂow:

(a) glass stopcock with solid glass plug; (b) high-vacuum

stopcock with vacuum cup and hollow plug; (c) glass stop-

cock with Teﬂon plug; (d) threaded glass vacuum valve with

O-ring-sealed Teﬂon stem.

80 WORKING WITH GLASS

No lubrication is required, and the plug seldom freez es in

the body of the stopcock.

In glass vacuum systems, the stopcock illustrated in

Figure 2.3(b) is far more reliable than the simple solid plug

design.

The plug is hollow, and the small end of the body is

closed off by a vacuum cup so that the interior of the

stopcock can be evacuated. The plug is held securely in

place by atmospheric pressure.

Valves with threaded borosilicate glass bodies and

threaded Teﬂon plugs [Figure 2.3(d)] are rapidly replacing

con

ventional stopcocks for most applications. These

valves are no more expensive than good vacuum stop-

cocks. They require no lubrication; only glass and Teﬂon

are exposed to the interior of the system. They are suitable

for use with most liquids and gases and may be used at

pressures from 10

6

torr to 15 atm.

2.2.4 Graded Glass Seals and

Glass-to-Metal Seals

In general, glasses of dif ferent composition hav e different

coefﬁcients of thermal expansion. As a consequence, two

glasses of dif ferent composition usually cannot be joined,

since differing rates of expansion and contraction produce

destructive stresses as the fused joint cools. In practice two

glasses can be successfully joined if their coef ﬁcients of ther -

mal expansion differ by no more than about 1 3 10

6

1

The problem of joining two glasses with signiﬁcantly differ-

ent coefﬁcients of thermal expansionis solvedby interposing

several layers of glass, each with a coefﬁcient only slightly

different from its neighbors. This stack of glass when fused

together is called a graded seal. Tubing with graded seals

joining different glasses is manufactured commercially.

Borosilicate-to-soft-glass seals are available in tube

sizes from 7 to 20 mm. Seals graded from borosilicate

glass (for example Pyrex 7740) to quartz (Vycor 7913)

are available in tube sizes from 7 to 51 mm.

Glass tubing can, with care, be joined to metal tubing.

Ideally the glass and the metal should have the same coef-

ﬁcient of expansion. It has been demonstrated, however,

that glass tubing can be joined to metal tubing that has a

very different coefﬁcient provided that the end of the metal

tubing has been machined to a thin, sharp, feathered edge.

The stresses of thermal expansion and contraction can then

be taken up by stretching of the metal. The stresses created

by joining glass to metal can also be reduced by interpos-

ing glasses whose coefﬁcient of thermal expansion is inter-

mediate between that of the metal and the ﬁnal glass.

Direct tube seals between borosilicate glass and copper

or stainless steel are available in diameters from 6 mm to

50 mm. Graded glass seals between borosilicate glass and

Kovar, an iron–nickel–cobalt alloy, are available in sizes

from 3 mm to 75 mm. These graded seals are robust, and

far and away the most common glass-to-metal seal. Kovar is

easily silver-soldered or welded to most steels and brasses.

2.3 LABORATORY GLASSBLOWING

SKILLS*

Considering the range of components now available, it is

usually only necessary for the laboratory worker to be able

to join commercially produced components to assemble a

complete apparatus. The required skills consist primarily

of joining tubes in series or at right angles, cutting and

sealing-off tubing, and making simple bends. It is easiest

and often necessary to make a joint between a piece of

tubing held in the hand and a piece attached to an apparatus

or otherwise rigidly clamped. In the following sections

only the simplest glassblowing operations with borosili-

cate glass are described. There are certainly many more

elegant and complex manipulations that can be carried out

by a skilled glassblower using only hand tools. Workers

who ﬁnd a need for these operations or discover in them-

selves a ﬂair for glassblowing may consult a more com-

plete text on the subject.

2.3.1 The Glassblower’s Tools

The necessary equipment for laboratory glasswork is illus-

trated in Figure 2.4. The basic tool is, of course, a torch.

The

National type-3A blowpipe with #2, #3, or #4 tip is the

standard in the trade. A torch stand is essential to hold the

lighted torch when both hands are required to manipulate a

piece of glass. A source of natural gas and low-pressure

* Many of the simpliﬁed methods described in Section 2.3 were devel-

oped by John Trembly at the University of Maryland for use in his

remarkably successful introductory glassblowing classes.

LABORATORY GLASSBLOWING SKILLS 81

oxygen is required, along with two lengths of ﬂexible

rubber or Tygon tubing for connecting the gas supplies

to the torch. A rigid ring stand and appropriate clamps

with ﬁberglass-covered jaws are needed to support glass

being worked upon. The torch and stand should be set up

on a ﬁreproof bench top. Also required are a number of

small hand tools, inexpensively obtained from a scientiﬁc

supply house. These include a torch lighter, a wax pencil,

a glass-cutting knife, a swivel, a mouthpiece (an old

tobacco-pipe bit will do), glassblowing tweezers, a collec-

tion of corks and one-hole stoppers, and a variety of ream-

ing tools. These reaming tools consist of ﬂat triangular

pieces of brass ﬁtted with wooden ﬁle handles, and tapered

round or octagonal carbon rods in various sizes. Didymium

eyeglasses are necessary to ﬁlter out the intense sodium

D-line emission produced when glass is exposed to the

ﬂame. Without these it is impossible to see hot glass as

it is worked. Clip-on didymium lenses are available for

these who wear prescription eyeglasses.

A little preliminary practice with the hand torch is

advisable. The gas inlet may be connected directly to a

low-pressure natural-gas outlet in the lab. The outlet valve

is turned completely open and gas ﬂow is controlled by the

valve in the body of the torch. Oxygen is usually obtained

from a high-pressure cylinder. A pressure regulator for the

oxygen tank is essential. The outlet pressure should be

between 40 and 70 kN/m

(6 and 10 psi). Once again,

the ﬂow of oxygen gas is controlled by the valve in the

body of the hand torch. The proper procedure is to open the

gas control and ignite the gas ﬁrst. The gas should be

adjusted to give a ﬂame 5 to 8 cm long before the oxygen

is introduced. If the ﬂame blows out, the oxygen valve

should be closed and the gas permitted to ﬂow for a few

moments to purge the torch of the explosive gas–oxygen

mixture before reignition is attempted.

With a #3 torch tip it is possible to produce a range of

ﬂames suitable for work on tubing from a few millimeters

up to 50 mm in diameter. Opening the gas valve wide and

adding only a little oxygen gives a large, bushy yellow

ﬂame. This is a cool reducing ﬂame suitable for preheating

large pieces of glass and for annealing ﬁnished work. At

the opposite extreme, a sharp blue oxidizing ﬂame can be

obtained by restricting the gas ﬂow. For work on ﬁne tub-

ing and for cutting tubing it is possible to make a ﬂame no

more than 3 cm long and 3 mm in diameter. The hottest

ﬂame is made with an excess of oxygen. The hottest part of

the ﬂame is the tip of the blue inner cone.

Some practice will be required to master even the simple

operations described below. The neophyte should obtain

the necessary tools and a supply of clean dry borosilicate

glass tubing of 8–12 mm diameter. About ten hours of

practice is required before one can proﬁtably embark on

any serious apparatus construction.

2.3.2 Cutting Glass Tubing

Tubing up to about 12 mm diameter can be broken cleanly

by hand. The location of the desired break may be indi-

cated by marking the tubing with a wax pencil. The glass is

then scored with a glass knife or the edge of a triangular

ﬁle, as shown in Figure 2.5. The scratch should be perpen-

dicular

to the axis of the tube and need only be a few

millimeters in length. Use considerable pressure and make

only one stroke. Do not saw at the glass. Wet the scratch

and then, holding the tubing as shown in Figure 2.6 with

the

scratch toward you, push the ends apart. Applying a

Figure 2.4 Glassblower’s equipment.

82 WORKING WITH GLASS

force that tends to bend the ends of the tube away from

you, while simultaneously pulling, will facilitate a clean

break.

Tubing of 12 to 25 mm diameter can be cut by cracking

it with a ﬂame. First score the glass around approximately

one third of its circumference with the glass knife. Then

wet the scratch and touch the end of the scratch with a very

ﬁne sharp ﬂame that is oriented tangentially to the circum-

ference, as shown in Figure 2.7.

Lar

ge-diameter tubing can be parted by cracking it using

a resistively heated wire held in a yoke, as illustrated in

Figure 2.8. The tubing is placed on the resistance wire with

one

end butted against a stop. The wire is heated red-hot by

passing current through it, and the tube is rotated to heat a

narrow zone around its circumference. After a moment the

tube is quickly removed and the hot zone is brushed with a

wet pipe cleaner. The thermal shock thus produced should

result in a clean break.

The edge of the glass at a fresh break is sharp and

fragile. After cutting, the end of a tube can be ﬁre-polished

to relieve this hazardous condition. This is accomplished

simply by heating the end of the tube in the ﬂame until the

glass is soft enough that surface tension rounds and thick-

ens the sharp edge.

2.3.3 Pulling Points

Points are elongations on the end of a tube produced by

heating the glass and stretching it. These points serve as

Figure 2.6 Breaking glass tubing. The tubing is bent and

simultaneously pulled apart.

Figure 2.7 Cracking tubing with a ﬂame.

Figure 2.5 Scoring glass tubing in preparation for break-

ing. Use only one stroke with considerable force.

Figure 2.8 Device for cutting large-diameter glass tubing.

LABORATORY GLASSBLOWING SKILLS 83

handles for manipulating short pieces of tubing. Pulling a

point is the ﬁrst step in closing the end of a tube.

The procedure for pulling points depends upon whether

the tubing can be rotated or not. If the tubing is free, then

place the torch in its holder with the ﬂame pointed away

from you and hold the glass in both hands as illustrated in

Figure 2.9. Adjust the torch to give a fairly full, neutral

ﬂame.

Then, rotating the glass at a uniform rate, pass it

through the ﬂame to heat a zone about as wide as the tube

diameter. When the glass softens, remove it from the ﬂame

and pull the heated section to a length of about 20 cm.

Then quickly heat the center of the stretched section and

pull the glass in two, leaving a small bead at the end of

each point. It is important that the points be on the axis

of the original tube. This requires that the circumference of

the tube be heated uniformly and that the ends of the tube

be pulled straight away from one another. Some practice is

required to synchronize the motion of the hands so that

both ends of the tubing are rotated in such a way that the

tube does not twist or bend when it becomes pliable in the

ﬂame. Beginners tend to overheat glass, thus exacerbating

this problem of misalignment. When glass is sufﬁciently

plastic for proper manipulation, it is still rigid enough to

help support the end sections.

If one end of a tube is attached, so that the tube cannot

be rotated, then it becomes necessary to swing the torch

around the tubing rather than rotate the glass before the

stationary torch. Some practice is required to achieve a

smooth motion with the torch so that the tube is heated

uniformly around its circumference. The unattached end of

the tubing is supported with the free hand until the glass is

sufﬁciently hot to be pulled.

2.3.4 Sealing Off a Tube: The Test-Tube End

Tubing is closed off by forming a hemispherical bubble

similar to that found at the end of a test tube. In order for

the test-tube end to form a strong closure, it must be

smooth and of a uniform thickness. The hemispherical

shape is formed by closing off the tubing and then soften-

ing the glass in the ﬂame and blowing into the tube.

Begin by pulling a point on the tubing that is to be closed

off. If the tubing is not rigidly mounted, place it in a clamp

secured to a ring stand on the workbench. If possible the

work should be at chest height with the point upward. Press

a one-hole stopper, with a piece of soft rubber tubing

attached, into the open end of the tube as shown in Figure

2.10. Warm the glass at the base of the point with a soft

bush

y ﬂame. Adjust the gas–oxygen mixture to the torch to

give a fairly small ﬂame with a well-deﬁned, blue inner

cone. Heat the point close to the shoulder where it joins the

tube. Swing the torch around the work so that the glass is

heated uniformly. When the glass melts, pull the point off

the tube. Only a small bead of glass should be left behind.

A large blob of glass will result in a closure that is too thick

in relation to the wall of the tubing. A test-tube end that is

thick in the middle and thin at the sides will develop

destructive strains, since it does not cool at a uniform rate.

The key is to heat only a narrow zone of the point near the

shoulder and to perform the whole operation rather

quickly. If a large globule of glass is left after pulling off

the point, the excess must be removed. With a sharp ﬂame,

heat the globule until it melts. Remove the ﬂame, touch the

molten bead with the end of a piece of glass rod (‘‘cane’’),

and quickly pull the rod away. Excess glass will be pulled

away from the soft bead into a ﬁber which can be broken or

melted off. The test-tube end is completed by heating the

closed-off end as far as the shoulder with a somewhat larger

ﬂame until it is soft and the glass has ﬂowed into a fairly

uniform thickness. The ﬂame should be directed downward

at the end of the tube with a circular motion. Remove the

ﬂame and gently blow the end into a hemispherical shape.

Figure 2.9 Pulling points.

84 WORKING WITH GLASS

If a ﬂat end is desired, reheat the round end and gently

blow while pressing a ﬂat carbon block against the end.

2.3.5 Making a T-Seal

A tube is joined at a right angle to the side of another tube

with a T-seal. To make a T-seal, close one end of a tube

with a cork and attach the blow tube to the other. If pos-

sible, mount the tube horizontally at chest height. With a

sharp ﬂame heat a spot on the top side of the tube. Using a

circular motion of the torch, soften an area about the size

of the cross-section of the tube that is to be joined. Then

move the ﬂame away and gently blow out a hemispherical

bulge, as shown in Figure 2.11(b). Reheat the bulge and

blo

w out a thin-walled bubble. Finally, while blowing to

pressurize the inside of the tube, touch the bubble with the

tip of the ﬂame so that a hole is blown through it. Now heat

the edge of this hole so that surface tension pulls the glass

back to the edges of the original bubble. The result should

be a round opening slightly smaller than the diameter of

the tube that is to be joined, as shown in Figure 2.11(f).If

the

opening is too small or if the edge is irregular, the hole

can be reamed and shaped by softening the glass and shap-

ing the hole with a tapered carbon. A tool for this job can

be made by sharpening a 1/4 in. diameter carbon rod in a

pencil sharpener.

With a cork or a point, close off the end of the tube that

is to be sealed to the horizontal tube. Then, holding this

tube above the hole and tipped slightly back, simultane-

ously heat the edges of the tube and the hole until they

become soft and tacky. Bring the tube into contact with the

back edge of the hole, remove the ﬂame, and tip the tube

forward until it rests squarely on the hole. The tacky edges

should join together to produce an airtight seal. Blow to

check the seal. Small holes can be closed by heating the

seal all around until the glass is soft, and tipping the ver-

tical tube in the direction of the leak. It also is possible to

‘‘stitch’’ a gap closed with cane. This is done by pulling a

Figure 2.10 Blowing a test-tube end.

LABORATORY GLASSBLOWING SKILLS 85

point on a piece of glass rod. Then warm the gap which is

to be repaired, heat the point of the cane until it is molten

and deposit the tiny blob of molten glass thus produced

into the gap. The seal at this point is quite fragile because

the glass is too thick around the seal. Cracks will develop if

the glass is permitted to cool before the seal is blown out in

order to reduce the wall thickness.

Glassblowing around the seal proceeds in four steps.

Begin with a sharp ﬂame parallel to the axis of the horizon-

tal tube. Swing the torch back and forth to heat one quadrant

Figure 2.11 Steps in making a T-seal.

86 WORKING WITH GLASS

of the seal. When the glass softens, remove the ﬂame and

blow gently. Timing is important here. Blowing while the

glass is in the ﬂame will cause the thinnest parts to bulge. If,

however, one waits a moment after removing the ﬂame, the

thinnest parts will cool and blowing will preferentially thin

out the thick portions of the seal, yielding a more uniform

wall thickness. The joint between the vertical and horizontal

tubes should then be a smooth curve of glass. During the

blowing operation the vertical tube must be held with the

free hand to prevent its tipping or sagging into the horizontal

tube. Next repeat the heating and blowing operation on the

side diametrically opposite. Finally, in a third and fourth

step, blow out the remaining two quadrants.

2.3.6 Making a Straight Seal

A straight seal joins two tubes coaxially. There are two

simple procedures for making such a seal.

If the tubes are quite different in diameter, close off the

larger one with a test-tube end and mount it vertically with

the closed end up. Then blow a bubble of the appropriate

size in the test-tube end and proceed as in making a T-seal.

Alternatively, the smaller tube can be ﬂared out to the

diameter of the larger one. The ﬂaring operation is illus-

trated in Figure 2.12. With the torch in its stand, heat the

edge

of the tube by rotating it in a sharp ﬂame. Remove it

from the ﬂame, and while continuing to rotate the tube,

insert a tapered carbon and gently bring the soft edge of the

glass up against the taper. Do not attempt to produce a ﬂare

of the desired diameter in one rotation of the tube. It will

not come out round. The ﬂaring operation is much easier if

the tube is placed on a set of glassblower’s rollers.

As shown in Figure 2.13(a), the larger tube should

mounted vertically if possible. Suspend the smaller tube

with the ﬂare just above the larger one. With the upper tube

tipped back slightly, heat the edges of the larger tube and

the rim of the ﬂare until the glass is tacky. Bring them into

contact at the back of the seal, remove the ﬂame, and tip

the upper piece forward to join the two pieces. Proceed to

blow out the seal in four steps as for the T-seal. Minimize

the distance above and below the seal over which the glass

is heated.

2.3.7 Making a Ring Seal

A ring seal is used for sealing a tube inside a larger tube,

as in Figure 2.14(f), or for passing a tube through the wall

a container. There are many procedures for making

such se als. The s implest involves bulging the smaller-

diameter tube sufﬁciently for it to close off the hole

through which the tube must pass. A bulge in a tube is

known as a maria. Making a maria is a freehand oper-

ation and requires some practice.

Begin with the torch in its holder and the gas supply

adjusted to give a long, na rrow ﬂame. Then rotating

the tubing in both hands, heat a very narrow zone at the

desired location. As soon as the glass softens, drop the

tube out of the ﬂame, and, with your elbows braced on

the bench top or against your sides, push the e nds of the

tube toward one another. If the tube has been heated uni-

formly around and the ends are held coaxial, a bulge

should develop around the tube. If the heating is not uni-

form, the tube will bend. If the glass is too soft, the ends

Figure 2.12 Flaring the end of a tube.

LABORATORY GLASSBLOWING SKILLS 87

of the tube are liable to move out of alignment and an

eccentric bulge will result. When a uniform bulge is

attained, reheat it, remove it from the ﬂame, and push

again to increase the dia met er of the ma ria. The bulge

should be solid glass. If too wide a zone is heated, the

maria will be hollow and dangerously fragile.

To make a coaxial ring seal between two tubes, form on

the smaller tube a maria of the same diameter as the larger.

Mount the larger tube vertically, ﬁre-polish the top edge,

and rest the smaller tube on top, as in Figure 2.14(e). With

small ﬂame, heat the junction uniformly between the

maria and the edge of the larger tube. The weight of the

smaller tube should cause it to settle and become fused to

the larger one. Finally blow out the seal in four steps, as in

making a conventional seal. Exercise care to prevent the

wall of the outer tube from sagging into the inner tube. If

the inner tube is not centered, it can be realigned by soft-

ening the seal with a cool, bushy ﬂame and manipulating

its protruding end.

2.3.8 Bending Glass Tubing

Bends are best made beginning with the tubing vertical

[Figure 2.15(a)]. Close off the upper end with a cork or a

point

and attach the blowtube to the other end. While

supporting the upper end of the tube with the free hand,

apply a large bushy ﬂame at the location of the desired

bend. Heat the glass uniformly over a length equal to about

four times the diameter of the tube. When the glass

becomes pliable, remove the ﬂame and quickly bend the

upper end over to the desired angle. As soon as the bend is

completed, blow to remove any wrinkles which may have

developed and to restore the tubing to its original diameter.

Some reheating may be necessary.

A sharp right-angle bend can be produced by ﬁrst mak-

ing a T and then pulling off one running end of the T close

to the seal [Figure 2.15(b)]. Blow out a test-tube end where

the

tubing is pulled off.

2.3.9 Annealing

Even when a seal is carefully blown out to give a uniform

wall thickness, harmful stresses are inevitably frozen into

the glass. Worked glass must be annealed by heating to a

temperature above the annealing point (see Table 2.1) and

then

slowly cooling to the strain point. In a large profes-

sional glass shop, special ovens are employed for this

operation. In the lab, however, glass must be annealed in

the ﬂame of the torch. After a piece of glass has been

blown, it is heated uniformly over a wide area surrounding

the work with a large, slightly yellow, bushy ﬂame. For

Pyrex 7740 the glass should be brought to an incipient

red heat. Care must be taken to prevent the glass from

becoming so hot that it begins to sag under its own weight.

The heated work is then cooled by slowly reducing the

oxygen to the torch until the ﬂame becomes sooty.

Figure 2.13 Steps in making a straight seal.

88 WORKING WITH GLASS

When soot begins to adhere to the glass, the ﬂame can be

removed.

Areas in glass which are under stress will rotate the plane

of polarization of transmitted light. A polariscope can be

used to observe strain in glass in order to test the effective-

ness of the annealing operation. A polariscope can be pur-

chased from a laboratory supplier or can be constructed with

high-extinction sheet polarizers, as shown in Figure 2.16.

e polarizers are crossed so that unstrained glass appears

dark when placed between them. Areas of strain rotate the

plane of polarization and appear bright, as in Figure 2.17.A

rge stationary piece of glasswork, such as a vacuum mani-

fold, can be tested by illuminating it from behind with ver-

tically polarized light and then viewing the work through

Polaroid sunglasses (which transmit horizontally polarized

light). A suitable source can be constructed by placing a

100 watt lamp behind a diffuser in a ventilated, open-top

box, and covering the box with a sheet of polarizer sand-

wiched between glass plates.

2.3.10 Sealing Glass to Metal

Glass-to-metal seals are fragile and difﬁcult to produce in

the lab. The simplest means of attaching metal tubing

to a glass system or of passing a metallic electrode through

a glass wall is to make use of a commercially produced

glass-to-metal seal [Figure 3.28(b)]. If necessary a direct

Figure 2.14 Steps in making a ring seal.

Figure 2.15 Bending tubing.

LABORATORY GLASSBLOWING SKILLS 89

seal between a variety of metals and glasses can be pro-

duced with careful attention to design and fabrication.

these, the tungsten-to-Pyrex seal is most easily and reliably

fabricated in the lab.

Although the linear coefﬁcient of expa nsion of tung-

sten is about 50% greater than that of 7740 borosilicate

glass, it is possible to m ake a strong, vacuum-tight seal

between Pyrex and tungsten wire or rod of up to a milli-

meter diameter.

Since the glass will wet tungsten oxide,

but not tungsten, it is necessary that the metal surface be

properly prepared. Tungsten wire or rod usually has a

longitudinal grain by virtue of the method of manufac-

ture. The metal stock should be cut to length by grinding

to prevent splintering. To pr event gas from leaking

through the seal along the length of the wire it is good

practice to fuse the ends of the wire in an electric arc.

Alternatively, a copper or nickel wire can be welded to

each end of the tungsten wire. Tungsten electrodes with

co pper or nickel wires attached are also available from

commercial sources. Holding the wire in a pin vise, heat

the area to be sealed to a dull red and i mmediately rub the

hot metal with a stick of sodium nitrite. The salt com-

bines with the tungsten oxide to leave a clean metal sur-

face. Rinse the metal with tap water to remove the salt

and then rinse with distilled water. The metal must then

be reoxidized in an oxygen-rich ﬂame to produce an

oxide layer of the proper thickness. If the layer is too

thick it will pull away from the metal; if it is too thin it

may all dissolve into t he glass. The clean tungsten should

be gently heated only until the metal appears blue-green

when cool. A piece of 7740 glass, 2 cm long with a wall

thickness of about 1 mm and an inner diameter slightly

larger than the tungsten wire, is slipped over the wire and

slid along to the sealing position. Be careful not to

scratch the oxide layer. T he glass tube is fused to the

metal using a small, sharp ﬂame. Melting should proceed

from one end to the other with continuous rotation to

pr event trapping air. If t he metal is properly wett ed by

the glass, the wire will appear oversize where it passes

through the seal. A copper or amber color after the seal is

cool indicates a good seal. The beaded tungsten rod is

then sealed into the apparatus, as in making a ring seal

(Section 2.3.7). If necessary, a shoulder can be built up

around

the middle of the bead by fusing on a winding of

1 mm glass rod.

A tungsten-to-Pyrex seal makes an excellent electrical

feedthrough. Wires can be brazed or spot-welded to either

end of the tungsten rod. Since tungsten is not a good elec-

trical conductor, care must be taken to ensure that electri-

cal currents do not overheat the feedthrough. The safe

current-carrying capacity of the tungsten in this applica-

tion is about 8 Amm

Figure 2.16 A polariscope.

Figure 2.17 The appearance of strain in unannealed glass

as seen in the polariscope.

90 WORKING WITH GLASS

2.3.11 Grinding and Drilling Glass

In many instances the ends of a tube must be ground square

or at an angle, or a tube must be ground to a speciﬁc length.

The ends of a laser tube, for example, must be cut and

ground to Brewster’s angle before optical windows are

glued in place. Grinding a plane surface is performed in

a water slurry of abrasive on a smooth iron plate. It is done

with a circular motion while applying moderate pressure.

The work should be lifted from the surface frequently in

order to redistribute the abrasive. If the angle of the ground

surface relative to the workpiece is not critical, the work

can be grasped in the hand; otherwise, a wooden jig, such

as is shown in Figure 2.18, may be fabricated to orient the

work

with respect to the grinding surface.

Carborundum or silicon carbide grit of #30, 60, 120, and

220 mesh is used for coarse grinding, and emery of #220,

400, and 600 mesh is used for ﬁne grinding. In any grind-

ing operation, begin with the grit required to remove the

largest irregularities and proceed in sequence through the

ﬁner grits. Before changing from one grit to the next ﬁner,

the work and the grinding surface must be scrupulously

washed so that coarse abrasive does not become mixed

with the next ﬁner grade. Before changing from one grit

to the next, it is useful to inspect the ground surface under

a magnifying glass. If the abrasive in use has completed its

job, the scratch marks left by the abrasive should be of a

fairly uniform width.

Holes can be cut in glass, and round pieces of glass can be

cut from larger pieces, with a slotted brass tube drill – a

‘‘cookie cutter’’ – in a drill press (Figure 2.19). These drills

are

easily fabricated in sizes from several millimeters to

many centimeters in diameter. Either ﬂat or curved glass

can be drilled. Cutting is accomplished by continuously feed-

ing the drill with a slurry of #60 or #120 mesh abrasiv e. It is

usually most convenient to form a dam of soft wax or putty

around the hole location to hold the slurry of abrasi ve around

the drill. Work slo wly with a light touch at a drill speed of

50–150 rpm. The tool should be backed out frequently to

permit the abrasive to ﬂow under. Because grinding action

occurs along both the leading edge and the side of the drill

tube, the ﬁnished hole will be some what larger than the drill

body. Frequently the edges of the hole will chip where the

drill breaks through on the under side of the work. This can

be prevented when drilling ﬂat glass by backing up the work-

piece with a second piece of glass waxed onto the underside.

Glass can be sawn as well as drilled. Many glass shops

use a powered, diamond-grit cutting wheel for precision

cutting. In the absence of such a machine, it is possible to

cut glass in much the same manner as it is drilled. A hack-

saw with a strip of 20-gauge copper as a blade is used. The

Figure 2.18 A wooden jig used in grinding the face of

a piece of tubing.

Figure 2.19 Drilling glass with a tube drill.

LABORATORY GLASSBLOWING SKILLS 91

work is clamped in a miter box and sawn with a light touch

while feeding an abrasive slurry to the blade.

Cited References

1. W. G. Housekeeper, Trans, A.I.E.E., 42, 870, 1923.

2. F. Rosebury, Handbook of Electron Tube and Vacuum Tech-

niques, Addison-Wesley, Reading, MA, 1965, pp. 54–66.

3. J. Strong, Procedures in Experimental Physics, Prentice-Hall,

Englewood Cliffs, NJ, 1938, p. 24; G. W. Green, The Design

and Construction of Small Vacuum Systems, Chapman and

Hall, London, 1968, pp. 100–102.

General References

W. E. Barr and J. V. Anhorn, Scientiﬁc and Industrial Glass

Blowing and Laboratory Techniques, Instruments Publishing,

Pittsburgh, 1959.

Corning Glass Works, Laboratory Glass Blowing with Corning’s

Glasses, Publ. No. B-72, Corning Glass Works, Corning, NY.

J. E. Hammesfahr and C. L. Strong, Creative Glass Blowing,

Freeman, San Francisco, 1968.

W. Morey, The Properties of Glass, Reinhold, New York, 1954.

F. Rosebury, Handbook of Electron Tube and Vacuum

Techniques, Addison-Wesley, Reading, MA, 1965.

92 WORKING WITH GLASS

VACUUM TECHNOLOGY

In the modern laboratory, there are many occasions when a

gas-ﬁlled container must be emptied. Evacuation may sim-

ply be the ﬁrst step in creating a new gaseous environment.

In a distillation process, there may be a continuing require-

ment to remove gas as it evolves. Often it is necessary to

evacuate a container to prevent air from contaminating a

clean surface or interfering with a chemical reaction. Beams

of atomic particles must be handled in vacuo to prevent loss

of momentum through collisions with air molecules. Many

forms of radiation are absorbed by air and thus can prop-

agate over large distances only in a vacuum. A vacuum

system is an essential part of laboratory instruments such

as the mass spectrometer and the electron microscope. Far

infrared and far ultraviolet spectrometers are operated

within vacuum containers. Simple vacuum systems are used

for vacuum dehydration and freeze-drying. Nuclear particle

accelerators and thermonuclear devices require huge,

sophisticated vacuum systems. Many modern industrial

processes, most notably semiconductor device fabrication,

require carefully controlled vacuum environments.

3.1 GASES

The pressure and composition of residual gases in a vac-

uum system vary considerably with its design and history.

For some applications a residual gas density of tens of

billions of molecules per cubic centimeter is tolerable. In

other cases no more than a few hundred thousand mole-

cules per cubic centimeter constitutes an acceptable vac-

uum: ‘‘One man’s vacuum is another man’s sewer’’.

It is

necessary to understand the nature of a vacuum and of

vacuum apparatus to know what can and cannot be done,

to understand what is possible within economic con-

straints, and to choose components that are compatible

with one another as well as with one’s needs.

3.1.1 The Nature of the Residual Gases

in a Vacuum System

The pressure below one atmosphere is loosely divided into

vacuum categories. The pressure ranges and number

densities corresponding to these categories are listed in

Table 3.1. Vacuum science has been slow in adopting the

unit of pressure – the Pascal or Pa – preferring instead

torr or bar. We will follow this preference. For the purposes

of the discussion here, a pressure of 1 torr, 1 millibar, and

100 Pa can be taken as equivalent. As a point of reference

for vacuum work, it is useful to remember that the number

density at 1 mtorr is about 3.5 3 10

3

and that the

number density is proportional to the pressure.

The composition of gas in a vacuum system is modiﬁed

as the system is evacuated because the efﬁciency of a

vacuum pump is different for different gases. At low pres-

sures molecules desorbed from the walls make up the

residual gas. Initially, the bulk of the gas leaving the walls

is water vapor and carbon dioxide; at very low pressures, in

a container that has been baked, it is hydrogen.

3.1.2 Gas Kinetic Theory

In order to understand mass ﬂow and heat ﬂow in a vacuum

system it is necessary to appreciate the immense change in

CHAPTER

freedom of movement experienced by a gas molecule

as the pressure decreases.

The average velocity of a molecule can be deduced

from the Maxwell–Boltzmann velocity distribution law:



v ¼

8kT



1=2

ð3:1Þ

For an air molecule (molecular weight of about 30 amu)

at 20 ºC:



v  5 3 10

cm s

1

km s

1

ð3:2Þ

Each second a molecule sweeps out a volume with a diam-

eter twice that of the molecule and a length equal to the

distance traveled by the molecule in a second. As shown in

Figure 3.1, this molecule collides with any of its neighbors

whose center lies within the swept volume. The number of

collisions per second is equal to the number of neighbors

within the swept volume. On average, the number of col-

lisions per second (Z) is the number density of molecules

(n) times the volume swept by a molecule of velocity



v and

diameter n. More precisely:

Z ¼

ﬃﬃﬃ

npn



v ð3:3Þ

where the

ﬃﬃﬃ

accounts for the relative motion of the

molecules. The time between collisions is the reciprocal

of this collision frequency, and the average distance

between collisions, or mean free path, is:

k ¼



1

ﬃﬃﬃ

npn

ð3:4Þ

Note that the mean free path is independent of the temper-

ature and the molecular weight.

The mean free path is inversely proportional to the pres-

sure. For an N

or O

molecule, n  3 3 10

8

cm. The

number density at 1 mtorr is about 3.5 3 10

3

. Thus

the mean free path in air at 1 mtorr is about 5 cm. Recalling

Figure 3.1 The volume swept in one second by a

molecule of diameter n and velocity



v (cm/s). The molecule

will collide with any of its neighbors whose center lies within

the swept volume.

Table 3.1 Air at 20 ºC

Pressure

(torr)

Number Density

(cm

3

)

Mean Free

Path

(cm)

Surface Collision

Frequency

(cm

2

1

)

Time for

Monolayer

Formation

(s)

One atmosphere 760 2.7 3 10

7 3 10

6

3 3 10

3.3 3 10

9

Lower limit of:

Rough Vacuum 10

3

3.5 3 10

543 10

2.5 3 10

3

High Vacuum 10

6

3.5 3 10

5 3 10

4 3 10

2.5

Very High Vacuum 10

9

3.5 3 10

5 3 10

4 3 10

2.5 3 10

7Ultrahigh Vacuum 10

12

3.5 3 10

5 3 10

4 3 10

2.5 3 10

1 torr ¼1.33 mbarr ¼133 Pa

assumes unit sticking coefﬁcient and a molecular diameter of 3 3 10

8

94 VACUUM TECHNOLOGY

the relationship between k and P, a valuable rule of thumb

is that for air at 20 ºC:

k 

PðmtorrÞ

cm ð3:5Þ

3.1.3 Surface Collisions

The frequency of collisions of gas molecules with a sur-

face is:

surface

ðs

1

2

Þð3:6Þ

The sticking probability for most air molecules on a clean

surface at room temperature is between 0.1 and 1.0. For

water the sticking probability is about unity for most surfa-

ces. Assuming unit sticking probability and a molecular

diameter n  3 3 10

8

cm, the time required to form a

monolayer of adsorbed air molecules at 20 ºCis:

t ¼

2:5 3 10

6

PðtorrÞ

s ð3:6Þ

Thus to maintain a clean surface for a useful period of

time may require a gas pressure over the surface less than

9

torr.

3.1.4 Bulk Behavior versus

Molecular Behavior

The pressure of gas within a vacuum system may vary over

10 or more orders of magnitude as the system is evacuated

from atmospheric pressure to the lowest attainable pres-

sure. At high pressures, when the mean free path is much

smaller than the dimensions of the vacuum container, gas

behavior is dominated by intermolecular interactions.

These interactions, resulting in viscous forces, ensure good

communication among all regions of the gas. At high pres-

sures, a gas behaves as a homogeneous ﬂuid. When the gas

density is decreased to the extent that the mean free path is

much larger than the container, molecules rattle around

like the balls on a billiard table (not a pool table, where

the ball density can be high), and gas behavior is deter-

mined by the random motion of the molecules as they

bounce from wall to wall. Gas ﬂow in the high-pressure

regime is characterized as viscous ﬂow and in the low-

pressure regime as molecular ﬂow. In the typical laboratory

vacuum system the transition between the two ﬂow

regimes occurs at pressures in the vicinity of 100 mtorr.

In the viscous-ﬂow region where the mean free path is

relatively small, gas ﬂow improves with increasing pres-

sure because gas molecules tend to queue up and push on

their neighbors in front of them. Gas ﬂow is impeded by

turbulence and by viscous drag at the walls of the pipe that

is conducting the gas. In the viscous region the coefﬁcients

of viscosity and thermal conductivity are independent of

pressure.

In the molecular-ﬂow region, momentum transfer

occurs between molecules and the wall of a container,

but molecules seldom encounter one another. In the molec-

ular ﬂow regime, a gas is not characterized by a viscosity.

Gas ﬂows from a region of high pressure to one of low

pressure simply because the number of molecules leaving

a unit of volume is proportional to the number of mole-

cules within that volume. Gas ﬂow is a statistical process.

At very low pressure a molecule does not linger at a sur-

face for a sufﬁcient time to reach thermal equilibrium.

Thus thermal conductivity at low pressures is a function

of gas density, and the coefﬁcient of thermal conductivity

depends upon the pressure and upon the condition of the

surface.

3.2 GAS FLOW

3.2.1 Parameters for Specifying Gas Flow

Before discussing vacuum apparatus it is necessary to

deﬁne the parameters used by vacuum engineers to char-

acterize gas ﬂow.

The volume rate of ﬂow through an aperture or across

the cross section of a tube is deﬁned as the pumping speed

at that point:

S [

½Ls

1

;ft

min

1

ðcfmÞ ð3:7Þ

The capacity of a vacuum pump is speciﬁed by the speed

measured at its inlet:

[

ðat pump inletÞð3:8Þ

GAS FLOW 95

The mass rate of ﬂow through a vacuum system is

proportional to the throughput:

Q [ PS ½ðtorr L s

1

;Pam

1

; std cm

1

ða standard cubic centimeter

or std cm

or scc is 1 cm

273 K and 1 atm or 1:01 barÞ

ð3:9Þ

To determine the throughput it is necessary that the

pressure and speed be measured at the same place, since

these quantities vary throughout the system.

The ability of a tube to transmit gas is characterized by

its conductance C. The deﬁnition of conductance is anal-

ogous to Ohm’s law for electrical circuitry. The throughput

of a tube depends upon the conductance of the tube and the

driving force, which in this case is the pressure drop across

the tube:

Q ¼ P

 P

ðÞC ðP

> P

Þð3:10Þ

Notice that conductance has the same units as pumping

speed.

3.2.2 Network Equations

A complicated network of tubes can be reduced to a single

equivalent conductance for the purpose of analysis. In

analogy to electrical theory once again, a number of tubes

in series can be replaced by a single equivalent tube with

conductance C

series

given by:

series

...



1

ð3:11Þ

A parallel network can be replaced by an equivalent

conductor with conductance:

parallel

¼ C

þ C

þ ð3:12Þ

3.2.3 The Master Equation

By use of the network equations given above, an entire

vacuum system can be reduced to a single equivalent con-

ductance leading from a gas source to a pump, as shown in

Figure 3.2. The net speed of the system is:

S ¼

ð3:13Þ

and the speed at the pump inlet is:

ð3:14Þ

Notice that the throughput is the same at every point

in this system, since there is only one gas source. The

throughput of the conductance is:

Q ¼ðP

 P

ÞC ð3:15Þ

Upon substitution for P

and P

from the previous two

equations, this equation, after some rearrangement,

becomes:

ð3:16Þ

This is the master equation that relates the net speed of a

system to the capacity of the pump and the conductors

leading to the pump. From this equation we see that both

the conductance of a system and the speed of the pump

exceed the net speed of the system. In vacuum-system

design, economics should be considered. The cost of a

vacuum pump is usually greater than the cost of construct-

ing a tube leading from a vacuum container to the pump. In

order to achieve a given net speed for a system, it is most

economical to design a system whose equivalent conduc-

tance exceeds the required net speed by a factor of three or

four so that the speed of the pump need only exceed the net

speed by a small amount.

Figure 3.2 Analytical representation of a vacuum system.

96 VACUUM TECHNOLOGY

3.2.4 Conductance Formulae

In the viscous-ﬂow region the conductance of a tube

depends upon the gas pressure and viscosity.

For a tube

of circular cross-section and in the absence of turbulence,

the conductance from the Hagen – Poiseuille derivation is:

C ¼ 32 600

1

ð3:17Þ

when the diameter D and length L of the tube are in cen-

timeters, the average pressure P

is in torr, and the vis-

cosity of the gas, g, is in micropoise (lP). For air at 20 ºC

the conductance is:

C ¼ 180

1

ð3:18Þ

These equations are used for determining the dimen-

sions required for the lines connecting to a pump that

operates in the rough vacuum region. A complex system

is treated as a series of simple cylindrical tubes; the con-

ductance of each tube is calculated from the equation

above and the conductance of the whole system is deter-

mined using the network equations. Joints and elbows

between simple tubes will reduce the conductance of the

system so it is wise to specify tube diameters somewhat

oversize to offset conductance losses in the transitions

between simple cylindrical shapes.

In the molecular-ﬂow region, conductance is independ-

ent of pressure. The conductance of a tube of circular

cross-section is:

C ¼ 2:6310

4



1

ð3:19Þ

when the diameter and length are measured in centimeters

and the average molecular velocity



v is in cm/s. For air at

20 ºC the conductance is:

C ¼ 12

1

ð3:20Þ

These equations are useful in determining the dimen-

sions of a high-vacuum chamber and the size of the tubes

leading to and from the chamber. As an example of poor

design consider the case of a vacuum chamber connected

to a 100 L/s diffusion pump by a tube 2.5 cm in diameter

and 10 cm long. The net speed of the pump and connecting

tube is:

S ¼

100



1

¼ 16 L s

1

ð3:21Þ

The connecting tube is strangling the pump. Consider also

the pressure drop across the tube. Since the throughput is a

constant, one can write:

¼ S

¼ Q ð3:22Þ

thus:

¼ 6 ð3:23Þ

This result indicates the importance of proper location

of a pressure gauge. In this case a gauge at the mouth of the

pump would indicate a pressure six times lower than the

pressure in the vacuum container.

There are frequently occasions when a vacuum system

is divided into compartments at very different pressures

separated by a wall with an aperture whose diameter

exceeds its length (a so-called ‘‘thin aperture’’). In the

viscous-ﬂow regime, the conductance of an aperture at

20 ºC is approximately:

C  20 A Ls

1

ð3:24Þ

where A is the area in cm

. In the molecular-ﬂow region,

the conductance of an aperture for a gas of molecular

weight M is:

C ¼ 3:7



1=2

A Ls

1

ð3:25Þ

where A is the area in cm

. These equations are useful for

determining the rate of gas ﬂow into a vacuum chamber

through an aperture in a gas-ﬁlled collision chamber or ion

source.

There is a transition region between the viscous- and

molecular-ﬂow regions where the mean free path approx-

imately matches the dimensions of the container. For

laboratory-scale apparatus, the transition region falls in

the range of 500 mtorr down to 5 mtorr. A mathematical

description of this region is difﬁcult. Fortunately one ﬁnds in

most vacuum systems that the transition region is encoun-

tered only brieﬂy during pumpdown from atmosphere to

GAS FLOW 97

high vacuum. Conductance formulae, such as given above,

for ﬂow in the viscous (high-pressure) region compared

to conductance formulae in the molecular (low-pressure)

region show two important differences: gas ﬂow in the

viscous region depends upon the gas pressure and the

square of the cross-section of the conductor (i.e., D

whereas gas ﬂow in the molecular ﬂow region is independ-

ent of pressure and goes as the 3/2 power of the cross-

section. It follows that the formulae for conductance in

the molecular-ﬂow region will give a conservative estimate

of the conductance in the transition region.

3.2.5 Pumpdown Time

The time required to pump a chamber of volume V from

pressure P

to P is:

t ¼



ð3:26Þ

assuming a constant net pumping speed and considering

only the gas that resided in the container at the outset. A

typical high-vacuum system is rough-pumped to about 50

mtorr with a mechanical pump and then pumped to very

low pressures with a diffusion pump or some other pump

that works effectively in the molecular-ﬂow region. The

pumpdown calculation is performed in two steps corre-

sponding to these two operations. In the low-pressure

regime, gas desorbing from the container walls may con-

tribute to the gas load and the rate of desorption will need

to be considered in estimating the pumpdown time.

3.2.6 Outgassing

The rate at which the pressure falls in a chamber at pres-

sures below about 10

5

torr is largely determined by the

rate of evolution of gas from the walls of the chamber

rather than by the speed of the pump. The rate of gas

evolution – outgassing – from solid materials depends both

on the nature of the solid and the adsorbate. Water and

carbon dioxide from the air are adsorbed most tenaciously.

A rough, porous, or polar surface adsorbs more gas than a

clean polished surface. The outgassing rate from a surface

decreases slowly, roughly as e

at

(a a property of the sur-

face and the adsorbate, as well as a strong function of

temperature). Baking a vacuum chamber to 150 to

200 ºC under vacuum will encourage outgassing and result

in a lower ultimate pressure after the chamber cools.

Following exposure to air, stainless steel outgases at

roughly 10

8

torr L s

1

2

of surface area after an hour

of pumping at room temperature. A day of pumping may

be required to reduce this rate below 10

9

torr L s

1

2

The outgassing rate from aluminum is more than 10 times

greater than for stainless steel. Outgassing from plastics is

roughly 10 times worse than from aluminum, and outgas-

sing from elastomers (rubber) is 10 times worse yet. Plas-

tics and rubbers have no use in a vacuum system that is to

achieve pressures below about 10

7

torr.

Consider, for example, the problem of maintaining a

base pressure of 10

7

torr in a stainless-steel chamber. If

the outgassing rate is 10

9

torr L s

1

2

, a pumping

speed of 10

2

1

is required for every cm

of surface.

For a container 1 m in diameter and 1 m high, a pumping

speed of 400 L s

1

is needed. This speed is typical of a

high vacuum pump (a diffusion pump or turbomolecular

pump) with a nominal 4 in. (10 cm) diameter inlet port.

Without baking to further reduce the outgassing rate, a

pump 10 times larger (and nearly 10 times as expensive)

would be required to reduce the pressure to 10

8

torr;

ultrahigh vacuum is out of the question.

3.3 PRESSURE AND FLOW

MEASUREMENT

The pressure within a vacuum system may vary over more

than 13 orders of magnitude. No one gauge will operate

over this range, so most systems are equipped with several

different gauges.

The pressure ranges in which the various gauges are

useful are shown in Figure 3.7.

3.3.1 Mechanical Gauges

Hydrostatic Gauges. The simplest pressure gauges

are hydrostatic gauges such as the oil or mercury

manometer. A closed-end U-tube manometer ﬁlled with

mercury is useful down to 1 torr. Diffusion-pump oils,

such as Octoil, di-n-butyl phthalate, or Dow Corning

DC704 or DC705 silicone oils, may also be used as

98 VACUUM TECHNOLOGY

manometer ﬂuids. Because the density of these oils is much

less than that of mercury, oil-ﬁlled manometers are useful

down to about 0.1 torr. As shown in Figure 3.3,anoil

manometer

should be made of glass tubing of at least 1 cm

diameter in order to reduce the effects of capillary

depression. To prevent oil adhesion to the walls, the

manometer should be cleaned with dilute hydroﬂuoric acid

before ﬁlling. A heater is usually provided to drive dissolved

gas from the oil prior to use.

A number of manometers hav e

been designed to increase the surface area of oil exposed to

the vacuum in order to hasten outgassing.

Both oil and

mercury manometers will contaminate a vacuum system

with vapor of the working ﬂuid. If this is a problem, a cold

trap is placed between the gauge and the system to condense

the offending vapor. Mercury in a manometer can be isolated

and protected from chemical attack by ﬂoating a few drops

of silicone oil on top of the mercury column.

The McLeod gauge shown in Figure 3.4 is a complex

drostatic gauge and is sensitive to much lower pressures

than a simple U-tube manometer. In the McLeod gauge, a

sample of gas is trapped and compressed by a known amount

(typically 1000:1) by displacing the gas with mercury from

the original volume into a much smaller volume. The pres-

sure of the compressed gas is measured with a mercury

manometer and the original pressure determined from the

general gas law. Of course, it is not possible to use a McLeod

gauge to measure the pressure of a gas that condenses upon

compression. With care, a high-quality McLeod gauge will

provide accuracy of a few percent do wn to about 10

4

torr.

Some gauges can be used at even lower pressures, but it is

necessary to consider the error caused by the pumping action

of mercury vapor streaming out of the gauge.

The McLeod gauge is constructed of glass and is easily

broken. If the mercury is raised into the gas bulb too

quickly, it can acquire sufﬁcient momentum to shatter

Figure 3.4 McLeod gauge.

Figure 3.3 Oil manometer. The trap is intended to contain

the oil charge in the event that the low-pressure arm of the

manometer is accidentally open to the atmosphere.

PRESSURE AND FLOW MEASUREMENT 99

the glass. When a gauge is broken, the external air pressure

frequently drives a quantity of mercury into the vacuum

system. For this reason it is wise to place a ballast bulb of

sufﬁcient volume to contain the mercury charge of the

gauge between the gauge and the system.

Mechanical Gauges. A number of different gauges

depend upon the ﬂexure of a metal tube or diaphragm as

a measure of pressure. In the Bourdon gauge, a thin-wall,

curved tube, closed at one end, is attached to the vacuum

system. Pressure changes cause a change in curvature of

the tube. A mechanical linkage to the tube drives a needle

to give a pressure reading on a curved scale. Another type

of mechanical gauge contains a chamber divided in two by

a thin metal diaphragm. The volume on one side of the

diaphragm is sealed, while the volume on the other side is

attached to the system. A variation in pressure on one side

relative to the other causes the diaphragm to ﬂex, and this

movement is sensed by a system of gears and levers that

drives a needle on the face of the gauge. The precision of

these gauges is limited by hysteresis caused by friction in

the linkage. To overcome this friction it is helpful to gently

tap the gauge before making a reading. Unlike the liquid

manometer, mechanical gauges are not absolute gauges.

The pressure scale and zero location on these gauges

must be calibrated against a McLeod gauge or U-tube

manometer. Mechanical gauges are useful down to 1 torr

with an accuracy of about 0.5 torr. They offer the

advantage of being insensitive to the chemical or

physical nature of the gas.

Piezoelectric Pressure Transducers. A piezo

transducer is an absolute, direct-reading device that

senses the gas pressure on a piezoelectric crystal. They

function in the 10

1

to 1000 torr range. Typical gauges

include the transducer and the sensor electronics in a

single compact unit (for example, MKS Instruments).

They are useful for monitoring roughing and foreline

pressures, and for inclusion in an interlock system to

control vacuum system operation (see Sections 3.6.1,

6.6.9, 6.6.10).

Capacitance Manometers. A capacitance manometer

is a diaphragm manometer wherein the position of the

diaphragm is determined from a measurement of

electrical capacitance. The gauge head is divided into

two chambers by a thin metal diaphragm that serves as

one plate of a capacitor; the second plate of the capacitor

is ﬁxed in one of the chambers. A change in the pressure

difference between the two chambers results in a change in

capacitance as the ﬂexible diaphragm moves relative to the

ﬁxed plate. A sensitive capacitance bridge measures the

capacitance between the two plates and the capacitance is

converted to a reading of the pressure difference.

Capacitance manometers are inherently differential

pressure gauges; most, however, are manufactured to

read absolute pressure by sealing and evacuating one of

the chambers. This arrangement does not provide a truly

absolute gauge since the readout must be set to zero by

connecting the open chamber to a true zero pressure (i.e.,

several orders of magnitude less than the full-scale

reading). A capacitance manometer is designed so that

the ﬂexible diaphragm touches the opposing capacitor

plate at a small overpressure. This protects the fragile

diaphragm from a sudden inrush of gas. As might be

expected, the capacitance measurement is very sensitive

to the temperature of the ﬂexible diaphragm. High

precision gauge heads incorporate a heater and

temperature control that maintains the gauge head at a

constant temperature.

Capacitance manometers are available to measure pres-

sures from 1000 torr down to less than 10

4

torr. A single

gauge head is useful over a range of three to four orders of

magnitude with an accuracy of 0.01% full scale at the low

end of the pressure range and 0.5% or better at the high end

(e.g., a 1 torr gauge head reads 1 3 10

4

61 3 10

4

torr at

the low end and 1.0060.005 torr at the high end). Gauges

are calibrated by the manufacturer and have a reputation

for holding their calibration for years given careful use.

The electronics have a response time of about 10 ms. This

makes the capacitance manometer especially useful for

pressure control in a feedback loop.

3.3.2 Thermal-Conductivity Gauges

The thermal conductivity of a gas decreases from some

constant value above about 10 torr to essentially zero at

about 10

3

torr. This change in thermal conductivity is

used as an indication of pressure in the Pirani gauge and

the thermocouple gauge. In both gauges a wire ﬁlament is

100 VACUUM TECHNOLOGY

heated by the passage of an electrical current. The temper-

ature of the ﬁlament depends on the rate of heat loss to the

surrounding gas. In the thermocouple gauge, the pressure

is determined from the e.m.f. (electromotive force) pro-

duced by a thermocouple in contact with the ﬁlament

heated by the passage of a constant current (Figure 3.5).

the Pirani gauge, the heated ﬁlament is one arm of a

Wheatstone bridge. A change in temperature of the ﬁla-

ment produces a change of resistivity and hence a change

in the voltage across the ﬁlament. The resulting imbalance

of the bridge gives an indication of pressure. Alternatively,

a voltage can be applied to keep the bridge in balance and

this voltage becomes the indication of pressure.

The pressure indicated by a thermocouple gauge or a

Pirani gauge depends upon the thermal conductivity of the

gas. They are usually calibrated by the manufacturer for

use with air. For other gases these gauges must be recali-

brated point-by-point over their entire range, since thermal

conductivity is a nonlinear function of pressure. In routine

use, a thermal-conductivity gauge can only be expected to

be accurate to within a factor of two. This accuracy is

adequate when the gauge is used to sense the foreline

pressure of a diffusion pump or to determine whether the

pressure in a system is sufﬁciently low to begin diffusion-

pumping. The principal advantages of these gauges are

their ease of use, ruggedness, and low cost.

3.3.3 Viscous-Drag Gauges

Above about 1 torr, the viscosity of a gas is constant, but, in

the molecular-ﬂow regime, the viscous drag exerted by a

gas on a moving surface depends upon the gas density and

the mean velocity of the gas. It follows that below about

1 torr, a ﬁrst-principles calculation yields gas pressure from

a measurement of viscous drag for a gas of known temper-

ature and composition. This approach to absolute pressure

measurement is applied in the spinning-rotor gauges man-

ufactured by Leybold AG and MKS Instruments.

In the gauge head of a spinning-rotor gauge, a magneti-

cally suspended steel ball is spun up to a rotational speed

of about 415 Hz by a rotating magnetic ﬁeld. The drive is

interrupted and the ball is permitted to decelerate to a

preset lower speed, typically about 405 Hz. The pressure

is determined from a measurement of the time required for

a complete revolution of the coasting ball. The rate of

deceleration is very small – at 10

4

torr the deceleration

from 415 to 405 Hz takes many minutes. The measurement

of the ball rotation rate is repeated many times to obtain

satisfactory precision. A microprocessor in the controller

computes the statistical average of the deceleration rate

after many cycles.

Spinning-rotor gauges provide absolute pressure meas-

urement between 10

1

and 10

6

torr with an accuracy of a

few percent. At the lower end of this range, they are the

only available means for making highly accurate, repeat-

able, absolute-pressure measurements. Spinning-rotor

gauges are used as a transfer standard in calibrating other

types of gauges. These instruments must be maintained

with great care. They are expensive.

3.3.4 Ionization Gauges

In the region of molecular ﬂow, pressure is usually meas-

ured with an ionization gauge or ‘‘ion gauge.’’ In this type

of gauge, gas molecules are ionized by electron impact and

the resulting positive ions are collected at a negatively

biased electrode. The current to this electrode is a function

Figure 3.5 Thermocouple gauge.

PRESSURE AND FLOW MEASUREMENT 101

of pressure. There are two basic types of ion gauges, differ-

ing primarily in the mechanism of electron production. In

the hot cathode ionization gauge, electrons are produced

by thermionic emission from an electrically heated wire

ﬁlament. In cold cathode gauges, electrons and ions are

produced in a discharge initiated by a high-voltage elec-

trical discharge.

The most familiar conﬁguration of the hot cathode ion-

ization gauge is that devised by Bayard and Alpert and

illustrated in Figure 3.6. The gauge electrodes are mounted

a glass envelope with a side arm that is attached to the

vacuum system. Electrons from an electrically heated ﬁl-

ament (F) are accelerated through the gas toward a posi-

tively biased, helical wire grid (G). Collisions between the

accelerated electrons and gas molecules create ions that

are collected at a central wire electrode (C), and the pos-

itive ion current is measured by a sensitive electrometer.

These gauges are useful in the 10

3

to 10

10

torr range.

The ion current measured with an ionization gauge is a

linear function of pressure; the proportionality between

ion current depends upon the electron emission current

from the ﬁlament and upon the ionization efﬁciency of

the gas in the gauge. Commercial gauge controllers are

calibrated for use with air at a speciﬁed emission current,

typically about 10 mA. An adjustment on the controller

permits the user to set the emission current. For gases other

than air, the indicated pressure is multiplied by a sensitiv-

ity factor that is inversely proportional to the electron-

impact-ionization cross-section for the gas in question.

Sensitivity factors for some common gases are given in

Table 3.2.

Ion

gauges have the sometimes useful and sometimes

detrimental property of functioning as pumps. There are

two mechanisms for pumping. Ionized gas molecules

accelerated to and embedded in the collector are effec-

tively removed from the system. In addition, metal evapo-

rated from the ﬁlament deposits on the glass envelope of

the gauge to produce a clean, chemically active surface

that adsorbs nitrogen, oxygen, and water. At pressures

below 10

7

torr this pumping action may create a signiﬁ-

cant pressure gradient between the gauge tube and the

system to which it is attached, resulting in a pressure read-

ing that is lower than that in the system. For ultrahigh-

vacuum systems the pumping problem is circumvented

by the use of ‘‘nude’’ gauges that consist of the gauge

electrodes mounted to a ﬂange that is installed so that

the electrodes protrude into the system proper; there is

no envelope or tubulation joining the gauge to the system.

The pressure indicated by an ionization gauge is also

affected by the emission of gas adsorbed on the gauge

electrodes and envelope. To overcome this problem the

gauge is periodically degassed by heating the electrodes

Figure 3.6 Bayard–Alpert ionization gauge.

Table 3.2 Sensitivity factors for ionization gauges

Gas Formula Multiplicative

Factor

Air 1.0

Nitrogen N

1.0

Oxygen O

0.9

Hydrogen H

2.4

Carbon dioxide CO

0.7

Methane CH

0.7

Hydrocarbons C

and up 0.2

Argon Ar 0.9

Neon Ne 3.5

Helium He 6.8

Calibrated for air. Recommended values based primarily upon

the survey published by R. L. Summers, NASA Tech. Note: TN

D-5285, and an assumed nominal acceleration potential of 150V.

102 VACUUM TECHNOLOGY

and the envelope. This is accomplished by the gauge con-

troller in the ‘‘degas’’ mode in which an AC current is passed

through the grid to heat it to incandescence. Radiative

heating of the surrounding components encourages outgas-

sing. A hot cathode ionization gauge is activated when the

pressure falls below 10

3

torr – turn-on at higher temper-

atures will cause the ﬁlament to burn out. The gauge should

be degassed for a few minutes when the pressure falls to

about 10

4

torr and the degassing should be repeated with

each decrease of two orders of magnitude in pressure.

The electron-emissive ﬁlament in the ion gauge is made

of tungsten or thoria-coated iridium. Tungsten ﬁlaments

operate at 1800 ºC. They provide the most stable operation,

however, their lifetime is signiﬁcantly shortened by expo-

sure to hydrocarbons at relatively high pressures. Thoria-

coated ﬁlaments operate at about 1200 ºC and can be

expected to be longer-lived than tungsten ﬁlaments. Many

gauge tubes provide two ﬁlaments with separate external

connections. Only one ﬁlament is activated at a time. When

the ﬁrst ﬁlament burns out the second can be used so that

it is not necessary to let the system up to air pressure

following the ﬁrst failure. When the ﬁlaments have failed

in a glass-enclosed gauge, the entire gauge is replaced.

Individual ﬁlaments are replaceable in nude gauges.

Cold cathode ionization gauges in various conﬁgura-

tions are identiﬁed as Penning gauges, magnetrons,

inverted magnetrons, and Philips gauges. In these gauges

an electrical discharge is struck in a low-pressure gas

between two electrodes maintained at a potential differ-

ence of several kV. The range of stability of the discharge

is extended by a magnetic ﬁeld provided by a permanent

magnet that is an integral part of the gauge head. The

magnetic ﬁeld conﬁnes the electrons in the discharge so

as to increase their pathlength through the gas. The dis-

charge current measured at one of the electrodes provides a

measure of the gas pressure. The measured current is rel-

atively much larger than that obtained with a hot-cathode

gauge – of the order of 1 A torr – thus greatly simplifying

the controller electronics. Cold cathode gauges operate in

the 10

2

to 10

7

torr range with an accuracy of a factor of

two at best. The pressure range is extended down to less

than 10

9

torr in some more complex designs. Without the

fragile ﬁlament of the hot cathode gauge, cold cathode

gauges are robust and economical, suffering primarily only

from their limited range of applicability.

The operating pressure ranges of the vacuum gauges is

shown in Figure 3.7.

3.3.5 Mass Spectrometers

A mass spectrometer can be used to determine the partial

pressures of residual gases in a system and to detect

leaks. Small, relatively inexpensive mass spectrometers

designed speciﬁcally for these purposes are called resid-

ual-gas analyzers (RGAs). These instruments employ quad-

rupole or magnetic-deﬂection type analyzers and typically

cover the mass range from 2 to 100 amu. They are sensitive

to partial pressures as low as 5 3 10

14

torr. Fixed-focus

mass spectrometers set to detect helium are widely used as

sensitive leak detectors. Leaks are located by monitoring

the helium concentration within a vacuum system while the

exterior of the system is probed with a small jet of helium.

The minimum detectable leak rate of commercial helium

leak detectors is less than 10

11

torr L s

1

3.3.6 Flowmeters

Gas ﬂow can be measured as a throughput or as a mass

ﬂow. Flow rate, as a throughput, is determined from a

measurement of the pressure drop across a tube or system

of tubes of known conductance. The mass ﬂow rate can be

determined from a measurement of the power required to

Figure 3.7 Operating ranges of pressure gauges.

PRESSURE AND FLOW MEASUREMENT 103

maintain a given temperature gradient across a tube

through which a gas ﬂows.

Differential Pressure Flowmeters. For gas

ﬂowing through a tube, the throughput depends upon the

pressure difference between the entrance and exit of the

tube and the conductance of the tube [from Section 3.2.1,

Q ¼ (P

 P

)C]. Obviously two pressure gauges are

required to determine the throughput. In addition the gas

temperature must be measured and the dimensions of the

tube must be chosen so that the gas ﬂow remains in a

deﬁnable ﬂow regime (either viscous ﬂow or molecular

ﬂow) so that the conductance of the tube can be

calculated from the tube dimensions. The length of the

tube should exceed the diameter by at least a factor of

10 so that end effects on the conductance can be

ignored. A capillary of 1 mm inner diameter and several

centimeters in length would assure viscous ﬂow conditions

at downstream pressures above 1 torr and the conductance

could be calculated from the Hagen – Poiseuille relation

(Section 3.2.4). To operate in the molecular-ﬂow regime, a

tube

of macroscopic dimensions would be only useful at

very low ﬂows and low downstream pressures. In practice,

the ﬂowrate in the molecular-ﬂow regime is measured

using a parallel array of capillary tubes, the dimension of

each tube being sufﬁciently small to assure molecular ﬂow

at pressures up to 1 torr. Capillary arrays with thousands of

parallel channels each 1 mm long with diameters as small

as 25 micrometers (lm) are available for this purpose.

The differential pressure ﬂowmeter is appealing in that

ﬂow rate is accurately determinable from ﬁrst-principles

calculation; in practice, however, these gauges are used

primarily for calibration purposes.

Thermal Mass Flowmeters. Commercial ﬂow-

meters for routine use are of the thermal mas s ﬂow

type. The mass ﬂow of gas through a tube can be

calculated from the temperature rise i n the ﬂowing gas

as heat is added or from the power required to maintain a

given t empera ture rise; t he latter sc heme is the basis o f

most c ommerc ially availabl e gauges. Thermal mass ﬂow

gauges operate in the viscous ﬂ ow regime where thermal

conductivity of a gas is essentially constant. The

ﬂowmeter consists of a tube that is surrounded by a

series of heaters that establish a temperature p roﬁle

along the tube. Gas ﬂowing through the tube modiﬁes

the temperature proﬁle and t his change of temperature

canbeusedasameasureofthegasﬂowrate.

Alternatively, the power to the heaters is a djusted by a

sensitive bridge to keep the temperature proﬁle ﬁxed. The

power to the heaters then becomes a measure of the mass

ﬂow rate. These gauges are usually cal ibr ated f or ai r. For

other gases, a correction fac tor, inversely proportional to

the heat capacity and density of the gas, is applied.

Thermal mass ﬂowmeters determine mass ﬂow from a

measurement of heat ﬂow; the instruments are, however,

calibrated in throughput units of standard cubic centi-

meters per minute (sccm) of air or N

. One standard cubic

centimeter is the amount of gas contained in 1 cm

at 1 atm

pressure and 0 ºC. Flowmeters are available with full-scale

ranges of 10 to 50 000 sccm and an accuracy of about 1%

of the full-scale reading. Because thermal mass ﬂowmeters

operate in the laminar viscous-ﬂow regime, they are

always placed on the delivery side of a ﬂow system. In

choosing a gauge one must consider the delivery pressure

and the pressure drop across the gauge element. For con-

densable gases it may be necessary to choose a gauge with

a range larger than required, in order to keep the delivery

pressure below the vapor pressure of the sample. Thermal

mass ﬂowmeters have a response time of the order of 1 s

and can be used in a feedback loop to control gas ﬂow rate.

Controllers incorporating a ﬂowmeter and an electrically

driven metering valve are commercially available.

3.4 VACUUM PUMPS

Vacuum pumps are classiﬁed according to the chemical or

physical phenomenon responsible for moving gas mole-

cules out of the vacuum vessel. Like pressure gauges,

every vacuum pump operates in a limited pressure range.

The useful range of a pump is also limited by the vapor

pressure of the materials of construction and the working

ﬂuids within the pump. In general, a pump that operates in

the viscous-ﬂow region will not operate in the molecular-

ﬂow region and vice versa. To achieve very low pressures,

two or more pumps are used in series. In addition, some

pumps are more efﬁcient for high-molecular-weight gases

than others, and some pump low boiling gases (e.g., H

and

He) more efﬁciently than others. To achieve ultrahigh

104 VACUUM TECHNOLOGY

vacuum it is common practice to employ pumps with com-

plimentary characteristics in parallel.

Mechanical pumps operating in the rough vacuum

region with ultimate low-pressure limits of 5 torr to 5 mtorr

serve two important functions in attaining high and ultra-

high vacuum. A pump that will achieve a high vacuum at

its inlet will invariably have a maximum tolerable outlet

pressure; this is the critical backing pressure. A mechan-

ical pump is employed to maintain the high-vacuum pump

exhaust pressure below the critical pressure and in this

function the mechanical pump is referred to as a backing

pump or forepump. In addition, it is necessary for the

pressure in a vacuum chamber to be below some pressure

before the high-vacuum pump can be put into operation;

this pressure is sometimes referred to as the stall pressure.

A mechanical pump is used to attain this maximum start-

ing pressure in the chamber and in this function the pump

is referred to as a roughing pump.

3.4.1 Mechanical Pumps

Oil-Sealed Rotary Vane Pumps. The pump most

commonly used for attaining pressures down to a few

millitorr is the oil-sealed rotary vane pump shown

schematically in Figure 3.8. In this pump a rotor turns

f-center within a cylindrical stator. The interior of the

pump is divided into two volumes by spring-loaded vanes

attached to the rotor. Gas from the pump inlet enters one of

these volumes and is compressed and forced through a one-

way valve to the exhaust. A thin ﬁlm of oil maintains the

seal between the vanes and the stator. The oil used in these

pumps is good-quality hydrocarbon oil from which the

high-vapor-pressure fraction has been removed. These

pumps are also made in a two-stage version in which two

pumps with rotors on a common shaft operate in series.

Rotary pumps to be used for pumping condensable vapors,

water vapor in particular, are provided with a gas ballast.

This is a valve that admits air to the compressed gas just

prior to the exhaust cycle. This additional air causes the

exhaust valve to open before the pressures of condensable

vapors exceed their vapor pressure and thus prevents these

vapors from condensing inside the pump.

Oil-sealed rotary vane pumps will operate for years

without attention if the inner surfaces do not rust and the

oil maintains its lubricating properties. It is wise to leave

these pumps operating continuously so that the oil stays

warm and dry. In use, an increase in the lowest attainable

pressure (the base pressure) indicates that the oil has been

contaminated with volatile materials. The dirty oil should

be drained while the pump is warm. The pump should be

ﬁlled with new oil, run for several minutes, drained, and

reﬁlled with a second charge of new oil. For storage, a

pump should be ﬁlled with new oil and the ports sealed.

Rotary pumps are av aila ble with capacities of 1 to 500

1

.Asingle-stagepumpisusefuldownto50mtorr,anda

two-stage pump to 5 mtorr . Typical perfo rmance of a single-

stage pump is indicated by the pumping-speed curve in Fig-

ure

3.8. A two-stage pump is to be preferred as a backing

pump

for a diffusion pump. W ith a two-stage pump, a base

Figure 3.8 Oil-sealed rotary vane pump.

VACUUM PUMPS 105

pressure of 10

4

torr can be achieved after a long pumping

time, if the back diffusion of oil vapor from the pump is

suppressed by use of a sorption or liquid-air trap on the pump

inlet. This is a simple scheme for evacuating small spe-

ctrometers and Dewar ﬂasks or other vacuum-type thermal

insulators.

The exhaust gases from an oil-sealed mechanical vac-

uum pump contain a mist of ﬁne droplets of oil. This oil

smoke is especially dense when the inlet pressure exceeds

100 torr. The oil droplets are extremely small, usually less

than 5 microns. Over the course of time, this oil settles on

the pump and its surroundings, and collects dirt and grime.

Furthermore, breathing the ﬁnely dispersed oil may injure

the operator’s lungs. In addition, over the course of weeks

or months, this oil represents a signiﬁcant loss from the oil

charge in the pump, so a pump failure may result if the oil

level in the pump is not faithfully monitored. Most pump

manufacturers market ﬁlters that cause the exhaust oil mist

to coalesce and run back into the pump; their use is rec-

ommended. In addition, modern standards of laboratory

hygiene require venting a mechanical pump into the labo-

ratory fume hood. If toxic gases are being pumped it is of

course essential to pipe the exhaust out of the lab. Some-

times, a pretreatment involving passage of the exhaust

through a neutralizing chemical bath is required. In most

cases exhaust lines can be made of PVC drainpipe avail-

able from plumbing suppliers. The exhaust line should rise

vertically from the pump so that oil in the exhaust will

collect on the walls of the line and run downward back

to the pump. An exception to this scheme arises in the case

of a wet vacuum process. If considerable water is exhausted

from the pump, there is the danger that water will condense

in the exhaust line and run back into the pump.

Roots Blowers. A Roots blower is a displacement

pump. As illustrated in Figure 3.9, these pumps consist of

pair of counter-rotating two-lobed rotors on parallel shafts.

Rotational speeds are about 3000 rpm. There is a clearance

of a few thousandths of an inch between the rotors

themselves and between the rotors and the housing. A

volume of gas is trapped at the inlet and compressed as it

ismovedtotheexhaust.Thereisnooilinthebodyofthe

pump to maintain a high-pressure seal, but, owing to the high

speed of the rotors, a compression ratio as great as 40:1 can

be achiev ed. The virtue of the Roots blower is its relati v ely

high pumping speed in the 1 to 10

3

torr region. To achieve

an ultimate vacuum of 10

3

torr, a Roots blower is used in

series with a rotary pump at its exhaust. The required speed

of the rotary pump is smaller than that of the Roots pump by

a factor of the in v erse of the compression ratio of the Roots

pump. Roots blowers are available with speeds of a few

hundredtomanythousandL/s.

Piston Pumps. There are now available piston pumps

with Teﬂon-sealed pistons that do not contaminate the va-

cuum en vironment with oil, as do oil-sealed rotary pumps.

The Leybold EcoDry pump employs a novel diaphragm

exhaust valve that permits a higher compression ratio than

pumps with poppet valv es. The low-pressure limit of these

pumps is about 50 mtorr. Piston pumps are robust and

reliable, but they are also relativ ely expensiv e in com-

parison to rotary pumps. They ﬁnd use as backing pumps

for pumps such as turbomolecular pumps, when con-

tamination with hydrocarbons is not permissible.

Diaphragm Pumps. Diaphragm pumps are displace-

ment pumps employing the ﬂexure of a thin metal or Teﬂon

Figure 3.9 Roots blower.

106 VACUUM TECHNOLOGY

diaphragm to compress gas and drive it out through an

exhaust valve. These are small pumps of low pumping

speed and relatively modest ultimate vacuum. The low

pressure limit is typically about 0.3 torr. Diaphragm

pumps can be made completely free of hydrocarbons so

they are used as roughing pumps and, in some

applications, as backing pumps in ultraclean systems.

Molecular Drag Pumps. A molecular drag pump

incorporates a rotating cylinder within a closely ﬁtting,

stationary cylinder. The clearance between rotor and

stator is of the order of 0.01 in. Pumping occurs when

the surface velocity of the rotor approaches the velocity

of the molecules being pumped, so that molecules striking

the rotor acquire a signiﬁcant velocity component

tangential to the rotor – they are dragged along with the

rotor. Tangentially accelerated gas molecules rebounding

to the stator are decelerated: they ‘‘pile up,’’ thus yielding

compression. The process is repeated continuously around

the gap between rotor and stator. Helical grooves on the

surface of the rotor or stator direct the ﬂow of continually

compressing gas toward the pump outlet. Drag pumps

provide efﬁcient pumping at inlet pressures from nearly

1 torr down to about 10

6

torr. The compression ratio

for air (that is, the ratio of outlet to inlet pressure) is

typically 10

at the low-pressure end of this range. As a

consequence, the exhaust pressure, that is, the critical

backing pressure, falls in the 1 to 10 torr range. The

practical result is that a very small pump is required to

transfer the drag pump throughput to the atmosphere.

Small diaphragm pumps serve well as backing pumps for

molecular drag pumps.

The chamber pressure at the inlet must be below about

1 torr for a drag pump to begin to operate efﬁciently; a

roughing pump is necessary. The backing pump, pumping

through the drag pump, can serve to rough down the cham-

ber, however, the gap between rotor and stator is small and

restrictive in the viscous-ﬂow regime. A separate roughing

pump or a bypass (with a valve) from the chamber to the

backing pump should be provided.

Molecular drag pumps provide modest pumping speeds

at high vacuum – the inlet apert ure is effectively the gap

between rotor and stator. Drag pumps are currently avail-

able with pumping speeds of up to about 30 L/s. The great

virtue of the drag pump is the relatively high throughput in

the 1 to 10

3

torr pressure range. Displacement pumps such

as rotary-vane pumps, piston pumps, and Roots blowers, lose

efﬁciency below 0.1 torr. High-vacuum pumps such as dif-

fusion pumps, turbomolecular pumps, and ion/getter pumps,

‘‘stall’’ at pressures abov e 0.01 torr. If pumpdo wn time is an

important issue, a molecular drag pump may be a good

choice for a small vacuum system with an ultimate pressure

of 10

6

torr. With a 1 L s

1

roughing/backing pump and a

drag pump of 30 L s

1

, a volume of 100 L can be evacuated

to less than 10

4

torr in a matter of minutes.

Turbomolecular Pumps. Turbomolecular pumps

operate in the molecular-ﬂow regime. The construction is

similar to that of an aircraft-type jet turbine engine. A

series of bladed turbine rotors on a common shaft turn at

20 000 to 90 000 rpm. The edge speed of a rotor

approaches molecular velocities. The rotor blades are

canted so that a molecule striking a blade receives a

signiﬁcant component of velocity in the direction of the

pump exhaust (Figure 3.10). Bladed stators are interleaved

between

the rotors. The stator blades are canted in the

opposite direction from that of the rotors in order to

decelerate the molecules and compress the ﬂowing gas

before it is delivered downward to the next rotor–stator

pair. These pumps provide roughly the same pumping

speed for all gases; however, the compression ratio

Figure 3.10 Rotor of turbomolecular pump.

VACUUM PUMPS 107

depends upon the nature of the gas being pumped. A single

rotor–stator pair typically provides a compression ratio of

about 10 for N

. To a ﬁrst approximation, the logarithm

of the compression ratio is proportional to the square root

of the molecular weight of the gas; thus, for example, a

multistage pump with eight rotors may have a compression

ratio of 10

for N

, but only 10

to 10

for H

. A desirable

consequence of the strong dependence upon molecular

weight is that the compression ratio is very high for oil

vapor backstreaming from the pump bearings or from the

pump exhaust; thus a turbopump provides an essentially

oil-free vacuum. The compression ratio is extremely

sensitive to the pressure at the outlet of the pump. A

typical turbopump may have a compression ratio of 10

for air if the pressure at the exhaust is maintained below

0.1 torr, but if the exhaust pressure rises to 1.0 torr, the

compression ratio falls to 10.

A turbomolecular pump is usually run in series with a

conventional oil-sealed rotary pump as a backing pump.

The backing pump also serves as a forepump. With the

vacuum chamber at atmospheric pressure, the rotary pump

is activated to evacuate the chamber, drawing gas directly

through the body of the turbopump. Depending on the

manufacturer’s speciﬁcation, the turbo is activated at the

same time or somewhat later as the chamber pressure falls

so that the turbo is coming up to its operating speed as the

chamber pressure reaches a pressure of a few millitorr.

The critical elements of a turbomolecular pump include

the motor and the bearings. Typically, 400 Hz synchronous

motors are used. Active electronic control is employed to

maintain rotor speed over a wide range of loads and to

protect the pump in the event of an overload. The motor

driver and control represent a signiﬁcant fraction of the

total cost of a turbomolecular pumping system. Many tur-

bopumps use water-cooled, grease-packed bearings. Some

use oil as a bearing lubricant with the oil being circulated

to a water-cooled heat exchanger. Magnetic suspension

systems are the most recent development (Balzers, Osaka,

and Varian). There is no mechanical contact in a magnetic

bearing; there is essentially no friction and lubrication is

unnecessary. In some pumps the rotor is completely mag-

netically suspended, while in others a magnetic bearing is

used at the inlet end of the rotor with a conventional

grease-lubricated bearing at the outlet, relying upon the

high pumping speeds for hydrocarbons to suppress oil

backstreaming. Axial and radial magnetic ﬁelds to support

the rotor are provided by electromagnets in a feedback

system that senses the position of the rotor and makes

corrections to offset disturbing forces. A mechanical bear-

ing is provided to catch the rotor in the event of catastrophic

imbalance and to support the rotor when the pump is not in

operation. A backup electrical system is required to protect

against a sudden loss of power to the magnet system when

the pump is in operation. This may be simply a battery,

however, in sophisticated systems, the pump motor is oper-

ated as a generator when external power is lost, in order to

provide electricity for the magnetic bearings.

The most recent innovation is a compound pump design

incorporating a multistage turbomolecular pump mounted

on a common axis above a molecular drag pump, as shown

in Figure 3.11. These are sometimes called hybrid pumps

compound turbomolecular drag pumps; a complete

system effectively has three pumps operating in series: a

turbomolecular pump, a molecular drag pump, and a

displacement-type backing pump (Balzers). The hybrid

arrangement increases the compression ratio of the high-

vacuum pumping stage by several orders of magnitude,

with a concomitant increase in the outlet pressure.

Figure 3.11 Compound turbomolecular/molecular drag

pump.

108 VACUUM TECHNOLOGY

The tolerable backing pump pressure of a hybrid pump is

in the 1 to 10 torr range. With the increase in outlet pres-

sure comes a corresponding decrease in the volume ﬂow

rate at the exhaust. The important consequence is that

these pumps require only a small dry-diaphragm backing

pump that, with the inclusion of a magnetic rotor suspen-

sion, creates an ultrahigh vacuum pumping system that is

completely free of hydrocarbons. Complete turnkey sys-

tems are available that include a compound pump with a

motor controller, a backing pump, and all necessary inter-

locks to control startup and shutdown. Pressures below

10

torr are attainable.

The hi gh rotationa l speeds and close tolera nces in a

turbomolecular pump place a p rem ium upon careful

mounting, cleanli ness , and proper mainte na nce. Owing

to the very small clearances between moving and station-

ary components, twisting and bending forces that would

cause distortion cannot be applied to the pump body. The

pump should not be used as the mounting platform for the

vacuum system. The pump should be suspended by its

inlet ﬂange. Small particles can have disastrous effects

upon bearings and rotors at high speeds. The vacuum

container pumped by a turbopump must be kept scrupu-

lously clean. A protective screen, known as a splinter

shield, over the inlet is essential. W hen the vacuum con-

tainer is to be let up to at mosph eric pressure, gas should

be admitted slowly so that turbulence d oes not carry deb-

ris into the turbopump.

Careful and systematic startup and shutdown procedures

are essential to protect the turbopump and to exclude oil

from the vacuum system. As mentioned above, turbos are

usually operated without a valve at the inlet, however, a

valve is required in the foreline between the turbo outlet

and its backing pump. At startup with the turbo and the

vacuum system at atmospheric pressure, the backing pump

is activated and the foreline valve is opened. The rush of

dense gas into the backing pump prevents oil from back-

streaming. As the pressure falls, the turbo activation is

timed so that the turbo is up to at least 50% of its maximum

speed before the pressure at the pump inlet falls below a

few hundred millitorr. At this point the turbo compression

should be sufﬁcient to prevent oil vapor from backstream-

ing to the vacuum system. At shutdown, the foreline valve

is closed immediately after power is cut from the turbo.

The vacuum system should be vented before the rotor falls

below 50% of its maximum speed – again so that the

compression ratio is sufﬁcient to prevent backstreaming

of oil from the bearings. When the pressure has risen above

several hundred torr, backstreaming is essentially impos-

sible. It follows that a pump that is not operating should not

be stored under vacuum. It also should be emphasized that

the pump must be vented above the outlet. Many manu-

facturers sell turbopumps and controllers as a complete

system that incorporates the necessary valves and timing

circuits to automatically perform the startup and shutdown

procedures.

A turbomolecular pump offers many advantages for

high- or ultrahigh-vacuum systems. Of course these must

be weighed against the disadvantages, the main one being

the relatively high initial cost and the cost of major servic-

ing; a complete turbomolecular-pump system may cost

two or more times as much as a comparable diffusion-

pump system. Turbomolecular pumps with pumping

speeds from 10 to 1000 L/s are available. A turbopumped

system can achieve pressures below 10

10

torr. Most gases

can be pumped, although, as noted, turbos do not efﬁ-

ciently pump hydrogen and helium. Most corrosive gases

are acceptable, providing the bearing lubricant does not

come under attack. Turbopumps are compact and rela-

tively light in weight; they need not be mounted on the

underside of a vacuum system. For many types of pumps,

the mounting orientation is not critical – these can be

mounted with the axis horizontal. Turbos can be baked

to reduce outgassing; many are equipped with heating

jackets for this purpose. A turbo can be used on a system

that is to be baked, provided the inlet temperature does not

exceed 100 – 120 ºC. Magnetic ﬁelds can be a problem, as

eddy currents induced in the aluminum rotor assembly

cause heating. The speciﬁcation for most pumps calls for

magnetic ﬁelds not to exceed 50 to 100 gauss at the inlet. A

turbomolecular pump can run for one to three years with-

out attention. The major maintenance procedure usually

involves replacing the bearings and rebalancing the rotor.

These procedures often require the pump to be returned to

the manufacturer.

3.4.2 Vapor Diffusion Pumps

In a diffusion pump, gas molecules are moved from inlet to

outlet by momentum transfer from a directed stream of oil

VACUUM PUMPS 109

or mercury vapor. As shown in Figure 3.12, the working

ﬂuid is evaporated in an electrically heated boiler at the

bottom of the pump. Vapor is conducted upward through

a tower above the boiler to an array of nozzles from which

the vapor is emitted in a jet directed downward and outward

toward the pump walls. The walls of the pump are cooled,

so that molecules of the working-ﬂuid vapor condense

before their motion is randomized by repeated collisions.

The diffusion pump walls are usually water-cooled,

although in some small pumps they are air-cooled. The

condensate runs down the pump wall to return to the boiler.

Efﬁcient operation of a diffusion pump requires a temper-

ature gradient from top to bottom. The pump wall should

be lowest at the top of the pump – less that 30 ºC–to

effectively condense oil vapor, and highest at the bottom

to drive absorbed gas out of the oil condensate. For this

reason the cooling water ﬂows from top to bottom and the

ﬂow rate is regulated; too high a ﬂow rate results in too low

a temperature at the bottom of the pump.

Because the pumping action of a diffusion pump relies

on momentum transferred in collisions between the mole-

cules of the working ﬂuid vapor and the molecules being

pumped, the speed of the pump is greater for light gases

than for heavy gases. The inlet area essentially determines

the net speed of the pump. For air the pumping speed is

about 4 L s

1

2

of inlet area.

As indicated by the pumping-speed curve in Figure 3.12,

the

pumping action of a diffusion pump begins to fail when

the inlet pressure increases to the point where the mean

free path of the molecules being pumped is less than the

distance from the vapor-jet nozzle to the wall. When this

occurs the net downward momentum of vapor molecules is

lost and the vapor begins to diffuse upward into the vacuum

system. Diffusion pumping of a vacuum chamber may be

initiated at 50 to 100 mtorr, but the system pressure should

quickly fall below 1 mtorr or the chamber will become

signiﬁcantly contaminated with the vapor of the working

ﬂuid. Oil diffusion pumps can run against an outlet pres-

sure of 300 to 500 mtorr, and mercury pumps can tolerate

an outlet pressure of a few torr. A backing pump, usually

an oil-sealed rotary pump, is required. The speed of the

diffusion pump is insensitive to foreline pressure up to

some critical pressure. If this critical backing pressure is

exceeded, the pump is said to stall. This is a disaster,

because hot pump-ﬂuid vapor is ﬂushed backwards through

the pump into the chamber. The usual practice is to maintain

the oil-diffusion-pump foreline pressure below 50 mtorr.

The primary difﬁculty with diffusion pumps is the back-

streaming of oil vapor from the pump inlet. Without appro-

priate precautions this can amount to as much as a

microgram per minute for each cm

of pump inlet area.

Backstreaming is much worse if the foreline pressure of a

hot pump accidentally rises above the critical backing

pressure of a few hundred millitorr. It is essential to main-

tain the pump cooling system. Most diffusion pumps are

water-cooled. A ﬁlter in the cooling-water line is necessary

to reduce the possibility of clogging. Cooling water should

enter at the top of the pump so that the uppermost part of

the pump wall is at the lowest temperature. The next line of

defense is a ‘‘cold cap’’ typically consisting of a conical

shield over the top of the jet tower. The cold cap is cooled

by water ﬂow or by solid thermal contact with the pump

body. Diffusion pumps usually are supplied with a cold cap

installed. In most installations a water- or refrigerant-

cooled bafﬂe ( Figure 3.26) is mounted on top of the pump.

The

cold cap and bafﬂe together reduce backstreaming by

Figure 3.12 Diffusion pump.

110 VACUUM TECHNOLOGY

as much as three orders of magnitude with a loss of pump-

ing speed of perhaps 50%. For many purposes, the vacuum

above the bafﬂe can be considered oil-free. Oil can reach

the vacuum chamber as a liquid ﬁlm that creeps up the

walls above the pump. To eliminate this problem, an anti-

creep barrier consisting of an annular ring made of Teﬂon,

a material not wetted by oil, can be installed on top of the

bafﬂe. The ultimate performance and the cleanest vacuum

are obtained with the installation of a liquid-nitrogen-

cooled trap (Figure 3.25) above the bafﬂe.

The

properties of diffusion-pump ﬂuids are given in

Table 3.3; included are hydrocarbon, perﬂuorocarbon and

silicone

oils, and mercury. The various diffusion pump oils

can be used interchangeably in an oil diffusion pump. The

choice depends upon the desired ultimate pressure, the

demands of the particular application, and the cost. The

matter of economics is signiﬁcant; the cost of the oils listed

in Table 3.3 ranges over more than a factor of 20. The

perﬂuorocarbon

and polyether oils are sufﬁciently costly

that it is economical to reclaim them; many vacuum hard-

ware companies offer this service. The absolute lowest

pressure attainable with an untrapped diffusion pump is

the room-temperature vapor pressure of the working ﬂuid.

The silicone oils are the least expensive of the high-per-

formance (i.e., low ultimate pressure) pump ﬂuids. They are

exceptionally resistant to oxidation and chemical attack,

except in the presence of BCl

and, to a lesser extent, CF

and CCl

. The main drawback to silicone oils is that the

residue of backstreaming oil found on surfaces in the vacuum

system will decompose and polymerize to produce insulating

ﬁlms upon exposure to heat and charged-particle bombard-

ment; silicone oils are unsuitable for diffusion pumps on

instruments such as mass spectrometers or electron micro-

scopes. The phthalate and sebacate oils are ine xpensi v e ﬂu-

ids suitable for many applications. Decomposition of these

hydrocarbon oils yields carbonaceous deposits that are con-

ductiv e. Polyphenylether oils of fer exceptional chemical and

thermal stability. These are well suited for use with mass

spectrometers and other charged-particle-beam instruments.

The perﬂuorocarbon oils are suitable for pumping corrosive

gases, with the exception of Lewis acids such as BCl

and

AlF

. Their performance under charged-particle bombard-

ment is probably the best of all pump ﬂuids.

Mercury diffusion pumps ﬁnd only a few specialized

uses that rely upon the chemical inertness of mercury

vapor. They are occasionally used on mass spectrometers

because of the simple, easily identiﬁed spectrum of mer-

cury vapor. Mercury diffusion pumps are most often made

of Pyrex glass and are intended for use with glass vacuum

systems used to handle and distill small quantities of

volatile chemicals. Mercury diffusion pumps tolerate inlet

pressures 10 times greater than the maximum inlet pres-

sure tolerated by oil pumps. In addition the critical foreline

pressure for a mercury pump is much higher. Because the

room-temperature vapor pressure of mercury is about 10

3

torr, an inlet cold trap is required to prevent bulk migration

of mercury into the vacuum system. Mercury vapor is

toxic, and care must be taken to properly trap and vent

the backing-pump exhaust.

Table 3.3 Properties of diffusion-pump ﬂuids

Trade Names

(chemical composition)

Boiling

Point at

1 torr

(ºC)

Approximate

Vapor

Pressure

@20 ºC

(torr)

(Mercury) 120 2 3 10

3

(Di-n-butyl phthalate) 140 2 3 10

5

Octoil, Diffoil

(di-2-ethylhexylphthalate)

200 3 3 10

7

Octoil-S, Diffoil-S

(di-2-ethylhexylsebacate)

210 3 3 10

8

Convoil-20

(saturated hydrocarbon)

190 5 3 10

7

Neovac Sy

(alkyldiphenylether)

240 1 3 10

8

Convalex-10

(polyphenyl ether)

280 7 3 10

10

Santovac-5

(pentaphenyl ether)

280 5 3 10

10

D.C.704

(tetraphenyl tetramethyl

trisiloxane)

240 3 3 10

8

D.C.705

(pentaphenyl trimethyl

trisiloxane)

250 5 3 10

10

FomblinY-VAC 25/9

(perﬂuoropolyether)

230 2 3 10

9

Krytox1625

(perﬂuoropolyether)

250 2 3 10

9

VACUUM PUMPS 111

Diffusion pumps with speeds of 50 to 50 000 L/s and

with nominal inlet port diameters of 2 to 100 cm are avail-

able. Diffusion pumps are constructed of Pyrex glass, mild

steel, or stainless steel. The jets and towers of pumps with

steel barrels are aluminum. The choice of glass or steel

usually depends upon the material that is used to construct

the vacuum container, although it is also relatively simple

to mate glass to steel with an elastomer gasket or through a

metal-to-glass seal. For those systems that are intended to

handle reactive gases, glass is the preferred material; how-

ever, glass pumps are available only in small sizes.

Diffusion pump maintenance involves assuring the qual-

ity and quantity of the pump ﬂuid and checking that the

heaters are operating. Some reaction of the pumped gas

with the pump ﬂuid is inevitable, so periodic inspection

of the pump innards is essential. Moderate discoloration

of the oil is not signiﬁcant, however, if the oil is opaque it

should be replaced. The interior of the pump must be thor-

oughly cleaned before adding new oil, especially if a differ-

ent type of oil is being installed. Scrubbing with acetone,

followed by an acetone and an ethanol rinse will remove

hydrocarbon oils and, with persistence, silicone oils. Depos-

its of badly decomposed oil can be removed with naphtha-

lene. Polyphenylether oils are soluble in trichloroethylene

and 1,1,1-trichloroethane. Both these solvents should be

used with care in a well-ventilated environment. Fluorocar-

bon oils are soluble in ﬂuorinated alkanes such as trichlor-

otriﬂuoroethane and perﬂuorooctane. Severe decomposition

of the oil results in black, carbonaceous deposits on the jet

tower. These must be removed mechanically by scrubbing

with ﬁne abrasi ve or by glass-bead blasting. The tower must

be carefully cleaned before reinstallation in the pump.

There is a close ﬁt between the tower and the pump body.

A residue of abrasive cleaning materials will result in the

tower becoming jammed in the pump body.

Diffusion pumps use ﬂat ‘‘pancake’’ heating elements

bolted to the bottom of the pump or cylindrical ‘‘cartridge’’

heaters inserted in close-ﬁtting holes in the bottom of the

pump. As many as six cartridge heaters wired in parallel

may be used. The advantage to multiple heaters is that the

pump continues to operate if one or more heaters burn out,

albeit with some loss of efﬁciency. On the other hand, the

loss of one or more heaters may go unnoticed until signiﬁ-

cant contamination of the vacuum has occurred. The indi-

vidual cartridge heaters may be disconnected from one

another and individually checked for electrical continuity.

It is essential that diffusion pump heaters be in good ther-

mal contact with the pump over their entire mating surfa-

ces or the heaters will burn out prematurely. A coating of

‘‘milk of magnesia’’ (a slurry of MgO in water) will assure

good contact and facilitate removal at a later time by pre-

venting the heater from sticking to the pump because of

corrosion or cold welding.

A diffusion-pumped system is the most economical

route to high and even ultrahigh vacuum in chambers of

moderate size. With no moving parts and no critical

dimensions, diffusion pumps are robust and long-lived.

Decades-old pumps can be perfectly serviceable. This is

a boon for researchers on a limited budget, since used

pumps are available at little or no cost.

3.4.3 Entrainment Pumps

A variety of vacuum pumps remove gas from a system by

chemically or physically tying up molecules on a surface

or by trapping them in the interior of a solid. Two of the

principal advantages of these pumps are that they require

no backing pump and they contain no ﬂuids to contaminate

the vacuum.

Sorption Pumps. The simplest of the entrainment

pumps is the sorption pump ill ustrated in Figure 3.13.

The

sorbent material is activated char coal or one of the

synthetic zeolite mater ials k nown as molecular sieves.

These ma ter ial s are effective sorbent s partly be ca us e of

their huge surface area – of the order of thousands of

square meters per gram. The most common molecular

sieves are zeolite 5A o r 13X. The number in the sieve

code speciﬁes the pore size: 5A is preferred for air

pumping, while 13X is used for trapping hydrocarbons.

All of these materials will pump water and hydrocarbon

vapors at room te mpe ratur e, but they must be cooled

to liquid-nitrogen temperature to absorb air. Sorbe nt

materials do not trap hydrogen or helium at liquid-

nitrogen temperature. Without some a uxiliary means of

removing hydrogen and helium, the partial pressures of

these gases in a system will establish the lowest attainable

pressure. Sorption pumps must be provided with a poppet

valve becaus e the sorbent materi al releas es all of its

absorbed air as it warms to room temperature.

112 VACUUM TECHNOLOGY

The sorbent is initially activated by baking to 250 ºC.

After several pumping cycles the pores of the sorbent

material will become clogged with water and the efﬁciency

of the pump will deteriorate. Water is removed by baking

the pump to 250 ºC with the poppet valve open and then

cooling to room temperature with the valve closed so that

moisture from the room is not reabsorbed. Baking can be

accomplished by wrapping the pump with heating tape.

Custom-made heating mantles can be obtained inexpen-

sively from the Glas-Col Company.

In a well-designed pump, 1 kg of dry Linde 5A molec-

ular sieve will pump a 100 L volume from atmosphere to

less than 10

2

torr in about 20 minutes. The pump must be

designed to provide good thermal contact between the

sieve and the coolant to obtain the maximum pumping

speed. A thin-walled inlet tube will minimize heat conduc-

tion into the pump. Sorption pumps similar to that in the

ﬁgure are available from suppliers of vacuum hardware.

Pressures below 10

6

may be attained in a system that has

been roughed down. A simple way to achieve low pres-

sures with sorption pumping is to use two or three pumps

on a manifold. Each pump is equipped with a shutoff valve.

Starting at atmospheric pressure, one pump valve is opened

to rough down the system. This pump should be of a size

such that the pressure falls to less than 1 torr. This pump is

valved off and the next pump is brought on line and so on.

To attain the lowest possible pressure with this arrange-

ment, the vacuum chamber can be purged of hydrogen

and helium before ev acuation proceeds. This can be accom-

plished by ﬂushing the vacuum chamber with dry air or dry

nitrogen before initiating pumping with the sorption pumps.

Getter Pumps. Clean surfaces of refractory metals

such as titanium, molybdenum, tantalum, or zirconium

will pump most gases by chemisorption. This process is

called gettering. In a getter pump, the active metal surface

is produced in vacuo. Titanium or a titanium/molybdenum

alloy is the preferred metal. A getter pump employing a

freshly evaporated titanium surface is called a titanium

sublimation pump. At room temperature a titanium

surface pumps H

,CO

, and H

O at rates of

several L/s per cm

of exposed surface. Cooling the

surface to liquid nitrogen temperatures may double or

triple the pumping speed for N

and H

. Methane and

the noble gases, such as Ar and He, are not pumped at all.

A titanium sublimation pump consists of a titanium sub-

limator and the surface surrounding the sublimator. The

surface may or may not be cooled. These pumps operate

effectively between 10

3

and 10

11

torr, however, the inert

gases must be removed before ultrahigh vacuum can be

achieved. This can be accomplished with a small ion pump

in parallel with the getter pump. An alternative method to

(at least initially) remove rare gases is to purge the system

with pure dry nitrogen prior to evacuation. The titanium

surface must be renewed at a rate roughly equal to the rate

at which a monolayer of gas is adsorbed. Down to about

7

torr the titanium surface is continuously deposited.

Below 10

7

torr the titanium need only be deposited peri-

odically. The capacity of a titanium sublimation pump is

about 30 torr L per gram Ti. A forepump is not required,

but a mechanical or sorption roughing pump is needed to

reach a starting pressure of about 10

3

torr.

Titanium sublimation pumps are quite simple in design

and correspondingly inexpensive. Commercially available

sublimators consist of two to four electrical feedthroughs

in a ﬂange with titanium ﬁlaments suspended between the

Figure 3.13 Sorption pump.

VACUUM PUMPS 113

feedthroughs, as illustrated in Figure 3.14. A controller

supplies electrical current through the ﬁlaments at a rate

appropriate for the vacuum conditions. The sublimator can

be inserted in a side arm on the vacuum system with bafﬂes

or an elbow arranged to prevent titanium vapor from enter-

ing the main part of the vacuum chamber. The walls of the

sidearm then serve as the pump. The pumping speed with

this arrangement will usually correspond to the conduc-

tance of the sidearm with its bafﬂes. Vacuum housings with

water- or liquid nitrogen-cooled bafﬂes are available to

contain the sublimator. These are designed to be mounted

directly atop a turbomolecular pump in an ultrahigh vac-

uum system. For a glass vacuum system, a simple pump

can be made by wrapping titanium wire around a tungsten

wire sealed in a glass bulb, as shown in Figure 3.15. The

tungsten

ﬁlament is electrically heated to evaporate the

titanium that in turn condenses on the walls of the bulb.

A new class of getter pumps employing so-called ‘‘non-

evaporable’’ getters has recently come into use (see, for

example, SAES Getters, S.p.A.). These employ a porous,

sintered, zirconium alloy that strongly absorbs and reacts

with active gases. The getter is activated by heating to 700

to 900 ºC in vacuo to remove any surface oxide. In oper-

ation the getter is maintained at a temperature of about

400 ºC. CO, CO

, and O

are irreversibly adsorbed.

Water vapor and hydrocarbons are dissociatively adsorbed.

is reversibly adsorbed; there is no sorption of the rare

gases. Nonevaporable getter pumps operate down to 10

12

torr. The pumping speed is highest for H

and H

O. These

pumps are an excellent adjunct to a turbomolecular pump

in a UHV system.

Cryopumps. Any surface will act as a pump for a gas

that condenses at the temperature of the surface. A pump

that relies primarily upon condensation on a cold surface is

called a cryopump. Commercial versions of these pumps

employ a closed-circuit helium refrigerator to cool the

active surfaces. Working temperatures are typically

below 20 K. These pumps usually employ two stages. In

the ﬁrst stage a metal surface is maintained at 30 to 50 K to

trap water vapor, carbon dioxide, and the major

components of air. In some designs a liquid-nitrogen-

cooled bafﬂe to reduce the load of water vapor on the

subsequent stages precedes this ﬁrst stage. The second

stage, maintained at 10 to 20 K, is coated with a

cryosorbent material such as activated charcoal to

provide pumping of neon, hydrogen, and helium.

Cryopumps provide a high pumping speed for the easily

condensed gases. Their performance with helium depends

critically upon the quality and recent history of the

cryosorbent surface. The gas captured by a cryopump is

Figure 3.14 Titanium sublimator on a

UHV ﬂange.

Figure 3.15 Simple titanium sublimation pump as an

appendage on a glass vacuum system.

114 VACUUM TECHNOLOGY

not permanently bound. The pump must periodically be

warmed to regenerate the pumping surfaces. Because of

the limited capacity of the pump, a roughing pump is

necessary, as is a valve between the cryopump and the

vacuum chamber so that the vacuum system can be

rough pumped to a pressure less than about 10

3

torr

before cryopumping is initiated.

Ion Pumps. An ion pump combines getter pumping

with the pumping action exhibited by an ionization

gauge. Within these pumps a magnetically conﬁned

discharge is maintained between a stainless-steel anode

and a titanium cathode. The discharge is initiated by

ﬁeld emission when a potential of about 7 kV is placed

across the electrodes. After the discharge is struck, a

current-limiting power supply maintains the discharge

rate at 0.2 to 1.5 A, depending on the size of the pump.

Inert-gas molecules, and other molecules as well, are

ionized in the discharge and accelerated into the cathode

with sufﬁcient kinetic energy that they are permanently

buried. Active gases are chemisorbed by titanium that

has been sputtered off the cathode by ion bombardment

and deposited on the anode.

Ion pumps function between 10

2

and 10

11

torr. A

forepump is needed to reach the starting pressure. Since

ion pumps are completely free of hydrocarbons, an oil-free

rough pump is called for. A well-trapped oil-sealed rotary

pump can be used, but roughing with sorption pumps will

guarantee that the vacuum chamber remains clean. An ion

pump has a limited lifetime of operation due largely to the

rate at which the cathode erodes during operation. The

operational lifetime is an inverse function of pressure.

Under continuous operation at 10

3

torr, the lifetime of a

typical pump is only 20 to 50 hours, whereas operation at

6

torr can continue for 20 000 to 50 000 hours (6 yrs).

At ultrahigh vacuum the lifetime is essentially inﬁnite.

Ideally, an ion pump is only operated below 10

5

torr,

but because this pressure is difﬁcult to attain with most

roughing systems, pumping can be initiated at 10

3

torr

provided that the gas load is such that the pressure quickly

falls into the desirable range. Ion pumps are frequently

used in conjunction with titanium sublimation pumps. In

fact, some ion pump designs include an integral sublima-

tion pump. The sublimation pump can serve to lower the

pressure from 10

3

torr to 10

5

torr before power is

applied to the ion pump. At lower pressures the titanium

sublimation pump signiﬁcantly increases the pumping

speed for getterable gases. To attain the lowest possible

pressures, an ion pump can be baked to at least 300 ºC.

Most pumps are equipped with integral heaters for this

purpose. Baking should be initiated only while the pump

is in operation.

The positive-ion current to the cathode of an ion pump is

a function of pressure; the pump serves as its own pressure

gauge. The power supply and control unit for most ion

pumps includes a pressure readout. This is a signiﬁcant

consideration in the design of a very small ultrahigh vac-

uum system; the cost of a 1 to 5 L/s ion pump with its

control unit is little more than the cost of an ion gauge

and controller.

Ion pumps require no cooling water or backing pump.

They continue pumping by getter action even if the power

fails. Ion pumps do not introduce hydrocarbon or mercury

vapors into the vacuum. Pumps with speeds from one to

many thousands of liters per second are available. The

limited capacity in the 10

3

torr to 10

5

torr range can

be a disadvantage. Stray magnetic and electric ﬁelds may

also present a problem; ion pumps may produce a mag-

netic ﬁeld of a few gauss at a distance of one inlet diameter.

There may also be a problem with ions escaping the pump;

ion emission can be suppressed by placing a suitably

biased screen above the pump inlet. An ion pump with

controller can cost two to three times as much as a com-

parable diffusion pump with an appropriately sized liquid-

nitrogen-cooled bafﬂe.

3.5 VACUUM HARDWARE

3.5.1 Materials

Glass. Two glasses are used in vacuum work: borosilicate

glass or ‘‘hard glass’’ such as Pyrex or Kimax that is about

70% SiO

, and quartz glass that is pure silica. Both

materials have a low coefﬁcient of thermal expansion and

are remarkably resistant to fracture under large temperature

gradients (thermal shock). Borosilicate glass has a broad

softening temperature range allowing glass vacuum

apparatus to be constructed and modiﬁed in situ by a

moderately competent glassblower as described in

Chapter 2. Quartz has a very high softening temperature

VACUUM HARDWARE 115

and a narrow softening temperature range and requires a

skillful glassblower. Quartz can be used in continuous

operation at temperatures up to 1000 ºC. Quartz is used

primarily when its high temperature strength or broad

range of optical transmission is to be exploited.

The permeability of helium through quartz is surprisingly

large – about 10

11

torr L s

1

mm cm

2

torr

1

[throughput

(torr L s

1

) through unit thickness (mm) per unit area (cm

)

per unit helium pressure differential (torr)] at room

temperature and increasing rapidly with increasing

temperature. This can be a problem with quartz windows

in UHV systems. Even when the permeation of atmospheric

helium is not signiﬁcant, the permeation of helium through a

quartz window can give rise to false signals when helium

leak-testing.

Hard glass tubing and glass vacuum accessories are

inexpensive. Stopcocks and Teﬂon-sealed vacuum valves;

ball joints, taper joints, and O-ring-sealed joints; traps; and

diffusion pumps are all easily obtained at low cost. In most

cases only the glassblowing ability to make straight butt

joints and T-seals is required to make a complete system

from standard glass accessories.

Glass pipe and pipe ﬁttings are manufactured for the

chemical industry. A variety of standard shapes, such as

elbows, tees, and crosses, are available in pipe diameters of

1/2 to 6 in. Glass process pipe with Teﬂon seals can be used

to make inexpensive vacuum equipment for use down to

8

torr. Couplings are also available for joining glass

pipe to metal pipe and to standard metal ﬂanges and pipe

ﬁttings so it is easy to make a system that combines glass

and metal vacuum components.

Glass and metal parts can be mated through a graded

glass seal. Typically a graded seal appears to be simply a

section of glass tubing butt-sealed to a section of Kovar

metal tube. In fact, the glass tubing consists of a series of

short pieces of glass whose coefﬁcients of thermal expan-

sion vary in small increments from that of hard glass to that

of the metal. Graded seals are useful for joining glass

accessories such as ion-gauge tubes to metal systems.

Alternatively, a graded seal can be employed to insert metal

hardware, such as a valve or an electrical feedthrough, into

a glass vacuum line. Inexpensive graded seals in sizes up to

5 cm diameter are available from commercial sources.

Windows in vacuum systems are often made of quartz.

For high-vacuum work the window can be sealed to the

vacuum wall with an elastomer gasket or O-ring. For ultra-

high vacuum, the edge of the quartz window is metalized

so that the window can be brazed into a metal ﬂange for

installation in a vacuum wall. Window/ﬂange assemblies

are available from most vacuum equipment suppliers.

Ceramics. Ceramics are used as electrical insulators and

thermal isolators. There are literally hundreds of different

kinds of ceramic materials; two ﬁnd frequent use in vacuum

apparatus: steatite, a magnesium silicate, and alumina

ceramics containing at least 96% Al

. Fabrication of

parts from these materials requires specialized grinding

equipment not ordinarily immediately available to a

laboratory scientist, however, there are many specialized

shops that provide grinding services under contract.

Standard shapes, such as rod, tubing, plate, and spheres,

are available in alumina (Coors Ceramics Co., McDanel

Refractory Porcelain Co., Industrial T ectonics, Inc.). It is

often possible to design an insulator that incorporates

these simple shapes into a more complex assembly.

Threaded steatite standoff insulators inexpensively avai-

lable from electronics suppliers can be used as structural

elements in vacuum apparatus. Corning produces

MACOR, a machinable ceramic that can be fashioned

into complex shapes with ordinary shop machine tools.

Brass and Copper. Brass has the advantage of being

easily machined, and brass parts can be joined by either

soft solder or silver solder. Unfortunately, brass contains a

large percentage of zinc whose volatility limits the use of

brass to pressures above about 10

6

torr. Heating brass

causes it to lose zinc quite rapidly. The vapor pressure of

zinc is about 10

6

torr at 170 ºC and 10

3

torr at 300 ºC.

Forelines for diffusion pumps are conveniently con-

structed of brass or copper tubing and standard plumbing

elbows and tees. Ordinary copper water pipe is acceptable

for forelines and other rough vacuum applications;

however, oxygen-free high-conductivity (OFHC) copper

should be used for high-temperature and high-vacuum

work. A skilled technician can weld copper.

Stainless Steel. The most desirable alloys for the

construction of high-vacuum and ultrahigh-vacuum

apparatus are the (American AISI) 300 series austenitic

stainless steels, especially type 304 and type 316

116 VACUUM TECHNOLOGY

stainless steels; type 303 is not ordinarily used as it contains

volatile elements added to improve machinability. Stainless

steel is strong, reasonably easy to machine, bakeable, and

easy to clean after fabrication. 304 and 316 stainless steels

are essentially nonmagnetic with magnetic permeabilities

less than about 1.01. Stainless-steel parts may be brazed or

silver-soldered. Low-melting (230 ºC) silver–tin solders are

useful for joining stainless-steel parts in the laboratory;

however, it is best if stainless parts are fused together by

arc welding using a nonconsumable tungsten electrode in

an argon atmosphere. This process, known commonly as

heliarc fusion welding o r tungsten-inert-gas (TIG)

welding, produces a very strong joint, and, because no

ﬂux or welding rod is used, such a joint is ea sily cleaned

after welding . M ost machine shops are p rep ared to d o

TIG welding on a routine basis.

The bulk of commercial vacuum ﬁttings (ﬂanges and

shapes such as te es, crosses, and nipples) are fabricated of

type 304 stainless steel. In additi on, type 304 stainless is

widely used in the milk- and food-processing industry. As

a result, many stock shapes are comme rcially available at

low cost. E lbows, te es , crosses, Ys, and many other ﬁt-

tings in sizes up to a t least 6 in. diameter may be pur-

chased from the Ladish Company or Alloy Products

Company.

Aluminum. Aluminum alloys, particularly the 6000

series allo ys, are used for vacuum apparatus. Aluminum

has the advantage over stainless steel of being lighter and

stiffer per unit weight, and much easier to machine. It is

nonmagnetic. The chief disadvantages of aluminum stem

from it s poros ity and the oxide layer that covers the

surface. The rate of outgassing from aluminum is ﬁve to

ten times greater than for stainless steel. Aluminum can

be ano dized bl ack (black chrome) to reduce reﬂectivity

in optic al devices, however, a nodizing may signiﬁcantly

increase outgassing rates. Welds in aluminum are not

as reliable as welds in stainless and tend to outgas

volatile materials that have been occluded in the weld;

nevertheless, welded aluminum vacuum c ontainers are

used down to at least 10

7

torr. The hard oxide layer

that forms instantl y on a clean aluminum surface is an

electrical insu lator. Th is insulatin g surface tends to

collect electrons or ions to produce an electric ﬁeld that

is undesirable in some applications. Copper or gold

plating on aluminum or a coating of col loidal graphite

(see Section 5.6.1) should eliminate the accumulation of

urface charge.

Plastics. Plastics are used as ﬁxtures, electrical

insulators, bearings, and windows in vacuum systems at

pressures down to 10

7

torr. Their use is limited to varying

degrees because they outgas air, water, and plasticizers,

and because they cannot be heated to high temperatures.

Polyamide (e.g., Nylon) and acetal-resin-based plastics

(e.g., Delrin) are used for mechanical elements in vacuum

systems at temperatures below 100 ºC. These plastics are

hard and machinable. Nylons are self-lubricating and make

excellent bearings. Nylon is hygroscopic and outgasses

water vapor after exposure to air. Outgassing is less of a

problem with Delrin. Windows in vacuum systems may

be made of polymethylmethacrylate (e.g., Plexiglas or

Lucite) or polycarbonate (e.g., Lexan) plastics. Lexan is

especially strong, tough, and machinable, well suited for

use as a structural material or as an electrical insulator.

Fluorocarbon polymers have superior high-temperature

characteristics. Polytetraﬂuoroethylene (PTFE) (e.g.,

Teﬂon) can withstand temperatures up to 250 ºC. The

outgassing rate falls below 10

8

torr L s

1

2

after an

initial pumpdown of a day at 100 ºC. Unfortunately, Teﬂon

is relatively soft, and cold-ﬂows under mechanical

pressure, thus limiting its usefulness as a structural

element. Various polyimides, although expensive, are

ﬁnding use in vacuum systems that are to be baked.

Polyetherimide (Ultem) can be used at temperatures to

200 ºC. Polyamide/imide (Torlon) is the highest strength

thermoplastic. Polyimide (Vespel, Kapton) is the ultimate

material for both mechanical elements and electrical

insulation at high temperatures. Vespel has been used

continuously at temperatures approaching 300 ºC in high

vacuum. Polyimide is somewhat hygroscopic, but can be

baked to reduce outgassing. Kapton is polyimide sheet

used for electrical insulation. Kapton-insulated wire is

supplied for high-temperature use in high vacuum and

even ultrahigh vacuum.

A variety of low-vapor-pressure sealers and adhesives

have vacuum applications. Apiezon M grease, Dow-Corning

silicone high-vacuum grease, and FOMBLIN perﬂuorinated

grease are used to seal stopcocks and ground-glass taper

joints and, in some instances, as low-speed lubricants.

VACUUM HARDWARE 117

Apiezon compounds are used to seal joints and windo ws as

well as to ﬁll small gaps in vacuum systems. These wax-like

materials soften at temperatures of 45 to 100 ºCandhave

vapor pressures between 10

4

and 10

8

torr at room temper -

ature. A variety of resin-based sealers in spray cans are mar-

keted for sealing very small leaks in high-vacuum and e ven

ultrahigh-vacuum systems while they are under v acuum.

Epoxy resins are particularly useful. Epoxy cements

consist of a resin and a catalytic hardener that are com-

bined immediately before use. The proportions of resin

and hardener and subsequent curing must be carefully con-

trolled to prevent excessive outgassing from the hardened

material. Small epoxy kits with resin and catalyst pre-

packaged in the correct proportions are available, as are

silver-ﬁlled epoxy formulations that conduct both electric-

ity and heat.

3.5.2 Demountable Vacuum Connections

Vacuum systems require detachable joints for convenience

in assembling and servicing. There are basically three

means of creating a vacuum-tight seal between mating

connectors: pipe threads with a sealant in the joint, elasto-

mer gaskets or ‘‘O’’-rings, and deformable metal gaskets.

Pipe Threads. The threaded parts of a pipe joint are

tapered so that the joint becomes tighter and tighter as the

two are screwed together. The two parts are not made with

sufﬁcient precision to assure a vacuum-tight seal even

though signiﬁcant distortion of the metal threads can

occur as the parts are joined. To assure a seal, the male

part is covered with a thin layer of Teﬂon tape prior to

assembly. Teﬂon thread tape, or thread ‘‘dope,’’ is sold in

hardware stores for use with plumbing ﬁxtures. The tape is

wrapped around the threaded end. No more than two layers

are required and the tape should be stretched as it is wound

on to make a very thin layer. Looking at the end of the male

part, the tape should be wound in a counterclockwise

direction so that the exposed tag end does not get caught

up in the female threads as the joint is assembled. The tape

must be replaced upon reassembly. A signiﬁcant volume of

gas is trapped in an assembled pipe thread joint. Pipe

thread joints are not appropriate for ultrahigh-vacuum

systems, and their use is to be avoided as much as

possible in high-vacuum systems.

‘‘O’’-Ring Joints. For pressures down to about 10

7

torr, vacuum connections are most often sealed with

rubber O-rings. Several O-ring-sealed joints are illustrated

in Figure 3.16. O-rings are circular gaskets with a round

oss-section. They are available in hundreds of sizes

from 3 mm (.125 in.) I.D. (inner diameter) with a cord

diameter of 2 mm [.070 in. (nominally 1/16 in.)] to 60 cm

(2 ft.) I.D. with a cord diameter of 7 mm [.275 in.

(nominally 1/4 in.)]. Very large rings may be made from

lengths of cord stock with the ends butted together and

glued with cyanoacrylate adhesive (Eastman 910). O-rings

are made of a variety of elastomers. The most common are

Buna-N, a synthetic rubber, and Viton-A, a ﬂuorocarbon

polymer. Buna-N may be heated to 80 ºC and will not

take a set after long periods of compression. Unfortunately

this material outgasses badly, particularly after exposure to

cleaning solvents. Viton-A has a low outgassing rate and

will withstand temperatures up to 250 ºC, but will take

a set after baking. Generally, the advantages of Viton-A

O-rings offset their higher cost.

O-ring-sealed ﬂanges and ‘‘quick connects’’ are easily

fabricated and they are also available ready-made. Mating

ﬂanges have a groove that contains the ring after the

ﬂanges have been pulled into contact with one another.

Usually, one ﬂange is ﬂat and a rectangular-cross-section

groove is cut into the mating ﬂange; ﬂanges can be made

sexless by cutting a groove of half the required depth in

both ﬂanges. Groove design is critical to obtaining a reli-

able seal, as is the surface ﬁnish of the ﬂange and inside

the groove. Surface roughness should not exceed 1 lm

(32 microinches). The ﬂange surface and groove should

be cut on a lathe so that tool marks run circumferentially.

Radial scratches are one of the most common causes of

seal failure. To obtain the correct compression of the

O-ring material, the groove depth should be about 80%

of the actual cord diameter for static seals and 85% of

the diameter for dynamic seals. Rubber is deformable,

but incompressible; the width of the groove should be such

that the cross-sectional area of the groove exceeds that of

the O-ring by 30 to 40%. The ID of the groove should

match the O-ring ID; the O-ring is not to be stretched into

its groove. It is sometimes convenient to undercut the sides

of the groove slightly to give a closed dovetail cross-section

rather than a rectangular cross-section, so that the ring is

118 VACUUM TECHNOLOGY

retained in the groove during assembly. For rings up to 30

cm (12 in.) in diameter, the nominal cord diameter should be

3 mm (1/8 in.) or less. Choose a ring to ﬁt in a groove that is

as close to the ﬂange ID as possible, in order to minimize the

amount of gas trapped in the narrow space between the

mated ﬂanges. The bolts or clamps that pull the ﬂanges

together should be as close to the groove as possible to

prevent ﬂange distortion. For static seals, O-rings should

be used dry. Before assembly, the groove should be cleaned

with solvent and the ring wiped free of mold powder with a

dry, lint-free cloth; O-rings should not be cleaned with sol-

vents. For rotating seals a very light ﬁlm of vacuum grease

on the ring will prevent abrasion. Occasionally a ﬁlm of

grease may be required on a static O-ring to help make a

seal on an irregular surface. Grease is a liability, however, as

it tends to pick up debris that may disrupt the seal.

For very high temperatures, elastomer O-rings can be

replaced by metal O-rings composed of a thin metal sleeve

with an internal spring to provide resiliency. These are

manufactured by Helicoﬂex in aluminum, silver, copper,

nickel, and other materials suitable for temperatures from

300 to 600 ºC and in sizes comparable to those of standard

rubber O-rings. The groove design is essentially the same

as for rubber O-rings; detailed design instructions are

available from the manufacturer.

There are three standard types of O-ring sealed joints:

ASA, QF (or KF), and ISO. Examples are shown in Figure

16. The ASA design dates back to an early steamﬁtters’

andard, ﬂange. ASA design consists of two ﬂat ﬂanges

with an O-ring groove in one ﬂange and a circle of bolt

holes well outside of the groove. These ﬂanges are bulky

and require fasteners much larger than needed to resist

atmospheric pressure. The sizing of ASA ﬂanges refers to

the nominal ID of the ﬂange or the nominal OD of the tube

to which it is attached: the bore of a 4 in ASA ﬂange is about

4 in; the OD of the ﬂange is 9 in. Some commercial vacuum

hardware, including large diffusion pumps, large mechani-

cal pumps, and Roots blowers, still use ASA ﬂanges.

The QF (quick ﬂange) or KF (Klein ﬂange) design

employs two, ﬂat, and therefore sexless, ﬂanges with an

outer diameter only slightly larger than that of the O-ring.

The O-ring is mounted around a separate, aluminum ‘‘cen-

tering ring’’ that prevents the O-ring from being forced

inward by external pressure and whose thickness deter-

mines the extent of compression of the O-ring. The center-

ing ring has a lip on both sides that engages the inner

circumference of each ﬂange so that the O-ring is correctly

located on the ﬂanges. A jointed, circular clamp is installed

around the assembled pair of ﬂanges and a thumbscrew is

tightened to draw the two ﬂanges together, compressing

the O-ring. They are compact and, with only a single screw

to tighten, quite convenient to use; a QF ﬁtting can be

assembled with one hand. QF ﬂanges are available in

brass, aluminum, and type 304 and 316 stainless steel in

conﬁgurations suitable for a brazed or welded butt joint

or socket joint to tube sizes from 10 mm (1/2 in) to 50 mm

(2 in). A remarkable range of components is available with

QF ﬁttings, including nipples, elbows, tees, 4-, 5-, and 6-

way crosses, as well as adapters to mate QF with other

styles of connectors. In the spirit of ‘‘Tinker Toys,’’ it is

Figure 3.16 O-ring-sealed vacuum connections: (a) an exploded view of an O-ring-sealed ﬂange joint; (b) assembled ASA-style

ﬂange joint; (c) O-ring tube coupling (Cajon VCO); (d) a quick connect; (e) QF(or KF) joint; (f) ISO joint with K-style ﬂanges.

VACUUM HARDWARE 119

often possible to assemble a large part of a vacuum system

using only these standard components.

ISO ﬂanges are similar to QF ﬂanges but are sized for

larger tubing: nominal bore sizes range from 63 to 630 mm.

The ISO ﬁtting is comprised of two ﬂat ﬂanges with a

combination centering ring and O-ring mounted between

them. The centering ring has a lip on each side that engages

a counterbore near the ID of the ﬂange. ISO ﬂanges are

designed for one of two methods of joining a pair of ﬂanges.

K-style ISO ﬂanges employ clamps that hook over the outer

edges of the mating ﬂanges. F-style ﬂanges have holes for

bolts to draw the two ﬂanges together. K-style ﬂanges are

more compact than F-style ﬂanges. F-style ﬂanges make a

stronger structure appropriate for joining tubing that must

support large transverse forces. An all-metal C-Flex assem-

bly manufactured by EG&G Engineered Products can

replace the centering ring/O-ring assembly in a QF or ISO

joint. These employ a springy, tin-coated, Inconel element

to replace the elastomer O-ring. They can be baked at mod-

est temperatures and are said to be usable at UHV pressures.

The A&N Corporation ULRIC

ﬂange system is similar in

conﬁguration to the ISO ﬂange system and can incorporate a

copper gasket to make a ﬁtting that is bakeable and useable

for ultrahigh vacuum.

Metal Gaskets. Metal sealing materials are required

for ultrahigh-vacuum (UHV). Elastomers are unacceptable

because they outgas and because they cannot be baked

to high temperatures. The ConFlat design developed by

Varian has become the industry standard. Flanges of this

design, now generally known as CF (for ConFlat-

compatible) ﬂanges, are now manufactured by many

vacuum equipment suppliers. The CF sealing system is

composed of two identical ﬂanges and a ﬂat OFHC

copper gasket, as shown in Figure 3.17. Annular knife-

edge

ridges in each ﬂange cut into the gasket to make a

seal as the ﬂanges are drawn together by bolts that pass

through holes in the ﬂanges outboard of the copper gasket.

The entire assembly can be baked to 450 ºC. A great deal

of force is required to make the seal, so many high-tensile-

strength bolts are used, closely spaced around the ﬂange.

The knife-edge is designed so that the correct deformation

of the gasket is obtained when the ﬂanges are drawn into

contact. Careful assembly is important to avoid warping

the ﬂanges. The joint is initially assembled with all the bolts

just ﬁnger tight. Then, using good-ﬁtting wrenches and

working in sequence around the ﬂange, each bolt is

tightened no more than one half turn. Going round and

round the ﬂange, the bolts are drawn up just until the

ﬂange surfaces touch. The copper gaskets are permanently

deformed during installation and hence are used only once.

Bolts wear and stretch and must be replaced after perhaps

a dozen assembly cycles. Baking a CF ﬂange encourages

the bolts to seize in their nuts. A very thin coating of

molybdenum disulﬁde grease helps avoid this problem.

Silver-plated bolts are available to help reduce galling and

seizing in systems that are baked frequently to high

temperatures. CF ﬂanges are speciﬁed by the ﬂange OD in

sizes that run from 1.33 in (or 34 mm) to 12 in (305 mm) to

16 1/2 in. These are used with tube sizes from .75 in (or 16

mm in metric sizes) to 10 in (or 250 mm) to 14 in. In UHV

systems, circular cross-section tubes larger than 14 in

diameter are joined with Wheeler ﬂanges that employ a 2

mm diameter OFHC copper wire as a deformable gasket.

Wire-sealed ﬂanges are heavy and very large forces are

required to achieve a seal. They are available from many

manufacturers in sizes up to about 30 in.

3.5.3 Valves

A wide variety of valves are available commercially for use

in glass systems and in high-vacuum and ultrahigh-vacuum

metal systems. Characteristics to be considered in choosing

a valve (roughly in order of importance) include: (i) con-

ductance; (ii) operating temperature; (iii) leak rate around

Figure 3.17 Detail of a bakeable, ultrahigh-vacuum CF

ﬂange.

120 VACUUM TECHNOLOGY

the valve-operating mechanism and the valve seat; (iv)

material of construction [related to (ii)]; (v) conﬁguration;

(vi) cost; (vii) reliability; (viii) ease of maintenance.

Metal valves are always used in metal vacuum systems.

The construction of glass systems is easiest if glass valves

are used; however, glass valves (stopcocks) have relatively

low conductance. The clear passage through an open stop-

cock is typically only a few millimeters in diameter. When

a large-bore, high-conductance, valve is required in a glass

system, a metal valve of suitable size can be inserted using

a glass-to-metal transition on each side of valve. The two

most common glass valves are illustrated in Figure 3.18.

One

(a) is a vacuum stopcock consisting of a tapered glass

plug that is ﬁtted into a glass body by lapping. The mating

parts are sealed with a ﬁlm of high-vacuum grease. As

shown, these stopcocks are designed so that atmospheric

pressure forces the plug into the body of the valve. The

more modern type of glass valve (b) has a Teﬂon plug

threaded into a glass body. The plug is sealed to the body

with an O-ring. It is generally advisable to apply a light

ﬁlm of vacuum grease to the O-ring.

There are three basic designs for metal vacuum valves –

an example of each is shown in Figure 3.19. The differ-

ences

between the three designs have to do with the motion

of the sealing plate as it approaches the valve seat. The

valve in Figure 3.19(a) is a piston-type, or poppet, valve in

which

an actuator moves the sealing plate axially as the

valve is opened and closed. The piston valve is inherently a

‘‘right-angle’’ valve with the inlet and outlet ports at 90º to

one another; the design may, however, be modiﬁed to a

‘‘quasi-straight-through,’’ or ‘‘in-line,’’ valve by introduc-

ing a bend in the downward-facing inlet port, so that it

enters on the side opposite the outlet port with its center-

line parallel to that of the outlet port. The conductance of

inline valves is not as high as might be expected, since the

ﬂow through the valve encounters two right-angle turns.

The valve shown in Figure 3.19(b) is a swing valve or

‘

‘butterﬂy’’ valve. The sealing plate rotates about an axis

along its diameter as the valve is opened and closed. The

actuator mechanism need only rotate one quarter of a turn.

The obvious advantage of the butterﬂy valve is the low

proﬁle that provides the shortest possible path for gas

and hence the highest possible conductance. The butterﬂy

valve must be installed so that there is clearance for the

valve plate in the open position. The valve shown in Figure

3.19(c) is a sliding-gate valve. The sealing plate moves

radially

with respect to the valve seat and the direction

of gas ﬂow; a cam drives the sealing plate against the valve

seat once the plate is positioned above the seat. Vacuum

valves of the three basic designs are available with bores

ranging from less than a centimeter to more than 20 cm.

Figure 3.18 Glass vacuum valves: (a) a stopcock; (b) a glass

valve with Teﬂon plug.

Figure 3.19 Metal high-vacuum valves: (a) bellows-sealed

valve; (b) swing or ‘‘butterﬂy’’ valve; (c) sliding-gate valve.

VACUUM HARDWARE 121

Vacuum valves are fabricated of brass, cast aluminum,

machined aluminum, or stainless steel. The cost increases,

and the low-pressure limit of usability decreases, in the

same order. Brass contains the volatile metal zinc and

hence should not be used above room temperature. Small

piston-type valves are often manufactured of brass. These

are suitable for rough vacuum applications, such as diffu-

sion pump forelines. Cast aluminum is porous and out-

gasses in vacuum. Inexpensive cast aluminum valves can

be used in high vacuum. Valves manufactured of high-

quality, vacuum-cast aluminum can be used down to at

least 10

9

torr. Valves made of aluminum machined from

solid stock, with the appropriate seals, ﬁnd some use at

ultrahigh vacuum. Stainless steel is the standard for valves

used in high vacuum and UHV. In addition to a much lower

outgassing rate (compared to aluminum), stainless steel

withstands higher bakeout temperatures and is much more

resistant to corrosive gases such as are used in semicon-

ductor processing. The vacuum seal between inlet and out-

let of most vacuum valves is made by an O-ring installed in

the valve plate coming into contact with a smooth seating

surface machined into the valve body. Viton is the standard

O-ring material. A valve with Viton seals can be baked to

200 ºC. Valves with a polyimide seal are available for use

up to 300 ºC. The sealing materials in a true UHV valve

must be metal. Most designs employ a copper pad on the

actuator plate that is driven onto a stainless-steel knife-

edge seat in the valve body. An all-metal UHV valve can

be baked to 450 ºC. The soft copper sealing pad is effective

for a limited number of cycles and must be replaced fre-

quently. This problem, along with the relatively high cost

of UHV valves, encourages UHV system designs with as

few valves as possible.

All valves require an actuator mechanism that passes

from the atmosphere to the evacuated innards of the valve.

In butterﬂy valves this is a rotating shaft; in some piston-

type valves and gate valves, a rotating shaft passes through

the vacuum wall to drive a screw mechanism that provides

the linear motion required to move the valve plate; in other

designs the linear motion is transmitted through the vac-

uum wall by a linearly translating shaft. In butterﬂy valves

and inexpensive piston and gate valves, the actuator shaft

is sealed with an O-ring. Leakage around this seal is inevi-

tably the source of vacuum failure in these valves. In high-

quality piston and gate valves, linear motion is transmitted

through the vacuum wall and the drive mechanism is

located outside the vacuum. A bellows that ﬂexes to follow

the driver in and out as the valve is closed and opened seals

the actuator shaft. The life of a bellows shaft seal ranges

from 10 000 to more than 100 000 cycles.

The drive mechanism in a vacuum valve may be mechan-

ical, electromagnetic, or pneumatic. The most robust actua-

tors are driven by a rotating handwheel or crank. These

designs make for slow opening and closing, since the valve

plate in a vacuum valve must be moved over a relatively

large distance to provide good conductance when the valve

is open. A large gate valve may require as many as 30 turns

to open or close. Some piston and gate valves employ a

toggle mechanism. The toggle handle swings through 90º

or 180º. Considerable force is required at the end of the

swing to affect a seal so the valve body must be mounted

very securely. Valves with toggle actuators are rarely used in

the laboratory. Valves with electromagnetic actuators are

available for use with tubing of up to 40 mm or 1.5 in.

OD. These valves are actuated by an electrical current to

a solenoid that drives a plunger that opens the valve. The

plunger is spring-loaded so that the valve automatically

closes if power is lost. Piston-type valves and gate valves

of all sizes are available with pneumatic actuators. Com-

pressed air is admitted to a cylinder to drive a piston that is

connected to the valve actuator. The motion is reversed by

venting air on one side of the piston and admitting com-

pressed air to the opposite side. An electromagnetic valve in

the compressed air circuit controls the airﬂow. The electro-

magnetic valve is designed so that air is directed to the side

that closes the valve when electrical power is lost. Some

small valves use a simpler pneumatic circuit employing a

spring to close the valve. Pneumatic valves typically require

compressed air at 0.5 to 0.7 MPa (80 to 100 psi).

It is often necessary to admit gas at a low rate into a

vacuum system. The gas source may be at a high pressure.

For example, the pressure in a commercial gas cylinder

may exceed 10 MPa (1500 psi). Metering valves or ‘‘leak’’

valves are available for this purpose. Valves providing ﬂow

rates spanning several decades and with minimum control-

lable ﬂow rates as low as 10

10

torr L s

1

are available.

There are a variety of designs. Some are simply needle

valves employing a long, gently tapering needle moving

in a conical seat. Another design incorporates a metal or

sapphire plate moving against a metal knife-edge. All

122 VACUUM TECHNOLOGY

provide a more or less precise micrometer drive to control

the moving element. In general, a leak valve should never

be used to shut off the ﬂow of gas, as deformation of one of

the two elements will result in a loss of low-ﬂow control. A

shutoff valve, if required, should go on the upstream side

of a leak valve and as close to the inlet as possible to

minimize the ‘‘dead’’ volume of gas that must be pumped

through the leak valve. A sintered metal ﬁlter should

always be used at the inlet of a leak valve. The smallest

piece of solid material compressed against the seat of a

leak valve will certainly cause irreversible damage.

3.5.4 Mechanical Motion in the

Vacuum System

Mechanical motion can be transmitted through the vacuum

wall using a sliding seal, a ﬂexible wall, or a magnetic

coupling.

Rotary motion at speeds up to 100 rpm may be trans-

mitted through an O-ring-sealed shaft. These seals are

inexpensive, but may fail if the O-ring becomes abraded.

In addition, lubricants and the elastomer O-ring material

are exposed to the vacuum.

A bellows seal to a shaft is the most common means to

permit motion to pass through the vacuum wall. A simple

and inexpensive linear-motion feedthrough can be made

from the actuator mechanism of a small bellows-sealed

vacuum valve. As shown in Figure 3.20, the valve body

truncated above the seat, a mounting ﬂange is brazed to

the body, and a ﬁxture is brazed or screwed to the valve

plate for attaching the mechanism to be driven inside the

vacuum. Rotary motion may be transmitted through a

bellows-sealed ‘‘wobble driv e,’’ illustrated in Figure 3.21.

Relati

vely inexpensive rotary drives of this type are avail-

able from most vacuum-hardware suppliers. Much more

expensive and more complex drives are also available,

including drives that provide three-axis rotation and

three-axis translation.

Moving parts can be magnetically coupled through a

vacuum wall. This scheme is particularly useful for the

transmission of linear motion through the wall of a glass

vacuum system. The driven element is attached to a block

of magnetic material such as iron or nickel that is placed

against the inside of the vacuum wall. A magnet can then

drag the driven element along the wall. A more exotic

Figure 3.20 A bellows-sealed valve [Figure 3.19(a)]

converted to a linear-motion feedthrough.

Figure 3.21 Bellows-sealed, wobble-drive, rotary-motion

feedthrough.

VACUUM HARDWARE 123

application of magnetic forces is found in the use of ferro-

magnetic ﬂuids as shaft seals held in place by magnetic

ﬁelds. Ferroﬂuidic shaft seals rated for 5000 rpm at 10

9

torr are commercially available (A&N Super-Seal

Metal surfaces become very clean in vacuo, particularly

after baking, and metals in close contact tend to cold-weld.

Because of this, unlubricated bearing surfaces within a

vacuum system often become very rough after only a little

use. Liquid lubricants can be used if they are thoroughly

outgassed before installation. The vapor pressure of the

lubricant will be the limiting factor. Diffusion pump oils

can be used in diffusion-pumped vacuum systems, since the

ultimate pressure is determined by the room-temperature

vapor pressure of the oil in the pump. Polyphenylether

oils lubricate well and are among the lowest-vapor-pressure

oils. Perﬂuorinated oils, such as DuPont Krytox 143AZ,

are an excellent choice for liquid lubrication in a vacuum.

A difﬁculty with liquid lubricants is their tendency to creep

out of a bearing and along the surface of a shaft. A creep

barrier can be placed between a lubricated bearing surface

and the surroundings. This may consist of a coating or a

plastic lip of a material such as Teﬂon that is not wetted by

the lubricant.

There are a number of methods of improving bearing

performance in a vacuum system without introducing

high-vapor-pressure oils into the vacuum. The tendency

for a bearing to gall is reduced if the two mating bearing

surfaces are made of different metals. For example, a steel

shaft rotating without lubrication in a brass or bronze journal

will hold up better than in a steel bushing. A solid lubricant

may be applied to one of the bearing surfaces. Silver, lead–

indium, and molybdenum disulﬁde have been used for this

purpose. Graphite does not lubricate in a vacuum; MoS

probably best. The lubricant should be burnished into the

bearing surface. The part to be lubricated is placed in a lathe.

As the part turns, the lubricant is applied and rubbed into the

surface with the rounded end of a hardwood stick. By this

means, the lubricant is forced into the pores. After burnish-

ing, the surface should be wiped free of loose lubricant.

One component of a bearing may be fabricated of a self-

lubricating material such as nylon, Delrin, T eﬂon, or poly-

imide. Teﬂon is good for this purpose, but its propensity to

cold-ﬂow will cause the bearing to become sloppy with time.

Polyimide can be used in ultrahigh vacuum after baking to

250–300 ºC. Brown, Sowinski, and Pertel

have overcome

the cold-ﬂow problem in the design of a dri v e screw for use

in a vacuum. Both the screw and its nut are steel, and lubri-

cation is accomplished by placing a Teﬂon ke y in a slot cut in

the side of the screw. Teﬂon is then continuously wiped onto

the screw threads as the screw turns.

For very precise location of rotating parts and for high

rotational speeds, ball bearings are required. Precision,

bakeable ball bearings can be fabricated using sapphire

balls running in a stainless-steel race. Inexpensive preci-

sion sapphire balls are available from Industrial Tectonics.

A ball retainer is required to prevent the balls from rubbing

against one another (see Section 1.7.3). Without grease or

oil lubrication, it is helpful to burnish the race with MoS

For high-speed applications a ﬂuid lubricant is necessary.

The following process has been developed at NASA-

Goddard Space Flight Center:

purchase high-quality stain-

less-steel ball bearings with side shields and phenolic ball

retainers, such as the New Hampshire PPT series or Barden

SST3 series. Remove the shields and leach clean the phe-

nolic by boiling the bearings in chloroform – acetone, and

then vacuum-dry at 100 ºC. The bearings are then lubricated

by impregnating the phenolic with DuPont Krytox 143AZ, a

ﬂuorinated hydrocarbon. Impregnation is accomplished by

immersing the bearing in the lubricant and heating to 100 ºC

at a pressure of 1 torr or less until air stops bubbling out of

the phenolic. After this process the bearing must be wiped

almost dry of lubricant. The Texwipe Company makes

ultraclean foam cubes for this process. The amount of lubri-

cant in the bearing is determined by weighing before and

after impregnation. About 25 mg of Krytox is required for

an R4 (1/4in.) bearing, and about 50 mg is needed for an R8

(1/2 in.) bearing. This lubrication process should be carried

out in a very clean environment, and the bearing should be

inspected under a microscope for cleanliness before the side

shields are replaced. Bearings treated in this manner have

been run at speeds up to 60 000 rpm in vacuo.

3.5.5 Traps and Bafﬂes

Traps are used in vacuum systems to intercept condensable

vapors by means of chemisorption or physical condensa-

tion. When an oil-sealed mechanical pump is used as the

backing pump for a diffusion pump or a turbomolecular

pump, a trap is placed in the foreline between the backing

pump and the high vacuum pump to prevent backstreaming

124 VACUUM TECHNOLOGY

of mechanical pump oil vapor. This is absolutely essential

for the creation of a hydrocarbon-free vacuum. In some

applications, such as vacuum processes employed in the

semiconductor industry, the foreline trap is intended to

condense corrosive gases from the process chamber in

order to prevent harm to the forepump. In addition, a trap

is placed between a diffusion pump and a vacuum chamber

to pump water vapor and to remove diffusion-pump ﬂuid

vapors that migrate backwards from the pump toward the

chamber.

In many foreline traps, an ultraporous artiﬁcial zeolite

known as molecular sieve is employed to adsorb oil vapor.

These traps are similar in design to the molecular-sieve

sorption pumps previously described, except, of course,

that a trap must have both an inlet and an outlet. A typical

foreline trap ﬁlled with zeolite 13X molecular sieve is

shown in Figure 3.22 . The molecular sieve is initially acti-

ated by baking to 300 ºC for several hours. In use the

sieve material is regenerated at intervals of about two

weeks by baking under vacuum to drive out adsorbed oil

and water. Care must be taken to prevent the oil driven out

of the trap from condensing upstream of the trap, thus

doing more harm than good. A valve on the upstream side

of the trap can be closed to prevent oil vapor from back-

streaming, provided that the valve and the connection to

the trap are themselves heated to prevent condensation

while the trap is being baked. It is also possible that vapor

driven from the trap will contaminate the forepump. Some

trap designs provide a third connection for a separate

pump to be used during the bakeout. Another trap design

provides a removable basket for the sieve charge that can

be baked in a separate oven. For a system that must be kept

in continuous operation, two traps in parallel are used.

Valves on each side of both traps allow one trap to be

isolated for regeneration. An auxiliary pump (with suitable

valving) is used to evacuate the trap being regenerated.

The lowest pressure attai nable with a two-stage oi l-

sealed mechanical pump is initially determined by the

vapor pressure of the o il in the pump. By using a molec-

ular-si eve tr ap in series with a mechanical pump to

remove oil vapor, it is possible to achieve p ressures as

low as 10

4

torr in a small system with no gas load. This

is an e ffective scheme for maintaining a vacuum for ther-

mal insulation.

Molecular sieve may also be used in a high-vacuum

trap over the inlet of an oil diffusion pump. As shown in

Figure 3.23, these traps are designed to be optically

opaque,

so that a molecule cannot pass through the trap

in a straight line. This precaution is necessary because this

type of trap is intended for use at pressures where the

mean free path of a molecule is very long. To ensure high

conductance, the inlet and outlet ports should have the

same cross-sectional area as the inlet of the attached pump.

Also, the cross-section perpendicular to the ﬂow path

Figure 3.22 A foreline trap ﬁlled with

molecular sieve.

Figure 3.23 High-vacuum molecular-sieve trap for use over

the inlet of a diffusion pump.

VACUUM HARDWARE 125

through the trap (indicated by an arrow in Figure 3.23)

should be at least as large as that of the inlet and outlet

ports. The molecular sieve is activated by baking under

vacuum to 300 ºC for at least six hours. The trap may be

heated with heavily insulated heating tape or a custom-

made heating mantle such as those obtained from the

Glas-Col Apparatus Company. The ﬂanges of the trap

are water-cooled to prevent overheating the seals.

The maintenance of a high-vacuum trap is different

from that of a foreline trap. A high-vacuum molecular-

sieve trap is placed above an oil diffusion pump, and a gate

valve is located above the trap to permit isolation of

the trap and pump stack from the vacuum chamber.

After the initial bakeout the pump is run continuously, so

that the trap is always under vacuum. The isolation valve is

closed whenever it is necessary to open the chamber to the

atmosphere, and the chamber is rough-pumped before

reopening the isolation valve. The molecular sieve cannot

be regenerated after the ﬁrst bakeout. The initial bake of

the sieve results in the evolution of water vapor, but sub-

sequent baking would drive out absorbed pump-ﬂuid

vapor. This oil vapor would condense on the bottom of

the isolation-valve gate and be exposed to the vacuum

when the valve is open. After the initial bakeout, the

molecular sieve will trap oil vapor effectively for a period

of several months if it is not exposed to moist air during

that period. When the sieve becomes clogged with

absorbed vapor, the base pressure of the pump-and-trap

combination will begin to rise. At this time the molecu-

lar-sieve charge should be replaced. If it is absolutely nec-

essary to stop the diffusion pump, the pump and trap

should be ﬁlled with argon or dry nitrogen and isolated

from the atmosphere in order to preserve the molecular

sieve.

Condensation traps employing cold surfaces – cold

traps – are used as foreline traps as well as inlet traps over

diffusion pumps. The coolant may be simply a ﬂow of cold

water, an actively cooled refrigerant (Freon), or liquid

nitrogen. In principal, a trap cooled to liquid nitrogen

temperature would seem most effective, however, the

vapor pressure of most pump ﬂuids is below 10

12

torr

at 40 ºC, a temperature easily achieved with a Freon

refrigerator.

A simple ‘‘thimble’’ trap is shown in Figure 3.24. These

trap

s are used as foreline traps or over a small diffusion

pump. For periodic operation, the thimble can be ﬁlled with

liquid nitrogen. The coolant must be replenished every few

hours. For continuous, long-term operation, an alternative,

shown in the ﬁgure, is to ﬁll the trap with a low-melting

liquid, such as isopropyl alcohol, and refrigerate the liquid

with an immersion cooler (Neslab Instruments; FTS

Systems). These coolers consist of a refrigerator housed in

a small console, with a hose to carry refrigerant to a ﬂexible

probe that is inserted in the bath in the trap. A temperature

of 40 ºC is easily attained with the smallest unit since the

only heat load is thermal leakage from the surroundings into

the trap. A liquid-nitrogen-cooled cryotrap for use over a

large diffusion pump is illustrated in Figure 3.25. These

aps are connected to a large liquid-nitrogen Dewar with

a valve operated by a sensor that detects the coolant level in

the trap. When a cold trap is permitted to warm up, it must

be isolated from the vacuum chamber so that condensed

material does not migrate into the chamber. Also the trap

should be vented so that the evaporating condensate does

not build up a dangerously high pressure.

Figure 3.24 A thimble trap cooled by the ﬂexible, cooled

probe of an immersion cooler.

126 VACUUM TECHNOLOGY

An optically dense ‘‘chevron’’ bafﬂe of the type shown

in Figure 3.26 is usually placed over the inlet of a diffusion

pump.

These bafﬂes may be air-cooled, water-cooled, or

cooled by refrigerant from a small refrigerator. Recently,

bafﬂes with thermoelectric coolers operating at 35 ºC

have become available. In addition to reducing back-

streaming of pump-ﬂuid vapor, a bafﬂe serves as a radia-

tion barrier between the hot pump and the cold trap or

vacuum system above the bafﬂe.

3.5.6 Molecular Beams and Gas Jets

Often it is necessary to introduce a gaseous sample into a

vacuum system. The sample may be contained in a small

chamber with holes suitably located to admit probes such

as light beams or electron beams; however, the walls of

such a chamber may prove a hindrance to the proposed

experiment. Alternatively, a gas can be introduced as an

uncontained, but directed, beam of atoms or molecules.

The absence of walls is only one of the advantages to using

a gas beam. Because of the directed velocities of the par-

ticles in the beam, it is possible to maintain the sample in a

collisionless environment while still obtaining useful den-

sities. The beam can be crossed with another beam or

directed at a surface to obtain collisions of a speciﬁed

orientation. Under appropriate conditions, the expansion

of a jet of gas results in extreme cooling to give a very

narrow population distribution among quantum states of

molecules in the gas. Lucas succinctly stated the case for

atomic or molecular beams when he observed that ‘‘beams

are employed in experiments where collisions ...are

either to be studied, or to be avoided.’’

Permitting gas to ﬂow into a vacuum through a tube

creates a gas beam. The nature of the beam depends upon

whether the ﬂow exiting the tube is in the molecular- or the

viscous-ﬂow regime. Apertures placed downstream of the

channel through which the gas ﬂows into the vacuum can

establish the shape of the beam.

We begin with the molecular-ﬂow case, where the mean

free path, k, at the outlet of the gas channel is greater than

the diameter d of the channel. For the case of ﬂow from a

region of relatively high pressure into a vacuum through a

round aperture (that is, a tube of length l ¼ 0), the ﬂux

distribution in the direction speciﬁed by the angle h rela-

tive to the normal to the aperture surface is:

I hðÞ¼I h ¼ 0ðÞcos h ðatoms s

1

Þð3:27Þ

The beam width H speciﬁed as the full angular width meas-

ured at the angle where the ﬂux has fallen by half is 120º.

Increasing the length l of the tube or channel through which

the gas ﬂows into the vacuum can narrow the beam. Any

description of the gas beam issuing from such a channel must

consider the molecular diameter and the nature of the scatter-

ing of molecules from the walls of the tube. Both theoretical

and experimental inv estigations have been carried out in an

effort to describe a gas beam in terms of easily measured

parameters. In comparing experiment and theory it has turned

out that the observed ﬂux and the sharpness of the beam fall

short of theoretical expectations by a factor of two to ﬁv e.

In general, both experimental and theoretical results imply

that to obtain useful ﬂuxes and reasonable collimation, a

beam source consisting of a tube or channel must be at least

10 times greater in length than its diameter, and the gas

pressure behind this channel should be such that d < k < l.

Lucas has devised a succinct description of gas beams in

the molecular-ﬂow regime in terms of a set of reduced

parameters.

The gas pressure P behind the channel (in

Figure 3.25 Liquid-nitrogen-cooled cryotrap for a diffusion

pump.

Figure 3.26 Cooled bafﬂe.

VACUUM HARDWARE 127

torr), the beam width H (degrees), and the gas particle ﬂux

I [atoms s

1

(on axis)] and throughput q (atoms s

1

)

are related to the corresponding reduced parameters by:

P ¼

H ¼

I ¼

295M



1=2

q ¼

295M



1=2

ð3:28Þ

where T is the absolute temperature, M is the molecular

weight, d and l are in cm, and r is the molecular diameter

in A

(10

8

cm). For pressures roughly in the range where

d < k < l, the reduced half angle, ﬂux, and throughput

are related to the reduced pressure by:

¼ 2:48 3 10

ﬃﬃﬃﬃﬃﬃ

¼ 1:69 3 10

ﬃﬃﬃﬃﬃﬃ

¼ 2:16 3 10

ð3:29Þ

From model calculations, Lucas found that to obtain max-

imum intensity for a given angular width H, the reduced

pressure P

should not be less than unity.

For design work, a useful ‘‘optimum’’ equation can be

derived by combining the above and setting P

¼1 to give:

I ¼ 6:7 3 10

295M



1=2

ð3:30Þ

the optimum axial intensity for a given channel diameter and

desired angular width. The tube length is ﬁxed by the equa-

tions for H and H

¼ 1) above, and the input pressure

by the equation for P. Operating at somewhat higher pres-

sures gives some control over the ﬂux and throughput with-

out signiﬁcantly departing from the optimum condition.

The construction of low-pressure, single-channel gas-

beam sources is fairly straightforward. An excellent source

can be made of a hypodermic needle cut to the appropriate

length. These needles are made of stainless steel, they are

av ailable in a wide range of lengths and di ameters, and they

come with a mounting ﬁxture that is reasonably gas tight.

The goal of high intensity in a sharp beam is incompat-

ible with a single-channel source because, for a given

beam width, the gas load (throughput) increases more

rapidly than the ﬂux as the channel diameter is increased.

The solution to this problem is to use an array of many

tubes, each having a small aspect ratio (i.e., d/l << 1).

Tubes with diameters as small as 2 3 10

4

cm and lengths

of 1 3 10

1

cm arranged in an array a centimeter or more

across are commercially available in glass (Burle Electro-

Optics, Pegasus Glassworks, Hamamatsu).

When the gas pressure behind an aperture or nozzle

leading to a vacuum is increased to the extent that the mean

free path is much smaller than the dimensions of the aper-

ture, a whole new situation arises. Not only is the density

of the resultant gas jet much greater than in the molecular-

ﬂow case, but also the shape of the jet changes and the gas

becomes remarkably cold. This is a direct result of colli-

sions between molecules in the gas as it expands from

the oriﬁce into the vacuum. Because of collisions, the

velocities of individual molecules tend toward that

of the bulk gas ﬂow, just as an individual in a crowd

tends t o be dragged along with the crowd. The transla-

tional temperature of the gas, deﬁned by the width of its

velocity distribution, decreases, while the bulk-ﬂow

velocity increases. The c onversion of random molecular

motion into directed motion continues until the gas

becomes too greatly rareﬁed by expansion, at which point

the ﬁnal temperature is frozen in. Because the mass-ﬂow

velocity increases while the local speed of sound, propor-

tional to the sq uare root of the translational temperatur e,

decreases, the Mach number rise s and the ﬂow becomes

supersonic. Inelastic molecu lar collisions in the expand-

ing gas also cause internal molecular e nergy to ﬂow into

the kinetic energy of bulk ﬂow, with the result that there

may be substantial rotational and vibrational relaxation.

Rotational tempe ratures less than 1 K and vibrational

temperatures less than 50 K have been obtained. At these

low temperature s only a small number of qua nt um states

are occupied, an ideal c ondition for a variety of spectro-

scopic studies.

The low temperatures obtained in a supersonic jet can

present some problems. Chief among these is that of

condensation. Collisions in the high-density region of the

jet cause dimer or even polymer formation. With high-

boiling samples, bulk condensation may occur. Of course,

128 VACUUM TECHNOLOGY

if one wishes to study dimers or clusters, this condensation

is desirable. To avoid dimer formation, the sample gas is

mixed at low concentration with helium. This seeded gas

sample is then expanded in a jet. Adjusting its concentra-

tion in the helium carrier controls the degree of clustering

of the seed-gas molecules.

The cooling effect, as well as the directionality of the

jet, is lost if the expanding gas encounters a signiﬁcant

pressure of background gas in the vacuum chamber.

Unfortunately, optimum operating conditions require a

large throughput of gas into the chamber. The extent of

cooling depends upon the probability of binary collisions,

which is proportional to the product P

d of the pressure

behind the nozzle and the diameter of the nozzle. Further-

more, to minimize condensation, the ratio d/P

should be

as large as possible. The result, in practice, is that a large-

capacity vacuum pumping system is needed. In typical

continuously operating supersonic-jet apparatus, source

pressures of 10 to 100 atm have been used with nozzle

diameters of 0.01 cm down to 0.0025 cm. The conductance

of an aperture under these conditions is roughly:

C ¼ 15 d

1

ð3:31Þ

when the diameter is in centimeters. This implies a

throughput on the order of 10 torr L s

1

. To obtain a mean

free path of several tens of centimeters, a base pressure of

about 10

4

torr is required. A pump speed approaching

10 000 L s

1

may be necessary. Typically, several large

diffusion pumps are used. When possible the jet is aimed

straight down the throat of a pump.

In many experiments the cold molecules in a supersonic

jet are only probed periodically – as, for example, when

doing laser spectroscopy with a pulsed laser. Operation of

the jet in a synchronously pulsed mode can reduce the gas

load on the pump by several orders of magnitude compared

to that in the continuous mode. A number of fast valves for

this purpose have been devised.

The simplest are based

upon inexpensive automobile fuel injector valves.

Gen-

eral Valve produces a system consisting of a pulsed valve

and driver that operates at pulse rates as high as 250 Hz

with a pulse width as small as 160 ls.

Another efﬁcient means of dealing with the background-

gas problem has been demonstrated.

This relies upon the

fact that interaction of the expanding gas with the back-

ground gas gives rise to a shock wave surrounding the gas

jet. If the pressure P

behind the nozzle is increased, it is

possible to achieve a mode of operation where a rareﬁed

region is created behind the shock wave. In the region

upstream of the shock front, the gas behaves like a free

jet expanding into a perfect vacuum. The distance from the

nozzle to the shock front is:

‘ ¼ 0:67d



1=2

ð3:32Þ

where P

is the pressure in the nozzle, P the background

pressure, and d the nozzle diameter. When the nozzle pres-

sure is sufﬁciently high to achieve a free jet length of

usable dimensions, the background pressure will increase

greatly. This state of affairs has a distinct advantage, since

at a high background pressure, a large throughput can be

achieved with a pump of moderate speed. For example, to

obtain a free length ‘ ¼ 1 cm with a 0.01 cm nozzle and a

source pressure of 10 atm, the background pressure should

be about 400 mtorr. The throughput in this case is about

10 torr L s

1

and the required pumping speed, 25 L s

1

could be achieved by a large rotary mechanical pump or a

Roots pump of modest capacity.

The fabrication of a nozzle is straightforward, although

some difﬁculty may be encountered in making the neces-

sary small hole. A skillful mechanical technician can drill

a hole as small as 0.01 cm diameter. Smaller holes can be

made by spark or electrolytic erosion, or by swaging a hole

closed on a piece of hard wire and then withdrawing the

wire. One of the ﬁrst small, high-pressure nozzles

was

made by drilling down the axis of a stainless-steel rod to

within 0.1 mm of the end with a drill bit having a sharp

conical point. A 0.0025 cm diameter hole was then made

through the remaining metal by spark erosion.

For many experiments, the gas ﬂowing into a vacuum

system through an aperture or a channel produces a beam

that is too broad or too divergent for the intended applica-

tion. In this case one or more apertures placed downstream

from the source can deﬁne the beam shape. Often it is

advantageous to build these apertures into partitions that

separate the vacuum housing into a succession of cham-

bers. Each chamber can be evacuated with a separate

pump. The pressure in the ﬁrst will be highest, so that

the large throughput obtained here will signiﬁcantly reduce

VACUUM HARDWARE 129

the gas load on the next pump. This scheme is called differ-

ential pumping (see Section 3.6.2).

aperture downstream of a supersonic jet, but close

enough to be in the viscous-ﬂow region, is called a skimmer.

The design of these skimmers is critical, since they tend to

produce turbulence that will destroy the directionality of

the ﬂowing gas. A skimmer is usually a cone with its tip cut

off and the truncated edge ground to knife sharpness. The

details of the design, location, and fabrication of a skimmer

are beyond the scope of this book, and the interested reader

should refer to a specialized text on this subject.

3.5.7 Electronics and Electricity in Vacuo

At low frequencies the vacuum between electrodes or wires

provides excellent insulation. At pressures below 10

4

torr,

the breakdown voltage between smooth, gently rounded

surfaces is in excess of 1000 V for each millimeter of

separation. Occasionally sparking will occur between

newly made parts because of high ﬁeld gradients around

whiskers of metal. These whiskers quickly evaporate and

sparks do not recur. The challenge in making electrical

devices function in vacuum is in the design of spacers

and other elements that locate electrodes and wires that

are at different electrical potentials. Insulating materials

must possess adequate mechanical strength and be compat-

ible with the vacuum environment and available fabrication

processes. In addition, insulators must be very clean. Elec-

trical breakdown in the vacuum is usually initiated by a

discharge traveling along the surface of an insulator.

Ceramic materials are the best insulators and, among

these, alumina (at least 96% Al

) is probably the best.

Simple shapes such as rods, tubes, and balls are readily

available to be incorporated in insulator asse mblies (see

Figures 5.40 and 5.41). More complex shapes require spe-

cia

lized grinding techniques. Alumina circuit board

substrate is available as plate .010 in. to .060 in. thick

and 6 in. square. Owing to the scale of the circuit-board

industry, the faci lities for custom fabrication by laser cut-

ting of alumina plate are widely available. The d esigner of

vacuum apparatus can n ow spe cify quite complex shapes

cut from al umina plate at a cost of just a few dollars a

piece. A simple scheme employing alumina washers to

locate and insulate electrically isolated parts is illustrated

in Figure 3.27(c).

Alumina

can be metalized and subsequently joined by

brazing to stainless steel or Kovar structures. It is imprac-

tical to attempt this process in the lab; however, this

technology is employed in many standard vacuum compo-

nents, such as electrical feedthroughs (Ceramseal, Insula-

tor Seal) to be inserted in the vacuum wall [Figure 3.27(d)]

and

ceramic ‘‘breaks’’ built into the middle of a length of

metal vacuum tubing [Figure 3.27(e)].

few precautions should be observed in designing and

mounting ceramic parts. Ceramic materials are strongest in

compression and cannot be plastically deformed. The best

design of an assembly with ceramic components captures

each ceramic part between smooth surfaces that are

aligned with the face of the part so that shear forces are

not applied to the ceramic material.

Ceramics are often used simultaneously for electrical

insulation and thermal isolation. In this case it is impor-

tant to be aware of the strong dependence of electrical

resistivity on temperature. The resistivity of a ceramic

material falls by roughly a factor of 10 for every 100 ºC

increase in temperature.

For example, the resistivity of

alumina is greater than 10

ohm cm at 100 ºC and falls

below 10

ohmcmat1000ºC.

The surface of a ceramic part is more or less porous

and susceptible to trapping contaminates. In handling

ceramic parts, inorganic salts from skin oils may be

transferred fr om the ﬁngers to the surface of the ceramic.

Salts absorb water a nd encourage electrica l conduction

across the surface. A part should be c leaned with organic

solvents to remove oils followed by a ﬁnal rinsing in hot

distilled water to remove these salts. Rinsing with pure

methanol and heating can dry the part. Surgical gloves

should be worn to handle a part after it has been cleaned.

If the spacing between wires in a vacuum system cannot

be reliably maintained, then insulation is required. Ordinary

Teﬂon-insulated, solid, hookup wire may be used down to

7

torr, although air bleeding out from under the insu-

lation will slow pumpdown. Stranded wire should never be

used, as gas is trapped between the strands. At very low

pressures and high temperatures, wires can be insulated by

stringing ceramic ‘‘ﬁsh spine’’ beads (from Coors) [Figure

3.27(a)] or pieces of Pyrex tubing over them. The spacing

between

wires can be maintained with ceramic wire looms

[Figure 3.27(b)] available from many suppliers of vacuum

apparatus.

Wire insulated with a Kapton (polyimide) ﬁlm

130 VACUUM TECHNOLOGY

or a ceramic coating is available from vacuum-equipment

suppliers for use in UHV. The latter is better for use at

elevated temperatures, but has the disadvantage of shed-

ding bits of ceramic material when ﬂexed. Electrical solder

should not be used for electrical connections in a vacuum

system because the lead in solder and soldering ﬂux con-

taminate the vacuum. Mechanical connections are prefera-

ble. Wrapping a wire under the head of a screw and

tightening the screw can make connections to electrodes.

Wires may be jointed by slipping the ends into a close-

ﬁtting piece of tubing and crimping the tubing onto the wire.

A variety of wire connectors are available from vacuum-

equipment suppliers. Tungsten, molybdenum, nichrome, or

stainless-steel wires may be spot-welded together. In weld-

ing refractory metals, a more secure weld is obtained if a

piece of nickel foil is interposed between the wires.

Electronic devices tend to overheat in a vacuum since

the only cooling is by radiation. Electronic components

such as power transistors and integrated circuits that must

dissipate more than about 2 watt are particularly unreliable.

Such devices can be placed in vacuum-tight, gas-ﬁlled

boxes that are thermally connected to the vacuum wall.

Electrical feedthroughs for wires passing through the wall

of a glass vacuum system are illustrated in Figure 3.28.As

scribed in Section 2.3.10, an electrical feedthrough can be

de by sealing a tungsten rod directly into a hard glass

wall. An easier solution is to braze an electrode into the

metallic end of a standard Kovar-to-glass graded seal and

join the glass end of the seal to the glass vacuum wall.

3.6 VACUUM-SYSTEM DESIGN

AND CONSTRUCTION

Before beginning the design of a vacuum system, a number

of parameters must be speciﬁed in at least a semiquantitati v e

Figure 3.27 Applications of ceramics for electrical insulation in vacuum systems: (a) ceramic

‘‘ﬁsh spine’’ beads threaded on a wir e as insulation; (b) ceramic disk with holes used as a

wire-loom to keep wires in a bundle from touching one another; (c) design for electrodes

located and electrically isolated with spacers laser-cut from alumina circuit-board substrate;

(d) a ceramic-insulated electrical feedthrough; (e) a ceramic break in a vacuum line

mounted between two standard vacuum ﬂanges.

VACUUM-SYSTEM DESIGN 131

manner. The size and shape of the vacuum chamber must

be determined. The desired ultimate pressure and the com-

position of the residual gas in the chamber must be speci-

ﬁed. One must estimate the gas load on the pumps. The

amount of money and time available are also important

considerations. It is instructive to spend a few evenings

leaﬁng through vacuum-equipment manufacturers’ cata-

logs to become familiar with the speciﬁcations and cost

of commercial vacuum components. The author has found

the Kurt J. Lesker, Co., Leybold AG, and Varian Vacuum

catalogs to be especially informative.

The ultimate pressure requirement dictates the choice of

the primary pump. Cost and limitations on hydrocarbon

contamination will determine the choice of roughing and

backing pumps. An ultimate pressure down to about 1 mtorr

can be achiev ed with a mechanical pump with an appropriate

trap. Sorption pumps can be used on a system requiring an

ultimate pressure of 1 mtorr if there is not a large continuous

gas load. Ultimate pressures in the high-vacuum range do wn

to about 10

9

torr can be achieved with a diffusion pump, a

turbomolecular pump, or a cryopump. True ultrahigh-

va cuum systems ordinarily use ion pumps and titanium sub-

limation pumps. Ultrahigh vacuum can also be achiev ed with

turbomolecular pumps. To reach UHV starting from a back-

ing pressure near 1 torr requires a compression ratio

approaching 10

. This can be accomplished with two turbo-

molecular pumps operating in series, a turbo backed with a

drag pump, or with a compound turbomolecular/drag pump.

The cost of a vacuum system is about equally divided

between the cost of the pumps and the cost of the v acuum

vessel and ancillary hardware, such as gauges and valves. In

terms of cost per unit pumping speed, mechanical pumps are

most expensive – on the order of $100 per L/s. Most systems

require a mechanical pump as either the primary pump or a

backing pump; howe ver, since they operate at relativ ely high

pressures and correspondingly high throughputs, one ordina-

rily ﬁnds that for laboratory apparatus only modest pumping

speed is required of a mechanical pump – a few L/s to a fe w

tens of L/s. For high-vacuum systems, diffusion pumps are

most cost effecti ve although sorption or cold traps needed to

prev ent hydrocarbon contamination will add to the total cost.

The cost of a diffusion pump amounts to $2 to $5 per L/s of

pumping speed. A turbomolecular pump with its controller, a

cryopump with a refrigerator, or an ion pump and controller

will cost ﬁve to ten times as much as a diffusion pump of

comparable pumping speed.

There are three sources of gas that must be pumped out

of a vacuum vessel: molecules adsorbed on the walls of the

container, as well as the components therein, gas intention-

ally admitted as part of the process under study, and leaks.

The rate of outgassing of adsorbed water, carbon dioxide,

and hydrocarbons, and, ultimately, hydrogen, from the

surface of materials is difﬁcult to measure. A summary

of published data is given in O’Hanlon’s book.

With care

in the choice and processing of the materials of construc-

tion of vacuum apparatus, it is generally possible to reduce

outgassing rates below 10

9

torr L s

1

2

; lower yet

with baking. Similarly, actual leaks can be eliminated by

careful design and construction; so-called virtual leaks are,

however, more or less of a problem in all systems. Virtual

leaks are the result of gas being tapped in small occlusions

within the vacuum vessel. These typically occur where

parts are ﬁtted together. Gas will be trapped between mated

surfaces and the conductance through the space between

such surfaces will be very small. The trapped gas may take

weeks to be pumped away and thus acts as a continual gas

load on the pump. Every effort should be made to vent

these spaces with pumpout holes (Figure 3.40).

3.6.1 Some Typical Vacuum Systems

Diffusion-Pumped System. A diffusion-pumped

vacuum system is shown schematically in Figure 3.29.

Figure 3.28 Electrical feedthroughs in a glass vacuum wall

employing (a) a tungsten-to-metal seal; (b) a standard

Kovar-to-glass seal.

132 VACUUM TECHNOLOGY

For illustration, suppose the vacuum chamber is constructed

of stainless steel and is 30 cm in diameter and 30 cm high

with a surface area of 5000 cm

. If the pump stack consists

of a 2 in. oil diffusion pump with a speed of 150 L s

1

, and

a trap and bafﬂe with a conductance of 200 L s

1

, the net

speed of the pump stack will be:

S ¼



1

150 L s

1

200 L s

1



1

¼ 85 L s

1

ð3:33Þ

Assuming an initial outgassing rate of 10

9

torr L s

1

2

the vacuum vessel will pump down to:

P ¼

5000 cm



3 10

8

torr L s

1

2



85 L s

1

¼ 6310

7

torr ð3:34Þ

within a few hours. After a day of pumping and perhaps a

light bake to 100 ºC, the outgassing rate should fall below

9

torr L s

1

2

and an ultimate pressure in the 10

8

torr range should be achievable.

The size of the backing pump is determined from

the maximum throughput of the diffusion pump. This

occurs after the vacuum vessel is rough pumped and the

gate valve over the diffusion pump is ﬁrst opened. The

pressure in the vessel at this time should not be greater than

about 50 mtorr. The maximum throughput will then be:

max

¼ P

max

S ¼ 5 3 10

2

torr



3 85 L s

1



¼ 4 torr L s

1

ð3:35Þ

The foreline pressure must always remain below about 200

mtorr so the speed of the backing pump should be:

p,backing

max

backing

4 torr L s

1

2310

1

torr

¼ 20 L s

1

: ð3:36Þ

A small two-stage mechanical pump can meet this

requirement.

The conductance of the foreline should be at least twice

the speed of the forepump so that the forepump is not

strangled by the foreline. To achieve a conductance of

Figure 3.29 Schematic diagram of diffusion-pumped high-vacuum system.

VACUUM-SYSTEM DESIGN 133

40 L s

1

at a pressure of 200 mtorr in a foreline a half

meter long, the diameter (from Section 3.2.4) must be:

D ¼

180P



1=4

cm ðL in cmÞ

40 3 50

180 3 2 3 10

1



1=4

¼ 2:7cm ð3:37Þ

In this case l in. copper water pipe would make an excel-

lent foreline.

To activate a system of the type shown in Figure 3.29,

starting

with all valves closed and the pumps off, proceed

as follows:

(1) Turn on the mechanical pump.

(2) When the pressure indicated by thermocouple gauge

1 (TC1) is below 200 mtorr, open the foreline valve.

(3) When TC1 again indicates a pressure below 200 mtorr,

turn on the cooling water and activate the diffusion

pump. The pump will require about 20 minutes to

reach operating temperature. When operating it makes

a crackling sound.

(4) Before pumping on the chamber with the diffusion

pump, the pressure in the chamber must be reduced to

a rough vacuum. Close the foreline valve and op en

the roughing valve. When the pressure indicated by

TC2 is below 50 mtorr, close the roughing valve and

open the foreline valve. The diffusion pump should

not be operated for more than two minutes with the

foreline valve closed. If necessary, interrupt the

roughing procedure, c lose the roughing valve, wait

for TC1 to indicate less than 200 mtorr, and reopen

the foreline valve for a moment to ensure that the

diffusion-pump outlet pressure does not rise above

about 200 mtorr.

(5) Slowly open the gate valve that isolates the diffusion

pump from the chamber. In less than 10 s the pressure

indicated by TC2 should fall below 1 millitorr and the

ionization gauge can be turned on.

A diffusion-pumped system of the type shown in Figure

3.29 is one of the most convenient and least expensive

systems

for obtaining high or even ultrahigh vacuum.

The system can be fabricated of metal or glass. A bafﬂed,

but untrapped, oil diffusion pump on this system should

result in an ultimate pressure slightly below 10

6

torr.

With a cold trap an ultimate pressure of 10

9

torr is pos-

sible if the vacuum chamber is baked and only low-vapor-

pressure materials are exposed to the vacuum.

A number of inexpensive safeguards are incorporated

in the design in Figure 3.29 to avoid contamination or

damage

in the event of a loss of electrical power. A nor-

mally open (N.O.) sole noid-operated water valve in par-

allel with the pump heater admits water to the diffusion

pump, quick-cooling coils if the power fails. The diffu-

sion pump is isolated from the mechanical pump by a

nor mally closed (N.C. ) s olenoid valve to prevent air or

oil from being sucked through the mechanical pump into

the foreline. Special mechanical pump inlet valves are

available for this purpose (HPS Vacuum SentryÒ and

Leybold SECUVACÒ). These valves close automatically

when power is lost and vent the pump to atmosphere;

when power is reg ained, the valve does not reopen until

the pressure o n th e pu mp side falls to a few hundred

millitorr. The SECUVAC valve is also designed to c lose

in the even t of a sudden rise in inlet pressure. It is helpful

to place a ballast volume in the foreline to m aintain a

low foreline pressure while the diffusion pump cools

after a power outage. A relatively large foreline trap will

also serve as a ballast. A ballast tank of 5 to 10 L in the

foreline will permit the continued operation of the dif-

fusion pump for a period of perhaps 10 to 20 minutes

if the backing pump is turned off and the valve at the

inlet to the backing pump is closed. This intermittent

mode of operation can be useful in the event that vibra-

tion of the mechanical pump ha s an adverse effect on an

instrument housed in the h igh-vacuum chamber. For

example, this mode of opera tion is used on some electron

microscopes.

A useful fail-safe mechanism, not shown in Figure

29, would be a water-pressure sensor in the water line

interrupt the electrical power if the water fails. Alter-

natively, a heavy-duty, normally closed (N.C.), bimetal-

lic temperature switch wired in series with the diffusion

pump heater may be mounted to the bottom turn of the

water-cooling coil. Then if the cooling-water ﬂow is

inadequate, the rising temperature of the pump barrel

will interrupt the electricity to the pump heater. Many

diffusion pumps are equipped with a mounting plate for a

temperature switch that can be obtained from the pump

manufacturer.

134 VACUUM TECHNOLOGY

A power interruption in the operator’s absence threatens

serious contamination of the vacuum vessel, both at the

time the power goes off and when it comes back on again.

When the power goes off it is essential that the diffusion

pump stops operating before the foreline pressure rises

above the critical backing pressure. This is the purpose

of the quick-cool water valve described above. When

power is restored in the operator’s absence there is no

provision to rough out the vacuum vessel or otherwise

follow the orderly initiation of pumping described above.

As a minimum safeguard against a power failure, the

power to the system’s components should be supplied

through power relays that are wired to latch ‘‘off’’ until

reactivated by the operator. A latching relay circuit is

shown in Figure 3.30.

or a vacuum system that operates for long periods of

time without close supervision, it is worthwhile incorpo-

rating a control system that monitors the pressure in the

chamber and the foreline. Many high-quality commercial

thermocouple-gauge and ionization-gauge controllers

include relays that can be set to trip at a predetermined

pressure. The relay controlled by the foreline thermo-

couplegauge(TC1)canbesettotripat200–300mtorr.

This relay can be wired to operate a second, heavy-duty

relay that removes power from the diffusion pump and

simultaneously opens the quick-cool water valve and

closes the foreline sole noid valve at the mechanical

pump. The overpressure relay controlled by the ion

gauge can be employ ed to isolate the high-vacuum c ham-

ber by means of an electrically controlled, pneumatically

activated gate valve when the pressure in the chamber

rises above a few millitorr. In lieu of a gauge controller

with control relays, there are now available inexpensive,

modular, Pirani vacuum sensors with built-in pressure

switches (for example, the HPS Moducell). These can be

set to trip in the range 5 3 10

3

to 30 torr, making them

suitable for monitoring either the high-vacuum chamber or

the foreline. The design of a logical interlock system

employing temperature and pressure sensors to protect a

vacuum system is discussed in Sections 6.6.9 and 6.6.10.

A Small, Inexpensive Ultrahigh-Vacuum

System.

A small, inexpensive system, capable of

producing a vacuum of about 10

10

torr in a 1 L volume,

is illustrated in Figure 3.31. The entire system can be made

Pyrex. Constrictions in the glass tubing joining

Figure. 3.30 Relay circuit to latch ‘‘off’’ a diffusion-pumped vacuum system in the event of

a power failure.

VACUUM-SYSTEM DESIGN 135

components of the system are fused closed with a

glassblower’s torch to seal off each part of the system as

evacuation proceeds. Rough pumping is initiated with a

water aspirator or alternatively a compressed-air Venturi

pump. High vacuum is achiev ed with sorption pumps

operated in sequence and ultrahigh vacuum is reached with

a titanium sublimation pump, possibly with the aid of a

small ion pump.

To achieve UHV, special precautions

are taken to displace rare gases from the system and to

remove water and carbon dioxide adsorbed on the walls of

the system. Neither sorption pumping nor gettering

efﬁ ciently pumps rare gases, helium in particular. The rare

gases are swept from the system by a ﬂow of dry nitrogen

before ev acuation is begun. The entire system is maintained

at a moderately high temperature throughout the entire

pumpdown procedure in order to driv e adsorbed gases off

the walls and into the pumps.

The pumpdown procedure for this vacuum system is as

follows:

(1) Flow pure dry nitrogen through the system from S

the aspirator. Do not activate the aspirator. Pure dry

nitrogen gas can be obtained from the headspace over

liquid nitrogen in a Dewar.

(2) As nitrogen ﬂows through the system, the molecular-

sieve sorption pumps are heated to 300 ºC and the trap

is cooled with liquid nitrogen. The remainder of the

system should be heated to about 100 ºC with heating

tape or by brushing the glass with a cold ﬂame or with

hot air from a heat gun.

(3) After about an hour, close pinchoff S

by heating the

glass with a torch and turn on the aspirator. The pres-

sure will quickly fall to about 20 torr.

(4) Seal off constriction S

and refrigerate the ﬁrst molec-

ular-sieve pump. The pressure will fall to about 10

4

torr. Continue to heat the system.

(5) Seal off S

and cool the second sorption pump. The

pressure will fall to about 10

7

torr. Continue heating

the system for a short time to drive off the remaining

adsorbed gases.

(6) Pass a current through the ﬁlament of the titanium

pump to evaporate a layer of titanium onto the glass

envelope, and activate the ion pump.

(7) Seal off S

and deposit a fresh layer of titanium. The

pressure should fall well below 10

9

torr.

When sealing off a constriction, it is wise to proceed

slowly so that the pumps have time to take up any gas that

is liberated.

A similar system can be made with the pinchoffs

replaced by all-metal high-vacuum valves. In this case it

would also be possible to construct the entire system of

stainless steel.

An Oil-Free Ultrahigh-Vacuum System. A large,

oil-free ultrahigh-vacuum system is illustrated in Figure

3.32. The system is roughed down with sorption pumps,

and

the ion pump is depended upon for the removal of rare

gases. The system must be baked. A number of variations

on this system are possible. The rough-pumping operation

can be accelerated and the gas load on the sorption pumps

reduced if the system is ﬁrst roughed down with one of

the compressed-air aspirators (Venturi pumps) sold for this

purpose. Alternatively, one can employ one of the oil-free

mechanical pumps that have recently appeared on the

market. Varian, for example, manufactures a reciprocating

piston pump with Teﬂon seals that would be suitable as

a roughing pump. The pumping at high vacuum can be

carried out with a cryopump rather than a getter pump.

The choice of the high-vacuum pump or combination

of pumps depends upon the composition of the residual

Figure 3.31 A small inexpensive ultrahigh-vacuum system

made of Pyrex glass. Constrictions (labeled ‘‘S’’) between

components are heated with a glassblowers torch until they

collapse and fuse under the external atmospheric pressure

to seal off and isolate components as evacuation proceeds.

136 VACUUM TECHNOLOGY

gas, as well as the composition of gases that may be

admitted to the system at high vacuum.

Small, Oil-Free, Turbomolecular Pumped UHV

System.

W ith appropriate precautions, hydrocarbon-free

vacuum belo w 10

11

torr can be attained with a turbo-

molecular pump. The compression ratio of a turbo-

molecular pump for air is typically 10

to 10

,soaforeline

pressure well below 10

2

torr is required to achiev e UHV.

This is accomplished with a small high-vacuum pump

between the turbomolecular pump and the mechanical

foreline pump. One possibility is to back the turbo with a

diffusion pump backed by a mechanical pump. The

intermediate pump might just as well be another turbo or a

molecular-drag pump. These intermediate pumps can be

very small: in principle, the speed of these pumps need

only be that of the primary turbopump di vided by its

compression ratio in order to deal with the throughput of

the primary turbo!

The compression ratio of a turbomolecular pump

exceeds 10

for gases with molecular weights greater than

100, so when the pump is running there is essentially no

backstreaming of hydrocarbons from oil-lubricated bear-

ings or from an oil-sealed mechanical forepump; however,

hydrocarbon contamination of the UHV chamber is possi-

ble when the turbo is not operating. There are two essential

precautions. When the turbo is turned off it should be

vented to atmospheric pressure. Dense gas in the pump

will prevent backstreaming from bearings at the bottom

of the pump into the upper stages. There is usually no need

for a valve between a turbo pump and the vacuum chamber

so the chamber is also vented to atmospheric pressure

when the pump is vented. On the other hand, there must

be a valve at the turbopump exhaust. This valve must be

kept closed except when the pump is activated. In a turbo-

molecular-pumped system, the chamber is rough-pumped

directly through the turbopump. To initiate pumping, the

mechanical backing pump is turned on, the valve at the

turbo exhaust is opened, and the turbo is then immediately

activated so that roughing and turbo spin-up occur simul-

taneously. The intermediate pump can also be activated

at this time. By following this procedure, the initial ﬂow

of dense gas from the chamber will prevent backstreaming

while the turbo is coming up to speed. Of course, the best,

albeit most expensive, means for eliminating hydrocarbons

is to employ pumps that contain no hydrocarbons: turbo-

molecular pumps and molecular drag pumps with magneti-

cally suspended rotors and a diaphragm pump as a

forepump (see Section 3.4.1).

The

ultimate pressure in a UHV chamber with a turbo-

molecular pump is determined by the compression ratio for

and the partial pressure of H

in the foreline. The com-

pression ratio for H

in modern pumps is in the range from

to 10

. The exclusion of hydrocarbon oils and elasto-

mer seals in the foreline helps reduce the hydrogen partial

pressure in the foreline. In any event it has been found that

hydrogen represents 80 to 90% of the residual gas in a

turbopumped chamber at pressures below about 10

10

torr.

When this is a problem for a particular experiment, a tita-

nium sublimation pump can be installed above the turbo. It

would not be necessary for titanium to be continuously

evaporated once UHV conditions are achieved.

Custom-made UHV chambers can be quite expensive

especially when many access ports are required for com-

ponents, such as mechanical and electrical feedthroughs,

and windows. When a relatively small volume is required

(a few hundred cubic inches or a few thousand cubic cen-

timeters), it is often possible to make up the chamber of

standard UHV components, such as tees and crosses. In

the author’s laboratory a 6 in. cube cross (Kurt J. Lesker

Figure 3.32 An oil-free ultrahigh-vacuum system.

VACUUM-SYSTEM DESIGN 137

Company) is used as a small UHV chamber. The pump is

mounted on one face and the remaining ﬁve faces provide

ports for mounting components. The cube was ordered 0.5

in oversize (i.e., 6.5 in. 3 6.5 in. 3 6.5 in.). With the addi-

tional size it is possible to bore .375 in diameter holes

through the cube close to each vertical edge. Cartridge

heaters inserted in the holes are used for bakeout.

3.6.2 Differential Pumping

One is occasionally required to design a system wherein gas

is maintained at two very different pressures. Often two or

more pumps with interconnecting tubing must be balanced

against one another to obtain the desired pressure differential.

As an example we will consider the problem of making

a mass-spectrometric analysis o f trace constituents in

argon ﬂowing through a t ube at a pressure P

of 1.0 tor r.

As illustrated schematically in Figu re 3.33(a),thesample

to be withdrawn through a hole in the ﬂow tube. The

mass s pectrometer must be operated at a pressure P

5 3 10

7

torr. To begin, let us suppose that a 6 in. diffusion

pump is to be used to maintain the pressure P

. A properly

trapped 6 in. diffusion pump has a speed of about 900 L s

1

over the range 10

3

–10

9

torr (see Figure 3.12). The

throughput is then:

Q ¼ P

S ¼ð5 3 10

7

torrÞð900 L s

1

¼ 4:5 3 10

4

torr L s

1

ð3:38Þ

The conductance of the sampling aperture that provides

this throughput is:

C ¼

 P

4:5 3 10

4

torr L s

1

1:0 torr

¼ 4:5 3 10

4

1

ð3:39Þ

The ﬂow through this aperture is in the viscous-ﬂow

regime. The area of the aperture that provides this conduc-

tance (from Section 3.2.4) is approximately:

A ¼

C Ls

1

ðÞ

4:5 3 10

4

¼ 2:3310

5

ð3:40Þ

corresponding to a diameter of 0.05 mm for a circular

aperture. There ar e two problems associated with this

small aperture. Firstly, there is the mechanical difﬁculty

of creating suc h a small hole . Secondly, this tiny hole

may impose a severe limitation upon the sensitivity of

the measurement, particularly if the analyzer samples

only atoms moving along the line of sight from aperture

to analyzer. A solution to these problems is to incorpo-

rate several stages of pumping – a scheme known as

differential pumping.

A two-stage differentially pumped system is illustrated

in Figure 3.33(b). An intermediate-pressure chamber with

its

own pump is interposed between the sample and ana-

lyzer volumes. There are two apertures now and the pres-

sure drop occurs in two steps. For comparability with the

previous example, suppose the intermediate chamber

and the analyzer chamber are each evacuated with 4 in.

Figure 3.33 (a) Schematic representation of

an analyzer in high vacuum (5 x 10

7

torr) used

to sample a gas at high pressure (1 torr).

(b) Differential pumping arrangement that

permits a much larger sampling aperture with

the same total pumping speed for the analyzer.

138 VACUUM TECHNOLOGY

diffusion pumps, each with a speed of 400 L s

1

. Take the

ratio of pressures across each aperture to be the same, so

that P

¼ P

and the pressure P

in the intermediate

chamber is then 7 3 10

4

torr. The throughput of the pump

on the lowest pressure chamber is:

¼ P

¼ð5 3 10

7

torrÞð400 L s

1

¼ 2 3 10

4

torr L s

1

ð3:41Þ

The conductance C

of the aperture separating the region

of pressure P

from the region of pressure P

must main-

tain this throughput:

 P

2 3 10

4

torr L s

1

7 3 10

4

torr

¼ 0:3Ls

1

ð3:42Þ

The ﬂow through this aperture is in the molecular-ﬂow

regime. The area of the aperture that provides this conduc-

tance (from Section 3.2.4) for argon at 300 K is:

¼ C 3:7



1=2

1

¼ 0:03 cm

ð3:43Þ

corresponding to a diameter of about 2 mm for a circular

aperture. Similarly, the conductance of the aperture sepa-

rating the high- and intermediate-pressure regions must

match the throughput of the intermediate pump:

¼ P

¼ð7 3 10

4

torrÞð400 L s

1

¼ 0:3 torr L s

1

ð3:44Þ

so that:

 P

0:3 torr L s

1

1 torr

¼ 0:3Ls

1

ð3:45Þ

The ﬂow through this aperture is in the viscous-ﬂow

regime. The area of the aperture that provides this conduc-

tance (from Section 3.2.4) is approximately:

C Ls

1

ðÞ

0:3

¼ 0:015 cm

ð3:46Þ

corresponding to a diameter of about 1 mm for a circular

aperture. In this example, we ﬁnd that, by pumping in

stages, and without an increase in total pumping speed,

the required pressure differential can be maintained across

apertures that are hundreds of times larger than if all the

available pumping speed had been applied in a single

stage. Furthermore, assuming that the gas ﬂow through

ﬁrst aperture is directional, the sensitivity of the measure-

ment is greatly increased by aligning the second aperture

and analyzer with the ﬂow through the ﬁrst aperture, as

suggested in the ﬁgure.

3.6.3 The Construction of

Metal Vacuum Apparatus

Metal vacuum chambers are often built up of one or more

cylindrical sections. Tube stock is readily available and a

cylindrical shape is second only to a spherical shape in

strength to withstand external pressure. Even when tube

stock is unavailable, a cylindrical section is easily fabri-

cated by rolling up sheet stock. The ends of a cylindrical

chamber are most conveniently closed with ﬂat plates, as

shown in Figure 3.34. A ﬂat end plate must be quite thick

withstand atmospheric pressure, as discussed below.

Domed or spherical end caps are much stronger, but more

expensive to fabricate.

The ability of a cylinder to resist collapsing under external

pressure depends upon the length of the cylinder between

supporting ﬂanges, the diameter, the wall thickness, and the

strength of the material. The ASME has published standards

for the wall thickness of cylindrical vessels under external

pressure.

The data in Figure 3.35 have been abstracted

from the ASME speciﬁcations for type 3003-T0 aluminum

alloy and type 304 stainless steel respectively. These recom-

mendations should be more than adequate for any of the

4000, 6000, or 7000 series tempered aluminum alloys (such

as 2024-T4, 6061-T6, or 7075-T6) and adequate for most

VACUUM-SYSTEM DESIGN 139

stainless steels. Soft aluminum, such as the 1000-series

alloys, should not be used for vacuum chambers. Holes

cut for ports in the side of a cylinder reduce the strength

of the cylinder and should be avoided. If side ports are

necessary, the wall thickness should be increased over the

recommendations of the code. Dents and out-of-roundness

in a cylinder weaken it and should be avoided.

A ﬂat end plate will bend a surprising amount under

atmospheric pressure. Assuming the plate caps a cylindri-

cal shape, the nature of the stress in the plate and the

maximum deﬂection depend upon whether or not the edges

of the plate are clamped to the cylinder. In this case

‘‘clamped’’ implies that the plate is welded to the cylinder.

A removable end plate bolted in place should be consid-

ered ‘‘unclamped’’ when designing a vacuum chamber.

The deﬂection at the center of a ﬂat circular end plate

clamped at its edges is:

d ¼

3PR

ð1  l

16Ed

ðedge clampedÞð3:47Þ

where P the external pressure, R is the radius of the plate, d

the thickness, l Poisson’s ratio, and E the modulus of

elasticity or Young’s modulus of the material.

In this

case, the maximum tensile stress is at the edge of the plate

(see Section 1.6.3).

The

deﬂection of a demountable end plate is greater than

that of a permanent end cap. For a circular plate with

unclamped edges:

d ¼

3PR

ð5 þ lÞð1  lÞ

16Ed

ðunclampedÞð3:48Þ

The maximum stress is at the center of the plate (see

Section 1.6.3).

he deﬂection of ﬂat end plates of steel or aluminum

under atmospheric pressure is plotted in Figure 3.36. In most

ses, relative deﬂection, (d/R), in the range 0.001 to 0.005

should be acceptable, otherwise the plate may be too heavy.

Steel is about three times more dense than aluminum. For a

given maximum deﬂection, an aluminum plate is less than

half as heavy as a steel plate. A vacuum-chamber design that

incorporates a stainless-steel cylinder with a demountable

aluminum end plate has much to say in its favor. Welds in

the stainless cylinder are much stronger and more reliable

than would be the case if the cylinder were made of alumi-

num. A removable aluminum end plate is lighter and much

less expensive to machine than one of steel.

Figure 3.34 Typical aluminum or steel vacuum chamber

resting on a baseplate. The pump, gauges, and electrical

and mechanical feedthroughs are most conveniently

mounted to the baseplate.

Figure 3.35 Recommended minimum wall thickness

(scaled to diameter) for evacuated aluminum-alloy

and stainless-steel tubes under external atmospheric

pressure, as a function of tube length (scaled to

diameter) between supporting ﬂanges.

140 VACUUM TECHNOLOGY

The deﬂection of the walls of a vacuum chamber must be

accounted for in designing the mounting for a vacuum sys-

tem. If both the chamber and the pump are securely

mounted, severe stresses will dev elop as the chamber is

evacuated. The correct practice is to securely mount the

vacuum chamber and leave the pump suspended from a

ﬂange on the chamber , or, alternati v ely, to mount the pump

and permit the chamber to rest on top of the pump with no

further constraint. In the latter case, it is important that forces

generated by the apparatus resting on the top of the pump do

not distort the pump. This is particularly important for

pumps requiring a high degree of mechanical precision, such

as a turbomolecular pump or a molecular drag pump. It is

generally recommended that turbopumps and drag pumps be

suspended by their inlet ﬂange with no other attachment.

Using standard, commercially av ail able components save s

both time and money. In fact, even quite large systems can

be built entirely of standard parts. In the author’s laboratory

a chamber 50 cm (20 in.) in diameter and 100 cm (40 in.)

high was created from a pair of ISO 500 half nipples that

were ordered with domed end caps. Ports were added to the

lower half nipple for feedthroughs and for a pump, as shown

in Figure 3.37. The total cost was about $5000 in 1994.

tal parts may be joined by soldering, brazing, or weld-

ing. Tungsten – inert-gas welds (so-called ‘‘TIG’’ or ‘‘heli-

arc’’ welds) produce the cleanest, strongest joints in stainless

steel. Soldering and brazing result in less distortion of the

joined parts and are more convenient operations in the labo-

ratory. As shown in Figure 3.38, a joint that is to be soldered

brazed should be designed so that the metal parts take the

thrust of the atmosphere and the solder or brazing alloy

serves only as a sealant. If possible, the joint should be

Figure 3.36 Deﬂection of ﬂat circular plates under

atmospheric pressure. A clamped end plate caps a cylindrical

tube and is welded in place, otherwise the plate should be

considered as unclamped. These curves assume a Poisson’s

ratio of 0.3 and a Young’s modulus of 210 GN m

2

(3 3 10

psi) for steel and 70 GN m

2

(1 3 10

psi) for aluminium.

Figure 3.37 A vacuum chamber composed of a pair of

ISO-500 (500 mm diameter) half nipples with domed

end caps.

Figure 3.38 The design of joints to be soldered or brazed.

VACUUM-SYSTEM DESIGN 141

designed to provide positive location of mating parts. The

surfaces to be joined should be cleaned before assembly by

sandblasting or by polishing with sandpaper so that the sol-

der or brazing metal will ﬂow into and completely ﬁll the

joint. This is necessary to achieve maximum strength and to

eliminate a narrow gap that is difﬁcult to pump out and is

liable to collect ﬂux and other material that will contaminate

the vacuum system. Tin-alloy solders (plumbing solder)

should only be used for rough vacuum applications such

as a diffusion-pump foreline. Brazed joints are acceptable

in high vacuum. The copper–silver eutectic alloy is the pre-

ferred brazing material. Brazing is an excellent way of

attaching thin metal parts, such as bellows, that can easily

be burned through in a welding operation.

Welded joints are designed to minimized distortion in

the welding process and to avoid occlusions on the vac-

uum side of the joint that may trap contaminates or a ct as

virtual l eaks. Parts to be joined by welding are designed

so that the rate of heat dissipation while welding is the

same to each part. This is necessary to prevent destruc-

tive thermal stresses from being frozen into the ﬁnished

joint. When joining a heavy ﬂange to a thin tube, a notch

or a groove is cut in the thick part near the joint to control

the rate at whic h heat is dissipa ted, as shown in Figure

3.3

9. To join a very thin part to a ﬂ ange, extra material,

such

as the welding ring shown in the ﬁgure, is added to

back up the weld. Whenever possible, welds should be

on the vacuum side, that is, on the inside of the vacuum

wall. Locational welds or ‘‘tack welds’’ should be on the

outside and should be intermittent. For material up to about

3 mm (1/8 in.) thick, full-penetration welds should be

speciﬁed. A weld from the outside, often necessary when

joining a small diameter tube to a ﬂange, should be a full

penetration weld if possible. When an outside weld is

unavoidable, the joint should be designed to minimize

the trapped volume on the inside, as shown in the ﬁgure.

Metal parts inside a vacuum system may be joined by

welding or brazing, but in most cases nut-and-bolt assem-

bly is more convenient. Special care must be taken to

prevent air from being trapped under a screw in a blind

hole. The placement of pumpout holes for blind screw

holes is illustrated in Figure 3.40.

3.6.4 Surface Preparation

Surfaces that are to be exposed to a vacuum should be free

of substances that have a signiﬁcant vapor pressure, and

they should be as smooth as possible to minimize the

microscopic surface area and thus minimize the amount

of adsorbed gas. The substances that must be removed

from the surfaces of vacuum apparatus are mainly hydro-

carbon oils and greases, and inorganic salts that are hygro-

scopic and outgas water vapor.

The two preferred treatments for metal vacuum-system

surfaces are electropolishing and bead blasting. Con ventional

wheel polishing and bufﬁng is unsatisfactory, since these

processes tend to ﬂatten surface burrs and trap gas under-

neath. Electropolishing is con v eniently carried out in the

laboratory, although most machine shops are prepared to

do it routinely. An electropolishing solution for stainless steel

Figure 3.39 Welded joints in a vacuum system.

142 VACUUM TECHNOLOGY

recommended by Armco Steel consists of 50 parts by volume

of citric acid and 15 parts by volu me of sulfuric acid, plus

enough water to make 100 parts of solution. The solution

should be used at a temperature of 90 ºC. A current density of

about 0.1 A/cm

at 6 to 12 V is required. A copper cathode is

used with the piece to be polished serving as the anode.

Blasting with 20–30 micron glass beads effectively

reduces the adsorbing area of a metal surface and thus

reduces the rate of outgassing from the surface. Glass

beading can be carried out in a conventional sandblasting

apparatus. The machine should be carefully cleaned of

coarse grits before use.

Shop processes such as welding, plasma cutting, and

high-speed turning can leave surfaces with a heavy layer

of oxides and other contaminants. Bead blasting or, alter-

natively, the chemical process known as pickling may

remove this layer. A pickling solution for stainless steel

consists of 2% (by volume) concentrated nitric acid

(HNO

) and 25% hydrochloric acid (HCl) in distilled

water at 60 ºC. This solution is known as ‘‘bright dip’’ in

the shop. After dipping in this solution, the part should be

thoroughly rinsed and its surface neutralized by immersion

in an alkaline solution. Aluminum is pickled in a 10%

solution of sodium hydroxide (NaOH) saturated with com-

mon salt (NaCl) at 80 ºC. After about half a minute in this

solution the part is transferred to a 10% solution of hydro-

chloric acid to obtain a bright ﬁnish.

An ultrasonic cleaner is particularly effective for prepar-

ing vacuum parts. The cleaner should be ﬁred with a deter-

gent solution. If two cleaners are available, ﬁll one with

detergent solution and the other with distilled water, and

use them in sequence with a hot-water rinse between.

Diffusion-pump oil is especially difﬁcult to remove.

Nevertheless, a diffusion pump must be thoroughly

cleaned when replacing old oil with new or when changing

from one type of oil to another. Hydrocarbon oils, poly-

phenylethers, and silicone ﬂuids can be dissolved in tri-

chloroethylene followed by acetone and then ethyl alcohol.

Trichloroethylene is somewhat toxic, and acetone and

ethanol are ﬂammable, so this cleaning should be carried

out carefully in a fume hood. Avoid skin contact with these

solvents. Fluorinated diffusion-pump ﬂuids, such as the

perﬂuoropolyethers (Fomblin), are soluble in ﬂuorinated

solvents such as chlorotriﬂuoroethane.

Glass can usually be effectively cleaned by washing in a

detergent solution followed by a rinse in hot water and

immersion in a 10–20% solution of hydroﬂuoric acid.

The glass is then rinsed with water, neutralized with an

alkaline solution, and rinsed with distilled water. Protect

eyes and skin during these operations. Hydroﬂuoric acid

burns are especially painful and persistent.

After surface treatment as required for particular com-

ponents, the ﬁnal cleaning procedure for all components of

a vacuum system should proceed as follows:

(1) Scrub with a strong solution of detergent (Alconox or

liquid dishwashing detergent is ﬁne).

(2) Rinse with very hot water.

(3) Rinse with distilled water.

(4) Rinse with pure methanol.

Do not touch clean parts with bare hands. Disposable plas-

tic gloves (free of talc) are convenient for handling vacuum

apparatus after cleaning.

3.6.5 Leak Detection

A leak that raises the base pressure of a system above

about 10

6

torrcanusuallybefoundbyprobingsus-

pected locations on the outside of the vacuum chamber

with a liquid or vapor for which the gauge sensitivity or

pump speed is very different from that for air. A squeeze

bottle of acetone or a spray can of a Freon cleaner is a

useful tool. These liquids w ill usually cause a very abrupt

increase in indicated pressure as they ﬂow through a leak,

Figure 3.40 Pumpout holes for blind screw holes.

VACUUM-SYSTEM DESIGN 143

but somet imes rapid evaporation of a li quid t hrough a

leak will cause the liquid to freeze and temporarily plug

the leak, causing the pressure to fall. A disadvantage of

this method is that the solvent may contaminate O-rings.

A small jet of helium is also a useful leak probe because

an ionization gauge is quite insensitive to helium. The

indicated pressure will fall when helium i s introduced

into a leak.

In a glass system, a leak that raises the pressure into the

10 mtorr to several torr range can be located with a Tesla

coil. The surface of the glass is brushed with the discharge

from the Tesla coil. The discharge is preferentially directed

toward the leak, and a bright white spot will reveal the

location as the discharge passes through. Avoid very thin

glass walls and glass-to-metal seals, as the Tesla discharge

can hole the glass in these fragile areas.

For very small leaks in high-vacuum systems, a mass-

spectrometer leak detector is needed (see Section 3.3.5).

3.6.6 Ultrahigh Vacuum

To achieve pressures much below 10

7

torr, baking is

required to remove water and hydrocarbons from vac-

uum-system walls. Heating to 50–100 ºC for several hours

will improve the ultimate pressure of most systems by an

order of magnitude. A true ultrahigh-vacuum system must

be baked to at least 250 ºC for several hours during the

initial pump out. A system contaminated with hydrocar-

bons may require a bakeout at temperatures approaching

400 ºC. After a hard preliminary bake in vacuo to remove

deeply adsorbed material, the system can be baked more

gently after subsequent exposures to air.

A small system can be wrapped with heating tape and

then covered with ﬁberglass insulation. For larger systems,

an oven constructed of sheet metal insulated with ﬁber-

glass can be erected around the vacuum chamber and

heated with bar heaters. Batts of ﬁberglass insulation

intended for use in automobile engine compartments are

readily available. Do not use home-insulating ﬁberglass

materials. Metal seals must be used in a metal vacuum

system that is to be baked. It is, however, often necessary

to join the vacuum chamber to its pumping station with an

O-ring-sealed ﬂange. In this case, a cooling coil should be

installed around the ﬂange (as in Figure 3.23) to prevent

damage

to the O-ring while the chamber is being baked.

Alternatively a metal O-ring can be used, as described in

Section 3.5.2.

Quartz

lamp heaters can be installed inside a vacuum

system to directly heat the surfaces that need to be out-

gased. This method is frequently faster and more econom-

ical than heating from the outside. A recent innovation for

removing water absorbed on the walls of vacuum appara-

tus employs ultraviolet radiation rather than heat. A lamp

known as a Phototron, manufactured by Danielson, is

inserted in the vacuum system. This lamp radiates at a wave-

length absorbed by water molecules and imparts sufﬁcient

energy to break the bond holding the water to the walls. This

method is not so effective as a high-temperature bakeout,

since the radiation is fairly speciﬁc for water and, in addi-

tion, the radiation cannot be expected to penetrate into small

involutions where water may be trapped. The method is

faster than a thermal bakeout and can be used in a system

that contains materials that are degraded by heat. It is

claimed to be 80 to 90% as effective as a bakeout.

Hydrocarbons from pump oils, cleaning ﬂuids and shop

processes are ubiquitous contaminates in vacuum systems.

Hydrocarbons create insulating layers on electrodes in elec-

tron microscopes and mass spectrometers. Their presence is

a particular problem in mass spectrometer experiments

since the hydrocarbon spectrum is very rich. XEI Scientiﬁc

has developed a device (the Evactron) that produces a low-

pressure plasma in oxygen to make radicals that react with

hydrocarbons in the vacuum system leaving only low-

vapor-pressure residues (‘‘ash’’).

To reduce outgassing to a minimum in an ultrahigh-

vacuum system it is common practice to preﬁre (‘‘stove’’)

components before they are assembled, in order to clean

the surfaces and to drive out dissolved gases. The usual

shop practice is to ﬁre components in a hydrogen atmos-

phere such as is provided by a hydrogen furnace or a dis-

sociated-ammonia furnace. This has the advantage of

effectively removing oxides from surfaces. The disadvant-

age to this procedure is that hydrogen is left to outgas at

lower temperatures. Copper parts containing trapped or

dissolved oxygen are also subject to embrittlement as a

result of hydrogen ﬁring. It is for this reason that oxy-

gen-free high-conductivity (OFHC) copper should be used

in constructing vacuum apparatus. High-temperature bak-

ing in vacuum or under an inert atmosphere is the preferred

treatment. Iron, steel, stainless-steel, and nickel-alloy parts

144 VACUUM TECHNOLOGY

are ﬁred at a temperature of about 900 ºC for up to eight

hours. Copper is ﬁred at 500 ºC.

Cited References

1. N. Milleron, Res. Dev., 21(9), 40, 1970.

2. Derivations of the conductance formulae are given by C. M.

VanAtta, Vacuum Science and Engineering, McGraw-Hill,

New York, 1965, pp. 44–62 and J. F. O’Hanlon, A User’s

Guide to Vacuum Technology, 2nd edn., John Wiley & Sons,

Inc., New York, 1989, Chap. 3.

3. M. A. Biondi, Rev. Sci. Instr., 24, 989, 1953.

4. A. T. J. Hayward, J. Sci. Instr., 40, 173, 1963; C. Veillon,

Rev. Sci. Instr., 41, 489, 1970.

5. H. Ishii and K. Nakayama, Transactions of the 2nd

International Congress on Vacuum Science and

Technology, Vol. 1, Pergamon Press, Elmsford, NY, 1961, p.

519; R. J. Tunnicliffe and J. A. Rees, Vacuum, 17, 457,

1967; T. Edmonds and J. P. Hobson, J. Vac. Sci. Tech., 2,

182, 1965.

6. G. R. Brown, P. J. Sowinski, and R. Pertel, Rev. Sci. Instr.,

43, 334, 1972.

7. An application of this process is described by J. H. Moore

and C. B. Opal, Space Sci. Instr., 1, 377, 1975.

8. C. B. Lucas, Vacuum, 23, 395, 1973.

9. R. H. Jones, D. R. Olander, and V. R. Kruger, J. Appl. Phys.,

40, 4641,1969; D. R. Olander, J. Appl. Phys ., 40, 4650,

1969; D. R. Olander, J. Appl. Phys., 41, 2769, 1970; D. R.

Olander, R. H. Jones, and W. J. Siekhaus, J. Appl. Phys., 41,

4388, 1970; W. J. Siekhaus and R. H. Jones, J. Appl. Phys.,

41, 4392, 1970.

10. M. G. Liverman, S. M. Beck, D. L. Monts, and R. E.

Smalley, J. Chem. Phys., 70, 192, 1979; W. R. Gentry and

C. F. Giese, Rev. Sci. Instr., 49, 595, 1978; C. M. Lovejoy

and D. J. Nesbitt, J. Chem. Phys., 86, 3151, 1987.

11. D. Bassi, S. Iannotta, and S. Niccolini,

Rev. Sci. Instr., 52,8

1981; F. M. Behlen, Chem. Phys. Lett., 60, 364, 1979.

12. R. E. Smalley, D. H. Levy, and L. Wharton, J. Chem. Phys.,

64, 3266, 1976.

13. J. B. Anderson, R. P. Andres, and J. B. Fenn, in Advances in

Chemical Physics,Vol.10,Molecular Beams, J. Ross (Ed.),

John Wiley & Sons, Inc., New York, 1966, Chapter 8; H.

Pauly and J. P. Toennies, in Methods of Experimental

Physics, Vol. 7, Part A, B. Bederson and W. L. Fite, (Eds.),

Academic Press, New York, 1968, Chapter 3.1; D. R. Miller,

in Atomic and Molecular Beam Methods, Vol. I, G. Scoles,

(Ed.), Oxford University Press, Oxford, 1988, pp. 14–53.

14. W. D. Kingery, H. K. Bowen, and D. R. Uhlmann,

Introduction to Ceramics, 2nd edn., John Wiley & Sons,

Inc., New York, 1976, Chapter 17.

15. J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd

edn., Wiley, Hoboken, NJ, 2003, pp. 366–369.

16. This system is an adaptation of a design described by N. W.

Robinson, Ultra-high Vacuum, Chapman and Hall, London,

1968, pp. 72–73.

17. A.S.M.E. Boiler and Pressure Vessel Code, Section VIII,

Division 1, Appendix V, 1974.

18. Clifford Mathews, A.S.M.E. Engineer’s Data Book, 2nd

edn., ASME Press, NY, 2001, p. 75; J. F. Harvey, Pressure

Vessel Design, Van Nostrand, Princeton, NJ, 1963, pp.

89–91.

General References

Comprehensive Texts on

Vacuum Technology

S. Dushman, Scientiﬁc Foundations of Vacuum Technique,

2nd edn., J. M. Lafferty (Ed.), John Wiley & Sons Inc.,

New York, 1961.

M. Hablanian, High-Vacuum Technology, Dekker, New York,

1990.

G. Lewin, Fundamentals of Vacuum Science and Technology,

McGraw-Hill, New York, 1965.

J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 3rd edn.,

Wiley, Hoboken, NJ, 2003.

J. M. Lafferty (Ed.), Foundations of Vacuum Science

and Technology, Joh n Wiley & Son s, In c., New York,

1998.

C. M. Van Atta, Vacuum Science and Engineering, McGraw-Hill,

New York, 1965.

‘‘Vacuum Technology: Its Foundations, Formulae and Tables’’,

until 1996 published as an appendix of the Leybold AG

catalog, Product and Vacuum Technology Reference Book,

Leybold, Inc., San Jose, CA.

Detailed Calculation of Gas Flow

R. A. Roth, Vacuum Technology, 2nd edn., North-Holland,

Amsterdam, 1982.

R. G. Livesey, ‘‘Flow of Gases through Tubes and Oriﬁces’’ in

Foundations of Vacuum Science and Technology, J. M. Lafferty

(Ed.), John Wiley & Sons, Inc., New York, 1998.

REFERENCES 145

Design of Vacuum Systems

N. T. M. Dennis and T. A. Heppell, Vacuum System Design,

Chapman and Hall, London, 1968.

G. W. Green, The Design and Construction of Small Vacuum

Systems, Chapman and Hall, London, 1968.

R. P. LaPelle, Practical Vacuum Systems, McGraw-Hill,

New York, 1972.

Outgassing Data

W. A. Campbell, Jr., R. S. Marriott, and J. J. Park,

A Compilation of Outgassing Data for Spacecraft Materials,

NASA Technical Note TND-7362, NASA, Washington,

DC, 1973.

Properties of Materials Used in Vacuum

Systems

W. Espe, Materials of High Vacuum Technology: Vol. 1, Metals

and Metaloids; Vol. 2, Silicates; Vol. 3, Auxiliary Materials,

Pergamon Press, Oxford, 1968 (a translation of the original

German published in 1960).

Sealing Ceramics and Glass to Metal,

Heat-Treating, Cleaning, Building Joints,

and Feedthroughs

F. Rosebury, Handbook of Electron Tube and Vacuum

Techniques, Addison-Wesley, Reading, Mass., 1969.

A. Roth, Vacuum Sealing Techniques, Pergamon Press,

New York, 1966 and American Vacuum Society Classics,

American Institute of Physics, New York, 1994.

Ultrahigh Vacuum

P. A. Redhead, J. P. Hobson, and E.V. Kornelsen, The

Physical Basis of Ultrahigh Vacuum, Chapman and Hall,

London, 1968.

R. W. Roberts and T. A. Vanderslice, Ultrahigh Vacuum and

Its Applications, Prentice-Hall, Englewood Cliffs, NJ, 1963.

W. Robinson, The Physical Principles of Ultrahigh Vacuum

Systems and Equipment, Chapman and Hall, London, 1968.

G. F. Weston, Ultrahigh Vacuum Practice, Butterworths, London,

1985.

J. T. Yates, Jr., Experimental Innovations in Surface Science,

Springer-Verlag, New York, 1998.

146 VACUUM TECHNOLOGY

OPTICAL SYSTEMS

Physical, chemical, and biological phenomena are regu-

larly studied or induced optically. Such experiments can

involve light absorption, light emission, or light scattering.

We can characterize any experimental arrangement where

light is used, produced, measured, modiﬁed, or detected as

an overall optical system. Any such optical system will

always be reducible to three parts: a source of light, a

detector of that light, and everything in between. We will

frequently refer to this important and varied intermediary

arrangement as the optical system. Consequently, our dis-

cussion of overall optical system design and construction

will involve three key topics: sources, optical systems, and

detectors (to be discussed in detail in Chapter 7). The light

source may be a laser, lamp, light-emitting diode, or the

Sun. The detector may be a vacuum tube, solid-state device,

or even the eye. Light intensity may vary from continuous

wave (CW) to pulsed, and these pulses may have durations

as short as a few femtoseconds. Passive elements in the

system may transmit, reﬂect, combine, polarize, or sepa-

rate light according to its spectral content. Nonlinear opti-

cal elements change the spectral content of light.

It is our aim in this chapter to explain the basic concepts

that need to be understood by the experimentalist who uses

optical techniques. In addition, we will provide examples

of useful techniques for producing, controlling, analyzing,

and modulating light.

4.1 OPTICAL TERMINOLOGY

Light is one form of electromagnetic radiation, the many

categories of which make up the electromagnetic spectrum.

Electromagnetic radiation, which transports energy from

point to point at the velocity of light, can be described in

terms of both wave and particle ‘‘pictures’’ or ‘‘models’’.

This is the famous ‘‘wave-particle’’ duality of all ﬁelds or

particles in our model of the Universe. In the electromag-

netic-wave picture, waves are characterized by their fre-

quency m, wavelength k, and the velocity of light c, which

are related by c ¼ mk. A propagating electromagnetic wave

is characterized by a number of ﬁeld vectors, which vary in

time and space. These include the electric ﬁeld E (meas-

ured in Volt/m), the magnetic ﬁeld H (measured in Amp/

m), the displacement vector D (measured in Coulomb/m

and the magnetic ﬂux density B (measured in Webers/m

or Tesla). For a complete description the polarization state

of the wave must also be speciﬁed. Linearly polarized

waves have ﬁxed directions for their ﬁeld vectors, which

do not re-orient themselves as the wave propagates. Circu-

lar or elliptically polarized waves have ﬁeld vectors that

trace out circular or elliptic helical paths as the wave trav-

els along. In the particle picture, electromagnetic energy is

carried from point to point as quantized packets of energy

called photons. The energy of a photon of frequency m is hm,

where h is Planck’s constant – 6.626 3 10

–34

J s. Photons

have zero mass, travel at the velocity of light, and also carry

both linear and angular momentum. The linear momentum

of a photon of wavelength is p ¼ h/k, the angular momen-

tum depends on the equivalent polarization state of the cor-

responding wave. Circularly polarized photons have angular

momentum h/2p ¼

Our everyday experience of ‘‘light’’ generally only

encompasses the small part of the electromagnetic spectrum

to which the human eye is sensitive, a wavelength range

running roughly from 400–700 nm. The full electromagnetic

147

CHAPTER

spectrum, going from low to high frequencies, is divided

into radiowaves (0–1 GHz), microwaves (1–300 GHz),

infrared waves (k 0.7 –1000 lm) (300 GHz–430 THz)

visible light (k 400–700 nm), ultraviolet light (k 10–

400 nm), X-rays (k 0.1–10 nm), and c waves (k < 0.1 nm).

The wavelength region between 10 nm and 200 nm is

often called the vacuum-ultraviolet region because these

wavelengths are absorbed by air and most gases. Optical

systems can somewhat arbitrarily be classiﬁed as systems

that handle light in the spectral region between 10 nm and

100 lm. Beyond the far-infrared, between 100 and 1000 lm

(the submillimeter wave region of the spectrum), lies a

spectral region where conventional optical methods can still

be used, but become difﬁcult, as does the extension of

microwave techniques for the centimeter- and millimeter-

wave regions. The use of optical techniques in this region,

and even in the millimeter region, is often called quasi-

optics.

1–4

Only a few experimental techniques and devices

that are noteworthy in this region will be mentioned.

Table 4.1 summarizes the important parameters that are

used

to characterize light and the media through which it

passes. A few comments on the table are appropriate.

Table 4.1 Fundamental parameters of electromagnetic radiation and optical media

Parameter Symbol Value Units

Velocity of light in tacuo c

¼(l

)

1/2

2.99792458 3 10

m/sec

Permeability of free space l

4p 3 10

7

henry/m

Permittivity of free space e

8.85416 3 10

12

farad/m

Velocity of light in a medium c ¼(l

)

1/2

¼c

/n m/sec

Refractive index n ¼(l

)

1/2

(dimensionless)

Relative permeability of a medium l

Usually 1 (dimensionless)

Dielectric constant of a medium e

(dimensionless)

Frequency m ¼c/k Hz

Hz ¼1 GHz (gigahertz)

Hz ¼1 THz (terahertz)

Wavelength in tacuo k

¼c

Wavelength in a medium k ¼c/m ¼ k

/n m

3

m ¼1 mm (millimeter)

6

m ¼1 lm (micrometer)

¼1 l (micron)

9

m ¼1 nm (nanometer)

¼1ml (millimicron)

12

m ¼1 pm (picometer)

10

m ¼1 A (Angstrom)

Wavenumber



m ¼ 1=k cm

1

(kayser)

Wavevector k,|k| ¼2p/k m

1

Photon energy E ¼hm J

1.60202 3 10

J ¼1eV

(electron volt)

Electric ﬁeld of wave E V/m

Magnetic ﬁeld of wave H A/m

Poynting vector P ¼E 3 H W/m

Intensity I ¼ <|P|>

¼|E|

/2Z W/m

Impedance of medium

Z ¼

¼



1=2

Impedance of free space Z

¼(l

)

1/2

376.7 X

148 OPTICAL SYSTEMS

Although the v elocity of light in a medium depends both on

the relative magnetic permeability l

, and dielectric constant

of the medium, for all practical optical materials l

¼1, so

the refractiv e index and dielectric constant are related by:

n ¼

ﬃﬃﬃﬃ

ð4:1Þ

When light propagates in an anisotropic medium, such

as a crystal of lower than cubic symmetry, n and e

will, in

general, depend on the direction of propagation of the

wave and its polarization state. The velocity of light in

vacuo is currently the most precisely known of all the

physical constants – its value is known

within 40 cm/s.

A redeﬁnition of the meter has been adopted

based on the

cesium-atomic-clock frequency standard

and a velocity of

light in a vacuum of exactly 2.99792458 3 10

m/s. Con-

sequently, the meter is now a derived SI unit, deﬁned as the

distance traveled in vacuo by light in 1/2.99792458 3 10

seconds. The velocity, wavelength, and wavenumber of

light traveling in the air have slightly different values than

they have in vacuo. Tables that give corresponding values

m in vacuo and in standard air are available.

A plane electromagnetic wave traveling in the z-direc-

tion can, in general, be decomposed into two independent,

linearly polarized components. The electric and magnetic

ﬁelds associated with each of these components are them-

selves mutually orthogonal and transverse to the direction

of propagation. They can be written as (E

, H

) and (E

). The ratio of the mutually orthogonal E and H compo-

nents is called the impedance Z of the medium:

¼

¼ Z ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð4:2Þ

Most optical materials have l

¼ 1. The negative sign in

Equation (4.2) arises because (y, x, z)

is not a right-handed

coordinate system. The Poynting vector:

P ¼ E 3 H ð4:3Þ

is a vector that points in the direction of energy propaga-

tion of the wave, as shown in Figure 4.1. The local direc-

tion

of the Poynting vector at a point in a medium is called

the ray direction. The average magnitude of the Poynting

vector is called the intensity and is given by:

I ¼ <jPj>

jEj

ð4:4Þ

The factor of two comes from time-averaging the square

of the sinusoidally varying electric ﬁeld.

The wavevector k points in the direction p erpendicu-

lar to the phase front of the wave (the surface of cons tant

phase). In an isotropic medium k and P are always

parallel.

The photon ﬂux corresponding to an electromagnetic

wave of average intensity I and frequency v is:

N ¼

ð4:5Þ

where h is Planck’s constant, 6.6 3 10

–34

J s. For a

wave of intensity 1 Wm

and wavelength 1 lm in vacuo,

N ¼ 5.04 3 10

photons sec

–1

–2

. Photon energy is

sometimes measured in electron volts (eV): 1 eV ¼

1.60202 3 10

–19

J. A photon of wavelength 1 lm has an

energy of 1.24 eV. It is often important, particularly in the

infrared, to know the correspondence between photon and

thermal energies. The characteristic thermal energy at

absolute temperature T is kT. At 300 K, kT ¼ 4.14 3

–21

J ¼ 208.6 cm

–1

¼ 0.026 eV.

Figure 4.1 Orientation of the mutually orthogonal

electric-ﬁeld vector E, magnetic-ﬁeld vector H,

and Poynting vector P.

OPTICAL TERMINOLOGY 149

4.2 CHARACTERIZATION AND

ANALYSIS OF OPTICAL

SYSTEMS

Before embarking on a detailed discussion of the properties

and uses of passive optical components and systems con-

taining them, it is worthwhile reviewing some of the param-

eters that are important in characterizing passive optical

systems and some of the methods that are useful in analyz-

ing the way in which light passes through an optical system.

Optical materials have refractive indices that vary with

wavelength. This phenomenon is called dispersion. It causes

a wavelength dependence of the properties of an optical

system containing transmissive components. The change of

index with wavelength is very gradual, and often negligible,

unless the wavelength approaches a region where the mate-

rial is not transparent. Most materials exhibit normal disper-

sion, where the refracti v e inde x decreases with wavelength.

In speciﬁc spectral regions they may exhibit anomalous dis-

persion, where the refractiv e index increases with wave-

length over a limited range of wavelengths. A description

of the performance of an optical system is often simpliﬁed

by assuming that the light is monoch romatic (light that con-

tains only a small spread of wavelength components).

4.2.1 Simple Reﬂection and

Refraction Analysis

The phenomena of reﬂection and refraction are most easily

understood in terms of plane electromagnetic waves –

those in which the direction of energy ﬂow (the ray direc-

tion) is unique. Other types of wave, such as spherical

waves and Gaussian beams, are also important in optical

science; however, the part of their wavefront that strikes an

optical component can frequently be approximated as a

plane wave, so plane-wave considerations of reﬂection

and refraction still hold true.

When light is reﬂected from a plane mirror, or the planar

boundary between two media of different refractive index,

the angle of incidence is always equal to the angle of

reﬂection, as shown in Figure 4.2. This is the fundamental

law

of reﬂection.

When a light ray crosses the boundary between two

media of different refractive index, the angle of refraction

, shown in Figure 4.2, is related to the angle of incidence

by Snell’s law:

sin h

ð4:6Þ

This result is modiﬁed if one or both of the media is

anisotropic.

If n

< n

there is a maximum angle of incidence for

which there can be a refracted wave, since sin h

cannot be

greater than unity for a real angle. This is called the critical

angle h

and is given by:

sin h

¼n

ð4:7Þ

as illustrated in Figure 4.3(a)

If h

exceeds h

, the boundary acts as a very good mirror,

as illustrated in Figure 4.3(b). This phenomenon is called

tal internal reﬂection. Several types of reﬂecting prisms

discussed in Section 4.3.4 operate this way. When total

internal reﬂection occurs, there is no transmission of energy

through the boundary. The ﬁelds of the wave do not, how-

ever, go abruptly to zero at the boundary. There is an evan-

escent wave on the other side of the boundary, the ﬁeld

Figure 4.2 Reﬂection and refraction of a light ray at the

boundary between two different isotropic media of

refractive indices n

and n

, respectively. The case shown

is for n

> n

. The incident, reﬂected, and transmitted

rays and the surface normal N are coplanar.

150 OPTICAL SYSTEMS

amplitudes of which decay exponentially with distance. For

this reason, other optical components should not be brought

too close to a totally reﬂecting surface, or energy will be

coupled to them via the evanescent wave and the efﬁciency

of total internal reﬂection will be reduced. With extreme

care this effect can be used to produce a variable-reﬂectivity,

totally internally reﬂecting surface, as can be seen in Figure

4. Studies of total internal reﬂection at interfaces are

portant in a number of optical measurement techniques,

such as attenuated total (internal) reﬂection

and photon

scanning tunneling microscopy.

One or both of the media in Figure 4.2 may be aniso-

tropic, like calcite, crystalline quartz, ammonium dihydro-

gen phosphate (ADP), potassium dihydrogen phosphate

(KDP), or tellurium. Then the incident wave in general

will split into two components, one of which obeys Snell’s

law directly (the ordinary wave) and one for which Snell’s

law is modiﬁed (the extraordinary wave). This phenom-

enon is called double refraction.

11–13

If an optical system contains only planar interfaces, the

path of a ray of light through the system can be easily

calculated using only the law of reﬂection and Snell’s

law. This simple approach neglects diffraction effects,

which become signiﬁcant unless the lateral dimensions

(apertures) of the system are all much larger than the

wavelength (say 10 times larger). The simple behavior of

light rays in more complex systems containing nonplanar

components, but where diffraction effects are negligible,

can be described with the aid of paraxial-ray analysis.

14,15

Transmitted and reﬂected intensities and polarization

states cannot be determined by the above methods and

are most easily determined by the method of impedances.

4.2.2 Paraxial-Ray Analysis

A plane wave is characterized by a unique propagation

direction given by the wave vector k. All ﬁelds associated

with the wave are, at a given time, equal at all points in

inﬁnite planes orthogonal to the propagation direction. In

real optical systems, ideal plane waves do not exist, as the

ﬁnite size of the elements of the system restricts the lateral

extent of the waves. Nonplanar optical components will

cause further deviations of the wave from planarity. Con-

sequently, the wave acquires a ray direction that varies from

point to point on the phase front. The behavior of the optical

system must be characterized in terms of the deviations its

elements cause to the bundle of rays that constitute the

propagating, laterally restricted wave. This is most easily

done in terms of paraxial rays. In a cylindrically symmetric

optical system (for example, a coaxial system of spherical

lenses or mirrors), paraxial rays are those rays whose direc-

tions of propagation occur at sufﬁciently small angles h to

the symmetry axis of the system that it is possible to replace

Figure 4.3 (a) Critical angle (n

> n

); (b) total internal

reﬂection (n

> n

). N is the surface normal.

Figure 4.4 Schema of an evanescent-wave coupler.

The amount of intensity reﬂected or coupled is varied by

adjusting the spacing d; shown greatly exaggerated in

the ﬁgure. This spacing is typically on the order of the

wavelength. The surface boundary and adjacent prism

face must be accurately ﬂat and parallel.

CHARACTERIZATION AND ANALYSIS 151

sin h or tan h by h – in other words, paraxial rays obey the

small-angle approximation:

sin h ’ tan h ’ h ð4:8Þ

Matrix Formulation. In an optical system whose

symmetry axis is in the z-direction, a paraxial ray in a

given cross-section (z ¼ constant) is characterized by its

distance r from the z-axis and the angle r9 it makes with

that axis. Suppose the values of these parameters at two

planes of the system (an input and an output plane) are r

and r

, r9

, respectively, as shown in Figure 4.5(a). Then

in the paraxial-ray approximation, there is a linear relation

between them of the form:

¼ Ar

þ Br

¼ Cr

þ Dr

ð4:9Þ

or, in matrix notation:



ð4:10Þ

Figure 4.5 (a) Generalized schematic diagram of an optical system, showing a typical ray

and its paraxial-ray parameters at the input and output planes; (b) focal points

and F

and principal rays of a generalized optical system.

152 OPTICAL SYSTEMS

Here:

M ¼



ð4:11Þ

is called the ray transfer matrix. If the media where the

input and output ray parameters are measured have the

same refractive index, then the determinant of the ray

transfer matrix is unity, i.e., AD  BC ¼ 1.

Optical systems made of isotropic material are generally

reversible – a ray that travels from right to left with input

parameters r

, r9

will leave the system with parameters r

. Thus:



ð4:12Þ

where the reverse ray transfer matrix is:



1

ð4:13Þ

The ray transfer matrix allows the properties of an optical

system to be escribed in general terms by the location of its

focal points and principal planes, whose location are deter-

mined from the elements of the matrix. The signiﬁcance of

these features of the system can be illustrated with the aid of

Figure 4.5(b). An input ray that passes through the ﬁr

st focal

point F

(or would pass through this point if it did not ﬁrst

enter the system) emerges traveling parallel to the axis. The

intersection point of the extended input and output rays,

point H

in Figure 4.5(b), deﬁnes the location of the ﬁrst

principal plane. Conversely, an input ray traveling parallel

to the axis will emerge at the output plane and pass through

the second focal point F

(or appear to have come from this

point). The intersection of the extension of these rays, point

, deﬁnes the location of the second principal plane. Rays

1and2inFigure 4.5(b) are called the pr

incipal rays of the

system. The location of the principal planes allows the cor-

responding emergent ray paths to be determined, as shown

in Figure 4.5(b). The dashed lines in this ﬁgure, which

rmit the geometric construction of the location of output

rays 1 and 2, are called virtual ray paths.BothF

and F

lie

on the axis of the system. The axis of the system intersects

the principal planes at the principal points, P

and P

,in

Figure 4.5(b). The distance, f

, from the ﬁrst principal plane

to the ﬁrst focal point is called the ﬁrst focal length; f

called the second focal length.

In many practical situations, the refractive indices of the

media to the left of the input plane (the object space) and to

the right of the output plane (the image space) are equal. In

this case, several simpliﬁcations arise:

¼ f

¼ f ¼

D  1

A  1

ð4:14Þ

and h

are the distances of the input and output planes

from the principal planes, measured in the sense shown in

Figure 4.5(b).

Thus,

if the elements of the transfer matrix are known,

the location of the focal points and principal planes is

determined. Graphical construction of ray paths through

the system using the methods of paraxial ray tracing is

then straightforward (see below).

In using the matrix method for optical analysis, a consis-

tent sign convention must be employed. In the present dis-

cussion, a ray is assumed to trav el in the positi v e z-direction

from left to right through the system. The distance from the

ﬁrst principal plane to an object is measured positive from

right to left – in the negati v e z-direction. The distance from

the second principal plane to an image is measured positive

from left to right – in the positiv e z-direction. The lateral

distance of the ray from the axis is positiv e in the upward

direction, negati ve in the downward direction. The acute

angle between the system-axis direction and the ray, say r

in Figure 4.5(a), is positi v e if a counterclockwise motion is

necessary to go from the positiv e z-direction to the ray direc-

tion. When the ray crosses a spherical interface, the radius of

curvature is positive if the interface is conve x to the input ray.

The use of ray transfer matrices in optical-system analysis

can be illustrated with some speciﬁc examples.

(i) Uniform optical medium. In a uniform optical

medium of length d, no change in ray angle occurs, as

illustrated in Figure 4.6(a); so:

¼ r

þ dr

ð4:15Þ

CHARACTERIZATION AND ANALYSIS 153

Figure 4.6 Simple optical systems for illustrating the application of ray transfer matrices, with

input and output planes marked 1 and 2: (a) uniform optical medium; (b) planar interface

between two different media; (c) a parallel-sided slab of refractive index n bounded on both

sides with media of refractive index 1; (d) thins lens (r9

isanegativeangle;forathinlens,r

); (e) a length of uniform medium plus a thin lens; (f) two thin lenses.

154 OPTICAL SYSTEMS

Therefore:

M ¼

1 d



ð4:16Þ

The focal length of this system is inﬁnite and it has no

speciﬁc principal planes.

(ii) Planar interface between two different media.

At the interface, as sho wn in Figure 4.6(b),wehaver

¼ r

and from Snell’s law , using the approximation sin h ’ h:

ð4:17Þ

Therefore:

M ¼

0 n



ð4:18Þ

(iii) A parallel-sided slab of refractive index n bounded

on both sides with media of refractive index I [Figure

4.6(c)]. In this case:

M ¼

1 d=n



ð4:19Þ

The principal planes of this system are the boundary faces

of the optically dense slab.

(iv) Thick lens. The ray transfer matrix of the thick lens

shown in Figure 4.7(a) is the product of the three transfer

matrices:

¼ðmatrix for second spherical interfaceÞ

3 ðmatrix for medium of length dÞ

3 ðmatrix for first spherical interface Þ

ð4:20Þ

Note the order of these three matrices; M

comes on the

right because it operates ﬁrst on the column vector that

describes the input ray.

At the ﬁrst spherical surface:

ðr

þ /

Þ¼nr ¼ nðr

þ /

Þð4:21Þ

and, since h

¼ r

, this equation can be rewritten as:

ðn

 nÞr

ð4:22Þ

The transfer matrix at the ﬁrst spherical surface is:

 n



ð4:23Þ

where D

¼ (n – n9)/R

is called the power of the

surface. If R

is measured in meters, the units of D

are

diopters.

In the paraxial approximation, all the rays passing

through the lens travel the same distance d in the lens.

Thus:

1 d



ð4:24Þ

The ray transfer matrix at the second interface is:

n  n



ð4:25Þ

which is identical in form to M

. Note that in this case both

and R

are negative. The overall transfer matrix of the

thick lens is:

M ¼ M

1 



1 

ð4:26Þ

If Equations (4.26) and (4.14) are compared, it is clear

that the locations of the principal planes of the thick lens

are:

1 þ





ð4:27Þ

1 þ





ð4:28Þ

A numerical example will best illustrate the location of

the principal planes for a biconvex thick lens. Suppose that:

¼ 1ðairÞ, n ¼ 1:5ðglassÞ

¼R

¼ 50 mm,

d ¼ 10 mm

ð4:29Þ

In this case, D

¼ D

¼ 0.01 mn and, from Equations

(4.27) and (4.28), h

¼ h

¼ 3.448 mm. These principal

CHARACTERIZATION AND ANALYSIS 155

planes are symmetrically placed inside the lens. Figure

4.7(b) shows how the principal planes can be used to trace

the

principal-ray paths through a thick lens.

From Equation (4.26):

¼

þ 1 



ð4:30Þ

where the focal length is:

f ¼

þ D





1

ð4:31Þ

If l

is the distance from the object O to the ﬁrst principal

plane, and l

the distance from the second principal plane to

Figure 4.7 (a) Diagram illustrating ray propagation through a thick lens; (b) diagram

showing the use of the principal planes to determine the principal-ray paths through the

lens. The dashed paths XABX9 and YCDY9 are the virtual-ray paths; the solid lines XX9 and

YY9 are the real-ray paths.

156 OPTICAL SYSTEMS

the image I in Figure 4.7(b), then from the similar triangles

OO9F

, P

, and P

, II9F

 f

ð4:32Þ

If the media on both sides of the lens are the same, then

¼ f

¼ f and it immediately follows that:

ð4:33Þ

This is the fundamental imaging equation.

(v) Thin lens. If a lens is sufﬁciently thin that to a good

approximation d ¼ 0, the transfer matrix is:

M ¼



þ D

ð4:34Þ

As shown in Figure 4.6(d), the principal planes of such a

thin lens are at the lens. The focal length of the thin lens is

f, where:

þ D

 1







ð4:35Þ

so the transfer matrix can be written very simply as:

M ¼

1=f 1



: ð4:36Þ

The focal length of the lens depends on the refractive

indices of the lens material and of the medium within

which it is immersed. In air:

¼ðn  1Þ





ð4:37Þ

For a biconvex lens, R

is negative and:

¼ðn  1Þ



ð4:38Þ

For a biconcave lens:

¼ðn 1Þ



ð4:39Þ

The focal length of any diverging lens is negative. For

a thin lens the object and image distances are measured

to a common point. It is common practice to rename the

distances l

and l

in this case, so that the imaging Equation

(4.33) reduces to its familiar form:

ð4:40Þ

Then u is called the object distance (or object conjugate)

and v the image distance (or image conjugate).

(vi) A length of uniform medium plus a thin lens

[Figure 4.6(e)]. This is a combination of the systems in

(i) and (v); its overall transfer matrix is found from Equa-

tions (4.16) and (4.36) as:

M ¼

1=f 1



1 d



1 d

1=f 1  d = f



ð4:41Þ

(vii) Two thin lenses. As a ﬁnal example of the use of ray

transfer matrices, consider the combination of two thin

lenses shown in Figure 4.6(f). The transfer matrix of this

combination is:

M ¼ðmatrix of second lensÞ

3 ðmatrix of uniform medium of length d

3 ðmatrix of first lensÞ,

3 ðmatrix of uniform medium of length d

ð4:42Þ

which can be shown to be:

M ¼

1 

þ d



1 



ð4:43Þ

The focal length of the combination is:

f ¼

ðf

þ f

Þd

ð4:44Þ

The optical system consisting of two thin lenses is the

standard system used in analyses of the stability of lens

waveguides and optical resonators.

14–16

CHARACTERIZATION AND ANALYSIS 157

(viii) Optical systems with plane mirrors. Optical

systems in which a plane mirror is arranged perpen-

dicular to the system axis are most easily analyzed

by an unfolding technique. For, example if an optical

system with ray transfer matrix M is terminated by

a plane mirror, as shown in Figure 4.8(a), the

‘

‘unfolded’’ system is as shown in Figure 4.8(b). The ray

parameters

at the original input plane, after a ray has

Figure 4.8 (a) A simple optical system with two lenses and a plane mirror; (b) the equivalent ‘‘unfolded’’ system that

can be used for ray transfer matrix analysis.

158 OPTICAL SYSTEMS

passed back through the systems can be found as

follows:



¼ M

rev



ð4:45Þ

where M

rev

is the ray transfer matrix for the optical system in

the re v erse direction. Equation (4.45) can be also written as



¼ M

1

0 1



ð4:46Þ

(ix) Spherical mirrors. The object and image distances

from a spherical mirror also obey Equation (4.40), where

the

focal length of the mirror is R/2; f is positive for a

concave mirror, negative for a convex mirror. Positive

object and image distances for a mirror are measured pos-

itive in the normal direction away from its surface. If a

negative image distance results from Equation (4.40), this

implies

a virtual image (behind the mirror).

Ray Tracing. In designing an optical system, ray tracing is

a powerful technique for analyzing the design and assessing

its performance. Ray tracing follows the trajectorie s of light

rays through the system. These light rays represent, at each

point within the system, the local direction of energy ﬂow,

represented mathematically by the Poynting vector:

The trajectory of a light ray is governed by the laws of

reﬂection and refraction. At a mirror surface the angle of

reﬂection is equal to the angle of incidence. At the boun-

dary between two media of different refractive index n

, respectively, the angle of incidence, h

, and refraction,

, are related by Snell’s law

sin h

¼n

sin h

ð4:47Þ

In a medium where the refractive index varies from point

to point, Equation (4.47) still holds true, but it is better in

this

case to use the equation of light rays:



¼ grad n ð4:48Þ

where s is the distance measured along the path of the light

ray, and n(r) is the index of refraction at point r, measured

with respect to the origin.

Ray tracing provides an accurate description of the way

light passes through an optical system unless diffraction

effects become important. This happens when any aper-

tures in the system become comparable in size to the wave-

length, or when two adjacent apertures in the system

subtend angles that are comparable to the diffraction angle.

At a surface of diameter 2a, the diffraction angle for

light of wavelength k is:

diff

1:22k

ð4:49Þ

This is the angular position of the ﬁrst intensity minimum

in the ring-shaped diffraction pattern that results when a

plane-wave passes through a circular aperture. If a second

aperture of diameter 2a

is placed a distance d from the

ﬁrst, the angle subtended is:

h ¼

ð4:50Þ

For diffraction to be negligible requires h

diff

<< h, which

gives:

<< 1 ð4:51Þ

often called the Fresnel criterion.

Paraxial Ray Tracing. Practical implementation of

paraxial-ray analysis in optical-system design can be very

con veniently carried out graphically by paraxial ray tracing.

In ray tracing a few simple rules allow geometrical

construction of the principal-ray paths from an object point.

(These constructions do not take into account the nonideal

behavior, or aberrations, of real lenses, which will be

discussed later .) The ﬁrst principal ray from a point on the

object passes through (or its projection passes through) the

ﬁrst focal point. From the point where this ray, or its

projection, intersects the ﬁrst principal plane, the output ray

is drawn parallel to the axis. The actual ray path between input

andoutputplanescanbefoundinsimplecases–forexample,

the path XX9 in the thick lens shown in Figure 4.7(b).The

cond principal ray is directed parallel to the axis; from the

intersection of this ray, or its projection, with the second

principal plane, the output ray passes through (or appears to

have come from) the second focal point. The actual ray path

between input and output planes can again be found in

simple cases – for example, the path YY9 in the thick lens

shown in Figure 4.7(b). The intersection of the two principal

CHARACTERIZATION AND ANALYSIS 159

rays in the image space produces the image point that

corresponds to the original point on the object. If only the

back projections of the output principal rays appear to

intersect, this intersection point lies on a virtual image.

In the majority of applications of paraxial ray tracing, a

quick analysis of the system is desired. In this case, if all

lenses in the system are treated as thin lenses, the position of

the principal planes need not be calculated beforehand and

ray tracing becomes particularly easy. For each lens, the

position of the image of an object is obtained, and this image

then becomes the ‘‘object’’ for the next lens, and so on. For a

thin lens, a third principal ray is useful for determining the

image location. The ray from a point on the object that passes

through the center of the lens is not de viated by the lens.

The use of paraxial ray tracing to determine the size and

position of the real image produced by a convex lens, and

the virtual image produced by a concave lens are shown in

Figure 4.9. Figure 4.9(a) shows a converging lens; the input

Figure 4.9 Ray-tracing techniques for locating image and ray paths for:

(a) a converging thin lens; (b) a diverging thin lens. F ¼ focal point; C ¼ center

of lens. The principal rays and a general ray pencil are shown in each case.

160 OPTICAL SYSTEMS

principal ray parallel to the axis actually passes through the

focal point. Figure 4.9(b) shows a diverging lens; the above

ray

now emerges from the lens so as to appear to have come

from the focal point. More complex systems of lenses can

be analyzed the same way. Once the image location has

been determined by the use of the principal rays, the path of

any group of rays, a ray pencil, can be found. See, for

example, the cross-hatched ray pencils shown in Figure 4.9.

The

use of paraxial ray-tracing rules to analyze spher-

ical-mirror systems is similar to those described above,

except that the ray striking the center of the mirror in this

case reﬂects so that the angle of reﬂection equals the angle

of incidence. In all applications of ray tracing, a check on

whether this is being done correctly involves examining

the way in which a ray is bending at each surface. The

refraction (or reﬂection) relative to the local surface nor-

mal should be in the correct direction.

Imaging and Magniﬁcation. Imaging systems

include microscopes, telescopes, periscopes, endoscopes,

and cameras. They aim to reproduce at a particular plane in

the image space – the image plane – an exact replica in

terms of relative spatial luminous intensity distribution and

spectral content of an object located in the object plane.

Each point on the object is imaged to a unique point in the

image. The relative position and luminous intensity of

points in the image plane preserve these qualities from

their positions in the object plane. If the image is not a

faithful, scaled replica of the object, then the imaging

system suffers from aberrations.

In paraxial descriptions of an imaging system, often

called the Gaussian description of the system, the ray

transfer matrix from a point on the object to a point on

the image can be written as:



ð4:52Þ

For any ray angle of r9

leaving a point distant r

from the

axis on the object, the ray in the image plane must pass

through a point that is distant r

from the axis.

It is clear from Equation (4.52) that for this to be so, the

element B of

the ray transfer matrix must be zero. So:

¼ Ar

ð4:53Þ

The ratio of image height to object height is the linear

magniﬁcation m so:

m ¼A ¼r

ð4:54Þ

Note that if the image is inverted, m is negative. The angu-

lar magniﬁcation of the system is deﬁned as:



ð4:55Þ

so D ¼ m9.

If we use the focal length of the imaging system f ¼

–1/C, then the ray transfer matrix is:



m 0

1=fm



ð4:56Þ

If the media in the space where the object is located (the

object space) and the image space are the same then:

det



¼ 1 ð4:57Þ

which gives mm9 ¼ 1.

This is also a consequence of the conservation of bright-

ness in an optical system, which will be discussed later.

In Figure 4.9(a) the ratio of the height of the image, b to

the

height of the object a is called the magniﬁcation m.In

the case of a thin lens:

m ¼

¼

ð4:58Þ

Note that in Figure 4.9(a), b is

negative. In Figure 4.9(b), v

is negative, but b is positive. The ray transfer matrix M for

a complete description of the imaging systems in Figure

4.9 includes the entire system from object O to image I. So,

in Figure 4.9(a):

M ¼ðmatrix

for uniform medium of length vÞ

3ðmatrix for lensÞ

3ðmatrix for uniform medium of length uÞ

ð4:59Þ

Imaging and Nonimaging Optical Systems. The

techniques of optical-system analysis that we have

discussed so far will provide an approximate description

of simple systems. In many situations, however, a more

detailed analysis is needed. Additional parameters are also

introduced to characterize the system. More sophisticated

CHARACTERIZATION AND ANALYSIS 161

methods of analysis can be illustrated through a discussion

of imaging and nonimaging optical systems.

In any experimental setup that in v olv es the collection of

light from a source and its deli v ery to a light detection sys-

tem, the properties of the optical system between source and

detector should be optimized. This opt imization will take

different forms depending on the application. F or example,

in an experiment in which a weak ﬂuorescent signal from a

liquid in a curvette is to be detected, it is generally the aim to

maximize the amount of collected ﬂuorescence and deli v er

this light to the active surface of the detector. This applica-

tion does not require an imaging optical system, although an

imaging system is often quite satisfactory. On the other

hand, if an image of some object is being delivered to a

CCD camera, then an imaging optical system is required.

4.2.3 Nonimaging Light Collectors

The properties of a nonimaging optical system can be

described schematically with the aid of Figure 4.10. Light

that

enters the front aperture of the system within some

angular range, will leave the system through the exit aper-

ture. In such an arrangement, the brightness of the light

leaving the exit aperture cannot exceed the brightness of

the light entering the entrance aperture. The brightness of

an emitting object is measured in units of Wm

2

per stera-

dian.InFigure 4.10, if the brightness of the radiation

entering

the apertive is B

(W m

2

1

) then the power

entering S

from the source is:

¼pB

ð4:60Þ

where the angular range of the enetering rays is h

. Assum-

ing that R

>>S

, this angular range is h

’ 1=R

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

,or

’ S

=pR

. If all the power entering S

leaves through

, then the brightness of the emerging radiation is:

’

ð4:61Þ

where h

is the angular spread of emerging rays. So:

ð4:62Þ

and if B

< B



ﬃﬃﬃﬃﬃ

ð4:63Þ

Practical examples of these devices are given in Section

4.3.3.

4.2.4 Imaging Systems

Generalized Imaging Systems. In a generalized

imaging system, light from an object, located in the

object plane, passes through the system until it reaches

the image plane. In an ideal imaging system all the light

rays that leave a point on the object arrive at a single point

in the imaging plane. Furthermore, the locations of points

in the image plane are such as to preserve the scaling of the

image relative to the object. The image may be magniﬁed

or demagniﬁed, but it should not be distorted.

A type of imaging called aplanatic imaging occurs

when rays parallel to the axis produce a sharp image, inde-

pendent of their distance from the axis. More speciﬁcally,

if the angle of an input ray with the axis is h

and the output

angle with the axis h

, then an aplanatic system satisﬁes the

sine condition, namely:

sin h

¼ constant ð4:64Þ

for rays at all distances from the axis that can pass through the

system. Stigmatic imaging is sharp imaging of a point object

to a point image. An object point that is imaged to an image

point are together called conjugate points.

The Numerical Aperture. If an optical system is

illuminated by a point source on its axis, then the amount

of light collected by the system depends on the angle that

an effective aperture, called the entrance pupil, subtends at

Figure 4.10 Generalized diagram of a nonimaging system.

Light from the source enters the system though the aperture

over an angular range deﬁned by h

and leaves through

aperture S

over a range of angles deﬁned by h

162 OPTICAL SYSTEMS

the source. This concept will be discussed further in the

next section. In Figure 4.11 this angle is deﬁned by:

sin h ¼

ð4:65Þ

the numerical aperture of the system is:

NA ¼ n sin h ð4:66Þ

where n is the refractive index of the object space (which is

generally 1, but could be higher – for example in micro-

scopy, when an oil-immersion objective lens is used). Now,

a good imaging system obeys the sine condition, which

relates the angles subtended by the exit and entrance pupils

and the magniﬁcation m by:

m ¼

n sin h

sin h

ð4:67Þ

where the primed quantities refer to the image space. The

numerical aperture in the image space is:

ðNAÞ

¼ n

sinh

ð4:68Þ

The entrance pupil plays an important geometrical role

in determining the amount of light from an object (or light

source) that can enter and pass through an optical system.

For example, for an entrance pupil diameter (EPD) of D

located a distance d

from a point source of light, the

fraction of the light emitted by the source that will pass

through the system is:

F¼

ð1  cos hÞ¼

1  1 þ



1=2

, ð4:69Þ

where h is the angle shown in Figure 4.11.ForD << d

Equation (4.69) reduces to:

F¼

16d

ð4:70Þ

For a lens, the ratio of focal length to EPD is called the

f/number (f/#) of the lens. An f/1 lens has a ratio of its focal

length to aperture (the open lens diameter) equal to unity. For

a point source at the focal point of such a lens, F¼0 :067.

Apertures, Stops, and Pupils. Apertures controlthe

ray trajectories that can pass through an optical system. The

aperture stop is the aperture within the system that limits

the angular spread, or diameter, of a cone of rays from an

axial point on the object, which can pass through the

system. Another aperture in the system may restrict the

size or angular extent of an object that the system can

image. Awareness of the position and size of these stops

in an optical design is crucial in determining the light-

gathering power of the system, and its ability to deliver

light to an image or detector. The role of the aperture and

ﬁeld stop can be illustrated with Figure 4.12, which shows a

sin

gle lens being used to image light from a distant object.

The circular aperture behind the lens clearly limits the

diameter of a bundle of rays from an axial point on the

object and is clearly the aperture stop. The second stop,

placed in the image plane, clearly controls the maximum

angle at which rays from off-axis points on the object can

pass through the system. This is the ﬁeld stop in this case.

Whether a given aperture in an optical system is an aper-

ture stop or a ﬁeld stop is not always so easy to determine

as was the case in Figure 4.12. Figure 4.13 shows a three-

element

optical system, which actually constitutes what is

called a Gullstrand opthalmoscope

. The ﬁrst lens closest

to the object, called the objective lens, produces a real

inverted image, which is then re-inverted by the erector

lens, to form an image at the focal point of the eyepiece

lens. Aperture A is the aperture stop, and clearly restricts

the angular range of rays from an axial point on the object

that can pass through the system. Aperture B restricts from

what height on the object rays can originate, and still pass

through the system. This aperture is acting as a ﬁeld stop.

The entrance pupil is the image of the aperture stop

produced by all the elements of the system between the

aperture stop and the object. In Figure 4.13 the two

Figure 4.11 Single lens optical system to illustrate the

concepts of numerical aperture and entrance pupil.

CHARACTERIZATION AND ANALYSIS 163

elements producing the image are the erector lens and objec-

tiv e lens. The exit pupil is the image of the aperture stop

produced by all the elements between the aperture stop and

the image, which in Figure 4.13 is just the eye lens. The size

and

location of the entrance and exit pupils determines the

light-gathering and light-delivery properties of the system.

For example, if the entrance pupil has diameter D, and lies a

distance L from a point source of radiant power P (watts)

then the po wer entering the entrance pupil is:

ð1  cos hÞ, ð4:71Þ

where tan h ¼ D=2L:

For a point source that is far from the entrance pupil this

result becomes:

16L

: ð4:72Þ

The solid angle subtended by the entrance pupil in this

case is Dx ¼ D

=4L

The light that leaves the system can be characterized by

the total power that leaves the exit pupil, and the angular

range of the rays that leave the exit pupil.

Somewhere in an imaging system there is always an aper-

tur e stop. This may be an actual aperture in an opaque thin

screen placed on the system axis, or it may be the clear

aperture of a lens or mirror in the system. In either case the

aperture stop limits the range of rays that can pass through the

system. This concept is illustrated in Figure 4.14.Arayof

light

such as A, that enters the system and just passes the edge

of the aperture stop, is called a mar ginal ray.AraysuchasB,

that enters the system and passes through the center of the

aperture stop, is called a chief ray . An aperture stop will

always allow some light from every point on an object to

reach the corresponding point on the image. If the amount

of light from the edge of the object (say) that reaches the

corresponding point or the object is sev erely reduced this is

referred to as vignetting.

In Figure 4.13, a ray from an off-axis point on the object

that

passes through the center of the aperture stop is called the

principal ray of the cone of light from the off-axis point.

The ray that enters the system half-way between the high-

est and lowest rays of an oblique beam is called the chief

Figure 4.12 Single lens imaging system to illustrate the

concepts of aperture stop, ﬁeld stop, and entrance and exit

pupils.

Figure 4.13 Three-lens imaging system showing an aperture stop, a ﬁeld stop, and

the location of the entrance and exit pupils.

164 OPTICAL SYSTEMS

ray of the beam. In the absence of aberrations, the principal

ray and chief ray are the same, and both pass through the

center of the entrance pupil and aperture stop.

Vignetting. In our previous discussion we have

simpliﬁed the actual performance of a real optical system,

because for oblique rays passing through the system the

roles of aperture and ﬁeld stops become intertwined.

This can be illustrated with Figure 4.15, which shows a

simple

compound lens in which the apertures of the lenses

themselves restrict the rays that can pass through the sys-

tem. A family of oblique rays no longer ﬁlls the aperture

stop, because the following lens is acting as a stop. This is

called vignetting. In imaging systems it does not actually

remove points of the object from the image but parts of the

image that depend for their illumination on oblique rays

(especially at large angles) become less bright. Vignetting

is often deliberately allowed to occur in an imaging system

so as to remove certain rays from the system that would

otherwise suffer severe aberration.

Figure 4.14 Aperture stop in front of a single lens showing

vignetting of a family of rays from a distant off-axis point

passing through the lens.

Figure 4.15 Two-lens imaging system showing aperture stop, principal and marginal

rays, and vignetted rays.

CHARACTERIZATION AND ANALYSIS 165

4.2.5 Exact Ray Tracing and Aberrations

If an imaging system is built with a series of lenses and/or

mirrors, then there are inevitably various aberrations. For

refraction at a spherical surface this results because, for

angles of incidence and refraction h

, h

, respectively,

when light travels from a medium with refractive index

to one of refractive index n

sin h

¼n

sin h

ð4:73Þ

The paraxial approximation, which lacks aberrations,

fails because h

6¼ sin h

, whereas, in reality, sin h ¼

h  h

=3! þ h

=5!  h

=7!. The overall effect of aberra-

tions can be greatly reduced, and some types of aberrations

can be eliminated, by using several spherical surfaces, or in

some situations by using an appropriate aspheric surface, a

surface that is not part of a sphere but which is generally

describable in terms of some other conic function or power

series of the coordinates.

Analysis of imaging systems is most conv eniently carried

out using exact ray tracing techniques. In exact ray tracing the

small-angle approximation, Equation (4.8),isnotmadeand

Snell’

s Law is solved e xactly for each ray , at each interface.

By injecting many light rays into the system over some

deﬁning aperture or range of angles the performance of the

system in imaging, focusing, light collection, or light delivery

can be ev aluated precisely. These days this procedure is car-

ried out with optical design software. The most notable soft-

ware packages in this regard are Code V

, Zemax

,Oslo

Solstis

and Optikwerk

. The wide avai lability of these

software tools, and the essentially generic way in which they

are used, makes a brief description of ho w they work and are

used worthwhile. Just as an electronic circuit designer would

be likely to e v aluate a circuit with an analog design tool such

as PSpice, or a digital design tool such as Cadence, Magic, or

Xilinx, an optical designer can ultimately save time, and

avoid mistakes, by numerical simulation of a design.

We will illustrate the use of numerical ray tracing using

the set up procedures appropriate to Code V and with a

speciﬁc example: a double Gauss lens used for imaging.

The various optical elements that make up a double Gauss

lens are sho wn in Figure 4.16. For Code V analysis, the axial

position,

curvature, material, and aperture size (radius of

each surface perpendicular to the axis) must be speciﬁed

in an optical table showninthiscaseasTable 4.2.Note

the

entries that are speciﬁed in each column.

Figure 4.16 Double Gauss lens.

166 OPTICAL SYSTEMS

Table 4.2 Optical table for Code V analysis

Double Gauss – U.S. Patent 2, 532, 751

RDY THI RMD GLA CCY THC GLC

> OBJ: INFINITY INFINITY 100 100

1: 65.81739 8.746658 BSM24_OHARA 0 100

2: 179.17158 9.100796 0 0

3: 36.96542 12.424230 SK1_SCHOTT 0 100

4: INFINITY 3.776966 F15_SCHOTT 100 100

5: 24.34641 15.135377 0 0

STO: INFINITY 12.869768 100 0

7: 27.68891 3.776966 F15_SCHOTT 0 100

8: INFINITY 10.833928 SK16_SCHOTT 100 100

9: 37.46023 0.822290 0 0

10: 156.92645 6.858175 SK16_SCHOTT 0 100

11: 73.91040 63.268743 0 PIM

IMG: INFINITY 0.279291 100 0

SPECIFICATION DATA

EPD 50.00000

DIM MM

WL 656.30 587.60 486.10

REF 2

WTW 1 1 1

XAN 0.00000 0.00000 0.00000

YAN 0.00000 10.00000 14.00000

VUY 0.00000 0.20000 0.40000

VLY 0.00000 0.30000 0.40000

REFRACTIVE INDICES

GLASS CODE 656.30 587.60 486.10

BSM24_OHARA 1.614254 1.617644 1.625478

SK1_SCHOTT 1.606991 1.610248 1.617756

F15_SCHOTT 1.600935 1.605648 1.616951

SK16_SCHOTT 1.617271 1.620408 1.627559

SOLVES

PIM

NO Pickups deﬁned in system

INFINITE CONJUGATES

EFL 99.9866

EFL 63.2687

FFL 17.7398

FNO 1.9997

IMG DIS 62.9895

OAL 84.3452

PARAXIAL IMAGE

HT 24.9295

ANG 14.0000

ENTRANCE PUPIL

DIA 50.0000

THI 68.3242

EXIT PUPIL

DIA 58.0886

THI 52.8928

CHARACTERIZATION AND ANALYSIS 167

With ray tracing software the various parameters of this

lens system can be simultaneously optimized so as to pro-

duce the sharpest possible image of an object.

For the double Gauss lens, for example, th e curvatures

of the various surfaces, their spacings, and the type of

glass used for each element can be simultaneously var-

ied. In pr actice, various constr aints must be included in

this process: lens elements should not be too th ick or too

thin, and the glasses chosen must be available. The var-

iable paramete rs for a glass are its refractive index n and

its dispersion dn/dk, both of which vary with wave-

length.

The dispersion is frequently characterized by the Abbe V

number, which provides a relative measure of dispersion:

V ¼

 1

 n

ð4:74Þ

where the refractive index n is speciﬁed at the three

wavelengths d (the helium d line at 587.6 nm), F (the

hydrogen F line at 486.1 nm), and C (the hydrogen C line

at 656.3 nm). Some of the standard wavelengths that are

used in optical design are listed in Table 4.3. The different

glasses

that are available from a manufacturer are gener-

ally plotted on a glass chart, which plots (n

– 1) against V.

Figure 4.17 shows such a chart for glasses available from

Schott.

Other major suppliers of optical glass are Corning,

Hoya, and Ohara.

Two old classiﬁcations of glass into crown and ﬂint

glasses can be related to the glass chart. Crown glasses

are glasses with a V value greater than 55 if n

< 1.6 and

V >50ifn

> 1.6. The ﬂint glasses have V values below

these limits. The rare-earth glasses contain rare-earths

instead of SiO

, which is the primary constituent of crown

and ﬂint glasses.

Spot Diagram. If very many rays are launched from

a point on the objec t so as to cover the e ntrance pupil

of the system, the resulting p attern of ray intersections

with the image plane is called the spot diagram.A

tight spot diagram indicates t hat the effects of several

aberrations, notably spherical, astigmatism, coma, and

curvature of ﬁeld have been markedly reduced. It must

be remembered that this does not imply that the

aberrations themselves have necessarily been

eliminated, but that their effects have been reduced in

the situation examined. A tighter spot diagram can

always be produced by re ducing th e siz e of the

entrance pupil.

Figure 4.18 shows s uch a spot

diagram for a double Gauss lens being operated with a

relatively large entrance pupil.

Chromatic Aberrations. Because, in general, the

index of refraction increases with decreasing wavelength,

the focal length of a singlet lens

will, for example, be

shorter for blue light than it is for red light. This effect

leads to imperfect imaging, so that in white light

illumination both axial and off-axis object points will be

imaged, not as bright points, but as regions that show

blurring from red to blue. For axial object points this

blurring is spherically symmetric and results from the

image being closer to the lens for blue light than for red

light. This is simple chromatic aberration. For off-axis

object points, the magniﬁcation of the system varies with

wavelength, leading to what is called lateral color or

transverse chromatic aberration.

Table 4.3 Standard wavelengths used in optical design

Wavelength (nm) Designation Source

312.59 mercury

334.15 mercury

365.01 ‘ mercury

404.66 h mercury

435.83 g mercury

479.99 F9 mercury

486.13 F hydrogen

546.07 e mercury

587.56 d helium

589.29 D sodium (doublet)

632.80 He-Ne laser

643.85 c9 cadmium

656.27 c hydrogen

706.52 r helium

852.11 s cesium

1013.98 t mercury

1060.00 neodymium laser

1529.58 mercury

1970.09 mercury

2325.42 mercury

168 OPTICAL SYSTEMS

Chromatic aberration can be corrected for two colors

(generally red and blue) and the imaging of axial points.

Such lenses take the form of an achromatic doublet where

a doublet lens is generally fabricated from a positive (con-

verging) crown glass element and a negative (diverging)

ﬂint glass element.

If a compound lens is designed to remove c hromatic

aberration at three wavelengths it is called an apo-

chromat and if correcting for four wavelengths a

supe rachromat.

Achromatic doublets, because they have at least

three spherical surfaces (or four in an air-spaced

achromat), can also better correct for other aberrations

than a singlet lens. Such lenses are available in a

range of apertures an d focal lengths from many manu-

facturers.

Geometrical Aberrations. In a perfect imaging

system, all ra ys from a poin t on the objec t would

pass through an identical point on the image and there

Figure 4.17 The glass chart for glasses available from Schott.

CHARACTERIZATION AND ANALYSIS 169

would be a linear relation between the coordina tes of

points on t he image and corresponding points on th e

object.

For an axially symmetric system we can arbitrarily

choose the object point in Figure 4.19 to be at the

(x, y) p oint (0, h) i n the object. We take the polar coor-

dinates of a ray fro m this point to a point P in the

entrance pupil as (q, h). In the general case this ray will

intersect the image plane at point I9 with coordinates in

the image plan e ( x9, y9). The aberrations Dx9, Dy9 are the

displacements of (x9, y9) from the paraxial image point

I(x9

, y9

) for which there is a linear transformation from

the coordinates of the point on the object. The lowest-

order aberration terms contain terms in either h

, h

q,or

and are referred to as third-order aberrations .

Although there a re differences in terminology concern-

ing these terms in the literature we can write (following

Born and Wolf

)

¼ Bq

cos h  Fhq

ð2 þ cos ZhÞ

þð2C þ DÞh

q cos h  Eh

ð4:75Þ

¼ Bq

sin h  Fhq

sin 2h þ Dh

q sin h ð4: 76Þ

The coefﬁcients B, C, D, E, and F characterize the ﬁve

primary or Seidel aberrations. Their magnitude in any

given optical design can be calculated and visualized with

ray tracing optical software.

Spherical Aberration B 6¼0. When all the

coefﬁc ients in Equatio ns (4.75) and ( 4.76) are zero

except for B, the remaining effect is spherical

aberration. This aberration is strikingly observed in the

imaging of an axial point source, which will be imaged to

a circular bright region whose radius reveals the extent of

the aberration. For an axial point h ¼ 0 and from

Equations (4.75) and (4.76), Dy9 ¼ Bq

cos h, Dx9 ¼

sin h, which can be written as:

Dr ¼ Bq

ð4:77Þ

For focusing of parallel light the ‘‘best-form’’ singlet lens for

minimum spherical aberration is close to conv e x-plane (with

the con v ex surface towards the incoming parallel light).

Coma F 6¼ 0. Coma is the aberration in which the image

of an off-axis point varies for rays passing through

different regions of the entrance pupil. It is difﬁcult to

produce a lens where coma alone can be observed. The

spot diagram in Figure 4.18 shows the characteristic

‘‘ﬂaring’’ of the spot pattern, like a comet tail, which

gives the aberration its name. Coma can be controlled by

varying the curvatures of surfaces in the system.

Astigmatism C 6¼ 0. All the aberrations disc ussed so

far are defects in the imaging of meridional rays,thatis,

rays in the plane containing the axis of the lens and the

line from the object point through the center of the lens.

The imaging is different for sagittal rays, that is, ra ys in

the sagittal plane, which is perpendicular to the

meridional plane, as illustrated in Figure 4.20.The

Figure 4.18 Spot diagrams for a double Gauss

lens showing the spot diagrams for families of rays

entering the lens at angles of 0°,10°, and 14° – the

ﬁeld angles.

170 OPTICAL SYSTEMS

Figure 4.19 Diagram of a generalized imaging system used to discuss aberrations.

Figure 4.20 Illustrating astigmatism. Meridional rays PA and PA9 are imaged at P9

, sagittal

rays PB and PB9 are imaged at P9

. (After A. C. Hardy and F. H. Perrin, Principles of Optics,

McGraw-Hill, New York, 1932; by permission of McGraw-Hill Book Company, Inc.).

CHARACTERIZATION AND ANALYSIS 171

resulting aberration is called astigmatism.Itcanbe

controlled by lens curvature and refractive-index

variations a nd by the use of apertures to restric t the

range of angles and off-axis distances at which rays

can traverse the lens.

Distortion, E 6¼ 0. In distortion, the magniﬁcation

varies across the image plane. The height of the image

above the axis relative to the height of the object varies

across the image.

Each object point appear s as a point in the image, and

the images of object points on a plane orthogo nal to the

axis are also on such a plane. The magniﬁcation of an

object line segment may, however, vary with its distance

from the axis. This is called dis tortion . It takes two com-

mon fo r ms: pincushion and barrel distortion, as illus-

trated in Figure 4.21. Distortion is sensitive to the lens

shape

and spacing, and to the size and position of aper-

tures in the system – called stops.

For further details of aberrations and how to deal with

them, we refer the reader to specialized texts on optics

(especially lens design), such as those by Born and

Wolf,

Ditchburn,

Levi,

Smith,

25,26

Shannon,

and

Laikin.

Curvature of Field, D 6¼ 0. In this aberration, the

image of a plane object perpendicular to the axis is sharp

over a curved surface in the image space.

Modulation Transfer Function. A common way of

characterizing the performance of an imaging system is

through its modulation transfer function or MTF. This

refers to the a bility of the system to replicate in the

image, periodic features in the object. An optical test

pattern used to show this consists of a series of white

and black bands. These bands wi ll be smeared out in

the image to a greater or lesser extent be cause of

aberrations, and ultimately, if geometrical aberrations

are absent, by diffraction.

The relative brightness of the object and image will

appear schematically as shown in Figure 4.22.Wecan

chara

cterize the visibility, contrast or modulation of the

image as:

visibility ¼

max min

max þ min

ð4:78Þ

Figure 4.21 (a) ‘‘Pincushion’’ distortion;

(b) ‘‘barrel’’ distortion.

172 OPTICAL SYSTEMS

If the visibility is plotted versus the number of lines per

millimeter in the object in this case, this shows the mod-

ulation transfer function. Figure 4.23 shows an example for

the

double Gauss lens system shown in Figure 4.16. The

MTF

is ultimately limited by diffraction. In this case, for a

pattern with m lines per millimeter:

MTFðmÞ¼

ð2/  sin 2/Þð4:79Þ

where

/ ¼ cos

1

2NA



ð4:80Þ

In Equation (4.80) k

is measured in mm and NA is the

numerical aperture of the system.

A quantity, closely related to the MTF, for charactering

MTF, and also the focusing of a light beam, or laser beam,

is the Strehl ratio. The Strehl ratio is the ratio of the

Figure 4.22 (a) An object with sharp contrast between bright and dark bands;

(b) the corresponding image brightness variation for differing degrees of

modulation.

CHARACTERIZATION AND ANALYSIS 173

illumination at the center of a focused or circular image to

the illumination of an equivalent unaberrated image. The

interested reader can see a more detailed discussion in

Smith.

4.2.6 The Use of Impedances in Optics

The method of impedances is the easiest way to calculate

the fraction of incident intensity transmitted and reﬂected

in an optical system. It is also the easiest way to follow the

changes in polarization state that result when light passes

through an optical system.

As we have seen in Section 4.1, the impedance of a

plane

wave traveling in a medium of relative permeability

, and dielectric constant e

is:

Z ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

¼ Z

ﬃﬃﬃﬃﬃ

ð4:81Þ

If l

¼ 1, as is usually the case for optical media, the

impedance can be written as:

Z ¼ Z

=n ð4:82Þ

This impedance relates the transverse E and H ﬁelds of the

wave:

Z ¼

ð4:83Þ

When a plane wave crosses a planar boundary between

two different media, the components of both E and H

parallel to the boundary have to be continuous across that

boundary. Figure 4.24(a) illustrates a plane wave polarized

the plane of incidence striking a planar boundary

between two media of refractive indices n

and n

. In terms

of the magnitudes of the vectors involved:

cos h

þ E

cos h

¼ E

cos h

ð4:84Þ

 H

¼ H

ð4:85Þ

Equation (4.82) can be written as:



ð4:86Þ

Figure 4.23 Modulation transfer function (MTF) for a double Gauss lens.

The MTF for 0°,10°, and 14° ﬁelds in both the tangential and radial directions

are shown, and also the diffraction limit of an aberration-free system.

174 OPTICAL SYSTEMS

Figure 4.24 Reﬂection and refraction at a planar boundary between two different

dielectric media: (a) wave polarized in the plane of incidence (P-polarization);

(b) wave polarized perpendicular to the plane of incidence (S-polarization).

CHARACTERIZATION AND ANALYSIS 175

It is easy to eliminate E

between Equations (4.84) and

(4.86) to give:

q ¼

cos h

 Z

cos h

þ Z

cos h

ð4:87Þ

where q is the reﬂection coefﬁcient of the surface. The

fraction of the incident energy reﬂected from the surface

is called the reﬂectance, R ¼ q

. Similarly, the transmis-

sion coefﬁcient of the boundary is:

s ¼

cos h

þ Z

cos h

ð4:88Þ

By a similar treatment applied to the geometry shown in

Figure 4.24(b), it can be shown that for a plane wave

polarized

perpendicular to the plane of incidence:

q ¼

sec h

 Z

sec h

þ Z

cos h

ð4:89Þ

s ¼

2Z sec h

sec h

þ Z

sec h

ð4:90Þ

If the effective impedance for a plane wave polarized in

the plane of incidence (P-polarization)

and incident on a

boundary at angle h is deﬁned as:

¼ Z sec h ð4:91Þ

and for a wave polarized perpendicular to the plane of

incidence (S-polarization)

as:

¼ Z sec h ð4:92Þ

then a universal pair of formulae for q and s results:

q ¼

 Z

þ Z

ð4:93Þ

s ¼

þ Z

ð4:94Þ

It will be apparent from an inspection of Figure 4.24 that

Z9 i

s just the ratio of the electric-ﬁeld component parallel to

the boundary and the magnetic-ﬁeld component parallel to

the boundary. For reﬂection from an ideal mirror, Z9

¼ 0.

In normal incidence, Equations (4.87) and (4.89)

become

identical and can be written as:

q ¼

 Z

þ Z

 n

þ n

ð4:95Þ

Note that there is a change of phase of p in the reﬂected

ﬁeld relative to the incident ﬁeld when n

> n

Since intensity } (electric ﬁeld)

, the fraction of the

incident energy that is reﬂected is:

R ¼ q

 n



ð4:96Þ

R increases with the index mismatch between the two

media, as shown in Figure 4.25. If there is no absorption

energy at the boundary, the fraction of energy trans-

mitted, called the transmittance,is

T ¼ 1  R ¼

ðn

þ n

ð4:97Þ

Note that because the media on the two sides of the

boundary are different, T 6¼ | s |

Figure 4.25 Reﬂection loss per surface for normal inci-

dence as a function of refractive index.

176 OPTICAL SYSTEMS

Reﬂectance for Waves Incident on an

Interface at Oblique Angles.

If the wave is not

incident normally, it must be decomposed into two

linearly polarized components, one polarized in the plane

of incidence, and the other polarized perpendicular to the

plane of incidence.

For example, consider a plane-polarized wave incident on

an air glass (n ¼ 1.5) interface at an angle of incidence of

30°, with a polarization state exactly intermediate between

the S-polarization and the P-polarization. The angle of

refraction at the boundary is found from Snell’s law:

sin h

sin 308

1:5

ð4:98Þ

and so h

¼ 19.47°.

The effective impedance of the P-component in the air

is:

¼ 376:7 cos h

¼ 326:23 X ð4:99Þ

and in the glass:

376:7

1:5

cos h

¼ 236:77X ð4:100Þ

Thus, from Equation (4.87), the reﬂection coefﬁcient for

the P-component

is:

236:77  326:33

236:77 þ 326:23

¼0:159 ð4:101Þ

The fraction of the intensity associated with the P-compo-

nent that is reﬂected is q

¼ 0.0253.

For the S-component of the input wave:

376:7

cos h

¼ 434:98X ð4:102Þ

376:7

1:5 cos h

¼ 266:37X

266:37  434:98

266:37 þ 434:98

¼0:240

ð4:103Þ

The fraction of the intensity associated with the S-

polarization component that is reﬂected is q

0.0578. Sin ce the input wave conta ins equ al amo unts

of S-andP-polarization, the overall reﬂectance in this

case is:

R ¼ <q

¼ 0:0416 ’ 4% ð4:104Þ

Note that the reﬂected wave now contains more S-

polarization than P, so the polarization state of the

reﬂected wave has been changed – a phenomenon that

will be discussed further in Section 4.3.6.

Brewster’s Angle. Returning to Equation (4.87),it

might be asked whether the reﬂectance is ever zero. It is

clear that q will be zero if:

cos h

¼ n

cos h

ð4:105Þ

which, from Snell’s law [Equation (4.6)], gives:

cos h

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 



sin

ð4:106Þ

giving the solution:

¼ h

¼ arcsin

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ n

¼ arctan

ð4:107Þ

The angle h

is called Brewster’s angle. A wave polar-

ized in the plane of incidence and incident on a boundary at

this angle is totally transmitted. This allows the design of

low-reﬂection-loss windows in laser systems, as will be

seen in Section 4.6.2.IfEquation (4.89) is inspected care-

fully

, it will be seen that there is no angle of incidence that

yields zero reﬂection for a wave polarized perpendicular to

the plane of incidence.

Transformation of Impedance through

Multilayer Optical Systems.

The impedance

concept allows the reﬂection and transmission

characteristics of multilayer optical systems to be

evaluated very simply. If the incident light is incoherent

(a concept discussed in more detail later in Section 4.5.1),

then

the overall transmission of a multilayer structure

is just the product of the transmittances of its various

interfaces. For example, an air–glass interface transmits

CHARACTERIZATION AND ANALYSIS 177

about 96% of the light in normal incidence. The

transmittance of a parallel-sided slab is 0.96 3 0.96 ¼

92%. This simple result ignores the possibility of

interference effects between reﬂected and transmitted

waves at the two faces of the slab. If the faces of the

slab are very ﬂat and parallel, and if the light is

coherent, such effects cannot be ignored. In this case, the

method of transformed impedances is useful.

Consider the three-layer structure shown in Figure

4.26(a). The path of a ray of light through the structure

is shown. The angles h

, h

, and h

can be calculated from

Snell’s law. As an example, consider a wave polarized in

the plane of incidence. The effective impedances of media

1, 2, and 3 are

¼ Z

cos h

¼ Z

cos h

¼ Z

cos h

ð4:108Þ

It can be shown that the reﬂection coefﬁcient of the

structure is exactly the same as for the equivalent structure

in Figure 4.26(b) in normal incidence, where the effective

thickness of layer 2 is now:

¼ d cos h

ð4:109Þ

The reﬂection coefﬁcient of the structure can be calcu-

lated from its equivalent structure using the transformed

impedance concept.

15,29

The transformed impedance of medium 3 at the boun-

dary between media 1 and 2 is:

¼ Z

cos k

þ iZ

sin k

cos k

þ iZ

sin k



ð4:110Þ

where k

¼ 2p/k

¼ 2pn

. The reﬂection coefﬁcient of

the whole structure is now just:

q ¼

 Z

þ Z

ð4:111Þ

the reﬂectance of the whole structure is R ¼ |q|

, and its

transmittance is:

T ¼ 1  R ð4:112Þ

In a structure with more layers, the transformed impe-

dance formula [Equation (4.108)] can be used sequentially,

starting at the last optical surface and working back to

the ﬁrst. More examples of the use of the technique of

transformation of impedance will be given in Sections

4.3.1 and 4.3.7.

Optical System Design Software. As well as the

ray tracing optical design programs mentioned earlier, such

as Code V, there is a broad range of other software available

Figure 4.26 (a) Wave polarized in the plane of

incidence passing through a dielectric slab of

thickness d and impedance Z

separating two semi-

inﬁnite media of impedances Z

and Z

, respectively;

(b) equivalent structure for normal incidence.

178 OPTICAL SYSTEMS

commercially for optical system design including: laser

system design (GLAD, PARAXIA, ASC, and LASFIT);

atmospheric optical properties and sensors (ONTAR);

optical system solid modeling (LightTools, TracePro);

projection systems, ﬁber optics, and complex sources

(ASAP); beam propagation for integrated and ﬁber optics

(BeamProp); vector diffraction grating analysis software

and simulation (GSOLVER); optical thin-ﬁlm and coating

design, material analysis, ellipsometry, spectrophotometry

and thin-ﬁlm metrology; [Film Wizard, FilmSpectrum,

TFCalc, Thin Film Design Package (Thin Film Center)];

and analysis of laser beam propagation (FRESNEL).

4.2.7 Gaussian Beams

Gaussian beams are propagating-wave solutions of Max-

well’s equations that are restricted in lateral extent even in

free space. They do not need any beam-conﬁning reﬂective

planes, as do the conﬁned electromagnetic-ﬁeld modes of

waveguides.

Lasers frequently emit narrow beams of light

that are very close in character to ideal Gaussian beams.

The ﬁeld components of a plane transverse electromag-

netic wave of angular frequency x propagating in the

z-direction are of the form:

V ¼ V

iðxtkzÞ

ð4:113Þ

where V

is a constant. A Gaussian beam is of the form:

V ¼ Wðx, y, zÞ e

iðxtkzÞ

¼ Uðx, y , zÞe

ixt

ð4:114Þ

where, for example, for a particular value of z, W(x, y, z)

gives the spatial variation of the ﬁelds in the xy plane.



W gives the relative intensity distribution in the plane;

for a Gaussian beam this gives a localized intensity pattern.

The various Gaussian-beam solutions of Maxwell’s equa-

tions are denoted as TEM

modes; a detailed discussion

of their properties is given by Kogelnik and Li.

The out-

put beam from an ideal laser is generally a TEM mode or a

combination of TEM modes. Many laser systems operate

in the fundamental Gaussian mode, denoted TEM

. This

is the only mode that will be considered in detail here.

For the TEM

mode, W(x, y, z) has the form:

Wðx,y,zÞ¼exp iPðzÞþ

2qðzÞ



ð4:115Þ

where P(z)isaphase factor, q(z) is called the beam param-

eter, k equals 2p/k, and r

equals x

+ y

. The beam param-

eter, q(z), is usually written in terms of the phase-front

curvature of the beam R(z), and its spot size, w(z), as:



ð4:116Þ

q and P obey the following relations:

¼ 1 ð4:117Þ

¼

ð4:118Þ

For a particular value of z, the intensity variation in the

xy plane (the mode pattern) is, from Equation (4.115):



W ¼ exp

ikr

qðzÞ





ðzÞ



ð4:119Þ

which, from Equation (4.116) gives:



W ¼ e

2r

ð4:120Þ

Thus, w(z) is the distance from the axis of the beam (x ¼

y ¼ 0) where the intensity has fallen to 1/e

of its axial

value and the ﬁelds to 1/e of their axial magnitude. The

radial distribution of both intensity and ﬁeld strength of

the TEM

mode is Gaussian, as shown in Figure 4.27.

Clearly, from Equation (4.117):

q ¼ q

þ z ð4:121Þ

where q

is the value of the beam parameter at z ¼ 0. From

Equation (4.118):

PðzÞ¼

ilnq þ constant

¼ilnðq

þ zÞþconstant ð4:122Þ

Writing the constant in Equation (4.122) as h þ il

the full spatial variation of the Gaussian beam is:

U ¼ exp i kz iln 1 þ



þ h



RðzÞ





ð4:123Þ

CHARACTERIZATION AND ANALYSIS 179

The phase angle h is usually set equal to zero. In the plane

z ¼ 0:

U ¼ exp i

Rð0Þ



pwð0Þ

!()

ð4:124Þ

The surface of constant phase at this point is deﬁned by the

equation:

2Rð0Þ

¼ constant ð4:125Þ

If the constant is taken to be zero and R(0) inﬁnite, then r

becomes indeterminate and the surface of constant phase is

the plane z ¼ 0. In this case, w(0) can have its minimum

value anywhere. This minimum value is called the mini-

mum spot size w

, and the plane z ¼ 0 is called the beam

waist. At the beam waist:

ik

ð4:126Þ

Using Equations (4.116) and (4.121), for any arbitrary

alue of z:

ðzÞ¼w

1 þ



ð4:127Þ

The radius of curvature of the phase front at this point is:

RðzÞ¼z 1 þ



ð4:128Þ

From Equation (4.127) it can be seen that the Gaussian

am expands in both the positive and negative z-directions

from its beam waist along a hyperbola that has asymptotes

inclined to the axis at an angle:

beam

¼ arctan

ð4:129Þ

as illustrated in Figure 4.27(b). The surfaces of constant

phase

of the Gaussian beam are, in reality, parabolic. For

<< z

(which is generally true, except close to the beam

waist), they are spherical surfaces with the radius of cur-

vature R(z). Although they will not be discussed further

here, the higher-order Gaussian beams, denoted TEM

are also characterized by spot sizes and radii of curvature

that are identical to those of the TEM

mode and obey

Equations (4.127) and (4.128).

Focusing a Laser beam with a Lens. A lens can

be used to focus a laser beam to a small spot, or systems of

lenses may be used to expand the beam and recollimate it

(i.e., minimize the beam divergence). In such an

application a thin lens will not alter the transverse

intensity pattern of the beam at the lens, but it will alter

its radius of curvature. Far enough from the beam waist,

the radius of curvature of a Gaussian beam behaves exactly

Figure 4.27 (a) Radial amplitude variation of the

TEM

Gaussian beam; (b) contour of a Gaussian

beam.

180 OPTICAL SYSTEMS

as a true spherical wave, since, for z >> px

=k, Equation

(4.128) becomes:

RðzÞ¼z ð4:130Þ

w, when a spherical wave of radius R

strikes a thin

lens, the object distance is clearly also R

– the distance to the

point of origin of the wave. Therefore, the radius of curvature

immediately after passage through the lens must obey:



ð4:131Þ

as shown in Figure 4.28. Thus, if w is

unchanged at the

lens, the beam parameter after passage through the lens

obeys



ð4:132Þ

It is straightforward to use this result in conjunction with

Equations (4.116) and (4.121) to give the minimum spot

size w

of a TEM

Gaussian beam focused by a lens as:

f k

1 



1=2

ð4:133Þ

where w

and R

are the laser-beam spot size and radius of

curvature at the input face of the lens. If the lens is placed

very close to the waist of the beam being focused, Equation

(4.133) reduces to:

¼ f h

ð4:134Þ

where h

is the beam divergence at the input face of the

lens. If h

is a small angle, then w

is located almost at the

focal point of the l ens – in reality very slightly closer to

the lens. It is worthwhile comparing the result given b y

Equation (4.134) with the result obtained for a plane wave

eing foc us ed by a le ns. In the latter case, the lens diam-

eter D is the factor that limits the lateral extent of the

wave being focused. Diffraction theory

11,23

shows that,

in this case, 84% of the energy is focused into a region of

diameter:

S ¼ 2:44kf =D ð4:135Þ

This is the diameter of the focused Airy disk diffraction

pattern of the lens aperture.

It should be noted that the spot size to which a laser

beam can be focused cannot be reduced without limit

merely by reducing the focal length of the focusing lens.

In the limit the lens becomes a sphere and, of course, is

then no longer a thin lens. In practice, to focus a laser beam

to a small spot, the value of h

should be ﬁrst reduced by

expanding the beam and then recollimating it – generally

with a Galilean telescope, as will be seen in Section 4.3.3.

o prevent diffraction effects, the lens aperture should be

larger than the spot size at the lens: D ¼ 2.8w is a common

size used. In this case, if the focusing lens is placed at

the beam waist of the collimated beam, the focal-spot

diameter is:

5:6kf

1:78kf

ð4:136Þ

In practice, it is difﬁcult to manufacture spherical lenses

with very small values of f / D (called the f /# or f/ nu m-

ber) and at the same time achieve the diffraction-limited

performance pr edicted by this equation. Commer cially

available spherical lenses

achieve va lues of 2w

about 10k. Smaller spot sizes are possible with aspheric

lenses.

The Beam Parameter M

. Real laser beams are

often characterized by their M

parameter or focusability

parameter. Because of deviations from perfect Gaussian

behavior, whan a real laser beam is focused by an ideal

Figure 4.28 Transformation of a Gaussian beam by a thin

lens.

CHARACTERIZATION AND ANALYSIS 181

lens placed at the beam waist the focused spotsize is not

¼ fh

, as predicted by Equation (4.134), but is instead:

¼ M

f h

ð4:137Þ

For asymmetrical laser beams there will be two beam

parameters M

amd M

for the two lateral coordinates of

the laser beam. The M

parameter cannot be measured

from a single measurement of the laser beam. A series of

measurements on a focused beam are made, such as the

position of the focus relative to the focal length of the lens,

the new beam divergence angle after the focus,

the spotsize(s) at the focal point of the lens, and the new

minimum spotsize(s). Commercial instruments that meas-

ure M

are available from Coherent, Photon, Inc., and

Spiricon. Here, and wherever suppliers are mentioned in

the text, the list is intended to be representativ e, but not

necessarily exhaustive.

4.3 OPTICAL COMPONENTS

4.3.1 Mirrors

When light passes from one medium to another of different

refractiv e index, there is some reﬂection, so the interface acts

as a partially reﬂecting mirror . By applying an appropriate

single-layer or multilayer coating to the interface between

the two media, the reﬂection can be controlled so that the

reﬂectance has any desired value between 0 and 1. Both ﬂat

and spherical mirrors made in this way are available – there

are numerous suppliers.

If no transmitted light is required,

high-reﬂectance mirrors can be made from metal-coated

substrates or from metals themselves. Mirrors that reﬂect

and transmit roughly equal amounts of incident light are

oftenreferredtoasbeamsplitters.

Flat Mirrors. Flat mirrors are used to d eviate the path

of light ra ys w ithout any focusing. The se mirrors can

have their reﬂective surface on the front face of any

suitable substrate, or on the rear face of a transparent

substrate. Front-surface, totally reﬂecting mirrors have

the advantage of producing no unwanted additional or

ghost reﬂe ctions; however, their reﬂective su rfac e is

exposed. Rear-surface mirrors produce ghost reﬂections,

as illustrated in Figure 4.29, unless their front surface is

antir

eﬂection coate d; but the reﬂect ive surface is

protected. Most household mirrors are made this way.

The cost of ﬂat mirrors depends on their size and on the

degree of ﬂatness required.

Mirrors for high-precision applications – for example,

in visible lasers – are normally spec iﬁed to be ﬂat

between k/10 and k/20 f or visible light. This degree of

ﬂatness is not required when the mirror is merely for light

collection and redirection, for example to reﬂect light

onto the surface of a detector. Mirrors for this sort of

application are routinely ﬂat to within a few wavelengths

of visible light. Excellent mirrors for this purpose can be

made from ‘‘ﬂoat’’ plate glass,

whichisﬂatto1or2

wavelengths per inch.

New superpolishing techniques have allowed the pro-

duction of super mirrors, which have surf ace roughness

down to 0.1nm or below and loss (absorption plus scat-

tering) below 10

–6

per reﬂection. Super mirrors allow

the construction of optical resonators with very high Q

values, up to 1 million, for applications such as cavity

ring d own spectroscopy and high ﬁnesse interferometry

(see Section 4.7.4). Such mirrors are available from

s Gatos Researc h, Newport Corporation, an d the

Optical Corporation. More discussion of the issues

involved in fabricating such mirrors is available in

references 34–37.

Figure 4.29 Production of ghost reﬂections

by a rear-surface mirror whose front surface is

not antireﬂection coated.

182 OPTICAL SYSTEMS

Spherical Mirrors. Spherical mirrors are widely used

in laser construction, where the radii of curvature are

typically rather long – frequently 20 m radius or mor e.

They can be used whenever light must be collected and

focused; however, spherical mirrors are only good for

focusing nearly parallel beams of light that str ike the

mirror close to normal. In common with spherical

lenses, spherical mirrors suffer from various imaging

defects called aberrations, which have been discussed in

Section 4.2.5. A parallel beam of light

that strikes a

spherical mirror far from normal is not focused to a

small spot. When used this way the mirror is

astigmatic, that is, off-axis rays are focused at different

distances in the horizontal and vertical planes. This leads

to blurring of the i mage, or at best the focusing of a point

source into a line image.

A useful practical way to distinguish between a ﬂat

mirror and one with a large radius of curvat ure is to use

the mirror to view a sharp object in grazing incidence.

A cur ved mirror surface will reveal itself through the blur-

ring of the image, while a ﬂat mirror will give a sharp

image.

Paraboloidal and Ellipsoidal Mirrors. Paraboloidal

mirr ors will produce a parallel beam of light when a point

source is placed at the focus of the paraboloidal surface.

Thus, these mirrors are very useful in projection

systems. They are usually made of polished metal,

although versions using Pyrex sub strates are also

available. An important application of parabolic

mirrors is in the off-axis focusing of laser beams,

using off-axis mirrors in which the axis of the

paraboloid does not pass through the mirror. When

they are used in this way there is complete acces s to

the focal region withou t any sha dowing, as shown in

Figure 4.30. Spherical mirrors, on the other hand, do

not

focus well if they are used in this way. Off-axis

paraboloidal mirrors, as well as metal axial

paraboloidal mirrors, are available from Edmund

Optics, II-VI Infrared, Kugler, Lightwave Enterprises,

Melles Griot, Newport, Opti-Forms, OptoSigma, Space

Optics Research Lab, and Thorlabs.

Ellipsoidal mirrors are also used for light collecting.

Light that passes through one focus of the ellipsoid will,

after reﬂection, also pass through the other. These mirrors,

like all-metal paraboloidal mirrors, are generally made by

electroforming. The surface ﬁnish obtained in this way is

quite good, although not so good as can be obtained by

optical polishing. Rhodium-plated electroformed ellipsoi-

dal mirrors are available from Edmund Optics, Melles

Griot, Opti-Forms, and Spectrum Scientiﬁc.

Dielectric Coatings. Several dif ferent kinds of single-

layer and multilayer dielectric coatings are available

commercially on the surface of optical components. These

coatings can either reduce the reﬂectance or enhance it in

some spectral region.

(i) Single-layer antireﬂection coatings. The mode of

operation of a single-layer antireﬂection (AR) coating

can be conveniently illustrated by the method of trans-

formed impedances. Suppose medium 3 in Figure

4.31(a) is the surface to be AR coated. Apply to the surface

coating with an effective thickness:

¼ k

=4 ð4:138Þ

where k

¼ c

/mn

. The actual thickness of layer 2 is:

d ¼ d

= cos h

ð4:139Þ

Figure 4.30 Off-axis paraboloidal mirror.

OPTICAL COMPONENTS 183

The transformed impedance of medium 3 at the ﬁrst inter-

face is found by substitution in Equation (4.110):

¼ Z

ð4:140Þ

To reduce the reﬂection coefﬁcient to zero, we need

¼ Z9

; so the effective impedance of the antireﬂection

layer must be:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð4:141Þ

Thus, to eliminate reﬂection of waves linearly polarized

in the plane of incidence and incident at angle h

, n

must

be chosen to satisfy:

cos h

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

cos h

ð4:142Þ

For use in normal incidence, n

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

and d ¼ k

/4.

In normal incidence, an AR coating works for any incident

polarization. To minimize reﬂection at an air–ﬂint-glass

(n ¼ 1.7) interface, we would need:

ﬃﬃﬃﬃﬃﬃﬃ

1:7

¼ 1:3 ð4:143Þ

Magnesium ﬂuoride with a refractive index of 1.38

and cryolite (sodium aluminum ﬂuoride) with a refrac-

tive index of 1.36 come closest to meeting this require-

ment in the visible region of the spectrum. Optical

components such as camera lenses are us ually coated

with one of these materials to minimize reﬂection at

550 nm. The slightly greater Fresnel reﬂection that

results in the blue and red gives rise to the characteristic

purple color of these components in reﬂected light often

called ‘‘blooming’’.

(ii) Multilayer antireﬂection coatings. The minimum

reﬂectance of a single-layer antireﬂection-coated sub-

strate is (n

– n

)/(n

þ n

)

. Available robust

optical coating materials such as MgF

, however, do

not have a sufﬁciently low refractive index to reduce

the reﬂe ctance to zero with a single layer. Two-la yer

coatings, often called V-coatings because of the sh ape

of their transmission characteristic, reduce reﬂection

better than a single layer, as shown in Figure 4.31(b).

Multilayer

coatings can be used to reduce reﬂectance

over a broader wavelength region than a V-coating, as

shown in Figure 4.32. Such b road-band coatings are

ually of proprietary design: they are available

Figure 4.31 (a) Geometry of single-layer antireﬂection

coating; (b) reﬂectances of single- and double-layer antire-

ﬂection coatings on a substrate of refractive index 1.64.

(From Handbook of Lasers, R.J. Pressley (Ed.), CRC Press,

Cleveland, 1971; by permission of CRC Press, Inc.)

184 OPTICAL SYSTEMS

commercially from m any sourc es, as a re coatings of

other types.

Some companies offer both optical com-

ponents and coatings, while others specialize in coatings

and will coat customers’ own materials. Melles Griot

offer a HEBBAR (high efﬁciency broad-band antireﬂec-

tion) coating that provides very low reﬂectance over a

broad bandwidth, and is relatively insensitive to angle of

incidence, as shown in Figure 4.33.

(iii) High-reﬂectance coatings. The usually high reﬂec-

tance of a metal surface can be further enhanced, as shown

in Figure 4.34(a), by a multiple dielectric coating consist-

ing

of an even number of layers, each a quarter wavelength

thick, and of alternately high and low refractive index, with

a low-refractive-index material next to the metal. A very

high reﬂectance over a narrow wavelength range can be

achieved, as shown in Figure 4.34(b), by using a dielectric

substrate,

such as fused quartz, and an odd number of

quarter-wavelength layers of alternately high and low

refractive index with a high-index layer on the substrate.

Broad-band high-reﬂectance coatings are also available

where the thickness of the layers varies around an average

value of a quarter wavelength.

Beamsplitters. Beamsplitters are semitransparent mir-

rors that both reﬂect and transmit light over a range of wave-

lengths. A good beamsplitter has a multilayer dielectric

coating on a substrate that is slightly wedge-shaped to elim-

inate interference effects, and antireﬂection-coated on its

back surface to minimize ghost images. The ratio of reﬂec-

tance to transmittance of a beamsplitter depends on the

polarization state of the light. The performance is usually

speciﬁed for light linearly polarized in the plane of inci-

dence (P-polarization) or orthogonal to the plane of inci-

dence (S-polarization). Cube beamsplitters are pairs of

identical right-angle prisms cemented together on their

hypotenuse faces. Before cementing, a metal or dielectric

semireﬂecting layer is placed on one of the hypotenuse

Figure 4.32 Reﬂectance of a typical broad-band antireﬂec-

tion coating (BBAR) showing considerable reduction in

reﬂectance below the uncoated substrate. (From Handbook

of Lasers, R.J. Pressley (Ed.), CRC Press, Cleveland, 1971; by

permission of CRC Press, Inc.

Figure 4.33 The reﬂectance spectrum of an HEBBAR

high reﬂectance broad-band coating.

OPTICAL COMPONENTS 185

faces. Antireﬂection-coated cube prisms have virtually no

ghost image problems and are more rigid than plate type

beamsplitters. The operation of both types of beamsplitter is

illustrated in Figure 4.35.

Pellicles. Pellicles are beam-splitting mirrors made of

a high-tensile-strength polymer stretched over a ﬂat

metal frame. The polymer ﬁlm can be coated to modify

the reﬂection–transmission characteristics of the ﬁlm.

The polymer generally used, nitrocellulose, t ransmits in

the visible and near infrared to about 2lm. These devices

have some advantages over conventional coated-glass

or quartz beamsplitters; the thinness of the polymer

Figure 4.34 (a) Reﬂectance of a plain aluminum mirror

and an aluminum mirror with four dielectric overlayers.

(From Handbook of Lasers, R.J. Pressley (Ed.), CRC Press,

Cleveland, 1971; by permission of CRC Press); (b) typical

transmittance characteristic of a narrow-band,

maximum-reﬂectance, multilayer dielectric coating on

a dielectric substrate.

Figure 4.35 (a) Conventional planar beamsplitter (wedge

angle greatly exaggerated); (b) cube beamsplitter.

186 OPTICAL SYSTEMS

ﬁlm virtually eliminates spherical and chromatic aberrations

(see Section 4.3.3) when diverging or converging light

sses through them, and ghost-image problems are

virtually eliminated. They will, however, produce some

wavefront distortion, typically about two waves per

inch, and are not suitable for precision applications.

Pellicles are available from several suppliers

,suchas

Edmund Optics, Melles Griot, National Photocolor, and

Newport.

4.3.2 Windows

An optical window serves as a barrier between two media,

for example, as an observation window on a vacuum system

or on a liquid or gas cell, or as a Brewster window on a

laser. When light passes through a window that separates

two media, there is, in general, some reﬂection from the

window and a change in the state of polarization of both the

reﬂected and the transmitted light. If the window material is

not perfectly transparent at the wavelength of interest, there

is also absorption of light in the window, which at high light

intensities will cause the window to heat. This will cause

optical distortion of the transmitted wave, and at worst – in

high-power laser applications – damage the window on its

surface, internally, or both. Additionally, if the two surfaces

of a window are both very ﬂat (roughly speaking, one wave

per centimeter or better) and close to parallel, the window

will act as an etalon (see Sections 4.3.8 and 4.7.4) and

exhibit distinct variations in transmission with wavelength.

To circumvent this difﬁculty, which is a particular nuisance

in experiments using lasers, most precision ﬂat optical

windows are constructed as a slight wedge, with an angle

usually about 309.

The details of the reﬂection, refraction, and change of

polarization state that occur when light strikes a window

surface are dealt with in detail in Sections 4.2.6 and 4.3.6.

These considerations also apply when light strikes a lens or

prism. The reﬂection at such surfaces can be reduced by a

single-layer or multilayer dielectric antireﬂection coating. In

optical systems such as multielement camera lenses, where

light crosses many such surfaces, antireﬂection coatings are

very desirable. Otherwise a severe reduction in transmitted

light intensity will result, as illustrated in Figure 4.36.

Optical

cells, or cuvettes, are transparent containers,

generally made of glass or fused quartz, which are used

in absorption and ﬂuorescence spectrophotometers, in

light-scattering and turbidity measurements, and in many

other specialized experiments. These cells are usually rec-

tangular or cylindrical in shape and are available in many

sizes and conﬁgurations, including provision for liquid

circulation. Suppliers include Harrick Scientiﬁc, Hellma,

International Crystal Laboratories, Newport/Oriel, NSG

Precision Cells, Optiglas, Spectrocell, and Starna.

4.3.3 Lenses and Lens Systems

Singlet Lenses. Singlet lenses are the simplest and

most readily available lenses for nonexacting applications.

They come in six basic formats, shown in Figure 4.37.The

ns is speciﬁed by the material of which it is made, the

curvatures R

and R

of its two faces, the thickness d of

the lens at its mid point, and its aperture diameter D,

which also indirectly speciﬁes its thickness at the edge.

The lens has an effective focal length (EFL), f measured

from its principal planes, and front and back focal lengths,

which specify the distances of the focal points from the front

and back surfaces of the lens, as shown in Figure 4.38.A

convex lens has two generally spherical surfaces. In the

standard sign convention the ﬁrst of these has a positive

radius and the second a negative radius. A symmetrical

biconvex lens has R

¼ – R

.Aplano-convex lens has one

ﬂat face, while a convex meniscus lens has a ﬁrst surface of

positive radius and a second surface of a larger positive

radius. Biconvex, plano-convex, and convex meniscus

Figure 4.36 Transmittance of a multielement optical

system as a function of the refractive index of the

elements.

OPTICAL COMPONENTS 187

lenses all have a positive EFL. Biconcave, plano-concave,

and concave meniscus lenses have surface curvatures,

opposite in sign to their convex counterparts, and all have

anegativeEFL.

All singlet lenses suffer from spherical and chromatic

aberration. They are inexpensive, but suffer from signiﬁcant

amounts of aberration, so are not a good choice in imaging

situations. For focusing parallel light (inﬁnite object con-

jugate), or for producing a parallel beam of light, plano-

convex lenses or convex meniscus lenses that are close to

plano-convex exhibit the least spherical aberration for a

speciﬁed EFL. For best performance in these applications

the parallel light should pass through the more strongly

curved of the two surfaces. For imaging at different con-

jugate ratios the shape of singlet that produces the least

spherical aberration is called the best form lens for that

application. For example, for equal object and image dis-

tances (conjugate ratio ¼ 1) the best form singlet is a sym-

metrical biconvex lens. Singlet lenses can provide

satisfactory performance provided they are used with rel-

atively large f/numbers. If singlet lenses are used with

lasers then there is no chromatic aberration.

Doublets. If a positive focal length lens of one type of

glass is combined with a weaker negative lens made from a

different type of glass, then the lens combination can

exhibit reduced spherical and chromatic aberration.

Figure 4.37 The six basic singlet lens types:

(a) biconvex; (b) plano-convex; (c) convex

meniscus; (d) biconcave; (e) plano-concave;

(f) concave meniscus.

Figure 4.38 Diagram showing the effective focal length (EFL), the front focal length (FFL),

and the back focal length (BFL) of a thick lens.

188 OPTICAL SYSTEMS

Doublets can be either air-spaced or cemented. They are

widely available from many suppliers, such as CVI/Melles

Griot, Newport Corporation, OptoSigma, Rolyn, and

Thorlabs. For laser applications, even without the

concern for chromatic aberration, doublets will provide

superior focusing performance to singlets.

Camera lenses. Compound lenses involve more than

two spherical surfaces and can be designed to have reduced

aberrations. Camera lenses are multi element compound

lenses especially designed for imaging applications.

A wide variety of high-performance camera lenses is

available commercially from companies such as Canon,

Fujinon, Kodak, Leitz, Minolta, Nikon, Olympus, Sigma,

and Zeiss. The choice of camera lenses for a speciﬁc

application is generally guided by two parameters: (i) the

ﬁeld of view (FOV), which can be speciﬁed by the apex

angle of the cone of light that can be collected by the lens

and (ii) the aperture of the lens. Both these parameters

inﬂuence the light-gathering power of the lens.

Telecentric lenses are special compound lenses used in

applications such as machine vision and lithography where

object or image movement does not produce a change in

magniﬁcation.

33,38

For a lens with object space telecentric-

ity, a change in the object distance will not result in the

image changing size. For such a lens the aperture stop is

located in the back focal plane and the entrance pupil is at

inﬁnity. All the principal rays in object space are parallel to

the axis. For a lens with image space telecentricity, moving

the image plane to focus or defocus the system will not

change the size of the image. In this case the aperture stop

is located in the front focal plane and the exit pupil is at

inﬁnity. In the image space all the principal rays are parallel

to the axis. If a lens is telecentric for both the object

and image spaces it is called doubly telecentric. The primary

disadvantage of telecentric lenses is that they have a very

limited ﬁeld of view: object and image hav e to lie within a

cylindrical region whose radius in object and image space is

limited by the size of the lens elements. Telecentric lenses

are av ailable from Computer Optics, Edmund Optics,

Mekoptik, Navitar, Opto-Engineering, and Sill Optics.

Simple and Galilean Telescopes. The operation

of a simple telescope is illustrated in Figure 4.39(a).

The

objective is usually an achromat (a lens in which

chromatic aberration – the variation of focal length with

wavelength – has been minimiz ed). I t has a long focal

length f

and produces a real image of a distant object,

which can then be examined by the eyepiece lens of focal

length f

. This design, which produces an inverted image,

is often called an astronomical telescope. If desired, the

ﬁnal image c an be erected with a third lens, in which case

the device is called a terrestrial telescope.Theeyepiece

of the telescope can be a singlet lens, but composite eye-

piece designs such as the Ramsden and t he Kellner

are

also common. Most large astronomical telescopes use

spherical mirrors as obj ectives, and various conﬁgura-

tions are used, such as the Newtonian, C assegrain, and

Schmidt.

11,23–25

Since most telescope development has

been for astronomical applications, it is outside the scope

of thi s book to give a detailed discussion; for further

details the reader should consult Born and Wolf,

Levi,

Meinel,

or Brouwer and Walther.

Figure 4.39 Ray paths through telescopes in normal

adjustment (object and ﬁnal image at inﬁnity):

(a) astronomical telescope; (b) Galilean telescope.

OPTICAL COMPONENTS 189

Small astronomical and terrestrial telescopes are widely

available at relatively low cost. Two principal manufac-

turers are Celestron

and Meade.

The Galilean telescope illustrated in Figure 4.39(b),

ﬁrst constructed by G alileo in 1609, is the earli est tele-

scope of which there exists deﬁnite knowledge. It produ-

ces no real intermediate image, but the ﬁnal image is

erect. I n normal adjustment, the focal point of the diverg-

ing eyepiece is outside the telescope and coincident with

that of the obje ctive. In th e simple telescope the two focal

points also coincide, but are between the two. The mag-

niﬁcation M produced by either type of telescope can be

written as:

M ¼f

ð4:144Þ

Since the simple telescope has two positive (converging)

lenses, its overall magniﬁcation is negative, which indi-

cates that the ﬁnal image is inverted.

Simple and Galilean telescopes have practical uses in

the laboratory that are distinct from their traditional use for

observing distant objects.

Laser-Beam Expanders and Spatial

Filters.

Laser beams can be expanded and recollimated

(or focused and recollimated) with simple or Galilean tele-

scope arrangements, as illustrated in Figure 4.40. For opti-

mum

recollimation the spacing of the two lenses should be

adjustable, as ﬁne adjustment about the spacing f

þ f

will

be necessary for recollimating a Gaussian beam. In this

application the Galilean telescope has the advantage that

the laser beam is not brought to an intermediate focus

inside the beam expander. Gas breakdown at such an inter-

nal focus can occur with high-power laser beams, although

this problem can be solved in simple-telescope beam

expanders by evacuating the telescope. Since laser beams

are highly monochromatic, beam expanders need not be

constructed from achromatic lenses. Attempts should,

however, be made to minimize spherical aberration and

beam distortion. It is best to use precision antireﬂection-

coated lenses if possible. Laser-beam-expanding tele-

scopes that are very well corrected for spherical aberration

are available from Janos, Melles Griot, Newport/Oriel,

Rolyn, Sigma Koki, Space Optics Research Labs, and

Special Optics, among others.

Infrared laser-beam

expanders usually have ZnSe or germanium lenses. The

use of biconvex and biconcave lenses distributes the focus-

ing power of the lenses over their surfaces and minimizes

spherical aberration. Better cancellation of spherical aber-

ration is possible in Galilean beam expanders than with

simple telescopes.

If a small circular aperture is placed at the common

intermediate focus of a simple-telescope beam

expander, the device becomes a spatial ﬁlter as w ell.

Although ideally the output beam from a laser emitting

aTEM

mode has a Gaussian radial intensity proﬁle, in

practice the radial proﬁle may have some irregular struc-

ture. Such beam i rregularities may be produced in the

laser or by passage of the beam through some medium.

If such a beam is focused through a s mall enough aper-

ture and then recollimated, the irregular structure on the

radial intensity proﬁle can be removed and a smooth

Figure 4.40 Laser-beam expanders: (a) focusing type with

spatial ﬁlter; (b) Galilean type.

190 OPTICAL SYSTEMS

proﬁle restored, as illustrated in Figure 4.41.Thisis

called spatial ﬁltering. The minimum aperture diamete r

that should be used is

min

ð4:145Þ

where f

is the focal length of the focusing lens and w

the spot size at that lens. Typical aperture sizes used in

commercial spatial ﬁlters for visible lasers are on the order

of 10 lm. This aperture must be accurately and symmetri-

cally positioned at the focal point, so it is usually mounted

on an adjustable XY translation stage.

Lens Aberrations. As discussed in Section 4.2.5, real

lenses suffer from various forms of aberration, which lead

the image of an object to be an imperfect reconstruction of

it. If a particular aberration is judged to be detrimental in a

particular experimental situation, then a special lens combi-

nation can often be obtained that minimizes that aberration –

occasionally at the expense of worsening others.

(i) Chromatic aberrations. Because the refractive index

of the material of a lens varies with wavelength, so does its

focal length. Therefore rays of different wavelengths from

an object form images in different locations. Chromatic

aberration is almost eliminated with the use of an achro-

matic doublet. This is a pair of lenses, usually consisting of

a positive crown-glass lens and a negative ﬂint-glass lens,

cemented together. These two lenses cancel each other’s

chromatic aberrations exactly, at speciﬁc wavelengths in

the blue and red, and almost exactly in the region in

between. Good camera lenses are well corrected for chro-

matic aberrations.

Achromatic doublets are available from numerous sup-

pliers, including Edmund Optics.

(ii) Spherical aberration. This aberration can be mini-

mized in a single lens by distributing the curvature

between its two surfaces without altering the focal length.

So, for example, a biconvex lens will produce less spher-

ical aberration than a plano-convex one of the same focal

length. Spherical aberration can be minimized in an ach-

romatic doublet with appropriate choice of curvatures for

the constituent lens elements.

(iii) Coma. When an object point is off the axis of a lens,

its image is produced in different lateral positions by dif-

ferent zones of the lens. Coma can be controlled by an

appropriate choice of lens curvatures.

Other forms of aberration also occur, such as ﬁeld cur-

vature, in which an object plane orthogonal to the lens axis

is imaged as a curved surface.

(iv) Astigmatism. This aberration can be controlled by

lens curvature and index variations, and by the use of

apertures to restrict the range of angles and off-axis dis-

tances at which rays can traverse the lens.

Aspheric Lenses. If one face of a singlet lens is man-

ufactured as a nonspherical (or aspherical), surface then at

Figure 4.41 Intensity variation I (x) along a diameter

of a TEM

laser beam possessing spatial noise

structure: (a) before and (b) after spatial ﬁltering.

OPTICAL COMPONENTS 191

a speciﬁed design wavelength all spherical aberration can

be eliminated. With such a lens it is possible to obtain a

much smaller focal length than with a conventional spher-

ical lens of the same diameter, without increasing the

spherical aberration of the lens. An ideal aspheric lens

exactly cancels the spherical aberration that would other-

wise be present in the optical system. Such lenses can

produce the smallest focal spots when used with collimated

laser light. The collimated beam should enter the aspher-

ical surface and the focus will be on the opposite side, as

shown in Figure 4.42. The second face of an aspherical lens

often plane, or weakly spherical as shown in Figure 4.43.

optimum performance at a particular wavelength and

focal length is required, then a custom asphere can be

manufactured, but this can be expensive, unless a large

number of such lenses are required. Aspheres are often

made by molding, so once the mold has been manufactured

additional lenses are less expensive.

The standard formula that describes an aspheric surface

is:

z ¼



1 þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 ð1 þ KÞ

þ A

þA

þ A

þ ð4: 146Þ

where z is the depth (or sag) of the surface, r is the lateral

position, K is the conic constant of the surface, and R is the

effective curvature at the vertex of the surface, as shown in

Figure 4.42. The conic constant K has

the following values

for different surface proﬁles: K > 0 ellipse, K ¼ 0 sphere,

–1 < K < 0 ellipse, K ¼ –1 parabola, and K < –1 hyperbola.

Most aspherical designs use only the even order terms, as

shown in Equation (4.146), but the odd terms could also be

included.

Aspheric

lenses can collect and focus light rays over a

much larger solid angle than conventional lenses and can

be used at f/numbers as low as 0.6. Aspheric lenses save

space and energy. They can be used as collection lenses

very close to small optical sources, such as high-pressure

mercury or xenon arc lamps, and for collecting radiation

over a large solid angle and focusing it onto a detector

element. Such lenses are often referred to as condensers.

Condensers are widely used in microscopes, where they

focus light from the microscope light source onto a speci-

men. In such applications the aspherical surface should be

on the light source side. Because aspheric lenses are gen-

erally designed only to minimize spherical aberrations,

they will contribute to chromatic aberration, coma, distor-

tion, astigmatism, and curvature of ﬁeld. Consequently, an

aspheric lens should not be used under circumstances

where these aberrations will be compounded by transmis-

sion through additional components of the optical system.

Glass aspheric lenses are available in a range of diameters

and focal lengths from several suppliers,

such as Fresnel

Technologies, Melles Griot, Moritex, OptoSigma, and

Figure 4.42 Focusing light with an aspherical lens.

Figure 4.43 Cross-sections of three common types of

aspheric lens.

192 OPTICAL SYSTEMS

Thorlabs. Aspheric lenses in exotic materials can be

obtained as custom items.

Graded Index Lenses. Small lenses with a

convenient cylindrical shape can be made from graded

index material, which has a refractive index that varies

from point to point inside the material. A commonly

encountered axi-symmetric index variation is Gaussian,

or approximately so. The refractive index as a function

of distance r from the axis of symmetry is:

n ¼ n

r

=2r

ð4:147Þ

For distances from the axis that satisfy r  r, Equation

(4.147) can be written as

n ¼ n

ð1 

Þ¼n



ð4:148Þ

where n

¼ n

. This is a quadratic index proﬁle. A

cylindrical piece of such transparent material with ﬂat ends

has an overall ray transfer matrix from air, through a length

d of the graded medium and back into air:



0 n



cos



r sin





sin



cos



01=n



cos



sin





sin



cos



ð4:149Þ

The focal length of this GRIN lens is:

f ¼

sin



ð4:150Þ

which can also be written as:

f ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

sinðd

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð4:151Þ

Rays that enter a graded index lens follow sinusoidal

paths until they reach the back surface of the lens. The

oscillation pattern inside the lens describes its pitch. Figure

44 shows schematically how the pitch is deﬁned. A 1/4

tch graded index lens, for example, will take input parallel

light and bring it to a focus at the exit face of the lens.

Graded index lenses are very convenient to use in small

optical arrangements because their ﬂat ends make them easy

to couple to other structures, such as semiconductor lasers or

optical ﬁbers. They are available commercially as GRIN or

SELFOC lenses from suppliers such as LINOS Photonics,

Melles Griot, NSG, Red Optronics, Schott, and Thorlabs.

These lenses should not be used in precision imaging

applications because they generally suffer from relatively

severe aberrations, especially chromatic aberration.

Fresnel Lenses. A Fresnel lens is an aspheric lens

whose surface is broken up into many concentric annular

rings. Each ring refracts incident rays to a common focus,

so that a very large-aperture, small f/number, thin aspheric

lens results. Figure 4.45 illustrates the construction and

focusing

characteristics of such a lens. These lenses are

generally manufactured from precision-molded acrylic.

Because the refractive index of acrylic varies little with

wavelength, from 1.51 at 410 nm to 1.488 at 700 nm, these

lenses can be very free of chromatic and spherical aberra-

tion throughout the visible spectrum. Fresnel lenses should

Figure 4.44 Schematic operation of graded index lenses:

(a) a quarter pitch lens, which can be used to either focus

parallel light or collimate light from a point source on one

face of the lens; (b) a half pitch lens, which inverts an image

at its front face; (c) a three quarter pitch lens; (d) a whole

pitch lens.

OPTICAL COMPONENTS 193

Figure 4.45 (a) A Fresnel lens, made up of trapezoidal concentric secti ons (it

replaces a bulky asp heri c lens); (b) illustration of how the focusing characteristics

of a Fresnel lens result from refraction at the individual surface grooves. (Courtesy

of Melles Gri ot, I nc.)

194 OPTICAL SYSTEMS

be used so that they focus to the plane side of the lens, and

their surfaces should not be handled. They are inexpensive

and available from very many suppliers, including

Edmund Scientiﬁc, Fresnel Technologies, Lexitek, New-

port/Oriel, and Wavelength Optics. They should not be

considered for use in applications where a precision image

or diffraction-limited operation is required. Fresnel lenses

also scatter much more light than conventional lenses.

Fresnel lense s ar e an example of a more general

class of optics called d iffractive optics. These are struc-

tured optical elements that use diffraction to redirect

light, split a light beam into many separate beams, focus

light, produce di ffuse light, or c orrec t di storte d wave-

fronts. They are available from Holographix, MEMS Opti-

cal, Optocraft, RPC Photonics, Silios Technologies, and

Stocker Yale.

Cylindrical Lenses. Cylindrical lenses are pla nar

on one side and cylindrical on the other. I n planes

perpendicular to the cylinder axis they have focusin g

properties identical to a sph erical lens, but they do not

focus at all in planes containing the cylinder axis.

Cylindrical lenses focus an extended source into a

line, and so are very useful for imaging s ources onto

monochromator slits, although perfect matching of

f/numbers is not possible in this way. These lenses are

also widely used for focusing the output of solid-state

and nitrogen lasers into a line image in the dye cell of dye

lasers (see Section 4.6.3). Cylindrical lenses are

vailable from Bond Optics, Esco, Infrared Optical

Products, Melles Griot, Newport/Oriel, OFR (now

Thorlabs), Optimax, and Rolyn.

Optical Concentrators. Optical concentrators are

nonimaging light collectors that are useful in delivering

light to a detector. They effectively increase the

collection area of the detector, although they affect the

angles of light rays.

If light enters an optical system of entrance aperture

diameter 2a over a range of angles 2h and leaves through

an aperture of diameter 2a9 over a range of angles 2h9 then

in the paraxial approximation:

ah ¼ a

ð4:152Þ

which follows from the brightness theorem. If the refrac-

tive indices of the input and output media are n, n9, respec-

tively, then this relation becomes:

nah ¼ n

ð4:153Þ

The quantity n

, which is unchanged in going through

the system, is called the e

tendue of the system. Figure 4.46

shows two simple concentrator designs, a linear conical

concentrator

, and a compound parabolic concentrator

(CPC), often called a ‘‘Winston’’ Cone. These devices

are hollow or solid cones, which reﬂect entering rays one

or more times before they leave the exit aperture. The

range of light angles leaving such a device is greater than

the range of light angle entering, by the linear ratio be-

tween the entrance and exit apertures. Such a nonimaging

light collector could be used to collect light from a

diffusely emitting source and direct it onto a small area

Figure 4.46 Simple optical concentrator designs: (a) linear

cone; (b) compound parabolic concentrator.

OPTICAL COMPONENTS 195

photoelector; however, the detector’s active surface must

be placed close to the exit aperture because of the larger

range of angles of the emerging light rays.

Nonimaging light collectors are useful for collecting

light whose spatial distribution may be ﬂuctuating, yet

whose overall power may remain relatively constant, for

example, in the case of a laser beam that has passed

through a ﬂuctuating medium.

The concentration ratio is:

42,43

C ¼ a=a

sin h

n sin h

ð4:154Þ

In 2-D the maximum concentration ratio is:

max

n sin h



ð4:155Þ

and in 3-D for an axisymmetric concentrator:

max

n sin h



ð4:156Þ

The CPC can be fabricated from a solid transparent

material with refractive index n. For total internal reﬂec-

tion to occur for all internal rays that enter within a range

of angles h:

sin h

 1 



ð4:157Þ

sin h < n 

ð4:158Þ

To be useful as a material for a CPC it is clear that

n >

ﬃﬃﬃ

Since the rays leaving a concentrator can cover a solid

angle up to 2p sr, when the maximum concentration ratio

is used, a detector used in conjunction with the concentra-

tor would need to have its photosensitive surface directly at

the exit aperture.

Simple concentrators can be made by direct machining of

plastic material such as lexan (refractive index ~ 1.585)

using a numerically controlled lathe, followed by polishing.

Alternatively, a stainless-steel mandrel could be machined to

the required shape, and then a mold made by electroplating

over the stainless steel. After the hollow mold is made, then

plastic concentrators can be fabricated using transparent

epoxy resin placed into the mold and allowed to harden.

4.3.4 Prisms

Prisms are used for the dispersion of light into its various

wavelength components and for altering the direction of

beams of light. Prisms are generally available in most

materials that transmit ultraviolet, visible, and infrared

light. High-refractive-index semiconductor materials, such

as silicon, germanium, and gallium arsenide, however, are

rarely used for prisms. Consult Section 4.4 for a list of

suppliers

of optical materials.

The deviation and dispersion of a ray of light passing

through a simple prism can be described with the aid of

Figure 4.47. The various angles a, b, c, d satisfy

Snell’s law

irrespective of the polarization state of the input beam,

provided the prism is made of an isotropic material. It is

easy to show that:

sin d ¼ sin Aðn

 sin

aÞ

1=2

 cos A sin a ð4:159Þ

and:

D ¼ a þ d A ð4:160Þ

where A is the apex angle shown in Figure 4.47. The exit

ray

will not take the path shown if c is greater than the

critical angle.

Figure 4.47 Passage of a ray of light through a

prism.

196 OPTICAL SYSTEMS

The dispersion of the prism is deﬁned as:

ð4:161Þ

Substituting from Equation (4.159), this becomes:

dd ¼

sin A

cos b cos d

ð4:162Þ

When the prism is used in the position of minimum

deviation:

b ¼ c ¼

A ð4:163Þ

and:

a ¼ d ¼

ðD

min

þ AÞð4:164Þ

By the sine rule, Equation (4.162) can be written in the

form:

ð4:165Þ

where t is the distance traveled by the ray through the

prism and W is the dimension shown in Figure 4.47.

simple, yet important, application of a prism as a dis-

persing element is in the separation of a laser beam con-

taining several well-spaced wavelengths into its constituent

parts. Situations where this might be necessary include

isolation of the 488.8 nm line in the output of an argon

ion laser oscillating simultaneously at 476.5, 488.8, and

514.5 nm and other lines, or in nonlinear generation where

a fundamental and second harmonic must be separated. If

the spatial width of the laser beam is known, then an equa-

tion such as (4.165) will determine at what distance from

the prism the different wavelengths are spatially separated

from each other. The advantages of prisms in this applica-

tion are that they can introduce very little scattered light,

produce no troublesome ghost images, and can be cut so

that they operate with a ¼ d ¼ h

, thereby eliminating

reﬂection losses at their surfaces. Brewster-angle prisms

are used in this way inside the cavity of a laser to select

oscillation at a particular frequency. A modiﬁed prism

called a reﬂecting Littrow prism is frequently used in this

way, as shown in Figure 4.48. A Littrow prism is designed

that for a particular wavelength the refracted ray on

entering the prism travels normal to the exit face. Thus, if

the exit face is reﬂectively coated, for the speciﬁed wave-

length the incident light is returned along its original path.

Generally, a dispersing optical element used in Littrow has

this retroreﬂective characteristic at a particular wavelength.

If a beam of parallel monochromatic light passes

through a prism, unless the prism is used in the symmet-

rical minimum-deviation position, the width of the beam

will be increased or decreased in one dimension. This

effect is illustrated in Figure 4.49. By the use of two iden-

tical

prisms in an inverted conﬁguration, the compression

or expansion can be accomplished without an angular

Figure 4.48 Reﬂecting prism used in Littrow at Brewster’s

angle. Only light of a speciﬁc wavelength will be refracted at

the entrance face of the prism and then reﬂected back on

itself at the coated reﬂecting face.

Figure 4.49 (a) One-dimensional beam expansion

(or compression) with a prism; (b) one-dimensional beam

expansion without beam deﬂection using two oppositely

oriented, similar prisms.

OPTICAL COMPONENTS 197

change in beam direction. Prism beam expanders employ-

ing this principle are used in some commercial dye lasers

for expanding a small-diameter, intracavity laser beam

onto a diffraction grating to achieve greater laser line nar-

rowing. Such prism pairs can be used, in conjunction with

lenses, to produce anamorphic laser beam expanders.

These devices are important for the circularization and

collimation of the beams from semiconductor lasers. These

lasers generally emit an elliptical-shaped laser beam whose

beam divergence angle is different in two orthogonal

planes containing the beam axis.

Triangular prisms with a wide range of shapes and ver-

tex angles are available. The most common types are the

equilateral prism, the right-angle prism, and isosceles and

Littrow prisms designed for Brewster-angle operation.

Such prisms are readily available in glass and fused silica

from many suppliers.

Triangular and other prisms also

ﬁnd wide use as reﬂectors, utilizing total internal reﬂection

inside the prism or a reﬂective coating on appropriate

faces. Some speciﬁc reﬂective applications of prisms are

worthy of special note.

Right-Angle Prisms. Right-angle prisms can be used

to deviate a beam of light through 90°, as shown in Figure

4.50(a). Antireﬂection coatings on the faces shown are

sirable in exacting applications. A right-angle prism can

also be used to reﬂect a beam back parallel to its original

path, as shown in Figure 4.50(b). The retroreﬂected beam

shifted laterally. The prism will operate in this way

provided the incident beam is in the plane of the prism

cross-section. The retroreﬂection effect is thus independ-

ent of rotation about the axis A in Figure 4.50(b). If the

angle

of incidence differs signiﬁcantly from zero, the roof

faces of the prism need to be coated; otherwise total inter-

nal reﬂection at these surfaces may not result. If such a

prism is rotated about the axis B, only in a single orienta-

tion does retroreﬂection result. Roof prisms are available

from numerous suppliers, including Ealing, Edmund

Scientiﬁc, Melles Griot, Newport/Oriel, Opto-Sigma, and

Rolyn.

Porro prisms are roof prisms with rounded corners on

the hypoten use face and beveled edges. They are widely

Figure 4.50 (a) Right-angle prism used for 90° beam deﬂection;

(b) right-angle prism used for retroreﬂection. Incident and reﬂected ray are

parallel only if the incident beam is in the plane of the prism cross-section;

however, in this orientation, retroreﬂection is independent of orientation

about the axis A within a large angular range.

198 OPTICAL SYSTEMS

used in pairs for image erection in teles copes and binoc-

ulars, as shown in Figure 4.51(a). They are available from

Anchor

Optics, Edmund Optics, and Sunny Precision

Optics. Ami ci prisms are right-angle prisms where the

hypotenuse face has b een replaced by a 90° roof. They

are available from Anchor Optics, Edmund Optics, Red

Optronics, Starna, and TrustOptics. An image viewed

through an Amici prism is left-to-right reversed

(reverted) and top- to-bottom inve rted, as shown in Figure

4.5

1(b).

Dove, Penta, Polygon, Rhomboid, and Wedge

Prisms.

These prisms are illustrated in Figure 4.52.

Dove prisms are used to rotate the image in optica l

systems; rotation of the prism at a given angular rat e

causes the image to rotate at twice this rate. Dove prisms

have a length- to- aper tur e ratio of about ﬁve, so they must

be used with reasonably well-collimated light. They are

available from Anchor Optics, Edmund Opti cs, Esco

Optics, Melles Griot, Newport, Red Optronics, Rolyn,

TrustOptics, and Sunny Precision Optics.

Penta prisms deviate a ray of light by 90° without

inversion (turning upside down) or reversion (right-left

reversal) of the image. This 90° deviation appli es to all

rays incident on the useful aperture of the prism, irre-

spective of the ir angle of incidence. Penta prisms do not

operate by total internal reﬂection, so their reﬂective

surfaces are coated. Thes e prisms are useful for 90° devi-

ation when vibrations or other effects prevent their align-

ment being well controlled. They are available from

Anchor Optics, Edmund Optics, Melles Griot, Opto-

Sigma, Red Optronics, Rolyn, Sunny Precision Optics,

and TrustOptics.

Polygon prisms, usually octagonal, are available from

Rolyn and are used for high-speed light-ray deviation, for

example, in high-speed rotary prism cameras.

Rhomboid prisms are used for lateral deviation of a light

ray. When used in imaging applications, there is no change

of orientation of the image. Rhomboid prisms are available

from Edmund Optics, JML Optical, Precision Glass and

Optics, and Rolyn.

Wedge prisms are used in beam steering. The minimum

angular deviation D of a ray passing through a thin wedge

prism of apex angle A is:

D ¼ arcsinðn sin AÞA ’ðn  1ÞA ð4:166Þ

where n is the refractive index of the prism material.

A combination of two identical wedge prisms can be

used to steer a light ray in any direction lying within a cone

of semivertical angle 2D about the original ray direction.

Wedge prisms are available from Anchor Optics, Edmund

Figure 4.51 (a) Two Porro prisms used as an

image-erecting element; (b) Amici prism.

(Courtesy of Melles Griot, Inc.)

OPTICAL COMPONENTS 199

Optics, EKSPLA, Melles Griot, Precision Glass and Optics,

Red Optronics, Rolyn, and Sunny Precision Optics.

Corner-Cube Prisms (Retroreﬂectors). Corner-

cube prisms are exactly what their name implies, prisms

with the shape of a corner of a cube, cut off orthogonal to

one of its triad (body-diagonal) axes. The front face of the

resultant prism is usually polished into a circle as shown in

Figure 4.53. As a result of three total internal reﬂections, these

prisms

reﬂect an incident light ray back parallel to its original

direction, no matter what the angle of incidence is. The

reﬂected ray is shifted laterally by an amount that depends

on the angle of incidence and the point of entry of the incident

ray on the front surface of the prism. These prisms are

Figure 4.52 (a) Dove prism; (b) penta prism; (c) octagonal prism; (d) rhomboid

prism; (e) wedge prism, [(a), (b), and (e) courtesy of Melles Griot, Inc.]

200 OPTICAL SYSTEMS

in v aluable in experiments where a light beam must be

reﬂected back to its point of origin from some (usually

distant) point – for example, in long-path absorption

measurements through the atmosphere with a laser beam.

They are available commercially from Edmund Optics,

Knight Optical, Melles Griot, Newport, Precision Glass

and Optics, Precision Optical, Red Optronics, Rolyn, and

Sunny Precision Optics. The angular deviation of the

reﬂected ray from its original direction can be held to less

than a half second of arc in the best prisms. For infrared

applications beyond the transmission of fused silica, corner-

cube prisms are not readily available, but retroreﬂectors

can be made by using three square mirrors butted

together to form a hollow cube corner. Precision hollow

corner cubes of this type are available from PLX.

4.3.5 Diffraction Gratings

A diffraction grating is a planar or curved optical surface

covered with straight, parallel, equally spaced grooves.

They are manufactured in three principal ways: by direct

ruling on a substrate (called a master grating), by replication

from a master grating, and holographically. Such gratings

can be made for use in transmission, but are more com-

monly used in reﬂection. Light incident on the grooved face

of a reﬂection grating is diffracted by the grooves; the angu-

lar intensity distribution of the diffracted light depends on

the wavelength and angle of incidence of the incident light

and on the spacing of the grooves. This can be illustrated

with reference to the plane grating shown in Figure 4.54.

e grooves are usually produced in an aluminum or gold

Figure 4.53 Corner-cube prism.

(Courtesy of Melles Griot, Inc.)

Figure 4.54 Blazed groove proﬁle. The thickness of the

aluminum is generally equal to the blaze wavelength, and

the depth of the groove is about half the thickness. The

dimensions shown are approximately those for a grating

ruled with 1200 grooves per millimeter, blazed at 750 nm.

D ¼ depth of ruling; d ¼ groove spacing; L ¼ unruled land;

a ¼ angle of incidence; b ¼ angle of diffraction; c ¼ angle

of reﬂection; h ¼ blaze angle. The line N is normal to the

groove face F. (From D. Richardson, ‘‘Diffraction Gratings,’’

in Applied Optics and Optical Engineering, Vol. 5, R.

Kingslake (Ed.), Academic Press, New York, 1969; by

permission of Academic Press).

OPTICAL COMPONENTS 201

layer that has been evaporated onto a ﬂat optical substrate.

For high-intensity laser applications the substrate should

have high thermal conductivity. Master gratings ruled on

metal are available for this purpose from Diffraction Prod-

ucts, Jobin-Yvon, and Richardson Grating Laboratory

(through Newport). If the light diffracted at angle b from a

given groove differs in phase from light diffracted from the

adjacent groove by an integral multiple m of 2p, a max-

imum in diffracted intensity will be observed. This con-

dition can be expressed as:

mk ¼ dðsin a 6 sin bÞð4:167Þ

The plus s ign applies if the incident and the diffracted

ray lie on the same s ide of the normal to the grating

surface; m is called the order of the diffraction. For m

¼ 0, a ¼ b and the grating acts l ike a mirror. In any other

order, the diffraction maxima of different wavelengths

lie at different angles. The actual distribution of dif-

fracted intensity among the various or ders depe nds on

the proﬁle of the grating grooves. If the grooves are pla-

nar, cut a t an angle h to the plane of the grating, max-

imum diffracted intensity into a particular order results if

the angle of diffraction and the angle of reﬂection are the

same. In this case:

b  h ¼ c ð4:168Þ

h is called the blaze angle. The wavelength for which the

angle of reﬂection from the groove face and the diffraction

angle are the same is called the blaze wavelength, k

.Itis

common to use a grating in a Littrow conﬁguration so that

the diffracted ray lies in the same direction as the incident

ray. In this case:

mk ¼ 2d sin b ð4:169Þ

The wavelength at which the light reﬂects normally

from the grating groove satisﬁes:

¼ 2d sin h ð4:170Þ

Thus, for example, a grating could be speciﬁed to be

blazed at 600 nm in the ﬁrst order; it would, of course,

be simultaneously blazed in the second order for 300 nm,

the third order for 200 nm, and so on. Gratings are also

available with rectangular shaped (laminar proﬁle) or sinus-

oidal groove proﬁles. Laminar proﬁle grooves have low

second-order efﬁciency, which can be advantageous in vac-

uum ultraviolet applications: second-order rejection ﬁlters

are not available at such short wavelengths. Sinusoidal gra-

tings will operate over a broad spectral range, but their

diffraction efﬁciency into a particular order is at best

33%. There are many suppliers of both plane and concave

gratings, particularly Diffraction Products, Digital Optics,

Gentec, Jobin-Yvon, Newport, Optometrics, Spectrogon,

Spectrum Scientiﬁc, and TVC Jarrell-Ash.

Resolving Power. The resolving power of a grating is

a measure of its ability to separate two closely spaced

wavelengths. The resolving power depends both on the

dispersion and the size of the grating. For a ﬁxed angle

of incidence, the dispersion is deﬁned as:



d cos b

ð4:171Þ

Thus, the dispersion can be increased by increasing the

number of lines per millimeter (1/d), by operating in a high

order, and by using a large angle of incidence (grazing

incidence). The incidence, however, must not be so ﬂat as

to make the projection of the groove width perpendicular to

the incoming light smaller than the wavelength of the light.

The resolving power of a grating is Dk/k,wherek and k +

Dk are two closely spaced wavelengths that are just resolved

by the grating. The limiting resolution depends on the pro-

jected width of the grating perpendicular to the diffracted

beam. This width is Nd cos b,whereN is the total number

of lines in the grating. Diffraction theory predicts that

the angular resolution of an aperture of this size is

D/ ’ k=ðNd cos bÞ. The angle between the two closely

spaced wavelengths, from the dispersion relation, is:

Db ¼

mDk

d cos b

ð4:172Þ

In the limit of resolution, D/ ¼ Db, which gives:

k=Dk ¼ mN ð4:173Þ

Thus, from Equation (4.167):

Ndðsin a 6 sin bÞ

ð4:174Þ

202 OPTICAL SYSTEMS

and so it is clear that large gratings used at high angles give

the highest resolving power. The resolving powers avail-

able from 1 cm wide gratings range up to about 5 3 10

Concave gratings. These have long been used in short

wavelen gth applications because they provide diffracti v e and

focusing functions simultaneously. The development of

holographic concave gratings has made these devices widely

av ailable. They can be used to correct for aberrations which

occur when they are used in spectrometers (see Section 4.7),

and

to allow compact versions of such instruments to be

produced.

Efﬁciency. The efﬁciency of a grating is a measure of its

ability to diffract a given wavelength into a particular order

of the diffraction pattern. Blazing of the grating is the main

means for obtaining efﬁciency in a particular order;

without it, the diffracted energy is distributed over many

orders. Gratings are available with efﬁciencies of 95% or

more at their blaze wavelength, so they are virtually as

efﬁcient as a mirror, yet retain wavelength selectivity.

Defects in Diffraction Gratings. In principle, if an

ideal grating is illuminated with a plane monochromatic

beam of light, diffracted maxima occur only at angles that

satisfy the diffraction equation (4.167). In practice,

wever, this is not so. Gratings manufactured by ruling

a metal-coated substrate with a ruling engine exhibit

undesirable additional maxima.

Periodic errors in the spacing of the ruled grooves produce

Rowland ghosts. These are spurious intensity maxima, usu-

ally symmetrically placed with respect to an expected max-

imum and usually lying close to it. The strongest Rowland

ghosts from a modern ruled grating will be less than 0.1% of

the expected diffraction peaks. L yman ghosts occur at large

angular separations from their parent maximum, usually at

positions corresponding to a simple fraction of the wave-

length of the parent maximum – 4=9or5=9, for example.

They are also associated with slo w periodic errors in the

ruling process. Lyman-ghost intensities from modern gratings

are exceedingly weak (0.001% of the parent or less). Ghosts

can be a problem when used for the detection of weak emis-

sions in the presence of a strong laser signal, the ghosts of

which can (and have been) mistakenly identiﬁed as other real

spectral lines. If there is any suspicion of this, the weak signal

should be checked for its degree of correlation with the laser

signal – a linear correlation would be strong evidence for a

ghost. The development of unruled holographic gratings,

which are essentially perfect, plus the improvement of ruled

gratings made by interferometrically controlled ruling

engines, has considerably reduced the problem of ghosts.

There are other diffraction-grating defects. Satellites

are misplaced spectral lines, which can be numerous,

occurring very close to the parent, usually so close that

they can only be discerned under conditions of high res-

olution: they arise from small loc al varia tions in groove

spacing. Scattering gives rise to an appare nt weak contin-

uum over all diffraction angles w hen a grating is illumi-

nate d with an intense monochromatic source s uch as a

laser. Sc attering can arise from microscopic dust particles

or nongroove-like, ran dom d efects on the diffraction-

grating surface. In practice it does not follow th at a dif-

fraction grating that sh ows apparent bl emishes, such as

broad, shaded bands, will perform defec tively. One should

never attempt to remove such apparent visual bl emishes

by cleaning or polishing the grating.

Specialized Diffraction Gratings. Concave gra-

tings are frequently used in vacuum-ultraviolet spectrom-

eters and spectrographs, as they combine the functions of

both dispersing element and focusing optics. Thus, fewer

reﬂective surfaces are required – a highly desirable feature

of an instrument used at short wavelengths, where reﬂec-

tances of all materials decrease markedly.

Gratings for use at long wavelengths, above 50 lm,

use relatively few grooves per millimeter. Such gratings

are generally ruled directly on metal and are frequently

called echelettes (lit tle ladders) because of the shape of

their grooves.

Echelle gratings are special gratings designed to give

very high dispe rsion, up to 10

for ultraviolet wave-

lengths, when operated in a very high order. They have

the surface proﬁle illustrated in Figure 4.55,wherethe

dim

ension D is much larger than in a conventional gra-

ting, and can range up to several micrometers. Echelles

are widely used as the wavelength-tuning elemen t in

pulsed dye lasers because of their high dispersion and

efﬁcient operation. Other uses of diffraction gratings,

such as in the production of M oire

fringes and in inter-

ferometers, will not be discussed here. These subjects

have been dealt with by Girard and Jacquinot.

OPTICAL COMPONENTS 203

Practical Considerations in Using Diffraction

Gratings.

The main considerations in specifying a dif-

fraction grating are the wavelength region where maxi-

mum efﬁciency is required (which will specify the blaze

angle), and the number of grooves per millimeter and the

size of the grating (which will determine the resolving

power). Most gratings are rectangular or circular, the latter

being primarily for laser-cavity wavelength selection. Dif-

fraction gratings should be mounted with the care due all

precision components. Their surfaces should never be

touched and should be protected from dust. It is important

to note that if a grating is illuminated with a giv en wave-

length, say 300 nm, then dif fraction maxima will occur in the

same positions as would be found for 600 and 900 nm. This

dif ﬁculty can be av oided by using appropriate ﬁlters to pre-

vent unwanted wavelengths from passing through the system.

4.3.6 Polarizers

Polarized Light. If the electric vector of an

electromagnetic wave always points in the same

direction as the wave propagates through a medium, then

the wave is said to be linearly polarized. The direction of

linear polarization is deﬁned as the direction of the electric

displacement vector D, where:

D ¼ e

E ð4:175Þ

Except in anisotropic media, where e

is a tensor, D and

E are parallel and the direction of linear polarization can

be taken as the direction of E. If a combination of

two linearly polarized plane waves of the same frequency,

but having different phases, magnitudes, and polarization

directions, is propagating in the z-direction, the

resultant light is said t o be elliptical ly polarized.Such

a p air of waves, in genera l, have resultant electric ﬁelds

in the x-and y -directions t hat can be written as:

¼ E

cos xt ð4:176Þ

¼ E

cosðxt þ /Þð4:177Þ

where / is the phase difference between these two resul-

tant ﬁeld components. These are the parametric equations

of an ellipse. If / ¼ 6p/2 and E

¼ E

, then:

þ E

¼ E

ð4:178Þ

which is the equation of a circle. This represents circularly

polarized light. Then the instantaneous angle that the total

electric ﬁeld vector makes with the x-axis, as illustrated in

Figure 4.56, is:

a ¼ arctan

¼ arctan7 tan xt ¼ 7xt ð4:179Þ

Figure 4.56 Instantaneous direction of the electric vector

of an electromagnetic wave.

Figure 4.55 Echelle grating used in Littrow.

204 OPTICAL SYSTEMS

For / ¼ p/2, the resultant electric vector rotates coun-

terclockwiseviewedinthedirectionofpropagation–this

is right-hand circularly polarized light.If/ ¼ –p/2 the

rotation is clockwise – this is left-hand circularly polar-

ized light . The motion of the t otal electric vector as it

propagates is illustrated in Figure 4.57 .If/ ¼ 0o

we have linearly polarized light. Just as circularly p olar-

ized light can be viewed as a superposition of two linearly

polarized waves with orthogonal polarizations, a linearly

polarized wave can be regarded as a superposition of

left- and right-hand circularly po larized waves. If an el ec-

tromagnetic wave consists of a superposition of many

independent linearly p ola rized waves of independe nt

phase, amplitude, and polarization direction, it is said to

be unpolarized.

In anisotropic media – media with lower than cubic

symmetry – there is at least one direction, and at most

two directions, along which light can propagate with no

change in its state of polarization, independent of its state

of polarization. This direction is called the optic axis. Uni-

axial crystals have one such axis; biaxial crystals have

two. When a wave does not propagate along the optic axis

in such crystals, it is split into two polarized components

with orthogonal linear polarizations. In uniaxial crystals

these two components are called the ordinary and extraor-

dinary waves. They travel with different phase velocities,

characterized by two different refractive indices, n

and

(h), respectively, where h is the angle between the k vec-

tor of the wave and the optic axis. This phenomenon is

referred to as birefringence.

D and E are not necessarily parallel in an anisotropic

medium; however, D and H are orthogonal to the wave

vector of any propagating wave. Consequently the Poynt-

ing vector of the wave does not, in general, lie in the same

direction as the wave vector. The direction of the Poynting

vector is the direction of energy ﬂow – the ray direction.

When a plane wave crosses the boundary between an iso-

tropic and an anisotropic medium, the path of the ray will

not, in general, satisfy Snell’s law. The angles of refraction

of the ordinary and extraordinary rays will be different.

This phenomenon is called double refraction. In uniaxial

crystals, however, the ordinary ray direction at a boundary

does satisfy Snell’s law. For further details of these and

other optical characteristics of anisotropic media, the

reader should consult Born and Wolf,

Wahlstrom,

and Davis.

If linearly polarized light propagates into a birefringent

material, unless its polarization direction matches the

allowed direction of the ordinary or extraordinary wave,

it will be split into two components polarized in these two

allowed directions. These two components propagate at

different velocities and experience different phase changes

on passing through the crystal. For light of free-space

wavelength k

passing through a uniaxial crystal of length

L, the birefringent phase shift is:

D/ ¼

2pL

ðhÞn

½ð4:180Þ

In uniaxial crystals the allowed polarization directions

are perpendicular to the optic axis (for the ordinary wave)

and in the plane containing the propagation direction and

the optic axis (for the extraordinary wave), as shown in

Figure 4.57 Left-hand circularly polarized light. (From E.

Wahlstrom, Optical Crystallography, 3rd edn., John Wiley &

Sons, Inc., New York, 1960; by permission of John Wiley &

Sons, Inc.)

OPTICAL COMPONENTS 205

Figure 4.58. If the input wave is polarized at an angle b to

the ordinary polarization direction and D/ ¼ (2n þ 1)p,

the output wave will remain linearly polarized, but its

direction of polarization will have been rotated by an angle

of 2b. This rotation is always toward the ordinary polar-

ization direction, so a round-trip pass through the material

does not affect the polarization state. It is usual to make

b ¼ 45°, in which case the crystal rotates the plane of

polarization by 90°. Such a device is called a (2n þ 1)th-

order half-wave plate. On the other hand, if b ¼ 45° and

D/ ¼ (2n þ 1)p/2, the ordinary and extraordinary waves

recombine to form circularly polarized light. Such a device

is called a (2n + 1)th-order quarter-wave plate.Ifb is not

45°, a quarter-wave plate will convert linearly polarized

light into elliptically polarized light.

Polarization Changes on Reﬂection. As shown

in Section 4.2.6, if a linearly polarized wave reﬂects from

dielectric surface (or mirror), its state of linear polariza-

tion may be changed. For example, if a vertically polarized

wave traveling horizontally striking a mirror at 45° is

polarized in the plane of incidence, then after reﬂection

it will be traveling vertically and will be horizontally

polarized. A reﬂection off a second mirror at 45°,so

Figure 4.58 Cross-section of an ellipsoidal ﬁgure called the indicatrix, which allows

determination of the refractive indices and permitted polarization directions of a wave

traveling in a uniaxial crystal. The equation of the ellipse shown is (x

)+(z

) ¼ 1,

where OB ¼ n

and OC ¼ n

, OA ¼ n(h) is the effective extraordinary refractive index for a

wave traveling at angle h to the optic axis. The ordinary refractive index for this wave is still

and is independent of h.

206 OPTICAL SYSTEMS

oriented that the plane of incidence is perpendicular to the

polarization, will produce a horizontally traveling, hori-

zontally polarized wave. This exempliﬁes how successive

reﬂections can be used to rotate the plane of polarization of

a linearly polarized wave, and is illustrated in Figure 4.59.

circular or elliptically polarized light reﬂects from a

dielectric surface or mirror, its polarization state will, in

general, be changed. As an example, consider reﬂection at

a metal mirror. From Equations (4.87) and (4.89), for the

in-plane

and perpendicular polarized components of the

incident wave, respectively, we have:

¼1

ð4:181Þ

These reﬂection coefﬁcients ensure that the tangential

component of the electric ﬁeld goes to zero at the conduct-

ing surface of the mirror. As illustrated in Figure 4.60(a)

and

(b), this leads to a conversion of left- to right-hand

circularly

polarized light on reﬂection. The change of

polarization state on reﬂection from a dielectric interface

depends on the angle of incidence and whether n

> n

Figure 4.60 Changes of polarization state on reﬂection:

(a) and (b) conversion of left-hand

circularly polarized light (LHCP) to right-hand

circularly polarized light (RHCP) on reﬂection at

a perfect metal mirror; (c) conversion of LHCP to linear

polariation on reﬂection at Brewster’s angle.

Figure 4.59 Rotation of the plane of polarization

of a linearly polarized beam by successive reﬂection at two

mirrors.

OPTICAL COMPONENTS 207

A special case, illustrated in Figure 4.60(c), shows left-

hand circularly polarized light being converted to linearly

polarized light on reﬂection from an interface placed at

Brewster’s angle. Such changes of polarization state must

be taken into account when designing an optical system to

work with polarized light. The change in polarization of a

beam of light as it passes through a series of optical com-

ponents can be calculated very conveniently by the use of

Jones or Mueller calculus, which use matrix methods to

describe the state of polarization of the beam and its inter-

action with each component. Details of these techniques

are given by Shurcliff.

Linear Polarizers. A linear polarizer changes

unpolarized light to linearly polarized light or changes

polarized light to a desired linear polarization.

The simplest linear polarizers are made from dichroic

materials – materials that transmit one polarizat ion,

either ordinary or extraordinary, and strongly absorb

the other. Modern dichroic l inear polarizers , the com-

monest of which is Pola roid, ar e made of pol ymer ﬁlms

in which long- chain molecules with appropriate absorb-

ing side groups are oriented by stretching. The stretched

ﬁlm is then sandwiched between glass or plastic sheets .

These polarizers are inexpensive, but cannot be used to

transmit high intensities because they absorb all polariza-

tions to some degree. They cannot be fabricated to very high

optical quality, and generally only transmit about 50% of

light already linearly polarized for maximum transmission.

They do, however, work when the incident light strikes them

at any angle up to grazing incidence. The extinction coef-

ﬁcient K that can be achieved with crossed polarizers is

deﬁned as:

K ¼ log

ð4:182Þ

where T

and T

are the transmittances of parallel and

crossed polarizers, respectively. K is a useful quantity for

specifying a linear polarizer – the larger its value, the

better the polarizer. For dichroic polarizers, values of K

up to about 4 can be obtained. Polarizing beamsplitting

cubes provide linearly polarized light of relatively high

purity (98% or better) and can handle higher light inten-

sities. Corning manufacture a sheet polarizer called

Polacor made from glass containing billions of tiny silver

crystals. This material provides high throughput in the red

to near-infrared region, and extinction up to 4.

Higher quality, but more expensive, linear polarizers can

be made by using the phenomenon of double refraction in

transparent birefringent materials such as calcite, crystal-

line quartz, or magnesium ﬂuoride. Figure 4.61 shows

schematically

the way in which various polarizing prisms

of this type operate. Some of these polarizers generate two

orthogonally polarized output beams separated by an

angle, while others, for example the Glan–Taylor, reject

one polarization state by total internal reﬂection at a boun-

dary. Extinction coefﬁcients as high as 6 and good optical

quality can be obtained from such polarizers. The accept-

ance angle of these polarizers is generally quite small,

although it can range up to about 38° with an Ahrens

polarizer. Suppliers of polarizing prisms include Argyle

International, Gooch and Housego, Karl Lambrecht Cor-

poration, II-VI Infrared, Inrad, Lambda Research Optics,

Meadowlark Optics, Melles Griot, Newport/Oriel, Opto-

Sigmna, and Precision Optical.

Infrared polarizers (beyond about 7 lm) are often made

in the form of very many ﬁne, parallel, closely spaced

metal wires. Waves with their electric vector perpendicular

to the wires are transmitted; the parallel polarization is

reﬂected. Such polarizers are available from Coherent/

Molectron, Specac, and Thorlabs.

Linear polarizers for any wavelength where a transpar-

ent window material is available can be made using a stack

of plates placed at Brewster’s angle. Unpolarized light

passing through one such plate becomes slightly polarized,

since the component of incident light polarized in the plane

of incidence is completely transmitted, whereas only about

90% of the energy associated with the orthogonal polar-

ization is transmitted. A pile of 25 plates gives a high

degree of polarization. Stacked-plate polarizers are rather

cumbersome, but they are most useful for polarizing high-

energy laser beams where prism polarizers would suffer

optical damage. They are available commercially from

Inrad and II-VI Infrared (using ZnSe). For visible and

near-infrared light they can be easily made using a stack

of microscope slides.

Retardation Plates. Quarter-wave plates are gener-

ally used for converting linear to circularly polarized light.

208 OPTICAL SYSTEMS

Figure 4.61 Construction of various polarizers using birefringent crystals: (a) Ahrens polarizer – three calcite prisms cemented

together with Canada balsam, whose refractive index is intermediate between n

and n

for calcite. The O-ray suffers total

internal reﬂection at the cement and is absorbed in the black coating on the sides; (b) Glan–Foucault polarizer – two calcite

prisms separated with an air gap. The O-ray is totally internally reﬂected and either absorbed in the sides or transmitted

OPTICAL COMPONENTS 209

They should be used with the optic-axis direction at 45°

to the incident linear polarization direction. They are

available commercially in two forms: multiple- and single-

order. Multiple-order plates produce a phase change (retar-

dation) between the ordinary and extraordinary waves of

(2n +1)p/2. This phase difference is very temperature-

sensitive – a thickness change of one wavelength will pro-

duce a substantial change in retardation. Single-order

plates are very thin, their thickness being:

L ¼

4ðn

 n

ð4:183Þ

For example, with calcite, which has n

¼ 1.658, n

1.486, and with k

¼ 500 nm this thickness is only 726.7

nm. Consequently, most single-order plates are made by

stacking a (2n + 1)th-order quarter-wave plate on top of a

2nth-order plate whose optic axis is orthogonal to that of

the ﬁrst plate. The net retardation is just p/2 and is very

much less temperature-sensitive.

Direct single-order quarter-wave plates for low-inten-

sity applications can be made from mica, which cleaves

naturally in thin slices. The production of a plate for a

particular wavelength is a trial-and-error procedure.

12,45

Quarter-wave plates are invaluable, in combination with

a linear polarizer, for reducing reﬂected glare and for

reducing back reﬂections into an optical system, as shown

in Figure 4.62.

Half-wave

plates are generally used for rotating the

plane of polarization of linearly polarized radiation.

Figure 4.62 An optical isolator constructed from a linear polarizer and a

quarter-wave plate.

Caption for Figure 4.61 (cont.) if the sides are polished. A Glan–Thompson polarizer is similar; (c) Glan–Taylor polarizer –

similar to a Glan–Foucault polarizer except for the optic-axis orientation, which ensures that the transmitted E-ray passes

through the air gap nearly at Brewster’s angle; consequently, transmission losses are much reduced from those of a Glan–

Foucault. For high-power laser applications, the side faces can be polished at Brewster’s angle; (d) Rochon polarizer – two calcite

prisms with orthogonal optic axes cemented together with Canada balsam. / depends on the interface angle. The intensities of

the transmitted O- and E-rays are different. Other birefringent materials can be used; in the case of quartz, for example, the E-ray

would exit below the O-ray in the diagram shown here; (e) Senarmont polarizer – two calcite prisms cemented together with

Canada balsam. The angle / depends on h. This type of polarizer is less commonly used than the Rochon polarizer; (f) Wollaston

polarizer – two calcite prisms cemented together with Canada balsam. The O- and E-ray transmitted intensities are different. The

beam separation angle / depends on the interface angle h.

210 OPTICAL SYSTEMS

Multiple- and zero-order plates are available; as

in the case of quarter-wave plates, the operating

wavelength must be speciﬁed in buying one. This operat-

ing wavelength can be tuned to some extent by tilting

the retardation plate. Half-wave plates cannot be used

to make an optical isolator, as the polarization change

that occurs on one pass through the plate is reversed on

the return path.

Retardation plates only produce their speciﬁed retarda-

tion at a particular wavelength, and are usually speciﬁed

for normal, or almost normal incidence. Retardation plates

are available from several suppliers, including Karl Lam-

brecht Corporation, Optics for Research, Inrad, II-VI

Infrared, Esco, Melles Griot, Newport, OptoSigma and

Thorlabs. Continuously adjustable retardation plates,

called Babinet-Soleil compensators, are available from

Karl Lambrecht Corporation, Melles Griot, II-VI Infrared,

New Focus, Continental Optical, and OFR (now Thorlabs),

among others.

Retardation Rhombs. Because, in general, there is

a different phase shift on total internal reﬂection for

waves polarized in and perpendicular to the plane

of incidence, a r etarder that is virtually achromatic can

be made by the use of two internal reﬂections in a

rhomboidal prism of appropriate apex angle and refrac-

tive index. Two examples are shown in Figure 4.63.The

Fresne

l rhomb , for example, use s glass of index 1.51,

and with an apex angle of approximately 54.6° pr oduces

a retardation of exactly 90°. The op timum angle

must, h owever, be determined by trial and e rror, and

the desired retardation will only be obtained for a

speciﬁc angle of incid ence. Fresnel rhombs a re available

from II-VI Infrared, Karl Lambrecht (KLC), and

Newport/Oriel.

4.3.7 Optical Isolators

Optical isolators are devices that allow light to pass

through in one direction, but not in the reverse

direction. These devices contain t wo linear polarizers

and betwe en them a medium (generally a special

glass), which exhibits the Faraday effect. The medium

is placed in an axial magnetic ﬁeld provided by a

permanent magnet or magne ts. A Faraday-active

medium rotates the plane of an input linearly polarized

wave, and the direction of rotation depends on the

relative direction of light propagation and the magnetic

ﬁeld direction. In an isolator, the optical path

length through the Faraday material and the magnetic

ﬁeld strength are selected to provide a 45° rotation of the

input linear polarization, which then lines up with the

exit polarizer set at 45° to the input polarizer, as shown

Figure 4.63 Rhomb retarders: (a) Fresnel;

(b) Mooney.

OPTICAL COMPONENTS 211

in Figure 4.64. Light passing in the reverse direction has

its plane of linear polarization also rotated by 45°,butin

a sense that makes it o rthogonal to the next polarizer so

negligible light emerges. Co mmercially available Fara-

day isolators typically provide 30 dB isolation and must

be selected for the speciﬁc wavelength desired. Both

free space a nd optical- ﬁber-based devices are available

from companies such as AC Photonics, Conoptics, Elec-

tro-Optics Tech nology, Isowave, Leysop, Linos Pho-

tonics, Namiki, New Focus, Newport, a nd OFR (now

Thorlabs).

Optical isolators are particularly useful in certain preci-

sion experiments using lasers, to avoid feedback instabil-

ity. If some of the light from a laser re-enters the laser, the

amplitude and phase of the laser will ﬂuctuate, and this can

sometimes be very marked.

4.3.8 Filters

Filters are used to select a particular wavelength region from

light containing a broader range of wavelengths than is

desired. Thus, for example, they allow red light to be

obtained from a white light source, or they allow the isolation

of a particular sharp line from a lamp or laser in the presence

of other sharp lines or continuum emission. Although ﬁlters

do not have high resolving power (see Section 4.3.5), they

ve much higher optical ef ﬁ ciency at their operating wave-

length than higher-resolving-power, wavelength-selecti v e

instruments, such as prism or grating monochromators. That

is,theyhaveahighratiooftransmittedﬂuxtoinputﬂuxin

the wavelength region desired. Filters of several types are

av ailable for different applications.

Color Filters. A color ﬁlter selectively transmits a

particular spectral region while absorbing or reﬂecting

others. These simple ﬁlters are glasses or plastics

containing absorbing materials such as metal ions or

dyes, which have characteristic transmission spectra.

Such color ﬁlters are available from Chance-Pilkington,

Corning, CVI, Hoya, Kodak (Wratten ﬁlters), Kopp

Glass, Melles-Griot (now CVI-Melles-Griot), Newport,

Newport Thin Film Laboratory, Omega Optical,

Praezisions Glas & Optik, Schott, Rolyn, Rosco, and

Sterling Precision Optical. Transmission curves for these

ﬁlters are available from the manufacturers, and in

tabulations of physical and chemical data.

7,46

Care must be taken when color ﬁlters are being used to

block a strong light signal, such as a laser. These ﬁlters

may ﬂuoresce, so although the primary incident light is

blocked, a weak, longer-wavelength ﬂuorescence can

occur. We have seen this phenomenon quite strongly when

using orange plastic to block a blue/green laser.

Band-Pass Filters. A band-pass ﬁlter is usually a

Fabry–Perot etalon of small thickness. Although etalons

will be discussed in further detail in Section 4.7.4, a brief

discussion

is in order here.

In its simplest form, the Fabry–Perot etalon consists of a

plane, parallel-sided slab of optical material of refractive

index n and thickness d with air on both sides. In normal

incidence the device has maximum transmission for wave-

lengths for which the thickness of the device is an integral

number of half wavelengths. In this case, from Equation

(4.110):

¼ Z

ð4:184Þ

and there is zero reﬂection. For incidence at angle h,regard-

less of the polarization state of the light, there is maximum

transmission for wavelengths (in vacuo) that satisfy:

¼ 2d cos h

ð4:185Þ

where h

is the angle of refraction in the etalon.

A Fabry–Perot etalon is a ‘‘comb’’ ﬁlter. (Figure 4.159

shows an example of a transmission characteristic of such

device.) If the thickness of the etalon is small, the trans-

mission peaks are broad. In a typical band-pass ﬁlter oper-

ated as an etalon, all the transmission peaks but the desired

one can be suppressed by additional absorbing or multi-

layer reﬂective layers. The spectral width of the transmis-

sion peak of the ﬁlter can be reduced by stacking

Figure 4.64 Optical isolator that uses two linear polarizers

and a Faraday material producing a 45° polarization rotation.

212 OPTICAL SYSTEMS

individual etalon ﬁlters in series. A single etalon ﬁlter

might consist, for example, of two multilayer reﬂective

stacks separated by a half-wavelength-thick layer, as

shown in Figure 4.65(a), while a two-etalon ﬁlter would

hav

e two half-wavelength-thick layers bounded by multi-

layer reﬂective stacks. Commercially available band-pass

ﬁlters for use in the visible usually have a passband ranging

from below 1 nm to 50 nm (full width at half maximum

Figure 4.65 (a) Construction of an all-dielectric single-cavity Fabry–Perot

interference ﬁlter; (b) theoretical transmittance characteristics of single- and

double-cavity ﬁlters. (From Handbook of Lasers, R. J. Pressley (Ed.), CRC Press, Cleveland,

1971; by permission of CRC Press, Inc.)

OPTICAL COMPONENTS 213

transmission). The narrowest band-pass ﬁlters are fre-

quently called ‘‘spike ﬁlters.’’ Filters to transmit particu-

lar wavelengths, such as 632.8 nm (He-Ne laser), 514.5

and 488 nm (argon ion laser), 404.7, 435.8, 546.1, 577.0, and

671.6 nm (mercury lamp), 589.3 nm (sodium lamp), and

other wavelengths, are available as standard items.

Fil-

ters at nonstandard wavelengths can be fabricated as cus-

tom items. Band-pass ﬁlters for use in the ultraviolet

usually have lower transmittance, typically 20%, than ﬁl-

ters in the visible, whose transmittance usually ranges from

40% to 70%, being lowest for the narrowest passband.

Infrared band-pass ﬁlters are also readily obtained, at least

out to about 10 lm, and have good peak transmittance. The

typical available band-pass for a ﬁlter whose peak trans-

mission is k

peak

can usually be estimated as k

peak

/50,

although narrower band-pass ﬁlters can be obtained at

higher cost. Band-pass ﬁlters are available from many sup-

pliers, including Andover Optical, LOT-Oriel, Melles

Griot, Newport, Omega Optical, Spectrogon, Spectrum

Thin Films, and Sterling Precision Optical.

Band-pass ﬁlters are usually designed for use in normal

incidence. Their peak of transmission can be moved to shorter

wavelengths by tilting the ﬁlter, although the sharpness of the

transmission peak will be degraded by this procedure. If a

ﬁlter designed for peak wavelength k

is tilted by an angle

h, its transmission maximum will shift to a wav elength:

¼ k

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 

sin

ð4:186Þ

where n is the refractive index of the half-wavelength-thick

layer of the ﬁlter. For small tilt angles:

 k

sin

ð4:187Þ

Thus, a band-pass ﬁlter whose peak-transmission wave-

length is somewhat longer than desired can be optimized

by tilting.

Long- and Short-Wavelength-Pass Filters. A

long-wavelength-pass ﬁlter is one that transmits a broad

spectral region beyond a particular cutoff wavelength, k

min

A short-wavelength-pass ﬁlter transmits in a broad spectral

region below its cutof f wavelength k

max

. A combination of a

long-wavelength-pass and a short-wavelength-pass ﬁlter can

be used to produce a band-pass ﬁlter, as shown in Figure

4.6

6. Although long-and short-wavelength-pass ﬁlters usu-

ly involve multilayer dielectric stacks, the inherent

absorption and transmission characteristics of materials

can be utilized. Semiconductors exhibit fairly sharp long-

wavelength-pass behavior beginning at the band gap

energy. For example, germanium is a long-pass ﬁlter

with k

min

¼ 1.8 lm.

Holographic Notch Filters. These ﬁlters are special

diffractive structures that reﬂect a narrow range of wave-

lengths (~5 nm) very strongly, and consequently they

reduce transmitted light substantially (40–60 dB) over

the same narrow range. These ﬁlters are ideal for rejection

of laser light in experiments where a weaker light signal –

ﬂuorescence or Raman scattering – is being studied, and

some scattering or reﬂection of the excitation laser light is

occuring. These ﬁlters are available from Andor Technol-

ogy, Del Mar Ventures, Kaiser Optical Systems, MK Pho-

tonics, and Semrock.

Rugate Filters. Rugate ﬁlters are notch interfe rence

ﬁlters with high rejection of a narrow band of

wavelengths. In con trast to conventio nal multilayer

dielectric interference ﬁlters, in which the refractive

index variation from layer to layer is a square wave,

rugate ﬁlters use a sin usoidally variable refractive index

throughout the oxide ﬁlm layers. They can provide a

single notch band without harmonics, as shown in

Figure 4.66 Schematic transmission of long- and short-

pass optical ﬁlters showing the band-pass transmission

characteristics of the two in combination.

214 OPTICAL SYSTEMS

Figure 4.67. A rugate ﬁlter can look almost completely

colorless and transparent, and yet reject laser light at a

speciﬁed wavele ngth very efﬁciently. They are available

from Advanced Technology Coatings, Barr Associates,

Edmund Optics, Gist Optics, and Rugate Technologies.

Reststrahlen Filters. When ionic crystals are irradiated

in the infrared, they reﬂect strongly when their absorption

coefﬁcient is high, and their refractive index changes

sharply. This high reﬂection results from resonance

between the applied infrared frequency and the natural

vibrational frequency of ions in the crystal lattice. The

characteristic reﬂected light from different crystals, termed

Reststrahlen, allows speciﬁc broad spectral regions to be

isolated by reﬂection from the appropriate crystal. Some

examples of Reststrahlen ﬁlters are given in Figure 4.68.

Christiansen Filters. In the far infrared, the alkali

halides exhibit anomalous dispersion: at certain

wavelengths their refractive indices pass through unity.

Figure 4.67 Transmission characteristics of some rugate ﬁlters.

Figure 4.68 Reststrahlen ﬁlters. (Courtesy of Harshaw Chemical Co.)

OPTICAL COMPONENTS 215

(Normal dispersion involves an increase of refractive index

with wavelength.) Thus a po wdered alkali halide, which

would generally attenuate a transmitted wave sev erely

because of scattering, will transmit well at wav elengths

where its refractiv e inde x is the same as that of air. Filters

using such an alkali halide powder held between parallel

plates are called Christiansen ﬁlters and provide sharp

transmission peaks at certain wav elengths listed in Table 4.4.

Neutral-Density Filters. Neutral-density (ND) ﬁlters

are designed to attenuate light uniformly over some broad

spectral region. The ideal neutral-density ﬁlter should have

a transmittance that is independent of wavelength. These

ﬁlters are usually made by depositing a thin metal layer on

a transparent substrate. The layer is kept sufﬁciently thin

that some light is transmitted through it. The optical

density D of a neutral-density ﬁlter is deﬁned as:

D ¼ log

ð1=TÞð4:188Þ

where T is the transmittance of the ﬁlter. T is controlled

both by reﬂection from and by absorption in the metal

ﬁlm. If such ﬁlters are stacked in series, the optical density

of the combination is the sum of the optical densities of

the individual ﬁlters, provided the ﬁlters are positioned so

that multiple reﬂection effects do not occur between them

in the direction of interest.

Neutral-density ﬁlters are used for calibrating optical

detectors and for attenuating strong light signals falling

on detectors to ensure that they respond linearly. Because

neutral-density ﬁlters usually reﬂect and transmit light,

they can be used as beamsplitters and beamcombiners

for any desired intensity ratio. There are many suppliers.

Variable ND ﬁlters are available from HB Optical, Melles

Griot, Nova Phase, Reynard, and Singh-Ray.

Light Traps. If a beam of light must be totally absorbed

(for example, in an application where any reﬂected light

from a surface could interfere with some underlying weak

emission), a light trap can be constructed. The two types

illustrated in Figure 4.69 work well: the Wood’s horn, in

Figure 4.69 Light traps: (a) Wood’s horn; (b) stacked razor

blades.

Table 4.4 Christiansen ﬁlters

Crystal Wavelength of Maximum

Transmission (lm)

LiF 11.2

NaCl 32

NaBr 37

KCl 37

RbCl 45

NaI 49

CsCl 50

KBr 52

CsBr 60

TlBr 64

KI 64

RbBr 65

RbI 73

TlI 90

216 OPTICAL SYSTEMS

which a beam of light entering the trap is gradually

attenuated by a series of reﬂections at an absorbing

surface made in the form of a curved cone (usually made

of glass); and a stack of razor blades, which absorbs

incident light very efﬁciently.

4.3.9 Fiber Optics

As is well known, the use of o ptical ﬁbers has become

widespread in the telecommunications ﬁeld. Conse-

quently, there are numerous suppliers of the various

components and subsystems involved.

The use of

optical ﬁbers in scientiﬁc research can be a very valua-

ble technique, and one that is not particularly compli-

cated. For example, in experiments where radio

frequency (rf) interference, pickup, and ground loops

are a problem, an experimental signal can be used to

modulate a small light-emitting diode or laser. The

modulated optical signal is then passed along an optical

ﬁber to the observation location, where the original elec-

trical signal can be recovered with a photodiode. Com-

plete analog transmission systems of this kind are

available from A.A. Lab Systems, Alcatel, Analog

Modules, Force, J DS Uniphase, Luxlink, and Metrotek

Industries. A schematic diagram of the various compo-

nents of such a system is shown in Figure 4.70(a).

The

source may be supplied fabricated directly onto a

ﬁber. The modulator is frequ ently unnec essary, as th e

source itself can be directly amplitude-modulated. The

detector may also be supplied fabricated directly onto

the end of the ﬁber. A f ew spec iﬁc points are worthy of

note for the experimentalist who may wish to utilize this

technology.

For certain laboratory applications the construction of

a ﬁber system without any connectors is straightforward.

Light from the source is focused into the end of the ﬁber

with a microscope objective. Light emerging from the

other end of the ﬁber is focused onto the detector in a

Figure 4.70 (a) Fundamental components of a ﬁber-optic data link; (b) meridional section through a step-index optical

ﬁber. The core refractive index is n

; the cladding refractive index is n

. The core and cladding diameters are d and D,

respectively. A ray entering the ﬁber will be totally internally reﬂected provided its angle of incidence is less than h

, where

sin h

¼ NA.

OPTICAL COMPONENTS 217

similar way. A convenient range of microscope objec-

tives for this purpose is available from Newport, who

also supply a wide range of components for holding

and positioning ﬁbers. The choice of lens focal length

and placement is governed by the numerical aperture

(NA) of the ﬁber. The meaning of this parame ter ca n

be understood with reference to Figure 4.70(b),which

sho

ws a merid ional section through a so-called step-

index ﬁber. In this composite ﬁber the cylindrical core

has re fractive index n

, and the surrounding c ladding has

index n

, where for total internal reﬂection of rays to

occur in the core, n

> n

. Light entering the ﬁber at

angles < h

will totally internally reﬂect inside the core.

The NA is:

sin h

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

 n

ð4:189Þ

Commercially available ﬁbers typically have a

smoothly varying radial index proﬁle, but the NA is

still the appropriate parameter for determining the

acceptance angle. Two speciﬁc types of ﬁber are in

most common use: single-mode and multimode. Sin-

gle-mode ﬁbers typically have core diameters on the

order of 10 lm and cladding diamete rs of 125 lm.

They require very precise connectors and are only

needed in specialized experiments, for example in

high data rate optical communications, where the abil-

ity of the ﬁber to support only a single propagating

mode is important. Multimode ﬁbers have larger core

diameters, from 50 lmtoabove1mm,andcladding

diameters somewhat larger than their respective core

diameters. These ﬁbers are easy to use: the larger sizes

are frequently used to channel light for illumination

into pos itions that are difﬁcult to access, or to collect

light from o ne location a nd channe l it to a detector

somewhere else. Large ﬁbers that are suitable for these

purposes are available from AFL Telecommunications,

Berkshire Photonics, Edmund Optics, Fiberguide

Industries, Newport, P olymicro Technologies, and

3M Speciality Optical Fibers.

Fibers can be cut to provide a ﬂat end face with the aid

of specialist cleaving tool s of varying degrees of preci-

sion and complexity, available from suppliers such as

Newport and York. In s imple experimental setups an

adequate cleaved ﬂat face can be obtained in the follow-

ing way:

(1) Remove the outer plastic prot ect ive coating from

the cladding in the region that is to be cut by using

aﬁber-strippingtoolorbyimmersingthispartofthe

ﬁber in methylene chloride (the active ingredient in

most proprietary paint and varnish strippers). To

clean a ﬁber that has been stripped of its cladding

use Kimwipes or lens tissue moistened with pure iso-

propyl alcohol. Do not wipe the bare ﬁber with dry

tissue.

(2) Lightly scratch the cladding with a cleaving tool

(slightly more precise than a conventional glass cutter).

(3) Fasten one half of the ﬁber to a ﬂat surface with mask-

ing tape, and pull the other half of the ﬁber axially

away, keeping the ﬁber ﬂat on the surface.

This pro cedure usually g ives a ﬂat eno ugh face for

use w ith a microscope obje ctive. If ﬁbers are to be cut

and ﬁtted with connectors, they must be cut and pol-

ished according to the instructions supplied with the

connector.

Fiber Optic Connectors. If two identical ﬁbers are

to be joined together, this can be done with mechanical

coaxial connector s, with a mechanical splice, or the

ﬁbers can be fused together with a fusion splicer. In all

cases the ﬂat, cleaved faces of the two ﬁbers to be joined

must be brought together so that the two faces are in

close proximity, are parallel, and the ﬁbers are coaxial.

Proper alignments for orthogonal and angle c leaves are

shown in Figure 4.71(a) and (b) , respectively. Any

lateral

or tilt offset of the ﬁbers when they are joined

will reduce coupling efﬁciency. Precision mechanical

optical ﬁber connectors are able to couple two ﬁbers

together with losses in the range 0.1–0.2 dB.

Sometimes the connector contains a small amount of

index-matching gel that is squeezed in the gap

between the ﬁbers.

Mechanical ﬁber s plices are an inexpensive way to

join ﬁbers. They generally have a sleeve-like construc-

tion into which the two ﬁbers ar e pushed and then

glued or clamped in place. Better yet, a fusion splicer

can be used to fuse ﬁbers together; this is, however, an

expensive device. A good fusion splice can have a loss

218 OPTICAL SYSTEMS

below 0.1 dB. After two ﬁbers are f used together, a

splice protector should be included if the joined ﬁber

is to be protected from failure of the splice.

The use of optical ﬁber devices is much simpliﬁed

if these devices are purchased with appropriate ﬁber

optic connectors already attached. A convenient way

to obtain a connectorized ﬁber whe re access to one

free end is required is to buy a ﬁber jumper,which

is the optical equivalent of patch cord or coaxial

cable. By cutting the jumper cable, a length of ﬁber

with a conn ector on one end i s easily ob tained. Fiber

jumpers with various kinds of connectors, different

ﬁber optic cables, and of various lengths are readily

available (Cableorganizer.com, Datamax Technologies,

Fiberall, Fiber.com, Fiber Optic Cable Shop, L-Com,

Optica, Stonewall Cable, and Unicom). Fiber optic

connectors come in many types for both single-mode

and multimode ﬁbers: FC, LC, SMA, ST, SC, MT-RJ ,

MU, 50/125, D4, E20 00, 62.5/1 25, 9/125, and O pto-

clips. For special applications, angle-cleaved connec-

tors are available, which reduce the inevitable small

reﬂection that occurs at a ﬁber connector. A c ompre-

hensive discussion of practical ﬁber optics can be

found in Goff.

Polarization-maintaining (PM) ﬁber will preserve the

polarization state of launched light (to about 1% purity).

Special connectors and splicing techniques are needed for

PM ﬁber, as the azimuthal orientation of the two ﬁbers is

now important.

4.3.10 Precision Mechanical

Movement Systems

It is frequently necessary to be able to position compo-

nents in an optical system with high precision. The type

of stage with which this is done depends on the scale of

movement, the accuracy, repeatability resolution, and

freedom from backlash that is required. There a re a

large number of suppliers of stages, including transla-

tion, rotation, tilting, multi-ax is positioning and combi-

nations of these including Aerotech, Daedal, Melles

Griot, Newport, New Focus, Optosigma, Thor Labs,

and Velmex. Both manual and moto r-driven stages are

available. Although precision mechanica l stages can be

built in the laboratory, they are widely available com-

mercially. It is not likely that an experimentalist will

save money by building rather than buying a precision

stage.

The ac curacy of adjustment is the difference between

the actual and desired positions. Repeatability refers

to the ability to reproduce a desired position after a

movement of a stage to a different position. In a fair

comparison of stages this should involve signiﬁcant,

comparable movements away from, and t hen back to

a desired position. Resolution is the smallest motion

that a stage can make , which for a screw-driven

device will be limited by factors such as the number

of threads per inch in the lead screw, and friction. A

Figure 4.71 Alignment of optical ﬁbers for optical

connection: (a) correct alignment for perpendicular-cleaved

ﬁbers; (b) correct alignment for angle-cleaved ﬁbers;

OPTICAL COMPONENTS 219

precision micromete r might, for example, have a reso-

lution of about 1/10 of the smallest scale graduation

around the micrometer head. Another factor of impor-

tance i s cree p. A fter a stage has b een set to a desired

position does it stay there, or does removal of stress from

a positioning screw c ause it to relax? Absence of creep

means that a mount, once positioned, holds its position

for a long period. It is our experience that stainless-steel

mounts are less sus ceptible to creep than aluminum

mounts.

Resolution alone as a speciﬁcation does not mean

much without additional speciﬁcation of accuracy, repeat-

ability, and stability. The long-term stability of a mount

is also inﬂuenced by the thermal stability and expansion

of the materials from which the stage is made. The con-

venient materials of construction are aluminum alloy and

stainless steel.

Aluminum has a higher coefﬁcient of thermal expansion

(24 3 10

–6

/K) compared with stainless steel (10–16 3

–6

/K), but aluminum has a higher thermal conductivity

and reaches thermal equilibrium more quickly, which min-

imizes thermally induced strain. Aluminum takes a poor

thread and usually brass threaded inserts must be used for

brass or stainless-steel positioning screws.

The thermal stability of an optical mount can be

improved by using mounting assemblies constructed with

two dissimilar metals whose thermal expansions offset

each other. Commercially available mounts of the highest

precision may include this technology. The manufacturer’s

technical speciﬁcations should be consulted.

It is convenient to divide the movement scales available

into three broad categories.

(1) Medium – the scale of movement provided by manual

micrometer drives or precision lead screws. Typical

micrometer drives provide up to 50 mm travel with

accuracy on the order of 1 lm. Some commercial

drives claim a resolution below 0.1 lm, but, in prac-

tice, such claims must be reviewed with skepticism,

since the backlash, creep and repeatability of all

mechanical, screw-based, stages is likely to be worse

than this.

(2) Fine – The scales of movement, precision, and

repeatabily provided by motor-driven stages, which

may be driven either by a stepping motor or dc

motor. For repeatability, some form of encoding of

the position is needed, or feedback based o n the

characteristics of the state. Position encoding is usu-

ally done with either a shaft encoder, which tells

the drive motor on the lead screw exactly what its

angular position is, or with a linear encoder. A

linear encoder gives a more prec ise, r epeatable

measure of the actual location of the object being

moved. Precision drives incorporating encoders are

available from Grifﬁn Motion, Newport, Physik

Instrumente (PI), Quater, a nd Thorlabs. Precise

motor-driven stages are also available from Aerotech,

J.A. Noll, Daedal, Melles-Griot, Newport, and New

Focus.

(3) Nanoscale – p ositioning down to 1 nm resolution,

with varying degrees of repeatability. Positioning on

this scale requires the use of piezoelectric or electro-

static transducers. Piezoelectric transduc ers ge ner-

ally use a ceramic ma terial such as lead zirconate

titanate (PZT), which changes its shape in an

applied electric ﬁeld. Typical PZT transducers pro-

vide me chanical motion on the orde r of a few hun-

dreds o f nanometers for applied voltages on the

order of 1 kV. They provide resolution of 10 nm or

less, but do exhibit hysteresis, as shown i n Figure

72, unless some absolute position encoding

sch

eme is used. Individual PZT transduc ers are gen-

erally available either in the form of tubes or disks,

Figure 4.72 Hysteresis in the length change of

a piezoelectric element with applied voltage.

220 OPTICAL SYSTEMS

as shown in Figure 4.73 . Larger motions can be

obtained by stacking transducers in either a bimorph

or p olymorph arrangement. In a bimorph, two slabs

of PZT are driven so that one slab extends while the

other gets shorter, which ca uses the bimorp h to

bend, as shown in Figure 4.74.

a slab transducer, voltage is applied across the narrow

dimension of the slab, which will then change its thickness

with applied voltage. In a cylindrical transducer, voltage is

applied between the inner and outer metallized cylindrical

surface of the tube, which then changes its length in the

axial direction. Nanoscale precision piezoelectric drives

are available commercially from Attocube, Mad City

Labs, Melles Griot, Queensgate Instruments, Polytec,

Physik Instrumente, and Thorlabs, among others.

Bimorphs are available from FDK Products and Morgan

Electro Ceramics.

Small scale (~10 lm) precision motion in each of

three orthogonal axes can be accomplished inexpen-

sively with a mo diﬁed piezotube. A typical piezotube

is on the order of 30 mm long by 10 mm, and is generally

supplied with a metal coating on its inner and outer

cylindrical surfaces. The outer metallization should be

removedinfoursegementsapproximately1mmwide

spaced 90° apart on the outer cylindrical surface, as

shown in Figure 4.75. The four segements are then

riven by a ‘‘bridge’’ ampliﬁer current, in which oppo-

site pairs of electrodes are driven in a push-pull conﬁg-

uration, as shown schematically in Figure 4.76.Driving

lectrodes 1 and 2 produces an x-directed tilt of the tube,

electrodes 3 a nd 4 produce a y-directed tilt of the tube.

An additional ampliﬁer drives electrode 5 for z-directed

extension of the tube. Because the interelectrode

Figure 4.74 Operation of a bimorph piezoelectric element

in a parallel conﬁguration.

Figure 4.73 Simple piezoelectric elements: (a) slab; (b)

cylinder.

OPTICAL COMPONENTS 221

voltages used need to be as large as 1000 V, special op-

amps are required. Approp riate amplifers a re available

from Apex Microtec hnology Corporation. Piez o tubes

are available from Argillon, APC International, Boston

Piezo-Optics, Omega Pie zo Technologies, Physik

Instrumente (PI), and Sensor Technology.

4.3.11 Devices for Positional and

Orientational Adjustment of

Optical Components

For positioning a given component, the maximum number

of possible adjustments is six: translation along three

mutually orthogonal axes and rotation about these (or

other) axes. Mounts can be made that provide all six of

these adjustments simultaneously. Usually, however, they

are restricted and have no more degrees of freedom than

are necessary. Thus, for example, a translation stage is

usually designed for motion in only one dimension; inde-

pendent motion along other axes can then be obtained by

stacking one-dimensional translation stages. Orientation

stages are usually designed for rotation about one axis

(polar rotation) or two orthogonal axes (mirror mounts or

tilt tables). Once again, such mounts can be stacked to

provide additional degrees of freedom. It is often unneces-

sary for angular adjustment to take place about axes that

correspond to translation directions.

The ideal op tical mount provides independent

adjustment in each of its degrees of freedom without

any interaction with other potential degrees of free-

dom. It should be sturdy, insensitive to extraneous

vibrational disturbances, (such as air- or structure-

borne acoustic vibrations), and free of backlash during

adjustment. Generally it should be designed on k ine-

matic principles (see Section 1.7.1). The effect of tem-

perature

variations on an optical mount can also be

reduced, if desired, by constructing the mount from

Figure 4.76 Voltage drive scheme for a piezoelectric

element such as the one shown in Figure (4.69). Electrodes

1–4 are the quadrant electrodes, Electrode 5 is the inner

electrode.

Figure 4.75 A cylindical piezoelectric element with outer

quadrant electrodes. The element can be driven to provide

axial motion as well as tilt in two orthogonal axes.

222 OPTICAL SYSTEMS

low-coefﬁcient-of-expansion material, such as Invar, or

by using thermal-expansion compensation techniques.

Very high ridigity in an optical mount generally implies

massive construction. When weight is a limitation,

honeycombed material or material appropriately

machined to reduce excess weight can be used. Most

commercially available mounts are not excessively

massive, but represent a compromise between size,

weight, and rigidity. Generally, mounts do not need to

be made any more rigid than mechanical considerations

involving Young’s modulus and likely a pplied forces

on the mount would dictate.

The design of optical mounts on kinematic principles

involves constraining the mount just enough so that, once

adjusted, it has no degrees of freedom. Some examples

will illustrate how kinematic design is applied to optical

mounts.

Two-Axis Rotators. Within this category the

commonest devices are adjustable mirror or grating

mounts and tilt tables used for orienting components

such as prisms. Devices that adjust orientation n ear the

horizontal are usually called tilt adjusters. Mirror

holders, on the other hand, involve adjustment about

a vertical or near-vertical axis. A basic device of either

kind involves a ﬁxed stage equipped with three spherical

or hemispherical ball bearings, which locate,

respectively, in a V-groove, in a conical hole, and on a

plane surface machined on a movable stage. A typical

device is shown in Figure 4.77. The movable stage

makes

contact with the three balls on the ﬁxed stage at

just six points – sufﬁcient to prevent motion in its six

degrees of freedom – and is held in place with tension

springs between the ﬁxed and movable stages.

Adjustment is provided by making two of the locating

balls the ends of ﬁne-thread screws or micrometer heads.

Suitable micrometer heads for this purpose are

manufactured by Brown a nd Sharpe, Mitutoyo, Moore

and Wright, Shardlow, and Starrett, and are available

from most wholesale machine-tool suppliers. The ball

of the micrometer should be very accurately centered on

the spindle. The adju stment of the mo unt shown in

Figure 4.77 is about two almost orthogonal axes.

ere is s ome transla tion of the center of the movable

stage du ring ang ular adjustment, which can be avoided

by the use of a true gimbal mount.

A few of the constructional details of the mount in

Figure 4.77 are worthy of note. Stainless steel, brass,

and

aluminum are all suitable materials of construction;

an attempt to reduce the thermal expansion of the

mount by machining it from a low-expansion material

such as Invar may not meet with succe ss. Extensive

machining of low-expansion-coefﬁcient alloys gener-

ally increases the coefﬁcient, unless they are carefully

annealed afterward. Puttin g the component in boiling

water and letting it gradually cool will lead to partial

annealing. True kinematic design requires ball location

in a trihedr al hole, in a V-slot, a nd on a p lane surface

(or in three V-slo ts, but this no longer permits angular

adjustment about orthogona l axes) (see also Section

7.1). If the mount is made of aluminum, the locating

hole,

slot, and plane on the movable stage should be

made of stainless steel, or s ome other hard material,

shrunk-ﬁt into the main aluminum body. A true trihe-

dral slot can be made with a punch, as shown in

Figure 4.77 Kinematic double-hinge mirror mount.

OPTICAL COMPONENTS 223

Figure 4.78(a), or it can be machined with a 45° milling

cutter as shown in Figure 4. 78(b). A co nical hole i s not

ruly kinematic; a compromise design is shown in

Figure 4.79.

Altho

ugh motion of the mount in Figure 4.77 results

om direct micrometer adju stmen t, various c ommerc ial

mounts incorporate a reduc tion mechanism to increase

the s ensitivity of the mount. Typical schemes that are

used involve adjustment of a wedge-shaped surfac e by a

moving ball, as shown in Figure 4.80,ortheuseofa

ifferential screw drive . The two or more movable stages

of an adjustable mount can be held together with captive

tension springs, as in Figure 4.77. Designs involving only

small

angular adjustment can utilize the bending of a thin

section of material, as shown in Figure 4.81. The design of

such

mounts, called ﬂexures, is discussed in detail in

Section 1.7.6.

The

basic principle of a gimbal mount for two-axis

adjustment is shown in Figure 4.82. True orthogonal

motion

about two axes can be obtained in such a design

Figure 4.79 Compromise design for kinematic trihedral

hole.

Figure 4.78 Methods for making trihedral locating holes

for kinematic design; (a) trihedral steel punch; (b) trihedral

hollow machined with 45° milling tool; (c) steel balls ﬁtting

tightly in a hole.

224 OPTICAL SYSTEMS

without translation of the center of the adjusted compo-

nent. A kinematically designed gimbal mount is, however,

much more complicated in construction than the mount

shown in Figure 4.82. Precision gimbal mounts should

purchased rather than built. Very many companies man-

ufacture adequate devices with a variety of designs, and

their prices are lower than the cost of duplicating such

devices in the laboratory. Suppliers of gimbal mounts in-

clude Aerotech, Daedal, New Focus, Newport, J. A. Noll,

Standa, and Thorlabs. Most of these manufacturers also

manufacture good nongimbal mounts similar to the one

shown in Figure 4.77.

Translation Stages. Translation stages are generally

designed to provide linear motion in a single dimensio n

and can be stacked to provide additional degrees of free-

dom. Mounts fo r centering optical components, particu-

larly lenses, incorpor ate motion in two orthogonal (or

Figure 4.80 Cutaway views of a kinematic, single-axis rotator incorporating a

reduction mechanism involving a ball bearing on an angled surface. Two rotators of

this kind could be incorporated in a single mount to give two-axis gimbal adjustment.

Figure 4.81 Flexure type double-hinge mirror design.

OPTICAL COMPONENTS 225

near-or thogonal) axes in a single mount. The simplest

translation stages usu ally involve some sort of dovetail

groove arrangement, as shown in Figure 4.83(a).Greater

ecision can be obtained with ball bearings captured

between V-grooves with an arrangement to prevent adja-

cent balls from touching, as shown in Figure 4.83(b),or

ith crossed-roller bearings, as shown in Figure 4.83(c).A

simple

ball-bearing groove design is shown in Figure 4.84,

although

variants are possible. Suppliers of precision,

roller bearing translators include Aerotech, Daedal,

Melles Griot, Newport, OptoSigma, and Thorlabs. Vertical

translators using a ﬁne-thread screw drive are available

from Newport. Stages can be built to provide short-range,

highly stable, frictionless precision movement by using

ﬂexures, as shown in Figure 4.85. Typical travel of a ﬂex-

ure

stage is on the order of 10% to 15% of the dimensions

of the stage.

Less precise, but generally adequate, nonball-bearing

translation stages are available from Newport and Velmex.

Mounts for centering optical components such as lenses

are available from Aerotech, Ealing, and Newport, among

others. A simple kinematic design for a centering mount is

illustrated in Figure 4.86.

Rotators and Other Mounts. Rotators are used, for

example, for orienting polarizers, retardation plates,

prisms, and crystals. They provide rotation about a single

axis. Precision devices using ball bearings are available

from Aerotech, New Focus, Newport, OptoSigma, and

Thorlabs, among various other suppliers.

There are numerous more complicated optical mounts

than those described in the previous sections, which pro-

vide in a single mount any combination of degrees of free-

dom desired. Motor-driven and computer-controllable

versions of all these mounts are generally available. For

Figure 4.82 Schematic diagram of a true two-axis gimbal

mount. The center of the mounted component does not

translate during rotation.

Figure 4.83 Groove mounting arrangements for linear transation stages: (a) dovetail V-groove; (b) ball bearing;

226 OPTICAL SYSTEMS

details, the catalogs of the manufacturers previously men-

tioned should be consulted.

Optical Benches and Components. For optical

experiments that involve the use of one or more

optical compo nents in conjunctio n with a sou rce and/

or a detector in some sort of linear optical

arrangement, construction usin g an o ptical bench and

components is very convenient, particularly in

breadboarding applica tions. The commonest such

bench d esign is base d on the equilateral triangular bar

developed by Zeiss and typically machined from lengths

of stabilized cast iron. Aluminum benches of this type

are a lso available, but are less rigid. Components are

mounted on the bench in r od-mounted holders t hat ﬁt

into carriers that locate on the triangular ben ch. A cross-

sectional diagram of a typical bench and carrier is shown

in Figure 4.87.

Figure 4.84 Section drawings of a simple 1-D translation

stage.

Figure 4.85 Linear translation stage using ﬂexure

mounts.

Figure 4.86 A simple precision centering stage.

OPTICAL COMPONENTS 227

Coarse adjustment along the length of the bench is pro-

vided by moving the carrier manually. On many benches

this is accomplished with a rack-and-pinion arrangement. A

wide range of mounts and accessories are available, provid-

ing for vertical, lateral, and longitudinal adjustment of

mounted-component positions. Holders for ﬁlters, for cen-

tering lenses, and for holding and rotating prisms and polar-

izers are readily obtained. Precision gimbal mounts,

translators, and rotators can be readily incorporated into

the structure. Examples of devices that lend themselves well

to optical-bench construction are telescopes, collimators,

laser-beam expanders and spatial ﬁlters, optical isolators,

and electro-optic light modulators. Optical benches and

accessories are available from Edmund Optics, Lasico, Linos

Photonics, Melles Griot, and Ne wport. Optical benches are

no longer as commonly used or available as they once were

because of the wide availability of optical tables and mounts,

and the additional ﬂexibility provided by their use.

Piezoelectric Transducers. Most PZTs are made

from ferroelectric ceramics, such as lead zirconate titanate

or barium titanate, but polymers such as polyvinylidene

ﬂuoride (PVF) are also used. Simple ceramic transducers

are usually supplied as ﬂat discs with a metalized layer on

each ﬂat face, or as short hollow cylinders, in which case

the metalized electrodes are deposited on the inner and

outer cylindrical surfaces. The ﬂat discs change their thick-

ness with applied voltage, the cylindrical types change

their axial length. Typical length changes are on the order

of 10

–9

mV. Therefore, these devices are particularly suit-

able for very ﬁne (submicron) positioning. Much larger

motions can be obtained with bimorph PZTs. Bimorphs

can be stacked to provide macroscopic motions for modest

applied voltages. Excursions of several millimeters can be

obtained for voltages of 1 kV. Even larger motions can be

obtained with Inchworm transducers, available from

EXFO-Burleigh and Sensor Technology. Basic ceramic

transducer elements are available from EDO Electro-

Ceramic Products, Physik Instrumente (PI), Piezo Sys-

tems, CTS Piezoelectric Products, Polytec, and Queen-

sgate Instruments. PVF transducers are available from

Atochem North America (formerly Pennwalt). Complete

transducer assemblies are available from EXFO-Burleigh,

Newport/Klinger, and Polytec Optronics.

Voice Coil Actuators. Voice coil actuators are a con-

venient way to generate linear movement in the range

between micrometers and tens of millimeters, with zero

hysteresis, and up to audio frequencies. They are essen-

tially the same as the mechanism in a loudspeaker that

moves the diaphragm to generate sound. They are direct

drive linear actuators that incorporate magnets and an elec-

trical coil. The voice coil itself is a noncommutated, two-

terminal device. It has linear control characteristics, zero

hysteresis, zero backlash, and inﬁnite position sensitivity.

It has short mechanical and electrical time constants and a

high output power-to-weight ratio. A voice coil is gener-

ally operated in a control loop where a control signal is

provided from a position readout device. Voice coil

Figure 4.87 Typical dimensions of a Zeiss triangular optical

bench with carrier and mounted optical component.

(Courtesy of Ealing Corporation).

228 OPTICAL SYSTEMS

actuators are available from Airex, BEI Kimco, Equipment

Solutions, H2W Technologies, Innotics, and Orlin.

4.3.12 Optical Tables and

Vibration Isolation

A commercially made optical table provides the perfect

base for construction of an optical system. Such tables

have tops made of granite, steel, Invar, Superinvar (very

expensive), or ferromagnetic or nonmagnetic stainless

steel. When vibrational isolation of the table top is

required, the top is mounted on pneumatic legs. Such an

arrangement effectively isolates the table top from ﬂoor

vibrations above a few Hertz. To minimize acoustically

driven vibrations of the table top itself, the better metal

ones employ a laminated construction with a corrugated or

honeycomb metal cellular core bonded with epoxy to the

top and bottom table surfaces.

Granite table tops are very much less intrinsically reso-

nant than metal tops and represent the ultimate in dimen-

sional stability and freedom from undesirable vibrational

modes. Complete pneumatically isolated optical table sys-

tems, nonisolated tables, and table tops alone are available

from Kinetic Systems, Melles Griot, Newport, Standa,

Thorlabs, and TMC. In selecting a table, points of compar-

ison to look for include the following:

(1) The overall ﬂatness of the table top (ﬂatness within

50 lm is good, although greater ﬂatness can be obtained)

(2) The low-frequency vibration isolation characteristics

of the pneumatic legs

(3) The rigidity of the table top (how much it deforms with

an applied load at the center or end)

(4) The isolation from both vertical and horizontal vibra-

tions

(5) The frequencies and damping of the intrinsic vibra-

tional modes

(6) Are the threaded holes in the table top sealed so that

liquid spills do not disappear into the interior honey-

combs of the table?

Other criteria, such as cost and table weight, may be

important. Typical sizes of readily available tops range

up to 5 3 12 ft (larger tables are also available) and in

thickness from 8 in. to 2 ft. The thicker the table, the

greater its rigidity and stability. Most commercial tables

are available with 1= 4-20 threaded holes spaced on 1 in.

centers over the surface of the table. Better designs use

blind holes of this type so that liquids spilt on the table

do not vanish into its interior. Ferromagnetic table tops

permit the use of magnetic hold-down bases for mounting

optical components. Such mounts are available from

numerous optical suppliers. It is cheaper, and just as sat-

isfactory, to buy magnetic bases designed for machine-tool

use from a machine-tool supply company.

Steel and granite surface plates that can be used as

small, nonisolated optical tables are available from

machine-tool supply companies. If it is desired to construct

a vibration-isolated table in the laboratory, a 2 in. thick

aluminum plate resting on underinﬂated automobile-tire

inner tubes works rather well, although the plate will have

resonant frequencies. Very ﬂat aluminum plate, called jig

plate, can be obtained for this application at a cost not

much greater than ordinary aluminum plate. Just mounting

a heavy plate on dense polyurethane foam also works sur-

prisingly well. In fact, the vibrational isolation of a small

optical arrangement built on an aluminum plate and

mounted on a commercial optical table is increased by

having a layer of thick foam between plate and table top.

Even the best-constructed precision optical arrangement

on a pneumatic isolation table is subject to airborne acous-

tic disturbances. A very satisfactory solution to this prob-

lem is to surround the system with a wooden particle-board

box lined with acoustic absorber. Excellent absorber mate-

rial, a foam–lead–foam–lead–foam sandwich called Hush-

cloth DS, is available from American Acoustical Products.

4.3.13 Alignment of Optical Systems

Small helium–neon lasers are now so widely available and

inexpensive that they must be regarded as the universal tool

for the alignment of optical systems. Complex systems of

lenses, mirrors, beamsplitters, and so on can be readily

aligned with the aid of such a laser: even visible-opaque

infrared components can be aligned in this way by the use

of reﬂections from their surfaces. Fabry–Perot interferom-

eters, perhaps the optical instruments most difﬁcult to align,

are easily aligned with the aid of a laser. The laser beam is

shone orthogonally through the ﬁrst mirror of the interfer-

ometer (easily accomplished by observing part of the laser

OPTICAL COMPONENTS 229

beam reﬂect back on itself), and the second interferometer

mirror is adjusted until the resultant multiple-spot pattern

between the mirrors coalesces into one spot.

4.3.14 Mounting Optical Components

A very wide range of optical devices and systems can be

constructed using commercially available mounts

designed to hold prisms, lenses, windows, mirrors, light

sources, and detectors. Some commercially made optical

mounts merely hold the component without allowing pre-

cision adjustment of its position. Many of the rod-mounted

lens, mirror, and prism holders designed for use with stand-

ard optical benches fall into this category, although they

generally have some degree of coarse adjustability; how-

ever, a wide range of commercially available optical mounts

allow precision adjustment of the mounted component.

The construction of a complete optical system from

commercial mounts can be very expensive, while provid-

ing in many cases unnecessary, and consequently undesir-

able, degrees of freedom in the adjustment and orientation

of the various components of the system. Although extra

adjustability is often desirable when an optical system is in

the ‘‘breadboard’’ stage, in the ﬁnal version of the system it

reduces overall stability. An adjustable mount can never

provide the stability of a ﬁxed mount of comparable size

and mass. Stability in the mounting of optical components

is particularly important in the construction of precision

optical systems for use, for example, in interferometry and

holography.

A custom-made optical mount must allow the insertion

and stable retention of the optical component without dam-

age to the component, which is usually made of some

fragile (glassy or single-crystal) material. If possible, the

precision surface or surfaces of the component should not

contact any part of the mount. The component should be

clamped securely against a rigid surface of the mount. It

should not be clamped between two rigid metal parts:

thermal expansion or contraction of the metal may crack

the component or loosen it. The clamping force should be

applied by an intermediary rubber pad or ring. Some exam-

ples of how circular mirrors or windows can be mounted in

this way are shown in Figure 4.88. If a precision polished

surface

of the component must contact part of the mount

(for example, when a precision lens, window, mirror, or

prism is forming a vacuum-tight seal), the metal surface

should be ﬁnely machined: the edges of the mounting sur-

face must be free of burrs. Ideally, the metal with which the

component is in contact should have a lower hardness than

Figure 4.88 Ways for mounting delicate optical compo-

nents: (a) no contact between precision surface of compo-

nent and mount; (b) precision surface in minimal contact

with mount and held in place with retaining ring; (c) pre-

cision surface in minimal contact with bottom of recess in

mount and held in place with threaded plastic ring.

230 OPTICAL SYSTEMS

the component. A thin piece of paper placed between the

component and metal will protect the surface of the com-

ponent without signiﬁcantly detracting from the rigidity of

the mounting.

Generally speaking, unless an optical component has

one of a few standard shapes and sizes, it will not ﬁt

directly in a commercial mount and a custom adaptor will

need to be made.

It is often necessary to mount a precision optical com-

ponent (usually a ﬂat window or mirror, but occasionally a

lens or spherical mirror) so that it provides a vacuum- or

pressure-tight seal. There are two important questions to

be asked when this is done: can the component, of a certain

clear aperture and thickness, withstand the pressure differ-

ential to which it will be subjected, and will it be distorted

optically either by this pressure differential or the clamp-

ing forces holding it in place?

There are various ways of mounting a circular window

so that it makes a vacuum- or pressure-tight seal.

Demountable seals are generally made by the use of rub-

ber O-rings (see Section 3.5.2) for vacuum, or ﬂat rubber

skets for pressure. More-or-less permanent seals are

made with the use of epoxy resin, by running a molten

bead of silver chloride around the circumference of the

window where it sits on a metal ﬂange , or in cert ain cases

by directly soldering or fusing the window in place. Some

crystalline materials, such as germanium, can be soldered

to metal; many others can be soldered with indium if they,

and the part to which they are to be atta ched , are appro-

priately treated with gold paint beforehand.

If a window

is fused in place, its c oefﬁcient of expansion must be w ell

matched to that of the part to which it i s ﬁxed. Suitably

matched glass, fused silica, and sapphire windows on

metal are available. Either the glass and metal are them-

selves matched, or an intermediate graded seal is used

(see Section 2.2.4). To decide what thicknes s-t o-un sup-

por

ted-diameter ratio is appropriate for a given pressure

differential, it must be determined whether the method of

mounting corresponds to Figure 4.89(a) or (b). In either

case,

the maximum stress in the window must be kept

below the modulus of rupture Y of the window by an

appropriate safety factor S

. A safety factor of four is

generally adequate for determining a safe window

thickness, but a larger factor may be necessary to avoid

deformationofthewindowthatwouldleadtodistortion

of transmitted wavef ronts. The desired thickness-to-free-

diameter ratio for a pressure differential p is found from

the formula:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

KpS

ð4:190Þ

where K is a constant whose value can be taken as 0.75

for a clamped edge and 1.125 for a free edge (see also

Sections 1.6.3 and 3.6.3).

window mounted with an O-ring in a groove, as shown

in Figure 4.90, may not provide an adequate seal at mod-

erately

high pressures, say above 7MPa

, unless the clamp-

ing force of the window on the ring is great enough to

prevent the pressure differential deforming the ring in its

grooves and creating a leak. A better design for high-pres-

sure use, up to about 50MPa, is shown in Figure 4.90(b):

the

clamping force and internal pressure act in concert

to compress the ring into position. Clamping an optical-

quality window or an O-ring seal of the sort shown in

Figure 4.90(a) may cause slight bending of the window.

an optical window has been ﬁxed ‘‘permanently’’ in

place with epoxy resin, it may be possible to recover the

window, if it is made of a robust material, by heating the

seal to a few hundred degrees or by soaking it in methylene

chloride or a similar commercial epoxy remover.

If optical windows are to be used in pressure cells where

there is a pressure differential of more than 500 bars

(’ 7000 psi), O-rings are no longer adequate and special

window-mounting techniques for very high pressures must

be used.

50–52

Optical cells for use at pressures up to 3 kbar

are available from ISS, Inc.

Figure 4.89 Window mounting arrangements: (a) clamped

or ﬁxed edge (maximum stress at edge); (b) unclamped or

freely supported edge (maximum stress at center).

OPTICAL COMPONENTS 231

4.3.15 Cleaning Optical Components

It is always desirable for the components of an optical sys-

tem to be clean. At the very least, particles of dust on mirrors,

lenses, and windows increase scattering; organic ﬁlms lead

to unnecessary absorption, possible distortion of transmitted

wavefronts, and – in experiments with ultraviolet light sour -

ces – possible unwanted ﬂuorescence. In optical systems

employing lasers, dust and ﬁlms will frequently lead to visi-

ble, undesirable interference and diffraction effects. At

worst, dirty optical components exposed to high-intensity

laser beams can be permanently damaged, as absorbing dust

and ﬁlms can be burnt into the surface of the component.

The method used for cleaning optical components, such as

mirrors, lenses, windows, prisms, and crystals, will depend

on the nature of both the optical component and the type of

contaminant to be removed. For components made of hard

materials, such as borosilicate glass, sapphire, quartz, or

fused silica, gross amounts of contamination can be

removed by cleaning in an ultrasonic tank. The tank should

be ﬁlled with water and the components to be cleaned

placed in a suitable pure solvent, such as acetone or tri-

chloroethylene, contained in a clean glass or plastic

beaker. If trichloroethylene is used, the operation should

be performed inside a fume hood because there is evidence

that this solvent is a human carcinogen. The ultrasonic

cleaning is accomplished by placing the beaker in the tank

of water. Dust can be removed from the surface of hard

materials, including most modern hard dielectric reﬂecting

and antireﬂecting coatings, by brushing with a soft camels-

hair brush. Suitable brushes are available from most photo-

graphic stores. Lens tissue and solvent can be used to clean

contaminants from both hard and medium-hard surfaces,

provided the correct method is used. The category of

medium-hard materials includes materials such as arsenic

trisulﬁde, silicon, germanium, gallium arsenide, KRS-5,

and tellurium. Information about the relative hardness of

these and other materials is contained in Table 4.5. Dust

should

ﬁrst be removed from the component by wiping,

very gently, in one direction only, with a folded piece of

dry lens tissue. The tissue should be folded so that the

ﬁngers do not come near any part of the tissue that will

contact the surface. Better still, if a cylinder of dry nitrogen

is available, dust can be blown from the surface of the

component. Because the gas can itself contain particles,

it should be passed through a suitable ﬁlter, such as ﬁne

sintered glass, before use. Clean gas can be used in this

way to remove dust from the surface of even very delicate

components, such as aluminum- and gold-coated mirrors,

and diffraction gratings. The use of gas jets for dust

removal requires caution: delicate structures have been

damaged by the force of the gas. Commercial ‘‘dust-off’’

sprays are available that use a liquiﬁed propellant gas that

vaporizes on leaving the spray-can nozzle. These sprays

Figure 4.90 Mounting arrangements for optical windows in vacuum and pressure appli-

cations: (a) simple vacuum window; (b) high-pressure window.

232 OPTICAL SYSTEMS

Table 4.5 Characteristics of optical materials

Material Useful Transmission Range

(> 10% transmission)

in 2 mm Thickness

Index of Refraction [wavelength

(lm) in parentheses]

Knoop

Hardness

Melting

Point (°C)

LiF 0.104–7 1.60(0.125), 1.34(4.3) 100 870

MgF

0.126–9.7 n

¼ 1.3777, n

¼ 1.38950(0.589)

415 1396

CaF

0.125–12 1.47635(0.2288), 1.30756(9.724) 158 1360

BaF

0.1345–15 1.51217(0.3652), 1.39636(10.346) 65 1280

Sapphire(Al

) 0.15–6.3 n

¼ 1.8336(0.26520),

1525-2000

2040 6 10

¼1.5864(5.577)

, n

slightly less than n

Fused silica (SiO

) 0.165–4

1.54715(0.20254), 1.40601(3.5) 615 1600

Pyrex 7740 0.3–2.7 1.474(0.589), ’ 1.5(2.2) ’600 820

Vycor 7913 0.26–2.7 1.458(0.589) — 1200

0.6–0.13 2.84(1.0), 2.4(8) 109 300

RIR 2 ’0.4–4.7 1.75(2.2) ’600 ’900

RIR 20 ’0.4–5.5 1.82(2.2) 542 760

NaF 0.13–12 1.393(0.185), 0.24(24) 60 980

RIR 12 ¼0.4–5.7 1.62(2.2) 594 ’900

MgO 0.25–8.5 1.71(2.0) 692 2800

Acrylic 0.340–1.6 1.5066(0.4101), 1.4892(0.6563) — Distorts at 72

Silver chloride (AgCl) 0.4–32 2.134(0.43), 1.90149(20.5) 9.5 455

Silver bromide (AgBr) 0.45–42 2.313(0.496), 2.2318(0.671) > 9.5 432

Kel-F 0.34–3.8 — — —

Diamond (type IIA) 0.23–200+ 2.7151(0.2265), 2.4237(0.5461) 5700–10400

NaCl 0.21–25 1.89332(0.185), 1.3403(22.3) 18 803

KBr 0.205–25 1.55995(0.538), 1.46324(25.14) 7 730

KCl 0.18–30 1.78373(0.19), 1.3632(23) — 776

CsCl 0.19– ’30 1.8226(0.226), 1.6440(0.538) — 646

CsBr 0.21–50 1.75118(0.365), 2.55990(39.22) 19.5 636

KI 0.25–40 2.0548(0.248), 1.6381(1.083) 5 723

CsI 0.235–60 1.98704(0.297), 1.61925(53.12) — 621

SrTiO

0.4–7.4 2.23(2.2), 2.19(4.3) 620 2080

SrF

0.13–14 1.438(0.538) 130 1450

Rutile (TiO

) 0.4–7 n

¼ 2.5(1.0), n

¼ 2.7(1.0)

880 1825

Thallium bromide (TlBr) 0.45–45 2.652(0.436), 2.3(0.75) 12 460

Thallium bromoiodide (KRS-5) 0.56–60 2.62758(0.577), 2.21721(39.38) 40 414.5

Thallium chlorobromide (KRS-6) 0.4–32 2.3367(0.589), 2.0752(24) 39 423.5

ZnSe 0.5–22 2.40(10.6) 150 —

Irtran 2 (ZnS) 0.6–15.6 2.26(2.2), 2.25(4.3) 354 800

Si 1.1–15

3.42(5.0) 1150 1420

Ge 1.85–30

4.025(4.0), 4.002(12.0) 692 936

GaAs 1–15 3.5(1.0), 3.135(10.6) 750 1238

CdTe 0.9–16 2.83(1.0), 2.67(10.6) 45 1045

Te 3.8–8+ n

¼ 6.37(4.3), n

¼ 4.93(4.3)

— 450

CaCO

0.25–3 n

¼ 1.90284(0.200), n

¼ 1.57796(0.198)

——

¼ 1.62099(2.172), n

¼ 1.47392(3.324) 135 894.4

OPTICAL COMPONENTS 233

LiF 9 0.27 HF Scratches easily

MgF

16 7.6 3 10

–3

HNO

—

CaF

25 1.1 3 10

3

salts Not resistant to thermal or mechanical shock

BaF

26 0.12 NH

Cl Slightly hygroscopic, sensitive to thermal shock

6.66,

5.0

9.8 3 10

5

salts Very resistant to chemical attack, excellent material

SiO

0.55 0.00 HF Excellent material

Pyrex 3.25 0.00 HF, hot H

Excellent mechanical, optical properties

Vycor 0.8 0.00 HF, hot H

Excellent mechanical, optical properties

26 5 3 10

5

Alcohol Nonhygroscopic

RIR 2 8.3 0.00 1% HNO

Good mechanical, optical properties

RIR 20 9.6 — — Good mechanical, optical properties

NaF 36 4.2 HF Lowest ref. index of all known crystals

RIR 12 8.3 — — Good mechanical and optical properties

MgO 43 6.2 3 10

4

salts Nonhygroscopic; surface scum forms if stored in air

Acrylic 110–140 0.00 Methylene chloride Easily scratched, available in large sheets

AgCl 30 1.5 3 10

4

OH, KCN Corrosive, nonhygroscopic, cold-ﬂows

AgBr — 12 3 10

6

KCN Cold-ﬂows

Kel–F — — — Soft,easily scratched

Diamond 0.8 0.00 — Hardest material known; thermal conductivity

6 3 Cu at room temp., chemically inert

NaCl 44 36 H

O, glycerine Corrosive, hygroscopic

KBr — 65.2 H

O, glycerine Hygroscopic

KCl — 34.35 H

O, glycerine Hygroscopic

CsCl — 186 Alcohol Very hygroscopic

CsBr 48 124 H

O Soft, easily scratched, hygroscopic

KI — 144.5 Alcohol Soft, easily scratched, hygroscopic, sensitive to thermal

shock

CsI 50 160 Alcohol Soft, easily scratched, very hygroscopic

SrTiO

9.4 — — Refractive index ’

ﬃﬃﬃ

SrF

— 1.17 3 10

2

Hot HCl Slightly sensitive to thermal shock

TiO

9 0.00 H

Nonhygroscopic, nontoxic

TlBr — 0.0476 Alcohol Flows under pressure, toxic

KRS-5 51 <0.0476 HNO

, aqua regia Cold-ﬂows, nonhygroscopic, toxic

KRS-6 60 0.32 HNO

, aqua regia Cold-ﬂows, nonhygroscopic, toxic

ZnSe 8.5 0.001 — Very good infrared materials, also transparent to some

visible light

ZnS — 6.5 3 10

5

HNO

—

Si 4.2 0.00 HF + HNO

Resistant to corrosion, must be highly polished

Ge 5.5 0.00 Hot H

, aqua regia to reduce scattering losses at surface

Table 4.5 (cont.)

Material Thermal-

Expansion

Coefﬁcient

(10

–6

/K)

Solubility

in Water

[g/(100 g),

20°C]

Soluble in Comments

234 OPTICAL SYSTEMS

are not recommended for cleaning delicate or expensive

components. They can exert considerable force at close

range and can also deposit unvaporized propellant on the

component, or condense water vapor into the surface of a

hygroscopic material.

There are two good methods for cleaning hard and

medium-hard components with lens tissue and solvent. The

lens tissue should be folded as indicated previously, and a few

drops of solvent placed on the tissue in the area to be used for

the cleaning. The tissue should be wiped just once in a single

direction across the component and then discarded. Fingers

should be kept away from the solvent-impregnated part of the

tissue, and it may be desirable to hold the component to be

cleaned with a piece of dry tissue to avoid the transmission of

ﬁnger grease to its surface. Hemostats, av ailable from surgi-

cal supply stores, are very con venient for holding tissue dur-

ing cleaning operations. To clean a single, fairly ﬂat optical

surface, such as a dielectric coated mirror or window, place a

single lens tissue ﬂat on the surface. Put one drop of clean

solvent (spectroscopically pure grades are best) on the tissue

over the component. Then draw the tissue across the surface

of the component so that the dry portion of the tissue follows

the solvent-soaked part and dries off the surface.

Several suitable solvents exist for these cleaning oper-

ations, such as acetone, trichloroethylene, and methyl,

ethyl, and isopropyl alcohols. Diethyl ether is a very good

solvent for cleaning laser mirrors, but its extreme ﬂamma-

bility makes its use undesirable.

If there is any doubt as to the ability of an optical com-

ponent to withstand a particular solvent, the manufacturer

should be consulted. This applies particularly to specially

coated components used in ultraviolet and some infrared

systems. Some delicate or soft components cannot be

cleaned at all without running the risk of damaging them

permanently, although it is usually safe to remove dust

from them by blowing with clean, dust-free gas. It is worth

noting that diffraction gratings frequently look as though

they have surface blemishes. These blemishes frequently

look much worse than they actually are and do not notice-

ably affect performance. Never try to clean diffraction

gratings. It is also very difﬁcult to clean aluminum- or

gold-coated mirrors that are not overcoated with a hard

protective layer such as silicon monoxide. Copper mirrors

are soft and should be cleaned with extreme care.

Most optical components used in the visible and near-

ultraviolet regions of the spectrum are hard; soft materials

are often used in infrared systems. In this region several

soft crystalline materials such as sodium chloride, potas-

sium chloride, cesium bromide, and cesium iodide are

commonly used. These materials can be cleaned,

GaAs 5.7 0.00 — Very good high-power infrared-laser window material

CdTe 4.5 — — —

Te 16.8 0.00 H

, HNO

Poisonous, soft, easily scratched

CaCO

— 1.4 3 10

3

Acids, NH

Cl —

——— —

Table 4.5 (cont.)

Material Thermal-

Expansion

Coefﬁcient

(10

–6

/K)

Solubility

in Water

[g/(100 g),

20°C]

Soluble in Comments

Parallel to c-axis.

Perpendicular to c-axis.

Depends on crystal orientation.

Depends on grade.

Long-wavelength limit depends on purity of material.

Birefringent.

Softening temperature.

Decomposition temperature.

OPTICAL COMPONENTS 235

essentially by repolishing their surfaces. For sodium and

potassium chloride windows this is particularly straightfor-

ward. Fold a piece of soft, clean muslin several times to

form a large pad. Place the pad on a ﬂat surface – a piece of

glass is best. Stretch the pad tight on the surface and ﬁx it

securely at the edges with adhesive tape. Dampen an area

of the pad with a suitable solvent such as trichloroethylene

or alcohol. Place the window to be polished on the solvent-

soaked area, and work it back and forth in a ﬁgure-eight

motion. Gradually work the disc onto the dry portion of

the pad. This operation can be repeated as many times as

necessary to restore the surface of the window. Do not

attempt to clean windows of this kind, which are hygro-

scopic, by wiping them with solvent-soaked tissue. The

evaporation of solvent from the surface will condense

water vapor onto it and cause damage. The above recom-

mended cleaning procedure is quite satisfactory for clean-

ing even laser windows. Small residual surface blemishes

and slightly foggy areas do not detract signiﬁcantly from

the transmission of such windows in the middle infrared

and beyond – which in any case is the only spectral region

where they should be used. For removing slightly larger

blemishes and scratches from such soft windows, very ﬁne

aluminum oxide powder (available from Adolf Meller) can

be mixed with the cleaning solvent on the pad in the ﬁrst

stages of polishing. Perhaps the best way of all for cleaning

hard and medium-hard optical components is to vapor-

degrease them. This is a very general procedure for clean-

ing precision components. Place some trichloroethylene or

isopropyl alcohol in a large beaker (500 ml or larger) to a

depth of about 1 cm. Suspend the components to be

cleaned in the top of the beaker so that their critical sur-

faces face downward. An improvised wire rack is useful

for accomplishing this. Cover the top of the beaker tightly

with aluminum foil. Place the beaker on an electric hot

plate, and heat the solvent until it boils. The solvent vapor

thus produced is very pure. It condenses on, and drips off,

the suspended item being cleaned, effectively removing

grease and dirt. If large items are being cleaned, it may

be necessary to blow air on the aluminum foil with a small

fan. At the end of several minutes turn off the heat

and remove the clean items while they are still warm.

This cleaning procedure is recommended for components

that must be extremely clean, such as laser Brewster

windows.

4.4 OPTICAL MATERIALS

The choice of materials for the various components of an

optical system such as windows, prisms, lenses, mirrors,

and ﬁlters is governed by several factors:

(1) Wavelength range to be covered

(2) Environment and handling that components must

withstand

(3) Refractive-index considerations

(4) Intensity of radiation to be transmitted or reﬂected

(5) Cost.

4.4.1 Materials for Windows, Lenses,

and Prisms

For the purposes of classiﬁcation, the characteristics of

various materials for use in transmissive applications will

be considered in three spectral regions:

(1) Ultraviolet, 100–400 nm

(2) Visible and near infrared, 400 nm–2 lm

(3) Middle and far infrared, 2–1000 lm.

There are, of course, many materials that can be used in

part of two or even three of these regions. Table 4.5 sum-

marizes

the essential characteristics of all the common,

and most of the rarely used, materials in these three

regions. The useful transmission range given for each

material is only a guide; the transmission at the ends of

this range can be increased and the useful wavelength

range of the component extended by using thinner pieces

of material – if this is possible. The refractive index of all

these materials varies with wavelength, as is illustrated for

several materials in Figure 4.91. The Knoop hardness

is a

static measure of material hardness based on the size of

impression made in the material with a pyramidal diamond

indenter under speciﬁc conditions of loading, time, and

temperature. Roughly speaking, a material with a Knoop

hardness above about 60 is hard enough to withstand the

cleaning procedures described in Section 4.3.15.

ransmission curves for many of the useful optical

materials summarized in Table 4.5 are collected together

in Figures 4.92 – 4.101. Most of these materials are avail-

able

from several suppliers. Some of the materials listed in

Table 4.5 are worthy of brief extra comment.

236 OPTICAL SYSTEMS

Ultraviolet Transmissive Materials. The following

are suitable for use in the UV region.

(i) Lithium ﬂuoride. Lithium ﬂuoride (LiF, Figure 4.92)

s useful transmittance further into the vacuum ultraviolet

than any other common crystal. The transmission of vac-

uum-ultraviolet quality crystals is more than 50% at 121.6

nm for 2 mm thickness, and thinner crystals have useful

transmission down to 104 nm. The short-wavelength trans-

mission of the material deteriorates on exposure to atmos-

pheric moisture or high-energy radiation. Moisture does not

affect the infrared transmission, which extends to 7 lm.

Several grades of LiF are available. Vacuum-ultraviolet-

grade material is soft, but visible-grade material is hard.

Figure 4.91 The refractive indices of various optical materials. [Adapted, with permission,

from W. C. Wolfe and S. S. Ballard, Optical Materials, Films and Filters for Infrared

Instrumentation, Proceedings of the IRE, 47, 1540-1546, 1959. Ó 1959 IRE (now IEEE).]

OPTICAL MATERIALS 237

LiF can be used as a vacuum-tight window material by

sealing with either silver chloride or a suitable epoxy.

(ii) Magnesium ﬂuoride. Vacuum-ultraviolet-grade mag-

nesium ﬂuoride (MgF

, Figure 4.92) transmits farther into

the ultraviolet than any common material except LiF. The

transmission at 121.6 nm is 35% or more for a 2 mm thick-

ness. MgF

is recommended for use as an ultraviolet-trans-

missiv e component in space work, as it is only slightly affected

by ionizing radiation. MgF

is birefringent and is used for

making polarizing components in the ultraviolet. Irtran 1 is

a polycrystalline form of magnesium ﬂuoride manufactured

by Kodak, which is not suitable for ultra violet or visible appli-

cations. Its useful transmission extends from 500 nm to 9 lm.

(iii) Calcium ﬂuoride. Calcium ﬂuoride (CaF

, Figure

4.92) is an excellent, hard material that can be used

for

optical components from 125 nm to beyond 10 lm.

Vacuum-ultraviolet-grade material transmits more than

50% at 125.7 nm for a 2 mm path length. Calcium ﬂuoride

is not signiﬁcantly affected by atmospheric moisture at

ambient temperature. Calcium ﬂuoride lenses are available

from Argus, Janos Technology, Linos Photonics, Meller

Optics, Melles Griot, Newport, Optovac, Newport/Oriel

and Precision Optical. Irtran 3 is a polycrystalline form

of CaF

, which is not suitable for ultraviolet or visible

applications, but transmits in the infrared to 11.5 lm.

(iv) Barium ﬂuoride. Although barium ﬂuoride (BaF

Figure 4.93) is slightly more water soluble than calcium or

magnesium

ﬂuoride, it is more resistant than either of these

to ionizing radiation. It is a good general-purpose optical

material from ultraviolet to infrared. It has excellent trans-

mission to beyond 10 lm, and windows that are not too

thick (< 2 mm) can be used in CO

laser applications,

except at very high energy densities. Barium ﬂuoride

lenses are available from Infrared Optical Products and

International Scientiﬁc Products.

(v) Synthetic sapphire. Synthetic sapphire (corundum,

; Figure 4.93) is probably the ﬁnest optical material

av ailable in applications from 300 nm to 4 lm. It is v ery hard,

strong, and resistant to moisture and chemical attack (e ven HF

below 300 °C). The useful transmissive range extends from

150nmto6lm, the transmission of a 1 mm thickness being

21% and 34%, respectiv ely, at these two wavelengths. Sap-

phire optical components are available from many suppliers.

Sapphire is also resistant to ionizing radiation, has high

thermal conductivity, and can be very accurately fabricated

in a variety of forms. It has low dispersion, however, and is

not very useful as a prism material. Chromium-doped

(ruby) is used in laser applications.

(vi) Fused silica. Fused silica (SiO

, Figure 4.94)isthe

amorphous form of crystalline quartz. It is almost as good

Figure 4.92 Transmission curves of lithium ﬂuoride, magnesium ﬂuoride, and calcium

ﬂuoride windows of speciﬁed thicknesses.

238 OPTICAL SYSTEMS

an optical material as sapphire and is much cheaper . Its useful

transmission range extends from about 170 nm to about 4.5

lm. Special ultraviolet-transmitting grades are manufactured

(such as Spectrosil and Suprasil), as well as infrared grades

(such as Infrasil) from which undesirable absorption features

at 1.38, 2.22, and 2.72 lm, due to residual OH radicals, have

been removed. Fused silica has a very low coefﬁcient of

thermal expansion, 5 3 10

–7

/K in the temperature range from

20 to 900 °C, and is very useful as a spacer material in

applications such as Fabry–Perot etalons and laser cavities.

Fused-silica optical components such as windows, lenses,

prisms, and etalons are readily available. Crystalline quartz

is birefringent and is widely used in the manufacture of polar-

izing optics, particularly quarter-wa ve and half-wave plates.

Very pure fused silica is also the material of which most

optical ﬁbers are made. In ﬁber optic applications the index

gradient inside the ﬁber is generally produced by germania

(GeO

) doping. The pure silica used in optical ﬁbers is most

transparent in the infrared, generally near 1.55 lm.

(vii) Diamond. W indo ws made of type-IIA diamond (Fig-

ure

4.93) have a transmittance that extends from 230 nm to

yond 200 lm, although there is some absorption between

2.5 and 6.0 lm. The high refractiv e index of diamond, n ¼

2.4, over a very wide band, leads to a reﬂection loss of about

34% for two surfaces. Diamond windows are extremely

expensi ve, ($10,000–20,000 for a 1 cm diameter , 1 mm thick

window); howe v er, some properties of diamond are unique:

its thermal conductiv ity is six times that of pure copper at 20

°C, and it is the hardest material known, very resistant to

chemical attack, with a low thermal-expansion coefﬁcient

and high resistance to radiation damage.

Visible- and Near-Infrared-Transmissive

Materials.

The materials so far considered as

ultraviolet-transmitting are also excellent for use in the

visible and near infrared. There are, however, several

materials that transmit well in the visible and near

infrared, but are not suitable for ultraviolet use.

(i) Glasses. There is an extremely large number of types

of glass used in the manufacture of optical components.

They are available from many manufacturers, such as

Chance, Corning, Hoya, Ohara, and Schott.

Two old classiﬁcations of glass into cr own and ﬂint glasses

can be related to the glass chart. Cro wn glasses are glasses

with a V value greater than 55 if n

<1.6andV >50ifn

71.6. The ﬂint glasses have V v alues belo w these limits. The

rare earth glasses contain rare earths instead of SiO

,whichis

the primary constituent of crown and ﬂint glasses. Glasses

containing lanthanum contain the symbol La.

A few common glasses are widely used in the manufac-

ture of lenses, windows, prisms, and other components.

These include the borosilicate glasses Pyrex, BK7/A, and

crown (BSC), as well as Vycor, which is 96% fused quartz.

Transmission curves for Pyrex No. 7740 and Vycor No.

Figure 4.93 Transmission curves of sapphire, barium ﬂuoride, and

type IIA diamond windows of speciﬁed thicknesses.

OPTICAL MATERIALS 239

7913 are shown in Figure 4.95. These glasses are not very

useful above 2.5 lm, their transmission at 2.7 lmisdown

to 20% for a 10 mm thickness. In the spectral region

between 350 nm and 2.5 lm, however, they are excellent

transmissive materials. They are inexpensive, hard, and

chemically resistant, and can be fabricated and polished

to high precision. Special glasses for use further into the

infrared are available from Hoya and Corning. In window

applications these glasses do not appear to offer any par-

ticular advantages over more desirable materials such as

infrared-grade fused silica or sapphire; however, in speci-

alized applications, such as infrared lens design, their

higher refractive indices are useful.

For special applications, man y colored ﬁlter glasses can be

obtained. Glasses that transmit visible but not infrared, or vice

versa, or that transmit some near ultraviolet, but no visible,

Figure 4.95 Transmission curves for Pyrex 7740 and Vycor 7913.

Figure 4.94 Transmission characteristics of various grades of fused silica; all measurements made on 10 mm thick

materials. (Courtesy of Heraeus-Amersiol, Inc.)

240 OPTICAL SYSTEMS

and many other combinations are av ailable. The reader should

consult the catalogs published by the various manufacturers

and suppliers such as Chance-Pilkington, Corning, CVI,

Hoya, Kopp Glass, Melles-Griot (now CVI-Melles-Griot),

NPraezisions Glas & Optik, Schott, and Rolyn.

Special glasses whose expansion coefﬁcients match

selected metals can be made because the composition of

glass is continuously variable,. These glasses are useful for

sealing to the corresponding metals in order to make win-

dows on vacuum chambers. Corning glass No. 7056 is often

used in this way, as it can be sealed to the alloy Kovar.

Vacuum-chamber windows of quartz or sapphire are also

available,

but their construction is complex, and conse-

quently they are costly. Various grades of ﬂint glass are

available that have high refractive indices and are therefore

useful for prisms. For a tabulation of the types available the

reader is referred to Kaye and Laby.

The refractive indices

available range up to 1.93 for Chance-Pilkington Double

Extra Dense Flint glass No. 927210, but this and other high-

refractive-index glasses suffer long-term damage such as

darkening when exposed to the atmosphere.

(ii) Plastics. In certain noncritical applications, such as

observation windows, transparent plastics such as polyme-

thylmethacrylate (Acrylic, Plexiglas, Lucite, Perspex) or

polychlorotriﬂuoroethylene (Kel-F) are cheap and satisfac-

tory. They cannot be easily obtained in high optical quality

(with very good surface ﬂatness, for example) and are

easily scratched. The useful transmission range of Acrylic

windows 1 cm thick runs from about 340 nm to 1.6 lm.

A transmission-versus-wavelength curve for this material

is shown in Figure 4.96. One important application of

Acrylic

is in the manufacture of Fresnel lenses (see Section

4.3.3). Kel-F (polychlorotriﬂuoroethylene) is useful up to

about

3.8 lm, although it shows some decrease in trans-

mission near 3 lm. It is similar to polytetraﬂuoroethylene

(Teﬂon) and is very resistant to a wide range of chemicals –

even gaseous ﬂuorine.

(iii) Arsenic trisulﬁde. Arsenic trisulﬁde (As

, Figure

4.97) is a red glass that transmits well from 800 nm to 10

lm.

Its usefulness stems from its relatively low price, ease

of fabrication, nontoxicity, and resistance to moisture.

Although primarily an infrared-transmissive material, it is

also transmissive in the red, which facilitates the alignment

of optical systems containing it. As

is relatively soft and

will cold-ﬂow over a long period of time. A wide range of

lenses are available from Amorphous Materials,

OFR (Thorlabs), Recon Optical, and REFLEX Analytical.

Middle- and Far-Infrared-Transmissive Materials.

The following are useful well into the IR region.

(i) Sodium chloride. Sodium chloride (NaCl, Figure 4.98)

one of the most widely used materials for infrared-trans-

missive windows. Although it is soft and hygroscopic, it

can be repolished by simple techniques and maintained

exposed to the atmosphere for long periods without damage

simply by maintaining its temperature higher than ambient.

Figure 4.96 (a) Transmission curve for 3.175 mm thick

acrylic. (Courtesy of Melles Griot, Inc.); (b) Transmission

curve of various grades of acrylic available from Altumax

International.

OPTICAL MATERIALS 241

Two simple ways of doing this are to mount a small tung-

sten-ﬁlament bulb near the window, or to run a heated wire

around the periphery of small windows. High-precision

sodium chloride windows are in widespread use as Brew-

ster windows in high-energy, pulsed CO

laser systems.

(ii) Potassium chloride. Potassium chloride (KCI, Figure

4.98) is very similar to sodium chloride. It is also an excel-

lent

material for use as a Brewster window in pulsed CO

lasers, as its transmission at 10.6 lm is slightly greater than

that of sodium chloride.

Figure 4.97 Transmission curves for Irtran 2 (ZnS), Irtran 5 (MgO), and As

windows of

speciﬁed thicknesses.

Figure 4.98 Transmission curves for cesium bromide, potassium chloride, and sodium

chloride windows of speciﬁed thickness.

242 OPTICAL SYSTEMS

(iii) Cesium bromide. Cesium bromide (CsBr, Figure

4.98) is soft and extremely soluble in water, but has useful

transmission

to beyond 40 lm. It will suffer surface dam-

age if the relative humidity exceeds 35%.

(iv) Cesium iodide. Cesium iodide (CsI, Figure 4.99)is

used

for both infrared prisms and windows; it is similar to

CsBr, but its useful transmission extends beyond 60 lm.

(v) Thallium bromoiodide (KRS-5). Thallium bromoio-

dide (Figure 4.100), widely known as KRS-5, is an impor-

tant

material because of its wide transmission range in the

infrared – from 600 nm to beyond 40 lm for a 5-mm

thickness – and its low solubility in water. KRS-5 will

survive atmospheric exposure for long periods of time

and can even be used in liquid cells in direct contact with

aqueous solutions. Its refractive index is high: reﬂection

losses at 30 lm are 30% and it has a tendency to cold-ﬂow.

KRS-5 lenses are available from Almaz Optics, Infrared

Optical Products, ISP Optics, and Janos Technology.

(vi) Zinc selenide. Chemical-vapor-deposited zinc sele-

nide (ZnSe, Figure 4.100) is used widely in infrared-

laser

applications. It is transmissive from 500 nm to 22

lm. Zinc selenide is hard enough that it can be cleaned

easily. It is resistant to atmospheric moisture and can be

fabricated into precision windows and lenses. Its trans-

missive qualities in the visible (it is orange-yellow in

color) makes the alignment of infrare d systems using

it much more convenient than in systems using germa-

nium, silicon, or g allium arsenide. Irtran 4 is a polycrys-

talline form of zinc selenide originally developed by

Figure 4.99 Transmission curves for cesium iodide, silver bromide, and silver chloride

windows of speciﬁed thicknesses.

Figure 4.100 Transmission curves for zinc selenide,

cadmium telluride, and KRS-5 windows of speciﬁed

thicknesses.

OPTICAL MATERIALS 243

Kodak, which is available from Harrick Scientiﬁc and

Perkin Elmer.

(vii) Plastic ﬁlms. Several polymer materials are sold

commercially in ﬁlm form, including polyethylene (Poly-

thene, Polyphane, Poly-Fresh, Dinethene, etc.), polyviny-

lidene chloride copolymer (Saran Wrap), polythylene

terephthalate (Mylar, Melinex, Scotchpar), and poly-

carbonate (Lexan). These plastic materials can be used to

wrap hygroscopic crystalline optical components to pro-

tect them from atmospheric moisture. If the ﬁlm is wrap-

ped tightly, it will not substantially affect the optical

quality of the wrapped components in the infrared. Care

should be taken to use a polymer ﬁlm that transmits the

wavelength for which the protected component is to be

used. For example, several commercial plastic food wraps

can be used to wrap NaCI or KCI windows for use in CO

laser applications. Not all will prove satisfactory, however,

and a particular plastic ﬁlm should be tested for transmis-

sion before use. A note of caution: plastic ﬁlms contain

plasticizers, the vapor from which may be a problem.

(viii) Plastics and other materials for far-infrared use.

Plastics are widely used for windows, beamsplitters, and

light guides in the far-infrared. A Mylar ﬁlm is widely used

as the beam-splitting element in far-infrared Michelson

interferometers, and polyethylene, polystyrene, nylon,

and Teﬂon are used as windows in far-infrared spectrom-

eters and lasers. Black polyethylene excludes visible and

near-infrared radiation, but transmits far-infrared. Lenses

and stacked-sheet polarizers for far-infrared use can be

made from polyethylene. Several crystalline and semicon-

ducting materials, although they absorb in the middle infra-

red, begin to transmit again in the far infrared. A 1 mm

thick quartz window has 70% transmission at 100 lm and

more than 90% transmission from 300 to 1000 lm. The

alkali and alkaline-earth halides such as NaF, LiF, KBr,

KCI, NaCl, CaF

, SrF

, and BaF

show increasing trans-

mission for wavelengths above a critical value that varies

from one crystal to another but is in the 200–400 lm range.

Further details of the specialized area of far-infrared mate-

rials and instrumentation are available in the literature.

55–57

Semiconductor Materials. Several of the most

valuable infrared optical materials are semiconductors.

In very pure form these materials should be transmissive

to all infrared radiation with wavelengths longer than

that corresponding to the band gap. In practice the

long-wavelength transmission will be governed by the

presence of impurities – a fact that is put to good use in

the construction of infrared detectors. Semiconductors

make very convenient ‘‘cold mirrors,’’ as they reﬂect

visible radiation quite well but do not transmit it.

(i) Silicon. Silicon (Si, Figure 4.101) is a hard, chemically

resistant

material that transmits wavelengths beyond about

1.1 lm. It does, however, show some absorption near 9 lm,

so it is not suitable for CO

-laser windows. It has a high

refractive index (the reﬂection loss for two surfaces is 46%

at 10 lm), but can be antireﬂection-coated. Because of its

high refractive index it should always be highly polished to

reduce surface scattering. Silicon has a high thermal con-

ductivity and a low thermal expansion coefﬁcient, and it is

resistant to mechanical and thermal shock. Silicon mirrors

can therefore handle substantial infrared-laser power den-

sities. Silicon lenses are available from II-VI Infrared, ISP

Optics, Lambda Research Optics, Laser Research Optics,

Meller Optics, and V.A. Optical.

(ii) Germanium. Germanium (Ge, Figure 4.101) trans-

mits

beyond about 1.85 lm. Very pure samples can be

transparent into the microwave region. It is somewhat brit-

tle, but is still one of the most widely used window and lens

materials in infrared-laser applications. It is chemically

inert and can be fabricated to high precision. Germanium

Figure 4.101 Transmission curves for the semiconductor

materials germanium, gallium arsenide, and silicon.

244 OPTICAL SYSTEMS

has good thermal conductivity and a low coefﬁcient of

thermal expansion; it can be soldered to metal. In use, its

temperature should be kept below 40 °C, as it exhibits

thermal runaway – its absorption increases with increasing

temperature. A wide range of germanium lenses are avail-

able from Lambda Research Optical, Laser Research

Optics, Meller Optics, Umicore, and V.A. Optical.

(iii) Gallium arsenide. Gallium arsenide (GaAs, Figure

4.101) transmits from 1 to 15 lm.

It is a better, although

more expensive, material than germanium, particularly in

CO- and CO

-laser applications. It is hard and chemically

inert, and maintains a very good surface ﬁnish. It can han-

dle large infrared power densities because it does not

exhibit thermal runaway until it reaches 250 °C. It is also

used for manufacturing infrared-laser electro-optic modu-

lators. Gallium arsenide lenses are available from Infrared

Optical Products ISP Optics, Lambda Research Optics,

and REFLEX Analytical.

(iv) Cadmium telluride. Cadmium telluride (CdTe, Fig-

ure

4.100) is another excellent material for use between 1

and

15 lm. It is quite hard, chemically inert, and takes a

good surface ﬁnish. It is also used for manufacturing infra-

red-laser electro-optic modulators. Irtran 6 is a polycrystal-

line form of cadmium telluride available from Kodak; it

transmits to 31 lm. Cadmium telluride lenses are available

from ISP Optics and REFLEX Analytical.

(v) Tellurium. Tellurium is a soft material that is trans-

parent from 3.3 lm to beyond 11 lm. It is not affected by

water. Its properties are highly anisotropic; it can be used

for second harmonic generation with CO

-laser radiation.

Tellurium should not be handled, as it is toxic and can be

absorbed through the skin.

4.4.2 Materials for Mirrors

and Diffraction Gratings

Metal Mirrors. The best mirrors for general broad-

band use have pure metallic layers, vacuum-deposited or

electrolytically deposited on glass, fused-silica, or metal

substrates. The best metals for use in such reﬂective coat-

ings are aluminum, silver, gold, and rhodium. Solid metal

mirrors with highly polished surfaces made of metals such

as stainless steel, copper, zirconium-copper, and molybde-

num are also excellent, particularly in the infrared. The

reﬂectance of a good evaporated metal coating exceeds

that of the bulk metal. Flat solid-metal mirrors can be made

fairly cheaply by machining the mirror blank, surface-

grinding it, and ﬁnally polishing the surface. If precision

polishing facilities are not available, there are numerous

optical component suppliers who will undertake the pol-

ishing of such surface-ground blanks to ﬂatnesses as good

as k/10 in the visible. Finished ﬂat and spherical solid-

metal mirrors are available from II-VI Infrared, Opti-

Forms, Space Optics Research Labs (SORL), and Spawr.

Solid-metal mirrors are most valuable for handling high-

power infrared laser beams when metal-coated mirrors

cannot withstand the power dissipation in the slightly

absorbing mirror surface. Water-cooled copper mirrors

for handling very intense infrared laser beams are available

from Spawr and Umicore Laser Optics Ltd.

The spectral reﬂectanc es in normal inc idence of sev-

eral common metal coatings are compared in Figure

4.1

02. Several points are worthy of note. Gold and copper

are

not good for use as reﬂectors in the visible region.

Unprotected gold, silver, copper, and aluminum are very

soft. Aluminum rapidly acquires a protective layer of

oxide after deposi tion; this signiﬁcantly reduces the

reﬂectance in the vacuum ultraviolet and contributes to

increased scattering througho ut t he spectrum. Alum inum

and gold are frequently supplied commercially with a thin

protective dielectric layer, which increases their resist-

ance to abrasion without signiﬁcantly a ffecting their

reﬂectance, and also protects the aluminum from oxida-

tion. The protective layer is usually a k/2 layer (at 550

nm) of SiO for aluminum mirrors used in the visible

region of the spectrum. Aluminum coated with a thin

layerofMgF

canbeusedasareﬂectorinthevacuum

ultraviolet, although the reﬂectance is substantially

reduced below about 100 nm, as shown in Figure 4.103.

Man

y optical instruments operating in the vacuum ultra-

violet, including some spectrog raph s, have at leas t one

reﬂective component. Above 100 nm, coated aluminum is

almost always used for this reﬂector. Below 100 nm,

platinum and indium have superior reﬂectance to alumi-

num. At very short wavelengths, below about 40 nm, the

reﬂectance of platinum in normal incidence is down to

OPTICAL MATERIALS 245

only 10%, as shown in Figure 4.10 3. Therefore, reﬂective

components in this wavelength region are generally used

at grazing incidence, as the reﬂectance under these c on-

ditions can remain high. For example, at 0.832 nm the

reﬂectance of an a lum inum ﬁlm at a grazing angle of 0.5°

is above 90%.

Freshly evaporated silver has the highest reﬂectance of

any metal in the visible; however, it tarnishes so rapidly

that it is rarely used except on internal reﬂection surfaces.

In this case the external surface is protected with a layer of

Inconel or copper and a coat of paint.

Multilayer Dielectric Coatings. Extremely high-

reﬂectance mirrors (up to 99.99%) can be made by using

multilayer dielectric ﬁlms involving alternate high- and

low-refractive-index layers, ranging around k/4 thick,

deposited on glass, metal, or semiconductor substrates.

The layers are made from materials that are transparent

in the wavelength region where high reﬂectance is

required. Both narrow-band and broad-band reﬂective-

coated mirrors are available commercially. Figure

4.34(a) shows an example of each. Multilayer or single-

layer

dielectric-coated mirrors having almost any desired

reﬂectance at wavelengths from 150 nm to 20 lm are also

commercially available.

Substrates for Mirrors. The main factors inﬂuencing

the choice of substrate for a mirror are: (1) the dimensional

stability required; (2) thermal dissipation; (3) mechanical

considerations such as size and weight; and (4) cost. Glass

is an excellent substrate for most totally reﬂective mirror

applications throughout the spectrum, except where high

thermal dissipation is necessary. Glass is inexpensive and

strong, and takes a surface ﬁnish as good as k/200 in the

Figure 4.102 Reﬂectance of freshly deposited ﬁlms of aluminum, copper, gold, rhodium,

and coated silver, aluminum and rhodium as a function of wavelength from 0.2 to 10 lm.

246 OPTICAL SYSTEMS

visible. Fused silica and certain ceramic materials such as

Zerodur (available from Schott Glass) are superior, but

more expensive, alternatives to glass when greater

dimensional stability and a lower coefﬁcient of thermal

expansion (CTE) are required. Fused silica has the

lowest CTE, ~5 3 10

–7

/K of any readily available

material. The ceramic Zerodur has a CTE that can be 10

times smaller. The alloy Superinvar has a CTE similar to

quartz, but generally over a restricted temperature range.

Machining or poli shing of low CTE materials can produce

stresses in them and increase their expansion coefﬁcients.

Metal mirrors are frequently used when a very high light

ﬂux must be reﬂected, but even the small absorpti on loss in

the reﬂecting surface necessitates cooling of the substrate.

Metals are, however, not so dimensionally stable as glasses

or ceramics, and their use as mirrors should be avoided in

precision applications, particularly in the visible or

ultraviolet.

Partially reﬂecting, partially transmitting mirrors are

used in many optical systems, such as interferometers

and lasers. In this application the substrate for the mirror

has to transmit in the spectral region being handled. The

substrate material should possess the usually desirable

properties of hardness and dimensional stability, plus the

ability to be coated. For example, germanium, silicon, and

gallium arsenide are frequently used as partially trans-

mitting mirror substrates in the near infrared. Only the

least expensive partially reﬂecting mirrors use thin metal

coatings. Such coatings are absorbing, and multilayer,

dielectric-coated reﬂecti v e surfaces are much to be preferred.

There are numerous suppliers of totally and partially

reﬂecting mirrors.

The experimentalist need only deter-

mine the requirements and specify the mirror appropri-

ately.

Mirrors that reﬂect visible radiation and transmit infra-

red (cold mirrors) or transmit visible radiation and reﬂect

infrared (hot mirrors) are available as standard items from

several suppliers.

Diffraction Gratings. Diffraction gratings are generally

ruledonglass,whichmaythenbecoatedwithaluminum

or gold for visible or infrared reﬂective use, respectively.

Many commercial gratings are replicas made from a ruled

master, although high-quality holographic gratings are

available from several suppliers.

For high-power

infrared-laser applications, gold-coated replica gratings

are unsatisfactory and master gratings ruled on copper

should be used. Such gratings are available from Diffraction

Products, Jobin-Yvon, and Richardson Grating Laboratory

(through Newpo rt).

4.5 OPTICAL SOURCES

Optical sources f all into two categories: incoh erent sour-

ces such as me rcur y or xenon arc, tungsten ﬁlament, and

sodium lamps; and coherent sources (las ers). There are

many different types of laser, of which some exhibit a

high degree of coherence and others are not signiﬁcantly

more coherent than a line source, such as a low-pressure

mercury lam p.

Incoherent sources fall into two broad categories: line

sources and cont inuum sources. Line sources emit most

of their radiation at discret e wavelengths, which corre-

spond to strong spectral emission features of the excited

atom or ion that is the emitting species in the source.

Continuum sources emit over some broa d spectral

region, although their radiant intensity varies with wave-

length.

Figure 4.103 Normal-incidence reﬂectance of platinum,

aluminum with a 25 nm thick overcoat of MgF

, and

unprotected aluminum 24 hours after ﬁlm deposition.

OPTICAL SOURCES 247

4.5.1 Coherence

There are two basic coherence properties of an optical

source. One is a measure of its relative spectral purity. The

other depends on the degree to which the wavefronts coming

from the source are uni phase or of ﬁxed spatial phase varia-

tion. A wavefront is said to be uniphase if it has the same

phase at all points on the wavefront. The Gaussian TEM

mode emitted by many lasers has this property.

The two types of coherence are illustrated by Figure 4.104.If

the

phases of the electromagnetic ﬁeld at two points, A and B,

longitudin ally separate d in the direction of propagation, have a

ﬁxed relationship, then the wave is said to be temporally coher-

ent for times corresponding to the distance from A to B.The

existence of such a ﬁxed phase relationship could be demon-

strated by combining waves extracted at points separated like

A and B and producing an interference pattern. The Michelson

interferometer (see Section 4.7.6) demonstrates the existence

such a ﬁxed phase relationship. The maximum separation

of A and B for which a ﬁx ed phase relationship exists is called

the coher ence length of the source l

. The coherence length

of a source is related to its coherence time s

by:

¼ cs

ð4:191Þ

Conceptually l

is the average length of the uninterrupted

wave trains from the source between random phase inter-

ruptions. Fourier theory demonstrates that the longer in

time a sinusoidal wave train is observed, the narrower is

its frequency spread. Thus the spectral width of a source

can be related to its coherence time by writing:

Dm ’ 1=s

ð4:192Þ

The most coherent conventional lamp sources are stabi-

lized low-pressure mercury lamps, which can have s

rang-

ing up to about 10 ns. Lasers, however, can have s

ranging

up to at least 1 ms.

Spatial coherence is a measure of phase relationships in

the wavefront transverse to the direction of wave propaga-

tion. In Figure 4.104, if a ﬁxed phase relationship exists

tween points C and D in the wavefront, the wave is said

to be spatially coherent over this region. The area of coher-

ence is a region of the wavefront within which all points

have ﬁxed phase relationships. Spatial coherence can be

demonstrated by placing pinholes at different locations in

the wavefront and observing interference fringes. Tempo-

rally incoherent sources can exhibit spatial coherence.

Small sources (so-called point sources) fall into this cate-

gory. The light from a star can be spatially coherent.

Extended, temporally incoherent sources have a low

degree of spatial coherence because light coming from

different parts of the source has different phases. Lasers

emitting a TEM

(fundamental) mode have very good

spatial coherence over their whole beam diameter.

4.5.2 Radiometry: Units and Deﬁnitions

Radiometry deals with the measurement of amounts of

light. In radiometric terms the characteristics of a light

source can be speciﬁed in several ways.

Radiant power, W, measured in watts, is the total amount

of energy emitted by a light source per second. The spec-

tral variation of radiant power can be speciﬁed in terms of

the radiant power density per unit wavelength interval, W

Clearly:

W ¼

‘

dk ð4:193Þ

If a light source emits radiation only for some speciﬁc

duration – which may be quite short in the case of a ﬂash-

lamp – it is more useful to specify the source in terms of its

radiant energy output, Q

, measured in joules. If the source

emits radiation for a time T, we can write:

WðtÞdt ð4:194Þ

Figure 4.104 Temporal and spatial coherence.

248 OPTICAL SYSTEMS

The amount of power emitted by a source in a particular

direction per unit solid angle is called radiant intensity I

and is measured in watts per steradian. In general:

W ¼ I

ðxÞdx ð4:195Þ

where the integral is taken over a closed surface surround-

ing the source. If I

is the same in all directions, the source

is said to be an isotropic radiator. At a distance r from such

a source, if r is much greater than the dimensions of the

source, the radiant ﬂux crossing a small area DS is:

ð4:196Þ

The irradiance at this point, measured in W/m

, is:

ð4:197Þ

which is equal to the average value of the Poynting vector

measured at the point. The radiant ﬂux emitted per unit

area of a surface (whether this be emitting or merely

reﬂecting and scattering radiation) is called the radiant

emittance M

, and it is measured in W/m

. For an extended

source, the radiant ﬂux emitted per unit solid angle per unit

area of the source is called its radiance or brightness L

ð4:198Þ

where the area dS

is the projection of the surface element

of the source in the direction being considered. When the

light emitted from a source or scattered from a surface has

a radiance that is independent of viewing angle, the source

or scatterer is called a perfectly diffuse or Lambertian

radiator. Clearly, for such a source, the radiant intensity

at an angle h to the normal to the surface is:

ðhÞ¼I

ð0Þcos h ð4:199Þ

as illustrated in Figure 4.105.

The

total ﬂux emitted per unit area of such a surface is

its radiant emittance, which in this case is:

¼ pI

ð0Þð4:200Þ

Illuminated diffusing surfaces made of ﬁnely ground glass

or ﬁnely powered magnesium oxide will behave as Lam-

bertian radiators.

For plane waves, since all the energy in the wave is

transported in the same direction, the concepts of

radiant int ensity and emittance are not u seful. It is

customary to specify the radiant ﬂux crossing unit

area normal to the direction of propagation, and call this

the intensity I of the plane wave. Because lasers emit radi-

ation into an extremely small solid angle, they have very

high radiant intensity, and it is once again more usual to

refer simply to the intensity of the laser beam at a point as

the energy ﬂux per second per unit area. The total power

output of a laser is:

W ¼

beam

IdS ð4:201Þ

4.5.3 Photometry

Photometry is the measurement of light that is in, or close

to, the spectral region where the human eye responds. It is

related to radiometry, but its units are weighted by the

response of the human eye. The human eye provides a

nonlinear and wavelength-dependent subjective impres-

sion of radiometric quantities. The response function of

the human eye extends roughly from 360 to 700 nm, with

a peak at 555 nm for the photopic (light-adapted) eye,

where the cones are the dominant receptors. The dark-

adapted human eye exhibits the scotopic response, which

comes from the light- (but not color-) sensitive rods in the

periphery of the retina. The photopic and scotopic

response are shown in Figure 4.106. Measures in photo-

metry

take into account the so-called photopic spectral

luminous efﬁciency function V(k). Thus, for example, in

Figure 4.105 Radiant intensity characteristics of a

Lambertian radiator.

OPTICAL SOURCES 249

physiological photometry the luminous ﬂux F is related to

radiant ﬂux /

(k) by:

F ¼ K

‘

VðkÞ/

ðkÞdk ð4:202Þ

where K is a constant. When F is measured in lumens and

(k) in watts, K ¼ 683 lumen W

1

. In practice, the integral

in Equation (4.202) need only be evaluated between

360 nm and 830 nm, as V(k) is zero outside this range.

Other photometric quantities that may be encountered in

speciﬁcations of light sources are as follows:

(1) The luminous intensity I

measured as candela (Cd),

where:

1 candela ¼ 1 lumen per sr

This is the photometric equivalent of the radiometric

quantity radiant intensity. The formal scientiﬁc speci-

ﬁcation of the candela is that it is the luminous inten-

sity, in a given direction, of a source that emits

monochromatic radiation of wavelength 550 nm and

that has a radiant intensity in that direction of 1/683

watt per steradian.

(2) The illuminance, E

measured in lumen/m

[ lux;

lumen/cm

[ phot; or lumen/ft

[ footcandle.

(3) The luminance or brightness, L

measured in candela/m

[ nit; candela/cm

[ stilb; candela/p ft

[ footlambert;

candela/p m

[ apostilb; or candela/p cm

lambert.

(4) The luminous energy, Q

, measured in lumen seconds [

talbot. The correspondences between radiometric and

photometric quantities are summarized in Table 4.6.

For a Lambertian source the luminance is independent

the observation direction. Photometric description of the

characteristics of light sources should be avoided in strict

scientiﬁc work, but some catalogs of light sources use

photometric units to describe lamp performance. For fur-

ther details of photometry, and other concepts, such as

color in physiological optics, the reader should consult

Levi

or Fry.

Calibration standards and devices for radiometric and

photometric calibration of light sources are available from

Gamma Scientiﬁc, International Light, Optronic Labora-

tories, and UDT Instruments (formerly Graseby).

4.5.4 Line Sources

Line sources are used as wavelength standards for calibrat-

ing spectrometers and interferometers; as sources in

atomic absorption spectrometers; in interferometric

Figure 4.106 The photopic and scotopic spectral

response of the human eye.

Table 4.6 Correspondence between radiometric and photometric quantities

Radiometric Quantity Radiometric Unit Photometric Quantity Photometric Unit

Radiant power watt (W) Power lumen (lm)

Radiant emittance Wm

2

Illuminance lumen m

2

¼lux (lx)

Radiant intensity W/sr Luminous intensity lumen/sr ¼candela (cd)

Radiance (Brightness) Wm

2

1

Luminance (Brightness) lm m

2

1

¼cd m

2

¼nit

Radiant Energy Joule Luminous Energy lm s [ talbot

250 OPTICAL SYSTEMS

arrangements for testing optical components, such as

Twyman–Green interferometers (Section 4.7.6); in a few

special

cases for optically pumping solid-state and gas

lasers; and for illumination.

The emission lines from a line source are not inﬁnitely

sharp. Their shape is governed by the actual conditions and

physical processes occurring in the source. The variation

of the radiant intensity with frequency across a line whose

center frequency is v

is described by its lineshape function

g(v, v

), where:

‘

‘

gðv,v

Þdv ¼ 1 ð4:203Þ

The extension of the lower limit of this integral to neg-

ative frequencies is done for formal theoretical reasons

connected with Fourier theory and need not cause any

practical problems, since for a sharp line the major con-

tribution to the integral in Equation (4.203) comes from

frequencies

close to the center frequency v

. There are

three main types of lineshape function:

Lorentzian,

Gaussian, and Voigt.

The Lorentzian lineshape function is:

ðv,v

Þ¼

pDv

1 þ v  v

ðÞ=Dv½

ð4:204Þ

where Dv is the frequency spacing between the half-inten-

sity points of the line (the full width at half maximum

height, or FWHM). Spectral lines at long wavelengths

(in the middle and far infrared) and lines emitted by heavy

atoms at high pressures and/or low temperatures frequently

show this type of lineshape.

The Gaussian lineshape function is:

ðv,v

Þ¼

ln 2



1=2

exp  2

v  v



ln 2

()

ð4:205Þ

where Dv

is the FWHM. Spectral calibration lamps are

available from Avantes, Cathodeon, Gamma Scientiﬁc,

Heraus Nobleight, Newport/Oriel, Ocean Optics, Spectral

Products, and Resonance. Gaussian lineshapes are usually

associated with visible and near-infrared lines emitted by

light atoms in discharge-tube sources at moderate pres-

sures. In this case, the broadening comes from the varying

Doppler shifts of emitting species, whose velocity distri-

bution in the gas is Maxwellian. Emitting ions in real

crystals sometimes have this type of lineshape because

of the random variations of ion environment within a real

crystal produced by dislocations, impurities, and other lat-

tice defects. A Lorentzian and a Gaussian lineshape are

compared in Figure 4.107.

Frequently

, the broadening processes responsible for

Lorentzian and Gaussian broadening are simultaneously

operative, in which case the resultant lineshape is a con-

volution of the two and is called a Voigt proﬁle.

The low-pressure mercury lamp is the most commonly

used narrow-line source. These lamps actually operate

with a mercury–argon or mercury–neon mixture. The prin-

cipal lines from a mercury–argon lamp are listed in Table

4.7. Numerous other line sources are also available.

particular, hollow-cathode lamps emit the strongest

spectral line of any desired element for use in atomic

absorption spectrometry. Such lamps are available from

Bulbtronics, GBC Scientiﬁc Equipment, Hamamatsu,

Figure 4.107 Gaussian and Lorentzian lineshapes of the

same FWHM, Dm.

OPTICAL SOURCES 251

Hellma International, REFLEX Analytical, Semicon Asso-

ciates, and Vitro Technology, Ltd.

4.5.5 Continuum Sources

A continuum source in con junction with a mon ochroma-

tor can be used to obtain radiation whose wavelength

is tunable throughout the emission range of the source.

If the wavelength region transmitted by the monochro-

mator is made very small, not very much energy will

be available in th e wavelength region se lected. E ven

so, continuum sources ﬁnd extensive use in this way in

absorption and ﬂuorescence spectrometers. Certa in

continuum sources , called b lackbody sources, h ave

very well-characterized radiance as a function of wave-

length and are used for calibrating both the absolute

sensitivity of detecto rs and the absolute radiance of

other sources.

Blackbody Sources. All objects are continuously

emitting and absorbing radiation. The fraction of

incident radiation in a spectral band that is absorbed by

an object is called its absorbtivity. When an object is in

thermal equilibrium with its surroundings, it emits and

absorbs radiation in any spectral interval at equal rates.

An object that absorbs all radiation incident on it is

called a blackbody – its absorbtivity a is equal to unity.

The ability of a body to radiate energy in a particular

spectral band compared to a blackbody is its emissivity.

A blackbody is also the most efﬁcient of all emitters –

its emissivity e is also unity. In general, for any object

emitting and absorbing radiation at wavelength k, e

¼ a

Highly reﬂecting, opaque objects, such as polished metal

surfaces, do not absorb radiation efﬁciently; nor, when

heated, do they emit radiation efﬁciently.

The simplest model of a blackbody source is a heated

hollow object w ith a small hole in it. Any radi ation enter-

ing the hole has minimal chan ce of re-emerging. Conse-

quently, the radiation leaving the hole will be

characteristic of the interi or temperature of the object.

The e nergy density distribution of this blackbody radia-

tion in frequency is:

qðvÞ¼

8phv

hv=kT

 1

ð4:206Þ

where q(v)dv is the energy stored (J/m

) in a small fre-

quency band dv at v. The energy density distribution in

wavelength is:

qðkÞ¼

8phc

hc=kkT

 1

ð4:207Þ

This translates into a spectral emittance (the total power

emitted per unit wavelength interval into a solid angle 2p

by unit area of the blackbody) given by:

ðe

=kT

 1Þ

ð4:208Þ

where C

¼ 2phc

, called the ﬁrst radiation constant, has

the value 3.7418 3 10

–16

/s, and C

¼ ch/k, called the

second radiation constant, has the value 1.43877 3

–2

mK.

Table 4.7 Characteristic lines from a mercury lamp

Wavelength

(lm)

0.253652

0.313156

0.313184

0.365015

0.365483

0.366328

0.404656

0.435835

0.546074

0.576960

0.579066

0.69075

0.70820

0.77292

1.0140

1.1287

3.9425

Note: Extensive listings of calibration lines from other sources

cab be found in C.R. Harrison M.I.T. Wavelength Tables, M.I.T.

Press, Cambridge, Mass, 1969; and in A. R. Striganov and N. S.

Sventitskii, Tables of Spectral Lines of Neutral and Ionized

Atoms, IFT/Plenum Press, New York, 1968.

In tacuo.

252 OPTICAL SYSTEMS

A true blackbody is also a diffuse (Lambertian) radiator.

Its radiance is independent of the viewing angle. For such a

source:

¼ pL

ð4:209Þ

The variation of L

with wavelength for various values of

the temperature is shown in Figure 4.108. The wavelength

maximum emittance, k

at temperature T obeys Wien’s

displacement law:

T ¼ 2:8978 3 10

3

mK ð4:210Þ

The total radiant emittance of a blackbody at temper-

ature T is:

‘

dk ¼

15c

¼ rT

ð4:211Þ

This is a statement of the Stefan–Boltzmann law. The

coefﬁcient r, called the Stefan–Boltzmann constant, has

a value of 5.6705 3 10

–8

–2

–4

. The known param-

eters M

and M

of a blackbody allow it to be used as an

absolute calibration source in radiometry. If a detector

responds to photons, the spectral emittance in terms of

photons, N

, may be useful:

hc=k

ð4:212Þ

Curves of N

are given by Kruse, McGlauchlin, and

McQuistan.

A source whose spectral emittance is identical to that of

a blackbody apart from a constant multiplicative factor is

called a graybody. The constant of proportionality, e, is its

emissivity. Several continuum sources, such as tungsten-

ﬁlament lamps, carbon arcs, and ﬂashlamps, are approxi-

mately graybody emitters within certain wavelength regions.

Practical Blackbody Sources. The radiant emittance

of a blackbody increases at all wavelengths as the

temperature of the blackbody is raised, so a practical

blackbody should, ideally, be a heated body with a small

emitting aperture that is kept as small as possible. Kruse,

McGlauchlin, and McQuistan

describe such a source,

illustrated in Figure 4.109, that can be operated at

Figure 4.108 Spectral radiance L

of a blackbody source

at various temperatures.

Figure 4.109 Construction details of a simple

high-temperature blackbody source. (From P. W. Kruse,

L. D. McGlauchlin, and R. B. McQuistan, Elements of

Infrared Technology: Generation, Transmission, and

Detection, John Wiley & Sons, Inc., New York, 1962;

by permission of John Wiley & Sons, Inc.)

OPTICAL SOURCES 253

temperatures as high as 3000 K. A 25-lm-thick tungsten

ribbon 2 cm wide is rolled on a 3-mm-diameter copper

mandrel and seamed with a series of overlapping spot

welds. A hole about 0.75 mm in diameter is made in the

foil, and the copper dissolved out with nitric acid under a

fume hood. The resulting cylinder is mounted on 1-mm-

diameter Kovar or tungsten rod feedthroughs in a glass

envelope and heated from a high-current, low-voltage

power supply. The glass envelope should be ﬁtted with a

window that is transmissive to the wavelength region

desired from the source.

Another design of blackbody source is shown in Figure

4.110. This design is based on a heated copper cylinder,

containing

a conical cavity of 15° semivertical angle, that

is allowed to oxidize during operation (so that it becomes

nonreﬂective and consequently of high emissivity). The

cylinder is heated by an insulated heater wire wrapped

around its circumference. If nichrome wire is used, the

cylinder can be heated to about 1400 K. This assembly

is mounted in a ceramic tube (alumina is quite satisfactory)

or potted in high-temperature ceramic cement. For high-

temperature operation, the whole assembly can be

mounted inside a water-cooled block.

A popular blackbody source uses a ‘‘Globar,’’ a rod of

bonded silicon carbide. In the high-temperature blackbody

source supplied by Newport/Oriel this has been replaced

by pyrolytic graphite. For further details of the advantages

and disadvantages of this and various other blackbody

sources, the reader is referred to Hudson.

Blackbody

sources are available commercially from The Eppley Lab-

oratory, HGH Optronics, Infrared Industries, Isotech,

Micron, Omega, and Newport/Oriel.

Tungsten-Filament Lamps. T ungsten-ﬁlament lamps

are approximately graybodies in the visible with an

emittance between 0.45 and 0.5. Such lamps are

Figure 4.110 Construction details of an NBS-type blackbody source.

254 OPTICAL SYSTEMS

frequently desc ribed i n terms of their color temperature

, which is the temperature at which a blackbody would

have a spectral emittance closest in shape to the lamp’s.

The color temperature will depend on the operating

conditions of the lamp.

Tungsten-ﬁlament lamps can most conveniently be

operated in the laboratory with a variable transformer.

For best stability and freedom from ripple on their output,

however, they should be operated from a stabilized d.c.

supply. Typical supply requirements range up to a few

hundred volts. Lamps with wattage ratings up to 1 kW

are readily available.

Small tungsten-ﬁlament lamps that can be used as point

sources are available from Newport/Oriel. Very-long-life,

constant-efﬁciency tungsten–halogen lamps are available,

in which the lamp envelope usually contains a small

amount of iodine. In operation, the iodine vaporizes and

recombines with tungsten that has evaporated from the

ﬁlament and deposited on the inside of the lamp envelope.

The tungsten iodide thus formed diffuses to the hot ﬁla-

ment, where it decomposes, redepositing tungsten on the

ﬁlament. The constant replacement of the ﬁlament in this

way allows it to be operated at very high temperature and

radiant emittance. Because the lamp envelope must with-

stand the chemical action of hot iodine vapor and high

temperatures, it is made of quartz. Hence such lamps are

frequently called quartz–iodine lamps. Such lamps can be

quite compact: a 1 kW lamp will have a ﬁlament length of

about 1 cm. They are available from Bulb Direct and

Ocean Optics. The National Institute of Standards and

Technology (NIST) standard of spectral irradiance consists

of a quartz–iodine lamp with a coiled-coil tungsten ﬁla-

ment operating at about 3000 K and calibrated from

250 nm to 2.6 lm against a blackbody source. Such cali-

brated lamps are available from EG&G and Newport/

Oriel. Because they are intense sources of radiant energy,

these lamps can also be used for heating. In particular, they

are often placed inside complex vacuum systems to bake

out internal components that are well insulated thermally

from the chamber walls.

Continuous Arc Lamps. High-current electrical

discharges in gases, with currents that typically range

from 1 to 100 A, can be intense sources of continuum or

line emission, and sometimes both at the same time. For

substantial continuum emission the most popular such

lamps are the high-pressure xenon, high-pressure mercury,

and high-pressure mercury–xenon lamps. The arc in these

lamps typically ranges up to about 5 cm long and 6.2 mm in

diameter (for a 10 kW lamp – 100 V, 100 A input). Because

of their small size, arc lamps have much higher spectral

radiance (brightness) than quartz–iodine lamps of

comparable wattage. In the visible region at 500 nm, a

typical xenon arc lamp shows 1.9 times the output of a

quartz–iodine lamp; at 350 nm, 14 times; and at 250 nm,

200 times. In addition, because of their small size, high-

pressure arc lamps work well in the illumination of

monochromator slits in spectroscopic applications. Lower-

wattage arc lamps come close to being point sources and are

ideal for use in projection systems and for obtaining well-

collimated beams.

There are two different kinds of high-pressure arc

lamps: those where the discharge is conﬁned to a narrow

quartz capillary (which must be water-cooled), and those

where the discharge is not conﬁned (which usually

operate with forced-air cooling). The former are available

from Flashlamps (Verre et Quartz), ILC Technology,

Xenon Corp., and Ushio and are used for pumping

CW solid-state lasers. (Krypton arc lamps are better than

xenon arc lamps for pumping Nd

lasers, as their

emission is better matched to the absorption spectrum of

ions.)

Because high-pressure a rc lamps operate at very

high pressures when hot (up to 200 bar), they must be

housed in a rugged metal enclosure to contain a possible

lamp explosion. The mounting must be such as to

allow s tress-free expansion during warmup. Genera lly

speaking, commercial lamp assemblies should be used.

The power-supply requirements are somewhat unusual.

An initial high-voltage pulse is necessary to strike the

arc, and then a lower voltage, typically in the range 70–

120 V, to establish the arc. When the arc is fully estab-

lished, the operating voltage will drop to perhaps as low

as 10 V. Arcs containing mercury need a further increase

in operating voltage as they warm up and their internal

mercury pressure inc reases. Complete lamp assemblie s

and power supplies are available from several compa-

nies, among them, ILC Tec hnology, Newport/Oriel,

ORC Lighting Products, Perkin Elmer, and Spectral

Energy.

OPTICAL SOURCES 255

High-pressure arc lamps give substantial continuum

emission with superimposed line structure, as can be seen

in Figure 4.111. These lamps are not efﬁcient sources of

infrared

radiation. They give substantial UV emission,

however, and care should be taken in their use to avoid

eye or skin exposure. Their UV output will also generate

ozone, and provision should be made for venting this

safely from the lamp housing. They are available from

Bulbtronics, Hamamatsu, Laser Drive, Lighting Technol-

ogies International, and Newport/Oriel.

Deuterium lamps are efﬁcient sources of ultraviolet

emission with very little emission at longer wave-

lengths, as shown in Figure 4.111(a). They are available

from

Catheodeon, Hamamatsu, Newport/Oriel, Ocean

Optics, a nd Spectral Energy. Hollow-cathode lamps,

available from Hamamatsu and Hellma, emit stong spec-

tral lines characteristic of the material of which their

cathode is made. They can be used as wavelength cali-

bration sources.

Discharges in high-pressure noble gases can also be

used as intense continuum sources of vacuum-ultraviolet

radiation. This radiation arises from noble-gas excimer

emission, which in the case of helium, for example, arises

from a series of processes that can be represented as:

He þe ! He



þHe ! He



! He þ He þ hv

ð4:213Þ

The spectral regions covered by the excimer continua

are He, 10 5–400 nm; Ar, 107–165 nm; Kr, 124 –185 nm;

and Xe, 147–225 nm. Because there are no tra nsmissive

materials available for wavelengths below about 110

nm, sources below this wavelength are used without

windows. Radiation leaves the lamp through a small slit,

or through a multicapillary array. The latter is a close-

packed array of m any capillary tubes, which presents

considerable resistance to the passage of gas, but is

highly transparent to light. Multicapillary arrays can

be obtained from Burle Electro-Optics. To maintain

the lamp pressure, gas is continuously admitted. Gas

that passes from the lamp into the rest of the experiment

(for example a vacuum-ultraviolet monochromator) is

continuously pumped away by a high-speed vacuum

Figure 4.111 (a) Spectral irradiance of various moderate-power gas-discharge lamps (courtesy of Oriel Corporation,

Stamford, Conn.); (b) spectral energy distribution for a high-power (10 kW) xenon arc lamp with a long discharge column (from

A. A. Kruithof, ‘‘Modern Light Sources,’’ in Advanced Optical Techniques, A. C. S. Van Heel, Ed., North-Holland, Amsterdam,

1967; by permission of North-Holland Publishing Company).

256 OPTICAL SYSTEMS

pump, as shown in Figure 4.112. This technique is called

differential pumping (see Section 3.6.2). For further

tails of vacuum-ultraviolet sour ces and technolog y,

thereaderisreferredtoSamson.

Microwave Lamps. Small microwave-driven

discharge lamps are very useful where a low-power

atomic-emission line source is desired, particularly if the

atomic emission is desired from some reactive species

such as atomic chlorine or iodine. A small cylindrical

quartz cell containing the material to be excited, usually

with the addition of a buffer of helium or argon, is excited

by a microwave source inside a small tunable microwave

cavity, as shown in Figure 4.113. Suitable cavities for this

purpose,

designed for operation at 2450 MHz, are

available from Opthos Instruments; power supplies for

these lamps are available from Opthos and Cathodeon.

Flashlamps. The highest-brightness incoherent radiation

is obtained from short-pulse ﬂashlamps. By discharging a

capacitor through a gas-discharge tube, much higher

discharge currents and input powers are possible than in

d.c. operation. As the current density or pressure of a

ﬂashlamp is increased, the emission from the lamp shifts

from radiation that is characteristic of the ﬁll gas, with

lines superimposed on a continuum, to an increasingly

close approximation to blackbody emission corresponding

to the temperature of the discharge gas. Commercial

ﬂashlamps can be roughly divided into two categories. In

long-pulse lamps, fairly large capacitors (100–10 000 lF),

Figure 4.112 (a) Differential pumping arrangement (P

, P

are the light source, differential pumping unit, and

spectrometer operating pressures, respectively); (b) light source for the production of the noble-gas continua – in a

differentially pumped mode, no LiF window would be used. (From R. E. Huffman, Y. Tanaka, and J. C. Larrabee, ‘‘Helium

Continuum Light Source for Photoelectric Scanning in the 600–1100 A

Region,’’ Appl. Opt., 2, 617–623, 1963; by

permission of the Optical Society of America.)

OPTICAL SOURCES 257

charged to moderately high v oltages (typically up to about 5

kV), are discharged slowly (on time scales from 100 lsto1

ms) through high-pressure discharge tubes. In short-pulse,

high-peak-power lamps, smaller , low-inductance capacitors

(typically 0.1–10 lF), charged to high voltages (10–80 kV),

are discharged rapidly (on time scales down to 1 ls) through

lower -pressure discharge tubes. Suppliers of linear

ﬂashlamps include Continuum, Laser SOS Group, New

Source Technology, Perkin-Elmer Optoelectronics, and

Xenon Corporation.

(i) Long-pulse lamps. Long-pulse lamps are generally

ﬁlled with xenon,

but krypton lamps

(for pumping

lasers) and alkali-metal lamps are also available. Fill

pressures are typically on the order of 0.1–1 bar. Although

the discharge current in such lamps can run to tens of

thousands of A/cm

, at low repetition frequencies (< 0.1

Hz) ambient cooling is all that is necessary. Three of the

most commonly used circuits for operating such lamps are

shown in Figure 4.114. In all three of these circuits, the

capacitor

, or pulse-forming network shown in Figure 4.114

(c), is charged through a resistor R.

The capacitor is dis-

charged through the lamp by triggering the ﬂashlamp with

one of the trigger circuits shown in Figure 4.115. The lamp

itself

behaves both resistively and inductively when it is

ﬁred. If the inductance and resistance of the lamp are not

Figure 4.113 Microwave cavity for exciting a gas discharge in a cylindrical quartz tube

(design used by Opthos). (After F. C. Fehsenfeld, K. M. Evenson, and H. P. Broida,

‘‘Microwave Discharge Cavities Operating at 2450 MHz,’’ Rev. Sci. Instr., 36, 294–298,

1965; by permission of the American Institute of Physics.)

258 OPTICAL SYSTEMS

Figure 4.114 Operating circuits for ﬂashlamps (a ¼ lamp

anode; k ¼ lamp cathode): (a) RC discharge; (b) RLC

critically damped discharge; (c) pulse-forming network.

Figure 4.115 Flashlamp triggering schemes

(a ¼ lamp anode; k ¼ lamp cathode): (a) overvoltage trig-

gering (V > self-ﬂash voltage of ﬂashlamp; switching is

accomplished in this case with a

thyratron, but a triggered spark gap or ignitron can also be

used); (b) series triggering (a saturable

transformer is used with a fast-risetime 10–20 kV pulse with

sufﬁcient energy to trigger the lamp and saturate the core);

ﬂashlamp is ionized by a trigger wire wrapped around the

outside of the lamp and connected to the 5–15 kV

secondary of a high-voltage pulse transformer).

OPTICAL SOURCES 259

sufﬁciently large, the capacitor may discharge too rapidly,

which can lead to damage of both lamp and capacitor.

Generally speaking, an additional series inductor will be

desirable to control the discharge. The problem of select-

ing the appropriate inductor for a particular capacitor size

and lamp has been dealt with in detail by Markiewicz and

Emmett.

Slow ﬂashlamps have a nonlinear V-I character-

istic, which can be approximated by:

V ¼ K

ﬃﬃﬃﬃﬃ

jIj

ð4:214Þ

where the sign of V is taken to be the same as the sign of I.

The value of K

, measured in X A

1/2

, is a parameter speci-

ﬁed by a manufacturer for a given lamp. Given this value

and the capacitor size to be used, the calculations of Mar-

kiewicz and Emmett allow a suitable value of series induc-

tor to be chosen. Other factors must be taken into account

in designing the ﬂashlamp circuit: the maximum power

loading, usually speciﬁed as the explosion energy of the

lamp (which will depend on the discharge-pulse duration),

and the maximum repetition frequency of the lamp. Usu-

ally, the larger the capacitor-stored energy, the lower the

permitted repetition frequency will be. As lamps and dis-

charge energies get smaller, repetition frequencies can be

extended, to several kilohertz for the smallest low-energy

lamps, such as those used in stroboscopes. The explosion

energy of the lamp is the minimum input required to cause

lamp failure in one shot. To obtain long ﬂashlamp life, a

lamp should be operated only at a fraction of its explosion

energy. For example, at 50% of the explosion energy

the expected lifetime is from 100 to 1000 ﬂashes, while

at 20% it is from 10

to 10

ﬂashes. The lamp should be

mounted freely and not clamped rigidly at its ends when it

is operated.

The spectral output of a ﬂashlamp varies slightly during

the ﬂash. For moderate- and high-power lamps (> 100 J in 1

ms), the spectral output approaches that of a blackbody, as

shown in Figures 4.116 and 4.117.

Low-power lamps

exhibit the spectral feature of their ﬁll gas, as shown in

Figure 4.118. Figure 4.116 shows the transition from a spec-

rum with some line structure to a blackbody continuum as

the current density through the lamp is increased.

A word about the triggering schemes shown in Figure

4.115. External triggering, accomplished by switching a

high-v

oltage pulse from a transformer to a trigger wire

wrapped around the lamp, is perhaps the simplest scheme;

it is used only with long-pulse lamps and does not give

quite so good time synchronization as series-spark-gap or

thyratron-switched operation. The other methods are more

complex, but can be also used with short-pulse, high-

power lamps. Series triggering allows the incorporation

of triggering and lamp series inductance in a single unit.

Trigger transformers of various types are available from

EG&G and ILC. EG&G and EEV supply a range of excel-

lent thyratrons.

(ii) Short-pulse high-power lamps. Flashlamps that can

handle the rapid discharge of hundreds of joules on time-

scales down to a few microseconds are available commer-

cially from Flashlamps (Verre et Quartz), ILC Technology,

Perkin Elmer, and Xenon Corporation, among others. To

achieve such rapid discharges, these lamps are generally

operated in a low-inductance discharge circuit. When these

lamps are ﬁred at high-peak-power inputs, a severe shock

Figure 4.116 Output spectrum of a Perkin-Elmer FX-47A

xenon ﬂashlamp (0.4 atm) at two current densities:

1700A/cm

and 5300A/cm

260 OPTICAL SYSTEMS

wave is generated in the lamp. To withstand the shock

wave, the lamps are designed with special re-entrant elec-

trode seals. If lamps designed for long-pulse operation are

discharged too rapidly, their electrodes are quite likely to

break off because the electrode seals are not shock-

resistant.

The spectral emission of short-pulse, high-energy lamps

is generally quite close to that of a high-temperature black-

body, perhaps as hot as 30 000 K. The ﬁll pressure in these

lamps is often lower than in long-pulse lamps, typically

from 0.1 to a few tens of millibars. The ﬁll gas is usually

xenon, but other noble gases such as krypton or argon can

be used. If a short-pulse lamp has a narrow discharge-tube

cross-section, at high power inputs material can ablate

from the wall and a substantial part of the emission from

the lamp can come from this material. Such lamps can be

made with heavy-walled discharge-tube bodies of silica,

glass, or even Plexiglas. These lamps can be made fairly

simply. A good design described by Baker and King

illustrated in Figure 4.119. It can be operated in a non-

ablating

or ablating mode (at high or low pressure, respec-

tively). When operated in the ablating regime, such lamps

can be ﬁlled with air as the nature of the ﬁll gas is unim-

portant. Figure 4.119 also shows the use of a ﬁeld-distor-

tion-triggered

spark gap for ﬁring the lamp – a spark-gap

design that offers quiet, efﬁcient switching of rapid-

discharge capacitors. Rapid-discharge (low-inductance)

capacitors suitable for fast ﬂashlamp and other applica-

tions are available from CSI Technologies, Hipotronics,

and Maxwell Energy Products.

4.6 LASERS

Lasers are now so widely used in physics, chemistry, the

life sciences, and engineering that they must be regarded as

the experimentalist’s most important type of optical

source. With few exceptions, anyone who wants a laser

for an experiment should buy one. This is certainly true

in the case of helium–neon, argon–ion, and helium–

cadmium gas lasers and all solid-state crystalline, glass,

or semiconductor lasers. True, these lasers can be built in

the laboratory, but this is the province of the laser specialist

and will generally be found time-consuming and unpro-

ductive for scientists in other disciplines. On the other

hand, there are some lasers, such as nitrogen, Exciplex,

Figure 4.118 Spectral distribution of intensity from an

ILC 4L2 xenon ﬂashlamp (51 mm long by 4 mm bore)

operated in a critically damped mode with 10 J discharged

in 115 ls. (Courtesy of ILC).

Figure 4.117 Spectral distribution of power radiated by an

EG&G FX42 xenon-ﬁlled ﬂashlamp (76 mm long by 7 mm

bore) operated in a critically damped mode with 500 J

discharged in 1 ms. The spectral distribution was observed

0.7 ms from ﬂash initiation. The line is the blackbody

radiation curve of best ﬁt. (After J. G. Edwards, ‘‘Some

Factors Affecting the Pumping Efﬁciency of Optically

Pumped Lasers,’’ Appl. Opt., 6, 837–843, 1967; by per-

mission of the Optical Society of America.)

LASERS 261

, and CO gas lasers, and dye lasers, that it might occa-

sionally pay to build for oneself, even though models are

available commercially. A detailed discussion of how to

construct all these lasers will not be given here, but, to

illustrate how it is accomplished, design features of some

speciﬁc systems will be discussed.

Table 4.8 lists the primary wavelengths available from

the

more commonly used lasers presently available com-

mercially. For more detailed information about suppliers

and speciﬁcations consult a trade reference, such as the

Laser Focus or Photonics Spectra Buyers Guides. Laser

suppliers come and go, as does the availability of speciﬁc

types of laser. Before brieﬂy describing some of these laser

systems, some background material will be presented that

is pertinent to a discussion of lasers in general. More

detailed information regarding the physics of laser opera-

tion is given in the books by Davis,

Silfvast,

Saleh and

Teich,

Yariv,

and Siegman.

Figure 4.119 High-pulse-energy, fast ﬂashlamp design for conventional or

ablation-mode operation. (From H. J. Baker and T. A. King, ‘‘Optimization of Pulsed UV

by the Institute of Physics, used with permission).

262 OPTICAL SYSTEMS

Table 4.8 Wavelengths available from important lasers

CW Gas Lasers

Type Operating Wavelengths (nm)

Ar ion 229

244

348

257

275

333.4

333.6

351.1

363.8

454.5

457.9

465.8

476.5

488.0

496.5

50.17

514.5

528.7

1092.3

Kr ion 337.5

350.7

356.4

406.7

413.1

461.9

468.0

476.2

482.5

530.9

568.1

647.0

676.4

752.5

793.1

799.3

He–Ne 543

594.1

612

632.8

1152

3392

5400

11552

He-Cd 325.0

441.6

CO 5–6.5

9–11

10.6

LASERS 263

Pulsed Gas Lasers

Type Operating Wavelengths (nm)

Excimer

ArF 193.3

KrF 248.4–249.1

XeCl 307–308.43

XeF 348.8–354

Cu vapor 510.54

570

578.2

157

337.1

Type Operating Wavelengths (lm)

10.6

9–11

CW Solid-State Lasers

Type Operating Wavelengths (lm)

Alexandrite 365

0.370

0.730

0.760

Nd:YAG 266.8

355

0.532

1.064

(This is the primary line, Nd:YLF gives 1.047 lm and 1.053 lm,

Nd:YVO4 also gives 1064 nm)

1.318

Ti:Sapphire 0.7–1.02

Tunable

Pulsed Solid-State Lasers

Type Operating Wavelengths (lm)

Alexandrite 0.720–0.780 (tunable, can also provide 2nd, 3rd and 4th harmonic wavelengths)

Er:ﬁber lasers 1.2–2.0

Er:glass 1.534

Er:YAG 2.940

Er:glass 1.534

Ho:YAG 2.1

Nd:glass 0.266

0.355

0.532

1.06

Table 4.8 (cont.)

264 OPTICAL SYSTEMS

Ti:Sapphire 0.68–1

Tunable

Nd:YAG 0.213

0.265

0.355

0.53

1.064

Ruby 0.6943

Ytterbium:glass 1.030

Diode-Pumped Solid-State Lasers

Type Operating Wavelengths (nm)

266

355

460

473

488

515

532

670

1064

1030

1480

1535–1565

CW Tunable Dye Lasers

(pumped with ion lasers, frequency-doubled Nd:YAG lasers at 530nm, or frequency tripled Nd:YAG laser at 355 nm)

Tuning range (lm)

0.4–1.1 (The tuning range depends on the dye used. A typical dye provides 50–100 nm of tuning)

Pulsed Tunable Dye Lasers

Tuning Range (lm)

0.197–1.036

Produced by second harmonic generation of blue-green argon ion laser lines.

Strongest lines.

Most readily available wavelength.

Molecular lasers that offer discrete tunability over several lines.

Strongest line. Industrial CO

lasers generally operate only at 10.6 lm.

Frequency quadrupled from 1.06 lm output.

Frequency tripled from 1.06 lm output.

Frequency doubled from 1.06 lm output.

Phosphate glass gives 1.05 lm. Nd:YLF gives 1.053 lm

Fifth harmonic from1.06 lm output.

Table 4.8 (cont.)

Pulsed Solid-State Lasers (Cont.)

Type Operating Wavelengths (lm)

LASERS 265

The lasers listed in the table fall into two categories:

pulsed and CW (continuous wave). Many can be operated

in both ways, with the exception of nitrogen, copper v apor,

andexcimerlasers,whichcanonlyoperateinapulsedmode.

These three laser types are self-terminating: once they lase

they destroy their own population inversio n, and a period of

time must elapse before the upper laser lev el can be re-excited.

For pulsed lasers, the available energy outputs per

pulse can be c lassiﬁed as low (< 10 mJ) medium (10

mJ–1 J), high ( 1 J–100 J), and very high (> 100 J). Pulse

lengths depend on the type of laser and its mode of oper-

ation. Almost all pulsed solid-state lasers operate in a Q-

switched mode,

which typically provides a pulse length

in the 10 ns range, bu t varies somewhat from man ufac-

turer to manufacturer. Non Q-switched long-pulse (LP)

solid-state lasers have pulse lengths > 0.1 ms. Solid-state

anddyelasersarefrequentlyoperatedinamode-locked

(ML) conﬁguration, which provides pulse lengths in the

0.1–10 p s ra nge. A given las er can often be operated in

ML, Q, and LP modes. The energy output per pulse will

decrease as LP > Q > ML.

Continuous wave lasers can be classiﬁed by output

power as low (< 10 mW), medium (10 mW–1 W), high

(1–10 W), very high (10–100 W), and industrial (> 100 W).

Continuous wave gas lasers, in particular, provide power

outputs at many different wavelengths, and the available

power varies from line to line. These lasers are generally

supplied to operate in a speciﬁc wavelength range with

discrete tunability within that range. Ultraviolet gas lasers,

for example, are equipped with special optics, so do not

generally operate in the visible range as well.

The energy outputs available from pulsed lasers,

together with their available pulse-repetition rates and

pulse lengths, cover a very wide range. The highest

available energy outputs are generally available only

at the lowest pulse-repeti tion rates. In the ca se of CW

lasers, available power o utputs vary from line to line and

from manufacturer to manufacturer. To the intended pur-

chaser of a laser system, we recommend the following

questions:

(1) What ﬁxed wavelength or wavelengths must the laser

supply?

(2) Is tunability required?

(3) What frequency and amplitude stability are required?

(4) What laser linewidth is required?

(5) What power or pulse energy is required?

(6) Are high operating reliability and long operating life-

time required?

(7) For time-resolved experiments, what pulse length is

needed?

(8) Is the spatial proﬁle of the output beam important?

The desirable attributes in each of these areas are

unlikely to occur simultaneously. For example, frequency

tunability is not readily available throughout the spectrum

without resorting to the specialized techniques of nonlinear

optics.

14,15,71–75

In Table 4.8 the various categories of laser: CW gas,

pulsed gas, CW solid-state, pulsed solid state, CW dye

and pulsed dye frequently show tuning ranges and wave-

lengths that are obtained from these lasers by the use of

nonlinear optics. For example, shorter wavelengths from

argon ion, Nd:YAG, Ti:sapphire, and CO

can be obtained

by frequency doubling (tripling or even quadrupling) by

the use of a nonlinear crystal. The nonlinear crystal is

generally external to the primary laser, although it may

be housed in its own resonant structure. Generating second

or third harmonic light from a sufﬁciently powerful laser is

not especially difﬁcult, although this is still a relatively

specialized endeavor.

New frequency generation from a primary pump laser

can also be obtained by the use of an optical paramatic

oscillator (OPO). In such a device an appropriate nonlinear

crystal is pumped with a frequency m

and in this process

generates two new frequencies m

and m

, called the signal

and idler frequencies, respectively. In this process photon

energy must be conserved, so:

¼ m

þ m

ð4:215Þ

High-energy and high-power lasers are generally less sta-

ble, both in amplitude and in frequency, and will generally

be less reliable and need more ‘‘hands on’’ attention than

their low-energy or low-power counterparts. When a deci-

sion is made to purchase a laser system, compare the spec-

iﬁcations of lasers supplied by different manufacturers;

discuss the advantages and disadvantages of different sys-

tems with others who have purchased them previously.

Reputable laser manufacturers are generally very willing

to supply the names of previous purchasers.

266 OPTICAL SYSTEMS

To some experimental scientists a laser is merely a

rather monochromatic directional lightbulb; for others,

detailed knowledge of its operating principles and charac-

teristics is essential. Certain aspects of laser designs and

operating characteristics, however, are very general and

are worthy of some discussion.

4.6.1 General Principles of Laser Operation

A laser is an optical-frequency oscillator: in common with

electronic circuit oscillators, it consists of an ampliﬁer

with feedback. The optical-frequency amplifying part of

a laser can be a gas, a crystalline or glassy solid, a liquid, or

a semiconductor. This medium is maintained in an ampli-

fying state, either continuously or on a pulsed basis, by

pumping energy into it appropriately. In a gas laser the

input energy comes from electrons (in a gas discharge or

an electron beam), or from an optical pump (which may be

a lamp or a laser). Solid-state crystalline or glassy lasers

receive their pumping energy from continuous or pulsed

lamps, and in more and more cases from semiconductor

lasers. Liquid lasers can be pumped with a ﬂashlamp or, on

a continuous or pulsed basis, by another laser. Semicon-

ductor lasers are p-n junction devices and are operated by

passing pulsed or continuous electrical currents though

them.

The amplifying state in a laser medium results if a pop-

ulation inversion can be achieved between two sublevels of

the medium. The energy sublevels of a system are single

states with their own characteristic energy. A set of sub-

levels having the same energy is called an energy level.

This can be seen with reference to Figure 4.120, which

sho

ws a schematic partial energy-level diagram of a typi-

cal laser system. Input energy excites ground-state par-

ticles (atoms, molecules, or ions) of the medium into the

state (or states) indicated as 3. These particles then transfer

themselves or excite other particles preferentially to sub-

level 2. In an ideal system, negligible excitation of par-

ticles into sublevel 1 should occur. If the populations of the

sublevels 2 and 1 are n

and n

, respectively, and n

> n

this is called a population inversion. The medium then

becomes capable of amplifying radiation of frequency:

v ¼

 E

ð4:216Þ

where h is Planck’s constant. In practice, energy levels of

real systems are of ﬁnite width, so the medium will amplify

radiation over a ﬁnite bandwidth. The gain of the ampliﬁer

varies with frequency in this band and is speciﬁed by a gain

proﬁle g(v), as shown in Figure 4.121. Actual laser oscil-

lation

occurs when the amplifying medium is placed in an

optical resonator, which provides the necessary positive

feedback to turn the ampliﬁer into an oscillator. Most opti-

cal resonators consist of a pair of concave mirrors, or one

concave and one ﬂat mirror, placed at opposite ends of the

amplifying medium and aligned parallel. A laser resonator

is in essence a Fabry–Perot (see Section 4.7.4), generally

large spacing. The radii and spacing of the mirrors will

determine, to a large degree, the type of Gaussian beam

that the laser will emit. At least one of the mirrors is made

partially transmitting, so that useful output power can be

extracted. The choice of optimum mirror reﬂectance

depends on the type of laser and its gain.

Low-gain lasers such as the helium–neon have high-

reﬂectance mirrors, (98–99%), while higher-gain lasers

such as pulsed nitrogen, CO

,orNd

:YAG can operate

with much lower reﬂectance values. In certain circumstan-

ces, when their gain is very high, lasers will emit laser

radiation without any deliberately applied feedback.

Figure 4.120 Schematic partial energy-level diagram of a

laser system.

LASERS 267

Lasers that operate in this fashion are generally operating

in an ampliﬁed spontaneous emission (ASE) mode. Such

lasers are just amplifying their own spontaneous emission

very greatly in a single pass.

4.6.2 General Features of Laser Design

Even though the majority of laser users do not build their

own, an awareness of some general design features of laser

systems will help the user to understand what can and

cannot be done with a laser. It will also assist the user

who wishes to make modiﬁcations to a commercial laser

system to increase its usefulness or convenience in a par-

ticular experimental situation. Figure 4.122 shows a sche-

matic

diagram of a typical gas laser, which incorporates

most of the desirable design features of a precision system.

The amplifying medium of a gas laser is generally a high-

or low-pressure gas excited in a discharge tube. The exci-

tation may be pulsed (usually by capacitor discharge

through the tube), d.c., or occasionally a.c. Some gas lasers

are also excited by electron beams, by radiofrequency

energy, or by optical pumping with either a lamp or

another laser. Far-infrared lasers, in particular, are fre-

quently pumped with CO

lasers. Depending on the cur-

rents that must be passed through the discharge tube of the

laser, it can be made of Pyrex, quartz, beryllium oxide,

graphite, or segmented metal. These last three have been

used in high-current-density discharge tubes for CW ion

lasers. Several types of pulsed high-pressure or chemical

lasers, such as CO

, HF, DF, and HCI, can be excited in

structures built of Plexiglas or Kel-F.

Because most gas lasers are electrically inefﬁcient, a

large portion of their discharge power is dissipated as heat.

If ambient or forced-air cooling cannot keep the discharge

tube cool enough, water cooling is used. This can be done

in a closed cycle, using a heat exchanger. Some lasers need

the discharge tube to run at temperatures below ambient. In

such cases a refrigerated coolant such as ethylene glycol

can be used. Many gas lasers use discharge tubes ﬁtted

with windows placed at Brewster’s angle. This permits

linearly polarized laser oscillation to take place in the

direction indicated in Figure 4.122; light bouncing back

and

forth between the laser mirrors passes through the

windows without reﬂection loss. Mirrors ﬁxed directly

on the discharge tube can also be used – this is common

in commercial He–Ne lasers. In principle, such lasers

should be unpolarized, although in practice various slight

anisotropies of the structure often lead to at least some

polarization of the output beam. The two mirrors that con-

stitute the laser resonator, unless these are ﬁxed directly to

the discharge tube, should be mounted in kinematically

designed mounts and held at ﬁxed spacing ‘ by a thermally

stable resonator structure made of Invar or quartz. In this

structure an important parameter is the optical length, L,of

the structure. For a laser in which the whole space between

the two resonator mirrors is ﬁlled with a medium of refrac-

tive index n, the optical length is L ¼ n‘. For a composite

structure with regions of different refractive index this

result is easily generalized. Because the laser generates

one or more output frequencies which are close to integral

Figure 4.121 (a) Laser gain proﬁle showing position of

cavity resonances and potential laser oscillation frequencies

near cavity resonances where gain lies above loss (L is length

of laser cavity); (b) transmission characteristic of intracavity

etalon, on same frequency scale as (a), for single-mode

operation (l is the etalon thickness and F its ﬁnesse).

268 OPTICAL SYSTEMS

multiples of c/2L, any drift in mirror spacing L causes

changes in output frequency v. This frequency change Dv

satisﬁes:

ð4:217Þ

For a laser 1 m long, even with an Invar-spaced resonator

structure, the temperature of the structure would need to be

held constant within 10 mK to achieve a frequency stabil-

ity of only 1 part in 10

. The discharge tube should be

thermally isolated from the resonator structure unless the

whole forms part of a temperature-stabilized arrangement.

If single-frequency operation is desired, the laser should

be made very short – so that c/2L becomes larger than Dv in

Figure 4.121 – or operated with an intracavity etalon (see

Sections 4.6.4 and 4.7.4). Visible lasers that have the capa-

bility

of oscillating at several different wavelengths are

generally tuned from line to line by replacing one laser

mirror with a Littrow prism whose front face is set at

Brewster’s angle and whose back face is given a high-

reﬂectance coating, as shown in Figure 4.123(a). Alterna-

vely, as shown in Figure 4.123(b), one can use a separate

intracavity

prism, designed so the intracavity beam passes

through both its faces at Brewster’s angle. Infrared gas

lasers that can oscillate at several different wavelengths

are tuned by replacing one resonator mirror with a gold-

coated or solid metal diffraction grating mounted in Lit-

trow, as shown in Figure 4.123(c). The laser oscillation

wav

elength then satisﬁes:

mk ¼2d sin h ð4:218Þ

where d is the spacing of the grating grooves, h is the angle

of incidence, and m is an integer.

A laser will oscillate only if its gain exceeds all the

losses in the system, which include mirror transmission

losses, absorption and scattering at mirrors and windows,

Figure 4.122 Schematic diagram of a typical gas laser showing some of the desirable

features of a well-engineered research system. In high-discharge-

current systems, some form of internal or external gas-return path from cathode to anode

must be incorporated into the structure.

LASERS 269

and any inherent losses of the amplifying medium itself –

the last generally being signiﬁcant only in solid-state,

liquid, and semiconductor lasers. Consequently, it is par-

ticularly important to keep the mirrors and windows of a

laser system clean and free of dust. Most commercial sys-

tems incorporate a ﬂexible, sealed enclosure between

Brewster windows and mirrors to exclude contaminants.

Figure 4.124 shows some design features of a simple

lamp-pumped

solid-state laser oscillator. This design

incorporates a linear pulsed or continuous lamp and a

crystalline or glass laser rod with Brewster windows

mounted inside a metal elliptical reﬂector, which serves

to reﬂect pumping light efﬁciently into the laser rod.

Although such solid-state lasers are rarely used in experi-

ments where extreme frequency stability and narrow line-

width operation are required, it is still good practice to

incorporate features such as stable, kinematic resonator

design and thermal isolation of the hot lamp from the

resonator structure. Elliptical reﬂector housings for solid-

state lasers (and ﬂashlamp-pumped dye lasers) can be

made in two halves by horizontally milling a rectangular

aluminum block with the axis of rotation of the milling

cutter set at an angle of arccos(a/b), where a and b are the

semiminor and semimajor axes of the ellipse. This process

is repeated for a second aluminum block. The two halves

are then given a high polish, or plated, and joined together

with locating dowel pins. For further details of solid-state

laser design and particulars of other arrangements for opti-

cal pumping the reader should consult Ro

or Koech-

ner.

Flashlamp-pumped dye lasers share some design

features with solid-state lasers. The main difference is that

the former require excitation of short pulse duration

(< 1 ls) with special ﬂashlamps in low-inductance dis-

charge circuitry.

78–81

4.6.3 Speciﬁc Laser Systems

Gaseous Ion Lasers. Gaseous ion lasers, of which the

argon, krypton, and helium–cadmium are the most impor-

tant, generate narrow-linewidth, highly coherent visible

and ultraviolet radiation with powers in the range from

milliwatts to a few tens of watts CW. Pulsed ion lasers

operate at high current densities, but have low duty cycles,

so that ambient cooling is adequate. These lasers are not in

widespread experimental use. Helium–cadmium lasers use

low-current-density (a few A/cm

) air-cooled discharge

structures, which in many respects are similar to those of

helium–neon lasers. They are limited to a few tens of milli-

watts in conveniently available output power. They do,

however, provide UVoutput at 325 nm. Argon and krypton

ion lasers use very high-current-density discharges (100–

2000 A/cm

) in special refractory discharge structures

Figure 4.123 Methods for wavelength-selective reﬂection

in laser systems: (a) Brewster’s-angle Littrow prism; (b)

intracavity Brewster’s-angle prism; (c) reﬂective diffraction

grating. N ¼ surface normal.

270 OPTICAL SYSTEMS

usually made of tungsten disks with ceramic spacers, as

shown in Figure 4.125. In operation, these disks cool them-

selves

by radiating through an outer fused-silica envelope

surrounded by coolant water. Commercially available

powers range up to a few tens of watts, but outputs up to

1 kW in the visible have been reported. Low power (< 100

mW) argon ion lasers can be forced-air cooled. Compre-

hensive information about ion lasers can be found else-

where.

82,83

Argon and krypton ion lasers are available

commercially from Coherent, JSC Plasma, JDSU, Melles

Griot, and Spectra Physics (Newport Corporation). Argon

and krypton ion lasers have in the past been widely used

for pumping CW dye lasers and Ti:sapphire lasers. They

are, however, rapidly being replaced in these applications

by frequency-doubled Nd lasers, which are more and more

likely to be pumped themselves by semiconductor diode

lasers. Because of the large currents at which they operate,

argon and krypton ion lasers regularly need their plasma

tubes to be replaced (typically evey few thousand hours of

operation), which is an expensive business. It appears

Figure 4.124 Schematic diagram of a simple solid-state laser system.

LASERS 271

likely that these lasers will disappear from use and be uni-

versally replaced by diode-pumped solid-state (DPSS) lasers.

Helium–Neon Lasers. Of all types of laser, helium–

neon lasers come closest to being the ideal classical mono-

chromatic source. They can have very good amplitude

(’ 0.1%) and frequency stability (1 part in 10

without

servo frequency control). Servo-frequency-controlled ver-

sions are already in use as secondary frequency standards,

and have excellent temporal and spatial coherence.

Typical available power outputs range up to 50 mW. Sin-

gle-frequency versions with power outputs of 1 mW, which

are ideal for interferometry and optical heterodyne experi-

ments, are available from Spectra-Physics and Aerotech.

Although 632.8 nm is the routinely available wavelength

from He–Ne lasers, other wavelengths, such as 543 nm or

1.15 or 3.39 lm are also available. Helium–neon lasers of

low power are very inexpensive, costing from about $100,

and are ideal for alignment purposes. Because of their

superior spectral qualities compared to semiconductor

lasers that can operate at the same wavelength, they remain

a valuable source in applications such as interferometry

and metrology. Other suppliers include Newport/Spectra

Physics, Meles Griot, and Micro-Controle.

Helium–Cadmium Lasers. These lasers are similar

in many ways to helium–n eon lasers. They operate at

relatively low current densities and use discharge tube

structures that do not require water cooling. They are

quite important in applications requiring deep blue and

ultraviolet light at powers of ten of milliwatts. They

operate at 325 nm and 441.6 n m. Th ese wavelengths,

especially 325 nm, are useful in applications where a

photochemically active source is require d. They are

widely used in photolithography. Helium–cadmium

lasers are available from Kimmon Electric Co. and

Melles Griot.

Lasers. Both pulsed and CW CO

lasers are easy to

construct in the laboratory. A typical low-pressure CW

version would incorporate most of the features shown in

Figure 4.122. A water-cooled Pyrex discharge tube of

internal

diameter 10–15 mm, 1–2 m long, and operating

at a current of about 50 mA, is capable of generating tens

of watts output at 10.6 lm. The best operating gas mixture

is CO

–N

–He in the ratio 1:1:8 or 1:2:8, at a total pressure

of about 25 mbar in a 10 mm diameter tube. ZnSe is the

best material to use for the Brewster windows, as it is

transparent to red light and permits easy mirror

alignment. The optimum output mirror reﬂectance

depends on the ratio of the tube length to diameter, L/d,

roughly according to:

R ’ 1  L=500d ð4:219Þ

Figure 4.125 Construction of a high-power, water-cooled ion laser.

272 OPTICAL SYSTEMS

The output mirror is usually a dielectric-coated germa-

nium, gallium arsenide, or zinc selenide substrate. Such

mirrors are available from Janos, Laser Optics, Coherent,

Infrared Industries, Laser Research Optics, Unique Opti-

cal, and II-VI Infrared, and Rocky Mountain Instruments,

among others. The total reﬂector can be gold-coated in

lasers with outputs of a few tens of watts. For tunable

operation, gratings are available from American Holo-

graphic, Gentec, Jobin-Yvon, Perkin-Elmer, Richardson

Grating Laboratory, and Rochester Photonics. When a gra-

ting is used to tune a laser with Brewster windows, the

grating should be mounted so that the E vector of the laser

beam is orthogonal to the grating grooves. An excellent

review of low-pressure CW CO

gas lasers has been given

by Tyte.

Continuous wave CO

lasers can also be operated in a

waveguide conﬁguration, in which a much higher pressure

gas mixture is excited in a small size discharge capillary.

These lasers provide substantially greater power output per

volume than the low pressure variety. They can be excited

by direct current, but r. f. excitation is now popular, and has

now solved the unreliability problems that afﬂicted early

commercial versions. Current suppliers of these compact

lasers are Access Laser, Coherent, Edinburgh Instruments,

Infrared Optical Products, Roﬁn-Sinar, Synrad, Trumpf,

and Universal Laser Systems.

Transversely excited atmospheric-pressure (TEA) CO

lasers ar e widely us ed when high-energy, pulsed infrared

energy near 10 lm is required. These lasers operate in

discharge structures w her e the current ﬂow is transverse

to t he resonat or axis through a hig h- press ure (> 0.5 bar)

mixture of CO

, and He, typically in the ratio 1:1:5.

To achieve a uniform, pulsed glow discharge through a

high-pressur e g as , special electro de structur es and pre-

ionization techniques are used to inhibit the formation

of locali zed spark discharges. Many very-high-energy

types utilize electron-beam excit ation. Discharge-excited

TEA lasers are relatively easy to construct in the labora-

tory. A device with a discharge volume 60 cm long 3 5

cm wide with a 3 cm electrode spacing excited with a 0.2

lF c apacitor charged to 30 kV, will generate several

joules in a pulse about 150 ns long. There a re very many

different d esigns for CO

TEA lasers; particulars of var-

ious ty pe s can be found in the IEEE Journ al of Quantum

Electronics and the Journal of Applied Physics. A partic-

ularly good design that is easy to construct is derived

from a vacuum-ultraviolet photopreionized design

described by Seguin and Tulip.

A diagram of the dis-

charge structure is shown in Figure 4.126 , together with

ts associated capacitor-dischargecircuitry.Thecathode

is an aluminum Rogowski 2p/3 proﬁle;

the anode i s a

brass m esh, beneath which is a section of doub le -side d

copper-clad printed circuit board machined into a matrix

of separate copper sections on its top side. This printed

circuit b oard provides a source of very many surface

sparks for photopreion iza tion of the main discharge.

The laser is ﬁtted with two separate capacitor banks: e ach

circuit-boa rd spark chan ne l is energized by a 3600 pF

Sprague or similar ‘‘doorknob’’ capaci tor, while the main

discharge is energized with a 0.2 lF low-inductance

capacitor. S uch capacitors ar e available from CSI Tech-

nologies, Hi Voltage Compon ents, and Maxwell Labs.

Both capacitor banks are switched with a s ingle spark

gap, which incorporates a Champion marine spark plug

for triggering. The end of the spark plug, which has an

annular gap, i s ground down to it s ceramic insulator and

is triggered by an EG&G Model TM-11A Trigger gener-

ator. A good double Rogowski TEA laser design has been

given by Seguin, Manes, an d Tulip.

TEA lasers based

on the multiple-pin-discharge design ﬁrst described by

Beaulieu

arealsoeasytoconstruct,buttheydonotgive

output en ergies com para ble to those of volume-excited

designs. They do, however, lend themselves we ll to l aser

oscillation in many different gases – for example, HF

formed by discharge excitation of H

–F

mixtures.

CO Lasers. Continuous wave CO lasers are essentially

similar in construction to CO

lasers except that the dis-

charge tube must be maintained at low temperatures –

certainly below 0 °C. They operate in a complex mixture

of He, CO, N

, and Xe with (for example) 21 mbar He,

0.67 mbar N

, 0.013 mbar O

, and 0.4 mbar Xe. They are

available from Access Laser and Edinburgh Instruments.

Exciplex (Excimer) Lasers. Exciplex lasers operate

in high-pressure mixtures such as Xe–F

, Xe–Cl

, Kr–Cl

Kr–F

, and Ar–F

. They are commonly also called ‘‘exci-

mer’’ lasers, although this is not strictly correct scientiﬁc

terminology except in the case of the F

laser. Both dis-

charge TEA and E-beam-pumped conﬁgurations are used.

LASERS 273

Under electron bombardment, a series of reactions occur

that lead to the formation of an excited complex (exciplex)

such as XeF

, which is unstable in its ground state and so

dissociates immediately on emitting light. Excimer lasers

available commercially are sources of intense pulsed ultra-

violet radiation. The radiation from these lasers is not

inherently of narrow linewidth, because the laser transition

takes place from a bound to a repulsive state of the exci-

plex, and therefore is not of well-deﬁned energy. Excimer

lasers are attractive sources for pumping dye lasers and

whenever intense pulsed UV radiation is required in, for

example, photolithography or photochemistry.

The beam quality from an excimer laser is not normally

very high. These are ‘‘multimode’’ lasers, with often a

rectangular output beam proﬁle. These lasers are widely

available commercially from companies such as Gam

Laser, JP Sercel Associates (JPSA), Lambda Physik

(now Coherent), Optec, MPB Communications, and

SOPRA.

Excimer lasers share technological design features in

common with both CO

TEA lasers and nitrogen lasers.

They use rapid pulsed electrical discharges through the

appropriate high-pressure gas mixture. The discharge

design must be of low inductance and the excitation is

generally faster than is necessary to operate a CO

TEA

laser. Because these lasers use toxic gases, such as ﬂuorine

and chlorine, appropriate gas-handling safety precautions

must be taken in their use. The gases used, which are

usually diluted mixtures of a halogen in a noble gas, should

be housed in a vertical gas cabinet and exhaust gases from

the laser should be sent through a chemical ‘‘scrubber’’ or

ﬁlter cartridge before venting into the atmosphere.

Figure 4.126 Cutaway view of vacuum-ultraviolet photopreionized Rogowski TEA laser

structure.

274 OPTICAL SYSTEMS

Nitrogen (N

) Lasers. Molecular-nitrogen lasers are

sources of pulsed ultraviolet radiation at 337.1 nm. Com-

mercially available low-energy devices usually operate on

a ﬂowing nitrogen ﬁll at pressures of several tens of mbar,

and generate output powers up to about 1 MW in pulses up

to about 10 ns long. These lasers are reliable and easy to

operate, and are widely used for pumping low-energy

pulsed dye lasers. Nitrogen lasers, by virtue of their inter-

nal kinetics, only operate in a pulsed mode. They use very

rapid transversely excited discharges, usually between two

parallel, rounded electrodes energized with small, low-

inductance capacitors charged to about 20 kV. The whole

discharge arrangement must be constructed to have very

low inductance. Special care must be taken with insulation

in these devices; the very rapidly changing electric ﬁelds

present can punch through an insulating material to ground

under circumstances where the same applied d.c. voltage

would be very adequately insulated. There are several

good N

-laser designs in the literature.

91–96

These designs

fall into two general categories: Blumlein-type distributed-

capacitance discharge structures, and designs based on

discrete capacitors. The latter, although they do not give

such high-energy outputs from a given laser as the very

rapid-discharge Blumlein-type structures, are much easier

to construct in the laboratory and are likely to be much

more reliable. The capacitors used in these lasers need to

be of low inductance and capable of withstanding the high

voltage reversal and rapid discharge to which they will be

subjected. Suitable capacitors for this application can be

obtained from Murata or Sprague.

The output beam from a transversely excited N

laser is

by no means Gaussian. It generally takes the form of a

rectangular beam, typically ’ 0.5 cm 3 3 cm, with poor

spatial coherence. Such a beam can be focused into a line

image with a cylindrical lens for pumping a dye cell in a

pulsed dye laser. Nitrogen lasers are available commer-

cialy from LTB Lasertechnik and Spectr-Physics (now

Newport).

Copper Vapor Lasers. These are high-pulse-

repetition-frequency (prf) pulsed gas lasers that operate

using high-temperature gas mixtures of copper vapor in a

helium or neon buffer gas. With individual pulse energies

up to several millijoules and prf up to 20 kHz, these lasers

provide average powers up to several watts. They are used

for pumping pulsed dye lasers. The principal operating

wavelengths are 510.6 and 578.2 nm. Suppliers include

Laser Consultants and Oxford Laser. Pulsed gold vapor

lasers are also available commercially, which are similar

in most respects. They operate at 627.8 nm.

Continuous wave Solid-State Lasers. The most

important laser in this category is the Nd:YAG laser, where

YAG (yttrium aluminum garnet Y

) is the host

material for the actual lasing species – neodymium ions,

. Other host materials are also used: YLF (yttrium

lithium ﬂuoride, LiYF

), YVO

(yttrium vanadate), YALO

(yttrium aluminum oxide YAlO

) and GSGG (scandium-

substituted gadolinium gallium garnet, Gd

The principal neodymium output wavelength is 1.06 lm,

but other infrared wavelengths, especially 1.32 lm, are

available. There are many suppliers.

The 1.06 lm can

be efﬁciently doubled to yield a CW source of green radi-

ation. This source of green radiation has replaced the

argon-ion laser in many applications, especially since the

neodymium laser itself can be pumped so conveniently

with appropriate semiconductor lasers.

Ti:sapphire is an attractive laser material for generating

tunable radiation in the 700–1060 nm range. These lasers

are generally pumped by argon-ion lasers on frequency-

doubled neodymium lasers. Suppliers include Coherent,

Inc., Continuuum, Photonics Industries International, and

Quantronix.

Fiber lasers use a gain medium that is a ﬁber doped with

rare-earth ions such as erbium (Er

), neodymium (Nd

ytterbium (Yb

), thulium (Tm

), or praseodymium

(Pr

). They are pumped by one or more semiconductor

laser diodes.

A simple schematic of how they are con-

structed is shown in Figure 4.127. In practice, the pump

light

may be coupled in through the cladding of the ﬁber.

Very high-power ﬁber lasers with powers above 100 W are

increasingly being used in industrial applications. Suppli-

ers include B&W Tek, Fibercore, Fibertek, IPG Photonics,

Micro-Controle, Newport, Nufren, and Toptica. Fiber

lasers can be mode-locked to generate very short pulses

(< 1 ps) in the infrared. Pulsed Er

ﬁber lasers are avail-

able from Calmar Optcom, PriTel, and IPG Phtonics.

Pulsed Yb

lasers are available from Calmar Optcom,

Clark-MXR, IPG Photonics, Laser Photonics, and Quantel.

LASERS 275

An important application of erbium-doped ﬁber is in

erbium-doped optical ﬁber ampliﬁers (EDFAs), widely

used in ﬁber optic communication networks to amplify

1.55 lm semiconductor laser radiation.

F-center lasers

are doped-crystal lasers that are pumped

with argon, krypton, or dye lasers. They pr ovide tunable

operation in two regions: between 1.43 and 1.58 lmand

between 2.2 and 3.3 lm, but are somewhat inconvenient,

because the crystal must be cooled with liquid nitrogen.

They no longer appear to be av ailable commercially .

Pulsed Solid-State Lasers. Three lasers are most

important in this category Nd:YAG, Nd:glass, and ruby.

Nd:YAG and Nd:glass lasers oscillate at the same principal

wavelength, 1.06 lm. Nd:YAG is generally used in high-

pulse-repetition-rate systems and/or where good beam

quality is desired. High-energy Nd laser systems frequently

incorporate an Nd:YAG oscillator and a series of Nd:glass

ampliﬁers. There are many suppliers.

Ruby lasers,

despite being the ﬁrst laser to be demonstrated, are little

used in research. They have medical applications because

they provide a high-energy pulsed deep-red output (694.3

nm). They are available from Continuum.

All these pulsed solid-state lasers use fairly long ﬂash

excitation (’ 1 ms). Unless the laser pulse output is con-

trolled, they generate a very untidy optical output, consist-

ing of several hundred microseconds of random optical

pulses about 1 ls wide, spaced a few microseconds apart.

This mode of operation, called spiking, is rarely used. Usu-

ally the laser is operated in a Q-switched mode. In this mode

the laser cavity is blocked with an optical shutter such as an

electro-optic modulator or Kerr cell, as illustrated in Figure

128. An appropriate time after ﬂashlamp ignition, after the

pulation inversion in the laser rod has had time to build to

a high value, the shutter is opened. This operation, which

changes the Q of the laser cavity from a low to a high value,

causes the emission of a very large short pulse of laser

energy. The Q-switched pulse can contain nearly as much

energy as would be emitted in the ‘‘spiking’’ mode and is

Figure 4.127 Schematic construction of a ﬁber laser.

Figure 4.128 Schematic arrangement for Q-switching. Laser oscillation occurs when the

voltage bias on the Kerr cell or electro-optic crystal is removed, thereby allowing the reﬂected

beam to remain linearly polarized in the vertical direction.

276 OPTICAL SYSTEMS

typically 10–20 ns long. Passive Q-switching can also be

accomplished with a ‘‘bleachable’’ dye solution placed in an

optical cell inside the laser cavity. The dye is opaque at low

incident light intensities and inhibits the buildup of laser

oscillation. When, however, the laser acquires enough gain

to overcome the intracavity dye absorption loss, laser oscil-

lation begins, the dye bleaches, and a Q-switched pulse

results. A bleachable dye cell with a short relaxation time,

placed close to one of the laser mirrors, will frequently lead

to mode-locked operation

99–101

within the Q-switched pulse

(see Section 4.6.4).

Semiconductor Lasers. Five principal types of

semiconductor laser are available commercially:

(1) Wide bandgap semiconductor lasers based on GaN/

AlGaN, which, depending on stoichiometry, can emit

down to 375 nm. These UV, blue, and green diode

lasers have power outputs of several milliwatt and

above. The developer of the shortest wavelength laser

diodes based on GaN is Nichia, other manufacturers

include Coherent, Cree, Koheras, Micro Laser Sys-

tems, Sony, and Toptica. Wavelengths above 375 nm

are obtained from diodes with elements such as

indium, aluminum, gallium, or nitrogen added, which

produces laser diodes with wavelengths from 480 to

520 nm. The availability of short wavelength diode

and diode-pumped solid-state lasers has signiﬁcantly

reduced the market and applications for visible and

UV gas lasers such as argon ion, helium–cadmium,

helium–neon, and krypton ion.

(2) GaAs or GaAlAs lasers, which operate at ﬁxed wave-

lengths in the region between 0.75 and 0.9 lm. These

lasers are very inexpensi v e and reliable; they are widely

used in communication and information-processing sys-

tems, and in compact-disk players. High-po wer versions

are used as the pumping source in DPSS lasers.

(3) InGaAsP lasers operate principally in the 1.3 and

1.55 lm regions for telecommunications applications.

They have been developed to operate at the optimum

wavelengths for minimum dispersion and lowest loss

in optical-ﬁber communication systems. Near infrared

semiconductor lasers are described in detail in many

specialized texts.

102–110

(4) Tunable diode lasers, which utilize lead-salt semicon-

ductors such as PbSSe, PbSnSe, and PbSnTe can

provide tunable operation over limited regions any-

where between 3 and 30 lm. The tunable lead-salt

diode lasers are now commonly used in high-resolu-

tion spectroscopy.

111

They generally emit several

modes, which, because of the very short length of

the laser cavity, are spaced far enough in wavelength

for a single one to be isolated by a monochromator.

The output laser linewidths that are obtainable in this

way are about 10

–4

/cm

(3 MHz). Scanning is accom-

plished by changing the temperature of the cryogeni-

cally cooled semiconductor or the operating current.

Complete tunable-semiconductor-laser spectroscopic

systems are available from Quantum Associates or

Spectra-Physics (Laser Analytics).

(5) Quantum cascade lasers

112

can provide tunable oper-

ation over speciﬁc limited spectral regions within a

range from 3 to 211 lm. The wavelength range varies

from manufacturer to manufacturer. These lasers use

multiple quantum wells, a so-called superlattice,to

provide laser operation between sub-bands in the con-

duction bands of the structure. These lasers do not use

p-n junctions for their operation. Quantum cascade

lasers are available from Alpes, Boston Electronics,

Cascade Technologies, and Sacher Lasertechnik.

Semiconductor Laser Properties. Only researchers

involved in semiconductor laser development will fabricate

these lasers. Their laser performance is, however, strongly

inﬂuenced by their generally small size, and device

structure. Figures 4.129–4.132 give examples of some

Figure 4.129 Double heterostructure laser diode design

using a stripe excitation region conﬁned by an oxide layer

and deep zinc diffusion.

LASERS 277

representative structures that are used in current

semiconductor diode lasers. The basic laser structure

involves a p-n junction through which a drive current

ﬂows. In all these structures the current ﬂow through the

device is controlled so that a speciﬁc volume of the active

region is excited. This region is generally very small. The

active length is not generally more than 1–2 mm. The

lateral dimensions of the active region are generally in

the 5–10 lm range, however, in single quantum well

(SQW) and multiple quantum well (MQW) lasers, the

dimension of the active region in the direction of current

ﬂow can be as small as 10–100 nm.

Laser oscillation occurs in a resonant Fabry–Perot

structure made up of the two end facets of the laser.

The active region acts like a waveguide to c onﬁne the

laser beam, which ideally emerges from the emitting

facet as an elliptical Gaussian beam. This is a Gaussian

beam whose spot sizes w

, w

are different in the two

orthogonal (x, y) directions perpendicular to the z prop-

agation direction of the laser beam. The smaller spot size

is generally in the direction perpendicular to the junc-

tion. This asymmetry of the laser beam causes its beam

divergence to be larger in the direct ion perpendicular to

the jun ction than it is in the orthog onal direction, as

shown schematically in Figure 4.133. Commercial diode

lasers

are often supplied with an anamorphic beam

expander, whic h circularizes the laser beam and equal-

izes its orthogonal beam divergence angles, however, in

general the beam quality from any semiconductor laser is

Figure 4.130 Double heterostructure laser of a buried

stripe design.

Figure 4.131 Cladded ridge double heterostructure semiconductor laser design.

278 OPTICAL SYSTEMS

inferior to that from m ost gas lasers. A circular, clean,

output beam ca n be obtain ed from a ﬁber-coupled diode

laser. Vertical cavity surface emitting lasers (VCSELs)

also provide circular output beams.

The spectral purity of Fabry–Perot semiconductor lasers

is generally inferior to helium–neon lasers or diode-

pumped solid-state lasers. Semiconductor laser linewidths

are typically several MHz or more, so their coherence

lengths are short. This makes them less suitable in most

interferometric applications than most gas lasers or diode-

pumped solid-state (DPSS) lasers. Narrower linewidth

semiconductor lasers use an external cavity incorporating

a grating structure, or have a Bragg grating structure incor-

porated into the semiconductor material itself: so-called

distributed feedback (DFB) or distributed Bragg reﬂection

(DBR) lasers. Suppliers include Agere, AMS Technolo-

gies, EXFO, Inﬁneon, Lasermate, Sacher Lasertechnik,

and Toptica. These lasers are mostly available at the tele-

communications wavelengths of 1300 nm and 1550 nm.

Diode lasers have achieved their greatest commercial

importance in telecommunications systems, but the avail-

ability of diode lasers at many discrete wavelengths from

375 nm to beyond 2 lm

has increased their use in spec-

troscopic applications. They can provide some degree of

tunability by changing their operating temperature or drive

current. Suppliers include Applied Optronics, Coherent,

DILAS, Laser Diode, Lasermate Group, Lasertel, Melles

Griot, New Focus, Newport, Opton, Photonic Products,

Point Source, and QPC Lasers. Manufacturers’ data sheets

should be consulted for wavelengths, mode quality (single

or multimode), beam quality (circular or elliptical),

powers, and operational currents.

Many of these lasers

can be obtained coupled to an optical ﬁber, which provides

a clean, circular beam.

Some of the commonly available wavelengths (in nm)

from diode lasers are: 375, 405, 408, 440, 635, 640, 650,

670, 690, 730, 780, 808, 830, 915, 940, 980, 1300, 1370,

1470, 1550, 1720, 1850, 1907, 1950, 2004, and 2350.

High-power diode lasers are available with powers up to

and beyond 1 kW. They are widely used as pump sources

in diode-pumped solid-state lasers; however, as far as spec-

troscopy purity is concerned they are closer in character to

a light-emitting diode than they are to high-coherence

lasers such as helium–neon, helium–cadmium or diode-

pumped Nd:YAG.

Diode-Pumped CW Solid-State Lasers. Because

of a fortuitous coincidence between the output of GaAlAs

semiconductor lasers working near 809 nm and a strong

absorption of the neodymium ions (Nd

) in YAG, YLF, or

YVO

, it is very efﬁcient to optically pump Nd

lasers

Figure 4.133 Schematic diagram of how a semiconductor

laser emits a quasi-elliptical output beam because of

asymmetrical beam conﬁnement in two orthogonal

directions inside the laser structure.

Figure 4.132 Graded index separate conﬁnement

heterostructure (GRINSCH) semiconductor laser design.

Typical dimensions of the various layers are indicated. For a

narrow stripe laser w ~5lm, for a broad stripe laser w ~60

lm.

LASERS 279

with diode lasers. These lasers have become widely

available commercially. They can also be efﬁciently

frequency doubled to 530 nm, so have begun to replace

ion lasers in applications where intense green light is

required. Green output powers up to 70 W are available.

Diode-pumped lasers in which the semiconductor lasers

are arranged to inject their pump radiation through the cy-

lindrical faces of a laser rod are in many ways akin to

lamp-pumped lasers of the same kind. Because of the high

electrical efﬁciency of GaAlAs laser diodes (>10%) the

ov erall electrical-to-optical conversion ef ﬁcienc y of these

lasers is very high, approaching 10%. If the diode laser pump

radiation is injected along the axis and matched to the trans-

verse mode geometry of the solid-state laser then very stable,

narrow linewidth laser oscillation can be obtained: Figure

4.134 shows the clev er monolithic Nd:YA G laser design of

Kane

and Byer .

113

In this laser the magneto-optical proper-

ties of YAG are used to obtain unidirectional ampliﬁcation of

a trav eling wave in the laser cavity. This prev ents the spatial

hole-burning that can occur in a standing wav e homogene-

ously broadened laser, which can allow multiple longitudinal

modes to oscillate.

Frequency doubling of a DPSS laser is generally carried

out with an intracavity nonlinear crystal such as BBO (beta-

BaB

), PPLN (periodically poled lithium niobate), or

PPKTP [periodically poled potassium titanium oxide phos-

phate (KTiOPO

)], or with an external resonant cavity

containing a nonlinear crystal. Figure 4.135 shows how

tracavity frequency doubling is done with a Nd:YVO

coherent Verdi laser. This use of a ring laser resonator with

unidirectional laser oscillation provides single longitudinal

mode operation and a narrow linewidth. Frequency-tripled

operation of diode-pumped Nd

laser at 355 nm is avail-

able at powers in excess of 3 W, frequency-quadrupled oper-

ation at 266 nm provides powers up to 500 mW. There are

many suppliers of diode-pumped Nd

lasers, including A-

B Lasers, Alphalas, Cobolt AB, Coherent, Continuum, Lee

Laser, Lightwave Electronics, Melles Griot, Quantronix,

Spectra-Physics, TecOptics, and TRUMPF, among

others.

Diode-pumped solid-state lasers are also avail-

able at other wavelengths, notably 2.1 lm in holmium

(Ho

), 1.6 lm and 2.8 lm in erbium (Er

) and 2.3 lm

in thulium (Tm

The principal advantages of this type of laser are reliabl-

ity, narrow linewidth, and single-frequency operation.

Continuous Wave Dye Lasers. Continuous wave

dye lasers usually take the form of a planar jet of dye

solution continuously sprayed at Brewster’s angle from a

slit nozzle, collected, and recirculated. The jet stream is in

a spherical mirror laser cavity, where it is pumped by the

focused radiation of a CW ion laser or frequency-doubled

Nd:YAG laser, as shown in Figure 4.136. These lasers can

generally

be regarded as wavelength converters – they

have essentially the linewidth, frequency, and amplitude

stability of the pumping source. For example, narrow-line-

width operation requires an etalon-controlled single-fre-

quency ion laser. Continuous wave dye lasers are quite

efﬁcient at converting the wavelength of the pump laser;

at pump powers far enough above threshold, the conver-

sion efﬁciency ranges from 10 to 45%. Laser dyes are

available from Exciton Lambda Physik and Radiant Dyes

Laser Accessories, among others. Dye lasers are rapidly

being replaced, wherever possible, with tunable solid-state

devices. The dyes used photodegrade and liquid spills are

common. The laboratories of most dye-laser users are

stained with the dyes that they use! For further details of

CW-dye-laser operation consult Schafer.

Continuous

wave dye lasers are available from Big Sky Laser Technol-

ogies, Coherent, Quantel, and Spectra-Physics.

Figure 4.134 The ’’MISER’’ ring laser design of Kane

and Byer.

280 OPTICAL SYSTEMS

Pulsed Dye Lasers. Continuous wave dye lasers are

not as frequently constructed in the laboratory as are

pulsed dye lasers. In its simplest form, a pulsed dye laser

consists of a small rectangular glass or quartz cell placed

on the axis of an optical resonator and excited with a

focused line image from a pump laser. Two simple

geometrics are shown in Figure 4.137.

Temperature-Controlled

Etalon

Optical

Diode

Green

Output

Pump

HR@1064 nm

AR@632 nm

HR@1064 nm

HT@808 nm

HR@1064 nm

HR3

HR1

Nd:YV0

Astigmatic

Compensator

Beam Paths: 808 nm

1064 nm

1064+532 nm

532 nm

Ring Cavity Resonator of Coherent, Inc. Verdi Green DPSS Laser

LBO

Figure 4.135 The layout of the Coherent, Inc. ‘‘Verdi’’ laser where intracavity frequency doubling with a lithium

triborate LiB

(LBO) crystal is used to generate 530 nm from 1.06 lm. The initial laser oscillation is at 1.064 l using a

neodymium-doped yttrium vanadate (Nd:YVO

) crystal pumped with an 808 nm diode laser. In the diagram HR – high

reﬂectance mirror; OC – output coupling mirror.

Figure 4.136 Layout of a CW dye laser using a ﬂowing

dye jet.

Figure 4.137 Two simple pulsed dye laser arrangements:

(a) transverse pumping; (b) longitudinal pumping.

LASERS 281

The most commonly used pump lasers are N

and

frequency-doubled Nd:YAG, although ruby, excimer and

copper-vapor lasers are also used. In its simplest form, this

type of pulsed dye laser will generate a broad-band laser

output (5–10 nm). Various additional components are

added to the basic design to give tunable, narrow-linewidth

operation. A very popular design that incorporates all the

desirable features of a precision-tunable visible source has

been described by Ha

nsch.

114

The essential components of

aHa

nsch-type pulsed dye laser are shown in Figure 4.138.

The

pump laser is focused, with a cylindrical and/or a

spherical lens, to a line image in the front of a dye cell. The

line of excited dye solution (for example a 5 3 10

–3

molar

solution of Rhodamine 6G in ethanol) is the gain region of

the laser. The laser beam from the gain region is expanded

with a telescope in order to illuminate a large area of a high

dispersion, Littrow-mounted echelle grating. Rotation of

the grating tunes the center wavelength of the laser. With-

out the telescope, only a small portion of the grating is

illuminated, high resolution is not achieved, and the laser

linewidth will not be very narrow. With telescope and

grating alone, the laser linewidth will be on the order of

0.005 nm at 500 nm (’ 0.2 cm

1

). Even narrower linewidth

can be achieved by including a tilted Fabry–Perot etalon

in the cavity. A suitable etalon will have a ﬁnesse of 20 and

a free spectral range (see Section 4.7.4) below about 1 cm

1

in this case. Line widths as narrow as 4 3 10

–4

nm can be

achieved. A few experimental points are worthy of note:

the laser is tuned by adjusting grating and/or etalon; align-

ment of the telescope to give a parallel beam at the grating

is quite critical; the dye should be contained in a cell with

slightly skewed faces to prevent spurious oscillation; the

dye solution can remain static when low-power (10–100

kW) pump lasers are used, magnetically stirred when

pump lasers up to about 1 MW are used, or continuously

circulated from a reservoir when higher-energy or high-

repetition-rate pump lasers are used. Suitable dye cells are

available from Anderson Lasers, Esco, Hellma Cells and

NSG Precision Cells. Cells can be constructed from stain-

less steel with Brewster window faces when end-on pump-

ing with a high-energy laser is used (as shown in Figure

4.139). The dye can be magnetically stirred by placing a

small

Teﬂon-coated stirring button in the bottom of the dye

cell. When continuous circulation of dye is used, suitable

Figure 4.138 Ha

nsch-type pulsed dye laser.

Figure 4.139 Flowing dye cell for end-pumped operation.

N ¼ normal to windows; h

¼ Brewster’s angle,

approximately the same for both pump and dye laser

wavelengths; Dh ¼ a small angle. Dye solution ﬂows

laminarly in the channel between the windows.

282 OPTICAL SYSTEMS

pumps are available from Fluid-o-Tech and Micropump

Corporation.

Once a narrow-linewidth pulsed-dye-laser oscillator has

been constructed, its output power can be boosted by pass-

ing the laser beam through one or more additional dye

cells, which can be pumped with the same laser as the

oscillator. In a practical oscillator-ampliﬁer conﬁguration,

10% of the pump power will be used to drive the oscillator

and 90% to drive the ampliﬁer(s). Further details of

nsch-type dye-laser construction are available in several

publications.

115–119

Two other approaches to achieving narrow-linewidth

laser oscillation are worthy of note. The intracavity-

telescope beam expander can be replaced, by a multiple-

prism beam expander (see Section 4.3.4), which expands

the

beam onto the grating in one direction only. Such an

arrangement does not need to be focused. An alternative,

simple approach described by Littman

118,119

is to elimi-

nate the beam expander and instead use a Littrow-mounted

holographic grating in grazing incidence, as shown in Fig-

ure

4.140. Linewidths below 0.08 cm can be obtained with-

out

the additional use of an intracavity etalon.

Optical Parametric Oscillators. At one time, opti-

cal parametric oscillators (OPOs) were not readily avail-

able commercially, and were tricky to use. This has

changed. Optical parametric oscillators provide tunable

radiation typically in the range 210–5000 nm. They operate

by using nonlinear optical processes in a crystal.

15,120–124

The OPO requires a pump laser of frequency m

,whichis

passed through a nonlinear crystal such as PPLN. Two

new frequencies are generated in this process, a signal of

frequency m

, and an idler of frequency m

. Energy is con-

served in this process so that m

¼ m

– m

. Tunability results

by changing the angle of the pump beam with respect to the

optic axis of the crystal, or by changing the temperature of

the crystal. One or more of the three frequencies, pump,

signal, or idler, is resonated inside a resonant structure that

surrounds the nonlinear crystal. Figure 4.141 shows a sche-

mat

ic of an OPO with a resonant signal beam. An OPO

generally generates tunable radiation with relatively broad

linewidths (>1 cm). Special techniques are needed to gen-

erate narrow linewidths.

125

Optical parametric oscillators

are available from Coherent, Continuum, EKSPLA, Linos

Photonics, Opotek, Quantel, Radiantis, and Spectra Physics.

Pulsed OPOs are more readily available than CW OPs and

have larger tuning ranges. They can also generate very

short (femtosecond) pulses.

4.6.4 Laser Radiation

Laser radiation is highly monochromatic in most cases,

although ﬂashlamp-pumped dye lasers in a worst case

may have linewidths as large as 100 cm

1

(2.5 nm at 500

nm). The spectral characteristics of the radiation vary from

laser to laser, but will be speciﬁed by the manufacturer.

Lasers are usually speciﬁed as single-mode lasers or multi-

mode lasers.

Figure 4.140 Littman-type dye laser.

Figure 4.141 Schematic layout of an optical parametric

oscillator (OPO).

LASERS 283

A single-mode laser emits a single-frequency output.

Continuous wave CO

lasers and other middle- and far-

infrared lasers usually operate in this way, and helium–

neon and argon–ion lasers can also be caused to do so.

The single output frequency will itself ﬂuctuate randomly,

typically over a bandwidth of 100 kHz–1 MHz, unless

special precautions are taken to stabilize the laser – usually

by stabilizing the spacing between the two mirrors that

constitute its resonant cavity.

Multimode lasers emit several modes, called longitu-

dinal modes, spaced in freq uency by c

/2L,wherec

the velocity of light in vacuo and L is the optical path

length between the re sonator mirrors. In a med ium of

refractive index n and geometric length l, L ¼ nl.There

may, in fact, be several superposed combs of equally

spaced modes in the output of a multimode laser if it

is not operating in a single transverse mode. The trans-

verse modes specify the different spatial distributions of

intensity that are possible in the output beam. The most

desirable such mode, which is standard in most goo d

commercial lasers, is the fundamental TEM

mode,

which has a Gaussian radial intensity distribution (see

Section 4.2.4). A laser will generally operate on multi-

ple

longitudinal modes if the linewidth Dv of the ampli-

fying transition is much greater than c

/2L. In this case,

the output frequencies will spa n a frequency r ange o n

the order of Dv. In short-pulse lasers the radiation oscil-

lating in the laser cavity may not be able to make many

passes during the duration of the laser pulse, and (par-

ticularly if the linewidth of the amplifying transition is

very large) the individual modes may not have time to

become well characterized in frequency. T his is the sit-

uation that prevails in pulsed dye and excimer lasers.

Additional frequency-selective components must be

included in such lasers, such as etalons and/or diffrac-

tion gratings, to obtain narrow output linewidths.

Laser radiation is highly collimated: beam divergence

angles as small as 1 mrad are quite common. This makes a

laser the ideal way to align an optical system, far superior

to traditional methods using point sources and autocolli-

mators. As mentioned previously, lasers are highly coherent.

Single-mode lasers have the highest temporal coherence –

with coherence lengths that can extend to hundreds of

kilometers. Fundamental-transverse-mode lasers have the

highest spatial coherence.

In multimode lasers, the many output frequencies lie

underneath the gain proﬁle, as s hown in Figure 4.12 1.

Laser

oscillation can be restricted to a single transverse

mode by appropriate choice of mirror radii and spacing.

Then, the available output frequencies are uniformly

spaced longitudinal modes a frequency c

/2L apart,

where L is the optical spacing of the laser mirrors. Laser

oscillation can be restricted to a single one of these

longitudinal modes by placing an etalon inside the laser

cavity. The etalon should be of such a length l that its

free spectral range c/2l is greater than the width of the

gain proﬁle, Dv. Its ﬁnesse should be high enough so

that c/2lF < c

/2L. The etalon acts as a ﬁlter that allows

only one longitudinal mode to pass without incurring

high loss.

Many lasers ca n be operated in a mode -locked fash-

ion. Then the longitudinal modes of the laser cavity

become locked together in phase and the output of the

laser becomes a train of uniformly spaced, very narrow

pulses. The spacing between these pulses corresponds to

the round-trip time in the laser cavity, c

/2L.Thetem-

poral width of the p ulses is inversely proportional to the

gain band width; th us, the broader the gain proﬁle, the

narrower the o utput pulses in m ode-locked operation .

For example, an argon-ion laser with a gain proﬁle 5

GHz wide can yield mode-locked pulses 200 lswide.

A mode-locked dye laser with a linewidth of 100 cm

(3 3 10

Hz) can, in principle, give mode-locked pulses

as short as about 0. 3 ps.

Even shorter pulses than this can be obtained with ring-

dye lasers, with mode-locked Ti:sapphire lasers, or with

colliding pulse mode-locking techniques,

which, with

pulse compression techniques, can generate pulses a few

tens of femtoseconds (10

–15

s) long. Ultrafast laser systems

are available from Big Sky Laxer, Clark-MXR, Coherent,

Quantronix, and Spectra Physics (now Newport).

Pulse compressors are available from Calmar Optcom,

Femtochrome Research, and Swamp Optics.

4.6.5 Coupling Light from a Source to

an Aperture

A common problem in optical experiment design involves

either the delivery of light from a source to a target, or

284 OPTICAL SYSTEMS

collection of light from a source and delivery of the light to

a collection aperture. The collection aperture might be the

active area of a photodetector, the entrance slit of a spec-

trometer, or the facet of an optical ﬁber. A problem of

speciﬁc importance is the focusing of a laser beam to a

small spot. Sometimes the solution to one of these prob-

lems will involve a imaging system, but it might also

involve a nonimaging light collector.

(1) Collection of light from a point source and its delivery

to a target aperture. This situation is illustrated in

Figure 4.142. The solid angle DX sub

tended by a cir-

cular aperture S ¼ pa

at distance R from the source is:

DX ¼ 2pð1  cos hÞð4:220Þ

which for R >> a can be written as:

DX ¼

ð4:221Þ

If the radiant power of the source is P watts then the

power, collected by the aperture is:

¼ P

ð4:222Þ

To increase the light delivered to the aperture S, a lens

system can be placed between O and O9 as shown in

Figure 4.143. To maximize light collection, the lens

used

should have a small f/number (f/#). The point

source is placed close to the focal point of the lens,

so that:

cos h ’ f =

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ f

ð4:223Þ

and

1 

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ f

ð4:224Þ

Since the f/number is:

f =# ¼

ð4:225Þ

Equation (4.224) becomes:

¼ P



f =#

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ 4f =#

ð4:226Þ

Figure 4.143 Optical arrangements for optimizing cou-

pling of a point source to an aperture: (a) lens coupling; (b)

lens and spherical mirror coupling; (c) coupling of a point

source to an optical ﬁber.

Figure 4.142 Geometry used to determine the collection

efﬁciency of an aperture when it is illuminated by light from

a point source.

LASERS 285

With an f/1 lens

¼ P



ﬃﬃﬃ



¼ 0:053P ð4:227Þ

In practice an aspheric lens should be used in this

application, especially if the aperture S is of small size.

If a spherical reﬂector is placed behind the source, as

shown in Figure 4.143(b), so that the source lies at its

center

of curvature, then the collection efﬁciency can

be doubled.

(2) Coupling light from a point source to an optical ﬁber.

Whether the source is actually a point source or is of

small ﬁnite size relative to other distances in the geo-

metry of Figure 4.143(c) is not very important. For

coupling

light to a ﬁber, the source must be imaged

onto the front end of the cleaved ﬁber, but the light

rays must remain within the numerical aperture of the

ﬁber: sin h

< NA. In principle, this can be accom-

plished by placing the source close to the focal point of

the lens so that linear magniﬁcation (v/u) is large. In

practice, the maximum magniﬁcation that can be used

will be limited by the core diameter of the ﬁber and the

ﬁnite size of the source.

(3) Collection of light from an extended source and its

delivery to a aperture. This situation is shown in

Figure 4.144. It is not possible in this case to image

heextendedsourcetoapoint,thebestthatcanbe

done is to image as large an area of the source as

possible onto the aperture S. If an axial point on the

source is imaged to t he center of the aperture S,then

the a rea of the source that can be imaged onto the

aperture S is

source

ð4:228Þ

since m ¼ (v/u) is the linear magniﬁcation of the sys-

tem. A high-quality imaging system would need to be

used in this situation, especially if the aperture S is

small, otherwise, aberrations will affect the size of

the image.

If the brightness of the extended source in Figure 4.144

is B

(Wm

2

1

), then the power collected by the lens

is, approximately:

¼ 2pB

source

ð1  cos h

Þð4:229Þ

This light is imaged onto the collection aperture of

area S where it occupies a solid angle DX

determined

by the angle h

, where:

¼ 2pð1  cos h

Þð4:230Þ

The brightness of the image is:

2pSð1  cos h

source

ð1  cos h

ð4:231Þ

which gives:

sin

ðh

=2Þ

sin

ðh

=2Þ

ð4:232Þ

For a paraxial system sinðh

=2Þ’ðh

=2Þ, so:

ðh

ð4:233Þ

The ratio



is the angular magniﬁcation, m9, of the

system. Therefore, since mm9 ¼ 1:

¼ B

ð4:234Þ

This is an example of the brightness theorem, which

states that the brightness of an image can not be greater

than the brightness of the object.

Figure 4.144 Geometry of an extended source and

collection aperture used to describe the collection efﬁciency.

286 OPTICAL SYSTEMS

4.6.6 Optical Modulators

In many optical experiments, particularly those involving

the detection of weak light signals or weak electrical sig-

nals generated by some light-stimulated phenomenon, the

signal-to-noise ratio can be considerably improved by the

use of phase-sensitive detection. The principles underlying

this technique are discussed in Section 6.8.2. To modulate

the

intensity of a weak light signal falling on a detector, the

signal must be periodically interrupted. This is most easily

done with a mechanical chopper. Weak electrical signals

that result from optical stimulation of some phenomenon

can also be modulated in this way by chopping the radia-

tion from the stimulating source.

Modulation of narrow beams of light such as laser

beams, or of extended sources that can be focused onto a

small aperture with a lens, is easily accomplished with a

tuning-fork chopper. Such devices are available from

Boston Electronics, Electro-Optical Products, and Scitec

Instruments. The region chopped can range up to several

millimeters wide and a few centimeters long at frequencies

from 5 Hz to 3 kHz. For chopping emission from extended

sources, or over large apertures, rotating chopping wheels

are very convenient. The chopping wheel can be made of

any suitable rigid, opaque material and should have radi-

ally cut apertures of one of the forms indicated in Figure

4.145. This form of aperture ensures that the mark-to-space

ratio

of the modulated intensity is independent of where the

light passes through the wheels. By cutting very many slots

in the wheel, very high modulation rates can be achieved –

for example, up to 100 kHz with a 20 000 rpm motor and a

wheel with 300 slots. The chopping wheel should usually

be painted or anodized matt black. For chopping intense

laser beams (in excess of perhaps 1 W), it may be better to

make the wheel reﬂective so that unwanted beam energy

can be reﬂected into a beam dump. Reﬂective glass chop-

ping wheels can be used at low speeds in experiments

where a light beam must be periodically routed along

two different paths.

To obtain an electrical reference signal that is synchro-

nous with a mechanical chopping wheel, a small portion

of the transmitted beam, if the latter is intense enough, can

be reﬂected onto a photodiode or phototransistor. Alterna-

tively, an auxiliary tungsten ﬁlament lamp and photodiode

can be mounted on opposite sides of the wheel. If these are

mounted on a rotatable arm, the phase of the reference

signal they provide can be adjusted mechanically. Chop-

ping wheels with built-in speed control and electrical rota-

tion reference signals are available commercially from

Boston Electronics, DL Instrument, EG&G Princeton

Applied Research, Electro-Optical Products Corp., New

Focus, Stanford Research Systems, and Thorlabs.

Electro-optic modulators (Pockel’s cells) can also be

used in special circumstances, particularly for modulating

laser beams, or when mechanical vibration is undesirable.

The operation of these devices is shown schematically in

Figure 4.146. Light passing through the electro-optic crys-

tal

is plane-polarized before entry and then has its state of

polarization altered by an amount that depends on the

voltage applied to the crystal. The effect is to modulate

the intensity of the light transmitted through a second lin-

ear polarizer placed behind the electro-optic crystal. By

choosing the correct orientation of the input polarizer rela-

tive to the axes of the electro-optic crystal and omitting

the output polarizer, the device becomes an optical phase

modulator. For further details of these electro-optic ampli-

tude and phase modulators the reader is referred to the

books by Yariv,

Kaminow,

125

and Davis.

Electro-optic

modulators are available from Cleveland Crystals, Conop-

tics, II-VI, JDS Uniphase, Meadowlark Optics, New Focus,

and Quantum Technology, among others.

Acousto-optic modulators which operate by diffraction

effects induced by sound-wave-produced periodic density

variations in a crystal are also available.

126,127

The most

widely used materials for these devices are LiNbO

,TeO

and fused quartz. In their operation a radio-frequency (r.f.)

sound wave is driven through the material from a piezo-

electric transducer, usually fabricated from LiNbO

ZnO. A schematic diagram of how such an acousto-optic

modulator works is given in Figure 4.147. Incident light

Figure 4.145 Some chopping-wheel designs.

LASERS 287

that makes an appropriate angle h

, with the sound wave-

fronts will be diffracted if it simultaneously satisﬁes the

condition for constructive interference and reﬂection from

the sound wavefronts. This condition is sin h

¼ k/k

where k is the laser wavelength in the acousto-optic mate-

rial, and k

is the sound wavelength. The device is used as

an amplitude modulator by amplitude-modulating the

input r.f., which will be set to a speciﬁc optimum fre-

quency for the device being used. Increase of drive power

increases the diffracted power I

and reduces the power of

the undeviated beam I

and vice versa. The device also

functions as a frequency shifter. In Figure 4.147 the laser

beam

reﬂects off a moving sound wave and is Doppler

shifted so that the beam I

is at frequency x þ x

, where

is the frequency of the sound wave. Acousto-optic devi-

ces are available from many suppliers, including Crystal

Technology, Electro-Optical Products, IntraAction, Iso-

met, and NEOS Technologies. Further details about these

devices can be found in References 15, 126, and 127.

Very many liquids become optically active on applica-

tion of an electric ﬁeld; that is, they rotate the plane of

polarization of a linearly polarized beam passing through

them. This phenomena is the basis of the Kerr cell, which

can be used as a modulator, but is more commonly used as

an optical shutter (for example, in laser Q-switching appli-

cations as discussed in Section 4.6.3). A typical Kerr cell

uses

nitrobenzene placed between two plane electrodes

across which a high voltage is applied. This voltage is

typically several kilovolts and is sufﬁcient to rotate the

plane of polarization of the incident light passing between

the plates by 45 or 90°. Kerr cells are rarely used these days

and have been superseded by electro-optic modulators.

Figure 4.147 Schematic diagram showing the operation of

an acousto-optic device in the Bragg regime. For simplicity,

the refraction of the laser beam at X, Y,andZ is not shown.

Figure 4.146 An electro-optic amplitude modulator using a transversely operated

electro-optic crystal. The d.c. bias voltage can be used to adjust the operating point

of the modulator so that, in the absence of modulation, the output intensity is a

maximum, a minimum, or some intermediate value.

288 OPTICAL SYSTEMS

Closely related to optical modulators are optical deﬂec-

tors, which can be used for the spatial scanning or switch-

ing of light beams. Two principal types are commonly

used: electromechanical devices that utilize small mirrors

mounted on galvanometer suspensions (available from

Cambridge Technology, GSI Lumonics, and NEOS Tech-

nologies) and beam deﬂectors that utilize the acousto-optic

effect. In the latter the deﬂection angle shown in Figure

4.147 is controlled by changing the r.f. drive frequency.

These

devices are available from Crystal Technology,

IntraAction, Isomet, and NEOS Technologies. Electro-

optic scanners are also available, but are less widely used.

These devices are generally designed for small deﬂections.

They are available from Conoptics.

Spatial light modulators are multiple element devices,

which generally use liquid crystals, work in transmission,

and can modify the characteristics of an entire wavefront in

a pixellated fashion. They are available from Display Tech

and Meadowlark Optics.

4.6.7 How to Work Safely with

Light Sources

Light sources, whether coherent or incoherent, can present

several potential safety hazards in the laboratory. The pri-

mary hazard associated with the use of home-built optical

sources is usually their power supply. Lasers and ﬂash-

lamps in particular, generally operate with potentially

lethal high voltages, and the usual safety considerations

for constructing and operating such power supplies should

be followed in their design:

(1) Provide a good ground connection to the power supply

and light-source housing.

(2) Screen all areas where high voltages are present.

(3) Install a clearly visible indicator that shows when the

power supply is activated.

(4) HV power supplies, particularly those that operate

with pulsed power, can remain dangerous even after

the power is turned off, unless energy-storage capaci-

tors are automatically shunted to ground. Always short

the capacitors in such a unit to ground after the power

supply is turned off before working on the unit.

(5) As a rule of thumb, keep a gap of about 25 mm for

every 10 kV between high-voltage points and ground.

(6) To avoid excessive corona at voltages above about 20

kV, make sure that high-voltage components and con-

nections have no sharp edges. Where such points must

be exposed, corona can be reduced by installing a spher-

ical metal corona cap on exposed items such as bolts or

capacitor terminals. Resistor and diode stacks can be

potted in epoxy or silicone rubber to prevent corona.

(7) Sources that are powered inductively or capacitively

with r.f. or microwave power can burn ﬁngers that

come too close to the power source, even without

making contact.

Commercial optical sources are generally fairly safe

electrically and are likely to be equipped with safety fea-

tures, such as interlocks, which the experimentalist may

not bother to incorporate into home-built equipment. Cav-

eat emptor. Remember the maxim ‘‘it’s the volts that jolts

but it’s the mills that kills.’’

Other general precautions with regard to electric shock

include the following:

(1) Avoid wearing metallic objects such as watches,

watchbands, and rings.

(2) If any operations must be performed on a line circuit,

wear well-insulated shoes and, if possible, use only

one hand – ‘‘Always keep one hand in your pocket.’’

(3) Keep hands dry; do not handle electrical equipment if

you are sweating.

(4) Learn rescue and resuscitation procedures for victims

of electric shock: Turn off the equipment, remove the

victim by using insulated material; if the victim is not

breathing, start mouth-to-mouth resuscitation; if there

is no pulse, begin CPR procedures immediately; sum-

mon medical assistance; continue resuscitation proce-

dures until relieved by a physician. If the victim is

conscious, but continues to show symptoms of shock,

keep the person warm. Always call for professional

help. (Dial 911 in the USA.)

Other hazards in the use of light sources include the

possibility of eye damage, direct burning (particularly, by

exposure to the beam from a high-average-power laser), and

the production of toxic fumes. The last is most important in

the use of high-power CW arc lamps, which can generate

substantial amounts of ozone. The lamp housing should be

suitably ventilated and the ozone discharged into a fume

LASERS 289

hood or into the open air. Some lasers operate using a

supply of toxic gas, such as hydrogen ﬂuoride and the hal-

ogens. Workers operating such systems must be sufﬁciently

experienced to work safely with these materials. The Math-

eson Gas Data Book, published by Matheson Gas Products,

is a comprehensive guide to laboratory gases, detailing the

potential hazards and handling methods appropriate to each.

The potential eye hazard presented by most incoherent

sources is not great. If a source appears very bright, one

should not look at it, just as one should not look directly at

the Sun. Do not look at sources that emit substantial ultra-

violet radiation; at the least, severe eye irritation will result –

imagine having your eyes full of sand particles for several

days! Long-term exposure to UV radiation should be kept

below 0.5 lW/cm

. Ordinary eyeglasses will protect the

eyes from ultraviolet exposure to some extent, but plastic

goggles that wrap around the sides are better. Colored

plastic or glass provides better protection than clear mate-

rial. The manufacturer’s speciﬁcation of ultraviolet trans-

mission should be checked, since radiation below 320 nm

must be excluded from the cornea.

The use of lasers in the laboratory presents an optical

hazard of a different order. Because a laser beam is gen-

erally highly collimated and at least partially coherent, if

the beam from a visible or near-infrared laser enters the

pupil of the eye it will be focused to a very small spot on

the retina (unless the observer is very short-sighted). If this

focused spot happens to be on the optic nerve, total blind-

ness may result: if it falls elsewhere on the retina, an extra

blind spot may be generated. Although the constant motion

of the human eye tends to prevent the focused spot from

remaining at a particular point on the retina for very long,

always obey the following universal rule: Never look down

any laser beam either directly or by specular reﬂection.In

practice, laser beams below 1 mW CW are probably not an

eye hazard, but they should still be treated with respect. A

beam must be below about 10 lW before most workers

would regard it as really safe.

The safe exposure level for CW laser radiation depends

on the exposure time. For pulsed lasers, however, it is the

maximum energy that can enter the eye without causing

damage that is the important parameter. In the spectral

region between 380 and 1.5 lm, where the interior mate-

rial of the eye is transparent, the maximum safe dose is on

the order of 10

–7

J/cm

for Q-switched lasers and about

–6

J/cm

for non-Q-switched lasers. If any potential for

eye exposure to a laser beam or its direct or diffuse reﬂec-

tion exists, it is advisable to carry out the experiment in a

lighted laboratory: in a darkened laboratory, the fully dark-

adapted human eye with a pupil area of about 0.5 cm

presents a much larger target for accidental exposure.

The Laser Institute of America publishes a guide that

shows the maximum permitted exposure in terms of power

and direction for a range of laser wavelengths.

128

Infrared laser beams be yond about 1.5 lm are not a retinal

hazard, as they will not penetrate to the retina. Beams

between1.5and3lm penetrate the interior of the eye to

some degree. Because its energy is absorbed in a distributed

fashion in the interior of the eye, 1.55 lm is one of the safest

laser waveleng ths. Lasers beyond 3 lm are a burn hazard,

and eye exposure must be avoided for this reason. CO

lasers,

for example, which operate in the 10 lm region, are less

hazardous than equivalent-intensity argon-ion or neodymium

lasers. Neodymium lasers represent a particularly sev ere haz-

ard: they are widely used, emit substantial po wers and ener-

gies, and operate at the invisible wavelen gth of 1.06 lm. This

wavelength easily penetrates to the retina, and the careless

worker can suffer sev ere eye damage without any warning.

The use of safety goggles is strongly recommended when

using such lasers. These goggles absorb or reﬂect 1.06 lm,

but allow normal transmission in at least part of the visible

spectrum. Laser safety goggles are available commercially

from several sources, such as Bolle

, Control Optics, Glen-

dale, K entek, Lase-R Shield, Melles Griot, Newport, NOIR,

Thorlabs, and UVEX. The purchaser must usually specify

the laser wav elen gth(s) for which the goggles are to be used.

Unfortunately, one problem with goggles prevents their

universal use. Because the goggles prevent the laser wave-

length from reaching the eyes, they prevent the alignment

of a visible laser beam through an experiment by observa-

tion of diffuse reﬂection of the beam from components in

the system. When such a procedure must be carried out, we

recommend caution and the operation of the laser at its

lowest practical power level during alignment. Frequently,

a weak, subsidiary alignment laser can be used to check the

potential path of a high-power beam before this is turned

on – a strongly recommended procedure. For infrared laser

beams, thermal sensor cards are available that will reveal

the location of an infrared laser beam through thermally

activated ﬂuorescence or ﬂuorescence quenching. They are

290 OPTICAL SYSTEMS

available from Applied Scintillation Technology, Laser

S.O.S., Macken Instruments, Newport, and Solar TII.

Some of these sensor cards or plates, especially for

laser beam location, require illumination with a

UV source. Where an infrared laser beam strikes the illu-

minated surface a dark spot appears. Used Polaroid ﬁlm

and thermally sensitive duplicating paper are also useful

for infrared-beam tracking.

The beam from an ultraviolet laser can generally be

tracked with white paper, which ﬂuoresces where the beam

strikes it. A potential burn and ﬁre hazard exists for lasers

with power levels above about 1 W/cm

, although the ﬁre

hazard will depend on the target. Black paper burns most

easily. Very intense beams can be safely dumped onto

pieces of ﬁrebrick. Pulsed lasers will burn at output ener-

gies above about 1 J/cm

In the United States, commercial lasers are assigned a

rating by the FDA Center for Devices and Radiological

Health, which identiﬁes their type, power output range,

and potential hazard. It must be stressed, however, that

lasers are easy to use safely: accidents of any sort have been

rare. Their increasing use in laboratories requires that work-

ers be well-informed of the standard safety practices. For

further discussion of this and all aspects of laser safety and

related topics, we recommend both the book by Sliney and

Wolbarsht

129

and a series of articles on laser safety in the

CRC Handbook of Laser Science and Technology,Vol.1.

130

4.7 OPTICAL DISPERSING

INSTRUMENTS

Optical dispersing instruments allow the spectral analysis

of optical radiation or the extraction of radiation in a nar-

row spectral band from some broader spectral region.

In this general category we include interference ﬁlters,

prism and grating monochromators, spectrographs and

spectrophotometers, and interferometers. Interferometers

have additional uses over and above direct spectral

analysis – including studies of the phase variation over an

optical wavefront, which allow the optical quality of opti-

cal components to be measured. Spectrometers, or mono-

chromators as they are generally called, are optical ﬁlters of

tunable center wavelength and bandwidth. The output nar-

row-band radiation from these devices is generally detected

by a photon or thermal detector, which generates an elec-

trical signal output. Spectrographs, on the other hand,

record the entire spectral content of an extended bandwidth

region either photographically, or more commonly these

days with a linear detector area. Spectrophotometers are

complete commercial instruments, which generally incor-

porate a source or sources, a dispersing system (which may

involve interchangeable prisms and/or gratings), and a

detector. They are designed for recording ultraviolet, visi-

ble, or infrared absorption and emission spectra.

Spectroﬂuometers are instruments to record ﬂuorescence

spectra. In such an application two principal modes of spec-

tral usage exist. The emission ﬂuorescence spectrum is the

spectral distribution of emission produced by a particular

monochromatic excitation wavelength. The excitation

spectrum is the total ﬂuorescence emission recorded as

the wavelength of the excitation source is scanned.

Before giving a discussion of important design consider-

ations in the construction of various spectrometers and inter-

ferometers, it is worthwhile mentioning two important

ﬁgures of merit that allow the evaluation and comparison

of the performance of different types of optical dispersing

instruments. The ﬁrst is the resolving power , (<¼k/Dk,

which has already been discussed in connection with diffrac-

tion gratings (Section 4.3.5). The second is the luminosity,

which

is the ﬂux collected by a detector at the output of a

spectrometer when the source at the input has a radiance

of unity. The interrelation between resolving power and

luminosity for spectrometers using prisms, gratings, and

Fabry–Perot etalons has been dealt with in detail by Jacqui-

not.

131

Prism spectrometers have almost disappeared from use

in recent years, however, because of their simple mode of

operation they serve as an archetype in discussing spec-

trometer performance.

Figure 4.148, which shows the essential components of

prism monochromator, will serve to illustrate the points

made here. High resolution is clearly obtained in this

arrangement by using narrow entrance and exit slits. The

maximum light throughput of the spectrometer results

when the respective angular widths W

, W

of the input

and output slits h

, h

satisfy:

¼ W

ð4:235Þ

OPTICAL DISPERSING INSTRUMENTS 291

where

ðda=dkÞ

, W

ðdd=dkÞ

ð4:236Þ

The angles a are the same as those used in Figure 4.47.

The

input and output dispersions (da/dk)

and (dd/dk)

are

only equal in a position of minimum deviation, or with a

prism (or grating) used in a Littrow arrangement. If dif-

fraction at the slits is negligible, the intensity distribution

at the output slit when a monochromatic input is used is a

triangular function, as shown in Figure 4.149, where W is

the

spectral width of the slits given by:

W ¼ W

¼ W

ð4:237Þ

The limit of resolution of the monochromator is:

dk ¼ W ¼

ðdd=dkÞ

ð4:238Þ

The maximum ﬂux passing through the output slit is:

U ¼ TE

ðkÞSlh

ð4:239Þ

where S is the normal area of the output beam, T is the

transmittance of the prism (or efﬁciency of the grating in

the order used) at the wavelength being considered, l is the

height of the entrance and exit slits (equal), and E

(k) is the

radiance of the monochromatic source of wavelength k

illuminating the entrance slit. lh

is the solid angle that

the exit slit subtends at the output focusing lens. Equation

(4.239) can be written as:

U ¼

ðkÞSlkðdd=dkÞ

ð4:240Þ

which clearly shows that the output ﬂux is inversely pro-

portional to the resolving power [for a continuous source at

the entrance slit, Equation (4.240) is multiplied by an addi-

tional

factor k/<]. The efﬁciency E of the monochromator

is deﬁned by the equation:

E ¼

TSl



ð4:241Þ

where we have assumed the usual case in which

¼ f

¼ f.

To collect all the light from the collimating optics in

the arrangement of Figure 4.148 , the prism or g rating

should

have a normal area at least as large as the aperture

of the collimating optics. Thus, the height of the prism

(or diffraction grating) should be h > W. The ratio f/W,

which is a measure of the light-gathering power of the

monochromator, deﬁnes its f/number. The most efﬁcient

way to use a spectrometer of any kind is to send the input

radiation into the entrance slit within the cone of angles

deﬁned by the f/number. The maximum resolution is

obtained if the input f/number matches the spectrometer

f/number. If radiation enters the spectrometer with an f /

number that is too small, this radiation overﬁlls the dis-

persing element and some is wasted. This can be

Figure 4.149 Intensity distribution at the output slit of a

monochromator whose entrance and exit slits have the

same spectral width W.

Figure 4.148 Basic elements of a prism monochromator.

292 OPTICAL SYSTEMS

illustrated with the aid of Figure 4.150 , which sh ows t he

use of a point source directly at the entrance slit. In

Figure 4.150(b) a point source is imaged on the en trance

sli

t using a lens that matches the input radiation to the f/

number of the spectrometer. In Figure 4.150(a) the frac-

tional

useful light collection from the source is:

’

ð4:242Þ

where F is the f/number of the spectrometer. In contrast, in

Figure 4.150(b) it is approximately:

’

ð4:243Þ

which can be written as:

ðv  f Þ

ð4:244Þ

and substituting v/d ¼ F, f/d ¼ F9 (the f/number of the

lens), we have:

pðF=F

 1Þ

ðF

< FÞð4:245Þ

Thus, equally efﬁcient light gathering to that which would

be obtained with the point source at the entrance slit

results if:

¼ F=2 ð4:246Þ

More ef ﬁcient light gathering results if F9 is less than this

valu e, but , if the lens and point source are incorrec tly posi-

tioned so that v/d < F, then not all the light collected by the

lens reaches the dispersing element of the spectrometer.

It is quite common for spectrometers to be used with a

ﬁber optic light-delivery system. If the NA of the ﬁber is

too large and the ﬁber optic is placed at the entrance of the

spectrometer, then overﬁlling of the dispersing element

will occur. In this case correction optics must be included

to match the ﬁber to the f/number of the spectrometer.

4.7.1 Comparison of Prism and

Grating Spectrometers

Following Jacquinot,

131

we use Equation (4.240) to com-

pare prism and grating instruments. Assume identical val-

ues of l and f

, since, for a given degree of aberration of the

system, their values are identical for prisms and gratings.

Blazed-grating efﬁciencies can be high, so T is assumed to

be similar for prism and grating. Thus, the comparison of

luminosity under given operating conditions of wavelength

and resolution depends solely on the quantity S(dd/dk)

for

a prism and S(db/dk)

for a grating.

For the prism:

ð4:247Þ

where, for maximum dispersion, the whole prism face is

illuminated, so that t is the width of the prism base. S ¼ hW

and th ¼ A, the area of the prism base, and so:

¼ A

ð4:248Þ

For the grating:

d cos b

ð4:249Þ

S ¼ Acosb, where A is the area of the grating. If it is

assumed that the grating is used in Littrow, then mk ¼

2d sin b, and therefore:

2A sin b

ð4:250Þ

Figure 4.150 Schematic diagrams illustrating geometrical

factors involved in optimizing light-collection efﬁciency by a

spectrometer of aperture W: (a) point source directly at

entrance slit; (b) remote point source imaged on entrance

slit with a lens.

OPTICAL DISPERSING INSTRUMENTS 293

The ratio of luminosities for a prism and grating of com-

parable size is therefore:

q ¼

UðprismÞ

UðgratingÞ

kdn=dk

2 sin b

ð4:251Þ

This ratio can be improved by a factor of two if the

prism is also used in Littrow. For a typical value of 30°

for b, Equation (4.251) predicts that a grating is always

superior

to a prism instrument. Except for a few materi-

als in restricted regions of wavelength where dn/dk

becomes large and q may reach 0.2–0.3, a grating is

more luminous than a prism by a factor of 10 or more.

The only potential advantage of a prism instrument over a

grating is the absence of overlapping orders. A grating

instrument illuminated simultaneously with 300 and 600

nm, for example, will transmit both at the same angular

position; a prism instrument will not. This minor problem

is easily solved with an appropriate order-sorting color or

interference ﬁlter .

Jacquinot

131

has demonstrated that a Fabry–Perot etalon

or interferometer (see Section 4.7.4) used at a high or

moderate

resolving power is superior in luminosity to a

grating instrument by a factor that can range from 30 to

400 or more. In general, an etalon cannot be used alone,

because of its many potential overlapping orders. It is usual

to couple it with a grating or prism monochromator in

high-resolution spectroscopic applications, except in those

cases where the source is already highly monochromatic.

Table 4.9 gives a comparison of the performanc e char-

acte

ristics of prism and grating monochromators and

Table 4.9 Main characteristics of optical dispersing elements

Element Advantages Disadvantages

Multilayer dielectric

interference ﬁlter

High throughput at center frequency, ’50%. Low resolution – minimum bandwidth ’1 nm.

Tunable to some extent by tilting. None available at short wavelengths < 200 nm.

Prism spectrometer Dispersion and resolution increase near

absorption edge of prism (however,

transmission falls).

Cannot be used below 120 nm (with LiF prism).

No ghosts. Resolution not as good as grating spectrometer,

best ’0.01 nm.

Scattered light can be lower than in grating

spectrometer.

Resolution particularly poor in infrared

No order sorting necessary. .

Grating spectrometer Resolution can be high (<0.001 nm). Ghosts can be a problem.

Can be used from vacuum UV to far IR. Expensive if really low scattered light

required – may need double- or triple-grating

instrument.

Dispersion independent of wavelength. Need to remove unwanted orders (not necessarily

a serious problem).

Luminosity depends on blaze angle, but

generally much higher than for prism

spectrometer.

Fabry–Perot interferometer Very high light throughput – much higher

than for grating spectrometer.

Many orders generally transmitted

simultaneously.

Very high resolution – tens of MHz at

optical frequencies ( >10

–5

nm).

Cannot be used at short wavelengths

(<200 nm).

Transmission maximum can be scanned only over

narrow range.

Most difﬁcult dispersing element to use.

294 OPTICAL SYSTEMS

Fabry–Perot interferometers. From t he vacuum ultravio-

let (prism instruments c annot be used below ab out 1200

) to the far infrared, grating instruments are much supe-

rior to comparable-size prism instruments in both resolving

power and luminosity. In recent years, the advantages of

grating instruments over prism instruments has virtually

eliminated the latter. This has primarily resulted because

of improvements in grating fabrication. Holographic plane

gratings have fewer and weaker ghosts than metal gratings,

and holographic curved gratings have allowed aberration

reduction in spectrometers. Apart from the minor incon-

venience of potential overlapping orders, grating instru-

ments are almost always to be preferred over prism

instruments. There is one exception worth noting: when a

monochromator is being used to observe some weak opti-

cal emission in the simultaneous presence of a strong laser

beam, unless the optical emission is too close in wave-

length to the laser for prism resolution to be adequate. In

this application, a prism avoids the problems of ghost

emission or grating scattering. A good prism has very

low scattered light. It is common to predisperse a light

beam with a prism before sending the beam into the

entrance slit of a monochromator, in order to avoid both

the overlapping-order problem and spurious signals from a

very strong light signal at another wavelength. Fabry–Perot

interferometers have very high resolution and luminosity,

but require careful and regular adjustment to maintain

high performance. They are used only where their very

high resolution is essential, frequently in conjunction with

a grating monochromator for pre-isolation of a narrow

spectral region.

A ﬁnal point to note with regard to the use of grating

spectrometers: these instruments are polarization sensitive.

If unpolarized light strikes a grating, the diffracted light

will be partially polarized because the grating efﬁciency is

wavelength-, and S and P polarization-dependent.

4.7.2 Design of Spectrometers and

Spectrographs

The construction of monochromators and spectrographs is

a specialized undertaking. The availability of good com-

mercial instruments generally makes it unnecessary for

anyone but the enthusiast to contemplate their construction

in the laboratory. On the other hand, the principles that

underlie good design in a dispersing instrument are not

complex. Some essential features of such instruments

can be illustrated with reference to particular designs that

are used both in laboratory and commercial instruments.

Attention will be restricted to monochromators; spectro-

graphs are similar, apart from having an array detector or

photographic plate instead of an exit slit, as shown in

Figure 4.151. Spectrographs are also simpler in construc-

tion

because wavelength scanning is not required and all

optical components of the system remain ﬁxed. The dis-

cussion here should also allow intelligent evaluation and

comparison of commercial instruments. For further details

of the many different instrument designs that have been

used for the construction of monochromators, spectro-

graphs and spectrophotometers, References

132,133

, The

Photonics Design and Applications Handbook

134

, and

the catalogs of instrument manufacturers should be con-

sulted.

Figure 4.152 shows a Littrow prism monochromator.

The

light from the input slit is collimated with an off-axis

paraboloidal mirror. The output wavelength is changed by

rotating the Littrow mirror. If the output wavelength must

change uniformly with rotation of a drive shaft, then the

rotation of the mirror requires a cam. Figure 4.153 shows a

Czerny–T

urner prism conﬁguration. The collimating mir-

rors are spherical. In the geometry of Figure 4.153(a), the

coma

of one mirror compensates that of the other, while in

Figure 4.153(b) these comas are additive. The wavelength

changed by rotating the prism.

In any of these spectroscopic instruments, the optical

arrangement should be enclosed in a light-tight enclosure

Figure 4.151 Schematic diagram of a simple prism

spectrograph. (From R.J. Meltzer, ‘‘Spectrographs and

Monochromators,’’ in Applied Optics and Optical

Engineering, Vol. 5, R. Kingslake (Ed.), Academic Press,

New York, 1969; by permission of Academic Press.)

OPTICAL DISPERSING INSTRUMENTS 295

painted on its interior with black nonreﬂective paint. Table

4.10 lists the various ‘‘black’’ coatings that are available

for

this purpose and in any application where broad reﬂec-

tion over a range of angles from a surface must be mini-

mized. This helps to minimize scattered light. It is essential

that light passing through the entrance slit is not able to

reach the exit slit without going through the illuminating

optics and prism. To this end, it is common practice to

incorporate internal blackpainted bafﬂes in the monochro-

mator enclosure. The most likely source of scattered light

is overillumination of the input collimator: input radiation

should not enter with an f/number smaller than that of the

monochromator. To check for stray light, visual observa-

tion through the exit slit in a darkened room when the

entrance slit is illuminated with an intense source will

reveal where additional internal bafﬂes would be helpful.

Stray light is more likely to be a problem in a Littrow

arrangement than in a straight-through type, such as the

Czerny–Turner.

In the visible and near infrared, lens coll imating optics

can be used, as, for example, in the design shown in

Figure 4.151. Good lenses, such as camera lenses, should

used. Mirror collimating optics are useful over a much

broader wavelength region. For ult raviolet use they

should be aluminum overcoated with MgF

,andthey

are frequently of this type, even in instruments designed

for longer wavelengths.

Slit design is important in achieving high resolution.

Entrance and exit slits of equal width are generally used.

If the source is small, having a height much less than the

height of the prism or grating, parallel-sided slits are

adequate. Adjustable versions are available from Melles

Griot, Newport, and OptoSigma. Fixed slits can be easily

made using razor blades or purchased from Melles Griot or

National Aperture. If the source is high compared to the

height of the dispersing element, a straight entrance slit

produces a curved image at the exit slit. In the case of a

prism, this happens because light passing through the

prism at an angle inclined to the meridian plane suffers

slightly more deviation than light in the meridian plane.

Figure 4.153 Czerny–Turner monochromator

arrangements; (a) coma of one mirror compensates

that of the other; (b) comas are additive.

Figure 4.152 Littrow monochromator. (From R.J. Meltzer,

‘‘Spectrographs and Monochromators,’’ in Applied Optics and

Optical Engin eering, Vol. 5, R. Kingslake (Ed.), Academic

Press, New York, 1969; by permission of Academic Press.)

296 OPTICAL SYSTEMS

Light striking a grating in a plane that is not perpendicular

to the grating grooves sees an apparently smaller groove

spacing, and is consequently deviated more than light in

the plane perpendicular to the grating. To maintain high

resolution in the presence of image curvature, curved

entrance and exit slits should be used, each with a radius

equal to the distance of the slit from the axis of the system.

This slit arrangement is shown in Figure 4.154, which also

sho

ws a very good, and widely used, grating monochro-

mator design due to Fastie

135

(based on a design originally

described by Ebert

136

for use with a prism). It is also quite

common for the single spherical mirror in Figure 4.154 to

replaced by a pair, in which case the design becomes the

Czerny–Turner one. Such an arrangement is shown in Fig-

ure

4.155. In either case the wavelength is tuned by rotat-

ing

the grating. The wavelength variation at the exit slit is

much more nearly linear with grating rotation than with

prism rotation. If linearity is required, a cam, sine-drive, or

other such arrangement is used for rotating the grating or

prism.

133

In a Czerny–Turner grating instrument the

entrance and exit slits are generally arranged asymmetri-

cally with respect to the grating, as this allows coma to be

corrected in the working wavelength range. Czerny–Turner

monochromators are available from Edmund Optics, Gen-

esis Laboratory Systems (who now manufacture the for-

mer Jarrel-Ash line of spectrometers), Horiba Yobin Yvon,

McPherson, Minuteman Laboratories, Ocean Optics,

Princeton Intruments/Acton, and Thorlabs.

Grating monochromators for use in the vacuum ultra-

violet generally have a concave grating. Such a grating,

which has equally spaced grooves on the chord of a spher-

ical mirror, combines both dispersion and focusing in one

element. For maximum resol ution, both the object and

imageformedbyaconcavegratingmustbeonacircle

called the Rowland circle, whose diameter is the principal

radius of the s pherical surface on which the grating is

ruled, as shown in Figure 4.156. The use of a concave-

grating

monochromator (or spectrograph) entails mount-

ing grating and slits (or grating, slits, and photographic

plate) on a Rowland circle. Adjustment of the i nstrument

will involve moving the grating, slits, or plate on the

Figure 4.154 (a) Ebert–Fastie monochromator; (b) curved

entrance- and exit-slit conﬁguration for use with the above.

Table 4.10 Black materials and coatings

Material Absorptivity

Anodized black 0.88

Carbon lampblack 0.84

Chemglaze black paint Z306 0.91

Delrin black plastic 0.87

Electro-optical industries 0.965

Mid-temperature black

coating (up to 200 °C)

Electro-optical industries 0.93

High-temperature black

coating (up to 1400 °C)

Martin black velvet paint 0.94

3M black velvet paint 0.91

Parsons black paint 0.91

Polyethylene black plastic 0.92

Anodized aluminum 0.84

OPTICAL DISPERSING INSTRUMENTS 297

circle. Various mounting conﬁgurations, such as the

Abney, Eagle, Pasc hen, Rowland, and Wadsworth, and

grazing-incidence mounting have been used to accom-

plish this.

A convenient concave-grating design widely used

in vacuum-ultraviolet monochromator s is the Seya–

Namioka,

137,138

shown in Figure 4.157. In this arrange-

ment, by judicious choice of slit distances from the grating

and slit angular separation, the only adjustment needed

for wavelength adjustment is rotation of the grating. In

comparison with an ideal Rowland-circle mounting, only

a small resolution loss results over a wide wavelength

range. Vacuum-ultraviolet instruments possess the

added complication that all interior adjustments of the

instrument must be transmitted through the walls of the

vacuum chamber that houses the optical arrangement. Var-

ious kinds of rotary-shaft and bellows seals and magneti-

cally coupled drives exist for this purpose.

139

See also

Section 3.5.4.

Multiple

monochromators use multiple dispersing ele-

ments in series to obtain greater dispersion and/or lower

scattered light. For example, in a double-grating mono-

chromator, two diffraction gratings move simultaneously;

the desired diffracted wavelength from the ﬁrst grating is

diffracted once again from the second grating before being

focused on the exit slit. The considerable reduction

in scattered light that can be obtained with multiple

Figure 4.156 Rowland circle of a concave diffraction

grating. For maximum resolution, both object and image

must be on the Rowland circle. R ¼ object (entrance-slit)

distance: R

¼ image (exit-slit) distance. (From R. J. Meltzer,

‘‘Spectrographs and Monochromators,’’ in Applied Optics

and Optical Engineering, Vol. 5, R. Kingslake (Ed.),

Academic Press, New York, 1969; by permission of

Academic Press.)

Figure 4.157 Layout of the Seya–Namioka

monochromator.

Figire 4.155 Arrangement of a Czerny–Turner grating

monochromator.

298 OPTICAL SYSTEMS

monochromators makes them particularly useful for ana-

lyzing weak emissions close in wavelength to a strong

emission, as in Raman spectroscopy. Instruments with as

many as four gratings in series are available commercially.

Grating monochromators, spectrographs, and spectropho-

tometers are available from many manufacturers,

includ-

ing American Holographic, Coherent Scientiﬁc, CVI

Spectral Products, Horiba Jobin-Yvon (formerly Spex or

Instruments SA), Minuteman Laboratories, Newport/

Oriel, Olis, Princeton Instruments/Acton, and Thermo Sci-

entiﬁc (which incorporates the old companies Jarrell-Ash,

Aminco-Bowman, Unicam, and Varian Associates). Fiber-

coupled spectrometers are manufactured by Ocean Optics,

Photon Control, and Stellar Net. These instruments either

consist of a complete spectrometer on a PC card or are

compact units connected to a computer through a USB

port. McPherson, Minuteman Laboratories, and Princeton

Instruments/Acton are noted for their vacuum instruments,

Coherent Scientiﬁc, Horiba Jobin-Yvon, and Princeton

Instruments/Acton for their multiple grating spectrome-

ters, and Genesis Laboratory Systems for their high-reso-

lution spectrometers and spectrographs.

Imaging Spectrographs [sometimes called optical mul-

tichannel analysers (OMAs )] image an entire spectrum

onto eit her a linear photodiode area (PDA) or onto a

linear CCD. These instruments often have the capability

for recording complete spectra from several sources at

once. Manufa cturers include Horiba Jobin-Yvon, Instru-

ment Systems GmbH, Olis, Nomadics, Princeton Instru-

ments/Acton, and Roper Scientiﬁc. Note that CCD arrays

are approximately 100 times more sensitive than PDAs,

so are best u sed f or the lowest light-level applications.

Change -coupled devices must be used with appropriat e

shutters or light modulation otherwise i mage ‘‘smear’’

will occur. This happens if new light falls on the array

while the previous deposited charge distribution i s being

read out.

Wavemeters are optical devices that are designed to pro-

vide direct electronic readout of the wavelength of mono-

chromatic radiation that is directed into them. They are

most frequently used in conjunction with a tunable laser

system. These convenient instruments incorporate a Fabry–

Perot or Fizeau interferometer. Manufacturers include Bris-

tol Instruments, Elliott Scientiﬁc, Holo-Spectra, MK Pho-

tonics, and Specialise Instruments Marketing.

4.7.3 Calibration of Spectrometers

and Spectrographs

To calibrate the wavelength scale of a spectrometer or spec-

trograph, the entrance slit is illuminated with a reference

source that has characteristic spectral features of accurately

known wavelength. It is quite common to mount a small

reference lamp – mercury, neon, and hollow-cathode iron

lamps are the most popular – near the entrance slit and use

a small remov able mirror or beamsplitter to superimpose the

spectrum of the reference on the unkno wn spectrum under

study. To calibrate a grating instrument through its various

orders, a helium–neon laser is ideal. If the slits are set to their

narrowest position and a low-power (< 1 mW) He–Ne laser

is directed at the entrance slit, the various grating settings that

transmit a signal (which can be safely observed by eye at the

exit slit) correspond to the wavelengths 0, 632.8 nm, 632.8 3

2 nm, 632.8 3 3 nm, and so on. By interpolation between the

observed v alues, a reliable calibration curve can be obtained

ev en for instruments operating far into the infrared.

The efﬁciency of the instrument at a given wavelength

can be determined with any suitable detector. A laser or

other narrow-band source at the desired wavelength illu-

minates the entrance slit, or a duplicate of it, and the trans-

mitted power is measured with the detector placed directly

behind the slit. A similar measurement is then made at the

exit slit of the whole instrument. The relative spectral efﬁ-

ciency can be determined by illuminating the entrance slit

with a blackbody source. A lens should not be used for

focusing light on the entrance slit, as its collection and

focusing efﬁciency will vary with wavelength. The signal

at the output slit is then measured as a function of wave-

length with a spectrally ﬂat detector, such as a pyroelectric

detector, thermopile, or Golay cell (see Section 7.10), and

normalized

with respect to the blackbody distribution.

4.7.4 Fabry–Perot Interferometers

and Etalons

Fabry–Perot interferometers and etalons are optical ﬁlters

that operate by multiple-beam interference of light

reﬂected and transmitted by a pair of parallel ﬂat or coaxial

spherical reﬂecting interfaces. In its simplest form, an eta-

lon consists of a ﬂat, parallel-sided slab of transparent

OPTICAL DISPERSING INSTRUMENTS 299

material, which may or may not have semireﬂecting coat-

ings on each face. An etalon may also consist of a pair of

parallel, air-spaced ﬂat mirrors of ﬁxed spacing. If the

reﬂective surfaces have adjustable spacing, or if their

effective optical spacing can be adjusted by changing the

gas pressure between the surfaces, the device is called a

Fabry–Perot interferometer. These devices can be ana-

lyzed by the impedance concepts discussed in Section

4.2.6, but it is instructive to discuss their operation from

the

standpoint of multiple-beam interference.

Figure 4.158 shows the successive reﬂected and transmit-

ed ﬁeld amplitudes of a plane electromagnetic wave strik-

ing a plane-parallel Fabry–Perot etalon or interferometer at

angle of incidence h9. Although the reﬂection coefﬁcients at

the two reﬂecting interfaces may be different, only the case

where they are equal will be analyzed. Almost all practical

devices are built this way. The optical-path difference

between successive transmitted waves is 2nl cos h,where

l is the interface spacing and n is the refractive index of the

medium between these interfaces (air, glass, quartz, or sap-

phire, for example). If refraction occurs at the reﬂecting

interfaces, h and h9 will be related by Snell’s law. The phase

difference between successive transmitted waves is:

d ¼ 2kl cos h þ2 e ð4:252Þ

where:

k ¼

2pn

2pnv

ð4:253Þ

and e is the phase change (if any) on reﬂection.

The total resultant transmitted complex amplitude is:

¼ E

þ E

id

þ E

2id

þ ...

1  r

id

ð4:254Þ

Here r and t are the reﬂection and transmission coefﬁcients

of the waves passing from the medium of refractive index n

to that of refractive index n9 at each interface, r9 and t9 are

the corresponding coefﬁcients for passage from n9 to n, and

is the amplitude of the incident electric ﬁeld.

Figure 4.158 Paths of transmitted and reﬂected rays in a Fabry–Perot etalon. The complex

amplitude of the ﬁelds associated with the rays at various points is shown.

300 OPTICAL SYSTEMS

The total transmitted intensity is:

jtt

j1  r

id

: ð4:255Þ

Here |tt9| ¼ T and |r|

¼ |r9|

¼ R, where T and R are the

transmittance and reﬂectance of each interface. If there is

no energy lost in the reﬂection process:

T ¼ 1  R ð4:256Þ

If the etalon had slightly absorbing reﬂective layers, this

would no longer be true; if each layer absorbed a fraction

A of the incident energy, then:

T ¼ 1  R  A ð4:257Þ

If A ¼ 0, Equation (4.255) gives:

1 þ

ð1  RÞ

sin

ð4:258Þ

This variation of transmitted intensity with d is called an

Airy function and is illustrated in Figure 4.159 for several

alues of R. The variation of reﬂected intensity with d is

just the inverse of Figure 4.159, since:

¼ 1 

ð4:259Þ

If A 6¼ 0, Equation (4.258) becomes:

1  R



1 þ

ð1  RÞ

sin

ð4:260Þ

In either case, maximum transmitted intensity results when:

d ¼ 2mp ð4:261Þ

where m is an integer. If the phase change on reﬂection is

neglected, this reduces to:

2l cos h ¼ mk ð4:262Þ

where k is the wavelength of the light in the medium

between the two reﬂecting surfaces (plates). In normal

incidence, transmission maxima result when:

l ¼ mk=2 ð4:263Þ

Even if the phase change on reﬂection is included, the

adjustment in spacing necessary to go from one transmis-

sion maximum to the next is one half-wavelength. Thus,

for example, the transmitted intensity as a function of plate

separation when a Fabry–Perot interferometer is illumi-

nated normally with plane monochromatic light is also

as shown in Figure 4.159. In an ideal Fabry–Perot device,

Figure 4.159 Transmission and reﬂection characteristics of a Fabry-Perot etalon.

OPTICAL DISPERSING INSTRUMENTS 301

the overall transmittance at a transmission-intensity max-

imum is unity, whereas in a practical device, which will

invariably have some losses, the maximum overall trans-

mittance is reduced by a factor [T/(1 – R)]

. As is clear

from Figure 4.159, the transmission peaks of the device

become

very sharp as R approaches unity.

Free Spectral Range, Finesse, and Resolving

Power.

If a particular transmission maximum for ﬁxed

I occurs for normally incident light of frequency v

, then:

ð4:264Þ

where c is the velocity of light in the material between the

plates. Of course, the device will also show transmission

maxima at all frequencies v

6 pc/2l as well, where p is an

integer. The frequency between successive transmission

maxima is called the free spectral range:

Dv ¼

ð4:265Þ

When R is close to unity, all phase angles d within a

transmission maximum differ from the value 2mp by only

a small angle. Thus, we can write:

d ¼

4pvl

4pv

4pðv  v

Þl

ð4:266Þ

which can be written in the form:

d ¼ 2mp þ

2pðv  v

ð4:267Þ

Equation (4.258) becomes:

1 þ

4Rp

ð1  RÞ

v  v



ð4:268Þ

Writing p

ﬃﬃﬃ

=ð1  RÞ¼F, where F is called the ﬁnesse,

the shape of a narrow transmission maximum can be writ-

ten as:

1 þ 2ðv  v

Þ=Dv

1=2



ð4:269Þ

Here Dv

1/2

, the full width at half maximum transmission of

the transmission peak, is given by:

1=2

¼ Dm=F ð4:270Þ

The resolving power of a Fabry–Perot device is a measure

of its ability to distinguish between two closely spaced

monochromatic signals. A good criterion for determining

this is the Rayleigh criterion, which recognizes two closely

spaced lines as distinguishable if their half-intensity points

on opposite sides of the two line shapes are coincident, as

shown in Figure 4.160. Thus, for a Fabry–Perot device the

resolving

power is:

<¼

1=2

ð4:271Þ

It would appear that very high resolving powers can be

obtained by the use of high-reﬂectance plates (and con-

sequent high ﬁnesse values, as illustrated in Table 4.11)

and/or

large plate spacings (and consequent small free

spectral ranges). Additional practical considerations limit

how far these approaches to high resolution can act ually

be used.

Practical Operating Conﬁgurations and

Performance Limitations of Fabry–Perot

Systems.

The use of very high reﬂectance values to

obtain improved resolving power is limited by the ability

of the optical polisher to achieve ultraﬂat optical surfaces.

Very good-quality plates for use in the visible can be

obtained with ﬂatnesses of k/200 over regions a few

Figure 4.160 Two monochromatic spectral lines just

resolved according to the Rayleigh criterion.

302 OPTICAL SYSTEMS

centimeters in diameter. Some claims of ﬂatness in excess

of k/200 are also seen. These should be viewed with skep-

ticism – such a degree of ﬂatness is extremely difﬁcult to

verify. If the plates have surface roughness Ds, the average

error in plate spacing is

ﬃﬃﬃ

Ds. This gives rise to a spread in

the frequency of transmission maxima equal to:

’

mcDs

ﬃﬃﬃ

’

ﬃﬃﬃ

ð4:272Þ

Thus the ﬂatness-limited ﬁnesse is:

ﬃﬃﬃ



ﬃﬃﬃ

ð4:273Þ

For example, two plates with surface roughness of k/200

would have a ﬂatness-limited ﬁnesse of about 71. The use

of super mirrors has allowed ﬁnesse values to 30 000 to be

achieved. In practice, Fabry–Perot plates may not be ran-

domly rough, and their stated ﬂatness ﬁgure may represent

the average deviation from parallelism of the two plates. In

this case, the parallelism-limited ﬁnesse is:

2Ds

ð4:274Þ

where Ds is the deviation from parallelism over the used

aperture of the system. Thus, for example, with a 1 cm aper-

ture, a 1/100 arc-second deviation from parallelism would

imply Ds ¼ 4.84 nm and a parallelism-limited ﬁnesse of only

56 at 546 nm. Depending on the deﬁnition of what is meant

by surface roughness and deviation from parallelism, Equa-

tions (4.273) and (4.274) may take slightly different forms.

139

Fabry–Perot plates must be held very nearly parallel to

achieve high resolution. Also, their separation should not

be allowed to drift. A random variation of Ds will limit the

ﬁnesse, as predicted by Equation (4.273). A fractional

length change of 10

–6

in a 1 cm spacing Fabry–Perot

device will limit the ﬁnesse to only about 27. Thus it must

be isolated from vibrational interference to achieve high

ﬁnesse. Further, if the frequencies of the transmission max-

ima are not to drift, the change in plate spacing due to

thermal expansion must be minimized by constructing

the device of low-expansion materials such as Invar,

141

Superinvar,

142

fused silica,

143

or special ceramics.

144

The resolving power of a Fabry–Perot system is also

limited by the range of angles that can be transmitted

through the instrument. One popular conﬁguration is shown

in Figure 4.161. A small source, or light from an extended

source that passes through a small aperture, is collimated

by a lens, passes through the interferometer, and is focused

onto a second small aperture in front of a detector. The

maximum angular spread of rays passing through the sys-

tem will be governed by the aperture sizes W

and W

and

the two focal lengths f

and f

. In the paraxial-ray

Table 4.11 Properties of Fabry-Perot etalons

Plate Separation

l (cm)

Reﬂectance R (%) Free Spectral Range

Dt ¼c/2Z Hz

Finesse

F ¼ p

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1RðÞ

Resolving Power

R ¼Ft/Dm

0.1 80 1.5 3 10

14 5.6 3 10

0.1 90 1.5 3 10

30 1.2 3 10

0.1 95 1.5 3 10

61 2.44 3 10

0.1 99 1.5 3 10

313 1.25 3 10

1.0 80 1.5 3 10

14 5.6 3 10

1.0 90 1.5 3 10

30 1.2 3 10

1.0 95 1.5 3 10

61 2.44 3 10

1.0 99 1.5 3 10

313 1.25 3 10

10.0 80 1.5 3 10

14 5.6 3 10

10.0 90 1.5 3 10

30 1.2 3 10

10.0 95 1.5 3 10

61 2.44 3 10

10.0 99 1.5 3 10

313 1.25 3 10

Note: Properties shown are at 500 nm (600 THz).

OPTICAL DISPERSING INSTRUMENTS 303

approximation, the angular width 2Dh of the paraxial-ray

bundle that comes from, or is delivered to, an aperture of

diameter W is equal to the angular width 2Dh9 that traverses

the system, as illustrated in Figure 4.162. In this case:

Dh ’ W=2f ð4:275Þ

In Figure 4.161 the resolving power will be limited by

or W

, whichever is the larger. The transmitted

frequency spread associated with an angular spread Dh

around the normal direction is, from Equations (4.262)

and (4.264):

1=2

¼ v

ðDhÞ

=2 ð4:276Þ

The corresponding aperture-limited ﬁnesse is:

lðDhÞ

4kf

ð4:277Þ

For example, using a 1 mm diameter aperture, a 10 cm

focal-length lens, and a 1-cm air-spaced Fabry–Perot

device at 546.1 nm, the aperture-limited ﬁnesse is 218.

The operating conditions of a Fabry–Perot system should

be arranged so that F

is at least three times larger than the

desired operating ﬁnesse, which usually is ultimately

limited by the ﬂatness-limited ﬁnesse. The apertures in

Figure 4.161 should be circular and accurately coaxial

with both lenses, or the aperture ﬁnesse will be further

reduced. If the limiting aperture (either a lens or the

Fabry–Perot device itself) is D, there is also a diffraction

limit to the ﬁnesse, which on axis is:

knl

: ð4:278Þ

At the pth fringe off axis:

2pknl

ð4:279Þ

where n is the refractive index of the material between

the plates. The overall ﬁnesse of a Fabry–Perot system,

, is related to t he individual contributions to the ﬁnesse,

,by

2

¼ +

2

ð4:280Þ

Figure 4.161 (a) Operating scheme for a Fabry–Perot

interferometer, using collimated light; (b) detail of typical

plate conﬁguration (the wedge angle of the reﬂecting plates

is exaggerated).

Figure 4.162 Angular factors involved in the collection

of light transmitted through a Fabry–Perot interferometer

by a circular aperture. In the paraxial-ray

approximation, Dh9 ¼ Dh.

304 OPTICAL SYSTEMS

In the operating conﬁguration of Figure 4.161, if the plate

spacing is ﬁxed, then with a broad-band source, all frequen-

cies that satisfy Equation (4.280) will be transmitted. These

equencies become more closely spaced as the plate sepa-

ration l is increased. There is a concomitant increase in

resolution, but this may not prove useful if any of the spec-

tral features under study are broader than the free spectral

range. In this case, simultaneous transmission of two broad-

ened spectral features always occurs. For example, for two

lines of wavelength k

and k

and of FWHM Dk ,itis

usually possible to ﬁnd two integers m

and m

such that:

¼ 2l, jk

 k

j& Dk

¼ 2l, jk

 k

j& Dk

ð4:281Þ

Thus, for isolated, high-resolution studies of the spectral

feature at k

, say, all potential interference features such as

must be ﬁltered out. This is done with a color or inter-

ference ﬁlter, or a prism or grating monochromator, before

the signal is sent to the interferometer. The choice of pre-

ﬁltering element will depend on the relative wavelength

spacing of k

and k

The optical throughput of ﬁlters can

be very high, 50% or more, but will not allow preﬁltering

of lines closer than a few nanometers. When very high

throughput coupled with high resolution is essential, one

or more additional Fabry–Perot devices of appropriate free

spectral range can be used. For example, an etalon of spac-

ing 0.01 mm has a free spectral range of about 15 nm. If

it has a ﬁnesse of 50, its useful transmission bandwidth is

0.3 mn. Such an etalon could be coupled with etalons of

spacing 0.1 mm and 1 mm with similar ﬁnesse to isolate a

band only 0.003 nm wide from an original relatively broad

frequency band transmitted through a ﬁlter. The ﬁnal

transmitted wavelength of such a combination of etalons

can be tuned by tilting.

The wavelength of maximum transmission of a single

etalon varies as:

k ¼ k

cos h ð4:282Þ

where k

is the wavelength for maximum transmission in

normal incidence. In the interferometer arrangement

shown in Figure 4.161(a), wavelength scanning can be

complished in two ways: by p ress ure scann ing, or by

adjusting the axial position of one of the plates with a

piezoelectri c transducer.

145

To accomplish pressure scan-

ning, the interferometer is mounted in a vacuum- or

pressure-tight housing into which gas can be admitted

at a slow ste ady rate. The resultant change of refractive

index of the gas between the plates, which is approxi-

mately linear with pressure, ca uses a continuous, unidir-

ectional scanning of the center transmitted frequency.

The interferometer should b e mounted freely within

the housing so that the pressure differential between the

interior and exterior of the housing causes no deformation

of th e interf erome ter. Pressure scanning is no t conve-

nient where rapid or bidirectional scanning is required.

Because no geometrical dimensions of the interferometer

change during the scan, n o c h ange in ﬁnesse should oc cur

during scanning.

Piezoelectric scanning is very convenient, but the trans-

ducer material must be specially selected to give uniform

translation of the moving plate without any tilting – which

would cause ﬁnesse reduction during scanning. If separate

piezoelectric transducers

145

are mounted on the kinematic-

mounted alignment drives of the plate holders, it is possi-

ble to trim the ﬁnesse electronically after good mechanical

alignment has been achieved by micrometer adjustment.

The alignment of the plates during scanning can be main-

tained with a servo system.

146,147

A Fabry–Perot eta lon can be used in the conﬁguration

shown in Figure 4.163 to give a high-resolution display of

narrow-band s p ect ral featur e that cannot be displayed

with a scanning interferometer because (for example)

the optical signal is a short pulse. In the arrangement

shown in Figure 4.16 3, all rays from a monochromatic

source

that are incident at angle h

on the plates will be

transmitted and brought to a focus in a bright ring on a

screen if:

cos h

ð4:283Þ

In the paraxial approximation, h

is a small angle and the

radius q

of a ring on the screen is:

¼ f h

ð4:284Þ

which can be written as:

¼ f

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 

ð4:285Þ

OPTICAL DISPERSING INSTRUMENTS 305

The radius of the smallest ring corresponds to the largest

integer m, for which mk /2l < 1. Successive rings going out

from the center of the pattern correspond to integers m –1,

m – 2, and so on.

If there is a bright spot at the center of the ring pattern,

the radius of the pth ring from the center is:

¼ f

ﬃﬃﬃﬃﬃ

: ð4:286Þ

This ring will be diffuse because of the ﬁnite ﬁnesse of the

etalon, even if the source is highly monochromatic. The

FWHM at half maximum intensity of the pth ring in this

case is:

2pF

ð4:287Þ

which can be veriﬁed by expanding Equation (4.260) in the

angle h. This ring width is the same as would be produced

by a source of FWHM Dk ¼ k

/2lF.

Equation (4.287) predicts that the total ﬂux through each

ring of the pattern will be identical, since the area of each

ring is:

DA ¼ 2pq

¼ pf

=2lF ð4:288Þ

The ratio of ring width to ring spacing for the pth ring in

the pattern is:

p þ1

 q

¼ 2Fp 1 

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ

!"#

1

ð4:289Þ

which is close to 1/F except for the ﬁrst few rings. Thus

observation of the ring pattern from a quasimonochromatic

source will yield its approximate bandwidth Dk as:

Dk ’

p þ1

 q

ð4:290Þ

A convenient way of making a qualitative visual observa-

tion of this kind is to use an etalon in conjunction with a

small telescope, as shown in Figure 4.164.

Figure 4.164 Arrangement for visual observation of

Fabry–Perot fringes.

Figure 4.163 Arrangement for observing a ring interference pattern with a

Fabry–Perot etalon.

306 OPTICAL SYSTEMS

Luminosity, Throughput, Contrast Ratio, and

tendue.

The luminosity of a Fabry–Perot system is, as

already mentioned, much higher than that of any prism or

grating monochromator. In the arrangement of Figure

4.161, the luminosity is:

U ¼

1  R



ðkÞS

ð4:291Þ

where pW

/4f

is the solid angle subtended by the output

circular aperture at the output focusing lens, and S is the

illuminated area of the plates. If the system has an aper-

ture-limited ﬁnesse, then, from Equation (4.277) the lumi-

nosity

becomes:

U ¼

1  R



ðkÞ

pkS

ð4:292Þ

which can be written in terms of the resolving power < as:

U ¼

1  R



ðkÞ

2pS

ð4:293Þ

The factor [T/(1 – R)]

is called the throughput of the

system. To compare the luminosity predicted by Equation

(4.293) with that of a grating, we shall assume that the

throughput

of the Fabry–Perot system is equal to the cor-

responding efﬁciency factor T of the grating in Equation

(4.240). In this case, for identical resolving powers <,

from

Equations (4.293) and (4.240), we have:

UðF:P:Þ

UðgratingÞ

ðA sin bÞðl=f

ð4:294Þ

where l/f

is the angular slit height at the output-focusing

element of the grating monochromator. For a blaze angle

of 30° and equal Fabry–Perot aperture and grating area:

UðF:P:Þ

UðgratingÞ

l=f

ð4:295Þ

For a 0.3 m focal length grating instrument and a slit height

of 3 cm (which is a typical maximum value for a small

instrument of this size), the luminosity ratio is 71.4. This

probably represents an optimistic comparison as far as the

grating instrument is concerned, since high-resolution gra-

ting monochromators typically have focal lengths in

excess of 0.75 m.

The contrast ratio of a Fabry–Perot system is deﬁned as:

C ¼

ðI

max

ðI

min

ð4:296Þ

which from Equation (4.258) clearly has the value:

C ¼

1 þ R

1  R



¼ 1 þ

ð4:297Þ

The e

tendue U of a Fabry–Perot system is a measure of its

light-gathering power for a given frequency bandwidth

1/2

. It is deﬁned by:

U ¼ XS ð4:298Þ

where A is the area of the plates and X is the solid angle

within which incident rays can travel and be transmitted

with a speciﬁed frequency bandwidth. From Equation

(4.276), since X ¼ pDh

1=2

ð4:299Þ

Therefore:

U ¼ XS ¼

2pDv

1=2

ð4:300Þ

which can be written in the form:

U ¼ XS ¼

4lF

ð4:301Þ

Spherical Mirror Fabry–Perot Interferometers.

Fabry–Perot interferometers with spherical concave

mirrors are generally used in a confocal arrangement, as

shown in Figure 4.165. In this conﬁguration the various

chara

cteristics of the interferometer can be summarized as

follows:



max

2ð1  RÞ

ð4:302Þ

DvðFSRÞ¼c=4l ð4:303Þ

reflectivitylimited finesse ¼

ﬃﬃﬃ

ð1  RÞ

ð4:304Þ

OPTICAL DISPERSING INSTRUMENTS 307

The approximate optimum radius of the apertures used

in an arrangement similar to Figure 4.161 is 1.15 (kr

/f/)

1/4

where r is the radius of the spherical mirrors. Fabry–Perot

interferometers with spherical mirrors can achieve very

high ﬁnesse values.

The characteristics of all the possible combinations of

two spherical mirrors that can be used to form a Fabry–Perot

interferometer have been very extensively studied in con-

nection with the use of such mirror arrangements to form

the resonant cavities of laser oscillators.

14–16

In that appli-

cation, these spherical-mirror resonators support Gaussian

beam modes, and it is with such Gaussian beams that high-

est performance can be achieved with a spherical-mirror

Fabry–Perot interferometer. Thus, a confocal Fabry–Perot

interferometer is ideal for examining the spectral content of

a Gaussian laser beam. The beam to be studied should be

focused into the interferometer with a lens that matches

the phase-front curvature and spot size of the laser beam

to the radius of the Fabry–Perot mirror and the spot size of

the resonant modes. (See Section 4.2.7.)

4.7.5 Design Considerations for

Fabry–Perot Systems

Fabry–Perot interferometers and etalons are extremely

sensitive to angular misalignment and ﬂuctuations in plate

spacing. Consequently, their design and construction are

more demanding than for other laboratory optical instru-

ments. The plates must be extremely ﬂat, as already

mentioned, and must be held without any distortion in

high-precision alignment holders. The plate spacing must

be held constant to about 1 nm in a typical high-ﬁnesse

device for use in the visible, and the angular orientation

must be maintained to better than 0.01 second of arc.

Small-plate-spacing etalons are generally made commer-

cially by optically contacting two plates to a precision

spacer, or spacers, made of quartz. Such etalons are avail-

able from CVI Laser, II-VI Infrared, Michigan Aerospace,

OFR, Research Electro-Optics, Rocky Mountain Instru-

ment Co., TecOptics, Scientiﬁc Solutions, and SLS Optics,

among others. Etalons of thickness in excess of 1 or 2 mm

for use in the visible can be made from solid plane-parallel

pieces of quartz or sapphire with dielectric coatings on

their faces, or from materials, such as germanium or zinc

selenide, for infrared use. Fabry–Perot interferometer

plates are almost always slightly wedge-shaped and anti-

reﬂection-coated on their outside faces to eliminate

unwanted reﬂections, as shown in Figure 4.161(b). To pre-

vent distortion of the plates they should be kinematically

mounted in their holders. A good way to do this is to use

three quartz or sapphire balls cemented to the circumfer-

ences of the plates and held in ball, slot, and plane loca-

tions with small retaining clips. For further details see

Section 1.7.1 and Figures 1.52 and 1.53.

For the construction of Fabry–Perot interferometers,

low-expansion materials should be used. The plate holders

can be held at a ﬁxed spacing by having them spring-

loaded against three quartz or ceramic spacer rods or by

the use of an Invar or Super-Invar spacer structure.

After a Fabry–Perot interferometer is aligned mechan-

ically, it will creep slowly out of alignment, because of the

easing of micrometer threads, for example. The alignment

can be returned by having a piezoelectric element

145

incor-

porated in each plate-orientation adjustment screw.

Fabry–Perot interferometers are made commercially by

Bernhard Halle Nachﬂ. GmbH, Bristol Instruments (who

still provide service and parts for Burleigh interferome-

ters), Hovemere, SSI, and Thorlabs.

The Fizeau interferometer is closely related to the

Fabry–Perot, except that one of the mirrors is made totally

reﬂecting and a beamsplitter is used to extract the interfer-

ing waves. They measure the phase difference between a

reference surface and the object under test, as shown sche-

matically in Figure 4.166. These interferometers are

commonly used to test the ﬂatness of optical surfaces.

Figure 4.165 Confocal Fabry–Perot interferometer.

308 OPTICAL SYSTEMS

They are available commercially from 4D Technology,

Davidson Optronics, Logitech, Moeller-Wedel Optical

GmbH, Sigma Koki Co, Silo, and Zygo.

4.7.6 Double-Beam Interferometers

In a double-beam interferometer, waves from a source are

divided into two parts at a beamsplitter and then recom-

bined after traveling along different optical paths. The

most practically useful of these interferometers are the

Michelson and the Mach–Zehnder.

The Michelson Interferometer. The operation of a

Michelson interferome ter can be illus trated with

reference to Figure 4.167. Light from a n extended

source

is divided at a beamsplitter and sent to two plane

mirrors M

and M

. If observations of a broad-band

(temporally incoherent) source are being made, a

compensating plate of the same material and thickness

as the beamsplitter is included in arm 2 of the

interferometer. This p late compensates for the two

additional traverses of the beamsplitter substrate made

by the beam in arm 1. Because of the dispersion of the

beamsplitter material, it produces a phase difference t hat

is wavelength-dependent, and without the compensating

plate, interference fringes would not be observable with

broad-band illumination (such as white light).

A maximum of illumination results at angle h in Figure

4.167 if the phase difference between the two beams com-

ing

from M

and M

is an integral multiple of 2p.IfM9

represents the location of the reﬂection of M

in the beam-

splitter, the condition for a maximum at angle h is:

2l cos h ¼ mk: ð4:305Þ

The positioning of M

at M

corresponds to l ¼ 0, m ¼ 0. If

the output radiation is focused with a lens, a ring pattern is

produced. A clear ring pattern is only visible if:

2l cos h & l

ð4:306Þ

where l

, is the coherence length of the radiation from the

source. The clearness of the rings is usually described in

terms of their visibility V, deﬁned by the relation:

max

 I

min

max

þ I

min

ð4:307Þ

To obtain a ring-shaped interference pattern, M

and M

must be very nearly parallel; otherwise a pattern of curved

Figure 4.166 Fizeau interferometer. SF – spatial ﬁlter, BS – beamsplitter cube,

CL – collimating lens.

OPTICAL DISPERSING INSTRUMENTS 309

dark and light bands will result. To study the fringes, mirror

must be scanned in a direction perpendicular to its sur-

face. This can be done with a precision micrometer, or a

piezoelectric transducer, if only small motion is desired.

Because interference fringes are only observed with a

broad-band source illuminating a Michelson (or other dou-

ble-beam) interferometer when the two interferometer arms

are of almost equal length, this mode of operation is extra-

ordinarly sensitive. Such ‘‘white-light interferometry’’

forms the basis of a number of sensor systems for phenom-

ena such as vibration, temperature, and pressure.

149,150

In practice, Michelson interferometers are rarely used in

the conﬁguration shown in Figure 4.167, but are used

instead

with collimated illumination (a laser beam, or par-

allel light obtained by placing a point source at the focal

point of a converging lens) as shown in Figure 4.168.In

this

case, the output illumination is (almost) perfectly uni-

form, being a maximum if:

2l ¼ mk ð4:308Þ

where 2l is the path difference between the two arms.

If monochromatic illumination of angular frequency x

is used, we can write the ﬁelds of the waves from arms 1

and 2 as:

¼ V

iðxt/

¼ V

iðxt/

ð4:309Þ

where it is assumed that the beamsplitter divides the inci-

dent beam into two equal parts. /

and /

are the optical

phases of these two beams, which are dependent on the

optical path lengths traveled in arms 1 and 2.

The output intensity is:

I } ðV

þ V

ÞðV

þ V

Þð4:310Þ

which gives

I ¼ I

1 þ cosð/

 /

Þ½

¼ I

1 þ cos

4pvl



ð4:311Þ

Figure 4.167 Michelson interferometer.

310 OPTICAL SYSTEMS

in which I

is the intensity of the light from one arm alone.

Suppose an optical component such as a prism or lens is

placed in one arm of the interferometer, as shown in Figure

169, with the plane mirror replaced by an appropriate radius

herical mirror in the case of the lens, and quasi-monochro-

matic illumination is used. Then the output fringe pattern will

rev eal inhomogeneities and defects in the inserted component.

A Michelson interferometer used in this way for testing opti-

cal components is called a Twyman–Green interferometer.

Equation (4.302) illustrates why Michelson (and all

other double-beam) interferometers are not directly suit-

able for spectroscopy. The distance the movable mirror

must be adjusted to go from one maximum to the next is:

Dl ¼ k=2 ð4:312Þ

The distance required to go from a maximum- to a half-

maximum-intensity point is:

Dl ¼ k=8 ð4:313Þ

Thus the effective ﬁnesse is only 4: sharp spectral peaks

with monochromatic illumination are not obtained, as they

are in multiple-beam interferometers.

Fourier Transform Spectroscopy. In an arrange-

ment such as Figure 4.168, if the movable mirror is

scanned

at a steady velocity v, the resultant intensity as a

function of position can be used to obtain considerable

information about the spectrum of the source. If the

Figure 4.168 Simple Michelson interferometer for use with collimated input radiation.

OPTICAL DISPERSING INSTRUMENTS 311

source has intensity I(m)atm, the contribution to the

intensity from the small band dm at v is:

ðlÞ¼IðmÞ 1 þ cos

4pml



dm ð4:314Þ

where l ¼ mt. The total observed output from the full spec-

trum of the source is:

IðlÞ¼

‘

m ¼0

IðmÞ 1 þ cos

4pml



‘

m ¼0

IðmÞcos

4pml

ð4:315Þ

The second term on the second line is essentially the

cosine transform of I(v). Thus I(v) can be found as the

cosine transform of I(l)–(I

/2):

IðvÞ¼

‘

l ¼0

IðlÞ



cos

4plm

dl ð4:316Þ

This method for obtain ing the spectrum of a source as

the Fourier transform of an inte nsity recorded as a

function of scanning mirror p osition is called Fo uri er

transform spectroscopy. Such Fourier transform spec-

trometers have high luminosity and collect spectral

information very efﬁciently: the whole emission spec-

trum is in reality sampled all at once, rather than one

feature at a time, as in a conventional dispe rsive grating

spectrometer. This is often called the Fellgett or Jacqui-

not advantage.

Commercial fourier transform spectrometers have

become widely available and easy to use. Suppliers include

ABB Bomen, Bruker Optics, Melles Griot, MIDAC,

Newport/Oriel, Perkin-Elmer, ScienceTech, Shimadzu,

Thermo-Fischer Scientiﬁc (formerly Nicolet), and Varian

(previously Bio-Rad and Digilab). These instruments have

replaced grating instruments in many analytical applica-

tions, especially for infrared absorption spectroscopy.

They must be ‘‘zeroed’’ by running a spectrum of the

source itself before any absorbing material is included in

the sample path, and the absorption of the sample is

obtained by ratioing with respect to the empty sample path.

They can also be checked by measuring the absorption

spectrum of a known sample, such as a thin polystyrene

ﬁlm. Commercial instruments often have interchangeable

sources and detectors to cover different spectral regions.

Figure 4.169 Twyman–Green interferometer:

(a) arrangement for testing a prism; (b) arrangement for

testing a lens. S is a monochromatic source, L

is a

collimating lens, and L

is a focusing lens. (Adapted with

permission from M. Born and E. Wolf, Principles of Optics,

3rd edn., Pergamon Press, Oxford, copyright Ó 1965.)

312 OPTICAL SYSTEMS

For example they might use a hot ceramic (globar type)

source for infrared work, and germanium, InGaAs,

HgCdTe, or triglycine sulfate (TGS) detectors, depending

on the spectral region of interest.

The Mach–Zehnder Interferometer. The Mach–

Zehnder interferomete r, shown in Figure 4.170,iswidely

used

for studying refra ctive-index distributions in gases,

liquids, and solids. It is particularly widely used for

studying the density variations in compressible gas

ﬂows,

151

the thermally i nduced density (and consequent

refractive-index) changes behind shock fronts, and

thermally induced density changes produced by la ser

beams propagating through transparent media.

152,153

If the light entering the interferometer is perfectly

collimated, uniform output illumination results, which

is a maximum if the path difference between the two

arms is an integral number of wavelengths. If the image

of M

in beamsplitter B

is not parallel to M

, the ou tput

fringe pattern is essentially the interference pattern

observed from a wedge – a series of parallel bright and

dark bands. If the medium in arm 2 is perturbed i n

some way, so that a spatial variation in refractive index

results, the output fringe pattern changes. Analysis of

the new fringe pattern reveals the spatial distribution

of refractive-index variation al ong the beam path in

arm 2. Various design variations on the Mach–Zehnder

interferometer exist, notably the Jamin and the Sirks–

Pringsheim.

11,154

Figure 4.170 Mach-Zehnder interferometer. M

are totally reﬂecting mirrors;

are beamsplitters (usually equally reﬂective and transmissive). The

distribution of output illumination reﬂects the refractive-index distribution in

the sampled region.

OPTICAL DISPERSING INSTRUMENTS 313

Design Considerations for Double-Beam

Interferometers.

Michelson and Mach–Zehnder inter-

ferometers are much easier to build in the laboratory than

multiple-beam interferometers, such as the Fabry–Perot.

Because the beams only reﬂect off the interfero-

meter mirrors once, mirrors of ﬂatness k/10 or k/20 are quite

adequate for building a good instrument. The usual precau-

tions should be taken in construction: stable rigid mounts for

the mirrors and beamsplitters and, if long-term thermal

stability is required, low-expansion materials. Piezoelectric

control of mirror alignment is not generally necessary, as

these instruments are less sensitive to small angular mis-

alignments than Fabry–Perot interferometers. To achieve

freedom from alignment disturbances along one or two

orthogonal axes, the plane mirrors of a Michelson interfer-

ometer can be replaced with right-angle prisms or corner-

cube retroreﬂectors, respectively. Some care should be taken

to avoid source-polarization effects in these instruments; the

beamsplitters are generally designed to reﬂect and transmit

equal amounts only for a speciﬁc input polarization. If

polarizing materials are placed in either arm of the interfer-

ometer, no fringes will be seen if, by any chance, the beams

from the two arms emerge orthogonally polarized.

Endnotes

a 1 GHz (GigaHertz) ¼10

Hz, 1 THz (TeraHertz)

¼10

. The infrared range can also be somewhat

arbitrily divided up into the submillimeter region

(k ¼0.1–1 mm), far-infrared (k ¼20–100 lm), middle

infrared (k ¼3–20 lm), and the near infrared (k ¼0. 7 –

3 lm).

b At the boundary separating one or more anisotropic

media, Snell’s law must be used with some care as,

in anisotropic media, the ray direction is not in general

parallel to the wave vector (or wave normal), which is

also used to characterize the direction of the ray.

c Used by physicians for examining the retina of a

patient’s eye.

d A pinhole camera is free of all aberrations in a geomet-

rical optics description.

e A simple lens with just two spherical surfaces.

f Often called a TM wave.

g Often called a TE wave

h The old pressure unit of pounds per square inch (psi) ¼

6895 Pa

i The word rugate means corrugated, having alternating

ridges and depressions

j The phosphorous is often omitted, and the precise stoi-

chiometry of (In, Ga) and (As, P) determines the laser

wavelength

k In practice, in any real system, transmission losses and

aberrations will cause B

< B

Cited References

1. Proceedings of the Symposium on Quasi-Optics, New York,

June 8–10, 1964, J. Fox (Ed.), Polytechnic Press of the

Polytechnic Institute of Brooklyn, New York, 1964.

2. Pr oceedings of the Symposium on Submillimeter Waves,New

York, March 31–April 2, 1970, J. Fox (Ed.), Polytechnic Press

of the Polytechnic Institute of Brooklyn, Ne w York, 1964.

3. A. Mortazawi, T. Itoh, and J. Harvey, Active Antennas and

Quasi-Optical Arrays, Wiley-IEEE Press, New York, 1998.

4. J. Lesurf, Millimeter-Wave Optics, Devices and Systems,

Lavoisier, Chachan, 1990.

5. K. M. Baird, D. S. Smith, and B. G. Whitford, Conﬁrmation

of the currently accepted value 299792458 metres per second

for the speed of light, Opt. Commun., 31,367–368,1979.

6. E. R. Cohen and B. N. Taylor, Committee on Data

for Science and Technology , CODATA Bulletin,No.63, 1986.

7. G. W. C. Kaye and T. H. Laby, Tables of Physical and

Chemical Constants, 16th edn., Longman, London: 1995.

Now available free online at http://www.kayelaby.npl.

co.uk/

8. C. D. Coleman, W. R. Bozman, and W. F. Meggers, Table of

Wavenumbers, US Nat’l. Bur. Std. Monograph 3, Vols. 1–2,

1960.

9. M. W. Urban, Attenuated Total Reﬂectance Spectroscopy

of Polymers: Theory and Practice, American Chemical

Society, Washington, DC, 1996.

10. R. Wies endanger, Scanning Probe Microsocopy and

Spectroscopy, Cambridge Uni versity Press, Cambridge, 1994.

11. M. Born and E. Wolf, Principles of Optics, 7th ed.,

Cambridge University Press, Cambridge, 1999.

12. E. E. Wahlstrom, Optical Crystallography, 5th edn., John

Wiley & Sons, Inc., New York, 1979.

13. W. A. Shurcliff, Polarized Light: Production and Use,

Harvard University Press, Cambridge, MA, 1962.

14. A. Yariv, Optical Electronics in Modern Communications,

5th edn., Oxford University Press, New York, 1997.

314 OPTICAL SYSTEMS

15. C. C. Davis, Lasers and Electro-Optics, Cambridge

University Press, Cambridge, 1996.

16. H. Kogelnik and T. Li, Proc. IEEE, 54, 1312–1329, 1966.

17. R. Kingslake, Optical System Design, Academic Press,

Orlando, FL, 1983.

18. Code V. Available from Optical Research Associates.

19. Zemax. Available from Zemax Development

Corporation.

20. Oslo developed by Sinclair Optics, Inc. Distributed by

Lambda Research Corporation.

21. Solstis Odyssey. Available from Optis.

22. Optikwerk. Available from Optikwerk, Inc.

23. R. W. Ditchburn, Light, 3rd edn., Academic Press,

New York, 1976.

24. L. Levi, Applied Optics, Vol.1 John Wiley & Sons, Inc.,

New York, 1968.

25. W. J. Smith, Modern Optical Engineering, 3rd edn., SPIE

Press, Bellingham, WA, 2000.

26. W. J. Smith, Modern Lens Design: A Resource Manual,

McGraw-Hill, New York, 1992.

27. R. R. Shannon, The Art and Science of Optical Design,

Cambridge University Press, Cambridge, 1997.

28. M. Laikin, Lens Design, 3rd edn., Marcel Dekker, New

York, 2001.

29. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and

Waves in Communication Electronics, 3rd edn., John

Wiley & Sons, Inc., New York, 1994.

30. Diffraction-limited spherical lenses are available from

Melles Griot, Optics for Research, Newport, Special

Optics, and J. L. Wood Optical Systems, among others (see

following reference).

31. Laser Focus Buyers Guide, published annually by

Pennwell Publishing Co., 1421 South Sheridan, Tulsa, OK

74112 01460, lists a large number of suppliers of a wide

range of optical components and systems as does the

The Photonics Buyers’ Guide, published annually by

Photonics Spectra, Laurin Publishing Co., Berkshire

Common, P. O. Box 4949, Pittsﬁeld, MA 01202-4949.

Additional valuable listings of this sort are: Lasers and

Optronics Buying Guide, published a nnually by Cahners,

301 Gibral tar Drive, Box 650, Morris Plains,

NJ 07950-0650; and Lightwave, 98 Spit Brook Road,

Suite 100, Nashua, NH 03062–5737.

32. The ‘‘ﬂoat’’ method for manufacturing plate glass

(developed by Pilkington Glass) involves the drawing of the

molten glass from a furnace, where the molten glass ﬂoats on

the surface of liquid tin. The naturally ﬂat surface of the

liquid metal ensures the production of much larger sheets of

better-ﬂatness glass than was possible by earlier techniques.

33. Alexander Hornberg (Ed.), Handbook of Machine Vision,

John Wiley & Sons, Inc., New York, 2006.

34. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari,

Opt. Lett., 17, 363–365, 1992.

35. C. J. Hood, H. J. Kimble, and J. Ye, Phys. Rev. A, 64,033804,

2001.

36. H. R. Bilger, P. V. Wells, and G. E. Stedman, Appl. Opt., 33,

7390–7396, 1994.

37. H.-J. Cho, M.-J. Shin, and J.-C. Lee, Appl. Opt. 45, 1440–

1446, 2006.

38. A. B. Meinel, in Applied Optics and Optical Engineering,

Vol. 5, R. Kingslake (Ed.), Academic Press, New York,

1969.

39.

W. Brouwer and A. Walther, Design of optical instruments,

in Advanced Optical Techniques, A. C. S. Van Heel, (Ed.),

North-Bouand, Amsterdam, 1967.

40. Celestron Telescopes are available from Celestron

International, 2835 Columbia Street, P.O. Box 3578,

Torrance, CA 90503; (310) 328–9560.

41. Meade Telescopes are available from Meade Instruments

Corporation, 6001 Oak Canyon, Irvine, California

92618–5200, (949) 451–1450.

42. W. T. Wellford and R. Winston, High Collection Nonimaging

Optics, Academic Press, San Diego, CA, 1989.

43. R. Winston, J. C. Min

ano, and P. G. Benitez, Nonimaging

Optics, Elsevier, Amsterdam, 2005.

44. A. Girard and P. Jacquinot, in Advanced Optical

Techniques,A.C.S.VanHeel(Ed.),North-Bouand,

Amsterdam, 1967.

45. J. D. Strong, Procedures in Experimental Physics,

Prentice-Hall, Englewood Cliffs, NJ, 1938.

46. David R. Lide (Ed.), Handbook of Chemistry and Physics,

81st. edn., CRC Press, Boca Raton, FL, 2000.

47. D. R. Goff, Fiber Optic Reference Guide, 3rd edn., Focal

Press (Elsevier), Amsterdam, 2002.

48. U. Hochuli and P. Haldemann, Rev. Sci. Instr., 43, 1088–

1089, 1972.

49. Epoxy-removing solvents are available from Electron

Microscopy Services, Oakite, or Hydroclean.

50. T. C. Poulter, Phys. Rev., 35,297,1930.

51. W. Paul, W. W. Meis, and J. M. Besson, Rev. Sci. Instr., 39,

928–930, 1968.

52. I. L. Spain and J. Paawe (Eds.), High Pressure Technology,

Dekker, New York, 1967.

53. Compilation of ASTM Standard Deﬁnitions, 3rd edn.,

American Society for Testing and Materials, Philadelphia,

1976.

REFERENCES 315

54. Glass, quartz, and sapphire vacuum window assembles are

available from Adolf Meller, Ceramaseal, Varian, and

Vacuum Generators.

55. D. H. Martin (Ed.), Spectroscopic Techniques for Far

Infra-Red, Submillimetre and Millimetre Waves,

NorthHolland, Amsterdam, 1967.

56. K. D. Moller and W. G. Rothschild, Far-Infrared

Spectroscopy, Wiley-Interscience, New York, 1971.

57. A. Hadni, Essentials of Modern Physics Applied to the

Study of the Infrared, Pergamon Press, Oxford, 1967.

58. G. A. Fry, Applied Optics and Optical Engineering, Vol. 2,

R. Kingslake (Ed.), Academic Press, 1965.

59. C. C. Davis and R. A. McFarlane, J. Quant. Spect. Rad.

Trans., 18, 151–170, 1977.

60. P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan,

Elements of Infrared Technology: Generation,

Transmission and Detection, John Wiley & Sons, Inc.,

New York, 1962.

61. R. D. Hudson, Jr., Infrared System Engineering,

Wiley-Interscience, New York, 1969.

62. J. A. R. Samson, Techniques of Vacuum Ultraviolet

Spectroscopy, John Wiley & Sons, Inc., New York, 1967.

63. Available from EG&G Optoelectronics, ILC, Verre &

Quartz, and Xenon Corporation.

64. Available from EG&G Optoelectroncs, Verre & Quartz,

Resonance, and Xenon Corporation.

65. J. P. Markiewicz and J. L. Emmett, IEEE J. Quant. Elec-

tron., QE-2, 707–711, 1966.

66. J. G. Edwards, Appl. Opt., 6, 837–843, 1967.

67. H. J. Baker and T. A. King, J. Phys. E.: Sci. Instr., 8, 219–

223, 1975.

68. William T. Silfvast, Laser Fundamentals, 2nd edn.,

Cambridge University Press, Cambridge, 2004.

69. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics,

John Wiley & Sons, Inc., New York, 1991.

70. A. E. Siegman, Lasers, University Science Books, Mill

Valley, CA, 1986.

71. H. Rabin and C. L. Tang (Eds.), Quantum Electronics, Vols.

1A and 2A, Nonlinear Optics, Academic Press, New York,

1975.

72. Nonlinear Optics, Proceedings of the Sixteenth Scottish

Universities Summer School in Physics, 1975, P. G. Harper

and B. S. Wherrett (Eds.), Academic Press, London, 1977.

73. N. Bloembergen, Nonlinear Optics, Benjamin, New York,

1965.

74. F. Zernike and J. E. Midwinter, Applied Nonlinear Optics,

John Wiley & Sons, Inc., New York, 1973.

75. R. W. Boyd, Nonlinear Optics, Academic Press,

Boston, 1992.

76. D. Ro

ss, Lasers, Light Ampliﬁers and Oscillators,

Academic Press, New York, 1969.

77. W. Koechner, Solid

State Laser Engineering, 5th revised

and updated edn., Springer-Verlag, Berlin, 1999.

78. F. P. Scha

fer (Ed.), Topics in Applied Physics, Vol. 1, Dye

Lasers, 3rd revised and enlarged edn., Springer-Verlag,

Berlin, 1990.

79. H. W. Furumoto and H. L. Ceccon, Appl. Opt., 8, 1613–

1623, 1969.

80. J. F. Holzrichter and A. L. Schawlow, Ann. N.Y. Acad. Sci.,

168, 703–714, 1970.

81. T. B. Lucatorto, T. J. McIlrath, S. Mayo, and H. W.

Furumoto, Appl. Opt., 19, 3178–3180, 1980.

82. C. C. Davis and T. A. King, Advances in Quantum Elec-

tronics, Vol. 3, D. W. Goodwin (Ed.), Academic Press,

London, 1975, pp. 169–454.

83. W. B. Bridges, Handbook of Laser Science and Technology,

Vol. 1: Lasers in All Media, M. J. Weber (Ed.), CRC Press,

Boca Raton, FL, 1982.

84. C. C. Davis, Handbook of Lasers Science and Technology,

Vol. 1, Lasers in All Media, M. J. Weber (Ed.), CRC Press,

Boca Raton, FL, 1982.

85. D. C. Tyte, Advances in Quantum Electronics, Vol. 1, D. W.

Goodwin (Ed.), Academic Press, London, 1970.

86. J. J. Degnan, Appl. Phys., 11, 1–33, 1976.

87. H. Seguin and J. Tulip, Appl. Phys. Lett., 21, 414–415,

1972.

88. J. D. Cobine, Gaseous Conductors, Dover, New York, 1958.

89. H. J. Seguin, K. Manes, and J. Tulip, Rev. Sci. Instr., 43,

1134–1139, 1972.

90. A. J. Beaulieu, Appl. Phys. Lett., 16, 504–505, 1970.

91. D. Basting, F. P. Scha

fer, and B. Steyer, Opto-electron., 4,

43–49, 1972.

92. P. Schenck and H. Metcalf, Appl. Opt., 12, 183–186, 1973.

93. C. P. Wang, Rev. Sci. Instr., 47, 92–95, 1976.

94. A. J. Schwab and F. W. Bouinger, IEEE J. Quant,. Elec-

tron., QE-12

, 183–188, 1976.

95.

C. L. Sam, Appl. Phys. Lett., 29, 505–506, 1976.

96. M. Feldman, P. Lebow, F. Raab, and H. Metcalf, Appl. Opt.,

17, 774–777, 1978.

97. M. J. F. Digonnet (Ed.), Rare Earth Doped Fiber Lasers

And Ampliﬁers, 2nd Revised edn., Taylor & Francis Ltd.,

Abingdon, 2001.

98. L. F. Mollenauer, Opt. Lett., 1, 164, 1977 (see also Opt.

Lett. 3, 48–50, 1978; 4, 247–299, 1979; 5, 188–190,

1980).

99. R. C. Greenhow and A. J. Schmidt, Advances in Quantum

Electronics, Vol. 2, D. W. Goodwin (Ed.), Academic Press,

London, 1973.

316 OPTICAL SYSTEMS

100. S. L. Shapiro (Ed.), Ultrashort Light Pulses, Picosecond

Techniques and Applications, Topics in Applied Physics,

Vol. 18, Springer, Berlin, 1977.

101. C. H. Lee (Ed.), Picosecond Optoelectronic Devices,

Academic Press, Orlando, FL, 1984.

102. P. Bhattacharya, Semiconductor Optoelectronic Devi-

ces, 2nd edn., Prentice-Hall, Upper Saddle River, NJ,

1997.

103. J. Gowar, Optical Communication Systems, 2nd edn.,

Prentice-Hall, Englewood Cliffs, NJ, 1993.

104. D. Wood, Optoelectronic Semiconductor Devices,

Prentice-Hall, New York, 1994.

105. G. P. Agrawal and N. K. Dutta, Long-Wavelength

Semiconductor Lasers, Van Nostrand Reinhold,

New York, 1986.

106. G. H. B. Thompson, Physics of Semiconductor Laser

Devices, John Wiley & Sons, Ltd, Chichester, 1980.

107. S. L. Chuang, Physics of Optoelectronic Devices, John

Wiley & Sons, Inc., New York, 1995.

108. J. Singh, Semiconductor Optoelectronics, McGraw-Hill,

New York, 1995.

109. H. Kressel (Ed.), Semiconductor Devices for Optical

Communication, Vol. 39, Topics in Applied Physics, 2nd

updated edn., Springer-Verlag, Berlin, 1982.

110. E. Kapon (Ed.), Semiconductor Lasers, Vols. 1 and 2,

Academic Press, San Diego, CA, 1999.

111. E. D. Hinkley, K. W. Nill, and F. A. Blum, Topics in

Applied Physics, Vol. 2, H. Walther (Ed.), Springer, Ber-

lin, 1976, pp. 125–196.

112. J. Faist, F. Capasso, D. L. Sivco, et al., Science, 264

(5158), 553–556, 1994.

113. T. J. Kane and R. L. Byer, Optics Lett., 10, 65–67, 1985.

114. T. W. Ha

nsch, Appl. Opt., 11, 895–898, 1972.

115. R. Wallenstein and T. W. Ha

nsch, Appl. Opt., 13, 1625–

1628, 1974.

116. R. Wallenstein and T. W. Ha

nsch, Opt. Commun., 14, 353–

357, 1975.

117. G. L. Eesley and M. D. Levenson, IEEE J. Quant. Elec-

tron. QE-12, 440–442, 1976.

118. M. G. Littman and H. J. Metcalf, Appl. Opt., 17, 2224–

2227, 1978.

119. M. Littman and J. Montgomery, Laser Focus/Electro-

optics,

24,

70–86, 1988.

120. M. B. Radunsky, Laser Focus World, p. 107, October

1995.

121. B. J. Orr et al., Tunable Laser Applications, F. J. Duarte

(Ed.), Marcel Dekker, New York, 1995.

122. R. G. Batchko, D. R. Weise, T. Plettner, et al., Opt. Lett.

23(3), 168, 1998.

123. M. E. Klein, D.-H. Lee, J.-P. Meyn, K.-J. Boller, and

R. Wallenstein, Opt. Lett., 24, 1142–1144, 1999.

124. F. Mu

ller, G. von Basum, A. Popp, et al., Appl. Phys. 80,

307–313, 2004.

125. I. P. Kaminow, An Introduction to Electro-optic Devices,

Academic Press, New York, 1974.

126. A. Korpel, Acousto-Optics, Marcel Dekker, New York,

1988, see also Acousto-Optics – a review of fundamentals,

Proc. IEEE., 69, 48–53, 1981.

127. I. C. Chang, IEEE Trans. Sonics and Ultrasonics, SU-23,

2–22, 1976.

128. American National Standard for Safe Use of Lasers,

ANSI Z136-2-2000, Published by the Laser Institute of

America, Suite 128, 13501 Ingenuity Drive, Orlando, FL

32826.

129. D. Sliney and M. Wolbarsht, Safety with Lasers and Other

Optical Sources: A Comprehensive Handbook, Plenum,

New York, 1980.

130. M. J. Weber (Ed.), CRC Handbook of Laser Science and

Technology, Vol. 1, Lasers and Masers, CRC Press, Boca

Raton, FL, 1982.

131. P. Jacquinot, J. Opt. Soc. Am., 44, 761–765, 1954.

132. R. Kingslake (Ed.), Applied Optics and Optical Engi-

neering, Vol. 5: Optical Instruments Part II, Academic

Press, New York, 1969.

133. J. F. James and R. S. Sternberg, The Design of Optical

Spectrometers, Chapman and Hall, London, 1969.

134. The Photonics Design and Applications Handbook,

published annually by Laurin Publishing Co. Inc.,

Pittsﬁeld, MA.

135. W. G. Fastie, J. Opt. Soc. Am., 42, 641–647, 1952.

136. H. Ebert, Annalen der Physik und Chemie, 38, 489–493,

1889.

137. M. Seya, Sci. Light (Tokyo), 2, 8–17, 1952.

138. T. Namioka, Sci. Light (Tokyo),

15–24, 1952.

139. P. Atherton, N. Reay, J. Ring, and T. Hicks, Opt. Eng., 20,

806, 1981.

140. Available from numerous suppliers of vacuum equipment –

for example, Ceram Tec (Ceramaseal Division), Edwards,

Ferroﬂuidics Corp., Perkin Elmer, Vacuum Generators

(VG), Varian, and Veeco.

141. Available from Carpenter Technology, P.O. Box 14662,

Reading, PA 19612–4662; Tel: (800) 338–4592 and (610)

208–2000, FAX: (610) 208–2361.

142. Available from Burleigh.

143. Available from Heraeus-Amersil, Dynasil, Esco, and

Quartz Scientiﬁc, among others.

144. Available from Corning Glass Works, Optical Products

Department.

REFERENCES 317

145. Piezoelectric transducers are available from American

Piezo Ceramics, Burleigh, EDO, Polytec, Queensgate

Instruments, and Xinetics, among others.

146. C. F. Bruce, Appl. Opt., 5, 1447–1452, 1966.

147. Commercial Fabry–Perot Interferometers that can

incorporate this feature are available from Burleigh.

148. P. Hariharan, Optical Interferometry, 2nd edn., Academic

Press, 2003.

149. B. T. Meggitt and K. T. V. Grattan, Optical Fiber Sensor

Technology, Springer, New York, 1999.

150. James C. Wyant, White light interferometry, paper

presented at AeroSense, Orlando, Florida, 1–5 April

2002. (Available online at fttp://www.optics.arizona.edu/

jcwyant/pdf/Meeting_papers/WhiteLightInterferometry.pdf)

151. R. Ladenburg and D. Bershader, High Speed Aerody-

namics and Jet Propulsion, Vol. 9, Physical Measurements

in Gas Dynamics and Combustion, R. Ladenburg (Ed.),

Princeton University Press, Princeton, NJ, 1954.

152. P. R. Longaker and M. M. Litvak, J. Appl. Phys., 40,

4033–4041, 1969.

153. D.C. Smith, IEEE J. Quant. Electron., QE-5, 600–607, 1969.

154. H. Kuhn, Rep. Prog. Phys., 14, 64–94, 1951.

General References

Comprehensive (General)

Optics Texts

M. Born and E. Wolf, Principles of Optics, 7th edn., Cambridge

University Press, Cambridge, 1999.

E. Hecht, Optics, 3rd edn., Addison-Wesley, Reading, MA, 1998.

R. W. Ditchburn, Light, 3rd edn., Academic Press, New York, 1976.

F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th edn.,

McGraw-Hill, New York, 1976.

M. V. Klein and T. E. Furtak, Optics, 2nd edn., John Wiley &

Sons, Inc., New York, 1986.

R. S. Longhurst, Geometrical and Physical Optics, 3rd edn.,

Longman, London, 1973.

F. G. Smith and J. H. Thomson, Optics, 2nd edn., John Wiley &

Sons, Inc., Chichester, 1988.

J. Strong, Concepts of Classical Optics, Freeman, San Francisco,

CA, 1958.

Applied Optics

W. J. Smith, Modern Optical Engineering, 3rd edn., SPIE Press,

Bellingham, WA, 2000.

R. Kingslake (Ed.), Applied Optics and Optical Engineering

Academic, New York, Vol. 1, 1965; Vol. 2, 1965; Vol. 3, 1965;

Vol. 4, 1967; Vol. 5, 1969.

L. Levi, Applied Optics, John Wiley & Sons, Inc., New York,

Vol. 1, 1968; Vol. 2, 1980.

Lens Design

W. J. Smith, Modern Lens Design: A Resource Manual,

McGraw-Hill, New York, 1992.

R. R. Shannon, The Art and Science of Optical Design,

Cambridge University Press, Cambridge, 1997.

M. Laikin, Lens Design, 3rd edn., Marcel Dekker, New York,

2001.

Electro-Optic Devices

M. A. Karim, Electro-Optical Devices and Systems, PWS-Kent

Publishing, Boston, MA, 1990.

I. P. Kaminow, An Introduction to Electro-Optics, Academic

Press, New York, 1974.

A. Yariv, Optical Electronics in Modern Communications,

5th edn., Oxford University Press, New York, 1997.

Far-Infrared Techniques

M. F. Kimmitt, Far-Infrared Techniques, Routledge, 1970.

A. Hadni, Essentials of Modern Physics Applied to the Study

of the Infrared, Pergamon Press, Oxford, 1967.

K. D. Mo

ller and W. G. Rothschild, Far-Infrared Spectroscopy,

Wiley-Interscience, New York, 1971.

L. C. Robinson, Physical Principles of Far-Infrared Radiation,

Methods in Experimental Physics, Vol. 10, L. Marton (Ed.),

Academic Press, New York, 1973.

Fiber Optics

J. Hecht, Understanding Fiber Optics, 3rd edn., Prentice-Hall,

Upper Saddle River, NJ, 1999.

A. Ghatak and K. Thyagarajan, Introduction to Fiber

Optics, Cambridge University Press, Cambridge, 1998.

A. Ghatak, A , Sharma, and R. Tewari, Understanding

FiberOpticsonaPC, Viva Books P rivate Ltd., New

Delhi, 1994. P.K. Cheo, Fiber Optics and Optoelectronics,

2nd edn., Prentice-Hall, Englewood Cliffs, NJ, 1990. L.

Kazovsky, S. Benedetto, and A. Willner, Optical Fiber

Communication Systems,ArtechHouse,Boston,MA,

1996.

318 OPTICAL SYSTEMS

J. Gowar, Optical Communication Systems, 2nd edn. Prentice-

Hall, Englewood Cliffs, NJ, 1993.

M. K. Barnoski, (Ed.,) Introduction to Integrated Optics, Plenum,

New York, 1974.

D. Marcuse, Principles of Optical Fiber Measurements,

Academic Press, San Diego, CA., 1981.

T. Okoshi, Optical Fibers, Academic Press, New York, 1982.

D. Gloge (Ed.), Optical Fiber Technology, IEEE, New York,

1976.

J. C. Palais, Fiber Optic Communications, 5th edn.,

Prentice-Hall, Upper Saddle River, NJ, 2004.

A. D. Snyder and J. D. Love, Optical Waveguide Theory,

Chapman and Hall, London and New York, 1983.

Filters

D. R. Lide (Ed.), Handbook of Chemistry and Physics, 87th

edn., Taylor and Francis, Boca Raton, Florida, 2000. Also

available on line at http://www.hbcpnetbase.com/help/

default.asp

R. J. Pressley (Ed.), Handbook of Lasers, CRC Press, Cleveland,

OH, 1971.

L. Levi, Applied Optics, Vol. 2, John Wiley & Sons, Inc., New

York, 1980.

H. A. Macleod, Thin-Film Optical Filters, American Elsevier,

New York, 1969.

E. J. Bowen, Chemical Aspects of Light, 2nd revised edn., The

Clarendon Press, Oxford, 1946.

Fourier Transform Spectroscopy

P. Grifﬁths and J. deHaseth, Fourier Transform Infrared

Spectroscopy, John Wiley & Sons, Inc., New York,

1986.

B. C. Smith, Fundamentals of Fourier Transform Infrared

Spectroscopy, CRC Press Inc., Boca Raton, IL, 1996.

Incoherent Light Sources

A. C. S. Van Heel (Ed.), Advanced Optical Techniques,

North-Bouand, Amsterdam, 1967.

R. Kingslake (Ed.), Applied Optics and Optical Engineering,

Vol. 1, Academic Press, New York, 1965.

R. J. Pressley (Ed.), Handbook of Lasers, CRC Press, West Palm

Beach, FL, 1971.

L. Levi, Applied Optics, Vol. 1, John Wiley & Sons, Inc., New

York, 1968.

Photometry

C. DeCusatis, Handbook of Applied Photometry, AIP Press, New

York, (1997).

M. Rea (Ed.), Lighting Handbook: Reference and Application,

8th edn., Illuminating Engineering Society of North America,

New York, 1993.

Infrared Technology

W. L. Wolfe and G. J. Zissis (Eds.), The Infrared Handbook,

Ofﬁce of Naval Research, Washington, DC, 1985.

A. R. Jha, Infrared Technology, John Wiley & Sons, Inc., New

York, 2000.

A. Hadni, Essentials of Modern Physics Applied to the Study of

the Infrared, Pergamon Press, Oxford, 1967.

R. D. Hudson, Infrared System Engineering,

Wiley-Interscience, New York, 1969.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements

of Infrared Technology, John Wiley & Sons, Inc., New York,

1962.

Interferometers and Interferometry

P. Hariharan, Optical Interferometry, Academic Press, Orlando,

FL, 1985.

G. Hernandez, Fabry–Perot Interferometers, Cambridge

University Press, Cambridge, 1986.

R. Jones and C. Wykes, Holographic and Speckle

Interferometry, 2nd edn., Cambridge University Press,

Cambridge, 1989.

J. C. Dainty (Ed.), Laser Speckle and Related Phenomena, Topics

in Applied Physics, Vol. 9, Springer-Verlag, Berlin; New York,

1975.

M. Francon, Laser Speckle and Applications in Optics, Academic

Press, New York, 1979.

M. Born and E. Wolf, Principles of Optics, 7th edn., Cambridge

University Press, Cambridge, 1999.

M. Francon, Optical Interferometry, Academic Press, New York,

1966.

W. H. Steel, Interferometry, 2nd edn., Cambridge University

Press, Cambridge, 1983.

S. Tolansky, An Introduction to Interferometry, Longman,

London, 1955.

J. M. Vaughan, The Fabry–Perot Interferometer: History,

Theory, Practice and Applications, Adam Hilger, Bristol, UK,

1989.

REFERENCES 319

Fourier Optics and Holography

J. Goodman, Introduction to Fourier Optics, 2nd edn., McGraw-

Hill, New York, 1996.

P. Hariharan, Optical Holography, Cambridge University Press,

Cambridge, 1984.

Lasers

A. Yariv, Optical Electronics in Modern Communications, 5th

edn., Oxford University Press, New York, 1997.

C. C. Davis, Lasers and Electro-Optics, Cambridge University

Press, Cambridge, 1996.

C. R. Pollack, Fundamentals of Optoelectronics, Irwin, Chicago,

1995.

W. T. Silfvast, Laser Fundamentals, 2nd edn., Cambridge Uni-

versity Press, 2004.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd

edn., John Wiley & Sons, Inc., New York, 2007.

M. Weber (Ed.), Handbook of Laser Science and Technology,

Vol. 1, Lasers and Masers; Vol. II, Gas Lasers, CRC Press,

Boca Raton, FL, 1982.

A. Maitland and M. H. Dunn, Laser Physics, North

Holland, Amsterdam, 1969.

D. C. O’Shea, W. R. Callen, and W. T. Rhodes, Introduction to

Lasers and Their Applications, Addison-Wesley, Reading,

MA, 1977.

J. T. Verdeyen, Laser Electronics, 3rd edn., Prentice-Hall,

Englewood Cliffs, NJ, 1995.

A. Yariv, Quantum Electronics, 3rd edn., John Wiley & Sons,

Inc., New York, 1989.

A. E. Siegman, Lasers, University Science Books, Mill Valley,

CA, 1986.

Nonlinear Optics

R. W. Boyd, Nonlinear Optics, Academic Press, Boston, MA,

1992.

N. Bloembergen, Nonlinear Optics, Benjamin, New York, 1965.

P. G. Harper and B. S. Wherrett (Eds.), Nonlinear Optics,

Academic Press, New York, 1977.

C. L. Tang and H. Rabin, (Eds.), Quantum Electronics, Vols.

1A and 2A Nonlinear Optics, Academic Press, New York,

1975.

F. Zernike and J. E. Midwinter, Applied Non-Linear Optics, John

Wiley & Sons, Inc., New York, 1973.

Y. R. Shen, The Principles of Nonlinear Optics, John Wiley &

Sons, Inc., New York, 1984.

Optical Component and Instrument Design

A. C. S. Van Heel (Ed.), Advanced Optical Techniques,

North Holland, Amsterdam, 1967.

R. Kingslake (Ed.), Applied Optics and Optical Engineering,

Academic Press, New York, Vol. 3, 1965; Vol. 4, 1967; Vol. 5,

1969.

Optical Detectors

A. Rogalksi, Infrared Detectors, Gordon and Breadh, Amster-

dam, 2000.

J. Gowar, Optical Communication Systems, 2nd edn.,

Prentice-Hall, Englewood Cliffs, NJ, 1993.

E. L. Dereniak and G. D. Boreman, Infrared Detectors and

Systems, John Wiley & Sons, Inc., New York, 1996.

E. L. Dereniak and D. G. Crowe, Optical Radiation Detectors,

John Wiley & Sons, Inc., New York, 1984.

J. Graeme, Photodiode Ampliﬁers, McGraw-Hill, New York,

1996.

J. B. Dance, Photoelectronic Devices, Iliffe, London, 1969.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements

of Infrared Technology, John Wiley & Sons, Inc., New York,

1962.

L. Levi, Applied Optics, Vol. 2, John Wiley & Sons, Inc., New

York, 1980.

R. S. Keyes (Ed.), Optical and Infrared Detectors, Topics in

Applied Physics, Vol. 19, Springer, Berlin, 1977.

Optical Materials

R. Kingslake (Ed.), Applied Optics and Optical Engineering,

Vol. 1, Academic Press, New York, 1965.

M. Weber (Ed.), Handbook of Laser Science and Technology,

Vols. III–V, Optical Materials, CRC Press, Boca Raton, FL,

1986–87.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements

of Infrared Technology, John Wiley & Sons, Inc., New York,

1962.

A. J. Moses, Optical Material Properties, IFI/Plenum, New York,

1971.

Optical Safety

M. J. Weber (Ed.), Handbook of Laser Science and

Technology, Vol. 1, Lasers and Masers, CRC Press, Boca

Raton, FL, 1982.

320 OPTICAL SYSTEMS

D. Sliney and M. Wolbarsht, Safety with Lasers and Other

Optical Sources: A Comprehensive Handbook, Plenum, New

York, 1980.

Polarized Light and Crystal Optics

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized

Light, North-Bouand, Amsterdam, 1977.

D. Goldstein, Polarized Light, CRC Press, Boca Raton, FL, 2003.

W. A. Shurcliff, Polarized Light, Harvard University Press,

Cambridge, MA, 1962.

E. Wahlstrom, Optical Crystallography, 5th edn., John Wiley &

Sons, Inc., New York, 1979.

A. Yariv and P. Yeh, Optical Waves in Crystals,JohnWiley&Sons,

Inc., New York, 1983.

Spectrometers

N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to

Infrared and Raman Spectroscopy, 2nd edn., Academic Press,

New York, 1975.

Francis M. Mirabella Jr., (Ed.), Internal Reﬂection

Spectroscopy. Theory and Applications, CRC Press, Boca

Raton, 1993.

J. F. James and R. S. Sternberg, The Design of Optical

Spectrometers, Chapman & Hall, London, 1969.

H. S. Strobel and W. R. Heineman, Chemical Instrumentation,

3rd edn., John Wiley & Sons, Inc., New York, 1989.

Spectroscopy

M. Pinta (Ed.), Atomic Absorption Spectrometry, John Wiley &

Sons, Inc., New York, 1975.

J. R. Edisbury, Practical Hints on Absorption Spectrometry,

Hilger and Watts, London, 1966.

R. J. Reynolds and K. Aldous, Atomic Absorption Spectroscopy,

Barnes and Noble, New York, 1970.

A. Lee Smith, Applied Infrared Spectroscopy: Fundamentals,

Techniques and Analytical Problem-Solving, Vol. 54

(Chemical Analysis, Vol. 21), John Wiley & Sons, Inc.,

New York, 1979.

R. A. Sawyer, Experimental Spectroscopy, Prentice-Hall,

Englewood Cliffs, NJ, 1951.

D. Williams (Ed.), Methods of Experimental Physics, Vol. 13,

Spectroscopy, Parts A and B, Academic Press, New York,

1968.

S. Walker and H. Straw, Spectroscopy, Vol. I, Microwave and

Radio Frequency Spectroscopy; Vol. II, Ultraviolet, Visible,

Infrared and Raman Spectroscopy, Macmillan, New York,

1962.

Submillimeter Wave Techniques

K. J. Button, Infrared and Millimeter Waves:

Submillimeter Techniques, Academic Press, New York,

1980.

G. W. Chantry, Submillimeter Spectroscopy, Academic Press,

New York, 1971.

E. Kollberg (Ed.), Instrumentation for submillimeter

spectroscopy, SPIE Proceedings, Vol. 598, SPIE, Bellingham,

WA, 1986.

D. H. Martin (Ed.), Spectroscopic Techniques, North-Holland,

Amsterdam, 1967.

Tables of Physical and Chemical Constants

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical

Constants, 16th edn., Longman, London, 1995. Now available

free online at http://www.kayelaby.npl.co.uk/

Tables of Spectral and Laser Lines

M. J. Weber, Handbook of Lasers, CRC Press, Boca Raton, FL,

2001.

M. J. Weber, Handbook of Laser Wavelengths, CRC Press, Boca

Raton, FL, 1999.

G. R. Harrison, MIT Wavelength Tables, MIT Press, Cambridge,

MA, 1969.

A. R. Striganov and N. S. Sventitskii, Tables of Spectral Lines

of Neutral and Ionized Atoms, IFI/Plenum, New York,

1968.

A. N. Zaidel’, V. K. Prokof’ev, S. M. Raiskii, V. A. Slavnyi, and

E. Ya. Shreider, Tables of Spectral Lines, IFI/Plenum, New

York, 1970.

Ultraviolet and Vacuum-Ultraviolet

Technology

A. E. S. Green (Ed.), The Middle Ultraviolet: Its Science

and Technology, John Wiley & Sons, Inc., New York, 1966.

J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy,

John Wiley & Sons, Inc., New York, 1967.

REFERENCES 321

Suppliers of Optical Windows

Several of the suppliers listed will supply lenses, prisms, and

other components fabricated from these materials:

AMTIR (GeAsSe Glass): Harrick Scientiﬁc, Janos, REFLEX

Analytical

Arsenic trisulﬁde: Infrared Optical Products, REFLEX

Analytical, Spectrum Thin Films Corp.

Arsenic triselenide: Infrared Optical Products, REFLEX

Analytical, Spectrum Thin Films Corp.

Barium ﬂuoride: Crystran, Del Mar Photonics, Harrick Scientiﬁc,

Infrared Optical Products, ISP Optics, Janos, Koch Crystal

Finishing, Molecular Technology.

Cadmium sulﬁde: Cleveland Crystals, Molecular Technology.

Cadmium selenide: Cleveland Crystals, Molecular Technology.

Cadmium telluride (Irtran 6): Cleveland Crystals, ISP Optics,

Janos, Laser Research Optics, Molecular Technology.

Calcium carbonate (calcite): Crystran, Karl Lambrecht Corp

(KLC), Photox, Thin Film Lab.

Calcium ﬂuoride (Irtran 3): Argus International, Coherent, Inc.,

Crystran, Edmund Optics, EKSPLA, Gooch and Housego,

Hellma International, Infrared Optical Products, ISP Optics,

Janos, KLC, Koch Crystal Finishing, Lambda Research

Optics, Meller Optics, Molecular Technology, Newport,

Optimax, Opto-Sigma, Photox, REFLEX Analytical, Rocky

Mountain Instruments, Spectrum Thin Films, Thorlabs.

Cesium bromide: Argus International, Crystran, Harrick

Scientiﬁc, Janos.

Cesium iodide: Crystran, Koch Crystal Finishing, Molecular

Technology, REFLEX Analytical.

Diamond: Argus International, Gist Optics, Coherent

Photonics Group, II-VI Infrared, ISP Optics, Laser Power

Optics, REFLEX Analytical, Optics for Research,

Newport/Oriel.

Gallium arsenide: Argus International, Crystran, Infrared Optical

Products, II-VI Infrared, ISP Optics, Lambda Research Optics,

Laser Power Optics, Laser Research Optics, Meller Optics,

REFLEX Analytical, Rocky Mountain Instruments, Sterling

Precision Optics.

Germanium: Argus International, Coherent, Inc., Crystran,

Edmund Optics, Gooch and Housego, II-VI Infrared, ISP

Optics, Janos, Laser Power Optics, Laser Research Optics,

Meller Optics, Photox, REFLEX Analytical, Rocky Mountain

Instruments, Spectrogon, Spectrum Thin Films Corporation,

Sterling Precision Optics, Unicore.

Glasses: Coherent, Ealing, Edmund Optics, Newport,

Opto-Sigma, Rocky Mountain Instruments, Rolyn, Schott,

Sterling Precision Optics, Thorlabs.

Lithium ﬂuoride: Argus International, Crystran, Coherent, Inc.,

EKSPLA, Hellma International, Infrared Optical Products, ISP

Optics, Lambda Research Optics, Macrooptica, Molecular

Technology, OPCO, Photox, REFLEX Analytical, Rocky

Mountain Instrument Co., Sterling Precision Optics.

Magnesium ﬂuoride (Irtran 1): Argus International, Coherent,

Inc., Crystran, Edmund Optics, EKSPLA, Gooch and

Housego, Hellma International, Infrared Optical Products, ISP

Optics, KLC, Lambda Research Optics, Macrooptica, Meller

Optics, Molecular Technology, Newport, Optimax, Photox,

REFLEX Analytical, Rocky Mountain Instruments, Sterling

Precision Optics.

Magnesium oxide (Irtran 5): Crystran, Harrick Scientiﬁc.

Potassium bromide: Argus International, Crystran, EKSPLA,

Hilger Crystals, Infrared Optical products, ISP Optics, Janos,

Koch Crystal Finishing, Lambda Research Optics,

Macrooptica, Molecular Technology, OPCO, Photox,

REFLEX Analytical Corp., Spectrum Thin Films Corp.,

Thorlabs.

Potassium chloride: Crystran, ISP Optics, Janos, Koch Crystal

Finishing, Macrooptica, Molecular Technology, Optovac,

Photox.

Potassium iodide: Crystran.

Quartz (crystalline): Crystran, Esco, Infrared Optical Products,

ISP Optics, Janos, Meller Optics, Molecular Technology,

Newport, Opto-Sigma, Photox, REFLEX Analytical, Sterling

Precision Optics, Continental Optical, Optics for Research,

Newport/Oriel, Adolf Meller.

Sapphire: Crystran, Infrared Optical Products, ISP Optics, Laser

Power Optics, Meller Optics, Newport, Opto-Sigma, REFLEX

Analytical, Rocky Mountain Instruments, Rolyn, Sterling

Precision Optics.

Silica (fused): Esco, ISP Optics, Janos, Macrooptica, Meller

Optics, Newport, Opto-Sigma, Photox, REFLEX Analytical,

Rolyn, Schott, Sterling Precision Optics, Thorlabs, Continental

Optical, Optical Coating Lab (OCLI).

Silicon: Crystran, Infrared Optical Products, ISP Optics, Janos,

Laser Power Optics, Macrooptica, Meller Optics, Molecular

Technology, Photox, REFLEX Analytical, Rocky Mountain

Instruments, Sterling Precision Optics.

Silver bromide: Crystran, Harrick Scientiﬁc, ISP Optics,

REFLEX Analytical.

Silver chloride: Crystran, Harrick Scientiﬁc, ISP Optics,

REFLEX Analytical.

Sodium chloride: Crystran, ISP Optics, Koch Crystal Finishing,

Macrooptica, Molecular Technology, Photox.

Sodium ﬂuoride: Crystran.

Strontium ﬂuoride: Crystran, Harrick Scientiﬁc.

322 OPTICAL SYSTEMS

Strontium titanate: Commercial Crystal Labs, Harrick Scientiﬁc,

Hibshman-Paciﬁc Optical, Photox.

Tellurium: Molecular Technology.

Thallium bromide: Crystran, Korth Kristalle GmbH.

Thallium bromoiodide (KRS-5): Argus International, Crystran,

Infrared Optical Products, ISP Optics, Janos, Koch Crystal

Finishing, Macrooptica, Molecular Technology, Perkin-Elmer.

Thallium chlorobromide (KRS-6): Crystran, Macrooptica,

Molecular Technology.

Titanium dioxide (rutile): Commercial Crystal Labs, Crystran,

Harrick Scientiﬁc, ISP Optics, Molecular Technology, Thin

Film Lab.

Zinc selenide (Irtran 4): Argus International, Coherent, Inc.,

Crystran, CVI Laser, Edmund Optics, EKSPLA, Gooch and

Housego, Harrick Scientiﬁc, Hellma International, II-VI

Infrared, Infrared Optical Products, ISP Optics, Janos, Laser

Power Optics, Laser Research Optics, Meller Optics, Molec-

ular Technology, REFLEX Analytical, Rocky Mountain

Instruments, Sterling Precision Optics.

Zinc sulﬁde (Irtran 2): Crystran, Gooch a nd Housego, Infrared

Optical Products, Laser Power Optics, Laser Resea rch

Optics, Meller, OPCO, Optimax, REFLEX Analytical,

Rocky Mountain Instruments, Sterling Precision Optics,

Zirconium dioxide: Insaco.

REFERENCES 323

CHARGED-PARTICLE OPTICS

Fifty years ago devices employing charged-particle beams

were conﬁned to the purview of a small group of physicists

studying elementary processes. Today chemists, biologists,

and engineers employ beams of ions or electrons to probe

various materials and to investigate discrete processes.

Physicists are constructing beam machines to control the

momentum of interacting particles with energies from a

few tenths of an electron volt to trillions of electron volts.

Chemists routinely use mass spectrometers as analytical

tools and various electron spectrometers to probe molecular

structures. The electron microscope is one of the primary

tools of the modern biologist. Furthermore charged-

particle beam technology has spread to industry, where

electron-beam machines are used for cleaning surfaces

and welding, and ion-beam devices are used in the prepa-

ration of semiconductors.

The propertie s of c harged-par ticle beams are analo-

gous in many respe ct s to those of pho ton beams: hence

the a ppellation charged-pa r ticle optics. In the following

sections the laws of geometrical optics wi ll be covered

insofar as they apply to charged-partic le beams. The c on-

sequences of the coulombic i nteraction of charged par-

ticles will be considered. In addition we shall discuss the

design of electron and ion sources, as well as the design

of electrodes that constitute optical elements for manip-

ulating beams of charged part icles. We shall consider

primarily electrostatic focusing by elements of cylindri-

cal symmetry and restr ict discussion to particles of sufﬁ-

ciently low kinetic energies that relativistic effects can be

ignored.

A number of excellent books and review articles are

available to the reader who wishes to pursue the topic of

electron and ion optics in greater detail.

1–6

5.1 BASIC CONCEPTS OF

CHARGED-PARTICLE OPTICS

5.1.1 Brightness

The brightness, b, of a point on a luminous object is deter-

mined by the differential of current dI that passes through

an increment of area dA about the point and shines into a

solid angle dX:

b ¼

dAdX

ðlAcm

2

1

Þ: ð5:1Þ

In electron or ion optics, a luminous object is usually

deﬁned by an aperture, called a window, which is uni-

formly illuminated from one side by a stream of charged

particles. A second aperture called a pupil limits the angu-

lar spread of particles emanating from the window. This

situation, in the xz plane, is illustrated in Figure 5.1. It will

assumed that the system is cylindrically symmetric

about the z-axis and the distance between the window

and pupil is sufﬁciently great that the angular spread of

rays emanating from each point on the object is the same.

The science of charged-particle optics owes a great deal to the princi-

ples of design formulated by C. E. Kuyatt (1930–1998). The authors are

indebted to Dr. Kuyatt for his advice and for permission to present parts

of his ‘‘Electron Optics Lectures’’ in this chapter.

324

CHAPTER

Then the integrated brightness of the object outlined by the

window is

b ¼

ð5:2Þ

where x

is the radius of the window and h is the half angle

deﬁned by the pupil relative to a point at the window.

5.1.2 Snell’s Law

When a beam of charged particles enters an electric ﬁeld,

the particles will be accelerated or decelerated; the trajec-

tory will depend on the angle of incidence upon the equi-

potential surfaces of the ﬁeld. This effect is analogous to

the situation in optics when a light ray passes through a

medium in which there is a change of refractive index.

Figure 5.2 illustrates the behavior of a charged-particle

beam

as it passes from a region of uniform potential V

to a region of uniform potential V

. The initial and ﬁnal

kinetic energies of a particle of charge q that originates at

ground potential with no kinetic energy are E

¼qV

and

¼qV

, respectively (i.e., for V in volts and E in eV, the

charge q on an electron is 1, and the charge of a singly

charged positive ion is +1). a

and a

are the angles of

incidence and refraction with respect to the normals to

the equipotential surfaces that separate the ﬁeld-free

regions.

The quantity in charged-particle optics that corresponds

to the index of refraction is the particle velocity, propor-

tional to the square root of the particle energy. Thus, the

charged-particle analog of Snell’s law is

ﬃﬃﬃﬃﬃ

sin a

ﬃﬃﬃﬃﬃ

sin a

: ð5:3Þ

Clearly, this property can be exploited in charged-

particle optics, as in light optics, to make lenses by shaping

the equipotential surfaces. This is equivalent to varying the

refractive index and shape of lenses for light.

5.1.3 The Helmholtz–Lagrange Law

Consider the situation illustrated in Figure 5.3, in which an

object deﬁned by a window at z

is imaged at z

. The rays

emanating from a point ( x

, z

) at the edge of the object are

limited by a pupil to fall within a cone deﬁned by a half

angle h

; this is the pencil angle. The angle of incidence a

of the central ray from (x

, z

) on the plane of the pupil is

referred to as the beam angle. The rays emanating from

each point on the image appear to be limited by an aperture

that corresponds to the image of the object pupil. An image

pencil angle h

and beam angle a

from a point (x

, z

)at

the edge of the image are deﬁned with respect to this image

pupil.

For most practical electron-optical systems, the pencil

and beam angles are small and the approximation sin h ¼ h

is valid. The treatment of optics based on this approxima-

tion is called Gaussian or paraxial optics.

Figure 5.1 A pupil establishes the half angle h of the

bundle of rays emanating from each point on an object

deﬁned by a window.

Figure 5.2 A charged-particle trajectory exhibits

‘‘refraction’’ at a potential gradient. (The energies, E

speciﬁed in the ﬁgure assume the particle originated at

ground potential with no kinetic energy.)

BASIC CONCEPTS 325

The image pencil angle is determined by the object pencil

angle. This relation is given to ﬁrst order by the Helmholtz–

Lagrange law:

ﬃﬃﬃﬃﬃ

¼ x

ﬃﬃﬃﬃﬃ

¼ Mm; M ¼

, m ¼

ð5:4Þ

where M and m are the linear and angular magniﬁcations,

respectively.

The current I

through the object window, that falls within

the object pupil is the same as the current I

through the

image window and pupil. Setting I

¼ I

¼ I, it follows that:

ð5:5Þ

Furthermore, if b

and b

are the brightnesses of the object

and image, respectively, then this equality can be written:

ð5:6Þ

demonstrating that the ratio of brightness to energy is

conserved from object to image.

5.1.4 Vignetting

The foregoing discussion assumes that the object radiates

uniformly; to the extent that the pencil angles are the same

for all points on the object, it follows that the image is

uniformly illuminated. However, if, as illustrated in Figure

5.4, a second pupil is added to the system, the illumination

Figure 5.3 Relation of image pencil angle h

and beam angle a

to object pencil angle h

and beam angle a

Figure 5.4 Vignetting.

326 CHARGED-PARTICLE OPTICS

will vary across the image. Such a situation is called

vignetting. The one case in which an aperture, in addition

to the object window and pupil, does not produce vignet-

ting is when an aperture is placed at the location of the

image of the original window or pupil. Such an aperture is

sometimes employed to skim off stray current resulting

from scattering from slit edges and from aberrations. Also,

an aperture is placed at the exit window of an energy or

momentum analyzer to deﬁne its resolution. Except for

‘‘spatter apertures’’ or resolving apertures, an electron-

optical system should have only two apertures.

5.2 ELECTROSTATIC LENSES

It is a simple matter to produce axially symmetric electro-

des that, when electrically biased, will produce equipoten-

tial surfaces with shapes similar to those of optical lenses.

A charged particle passing across these surfaces will be

accelerated or decelerated, and its path will be curved so as

to produce a focusing effect. The chief difference between

such a charged-particle lens and an optical lens is that the

quantity analogous to the refractive index, namely the par-

ticle velocity, varies continuously across an electrostatic

lens, whereas a discontinuous change of refractive index

occurs at the surfaces of an optical lens. Charged-particle

lenses are ‘‘thick’’ lenses, meaning that their axial dimen-

sions are comparable to their focal lengths.

5.2.1 Geometrical Optics of Thick Lenses

In the case of a thick lens, it is not correct to measure focal

distances from a plane perpendicular to the axis through

the center of the lens. The focal points of a thick lens are

located by focal lengths, f

and f

, measured from principal

planes, H

and H

, respectively. As shown in Figure 5.5,

the principal planes of a charged-particle lens are always

crossed, and they are both located on the low-voltage side

of the midplane, M, of the physical lens. F

and F

locate

the focal points with respect to the central plane and hence

the distances from the central plane to the principal planes

are F

 f

and F

 f

, respectively. The object and image

distances with respect to the principal planes are p and q,

and, with respect to the central plane, are P and Q, respec-

tively. All distances are positive in the direction indicated

by the arrows in Figure 5.5.

Figure 5.5 Lens parameters. H

and H

are the principal planes. M is the midplane of the

physical lens.

ELECTROSTATIC LENSES 327

As in light optics, it is possible to graphically construct

the image produced by a lens if the cardinal points of the

lens are known. This procedure is illustrated in Figure 5.6.

is only necessary to trace two principal rays. From a

point on the object draw a ray through the ﬁrst focal point

and thence to the ﬁrst principal plane. From the point of

intersection with this plane draw a ray parallel to the axis.

Draw a second ray through the object point and parallel to

the axis. From the point of intersection of this ray with the

second principal plane, draw a ray through the second

focal point. The intersection of the ﬁrst and second princi-

pal rays gives the location of the image point correspond-

ing to the object point.

A number of important relationships can be derived

geometrically from Figure 5.6 . The linear and angular

magniﬁ

cations, M and m, respectively, are given by:

M ¼

 q

 p

ð5:7Þ

and

m ¼

 p

 q

ð5:8Þ

where negative magniﬁcation implies an inverted image.

The object and image distances from the central

plane are

P ¼ F



ð5:9Þ

and

Q ¼ F

 Mf

ð5:10Þ

The object and image distances from the principal planes

are related by Newton’s law:

p  f

ðÞq  f

ðÞ¼P  F

ðÞQ  F

ðÞ¼f

ð5:11Þ

and Newton’s formula:

¼ 1 ð5:12Þ

For lenses that are not very strong, the principal planes are

close to the central plane. Then:

p ! P

q ! Q

ð5:13Þ

and

 f

to give an approximate form of Newton’s formula that is

quite useful in the initial stages of design work:

: ð5:14Þ

Furthermore, Spangenberg

has observed that for the

lenses discussed in succeeding sections:

M 0:8

ð5:15Þ

Figure 5.6 Graphical construction of an image.

328 CHARGED-PARTICLE OPTICS

5.2.2 Cylinder Lenses

The most widely used lens for focusing charged particles

with energies of a few eV to several keV is that produced

by two cylindrical coaxial electrodes biased at voltages

corresponding to the desired initial and ﬁnal particle ener-

gies. Figure 5.7 illustrates the equipotential surfaces and

the

axial electrical potential associated with the ﬁeld pro-

duced by two coaxial cylinders biased at voltage V

and V

respectively.

The focal properties of a two-cylinder lens depend upon

the diameters of the cylinders, the spacing between them,

and the ratio E

of the ﬁnal to initial kinetic energies of

the transmitted particles. The lens properties scale with the

diameter, so all dimensions are taken in units of the diam-

eter D of the larger cylinder. If the gap between cylinders is

large, the focal properties become sensitive to the cylinder

wall thickness and external ﬁelds are liable to penetrate to

the lens. Most lenses are constructed with a gap g ¼ 0.1D.

The particle energies depend upon the electrical potentials

(bias voltages) applied to the elements. It is assumed that

the bias voltage supplies are referenced to the particle

source, so that V

¼ E

Focal properties are usually presented as g raphs (Figure

5.8)ortablesofF

, f

, F

,andf

as a fun ction of V

For simple lenses i t is also convenient to plot P versus Q

for different V

ratios, as in Figure 5.9. The c hief

Figure 5.7 Potential distribution in a two-cylinder lens.

Figure 5.8 Focal properties of a two-cylinder lens with

coaxial cylinders of the same diameter D and a gap

between of 0.1D. (From E. Harting and F. H. Read,

Electrostatic Lenses, Elsevier, New York, 1976; by

permission of Elsevier Publishing Company.)

ELECTROSTATIC LENSES 329

sources of information on the focal properties of electro-

static lenses are the book Electrostatic Lenses by Harting

and Read

and various journal articles by Read and his

coworkers.

These data are determined from numerical

solutions of the equation of motion of an electron in a lens

ﬁeld and are thought to be accurate to 1–3%. Unfortunately,

these sources contain no information applicable to systems

with virtual objects or images. For two-cylinder lenses,

Natali, DiChio, Uva, and Kuyatt

have computed P–Q

curves that extend to negative values of the object and

image distances.

To obtain desired focal properties with a given accel-

eration ratio, two or more two-cylinder lenses can be

used in series. The lens ﬁeld extends abou t one diameter

D on either side of the midplane g ap. When two gaps are

sufﬁciently close that their lens ﬁelds overlap, it is con-

venient to treat the combination as a single lens. Such a

three-cylinder lens has the advantage that it can produce

an image of a ﬁxed object at a ﬁxed image plane for a

range o f ﬁnal-to-initial energy ratios. Alternatively, it can

produce a variable image location with a ﬁxed energy

ratio.

A three-cylinder lens for which the initial and ﬁnal ener-

gies differ is called an asymmetric lens. It can be used with

an electron or ion source to produce a variable-energy

beam. Such lenses are also used to focus an image of the

exit slit of a monochromator on a target while allowing for

a variation of the particle acceleration between monochro-

mator and target.

The focal properties of three-cylinder lenses are not

conveniently presented graphically, since each focal length

is a function of two independent variables. These variables

are usually taken to be V

and V

, where V

, V

, and

are the voltages on the ﬁrst, second, and third lens

elements. Harting and Read

and Heddle

present data

on three-element lenses for V

values between 1.0 and

30.0 in the form of tables of lens parameters (f

, f

, F

)

as a function of V

. They also plot ‘‘zoom-lens curves’’

as graphs of V

versus V

for selected values of P

and Q. An example is given in Figure 5.10.

Figure 5.9 P–Q curves for a two-cylinder lens with equal

diameter cylinders and a gap of 0.1D.(FromE.Hartingand

F. H. Read, Electrostatic Lenses, Elsevier, New York, 1976;

by permission of Elsevier Publishing Company.)

Figure 5.10 Typical ‘‘zoom-lens’’ curve. (From A. Adams

and F. H. Read, ‘‘Electrostatic Cylinder Lenses III,’’ J. Phys.,

330 CHARGED-PARTICLE OPTICS

Read has deﬁned a length f that approximately satisﬁes

the relation

ð5:16Þ

for three-element lenses. For use in initial design work,

is graphed as a function of f/D for various values

of V

A three-element lens for which V

¼ 1 is called an

einzel lens or unipotential lens. Such a lens produces focus-

ing without an overall change in the energy of the trans-

mitted particle. The focal properties are symmetrical: f

¼ f and F

¼ F

¼ F. Figure 5.11 illustrates the focal

properties of a typical einzel lens. For any desired object

and image distance there are two focusing conditions: a

decelerating mode with V

< 1 and an acceler ating

mode with V

> 1. The ac celera ting mode is preferred,

because deceleration in the middle element causes expan-

sion of the transmitted beam, resulting in aberrations and

unwanted interactions with the lens surfaces.

5.2.3 Aperture Lenses

An aperture in a plane electrode separating two uniform-

ﬁeld regions will have a focusing effect if the ﬁeld on one

side is different from that on the other. As illustrated in

Figure 5.12, this lens results from a bulge in the equipo-

tential

surfaces caused by ﬁeld penetration through the

aperture. A lens of this type is called a Calbick lens.

Single-aperture focusing is important in electron gun and

ion-source design because these devices usually have an

aperture at their output.

The Calbick lens is the analog of a thin lens. The electric

ﬁelds are established by the potentials V

, V

, and V

applied to the three planar elements, as shown in Figure

5.12. In this case it is assumed that electrons or ions

originate

at potential V

with essentially no kinetic energy.

For a circular aperture:

¼ f

¼ F

 E

ð5:17Þ

where the electrical ﬁeld intensities in the uniform-ﬁeld

regions are:

 V

, E

 V

ð5:18Þ

Figure 5.12 Protrusion of equipotential

surfaces through an aperture separating

regions of different ﬁeld strength.

Figure 5.11 Focal properties of an einzel lens with the

intermediate cylinder of length A ¼ D and lens gaps

g ¼ 0.1D. (From E. Harting and F. H. Read, Electrostatic

Lenses, Elsevier, New York, 1976; by permission of

Elsevier Publishing Company.)

ELECTROSTATIC LENSES 331

The ratio of aperture potential to radius must be larger than

or E

. For a long slot in the xy plane:

 E

ð5:19Þ

and

 ‘ ð5:20Þ

when the short dimension of the slot is in the x-direction.

The focal properties of a slot are important in the design

of electron guns that employ a ribbon ﬁlament.

Lenses can also be constructed using two or more aper-

tures. Read has computed the properties of two-aperture

and three-aperture lenses.

In practice, concentric cylindrical mounts support circular-

aperture electrodes of an aperture lens. The focusing

effects of these cylindrical elements can be ignored if the

cylinder diameter is at least three times greater than the

aperture diameter.

5.2.4 Matrix Methods

A useful description of the charged-particle trajectories

through a focusing system can be formulated using

the matrix methods introduced in Section 4.2.2.A

rticle trajectory through a system that is cylindrically

symmetrical about the z-axis is determined by (r,dr/dz ¼

r#, z), where r is the radial distance of the trajectory

from the axis at z. A trajectory through a plane perpendic-

ular to the central axis at z is represented by a

vector:



ð5:21Þ

The effect of a displacement in a ﬁeld-free region from z

to z

is given by:



¼ M z

! z

ðÞ



ð5:22Þ

where the ray transfer matrix is:

M z

! z

ðÞ¼

1 Dz



, Dz ¼ z

 z

ð5:23Þ

A lens can be represented as if its effect were conﬁned to

the region between the principal planes. The matrix oper-

ating between the principal planes is:

M H

! H

ðÞ¼



ð5:24Þ

Consider, for example, a ray originating at a point on an

object at z

andpassingthroughapointonanimageatz

.The

trajectory at z

can be determined from the trajectory at z

by:



¼ M H

! z

ðÞM H

! H

ðÞM z

! H

ðÞ



ð5:25Þ

In terms of the parameters deﬁned in Figure 5.5, the

displacement

between the object and the ﬁrst principal

plane is P F

+ f

; thus:

M z

! H

ðÞ¼

1 P F

þ f



ð5:26Þ

and similarly:

M H

! z

ðÞ¼

1 Q F

þ f



ð5:27Þ

Substitution yields:

 Q

 Q F

ðÞP  F

ðÞ



 P

ð5:28Þ

This transformation matrix is generally applicable to the

problem of tracing a trajectory through the ﬁeld of a lens.

For the two-cylinder lens, DiChio, et al. have derived sim-

ple analytical expressions for the elements of the matrix.

When r

and r

refer to points in the object and image

planes, respectively, the diagonal elements of the transfor-

mation matrix are the linear and angular magniﬁcation.

Furthermore, the focusing condition given by Newton’s

formula requires the numerator of the upper right element

332 CHARGED-PARTICLE OPTICS

to be zero. Thus, the transformation matrix between object

and image is:

M object ! imageðÞ¼

M 0



ð5:29Þ

The matrix formulation is a desirable alternative to graph-

ical ray tracing for a system of lenses that are so close to

one another that an image does not appear between each

lens and the next. Consider, for example, the system of two

lenses in Figure 5.13. In this case the transformation

matrix

is:

M z

! z

ðÞ¼M H

! z

ðÞM H

! H

ðÞ

3 M H

! H

ðÞM H

! H

ðÞM z

! H

ðÞ

ð5:30Þ

In general, the image distance L

will be unknown initially.

It can be determined, however, from the focusing condition

that requires the upper right element of M z

! z

ðÞto be

zero.

It is occasionally necessary to determine a particle tra-

jectory in a region of uniform ﬁeld. The transformation

matrix from z

to z

in a uniform ﬁeld in the z-direction is:

M uniform fieldðÞ¼

2DzV

V

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

 1

q

ﬃﬃﬃﬃ

ð5:31Þ

where V

and V

are the potentials of the planar equipo-

tential surfaces perpendicular to the z-axis at z

and z

5.2.5 Aberrations

There are three types of aberrations that must be consid-

ered in designing charged-particle optics:

(1) Geometrical aberrations due to deviations from the

paraxial assumption that the angle h between a ray

and the central axis is sufﬁciently small that

h  sin h  tan h:

(2) Chromatic aberrations caused by variations in the

kinetic energies of transmitted particles.

(3) Space charge due to repulsive interactions between the

charged particles.

The geometrical aberration associated with a lens is

deﬁned in terms of the radius Dr

of a spot in the image

plane formed by rays within the pencil angle h

that ema-

nate from an object point on the axis, as shown in Figure

5.14. The important geometrical errors can be expressed in

terms

of the coefﬁcients of a power series in h

¼ bh

þ ch

... ð5:32Þ

Figure 5.13 A compound lens system.

ELECTROSTATIC LENSES 333

An imaging system is said to be second-order-focusing

if b ¼ 0, and third-order-focusing if c ¼ 0. An axially

symmetric system is always at least second-order-focusing,

since only terms of odd order appear in the expansion of

. The coefﬁcient c is referred to as the third-order-

aberration coefﬁcient. Higher-order coefﬁcients can usu-

ally be ignored. For an object point on a lens axis, the error

represented by c is spherical aberration. Harting and

Read

have computed spherical-aberration coefﬁcients

deﬁned by:

c ¼ MC

ð5:33Þ

for all of the lenses for which they give focal properties.

For object points off axis, other types of aberration must

be considered (coma, ﬁeld curvature, distortion, and

astigmatism). Most off-axis aberrations can be relate d

to the magnitude of C

. When the object is small com-

pared to the lens diameter, the spherical-aberration coef-

ﬁcient gives a reasonable measure of the total geome trical

aberration.

As can be seen from Figure 5.14, the pencil of ray s

manating from a n object point achieves a minimum

diameter at a point slightly in front of the image plane.

This minimum diameter is the circle of least c onfu sion .

To achieve the shar pe st focus it is often possib le to vary

the lens voltages so as to place the circle of least confu-

sion on the desi red image pla ne. The radi us of this circle

;thusC

can, i n practice, be redu ced by a factor

of four.

The diameter of the bundle of rays emanating from an

object is usually determined by a pupil that limits the

portion of the lens that is illuminated by rays from the

object. The extent of illumination is speciﬁed by a ﬁlling

factor, which is the ratio of the diameter of the bundle of

rays near the lens gap to the lens diameter. Because the

spherical aberration depends upon the third power of the

angle between the limiting ray and the axis, it is obvious

that aberration increases rapidly with increasing ﬁlling

factor. In practice, a lens system should not be designed

with a ﬁlling factor in excess of about 50%.

For an object of ﬁnite extent, the worst aberration occurs

for off-axis image points. The magnitude of the aberration

depends upon the maximum value of the angle of a ray

from the edge of the object relative to the central axis of

the lens system. From Figure 5.3 it can be seen that this

angle

is the sum of the object pencil angle and beam angle.

In many lens systems, the image produced by one lens

serves as an object for succeeding lenses. According to

the Helmholtz–Lagrange law, the pencil angle associated

with this intermediate image is determined by the pencil

Figure 5.14 Geometrical aberration of the image of a point.

334 CHARGED-PARTICLE OPTICS

angle associated with the initial object. There are, how-

ever, no such physical restrictions on the beam angle from

the intermediate image. In fact, as shown in Figure 5.15,if

object pupil is placed at the ﬁrst focal point of a lens,

then the corresponding image pupil is at inﬁnity and the

image beam angle is zero. Obviously such an arrangement

reduces aberrations produced by lenses that treat this

image as an object.

Chromatic aberration depends upon the relative spread

in particle energies, DE/E, passing through a lens. Varia-

tions in particle energies can occur because of conditions

in the particle source or within the lens. An energy spread

of 0.2 to 0.4 eV is characteristic of electron sources. Some

ion sources yield ions in an energy bandwidth as great as

30 eV. Energy variations may also be caused by ﬂuctua-

tions in the voltage from the power supplies that establish

both source and lens-element potentials.

For a given lens, the extent of chromatic aberration can

best be determined from a calculation of the image dis-

tances for particles with energies at the extremes of the

anticipated energy distribution. Consider, for example,

the case of a source at ground potential that produces

particles with energies between 0 and DE. For a lens of

voltage r atio V

,adistanceP from the source, deter-

mine the corresponding image position, Q ¼ f(P, V

Determine also:

Q þ DQ ¼ fP,

 DE = q



ð5:34Þ

Then a point on axis at the source yields an image at Q

of radius:

¼ h

DQ ð5:35Þ

or, by the Helmholtz–Lagrange law:

ﬃﬃﬃﬃﬃﬃ

ð5:36Þ

where h

and h

are the pencil angles at the source and the

image, respectively.

In electron-beam devices, the main cause of chromatic

aberration is the spread of electron kinetic energies emitted

from a thermionic cathode as well as the potential drop

across the emitting portion of the cathode. The energy of

electrons at the maximum of the current distribution from a

cathode is:

max

¼ 8:6 3 10

5

T eV ð5:37Þ

Figure 5.15 An object pupil at the ﬁrst focal point moves the image

pupil to inﬁnity and reduces the image beam angle a

to zero.

ELECTROSTATIC LENSES 335

The width of the distribution DE  E

max

For a bare tungsten ﬁlament, a temperature of

about 3000 K is required to produce signiﬁcant emission.

At this temperature DE  0:25 eV. An oxide-coated cath-

ode (available from Electron Technology) can be

operated at temperatures as low as 1200 K, where

DE  0:1 eV. The potential drop across the emitting por-

tion of the cathode may add several tenths of an eV to the

energy spread.

The space-charge effect arises from the mutual r epul-

sion of particles of like charge. The effect increases with

current density. As a result, even a focused beam will

give a diffuse image. Furthermore, the beam will diverge

away from the image more rapidly than predict ed by

geometrical optics.

Space charge places a limit on the current in a charged-

particle beam. As an example of practical value, consider

the problem of transmitting maximum current through

a cylindrical element of length L and diameter D.As

shown in Figure 5.16, the maximum current is achieved

focusing the beam on a point at the center of the

tube with a pencil angle h ¼ D/L. It can be shown that

the space-charged-limited current of electrons of energy

E ¼qV is

max

ðelectronsÞ¼38:5V

3=2



lA ð5:38Þ

and the maximum ion current is:

max

ðionsÞ¼0:90



1=2

3=2



lA ð5:39Þ

where V is in volts, M is in amu, and n is the charge state.

The

minimum beam diameter at the space-charge limit is 0.43D.

Space charge also limits the current available from a

surface that emits electrons or ions. The typical source

geometry is the plane diode consisting of a planar anode

at potential V, a distance d from the cathode. Charged

particles produced by thermionic emission from the cath-

ode are accelerated toward the anode. The maximum elec-

tron current density at the anode is:

max

ðelectronsÞ¼2:34

3=2

lAcm

2

ð5:40Þ

while for an ion-emitting cathode:

max

ðionsÞ¼0:054



1=2

3=2

lAcm

2

ð5:41Þ

with V in volts, d in cm, M in amu, and n the charge state.

5.2.6 Lens Design Example

Consider the problem of producing the image of the anode

aperture of an electron source on the entrance plane of an

energy analyzer, as illustrated in Figure 5.17. The anode

potential

is V

¼ 100 V, and the analyzer entrance-plane

potential is V

¼ 10 V. The anode aperture radius is

¼ 1.0 mm, and the distance from anode to analyzer is

l ¼10 cm. It is desired that the image of the anode aperture

serve as the entrance aperture for the analyzer with radius

¼ 0.5 mm. So as not to overﬁll the analyzer, one must

also have the image pencil angle h

¼ 0.14 and the image

beam angle a

¼ 0.

The lens to be designed is a decelerating lens with

¼ 0.1 and magniﬁcation M ¼ 0.5. Customarily only

the focal properties of accelerating lenses are tabulated.

Figure 5.17 A simple lens design.

Figure 5.16 A beam focused to give maximum current

through a tube.

336 CHARGED-PARTICLE OPTICS

The focal properties for the desired lens are just the reverse

of those of the accelerating lens, with V

¼ 10. From

Harting and Read,

the focal properties of the V

¼ 10

lens (identiﬁed by a prime) are:

¼ 0:80DF

¼ 1:62D

¼ 2:54DF

¼ 1:19D

ð5:42Þ

The corresponding parameters for the V

¼ 0.1 lens

are:

¼ 2:54DF

¼ 1:19D

¼ 0:80DF

¼ 1:62D

ð5:43Þ

From the P–Q curve of Figure 5.9 for V

¼ 10 and

M#¼ 1/M ¼ 2, we estimate:

P ¼ Q

¼ 6:20D

Q ¼ P

¼ 2:05D

ð5:44Þ

Taking P ¼ 6.20D, Newton’s law gives:

Q ¼

P  F

þ F

¼ 2:03D ð5: 45Þ

The overall length of the lens is:

l ¼ P þ Q ¼ 6:20D þ 2:03D ¼ 10 cm ð 5 :46Þ

and thus:

D ¼ 1:22 cm: ð5:47Þ

In order for the image beam angle to be zero, the

object pupil should be placed at the ﬁrst focal point of

the lens so that the image pupil is at inﬁnity. The object

pupil must deﬁne a pencil angle h

that is consistent with

the required image pencil angle. By the Helmholtz–

Lagrange law:

¼ Mh

ﬃﬃﬃﬃﬃﬃ

¼ 0:022 ð5:48Þ

This angle is determined by the radius r

of an aperture at

the ﬁrst focal point:

¼ h

P  F

ðÞ¼0:13 cm ð5:49Þ

To estimate the geometrical aberration of this lens, we

calculate the spherical aberration for the lens used in

reverse. This is necessary because spherical-aberration

coefﬁcients are available only for lenses with V

>1.

For V

¼ 10, Harting and Read give:

¼ 20 ð5:50Þ

Thus for the lens used in reverse, the image of a point is a

spot of diameter

¼ M

¼ 0:067 cm ð5:51Þ

For the lens used as designed, the size of the image of an

object point is:

Dr ¼ MDr

¼ 0:033 cm ð5:52Þ

Thus spherical aberration will enlarge the image by 67%

(Dr=r

¼ 0:033=0 :05); however, if the lens voltage is

adjusted slightly to bring the circle of least confusion onto

the image plane, the spherical aberration can be reduced

to 17%.

For a typical electron source, DE ¼ 0.3 eV. This energy

spread will result in chromatic aberration at the image. To

estimate this effect, calculate the image position Q + DQ

for electrons at the extreme of the energy distribution

where the deceleration ratio of the lens is:

ðV

DE=qÞ=ðV

DE=qÞ¼10:3=100:3 ¼ 0:103 ð5:53Þ

As before, the focal properties can be determined from

those of the corresponding accelerating lens. For the lens

with V

¼ 0.103,

¼ 2:58DF

¼ 1:22D

¼ 0:82DF

¼ 1:65D

ð5:54Þ

The image position by Newton’s law in this case is:

Q þ DQ ¼

P  F

þ F

¼ 2:07D ð5:55Þ

so:

DQ ¼ 0:04D ¼ 0:05 cm ð5:56Þ

This displacement of the image plane will cause the

image of a point object to appear as a disk of radius:

Dr ¼ DQh

¼ 0:007 cm ð5:57Þ

in the original image plane. Chromatic aberration enlarges

the image by about 14% (Dr=r

¼ 0:007=0:05).

ELECTROSTATIC LENSES 337

The overall aberration of the lens as designed is about

30%. The ﬁlling factor is:

2 h

þ a

ðÞP

¼ 54% ð5:58Þ

From the aberration calculations it can be seen that the

aberrations would become serious if the ﬁlling factor were

to exceed this value.

5.2.7 Computer Simulations

The re are a variety of progra ms available f or the compu-

tation of charged-particle t rajectories in the ﬁeld of an

array of electrodes. Thes e employ Green’s func tion,

ﬁnite-element, and surface- charge methods to compute

the electrical ﬁeld produced by the array. All provide

for the possibility of an applied magnetic ﬁeld and some

solvefortheﬁeldproducedbyanarrayofmagnets.A

particular virtue in computer-simulation programs is that

theycanbeusedtopredictthepropertiesofcompound

lenses that are more complex than the two- and three-

element lenses that are described above, and for which

there are tabulated values of focal lengths and focusing

properties. Among the most useful and widely used

simulation programs are Simion (Scientiﬁc Instrument

Services, Inc., www.simion.com) and CPO (CPO, Ltd.,

www.electronoptics.com).

It must be emphasized that computer simulation pro-

grams cannot substitute for an understanding of the basic

principles of electron optics described in this chapter. It is

impossible to obtain the desired performance in the design

of an electron-optical system by arbitrarily choosing an

array of electrodes and ‘‘ﬁddling’’ to obtain the desired

beam properties; the positions of lenses, windows, and,

especially, pupils should be determined from considera-

tions of basic principles before turning to the computer

to optimize a design or test its performance.

Figure 5.18(a) shows a computer simulation of the

simple

cylindrical lens discussed in Section 5.2.6 and

illustrated

in Figure 5.17. The computed electric ﬁeld at

the

lens gap is shown as equipotential surfaces. Electron

trajectories are traced from points at the center and the

upper edge of the object win dow. One of the three tra jec-

tories from each point passes through the center of the

pupil; the other two are the extreme rays t hat can pass

through the pupil. Figure 5.18(b), a bl owup of a portion of

18(a), shows the location of the image formed. It is

worth noting that the size of the image is half t hat of

the object, as predict ed in Section 5.2.6. The image dis-

tance, Q =1

.93D , is s om ewhat short of t ha t pred ic ted.

The bundle of rays from both the ce nter and the edge of

the object emerge from the image with their central axes

parallel to the axis of the lens; this implies that the beam

angle a

=0(seeFigure 5.15). Figure 5.18(c) shows a lens

system identical to that in 5.18(a), except the pupil has

been moved closer to the object and away from the ﬁrst

focal point of the lens. The result is a signiﬁcant increase

in the image beam angle, as well as noticeable geometric

aberration.

5.3 CHARGED-PARTICLE SOURCES

An electron or ion gun consists of a source of charged

particles, such as a hot metal ﬁlament or a plasma, and an

electrode structure that gathers particles from the source and

accelerates them in a particular direction to form a beam.

There is a wide range of practical electron and ion guns.

Some simple devices and their principles of operation will

be described in this section. In addition to simple devices

that can be conveniently constructed for laboratory use,

there are a number of very sophisticated guns that have been

developed commercially. These include electron guns for

cathode-ray tubes and electron-beam welders, and ion guns

for sputter-cleaning apparatus and for ion-implantation dop-

ing of semiconductors. Manufacturers of electron guns and

ion sources suitable for use in the laboratory include Kimble

Physics (electron and ion guns), Spectra-Mat (alkali-metal

ion sources), and Southwest Vacuum Devices and Clif-

tronics (both manufacturing CRT guns useful as electron

sources and both owned by Video Display Corporation).

5.3.1 Electron Guns

Electrons are produced by thermionic emission, ﬁeld

emission, photoe lectric emission, a nd electron-impact

ionization. Thermionic sources are the most common.

These sources typically consist of a wire ﬁlament of

some refractory metal, such as tungsten or tantalum,

338 CHARGED-PARTICLE OPTICS

which is heated by an ele ctrical current passing through

it. In some cases thermionic sources consist of a metal

cup o r button that is indirectly heated by an electrical

heater or by e lectron bombardment of the back surfac e.

The electrons from a hot ﬁlament possess energies of a

few tenths of an electron volt. Mutual repulsion will

cause the electrons to diffuse away from the source if

they are not immediately accelerated into a beam. M any

accelerator structures are us ed. Most us e either diod e

(two-electrode) or triode (thre e-electrode) geometries ,

Figure 5.18 (a) MacSimion simulation of the cylindrical lens shown in Figure 5.17 and

discussed in Section 5.2.6. The voltage ratio V

¼ 0.10; the object is deﬁned by an aperture

window and the object distance from the lens gap is P ¼ 6.20D (D is the diameter); a pupil is

placed at the ﬁrst focal point of the lens. The electric ﬁeld at the lens gap is shown by

equipotential surfaces computed by the program. The trajectories of 100 eV electrons

originating at the center and edge of the window have been traced by the computer program.

(b) A blowup showing the image formed. The image distance from the lens gap is Q ¼ 1.93D.

of the lens. The result is a signiﬁcant increase in the beam angle at the image.

(MacSimion, is a simulation program for MacIntosh developed by Don McGilvery and

coworkers, Department of Chemistry, Monash University, Clayton, Victoria, AUSTRALIA 3168)

CHARGED-PARTICLE SOURCES 339

although some TV tubes employ a pentode geometry.

The Pierce diode geometry is most common in labora-

tory devices.

Figure 5.19(a) ill ustrates a simple diode electron gun

consisting

of a plane emissive surface and a parallel

plane anode. Electrons leave the cathode with a nomin al

energy E

. The anode is b iased at a positive potential V

relative to the ca thode, so that electrons from a spot on

the cathode will appear at a spot on the anode with ener-

gies of approximately E

= qV

. To admit the acceler-

ated electrons to the system beyond, a hole is made in the

anode. If the cathode and anode were inﬁnite in extent, the

space-charge-limited current density given in Section 5.2.5

could be achieved at the anode, and the electron beam

emer

ging from the anode hole would be characterized by

a beam angle:

a ¼

ð5:59Þ

where r

is the radius of the anode hole and d the cathode-

to-anode spacing. Since the most divergent electron

arriving at the anode would be one emitted parallel t o

the cathode with energy E

, it can be seen that the pencil

angle characterizing the beam from the anode aperture

would be

h ¼

ﬃﬃﬃﬃﬃ

ð5:60Þ

For a cathode of ﬁnite extent, the space-charge interac-

tion causes the beam to spread laterally within the gap

between cathode and anode. Pierce

has shown that the

electric ﬁeld in an inﬁnite space-charge-limited diode

can be reproduced in the region of a ﬁnite cathode by

means of the conical cathode structure illustrated in Figure

5.19(b). The maximum current of electrons is:

max

¼ pr

max

¼ 7:35



3=2

lA ð5:61Þ

The corresponding ratio of brightness to energy (which is

conserved) is:

max

¼ 0:74

3=2

lAcm

2

1

ð5:62Þ

The design of multielectrode guns is a complicated

process involving time-consuming experimentation. A

number of special guns have been developed for such pur-

poses as producing low-energy electron beams or very

narrow beams. Klemperer and Barnett describe many of

these,

and most can be constructed easily if they are really

needed. In general, however, it is best to use the simplest

device that will fulﬁll one’s requirements.

The guns developed for TV tubes are the pro duct of

much industrial development. These guns will produce a

beam of electrons of several hundred eV to several tens

of thous ands eV th at is sharply focus ed to a spot at a

distance of 10 to 20 cm. Cathode-ray -tube guns can be

obtained quite inexpensively from commercial suppliers

such as Southwest Vac uum Devices and Cliftronics

(both owned by Video Display Corporation). Special-

ized guns of similar design are available from Kimble

Figure 5.19 (a) The plane diode; (b) the Pierce geometry

that simulates the ﬁeld of the plane diode.

340 CHARGED-PARTICLE OPTICS

Physics and other manufacturers of electron spe ctro-

meters.

5.3.2 Electron-Gun Design Example

Consider the problem of designing an electron gun consist-

ing of a Pierce diode and a lens system that can inject a

beam of 20–200 eVelectrons into a gas cell, as illustrated in

Figure 5.20. It is desired that the beam current approach the

ace-charge limit at 20 eV. The overall length of the gun is

to be about 10 cm, and the cell is to be located 4 cm in front

of the gun. The cell is 2 cm long, with an input aperture of

radius r

¼ 0.1 cm and an exit aperture of radius 0.15 cm.

Treat the exit aperture as though its radius r

were 0.1 cm, so

as to make the beam tight enough to minimize backscatter-

ing of electrons from the edges of this aperture.

Note that the electron gun system in Figure 5.20 is wired

such a way that the energies of the electrons through the

system, E

, E

, and E

, in electronvolts, are numerically

equal to the power supply voltages V

, V

, and V

. This is,

in general, a great convenience, since electron energies can

be read directly from the power supplies. In the following

discussion, E

and V

can be used interchangeably.

The maximum current through the cell can be taken as the

space-char ge-limite d current through a cylinder with a diam-

eter D equal to that of the gas-cell apertures and length L equal

to the length of the gas cell. From Section 5.2.5, the maximum

curr

ent of electrons with energy E

¼ 20 eV is, in this case

max

¼ 38:5V

3=2



¼ 34:4 lA

ð5:63Þ

To approach this limit, focus an image of the anode

aperture on the center of the cell. Make the image radius

¼ 0.43r

, the minimum size of the space-charge-limited

beam (note Section 5.2.5 and Figure 5.16).

The image

pencil angle will be h

¼ D/L ¼0.1 and the ratio of bright-

ness to energy at this image is:

max

¼ 9500 lAcm

2

1

ð5:64Þ

At the anode of the Pierce diode (Section 5.3.1), the ratio

brightness to energy is given by:

¼ 0:74

3=2

ð5:65Þ

where E

is the mean kinetic energy of electrons emitted

by the cathode, and E

is the energy of electrons at the

anode that is held at the potential V

relative to the cathode.

Now the ratio of brightness to energy is a conserved quan-

tity, so:

ð5:66Þ

Substituting from the previous two equations yields:



0:74



2=3

ð5:67Þ

For E

¼0.25 eV (Section 5.2.5), a cathode-to-anode spac-

ing d ¼ 0.5 cm, and a ﬁnal electron energy of 20 eV, the

kinetic energy of electrons at the anode, E

¼ 86 eV, and

the potential to be applied to the anode is:

ðE

¼ 20 eVÞ¼86 V ð5:68Þ

A similar calculation yields:

ðE

¼ 200 eVÞ¼185 V ð5:69Þ

The current from the diode depends upon the radius of

the anode aperture r

and the current density J at the anode:

I ¼ Jpr

ð5:70Þ

Figure 5.20 An electron gun system to inject a

variable-energy beam into a gas cell.

CHARGED-PARTICLE SOURCES 341

With the lens system tuned to inject 20 eV electrons into

the target cell (E

¼ 20 eV), the maximum current density

at the anode: is

max

2:34

3=2

; V

¼ V

ðE

¼ 20 eVÞ

¼ 7500 lAcm

2

ð5:71Þ

To achieve maximum current in the cell at 20 eV, we

choose the anode aperture to be:

max



1=2

¼ 0:04 cm ð5:72Þ

A similar calculation for E

¼ 200 eV would suggest

using a larger anode aperture; a larger aperture, however,

would produce an excess of current and thus many stray

electrons when the system is tuned to produce a low-

energy beam.

Note that when the system is designed to approach

the space-charge limit at 20 eV, the pencil angle at the

anode is consistent with the pencil angle deﬁned by the

cell apertures. The pencil angle characteristic of the Pierce

diode at the low-energy limit is:

ﬃﬃﬃﬃﬃ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

0:25

¼ 0:05 ð5:73Þ

and the anode pencil angle that gives the space-charge-

limited pencil angle in the cell can be determined from

the Helmholtz–Lagrange law:

ﬃﬃﬃﬃﬃ



¼ 0:05 ð5:74Þ

For ﬁnal energies greater than 20 eV, these pencil angles

will be less than the angle deﬁned by the cell apertures,

and scattering from the edges of the apertures will be

minimized.

It remains to design a lens system that will image the

anode aperture on the center of the gas cell. A variable-ratio

lens is required, and in this case a three-cylinder asymmetric

lens seems appropriate. The voltage ratios at the extremes

of the desired operating conditions are:

¼ 20 eVðÞ¼0:23 ð5:75Þ

and

¼ 200 eVðÞ¼1:1 ð5:76Þ

The desired magniﬁcation is

M ¼

 1 ð5:77Þ

The lens diameter must be chosen to give an acceptable

ﬁlling factor. As a starting point, recall that:

M  0:8

ð5:78Þ

The lens is to focus the anode aperture on the center of the

gas cell, so P + Q ¼ 10 cm + 4 cm + 1 cm ¼ 15 cm. The

distance from the anode to the middle of the lens will be:

P ¼

P þ Q



3 15 cm

P þ 1:25MP



3 15 cm

¼ 6:7cm

ð5:79Þ

For a ﬁnal energy of 20 eV, the maximum diameter of

the beam through the lens system will be approximately:

P ¼ 0:67 cm; h

ðE

¼ 20 eVÞð5:80Þ

Choose D ¼ 2.0 cm to achieve a ﬁlling factor less than

30%. Then:

P ¼ 3:35D

Q ¼ 4:15D

ð5:81Þ

and the nominal focal length of the desired lens (see Sec-

tion

5.2.2)is

f ¼



1

¼ 1:85D ð5:82Þ

The calculations of Adams and Read

or Harting and

Read

can then be used to determine the lens voltages that

correspond to this nominal focal length. Alternatively, the

lens system can be modeled by computer simulation and

the potential to be applied to the central element of the

342 CHARGED-PARTICLE OPTICS

three-cylinder lens can be determined empirically. Figure

5.21 shows the results of simulations for the projection of

and 200 eV electrons into the target cell. Figure 5.22

gives the central lens element voltage V

obtained from the

simulation.

5.3.3 Ion Sources

Many parameters must be considered in choosing or

designing an ion source. Foremost is the desired type of

ionic species and charge state. The physical and chemical

properties of the corresponding parent material determine

to a large extent the means of ion production. Other impor-

tant parameters are the desired current, brightness, and

energy distribution. In some cases it is also necessary to

consider the efﬁciency of utilization of the parent material.

In view of the number of variables involved, it is not

surprising that many different types of ion sources have

been developed to meet both scientiﬁc and industrial

demands.

Ion sources can be classiﬁed according to the ion pro-

duction mechanism employed. The two most common

Figure 5.21 MacSimion simulat ion of the electric ﬁeld and electron traject ories in the

electron gun system shown s chematically in Figure 5.20. The cathode-to-anode

distance

in the Pierce diode is d ¼ 0.5 cm and the radius of the aperture in the anode is

¼ 0.04 cm. The radii of the apertures in the target cell are r

¼ 0.1 cm and r

¼ 0.15

cm. The diameter of the lens D ¼ 2 cm, the length of the central element A ¼ 0.5D,and

the gap between lens elements is g ¼ 0.1D. (a) Trajectori es of electrons that pass

through the cell with energy E

¼ 20 eV; V

¼ 86 V, V

¼ 105 V, and V

¼ 20 V. (b)

Trajectories of electrons that pass through the cell with energy E

¼200 eV; V

¼185 V,

¼ 960 V, and V

¼ 200 V.

Figure 5.22 Lens voltages for the lens system of Figure 5.20.

CHARGED-PARTICLE SOURCES 343

means are surface ionization and electron impact. The

electron-impact sources include both electron-bombard-

ment sources and plasma sources. More exotic ion sources

employ ion impact, charge exchange, ﬁeld ionization, and

photoionization. Three typical sources, illustrating differ-

ent ion production mechanisms, will be discussed below.

In practice, the simplest means of producing ions is by

thermal excitation of neutral species. This process, known

as surface ionization, occurs efﬁciently when an atom or

molecule is brought in contact with a heated surface whose

work function exceeds the ionization potential of the atom

or molecule. This requirement is fulﬁlled for alkali atoms

(Li, Na, K, Rb, Cs) on surfaces of tungsten, iridium, or

platinum. In order for ionization to compete with vaporiza-

tion, it is necessary that the surface be sufﬁciently hot that

the substrate surface is only partially covered with neutrals,

so that the work function of the surface is characteristic of

the substrate rather than the material to be ionized.

In a surface-ionization ion gun, the source of neutral

atoms can either be remote from, or integral with, the ion-

izing surface. In the remote type, the alkali metal is con-

tained in an oven. A stream of metal vapor from the oven is

directed toward the ionizer, which is a heated metal ‘‘cath-

ode’’ located within an electrode structure similar to that

of an electron gun. The ‘‘anode’’ is negatively biased to

accelerate positive ions into a beam. The most convenient

alkali-ion emitter consists of a porous tungsten disk that

has been infused with an alkali-containing mineral and

mounted on an electrical heater. When heated, alkali atoms

are generated; the atoms diffuse to the surface of the disk,

and are ionized as they leave the surface. These emitters

with integral heaters are commercially available (Spectra-

Mat). As shown in Figure 5.23 , a source is constructed by

inserting

the emitter into the cathode of a Pierce diode or

into some other extractor electrode structure.

The majority of laboratory ion sources employ electron-

impact ionization. The simplest conﬁguration is illustrated

in Figure 5.24 . In this source, an electron beam from a

simple

diode gun is injected into an ionization chamber

containing an appropriate parent gas. A transverse electric

ﬁeld of a few V/cm causes ions produced by electron

impact to drift across the chamber and out through a slit

in the side of the chamber. An extractor electrode system

accelerates the ions into a beam. The ionic species pro-

duced will depend upon the parent gas, the gas pressure,

and the electron energy. Singly charged ions are produced

with maximum efﬁ ci enc y at electron energies of about 70 eV.

Higher electron energies favor multiply charged ions.

Lower electron energies yield only singly charged ions and

Figure 5.23 An alkali-ion source consisting of an indirectly

heated emitter in a Pierce diode.

Figure 5.24 An electron-impact ion source.

344 CHARGED-PARTICLE OPTICS

reduce the extent of fragmentation in the event that the

parent gas is a molecular species. Gas pressures are typi-

cally 1 to 10 mtorr. Higher pressures place an unreasonable

gas load on the vacuum system and impede the ﬂow of ions

from the ionization chamber.

Theefﬁciencyoftheelectron-impact ionization source can

be improved by imposing a magnetic ﬁeld of a few hundred

gauss coaxial with the electron beam. The ﬁeld conﬁnes the

electron beam to a spiral around the beam axis, thus increas-

ing the path length and maximizing the probability of

collision with the gas molecules. Electron-bombardment

sources of this type yield currents of a fe w tens of micro-

amperes. The chief advantages are simplicity of construction

and an energy spread in the product ions of only a few eV.

Relatively high ion densities can be achieved in an elec-

trical discharge through a gas. The ion density in a dis-

charge can be further increased if the discharge is conﬁned

and compressed by a magnetic ﬁeld. The duoplasmatron

source illustrated in Figure 5.25 is the prototypical dis-

charge-

type ion source.

Applying a potential of 300 to

500 V between the heated cathode and the anode produces

a discharge through a gas at about 100 mtorr. After the arc

is struck, the discharge is maintained by passing a current

of 0.5 to 2 A through the ionized gas. In the duoplasma-

tron, the intermediate element, known as the zwischen, is

one pole of a magnet. The axial magnetic ﬁeld at the tip

of the zwischen conﬁnes the discharge to a dense plasma

bubble at the anode. Plasma leaks through a hole in the

anode to ﬁll a cup on the front face of the anode. An

extractor electrode, biased at about 10 kV relative to the

anode, withdraws ions from the surface of the plasma. Ion

currents of 1 to 10 mA are easily obtained. In operation,

several hundred watts of electrical power are dissipated in

the arc and the electromagnet. In its original form, this

source was liquid-cooled. However, the author has found

air-cooling to be acceptable for slightly smaller versions.

The duoplasmatron is the brightest of ion sources. Copious

quantities of singly charged atomic and diatomic ions can

be obtained for these species for which an appropriate

gaseous parent can be found. It is also possible to obtain

a few microamperes of doubly charged ions, and in addi-

tion, negative ions can be obtained by reversing the extrac-

tion potential.

The chief disadvantages of plasma sources

are their complicated construction and the fact that stable

operation is only possible for a few days before cleaning

and ﬁlament replacement are necessary.

5.4 ENERGY ANALYZERS

There are three basic means of measuring the energy of

charged particles in a beam. These involve measuring the

time of ﬂight over a known distance, the retarding potential

required to stop the particles, or the extent of deﬂection in

an electric or magnetic ﬁeld.

Because of the great velocities involved, the ﬂight time

of a charged particle over any reasonable distance is very

short. Determination of the kinetic energy of a particle

from the time required to cover a distance of a few centi-

meters typically requires electronics with a response time

of a few nanoseconds. Time-of-ﬂight analyzers are used for

energy analysis of electrons with energies less than 10 eV

and ions below 1 keV.

Placing a grid or aperture in front of a particle collector

and var ying the potential on this element will perform an

energy analysis of the particles in a beam.

This is a retard-

ing potential analyzer. The current at the collector is the

integrated current of particles whose energy exceeds the

potential established by the grid. As the grid potential is

reduced from that at which all current is cut off, the collector

current increases. To obtain the energy distribution, the inte-

grated current as a function of retarding potential must be

differentiated. One drawback to this method is that only the

Figure 5.25 A duoplasmatron ion source.

ENERGY ANALYZERS 345

component of velo city normal to the retarding grid is

selected. There are also a number of practical difﬁculties.

The ratio of the initial energy to the energy at the potential

barrier varies rapidly for particles near the threshold for pen-

etrating the retarding barrier. This giv es rise to rapidly vary-

ing focusing effects near the threshold, so particles

approaching slightly off axis are often deﬂected away from

the collector. The result is that the transmission of the ana-

lyzer is unpredictable near the threshold. Another problem

with retarding-potential analyzers is that low-energy particles

near the retarding grid are seriou sly affected by space charge

and by stray electric and magnetic ﬁelds. Retarding potential

analyzers are very easily constructed and very compact, b ut

the vagaries of their performance suggests that their use for

high-resolution energy analysis be avoided if possible.

The energies of particles in a beam can be determined by

passing the beam through an electric or magnetic ﬁeld, so

that the deﬂection of the particle paths is a function of the

particle energy per unit charge or momentum per unit

charge. In these dispersive-type analyzers, the shape of

the deﬂection ﬁeld must be carefully controlled. Since it

is generally easier to produce a shaped electric ﬁeld than

a shaped magnetic ﬁeld, dispersive analyzers for particle

energies up to several keV are usually of the electrostatic

variety. For very high-energy particles, magnetic analyzers

are preferred, since production of the required electric ﬁelds

would demand inconveniently large electrical potentials.

The energy passband, DE, of an analyzer may be deﬁned

as the full width at half maximum (FWHM) of the peak that

appears in a plot of transmitted current versus energy. Ideally

the transmission function is triangular. For a real analyzer it

resembles a Gaussian. W e shall take DE to be half the full

width of the transmission function; such an approximation

overestimates the passband of a real analyzer.

To ﬁrst

order, entrance and exit slits or apertures, usually of equal

width w, establish the passband. The transmission function

also depends upon the maximum angular extent to which

particles can deviate from the central path leading from the

entrance to the exit slit. This angular deviation is deﬁned by

angles Da in the plane of deﬂection and Db in the perpen-

dicular plane. If E is the central energy of particles trans-

mitted through an analyzer , then the resolution is:

¼ aw þb DaðÞ

þc DbðÞ

ð5:83Þ

where a, b, and c are constants characteristic of the partic-

ular analyzer.

5.4.1 Parallel-Plate Analyzers

The simplest electrostatic analyzer employs a uniform

ﬁeld created by placing a potential difference across a pair

of plane parallel plates, as shown in Figure 5.26. With the

entrance

and exit slits in one of the plates, ﬁrst-order focus-

ing in the deﬂection plane is obtained when the angle of

incidence of entering particles is about a ¼ 45°.

The deﬂection potential V

(V), in relation to the inci-

dent energy E(eV), the plate spacing d, and the slit sepa-

ration L, is given by:

¼ E=qðÞ

ð5:84Þ

with the proviso that d > L/2, to prevent particles from

striking the back plate. The resolution is:

þ DaðÞ

DbðÞ

ð5:85Þ

Figure 5.26 Parallel-plate analyzers with (a) the

energy-resolving slits in one of the plates and (b) the slits in a

ﬁeld-free region.

346 CHARGED-PARTICLE OPTICS

A point at the entrance aperture is focused into a line of

length 2

ﬃﬃﬃ

LDb, and the length of the exit slit is corre-

spondingly greater than that of the entrance slit.

When the slits are placed in a ﬁeld-free region,

as in

Figure 5.26(b), optimum performance is obtained with the

angle

of incidence a ¼ 30°. The distance from the slits to

the entrance plate of the analyzer d

 0:1d

, where d

the plate spacing. The deﬂection potential is:

¼ 2:6 E=qðÞ



ð5:86Þ

This arrangement gives second-order focusing in the plane

of deﬂection. The resolution is:

¼ 1:5

þ 4:6 DaðÞ

þ 0:75 DbðÞ

ð5:87Þ

and the image of a point on the entrance slit is a line of

length 4LDb at the exit slit.

Although the parallel plate is an attracti ve design because

of its simple geometry, there are several problems. The

entrance apertures or slits in the front plate are at the boun-

dary of a strong ﬁeld and act as lenses to produce unwanted

aberrations. This problem can be alleviated for the design

with the energy-resolving slits in a ﬁeld-free region by

placing a ﬁne wire mesh over these entrance apertures to

mend the ﬁeld. A large electrical potential must be applied

to the back plate, creating a strong electrostatic ﬁeld outside

the analyzer. The apparatus in which the analyzer is installed

must often be shielded from this ﬁeld. In addition, because

the gap between the plates is large, the fringing ﬁeld at the

edges of the plates can penetrate into the deﬂection region.

This problem can be solved by extending the edges of the

plate well beyond the deﬂection region, or by placing com-

pensating electrodes at the edges of the gap, as in Figure 5.27.

5.4.2 Cylindrical Analyzers

Two electrostatic analyzers employ cylindrical electrodes.

These are the radial cylindrical analyzer and the cylindri-

cal mirror analyzer.

The radial cylindrical analyzer is shown in Figure 5.28.

The

radial electric ﬁeld is produced by an electrical poten-

tial placed across concentric cylindrical electrodes. Par-

ticles are injected midway between the electrodes in a

direction approximately tangent to the circular arc of

radius R

. First-order focusing is obtained if the cylindrical

electrodes subtend an angle of p=

ﬃﬃﬃ

¼ 127°. Assuming

a charged particle that originates at ground potential with

essentially no kinetic energy, and a mean pass energy E ¼

qV (that is, the energy of the particle that travels along

the central path of radius R

), the potentials to be applied

to the outer and inner cylindrical elements are:

outer

¼ V 1  2ln



ð5:88Þ

and

inner

¼ V 1  2ln



ð5:89Þ

Figure 5.27 Guard electrodes at the edges of a

parallel-plate analyzer to offset the distortion of the

ﬁeld caused by fringing.

Figure 5.28 The radial cylindrical analyzer.

ENERGY ANALYZERS 347

where R

and R

are the radii of the outer and inn er

cylinders, respectively. The potentials on the electrodes

are such that a charged particle that enters at the mid-

radius R

with an energy equal to the pass energy E will

lose an amount of energy e qual to 2E ln R

were it to

travel to the outer electrode, and would gain an amount

of energy equal to 2E ln R

were it to travel to the

inner electrod e.

The resolution of this analyzer is:

DaðÞ

DbðÞ

ð5:90Þ

It is good practice to limit the angle of divergence in the

plane of deﬂection so that:

Da <

ﬃﬃﬃ

ðR

 R

ð5:91Þ

in order to keep the ﬁlling factor below 50%. The radial-

ﬁeld analyzer gives focusing only in the plane of deﬂec-

tion. A point at the entrance slit is imaged as a line of

length

ﬃﬃﬃ

Db at the exit slit.

The cylindrical-mirro r analyzer is similar to the

parallel-plate analyzer except the deﬂection plates are

coaxial cylinders. In fact, the parallel-plate analyzer can

be considered a special case of the cylindrical mirror. In

the usual geometry, shown in Figure 5.29, the source is

cated on the axis, and particles emitted into a cone deﬁned

by polar angle a pass through an annular slot in the inner

cylinder. Particles of energy E are deﬂected so that they pass

through an exit slot and are focused to an image on the axis.

The cylindrical mirror is double-focusing (focusing occurs

in both the deﬂection plane and the perpendicular plane) so

that the image of a point at the source appears as a point at

the detector. An obvious advantage of this analyzer is that

particles at any azimuthal angle can be collected.

For optimum performance the entry angle a ¼ 42.3°,in

which case the distance from source to detector is L ¼

6.12R

The inner cylindrical plate is at the same poten-

tial as the source, and the potential on the outer cylinder,

relative to the inner cylinder, is:

outer

¼ 0:763 E=qðÞln

ð5:92Þ

It is wise to choose R

>2.5R

so that particles are

not scatte red from the outer electrode. The resolution

of the axial-focusing cylindrical-mirror analyzer is

approximately:

¼ 1:09



ð5:93Þ

for a source of axial extent w and an energy-resolving

aperture of diameter w

¼ w sin a perpendicular to the axis

(as shown in Figure 5.29).

the source is not small and well deﬁned, the entry

and exit slots in the inner cylinder can be used to

deﬁne the resolution of the cylindrical-mirror analyzer,

as in Figure 5.30; this arrangement is only ﬁrst-

ord

er-focusing.

5.4.3 Spherical Analyzers

For many applications, the most desirable ana lyzer

geometry employs an inverse-square-law ﬁeld cre ated

by placing a potential across a pair of concentric

spherical electrodes. Focusing in both the deﬂection

plane and the perpendicular plane can be obtained

using any sector portio n of a sphere. As shown in

Figure 5.31, the object and image lie on lines that are

Figure 5.29 Axial-focusing cylindrical-mirror analyzer.

Figure 5.30 Cylindrical-mirror analyzer with

energy-resolving slits in the inner electrode.

348 CHARGED-PARTICLE OPTICS

perpendicular to the entrance and exit planes, respec-

tively, and tangent to the circle described by the

midradius R

.Furthermore,byBarber’s rule, the object,

the center of curvature of the spheres, and the image lie

onacommonline.The180° spherical sector (Figure

32) is often used because of the c ompact geometry

that

results from folding the beam back onto a line

parallel to its original path. As with the cylindrical

mirror, the spherical analyzer can be used to collect

all particles emitted from a point source at or near a

particular polar angle.

Assuming a charged particle that originates at ground

potential with essentially no kinetic energy, and a mean

pass energy E ¼qV (that is, the energy of the particle

that travels along the central path of radius R

), the

potentials to be applied to the outer and inner spherical

elements are:

outer

¼ V 2

 1



ð5:94Þ

and:

Figure 5.32 The hemispherical analyzer: w is the width

of the entrance and exit apertures, Da the maximum

angular deviation of an incident trajectory, and w

the

maximum deviation of a trajectory from the central path

through the analyzer.

Figure 5.31 Focusing of a spherical analyzer.

ENERGY ANALYZERS 349

inner

¼ V 2

 1



ð5:95Þ

where R

and R

are the radii of the outer and inner spheres,

respectively; in general, the potentials on the electrodes are

such that a charged particle that enters at the midradius R

with an energy equal to the pass energy E will lose an

amount of energy equal to 2E 1 R

ðÞwere it to travel

to the outer electrode, and would gain an amount of energy

equal to 2ER

 1ðÞwere it to travel to the inner electrode.

The resolution of the 180° spherical sector (Figure 5.32)is:

DaðÞ

ð5:96Þ

and the maximum deviation, w

, of a trajectory from the

central path within the analyzer is given by:

þ Da þ

2Da



ð5:97Þ

For the truncated spherical sector shown in Figure 5.31, the

resolution

is approximately:

ð1  cos /Þþsin /

ð5:98Þ

where / is the angle subtended by the analyzer sector and l

is the distance from the exit boundary of the analyzer to the

exit aperture. Although it would appear that the resolution

could be increased arbitrarily by increasing l, the aberra-

tions increase rapidly as the system becomes asymmetric.

It is best to employ the symmetric geometry with / in the

range 60–180°.

In comparison with the parallel-plate or cylindrical-mir-

ror analyzers, the spherical analyzer has the advantage of

requiring relatively low electrical potentials on the electro-

des. Because the electrodes are closely spaced in the spher-

ical analyzer, fringing ﬁelds are less of a problem and more

easily controlled. The chief drawback of this type of ana-

lyzer is the difﬁculty of fabrication and mounting.

5.4.4 Preretardation

In all electros tatic-deﬂection analyzers, the passband DE

is a linear function of the transmitted energy. Thus, the

absolute energy resolution of these devices can be

improved by retarding the inci dent particles prior to t heir

entering the a nalyzer. In principle, the passband of an

analyzer can be reduced arbitrarily by preretardation;

in practice, there are limitations on this technique. A

decelerating lens as in the example given in Section

2.6 can slow charged particles incident on the entrance

aperture

of an analyzer. It would be very difﬁcult, how-

ever, to design a lens system to be used with analyz ers

that have an annular entrance slit. Space charge and stray

electric and magnetic ﬁelds must be considered. Because

the ﬂight path through an analyzer is long, it is usually

not possible to reduce the energy of transmitted particles

below about 2 eV before these effects result in severe

aberrations. Finally, it is important to recall that if

all particles of a particular energy in a b eam are to be

transmitted through an analyzer, the ratio of brightness

to energy must be conse rved (Section 5.1.3). As the

ener

gy of particles incident on an analyzer is decreased,

the current is ultimately reduced because the pencil

angle of the beam exceeds the acce ptance angle of the

analyzer.

When using a decelerating lens with an analyzer, it is

good prac tice to place an aperture on the high-energy

side of the lens and design the lens so that the image of

this aperture appears at the entrance plane of the ana-

lyzer. The need for a real entrance aperture is thereby

eliminated, and there are no metal surfaces in the vicinity of

the low-energy beam. Since space charge will cause the

low-energy beam to expand at the entrance plane of an

analyzer, current would be lost if a real entrance aperture

were used. As demonstrated by Kuyatt and Simpson,

space-charge expansion at a virtual aperture is compen-

sated by the spreading of the beam, with the result that

the beam appears to originate at an aperture of about the

same size as that in the absence of space charge

(see

Figure 5.16).

5.4.5 The Energy-Add Lens

An electrostatic energy analyzer can be used as a mono-

chromator to select the particles in a beam whose energies

fall within a narrow range, or as an analyzer to determine the

energy distribution of particles originating from a process

under study. In the latter application the passband of the

analyzer must be scanned over the energy range of interest.

350 CHARGED-PARTICLE OPTICS

Scanning can be accomplished by varying the potential dif-

ference between the analyzer electrodes; however, neither

the transmission nor the energy resolution will be constant.

A more satisfactory method for determining the energy dis-

tribution of particles in a beam is to ﬁx the analyzer poten-

tial at the voltage that allows transmission of particles of the

highest desired energy and preaccelerate the incident par-

ticles by a variable amount. The energy that must be added

to the particles so that they pass through the analyzer is then

a measure of the difference between their initial energy and

the energy necessary to transmit them with no preaccelera-

tion. In a scattering experiment, for example, the analyzer

might be set to transmit elastically-scattered particles, and

the distribution of energy lost by inelastically scattered par-

ticles would be scanned by monitoring the transmitted cur-

rent as a function of energy added.

An energy-add lens must add back energy without dis-

turbing the optics of the analyzer. Kuyatt

showed that the

electron-optical analog of the ﬁeld lens is suited to this

application. This lens is positioned so that its ﬁrst principal

plane coincides with the particle source to be examined.

The source is then imaged onto the second principal plane

with unit magniﬁcation. For a reasonably strong lens (V

> 3), the position of the principal planes is nearly independ-

ent of the voltage ratio and the separation of the planes is

small. Thus particles from the source can be accelerated by

a variable amount without changing the apparent position

of the source. An energy-add lens used in conjunction with

a ﬁxed-ratio decelerating lens for preretardation at the input

of an electron energy analyzer is schematically illustrated

in Figure 5.33. For transmission of electrons with energy A

(eV

) less than the maximum energy to be transmitted, the

Figure 5.33 An energy-add lens and ﬁxed-ratio retarding lens at the input of an analyzer.

The energies and corresponding lens voltages for electrons transmitted with no added

energy are given above the lens. Energies and voltages for transmission of electrons that

have lost energy A are shown below. The ‘‘source’’ is deﬁned by an aperture that is ﬁnally

imaged at the entrance plane of the analyzer.

ENERGY ANALYZERS 351

potential of the second element of the energy-add lens and

every electrode thereafter is increased by A (V). For a

positive ion analyzer, the potential would be decreased by

A/n (V), where n is the charge state of the ions.

A problem with the energy-add lens is that the object pupil

moves as the lens voltages change. Thus, while the apparent

source remains stationary, the beam angle may v ary over a

considerable range as the lens is tuned. As a result, the lenses

following the energy-add lens may be overﬁ lled. This can be

avoided by placing a second ﬁeld lens downstream from the

ﬁrst at an intermediate image of the apparent source. The

second ﬁeld lens is then tuned to gi v e a zero beam angle. An

einzel lens (Section 5.2.2) can be used so that there is no net

change

of energy as the beam angle is manipulated.

5.4.6 Fringing-Field Correction

For the radial-ﬁeld cylindrical analyzer or the spherical ana-

lyzer, particles must pass through the fringing ﬁeld at the

edge of the electrode gap as they enter the deﬂection region.

The electric ﬁeld at the edge bulges out of the gap, and this

curvature produces a focusing effect that causes undesirable

aberrations. Herzog

and Wollnik and Ewald

have shown

that a diaphragm at the entrance of the condenser gap can

largely eliminate this problem. As illustrated in Figure 5.34,

e diaphragm, when properly located, produces a ﬁeld that

has the same effect as a ﬁeld abruptly terminated at a dis-

tance d* in front of the condenser gap. The appropriate

location of the diaphragm as a function of the dimensions

given in Figure 5.34 can be determined for either a thick or

in diaphragm from the graphs in Figure 5.35.

Figure 5.34 A shielding diaphragm to correct for focusing

at the fringing ﬁeld at the edge of an electrostatic

condenser. The ﬁeld appears as if it were terminated

abruptly at a distance d* from the gap.

Figure 5.35 The distance of the apparent ﬁeld boundary

from the edge of the condenser electrodes as a function of

the dimensions given in Figure 5.34 for (a) a thick

diaphragm

and (b) a thin diaphragm. (From H. Wollnik and

H. Ewald, ‘‘The Inﬂuence of Magnetic and Electric Fringing

Fields on the Trajectories of Charged Particles,’’ Nucl. Instr.

Meth., 36, 93 (1965); by permission of North-Holland

Publishing Company.)

352 CHARGED-PARTICLE OPTICS

5.4.7 Magnetic Energy Analyzers

Magnetic ﬁelds are employed in se veral charged-particle-

energy analyzers and ﬁlters. The trochoidal analyzer

[Figure 5.36(a)] has proven quite useful for the dispersion

very-lo w-ener gy (0 to 10 eV) electrons and ions. This

device employs a magnetic ﬁeld aligned with the direction of

the charged-particle beam, and an electric ﬁeld perpendicu-

lar to this direction.

The trajectory of a particle injected

into this analyzer describes a spiral and the guiding center of

the spiral drifts in the remaining perpendicular direction. The

drift rate depends upon the particle energy; a beam entering

the device is dispersed in energy at the exit. The projection of

the trajectory on a plane perpendicular to the electric ﬁeld

direction is a trochoid, hence the name. The de vice requires a

very uniform magnetic ﬁeld of about 100 gauss. The ﬁeld is

usually produced by a relatively large Helmholtz pair (see

Section 5.6.5) mounted outside the vacuum system contain-

ing

the analyzer. The result is that the entire experiment is

immersed in the ﬁeld. This may be a drawback in some

cases, but, on the other hand, for low-energy electrons or

ions, the ﬁeld helps contain particles that otherwise would be

lost from coulombic repulsion (i.e., space charge).

The Wien ﬁlter [Figure 5.36(b)] similarly employs crossed

electric

and magnetic ﬁelds, howev er , the ﬁelds are perpendic-

ular to one another and both are perpendicular to the injected

beam direction.

The Coulomb force induced by the electric

ﬁeld E deﬂects charged particles in one direction and the

Lorentz force associated with the magnetic ﬁeld B tends to

deﬂect them in the opposite direction. The forces balance for

one velocity , v ¼ |E|/|B|, and particles of the corresponding

energy are transmitted straight through to the exit aperture.

A magnetic ﬁeld alone, perpendicular to the direction of

a charged-particle beam will provide energy dispersion,

provided that the particles are all of the same mass and

charge [Figure 5.36(c)]. Sector magnets such as those used

mass spectrometers are used in electron spectro-

meters for very-high-energy electrons and ions, the advant-

age over electrostatic deﬂectors being that large electrical

potentials are not required. Another advantage is that the

deﬂection is in the direction parallel to the magnet pole

face, making it possible to view the entire dispersed spec-

trum at one time. In contrast, energy dispersion in an

electrostatic device results in a signiﬁcant portion of the

dispersed particles striking one or the other electrode.

Figure 5.36 Charged-particle energy analyzers with

magnetic ﬁelds: (a) the trochoidal analyzer with an

electromagnet; (b) the Wien ﬁlter; (c) the sector

magnet analyzer. Trajectories for electrons of differ ent

energies are shown. Magnet polarities are for electrons.

ENERGY ANALYZERS 353

5.5 MASS ANALYZERS

Mass analysis is more complicated than energy analysis of

an isotopically pure beam, since energy and momentum

are independent variables in a mixed beam. A detailed

discussion of the many types of mass analyzers that have

been developed is beyond the scope of this book. The

principles of operation of a few representative analyzers

will be described.

5.5.1 Magnetic Sector Mass Analyzers

The deﬂection of ions in a perpendicular magnetic ﬁeld is

proportional to the particle momentum per unit charge. If

all particles entering a magnetic ﬁeld have the same

energy per unit charge, then the ﬁeld will separate par-

ticles according to their masses. In the usual c onﬁgura-

tion, a magnetic ﬁeld is produced between the two

parallel, sector-shaped polefaces of an electromagnet,

as illustrat ed in Figure 5.37. The focusing properties of

this

ﬁeld

are the same as those of the spherical electro-

static analyzer, a nd the locations of the e ntrance and exit

slits are given by Barber’s rule (Section 5.4.3). The

radiu

s of curvature of ions of energy E in a magnetic

ﬁeld of intensity B is:

R ¼

144

ﬃﬃﬃﬃﬃﬃﬃ

cm ð5:99Þ

with B in gauss, E in eV, m in amu, and n the charge state.

In terms of the parameters speciﬁed in Figure 5.37, the

resolution

is:

1  cos /ðÞþ‘ sin /

ð5:100Þ

where R

is the radius of curvature of the central trajec-

tory. To ﬁrst order, there is no focusing in the plane

perpendicular to the plane of deﬂection. When the cur-

vature of the fringing ﬁeld is taken into consi deration,

however, so me focusing in the perpendicula r plane

results. Incident ion trajectories should be normal to

the entrance pla ne to avoid focusing e ffects.

5.5.2 Wien Filter

The W ien ﬁlter , employing mutually perpendicular electric

andmagneticﬁeldsnormaltotheiontrajectory[Figure

.36(b)] can serve to disperse char ged particles according

either mass or energy.

Ions of a unique velocity v will

experience equal and opposite forces through interaction

with the two ﬁelds (the Coulomb force and the Lorentz

force) and be transmitted in a straight line. If all of the ions

injected into the ﬁelds of the Wien ﬁlter ha v e the same

kinetic energy, ions of a unique mass are transmitted straight

through; if the injected ions have all been accelerated

through the same potential (relativ e to their source), ions

of a unique mass-to-charge ratio are transmitted. In most

W ien ﬁlters a pair of permanent magnets supplies the mag-

netic ﬁeld, and the electric ﬁeld is produced by placing an

electrical potential V

across a pair of parallel electrodes

separated by a distance d. The velocity of ions transmitted

straight through the Wien ﬁlter is

v ¼ 10

cm s

1

ð5:101Þ

with V

in volts, d in cm, and B in gauss. Varying V

scans

the mass spectrum of ions. If slits of width w are placed at

the entrance and exit of a Wien ﬁlter of length L, the mass

resolution for ions of energy E is:

2dEw

ð5:102Þ

assuming the incident ion trajectories are normal to the

entrance plane. Boersch, Geiger, and Stickel have made a

detailed analysis of the focusing properties of the Wien ﬁlter.

Figure 5.37 Focusing of the magnetic sector.

354 CHARGED-PARTICLE OPTICS

5.5.3 Dynamic Mass Spectrometers

Dynamic mass spectrometers use time-varying electric or

magnetic ﬁelds or timing circuits to disperse ions accord-

ing to their masses.

The quadrupole mass analyzer and

the linear time-of-ﬂight mass spectrometer are the two

most successful designs of this type.

The quadrupole mass analyzer illustrated in Figure 5.38

employs a time-v arying electric quadrupole ﬁeld. For a par-

ticular

ﬁeld intensity and frequency, only ions of a unique

mass-to-charge ratio will follow a stable path and pass

through the ﬁeld. As shown in the ﬁgure, the quadrupole

ﬁeld is approximated by a square array of four cylindrical

electrodes parallel to the axis along which ions are injected.

The potential applied to the vertical pair of electrodes is:

¼ U þ V cos 2pft ð5:103Þ

while for the horizontal pair

¼U þV cos 2pft þpðÞ ð5:104Þ

where f refers to an r.f. frequency. For optimum perform-

ance the ratio of the d.c. ﬁeld to the r.f. ﬁeld is adjusted so

that U/V  0.17. For singly charged ions, the mass of the

ions that are transmitted is:

m ¼ 0:14

amu ð5:105Þ

with V in volts, r in cm, and f in MHz. Mass scanning is

usually accomplished by varying the r.f. amplitude V, while

ﬁxing the ratio of d.c.-to-r.f. voltage (U/V) and the fre-

quency (f). Quadrupole analyzers are compact and offer

the advantages of high transmission, fast scanning, and

insensitivity to the initial ion energy. These instruments

are available commercially as residual-gas analyzers for

high-vacuum systems and are suitable for use in many

scattering experiments.

The time-of-ﬂight mass spectrometer depends upon the

fact that the velocity of ions of the same kinetic energy is a

function of mass. In this spectrometer, positive (negative)

ions that have been accelerated to an energy of about 1 keV

are admitted to a long drift tube in short bursts by a

negative (positive) electrical pulse applied to a grid at

the entrance of the drift region. The lightest ions travel

most rapidly and are the ﬁrst to arrive at the detector

located at the end of the drift tube. Heavier ions arrive in

the order of their masses. The obvious advantage of this

design is that the entire mass spectrum is scanned in a few

microseconds. Furthermore, the spectrum can be scanned

thousands of times each second, making this system ideal

for studying rapidly varying processes. Its chief drawback

is its size, since the length of the ﬂight tube required

to achieve good resolution may be greater than a meter.

5.6 ELECTRON- AND ION-BEAM

DEVICES: CONSTRUCTION

To realize the design of a charged-particle optical system,

it is necessary to create an environment where a stream of

particles can travel without loss of momentum and to make

electrodes and pole pieces that faithfully produce the elec-

trical and magnetic ﬁelds necessary to deﬂect the particles.

5.6.1 Vacuum Requirements

Charged particles lose energy through interactions with

gas molecules; thus ions or electrons can only be trans-

ported in a vacuum. The required pressure depends upon

the distance they must travel. As noted in Section 3.1.2, the

mean

free path at a pressure of 1 mtorr is a few centimeters,

while at 10

5

torr this increases to a few meters. It follows

that high vacuum is required for the operation of a

charged-particle optical system.

Figure 5.38 The quadrupole mass analyzer.

ELECTRON- AND ION-BEAM DEVICES 355

Conducting surfaces must be kept clean, since contamina-

tion with an insulating material will result in the buildup of

surface charges that cause an unpredictable deﬂection of

charged particles passing nearby . Clean electrode surfaces are

particularly important for particles of energy less than 100 eV

and when high spatial resolution is required. All electrodes

must be clean and free of hydrocarbon contamination before

installation in the vacuum system (Section 3.6.3). An oil-free

acuum system with turbomolecular pumps, ion pumps, or

sorption pumps (Section 3.4.3) is most desirable, although a

system

ev acuated with a properly trapped oil diffusion pump

(Sections 3.5.5 and 3.4.2) is adequate in many cases.

Polyphen

yl ether diffusion-pump ﬂuids such as Con v alex-

10 (Consolidated Vacuum) or Neo v ac Sy (Varian) have been

found to be the least offensiv e diffusio n-pump oils for electron-

optical syste ms. In lo w-energy-beam de vices, a daily bake to

200–300 ° C will keep electrode surfaces clean and ensure

stable operation. Hydrocarbons on aperture surfaces exposed

to charged particles create a particularly obnoxious problem.

Bombardment of the adsorbed hydrocarbons produces an insu-

lating carbon polymer that adheres tenaciously to the under-

lyingmetal.Thiscarbonmaterialcanonlyberemovedby

high-temperature baking (400° C), by vigorous application

of an abrasi ve, or by etching with a strong solution of NaOH.

When baking is impractical, electrode surface quality and

stability are often impro v ed by a coating of carbon black. A

surface can be blacked by brushing with a sooty acetylene

ﬂame; howe v er, the coating produced in this manner does not

adhere well. A superior coating can be produced by spraying

or brushing the surface with a thin water or ethanol slurry of

colloidal graphite (Aquadag, made by Acheson Colloids Co.).

The tenacity of this coating is improved by preheating the

metal surface to about 100 °C before the slurry is applied.

5.6.2 Materials

The materials used to construct lens elements must be such

that the equipotential surfaces near the electrodes faithfully

follow the contours of the electrode surfaces. These surfaces

must be clean, and must withstand periodic cleansing by bak-

ing, bead blasting, electropolishing, or harsh chemical action.

The refractory metals such as tungsten, tantalum, and

particularly molybdenum are probably the best electrode

materials. These metals have a low, uniform, surface poten-

tial, they do not oxidize at ordinary temperatures, and they

are bakeable. Refractory metals are hard and rather brittle.

Only the wrought material can be machined or formed

easily. Stock produced by sintering is very difﬁcult to

machine. Electrodes spun from sheet molybdenum are

available in cylindrical and spherical shapes (Bomco, Inc.).

Oxygen-free high-conducti vity (OFHC) copper (Section

3.3) is often used for electrode fabrication, although Kuyatt

used

commercial, half-hard copper in some applications.

Exposed to air , copper forms a surface oxide, but this oxide

is conducting. Copper is bakeable and reasonably machinable.

Stainless steels (Section 1.3.1) contain domains of differ-

ent

composition, some of which may be ferromagnetic. The

magnetic properties of stainless steels vary considerably,

even between samples of the same net composition; these

materials are unsuitable for use with low-energy charged

particles unless they are carefully annealed to remove resid-

ual magnetism (Section 1.3.1). Stainless steels have the

adv

antage of being bakeable, strong, and easy to machine.

Aluminum (Section 1.3.4) is unsuitable, because its sur-

face

is rapidly attacked by oxygen in the air to form a hard,

insulting, layer of oxide. On the other hand, aluminum has

a low density, and most aluminum alloys are easy to

machine or form by bending, spinning, or rolling. When

these properties are important, the surface can be plated

with copper or gold to overcome the problem of oxidation.

Electrodes and lenses must be mounted on nonconducting

materials. Glass or ceramic (Section 1.3.7) or, in some cases,

plastic

(Section 1.3.6) can be used for this purpose. Of the

eramic materials, alumina is the best insulator and the stron-

gest. Precision-ground rods and balls are av ai lable commer-

cially. Alumina circuit board substrate in the form of thin

plates laser-cut in complex shapes can be obtained quite inex-

pensiv ely. There are also machinable ceramics from which

complicated shapes can be formed (MACOR from Corning).

As noted in Chapter 3, it is important to be aware that the

resistivity of a ceramic is strongly dependent upon temper-

ature. The resistivity of a ceramic material falls by roughly

a factor of 10 for ev ery 100 ° C increase in temperature.

For example, the resisti vity of alumina is greater than 10

ohm cm at 100 ° C and falls belo w 10

ohm cm at 1000 ° C.

Plastics are machinable and inexpensive. Unfortunately,

they are not bakeable; a further disadvantage is that they

contain hydrocarbons that can contaminate the vacuum

environment. Polyimide plastic sheet (Kapton) is a useful

insulator.

356 CHARGED-PARTICLE OPTICS

Mica in sheets is an excellent insulator (‘‘stove mica’’

from Spruce Pine Mica Co.).

5.6.3 Lens and Lens-Mount Design

Most electron-optical lenses are created by the ﬁelds in the

gap between coaxial cylindrically symmetric electrodes.

These electrodes must be designed so that electric ﬁelds

associated with the lens mounts and the vacuum-container

walls do not penetrate the gap between electrodes. The

involuted design illustrated in Figure 5.39 ensures that

the

lens gap is shielded. The step on the shoulder of the

lens elements is designed so that the inner gap is of the

correct size when the outer gap is adjusted to some stand-

ard width. In this way all the lenses in a system can be

correctly positioned with the aid of a single gauge.

There are two widely used, semikinematic schemes for

mounting lens elements. These are the rod mount and the

ball mount, illustrated in Figures 5.40 and 5.41, respectiv ely.

the rod mount, cylindrical lens elements rest on ceramic

rods that insulate the elements from one another and from

a grounded mounting plate. The critical dimensions are

the diameters of the lens elements and the width of the

channel in which the rods rest. In order for the lens element s

to be coaxial, their outer diameters must be identical. This

requirement is met by making all of the elements from a

single piece of rod stock that has been carefully turned to a

uniform diameter. To ensure that the elements are mounted

coaxially, it is then only necessary that the sides of the

Figure 5.39 Tube lens electrodes are constructed so that

external ﬁelds cannot penetrate the lens gap. When

mounting the lens elements, a gauge is inserted to ensure

correct spacing at the invisible lens gap.

Figure 5.40 Cylindrical lens elements mounted on ceramic

rods.

Figure 5.41 Lens elements mounted on ceramic balls.

ELECTRON- AND ION-BEAM DEVICES 357

channel in which the rods rest be parallel. This is easily

accomplished in a milling operation. If the ver ti cal position

of the lens axis is important, then the width of the channel

becomes a critical dimension. Of course, the diameter of the

rods is important, but, as noted elsewhere (Section 1.3.7),

alumina

rod, centerless-ground to high precision, is commer-

cially available. For maximum strength the rods should be

about 90° apart around the circumference of the lens element.

In the ball-mounting scheme, lens elements are insulated

from one another and positioned by ceramic balls that rest in

holes near the edges of the lenses. This system is preferred

when mounting very thin elements, as in an aperture-lens

system. Ideally only three balls should be used. The critical

dimensions are the locations of the holes and their diameter .

The holes should be bored, or drilled and reamed, in a milling

machine or jig borer using a dividing head or a precision

rotary table. For balls of diameter d, the hole diameter should

be d sin 45°, in which case the spacing between lens elements

will be d cos 45°. A lens system is assembled by stacking lens

elements alternating with balls. The stack must be clamped.

The clamp should hav e some spring and should bear on the

topmost element only at one or two points near the center of

the circle around which the balls are located. A rigid clamp

will tend to drive the balls into their holes and may crush the

edges of the holes. If the clamp bears too near the edge, there

is a danger that the stack may become cocked off axis.

5.6.4 Charged-Particle Detection

For particle energies up to a few tens of keV, a stream of

charged particles of sufﬁcient intensity can be collected

and measured directly as an electrical current. To achieve

the greatest sensitivity, individual ions or electrons can be

detected with an electron multiplier. Charged particles can

also be detected with photographic emulsions, scintilla-

tors, and various solid-state devices. Emulsions and scin-

tillators have largely been supplanted by the methods

mentioned above, and solid-state devices (Section 7.9.1)

are

only suitable for the detection of high-energy particles

(above 30 keV).

The collector for the direct detection of a current of

charged particles is called a Faraday cup. Typical designs

are illustrated in Figure 7.35. These simple collectors are

onnected directly to a current-measuring device and are

useful at currents down to the detection limits of modern

electrometers about 10

14

A. Their design and use is dis-

cussed in Section 7.9.

Single

charged particles can be detected with electron

multipliers. Their use and application is discussed in

Section 7.9.

5.6.5 Magnetic-Field Control

A magnetic ﬁeld may cause aberrations in a char ged-particle

optical system. The Earth’s magnetic ﬁeld is the usual source

of problems, but large concentrations of magnetic materials

nearby or large currents, such as those associated with a cyclo-

tron, may also produce magnetic ﬁelds of sufﬁcient intensity

to deﬂect the trajectories of electrons or ions in an optical

system. The Earth’ s magnetic ﬁeld is about 0.6 gauss directed

at an angle of elev ation in the north–south plane roughly equal

to the local latitude. Whether or not this is a problem depends

on the energy and mass of the transmitted charged particles,

and the dimensions of lens elements and apertures through

which the particles must pass. For example, the radius of

curvature of the path of a 10 eV electron moving perpendic-

ular to the Earth’ s ﬁeld is 15 cm; this amounts to a defection of

1.5 mm along a 1 cm path. For a low-energy (<100 eV)

electron spectrometer , such considerations may lead to a

residual-ﬁeld tolerance of less than 1 milligauss.

There are two methods to eliminate magnetic ﬁelds: an

opposing ﬁeld can be applied to cancel the offending ﬁeld

throughout the volume occupied by the apparatus, or the

apparatus can be enclosed in a shield of high permeability

ferromagnetic metal that shunt s the local ﬁeld around the

enclosure. An electromagnet constructed to make an oppos-

ing ﬁeld is the less expensive, but also the more ungainly,

approach; the dimensions of the coils may exceed by a factor

of 10 the dimensions of the apparatus to be shielded. In addi-

tion, without an elaborate feedback control, an electromagnet

can only cancel a constant (dipole) ﬁ eld. A magnetic shield

need be only large enough to contain the apparatus, but the

construction requires expensiv e fabrication and heat treat-

ment of the shielding alloy that is itself relatively expensi v e.

Electromagnets for canceling the ambient ﬁeld are

assembled from two or more pairs of current-carrying loops.

A continuous solenoid would be impractical, since access

to the interior volume is limited. Caprari has surveyed opti-

mal geometries for a range of possibilities.

The most

common arrangement consists of a pair of identical circular

358 CHARGED-PARTICLE OPTICS

magnet coils spaced apart by half the coil diameter. These

are referred to as Helmholtz pairs or Helmholtz coils.The

axis of the pair of coils must be oriented parallel to the ﬁeld

that is to be canceled. Alternatively, three pairs arranged

orthogonally can be used with the current to each adjusted

to give a net ﬁeld that opposes the offending ﬁeld. The

Helmholtz coil geometry is illustrated in Figure 5.42.The

ﬁ

eld along the axis of a round Helmholtz pair, a distance z

above the bottom coil is given by:

B ¼ 0:32

1 þ





3=2

þ 1 þ 1 





3=2

()

gauss

ð5:106Þ

where N is the total number of turns, I is in amperes, and R

and Z are in cm. For square coils, a similar expression with R

replaced by L/2 applies. The orientation of the coils and the

exact value of the current must be determined with the aid of

a magnetometer. The ﬁeld produced by a Helmholtz pair is

of high uniformity only in a small volume midway between

the coils and near the axis. For example, a uniformity

of 0.1% is achieved in a central volume of 2 3 10

2

cubic radii, a uniformity of 1% in a volume of 1.5 310

1

cubic radii, and a uniformity of 5% in a volume of 0.6 cubic

radii.

Thus, the coil dimensions must exceed those of the

apparatus to be shielded by at least a factor of 10 in order to

reduce the magnetic ﬁeld to a few milligauss. In addition, it

is important to recognize that a Helmholtz coil can only

cancel the dipole component of the ambient ﬁeld.

Shielding electron-optical devices from ambient magnetic

ﬁelds can be accomplished with an enclosure fabricated of

special high-permeab ility nickel–iron alloys.

These materi-

als are availab le as sheet or tubing and thus as a practical

matter are best formed into simple cylindrical shapes, either

with or without endcaps, depending on requirements of access

to the interior. Construction details are important in determin-

ing the performance of a magnetic shield. Removable parti-

tions and endcaps should be designed to overlap the ﬁxed

pieces to which they are attached and they should ﬁt tightly.

Permanent joints should be spot-welded lap joints or arc-

welded butt joints. Magnetic-shielding alloys only attain their

high permeability after annealing in a hydrogen atmosphere

follow ing a precisely deﬁ ned tempera ture schedule. Mechan-

ical stress degrades the permeability of the material so the

annealing is carried out after fabrication. It usually makes

sense to have a shield fabricated by a shop that is prepared

to do the annealing. Suppliers and fabricators of magnetic-

shielding mater ials include Amuneal Corp., Magnetic Metals

Co., and the Magnetic Shield Division of Perfection Mica Co.

A magnetic shield must be handled carefully. Bending or

sharp blows degrade the shielding properties, as will contact

with magnetic materials; magnetized tools are frequently the

culprits. The annealed material should not be heated above

400 °C. It must be emphasized that magnetic shielding cannot

be accomplished casually; a few sheets of ‘‘l-metal’’ wrapped

around a v acuum system will often do more harm than good.

The performance of a magnetic shield is speciﬁed by an

attenuation factor, A, given by the ratio of the magnetic ﬁeld

at a point in the absence of the shield to the ﬁeld strength

at the same point when it is surrounded by the shield:

A ¼

ð5:107Þ

Figure 5.42 Round and square Helmholtz coils.

ELECTRON- AND ION-BEAM DEVICES 359

The calculation of the attenuation factor is generally dif-

ﬁcult, howev er, since a shield is usually constructed of sheet

and tubing, a reasonable estimation can be made from

approximations to the attenuation factor for simple geomet-

ric shapes. The attenuation of a long cylindrical shield can be

approximated as that for an inﬁnitely long cylinder and the

attenuation of a closed box can be approximated as that for a

sphere. The attenuation factor depends upon the thickness of

the shielding material, the overall dimensions of the shield,

and l, the permeability of the shielding material. Low-

saturation alloys used to shield ﬁelds of the order of 1 gauss

have permeabilities of about 40 000. From the formulae

below it will be obvious that two or more nested shields of

thin material are much preferable to a single thick shield.

For a long cylinder, the attenuation factor is given

approximately by:

A 

ð5:108Þ

and for a sphere by

A 

2ld

ð5:109Þ

where R is the radius of the cylinder or sphere and d is the

thickness of the material. For a nested pair of cylinders or

spheres of radius R

and R

spaced apart by a distance

D ¼jR

 R

j, the attenuation factor:

A  A

ð5:110Þ

where A

and A

are the attenuation factors for each of the

cylinders or each of the spheres alone and R is the mean

radius of the two. Note that the attenuation increases with

the spacing between the two shields.

A sample calculation illustrates the advantage of multiple

shields: A single cylindrical shield, 20 cm in diameter of 1

mm thick material with a permeability of 40 000 gives an

attenuation factor of 200. Nested shields 20 cm and 22 cm in

diameter of the same material giv e an attenuation factor of

7000; for shielding from the Earth’ s magnetic ﬁeld, the dou-

ble shield reduces the ﬁeld well into the sub milligauss range.

An opening in a magnetic shield is often unavoidable. For

example a shield surrounding a vacuum system must be left

open at one end for attachment of the pump and for electrical

and mechanical feedthroughs. The external ﬁeld penetrates

into the opening. The attenuation near an opening reaches a

value of about two-thirds of the maximum attenuation of the

shield at a distance into the shield volume about equal to the

mean radius of the opening.

A skirt of shielding alloy

extending outward from an opening, thus effectively dis-

placing the opening outward from the shielded volume,

helps to alleviate the problem.

Cited References

1. K. R. Spangenberg, Vacuum Tubes, McGraw-Hill, New

York, 1948.

2. J. R. Pierce, Theory and Design of Electron Beams , 2nd edn.,

Van Nostrand, New York, 1954.

3. O. Klemperer and M. E. Barnett, Electron Optics, 3rd edn.,

Cambridge University Press, Cambridge, 1971.

4. V. E. Cosslett, Introduction to Electron Optics, Oxford

University Press, Oxford, 1946.

5. D. Roy and J. D. Carette Electron Spectroscopy, H. Ibach,

(Ed.), Topics in Current Physics, Springer, Berlin, 1977,

Chapter 2.

6. V. W. Hughes and H. L. Schultz (Eds.), Methods of Exper-

imental Physics, Vol. 4A, Atomic Sources and Detectors

Academic Press, New York, 1967.

7. E. Harting and F. H. Read, Electrostatic Lenses, Elsevier,

New York, 1976.

8. F . H. Read, J. Phys., E2, 165, 1969; (b) F. H. Read, J. Phys., E2,

679, 1969; (c) F. H. Read, A. Adams, and J. R. Soto-Montiel, J.

Phys., E4, 625, 1971; (d) A. Adams and F . H. Read, J. Phys., E5,

150, 1972; (e) A. Adams and F. H. Read, J. Phys., E5, 156, 1972.

9. S. Natali, D. DiChio, E. Uva, and C. E. Kuyatt, Rev. Sci.

Instr., 43, 80, 1972; D. DiChio, S. V. Natali, and C. E. Kuyatt,

Rev. Sci. Instr., 45, 559, 1974.

10. D. W. O. Heddle, Tables of Focal Properties of Three-

Element Electrostatic Cylinder Lenses, J.I.L.A. Report No.

104, University of Colorado, Boulder, 1970.

11. R. E. Collins, B. B. Aubrey, P. N. Eisner, and R. J. Celotta,

Rev. Sci. Instr., 41, 1403, 1970.

12. D. DiChio, S.V. Natali, C. E. Kuyatt, and A. Galejs, Rev. Sci.

Instr., 45, 566, 1974.

13. J. A. Simpson, in Methods of Experimental Physics, Vol. 4A,

V. W. Hughes and H. L. Schultz (Eds.), Academic Press, New

York, 1967, Section 1.15.

14. An estimation of image expansion at the space-charge limit

can be obtained from the data of W. Glaser, Grundlagen der

Elektronenoptik, Springer, Vienna, 1952, p. 75.

15. R. G. Wilson and G. R. Brewer, Ion Beams, Wiley, New

York, 1973.

360 CHARGED-PARTICLE OPTICS

16. C. D. Moak, H. E. Banta, J. N. Thurston, J. W. Johnson, and

R.F. King, Rev. Sci. Instr., 30, 694, 1959; M. von Ardenne,

Tabellen der Electronenghysit IonengRysik und Ubermilros-

kopie, Deutscher Verlag der Wissenschaften, Berlin, 1956.

17. W. Aberth and J. R. Peterson, Rev. Sci. Instr., 38, 745, 1967.

18. J. A. Simpson, Rev. Sci. Instr., 32, 1283, 1961.

19. M. E. Rudd Low Energy Electron Spectrometry,byK.D.

Sevier (Ed.), Wiley-Interscience, New York, 1972, Chapter

2, Section 3; A. Poulin and D. Roy, J. Phys., E11, 35, 1978.

20. T. S. Green and G. A. Proca, Rev. Sci. Instr., 41, 1409, 1970; G.

A. Proca and T. S. Green, Rev. Sci. Instr., 41, 1778, 1970.

21. V. V. Zashkvara, M. I. Korsunskii, and O. S. Kosmachev,

Soviet Phys. Tech. Phys., 11, 96, 1966; H. Sar-el, Rev. Sci.

Instr., 38, 1210, 1967, and 39, 533, 1968; J. S. Risley, Rev.

Sci. Instr., 43, 95, 1972.

22. C. E. Kuyatt and J. A. Simpson, Rev. Sci. Instr., 38, 103, 1967.

23. C. E. Kuyatt, unpublished lecture notes; see also A. J.

Williams, III, and J. P. Doering, J. Chem. Phys., 51, 2859,

1969; J. H. Moore, J. Chem. Phys., 55, 2760, 1971.

24. R. F. Herzog, Z. Phys., 89, 447, 1934; 97, 596, 1935; Phys.

Z., 41, 18, 1940.

25. H. Wollnik and H. Ewald, Nucl. Instr. Meth., 36, 93, 1965.

26. A. Stamatovic and G. J. Schulz, Rev. Sci. Instr., 39, 1752,

1968; A. Stamatovic and G. J. Schulz, Rev. Sci. Instr., 41,

423, 1970: L. Sanche and G. J. Schulz, Phys. Rev. A, 5

, 1672,

1972;

D. Roy, Rev. Sci. Instr., 43, 535, 1972.

27. R. L. Seliger, J. Appl. Phys., 43, 2352, 1972.

28. E. Segre, Experimental Nuclear Physics, Vol. 1, Wiley,

New York, 1953, part V.

29. H. Boersch, J. Geiger, and W. Stickel, Z. Phys., 180,415,

1964.

30. E. W. Blauth, Dynamic Mass Spectrometers, Elsevier,

Amsterdam, 1966; P. H. Dawson, Quadrupole Mass

Spectrometer, Elsevier, Amsterdam, 1976.

31. W. D. Kingery, H. K. Bowen, and D. R. Uhlmann,

Introduction to Ceramics, 2nd edn., John Wiley & Sons, Inc.,

New York, 1976, Chapter 17.

32. J. Millman and H. Taub, Pulse, Digital, and Switching

Waveforms, McGraw-Hill, New York, 1965, Chapter 3;

C. N. Winningstad, IRE Trans. Nucl. Sci., NS43, 26, 1959;

C. L. Ruthroff, Proc. IRE, 47, 1337, 1959.

33. L. J. Richter and W. Ho, Rev. Sci. Instr., 57, 1469, 1986; R. M.

T rom p, M. Copel, M. C. Reuter, etal.Rev.Sci.Instr., 62, 2679,

1991.

34. R. K. Cacak and J. R. Craig, Rev. Sci. Instr., 40, 1468, 1969.

35. R. Caprari, Meas. Sci. Technol., 6, 593, 1995.

36. The Deﬁnitive Guide to Magnetic Shielding, Amuneal Man-

ufacturing Corp., 4737 Darrah Street, Philadelphia PA 19124.

37. V. Schmidt, Electr on Spectr ometry of Atoms using Synchr o tr on

Radiation, Cambridge University Press, Cambridge, 1997, 403–

407.

38. W.G. Wadey, Rev. Sci. Instr., 27, 910, 1956.

REFERENCES 361

ELECTRONICS

This chapter dis cusses electronics at a level s omewhere

between that of a handbook, which consists essentially of

charts, tables, and graphs, and a textbook, whe re the

interesting, important, and useful conclusions come only

after well-developed discussions with examples. The aim

here is a presentation that has sufﬁcient continuity and

readability that individual sections can be proﬁtably read

without having to refer to preceding sections or ot her

texts. On the other hand, it is important to have useful

and frequently referenced material in the form of readily

accessible table s, gra phs , and di agrams that are sufﬁ-

ciently self-explanatory that very little reference to the

text material is necessary. Another important goal is

vocabulary. A large amount of jargon in electronics is

meaningless to the uninitiated, but when it is necessary

to understand the properties o f an elect ronic device from

a writ ten technical description, when writing the speciﬁ-

cations for electronic equipment, or when talking to an

electronics engineer, salesman, or technician, this

vocabulary is essential. With this i n mind, terms not cur-

rent outside of electronics are italicized.

To be used to best advantage, this chapter should be

supplemented with manufacturers’ catalogs, data books,

applications texts, handbooks, and more sp ecialized

texts that treat the topic of inter est in d epth. Manuf ac-

turers of laboratory electronic equipm ent, discrete devi-

ces, and integrated circuits have publications that

describe, in clear practical terms, the properties of their

products and their applications to a wide variety of tasks.

Much of this material is also available o n the internet,

and for this reason internet addresses are given when

available.

The material has been organized and written as

one explains it to a student or technician coming to work

in a laboratory for the ﬁrst time. The complexity of

modern electronics is such that the cut-and-try approach

is too inefﬁcient and costly in terms of material and

time. There are just too many possibilities when con-

necting devices and multiple-component circuits,

and it is important to establish a systematic approach

based on a limited number of simple, well-understood

principles. It is probably not reasonable in the labora tory

to expect quick solutions to problems that are entirely

outside one’s previous experience. The number of

really new situations that can arise is limi ted, however,

most probl ems being var iations on a few basic situations.

The ability to recognize this and to isolate the source

of difﬁculty comes with practice and mastery of basic

principles. When confronted with a new situation involv-

ing rack upon rack of equipment, t he tendency is to

believe that an understanding of how everything works

is beyond the capabilities of all but expert electronics

engineers. This is far from the truth. At the operational

level, present-day electronics is the most reliable, easy-to-

use, and easy-to-understand element of most experiments.

6.1 PRELIMINARIES

6.1.1 Circuit Theory

An understan ding o f e lementary c ircuit theory a nd the

accompanying vocabulary permits one to reduce com-

plex circuits consisting of many elements to a few

362

CHAPTER

essentials, predict the behavior of complex circuits,

specify the operation of components , an d un derstand

and use data sheets and operation manuals. In routine

laboratory wor k, it is not necessary to be skillful with

circuit theory. It is necessary to be able to isolate the

basic elements of a circuit and understand their beh av-

ior. With that ability, when circuits fail to operate cor-

rectly, the causes of the malfunction can be localized

and repaired.

Linear circuit theory applies to devices whose output

is d irectly proportional to the applie d input. If o ne

increases the current through a resistor by a factor

of two, for example, the voltage across it will double.

An example of a nonlinear device is a switch that is

either open or closed and whose state changes abruptly

at a threshold. A n onlinear device can often be tr eated

with linear theory by dividing the response of the

device into separate regions over which it beh aves in a

quasi-linear manner. This is called linearizing the

response curve. An example is the piecewise lineariza-

tion of a d iode’s current–voltage response, as shown

in Fig ure 6.1. The exponentially rising forward current

and

constant reverse current are represented by straight

lines of slop e 1/R

and 1/R

, which are joine d at

voltage V

We begin by considering only passive linear devices;

that is, devices that either dissipate energy (resistors) or

store energy in electric (capacitors) or magnetic (inductors,

transformers) ﬁelds. Active devices, such as transistors, can

supply energy to a circuit when appropriately powered by

external sources. The analysis of circuits with active devi-

ces is based on representations using equivalent circuits

consisting of passive devices.

Con v entional circuit analysis uses three lumped circuit

elements – resistors (R), capacitors (C), and inductors (L).

This way of analyzing circuits is valid at signal frequencies f

for which the wav elength k is much larger than the physical

dimensions of the circuit. Since k ¼ c/f,wherec is the speed

of light, this means that analysis in terms of lumped elements

is valid up to frequencies of a few hundred megahertz.

This frequency limitation also excludes waveforms with

signiﬁcant frequency components above a few hundred

megahertz, even though the repetition rate of the waveform

may be much less. A convenient way to estimate the fre-

quency of the highest-frequency component of a nonsinu-

soidal waveform is to divide 0.3 by the rise time of the

waveform, t

, deﬁned as the time between the 10% and

90% amplitude points on the leading edge of the wave-

form. A pulse with a 10 ns rise time, for example, has

signiﬁcant frequency components up to 30 MHz. The fall

Figure 6.1 (a) Real and (b) piecewise linear representation of the current–voltage

characteristics of a diode.

PRELIMINARIES 363

time, t

of a waveform is the time between the 10% and

90% amplitude points on the trailing edge. Figure 6.2

illustrates rise

time and fall time.

Even at low frequencies there are no ideal resistors, capaci-

tors, or inductors. Actual resistors have some capacitance and

inductance, while capacitors have resistance and inductance,

and inductors hav e resistance and capacitance. These depar-

tures from ideality are largely a matter of construction.

At high frequencies, stray capacitances and inductances

become signiﬁcant, and one commonly speaks of distributed

parameters, in contrast to the lumped parameters at low fre-

quencies. Coaxial cable is an example of a type of distributed

parameter circuit. The electrical properties of coaxial cable

are normally given in terms of resistance and attenuation

per unit length as a function of frequency. At high frequen-

cies, the resistance of conductors (eve n connecting wires)

increases due to what is termed skin effect. The magnitude

of this effect for round cross-section wires is gi ven in Table

6.1 as a function of frequency. High-frequency connections

are

best made with leads having a large surface area-to-

volume ratio, with ﬂat-ribbon geometry the best.

Conventional circuit theory is based on a few laws, prin-

ciples, and theorems. In the equations that follow, lowercase

letters represent instantaneous values of voltage and current,

whereas uppercase letters indicate effective or d.c. values. It

is also convenient to distinguish between root-mean-square

(rms), peak-to-peak, and average values of voltage and cur-

rent for sinusoidally varying voltages. If v ¼Vcos xt, where

v is the instantaneous value of voltage and V is the peak

value,thermsvalueisV=

ﬃﬃﬃ

, the peak-to-peak value is 2V,

and the average value is clearly zero. This is illustrated in

Figure 6.3. Common US line voltage is speciﬁed as 110 V

c., which is the rms value. The peak voltage is 156 V, so

the peak-to-peak voltage is 312 V.

Under certain conditions, the rms value is not sufﬁ cient

for specifying the output of an a.c. source. A source produc-

ing voltage spikes of large amplitude, but short duration

superimposed on a small sinusoidally varying voltage will

have an rms value very close to that without the spikes, but

the spikes can have a large effect on circuits connected to the

source. When specifying the output of a d.c. power supply,

the magnitude, frequency, and duration of nonsinusoidal

waveforms that appear at the output need to be speciﬁed,

as well as the rms value of any a.c. component of the output.

Laws

(i) Current–voltage relations. For resistors, capacitors,

and inductors we have:

¼ iR, v

idt, v

¼ L

ð6:1Þ

Figure 6.2 Rise time (t

) and fall time (t

) of a pulse.

Table 6.1 Ratio of a.c to d.c wire resistance

Wire Gauge R

Hz 10

#22 6.9 21.7 69 217

#18 10.9 34.5 109 345

#14 17.6 55.7 176 557

#10 27.6 87.3 276 873

Figure 6.3 Relation of rms and peak-to-peak voltages for a

sinusoidal waveform.

364 ELECTRONICS

respectively, where the resistance R is in ohms; the capaci-

tace C in farads; and the inductance L in henrys.

(ii) Loops and nodes (Kirchhoff’s laws). In these, the

sums are algebraic (signs taken into account):

(1) R (voltage drops around a closed loop) ¼ R (voltage

sources).

(2) R (current into a node) ¼ R (current out of a node),

where a node is a point where two or more elements

have a common connection.

Theorems

(i) Thevenin’s theorem. A real voltage source in a circuit

can always be replaced by an ideal voltage source in series

with a generalized resistance. An ideal voltage source is

one that can maintain a constant voltage across its termi-

nals regardless of the load across it. In other words, an

ideal voltage source has zero internal resistance. An auto-

mobile battery, with an internal resistance of a few hun-

dredths of an ohm, is a good approximation to an ideal

voltage source at currents of a few amperes. Electronically

regulated power supplies often have very low effective

internal resistances when operated within their voltage

and current ratings.

(ii) Norton’s theorem. A real current source in a circuit

can always be replaced by an ideal current source shunted

by a generalized resistance. An ideal current source is one

that supplies a constant current regardless of load – such a

source has an inﬁnite internal resistance. Photo-multiplier

and electron-multiplier devices provide currents, albeit

very low, that are almost independent of load, and they

approximate ideal current sources.

Superposition, Circuits with Multiple

Sources

For a circuit that contains several sources (voltage, current,

or a combination of both) the contribution of each source

to the voltage between any two points or the current past a

point can be considered separately with all the other sour-

ces represented by their internal resistances. The total volt-

age or total current is then the algebraic sum of the separate

contributions of each of the individual sources.

When connecting a source of current or voltage to a

circuit, it is often important to know the internal resistance

of the source. This can be determined by ﬁrst measuring the

open-circuit voltage of the source with a high internal-

resistance voltmeter and then connecting a variable

resistance across the source and adjusting it until the volt-

meter reading is one half the open-circuit value. The source

resistance is then equal to the value of the variable-resist-

ance setting. If the source has a very high internal resistance,

a current measurement can be substituted for the voltage

measurement. In this case, the output is shunted with an

ammeter and the so-called short-circuit current is measured.

Avariableresistanceisthenplacedinserieswiththe

ammeter and adjusted until the current through the ammeter

is one half the short-circuit current. The value of the variable

resistor at this point is equal to the internal resistance of the

source. Analogous measurements can be made for a.c. sour-

ces by using either a.c. voltmeters and ammeters or an

oscilloscope.

6.1.2 Circuit Analysis

For any given source, the choice of representation (Thevenin

or Norton) is arbitrary and, in fact, the series resistance in the

Thev enin representation is exactly equal to the parallel

resistance in the Norton representation. Thev enin’s and

Norton’s theorems simplify the application of the laws and

principles discussed above.

The most general method for solving circuit problems is

to apply Kirchhoff’s laws using the appropriate current–

voltage relations for each element in the circuit. This gives

rise to one or more linear differential equations, which,

when solved with the proper boundary conditions, give

the general solution. This is illustrated for RC circuits in

Section 6.1.3.

When

dealing with sinusoidal sources of angular fre-

quency x, circuit analysis can be greatly simpliﬁed when

only the steady-state solution is required. In this case, circuit

capacitances and inductances are replaced by r eactances:

capacitive reactance ¼ jX

, where X

1

inductive reactance ¼ jX

, where X

¼ xL

j ¼

ﬃﬃﬃﬃﬃﬃﬃ

1

ð6:2Þ

PRELIMINARIES 365

The impedance Z of a circuit is obtained by combining

reactances and resistances ac cording to the formula

Z ¼ R þ j(X

þ X

). These quantities can be represented

in the complex plane by vectors (see Figu re 6.4 ). The

angle

between Z and the real axis is /. By analogy with

the I–V relations for a pure resistance, X

is the ratio of

the a.c . voltage across a capacitor to the current t hrough

it, X

is the ratio of the a.c. voltage across an inductor to

the current through it, and Z is the net ratio of a.c. voltage

to current in a c ircuit composed of resistors, capacitors,

and inductors.

The fact that jX

and jX

are imaginary means that the

voltage and current are 90° out of phase with each other.

For a capacitor, the voltage lags the current by 90°, while

for an inductor the voltage leads the current by 90°.

Another quantity that is occasionally useful in circuit

analysis is the complex admittance Y, which is the recip-

rocal of the impedance. The SI unit of admittance is the

siemen. The usefulness of the admittance arises in circuits

with several parallel branches, where the net admittance is

the sum of the admittances of the branches.

In carrying out circuit analysis, the following results of

the above laws are useful:

Series Circuits. At any instant the current is the same

everywhere in a series circuit, and the algebraic sum of

the voltage drops around a circuit equals the algebraic

sum of the sources. For circuit elements of impedance

, Z

, ..., Z

in an N element series circuit, the total

impedance is Z ¼ Z

þ Z

þþZ

. If all the elements

are resistors, or inductors, or capacitors, the general

expression reduces, respectively, to:

R ¼ R

þ R

þþR

þþ

L ¼ L

þ L

þþL

ð6:3Þ

Parallel Circuits. For circuit elements in parallel, the

voltage drop across each branch is the same while the

current through each branch is inversely proportional to

the impedance of the branch. The total current through

all of the branches is the voltage across the network

divided by the equivalent impedance for the network.

The equivalent impedance Z and admittance Y for an N

branch parallel circuit are:

þþ

ð6:4Þ

and:

Y ¼ Y

þ Y

þþY

ð6:5Þ

where Z

, Z

, ..., Z

are the impedances of the branches

and Y

, Y

, ..., Y

are the admittances . In t he special cases

where all the c ircuit elements in the branches are of the

same type:

þþ

C ¼ C

þ C

þþC

þþ

ð6:6Þ

where R, C, and L are the net resistance, capacitance, and

inductance of the circuits.

Voltage Dividers. The voltage divider, illustrated in

Figure 6.5(a), is a very common circuit element. The

instantaneous

voltage across Z

is v

/(Z

þZ

þþZ

)]; that is, the fraction of v

that appears

Figure 6.4 Relations between reactance, resistance,

impedance, and phase angle.

366 ELECTRONICS

across any circuit element is the impedance o f that ele-

ment divided by the total impedance of the series circuit.

Voltage dividers provide a convenient way to obtain a

variable-voltage output from a ﬁxed-voltage input, but

there are l imitations. To avoid drawing too much current

from the voltage source, the impedance of the voltage

divider string should not be too small. If, in the interest of

conserving power, however, the impedance is made

large, the output impedance of the circuit will be large

and v

out

will depend critically on the load. This can be

seen f rom the Thevenin equivalent of the circuit given in

Figure 6.5(b) wh ere v

is the instantaneous voltage of the

ideal voltage source. When Z

is large, the voltage across

a load will depend critically on the value of the load.

Such loading of a divider is to be avoided. For noncritical

applications, Z

should be at mo st 1/10 of any anticip ated

load.

Precision, highly linear, multiturn potentiometers are

commonly used for position sensing. In this application,

the shaft of the potentiometer is coupled mechanically

to the moveable element whose position is to be

determined, and a stable voltage source is connected

across the ends of the potentiometer. The ratio of the

voltage from the variable contact of the potentiometer

to its e nd gives the angle through which the shaft has

rotated.

Equivalent Circuits. Two circuits are equivalent if

the relationships between the measurable currents and

voltages are identical. As has been seen, a circuit with

two external terminals can b e replaced by its Thevenin or

Norton equivalent. Common equivalence transformations

for circuit s with three terminals (Mill er and Y–D trans-

formations) are shown in Figures 6.6 and 6.7.Intheﬁrst

ller transformation of Figure 6.6, it is necessary to

kno

w t he ratio of the voltages at nodes 1 and 2; in the

second it is necessary to know the ratio of the currents

into nodes 1 and 2.

Discussions o f ampliﬁer circuits often refer to the

Miller effect. This occurs when the input and output

circuits of the ampliﬁer are coupled by an impedance

Z#. By using the transformation in Figure 6.6,Z# bet

ween

input terminal 1 and output terminal 2 can be transformed

into an equivalent circuit where Z# is replaced by Z

and

from terminals 1 and 2 to ground. The relations between

, and Z# are given in the ﬁgure. When the coupling

between terminals 1 and 2 is capacitive with Z# ¼ 1/jxC#,

and Z

are also capacitive impedances equal to

1/jxC#(1 K) and 1/jxC#K/(K 1), where K is the voltage

gain of the ampliﬁer, negative for the example shown in

Figure. 6.6.

Figure 6.5 (a) The voltage divider; (b) the Thevenin

equivalent.

PRELIMINARIES 367

Figure 6.6 Miller transformations for circuits with three terminals.

Figure 6.7 Y–D transformation for a circuit with three terminals.

368 ELECTRONICS

The Y–D transformation allows one to transform a cir-

cuit of three elements from a node to a loop conﬁguration.

6.1.3 High-Pass and Low-Pass Circuits

Analysis of the high-pass and low-pass circuits shown in

Figure 6.8 illustrates some of the above circuit-analysis

principles.

The combination of v

and R

represents a real

voltage source with instan taneous open-circuit voltage v

and internal resistance R

. For the high-pass or differentiat-

ing circuit, the output voltage v

is across the resistor R;

for the low-pass or integrating circuit, it is across

the capacitor C. Very often, the essential properties of

complex circuits can be understood in terms of one of

these two circuits, so it is useful to be acquainted with

their characteristics.

These circuits can be analyzed by the differential-

equation method. For either circuit:

ðtÞ¼iR

idt þiR ð6:7Þ

This equation uses the fact that the sum of the voltage drops

in the circuit equals the sum of the voltage sources and the

current is the same everywhere in a series circuit at any

instant. Differentiating with respect to time:

ðR

þ RÞþ

ð6:8Þ

The solution to the homogeneous equation (dv

/dt ¼ 0) is:

i ¼ Ae

t=R#C

ð6:9Þ

where R# ¼ R

þ R and A is the integration constant

determined from the initial conditions. The general

solution requires that the functional form of v

known. Consider three cas es:

(1) An a.c. voltage of amplitude V:

¼ V cosðxt þ /Þð6:10Þ

(2) A step voltage of amplitude V:

0 for t <0

V for t >0



ð6:11Þ

(3) A rectangular pulse of amplitude V and duration T:

V for 0 < t < T

V for t <0,t > T



ð6:12Þ

For case 1, the output voltage is sinusoidal at the same

frequency as the input voltage. The ratio of v

to v

as a

function of normalized frequency is shown in Figure 6.9(a).

the frequencies x ¼x

and x ¼ x

for the two circuits,

is 1=

ﬃﬃﬃ

of the maximum value. These frequencies are

called the upper and lower corner frequencies, respectively.

The maximum power that can be delivered to a load is

proportional to the square of the output voltage, so that at

x ¼ x

and x ¼ x

, the maximum power that the circuits

Figure 6.8 (a) High-pass or differentiating circuit; (b) low-pass or integrating circuit.

PRELIMINARIES 369

can deliver to a constant load is one-half the maximum

possible value. The usual way of expressing this is in terms

of decibels dB, where:

ratio in dB ¼ 10 log

power out

power in



¼ 10 log

out



ð6:13Þ

If R

out

¼R

, which is often assumed, then (ratio in dB) ¼

20 log

out

]. When m

out

ﬃﬃﬃﬃﬃﬃﬃﬃ

1=2

, this is a pprox -

imately 3, so that 3 dB represents a power reduction

of a factor of two. Since the frequency response of ampli-

ﬁers,ﬁlters,andtransducersisroutinelygivenindB,itis

important to keep in mind that the dB scale is logarith-

mic. Human sensory per ception is approximately loga-

rithmic, and a 3 dB change in sound level or light level is

barely perceptible.

Because of the reactive element in the RC circuits (the

capacitor), the voltage is not in phase with the current, as

illustrated in Figure 6.9(b). These plots of phase and log

(output

voltage) as a function of log(frequency) are called

Bode plots, after H. W. Bode.

It is often convenient to approximate frequency-

response curves by a piecewise linear function. Such ideal-

ized Bode plots are shown in Figure 6.10(a) and (b). The

corner

frequencies are where x/x

and x/x

¼ 1.0.

Figure 6.9 Output voltage as a function of frequency for: (a) high-pass and (b) low-pass

circuits; phase as a function of frequency for: (c) high-pass and (d) low-pass circuits.

370 ELECTRONICS

They correspond to the 3 dB points on the unapproxi-

mated Bode plots. For most purposes, the simpliﬁed curves

are satisfactory representations. From these curves, every

10-fold reduction in frequency below x

for the high-pass

circuit decreases the output voltage by 20 dB, and every

twofold reduction decreases it by 6 dB. The low-pass cir-

cuit has just the opposite properties: a 10-fold increase in

frequency above x

results in a 20 dB decrease in output

voltage, and a twofold increase results in a 6 dB decrease.

One often states these facts as 20 dB per decade and 6dB

per octave. The linearized phase-response curves are

shown in Figure 6.10(c). The 3

dB frequencies occur at

a phase shift of p/4 (45°) for the two circuits.

For the nonrepetitive input voltage waveforms of cases (2)

and (3), the output waveforms are given in Figure 6.11.

e output, waveforms for the rectan gular-wave

input function can be used to determine the RC time

constants for differentiating and integrating circuits.

This is called square-wave testing. Th e RC time con-

stant for the differentiating circuit is obtained by using a

square-wave input with a rise time much smaller than

RC and a period much larger than RC. For times small

compared with RC, the tilt of the top edge of the output,

as viewed with a fast-rise-time oscilloscope (see Figure

12) is directly related to RC.

The fractional decrease in

,intimet

is t

/RC, which can be set equal to (V  V#)/V

and solved for RC. For the integrating circuit, RC is

obtained by measuring the rise time of the output waveform

on a fast-rise-time oscilloscope. Using the deﬁnition of

the rise time t

, as the time between the 10% and 90% points

Figure 6.10 Idealized gain response for (a) high-pass and (b) low-pass circuits; idealized

phase response for (c) high-pass and (d) low-pass circuits

PRELIMINARIES 371

on the leading edge of the output waveform, one has the

relation:

¼ 2:2 RC ð6:14Þ

6.1.4 Resonant Circuits

The voltages and currents in circuits with capacitors, induc-

tors, and resistors show oscillatory properties much like

those of mechanical oscillators. Electronic circuits ha v e

Figure 6.11 Response of high-pass and low-pass circuits to a step voltage (a) and a

rectangular pulse of duration T (b).

372 ELECTRONICS

natural frequencies of oscillation and can be critically

damped, underdamped, or overdamped, depending on

the relations between the values of the circuit parameters.

Resonant circuits with ideal capacitors and inductors are of

the series or parallel type sho wn in Figure 6.13.Whendriven

y a sinusoidal input source, the capacitativ e reactance in the

series circuit will cancel the inducti v e reactance at the

resonant frequenc y x

, where 1/Cx

¼ x

L and

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1=LC

.Atx

the impedance of the series circuit is

a minimum and the current through it is a maximum.

For the parallel resonant circuit at low frequencies, the

L branch will have a very low reactance and the current

drawn from the source will ﬂow almost entirely through

that branch. At high frequencies, the current through the

RC branch is limited by the value of R. The total impe-

dance of the parallel circuit is therefore small at low and

high frequencies, passing through a maximum at the fre-

quency x

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1=LC

, provided that R << x

L. Graphs of

the currents in the two circuits as a function of driving

frequency are given in Figure 6.14. Real inductors have

associated resistance, which generally must also be

taken into account when analyzing circuits.

One measure of the resonance sharpness in the series and

parallel circuits is the Q or quality of the circuit. For prac-

tical purposes, Q ¼ x

/Dx where Dx is the full width at

half maximum of the peak or valley. In terms of the circuit

parameters, 1/Q ¼ x

L/R ¼ 1/x

RC. This is the ratio of the

energy stored (in the capacitor or inductor) to the energy

dissipated in the resistor per cycle at resonance. Values of Q

Figure 6.12 Square-wave testing of a high-pass circuit.

Figure 6.13 (a) Series resonant circuit; (b) parallel resonant

circuit.

Figure 6.14 Current as a function of frequency for: (a) the series resonant circuit and

(b) the parallel resonant circuit.

PRELIMINARIES 373

as large as 100 can be attained in electrical circuits while

mechanical oscillators can attain values as high as 10

. The

phase relationships between voltage and current in series

and parallel resonant circuits are shown in Figure 6.15.

hebehaviorofanLRC circuit upon the application of a

step or rectangular input is much like the response of a

mechanical system to a sudden impulse. Critically damped,

underdamped, and overdamped current ﬂows result.

6.1.5 The Laplace-Transform Method

A general technique for analyzing circuits for arbitrary

input voltage waveforms is the method of Laplace

transforms. With this method it i s possible to use onl y

algebra and lists of transforms – such as t hose given in

Table 6.2 – for the s olution of differential equations and

the

evaluation of boundary c onditions. The results of the

method will be presented without any proofs. The

vocabulary of Laplace transforms occurs in the discus-

sion of circuits and is included in this chapter for that

reason.

The method is based on an integral transform of the type:



f ðs Þ¼

‘

f ðtÞe

st

dt ð6:14Þ

where



f ðsÞ is the Laplace transform of f(t), written as

L [f(t)]. The function f(t) can involve integrals and dif-

ferentials. When L is applied to the second-order differ-

ential equations that arise in circuit analysis, rather

important simpliﬁcations occur a nd results can often be

written down by inspection. The Laplace transform of

the output voltage



ðsÞ of a circuit is the Laplace trans-

form of the input voltage



ðsÞ times the Laplace tra ns-

form of the transfer function



TðsÞ–thetransfer function

being the function relating the output to input. To obtain



TðsÞ, the values of all elements in the circuit are replaced

by their transform equivalents according to the recipe

R / R, C / 1/sC,andL / sL . In the simple case of

the voltage divider, the transfer function is t he ratio of the

impedance of the output-circuit element to the total

impedance of the circuit chain. T(s) is obtained in exactly

the same way, using the equivalences for R, C,andL.In

general,



TðsÞ is in the form of a ratio of two functions of

s, G(s)andH(s), which are polynomials in s:



TðsÞ¼

GðsÞ

HðsÞ

ð6:15Þ

The values of s for which G(s) is zero are called the zeros



TðsÞ; the values of s for which H(s) is zero are the

locations of the poles of



TðsÞ. In the most general case,

the zeros and poles are complex. The positions of the zeros

and poles of



TðsÞ in the complex plane give important

information on the properties of the circuit under analysis.

When the poles are complex, they occur in pairs, while

Figure 6.15 Phase relations between voltage and current in: (a) the series resonant

circuit and (b) the parallel resonant circuit.

374 ELECTRONICS

Table 6.2 Elementary Laplace Transforms

f(t)(t >0)

f ðsÞ

d(t)1

11/s

n1

/(n  1)! 1/s

(n a positive integer)

s  a

sin at

þ a

cos at

þ a

sinh at

 a

cosh at

 a

sin at

ðs

þ a

ðsin at  at cos atÞ

ðs

þ a

df ðt Þ

f ðsÞf

, f

¼ lim

t!0

f ðt Þ

f ðsÞsf

 f

, f

¼ lim

t!0

df ðt Þ

f ðt

Þdt

f ðsÞ

a  b

ðe

 e

ðs  aÞðs bÞ

a  b

ðae

 be

ðs  aÞðs bÞ

ð1  cos atÞ

sðs

þ a

ðat  sin atÞ

ðs

þ a

abðb

 a

ðb sin at a sin btÞ

ðs

þ a

Þðs

þ b

 a

ðcos at  cos btÞ

ðs

þ a

Þðs

þ b



at

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ b

sin½bt þ argð a þ ibÞ

s ðs þ aÞ

þ b

PRELIMINARIES 375

real-valued poles can occur singly or in pairs. The values of

the real and imaginary components of the pole coordinates,

usually labeled r and x, have important physical meaning.

The real component r is a measure of the damping in the

circuit while the imaginary part x is the natural frequency

of oscillation. Negative values of r give stable circuits in

which transient signals all decay to zero with time. Circuits

employing only passive elements behave in this way and

are stable. Circuits with active elements can behave in such

a way that the output increases with time in response to a

transient input signal. Such circuits are unstable and have

values of r greater than zero. They are to be avoided,

except in the case of oscillators, which must be unstable

in order to function.

The Laplace-transform equivalents of the high-pass

and low-pass circuits are shown in Figure 6.16. For the

high-pass

circuit, the output voltage across the resistor R

for the transformed circuit is:



ðsÞ¼



ðsÞ

ð1 þ

Þþ

SRC

ð6:16Þ

where



TðsÞ, the transfer function, has a pole at s ¼1/(R

+ R

)C. For the low-pass circuit, the ou tput voltage across

the capacitor for the transformed circuit is:



ðsÞ¼



ðsÞ

1 þð1 þ

ÞSRC

ð6:17Þ



TðsÞ has a pole at S ¼1=ðR þ R

ÞC. The steady-state

frequency and phase response of the circuits are obtained

from



TðsÞ by replacing s with jx. The transfer functions

are now, for the high-pass circuit:

TðxÞ¼

ð1 þ

Þj

ð6:18Þ

and:

TðxÞ¼

1 þ j

ð1 þ

ð6:19Þ

for the low-pass circuit. For these circuits x

¼ x

¼ 1/RC

for R

jR<<j.

Figure 6.16 Laplace-transform equivalents of: (a) the high-pass and (b) the low-pass

circuit.

376 ELECTRONICS

As seen previously, x

and x

are the corner

frequencies of the circuits. By rationalizing the denomina-

tors of the transfer functions, one obtains the phase

response. Since there are no inductive elements in the cir-

cuits, there is no natural frequency of oscillation. The poles

lie on the negative real axis because there are no active

elements in the circuit to cause sustained oscillations.

6.1.6 RLC Circuits

Consider the equivalent circuit and the Laplace transform

given in Figure 6.17. To analyze the circuit, consider the

parallel

combination of R and 1/sC, which is in series with

sL in a voltage-divider conﬁguration:

R=sC

R þ 1=sC

1 þ sRC

ð6:20Þ

Thus:



ðsÞ¼



ðsÞ

1 þ sL=R þ s

ð6:21Þ

The poles of



TðsÞ occur at:

s ¼

L=R6

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðL=RÞ

 4LC

2LC

ð6:22Þ

Letting the natural frequency of oscillation of the circuit be

¼ 1=

ﬃﬃﬃﬃﬃﬃ

,wehaveQ ¼ R/x

, and the poles can be

rewritten as:

s ¼



ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1=Q

 4

ð6:23Þ

There are three different possibilities for the roots of s:

(1) 1/Q

¼ 4: a single real root at s ¼x

/2Q

(2) 1/Q

 4 ¼ m

(m real): two real roots at s ¼x

/2Q

6 x

m/2.

(3) I/Q

4 ¼m

(m real): two conjugate complex roots

at s ¼x

/2Q 6 jx

m/2.

The magnitude of s in the r, jx plane is x

; in geometric

terms this means that the roots of s are conﬁned to a semi-

circle of radius x

in the left half of the complex plane (see

Figure 6.18).

Figure 6.17 An RLC circuit and the Laplace-transform

equivalent.

Figure 6.18 Pole trajectory for an RLC circuit.

PRELIMINARIES 377

6.1.7 Transient Response of

Resonant Circuits

The stability of a linear system subjected to a driving func-

tion depends on the system itself rather than the driving

function. For ease of analysis, consider the RLC circuit of

Figure 6.17 to be driven by a unit step input voltage of the

rm v

(t) ¼ 1 for t > 0. The Laplace transform of the output

voltage is then the transform of the input voltage,



ðsÞ,

multiplied by the transform of the transfer function



TðsÞ:



ðsÞ¼



ðsÞ



TðsÞð6:24Þ

For the unit step, input v

(s) ¼ 1/s from Table 6.2; therefo re



ðsÞ¼

sð1 þ sL=R þ s

LCÞ

ð6:25Þ

To ﬁnd v

(t) it is necessary to look up the inverse transform

in Table 6.2. The result is:

ðtÞ¼1 

kx

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1  k

sin

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1  k

þarctan

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1  k

ð6:26Þ

where k ¼ 1/2Q. Critical damping, overdamping, and

underdamping correspond to k ¼ 1, k > 1, and k <1,

respectively. The normalized response of the circuit for

various values of k is shown in Figure 6.19.

s can be seen, th e underdamped waveform overshoots

the steady-state value of one and oscillates about it with

decreasing amplitude. This is sometimes called ringing.

As damping is increased, the output waveform oscilla-

tions decrease in amplitude until, for k ¼1 (critical damp-

ing), the oscillations are completely gone. Increasing the

damping beyond k ¼ 1 only i ncreases the time for the

waveform to arrive at the steady-state value.

Overshoot, rise time, settling time, and error band are

terms used to characterize output waveforms. They are

illustrated in Figure 6.20. For critical damping, t

¼ 3.3/

. By decreasing the damping so that k <1,t

can be

further decreased, but at the expense of ringing. A suitable

compromise that is often used is k ¼ 0.707, under which

circumstance the overshoot is 4.3% and t

is reduced to

2.16/x

. Figure 6.21 is a graph of the percentage overshoot

as a function of k.

The abov e analysis is not restricted to passive circuits.

Ampliﬁers with negati v e feedback can have response

functions identical in form to those for RLC circuits. The

response of such ampliﬁers to nonrepetiti ve waveforms is

speciﬁed using the same terms as for the passi ve circuit

above. In pulse ampliﬁers, the transient response is the fun-

damental limitation on the pulse repetition rate. For critically

damped ampliﬁers, the width T of the impulse response and

the rise time t

are approximately related by T ¼ 1.5t

,sothat

pulsescannotbesentatarategreaterthan1/T per second. T,

in this case, is generally taken to be the time between the 50%

points on rising and falling edges of the output waveform.

For the precision control of temperature in a thermostat,

three-term control is often used. With this method, the

power applied to the heater element is set equal to a constant

background level plus a term proportional to the difference

between the set-point temperature T

and current temper-

ature T, a term proportional to the time integral of T

 T,

and a term proportional to the time derivative of T

 T.The

resulting differential equation is, under certain circumstan-

ces, analogous to that for the RLC circuit. Experimental

parameters are chosen to obtain the fastest time response

consistent with overall system stability. This is discussed in

further detail in Section 6.7.9 and in Chapter 7.

Figure 6.19 Response of a resonant circuit with no

damping (k=0), underdamping (k=0.2, 0.4), critical

damping (k=1), and overdamping (k=4).

378 ELECTRONICS

6.1.8 Transformers and Mutual Inductance

Transformers consist of primary and secondary windings

coupled by a core, which can be of magnetic material or

air. A voltage is induced in the secondary of the trans-

former when there is a change of current in the primary.

The reverse also occurs – indu ced volt age in the primary

due to a current change in the secondary. A transformer

circuit and the Laplace-transform equivalent are illus-

trated in Figure 6.22. T he dot associated with each

Figure 6.20 Output waveform in an underdamped resonant circuit.

Figure 6.21 Percentage overshoot as a function of

damping in a resonant circuit.

Figure 6.22 A transformer circuit and the

Laplace-transform equivalent. M, the mutual inductance,

is positive if i

and i

both ﬂow into or out of the dotted

ends of the coils.

PRELIMINARIES 379

winding of the transformer indicates the relative orienta-

tion of the windi ngs. The convention is that M,themutual

inductance, is positive if the currents i

and i

both ﬂow

into or out of the dotted ends of the coils, and negative

otherwise. The transfe r function



TðsÞ is obtained by

applying Kirchhoff’s laws to the two loops:



ðsÞ¼R



ðsÞþ



ðsÞ



ðsÞsL

 sM



ðsÞ

0 ¼



ðsÞsL



ðsÞsM þ



ðsÞsL



ðsÞR

ð6:27Þ



ðsÞ¼



ðsÞR

Eliminating



ðsÞ and substituting for



ðsÞ in the third

equation gives the result:

6.1.9 Compensation

It is often desired to modify the frequency response of a

given circuit. Two common methods are the addition of a

pole that is much smaller than the other poles of the trans-

fer function and the simultaneous addition of a pole and

zero to the transfer function. The addition of a pole is

accomplished with a resistor and capacitor in a low-pass

conﬁguration at the output of the circuit to be modiﬁed, as

illustrated in Figure 6.23(a). If the original circuit had a

pole x

and the introduction of the RC circuit produced a

pole at x

where x

<< x

, the overall response of the

circuit would be a 20 dB/decade decrease in gain from x

to x

followed by a 40 dB/decade decrease for frequencies

greater than x

The addition of a pole and a zero is accomplished with

the circuit in Figure 6.23(b). The transfer function for the

pole-zer

o compensation network is:

þ 1=sC

þ R

þ 1=sC

1 þ sR

1 þ sðR

þ R

ÞC

ð6:29Þ

with the zero at s ¼1/R

C and the pole at s ¼1/(R

)C. If the zero in the transfer function is chosen to

cancel the smallest pole of the original circuit, the overall

frequency response will be ﬂat up to the frequency

corresponding to the new pole. The gain will then decrease

by 20 dB/decade with increasing frequency up to the sec-

ond pole of the original circuit. The gain will then decrease

by 40 dB/decade up to the next high-frequency pole, after

which the decrease will be 60 dB/decade. The response of

the pole-zero-compensated circuit is sharper than that of

one with single-pole compensation.

6.1.10 Filters

Filters are generally classed as low-pass, high-pass, band-

pass, and band-reject. RC circuits are examples of the ﬁrst

two kinds, while the series and parallel RLC circuits illus-

trate the last two. A series of band-pass or band-reject

ﬁlters with pass bands at different, but closely spaced,

frequencies is called a comb ﬁlter.

Figure 6.23 Compensation by: (a) the addition of a pole

and (b) the addition of a pole and a zero to cancel the

lowest-frequency pole of the original circuit.



ðsÞ¼



ðsÞ

MCs

ðL

þ L

ÞM



þ R

ðL

þ L

ÞþR

½Cs

þ L

þ R

C½R

s þ R

ð6:28Þ

380 ELECTRONICS

The ideal ﬁlter would pass unattenuated all frequencies

in its pass band while completely rejecting frequencies

outside the pass band. The simple circuits we have exam-

ined thus far are only approximations to the ideal. There

are excellent approximations to the ideal ﬁlter that rely on

judicious choices of the transfer function poles of RC and

RLC circuits. There are four classes of ﬁlter design, each of

which has its advantages:

(1) Maximally ﬂat has the ﬂattest amplitude response within

the pass band. The Butterworth ﬁlter is an example.

(2) Equal ripple has ﬂuctuations in the pass band but

greater attenuation in the stop band than the maxi-

mally ﬂat ﬁlter.

(3) Elliptic has the maximum rate of attenuation between

the pass band and stop band. The Chebyshev ﬁlter is an

example of this type.

(4) Linear phase has a much less sharp cutof f than the others,

but maintains an almost linear phase response in the

pass band. The Bessel ﬁlter is an example of this type.

Methods of ﬁlter design are well established, and there

are many texts and handbooks that provide tables for ﬁlter

synthesis. Before designing or specifying a ﬁlter, it is

important to know, not only the cutoff and phase proper-

ties, but also the transient response and the input and out-

put impedances.

Ampliﬁers with negative feedback provided by resis-

tors and capacitors ca n have responses identical to RLC

circuits. By appropriate choices of the elements in a

feedback network, these ampliﬁers can be made into

ﬁlters. These so-called active ﬁlters are especially useful

at low frequencies, where large inductors with low resist-

ance are heavy a nd expensive. There are m any texts

and handbooks on active-ﬁlter design. Lancaster’s Active

Filter Cookbook (D. Lancaster, 2nd ed., Butt erworth-

Heinemann, Oxford, 1996) is written from a practical

point of view with a minimum of mathematics. Most

active-ﬁlter designs are based o n high-gain integrated-

circuit operationa l ampliﬁers. With the frequency

response of these ampliﬁers now extending well into

the megahertz region, active ﬁlters are ﬁnding increasing

application to high-frequency circuits. Stability is an

important factor in ﬁlter design, especially for large

values of Q. If drift is to be minimized, highl y stable

passive components are required.

6.1.11 Computer-Aided Circuit Analysis

The Simulation Program with Integrated-Circuit Emphasis

(SPICE) was originally intended for integrated circuit

design where the very large number of circuit elements

made traditional circuit analysis slow, cumbersome, and

subject to errors. The SPICE Program was ﬁrst limited to

use on mainframe computers with network access, but var-

ious versions are now available for personal computers

(PCs). One popular PC version of SPICE is PSPICE, now

available from Cadence. Because SPICE and PSPICE ﬁg-

ure prominently in electrical-engineering circuit-analysis

courses, they are usually available over university networks

and various versions, including student/faculty and evalua-

tion versions, can be downloaded from the web. Analysis of

digital circuits with SPICE requires detailed information

about waveforms and delays within individual units. Dig-

ital circuits are increasingly assembled from programmable

arrays and the manufacturers of the arrays generally supply

the required information with their programming software.

The following procedures should be followed when

using circuit-analysis programs:

(1) Create a schematic diagram of the circuit:

 Assemble components from the program library

 Import or create components unavailable in library

 Assign values to resistors, capacitors, and

inductors

 Make interconnections

(2) Create SPICE/PSPICE ﬁle:

 Specify temperature

 Specify sources

– Independent

– Controlled

 Verify interconnections (nodes)

(3) Analysis:

 D.c., quiescent

 Transient

 A.c., small signal

(4) Output:

 Graphs

– Bode plots

– Waveforms

– Numerical tables

(5) Adjust circuit to meet design criteria and reanalyze.

PRELIMINARIES 381

Analysis programs are extremely useful, but cannot

replace an understanding of circuit theory. It is unrealistic

to believe that one can begin with an approximate circuit

and use a program to arrange the values of the components

and the conﬁguration until the desired result is attained.

Even for a simple circuit of 10 components, the number of

possibilities is so large that an uninformed attempt to arrive

at a desired ﬁnal result cannot be successful. On the other

hand, an arbitrary circuit can be analyzed to determine

whether it will perform according to the requirements.

Most analysis programs come with libraries of common

active devices (transistors, diodes, operational ampliﬁers)

however, new devices appear on the market daily and

older devices become obsolete so th at it is imprac tical

for any single library to contain all possible devices. Add-

ing device speciﬁcations to analys is prog ra m libraries ca n

be time consuming and it is often more e fﬁcient to use

available devices with operating parameters close to those

of the device in question. This requires additional research,

but device speciﬁcations are now routinely available on the

websites of the manufacturers. In some cases, manufac-

turers provide SPICE ﬁles for their devices for loading

directly into libraries. An additional beneﬁt of analysis pro-

grams is compatibility with schematic capture and printed-

circuit-board layout software. This is discussed in more

detail in Section 6.10.3 on printed circuit boards.

6.2 PASSIVE COMPONENTS

In discussing passive components, emphasis will be placed

on choosing the correct type for the function to be per-

formed. It is rarely sufﬁcient to specify the nominal value

of a component. This can be appreciated by looking through

the catalog of any electronics supplier under resistors and

ﬁnding perhaps 50 different resistor types, each with a range

of resistance values. The following are some general con-

siderations in the choice of passive components:

(1) Nominal value and tolerance. An aspect of this is the

coding applied to the component. Color, letter, and

number codes are used.

(2) Stability. The nominal value as a function of temperature

[the temperature coefﬁcient (tempco) is often expressed

in % or in parts per million change per °Corppm/°C].

Age and en vironmental conditions such as humidity,

vibration, or shock also effect component v alues. On the

other hand, components can affect their environment –

for example, the outgassing of a capacitor in vacuum or

the heating of one component by another.

(3) Size and shape. Along with the reduction in size that

solid-state electronics has brought, there has been a

similar reduction in the size of passive components.

Generally, one uses the smallest practical size, but

power -density considerations can limit the packing den-

sity of power-dissipating components. Also, components

come in different shapes with dif fer ent lead geometries

depending on the intended mounting method. These are

discussed in the section on hardware.

(4) Power dissipation and voltage rating. A resistor has both

a po wer rating and a voltage rating. For very large values

of resistance, it is quite possible to operate well within

the resistor’s power rating, yet exceed the voltage rating.

The result is electrical breakdo wn and destruction of the

resistor. For moderate values of capacitance, capacitors

dissipate very little power and power rating is of no

importance. Very-high-capacitance capacitors with large

effective surface areas, however, have non-negligible

shunt conductances. The large currents that ﬂo w in such

capacitors can cause considerable heat to be generated

with potentially fatal (to the capacitor) results.

(5) Noise. Passive components can introduce noise into an

electronic circuit, and one must be particularly aware

of this problem in low-level circuits and choose appro-

priate low-noise components.

(6) Frequency characteristics. Pure resistors, capacitors,

and inductors are practically unrealizable, and the elec-

trical properties of real passive components depend on

frequency in a nonideal way. This is often indicated by

an equivalent circuit. Inductors and transformers with

magnetic cores, however, are inherently nonlinear and

can be treated only approximately in this way.

(7) Derating. This is an engineering term related to the

safety factors to be used when operating components

under a variety of conditions. Good design requires that

components be operated at no more than 50% of the

manufacturer’s recommended maximum ratings, partic-

ularly with respect to power and voltage. At high ambi-

ent temperatures, components should be derated by even

larger amounts. The resulting decrease in stress greatly

increases component lifetime. In laboratory equipment,

382 ELECTRONICS

large safety factors should always be used for enhanced

reliability. The abbreviation SOA, safe operating area,

speciﬁes the limits of voltage, current, and temperature

for semiconductors.

(8) Cost. For laboratory applications it is poor practice to

economize on passi v e components by using the least e x-

pensiv e ones that will do the job. Laboratory work is labor

intensiv e. The extra cost of top-grade components greatly

outweighs the time saved in troubleshooting and repair .

6.2.1 Fixed Resistors and Capacitors

The more common types of ﬁxed and variable resistors and

ﬁxed capacitors are listed in Tables 6.3 to 6.5.InTable 6.5,

the C range

and V range refer to the minimum and max-

imum values available for all types of a given dielectric. It

is not possible to have the maximum capacitance at the

maximum voltage. The larger capacitances have lower

working voltages (WV), while the smaller ones have the

Table 6.3 Fixed resistors

Carbon Composition Precision Wire-Wound (bobbin)

R range: 2.7 X to 22 MX R range: 0.1 X to 18 MX

Power range:

to 2W

Power range:

to 2W

Tolerances: 6 5, 6 10, 6 20% Tolerances: 6 0.05 to 6 5%

Temperature range: 55 to + 150 °C Temperature range: 55 to 6 145 °C

Temperature coefﬁcient 6 0.1%/°C Temperature coefﬁcient 6 0.0001 to 6 0.002%/°C

Voltage coefﬁcient 6 0.03%/V d.c. Noise: Low

Noise: Highest Frequency response: To 25 kHz for high-resistance values

unless noninductively wound

Typical capacitance: 0.25 pF, no inductance

Working voltage:

150V



to 750Vð2WÞ

Precision Carbon Film Power Wire-Wound

R range: 1 X to 100 MX R range: 0.1 X to 1.3 MX

Power range:

to 2W

Power range: 2 to 225 W

Tolerances: 6 0.5, 1, 2% Tolerances: 6 5%, 6 10%

Temperature range: 55 to 165 °C Operating temperature: 75 to +350 °C

Temperature coefﬁcient 0.02 to 0.05%/ °C Maximum rated-power

temperature:

25 °C

Noise: Low Temperature coefﬁcient: 6 0.026%/°C

Frequency response: To 1 MHz for R >1kX(spinal),

to 100 MHz for R <1kX

Frequency response: To 25 kHz for high-resistance values

unless noninductively wound

Precision Metal Film

R range: 10 X to 200 MX

Power range:

Tolerances: 6 0.1 to 6 1%

Temperature range: 55 to 165 °C

Temperature coefﬁcient 0.0025 to 0.01%/°C

Noise: Lowest

PASSIVE COMPONENTS 383

higher WV. The temperature coefﬁcients generally apply

only to a limited temperature range within the larger oper-

ating temperature range.

High component-density circuits use surface-mount

technology (SMT) chip resistors and capacitors. The se

are different from the more traditional wire lead types,

both in their conﬁguration and the way they are electri-

cally and mechanically connected to circuits. Chip resis-

tors and capacitors are common SMT components, but

semiconductors and integrated circuits are also m anu-

factured for surface mounting. Wh ile high packing de n-

sity is not often a primary consideration in laboratory

electronics, small component s ize can be an important

advantage for some circuits where stray capacitance and

inductance are factors. Surface-mount resistors and

capacitors have metalized contact surfaces and are con-

nected to circuit-board pads with solder that bridges the

SMT metallization and circuit-board pads. Surface-

mount technology resistors and capacitors can be little

larger that the end of a pencil lead and use special codes

to identify their values. The resistor code is a three- digit

code (for 2% and greater tolerances) and a tolerance

character. The ﬁrst two digits are the ﬁrst two signiﬁcant

ﬁgures of the resistance and the third digit is t he power

of ten multiplier. The code 563, for example, is 56

kohms. For resistances less than 100 ohms the letter R

is used to represent a decimal point. For example 33R is

a 33 ohm re sistor. The tolerance is s peciﬁed by a single

letterattheendofthenumericcode.Table 6.8 lists SMT

resistor

and capacitor codes.

Tantalum is the most stable of all ﬁlm-forming materi-

als. Tantalum-foil electrolytic capacitors have similar char-

acteristics to aluminum-foil electrolytic capacitors, but

offer superior stability and freedom from leaking. The

wet-slug type has the highest volumetric efﬁciency of

any capacitor. Tantalum solid-electrolyte capacitors have

much better stability, frequency, and temperature charac-

teristics than liquid-electrolyte types.

The equivalent circuits for ﬁxed resistors and capaci-

tors are given in Figure 6.24. Po

wer factor (PF),the

ratio of con sumed power to apparent power, is a way

of specif ying the nonideal properties of resistors, capaci-

tors, and inductors. The power factor of a pure resistance

is one, while the power factor o f a pure reactance

(capacitor or inductor) is zero. For resistors and capaci-

tors, power factor is speciﬁed at 10

to 10

Hz where X

is generally much smaller than X

. Figure 6.25 illustrates

common capacitor types. Coding is given in Tables 6.6,

7, and 6.8.

6.2.2 Variable Resistors

In electronic equipment, variable resistors are generally

called potentiometers. More speciﬁcally, they can be

classed as pote ntiome ters, trimmers, and rheostats. All

are three-te rminal devices with a terminal at each end

of the resistive element and the third terminal attached

to the sliding contact or tap. Potentiometers are designed

for r egular movement, trimmers for occasional changes,

and rheostats for current limiting in high-power circuits.

Some common type s of variable resistors are shown in

Figure 6.26. There are a number of different resistive-

ement materials for potentiometers. They are listed in

Table 6.4.

Gen

eral-purpose, single-turn potentiom eters come in

power ratings from 0.5 to 5 W and a variety of sizes and

tapers (taper is the change in resistance as a function of shaft

angle). Nonlinear tapers are often used in volume controls,

where an approximate logarithmic response is desired. Some

designs can be stacked on a common shaft, and it is often

also possible to incorporate an on–of f switch. Shafts with

locking nuts are very useful when it is necessary to ﬁx a

giv en setting. Precision potentiometers can be single-turn

or 3-, 5-, or 10-turn types. The resistiv e elements are wire,

conductiv e plastic, or a ceramic-metal substance called cer-

met. The rotating shaft is usually supported in a bushing,

which is mounted with a threaded collar . Power ratings are

Table 6.4 Variable resistors

Resistive

Element

Material

R Range Temperature

Coefﬁcient

(ppm/°C)

Linearity

(%)

Carbon composition 50 X to 1 MX 6 1000 5.0

Resistance wire 1 X to 100 kX 6 10 0.25

Conductive plastic 100 X to 5 MX 6 100 0.25

Cermet

100 X to 5 MX 6 100 0.25

Ceramic-metal hybrid.

384 ELECTRONICS

Table 6.5 Fixed capacitors

Air

C range: <100pF

Tolerances: To 0.01%

Stability: High

Temperature coefﬁcient 20 ppm/°C

Dissipation factor: 10

5

Mica and Glass

C range: pF to 1 lF

Tolerance: 6 1to6 20%

Operating temperature (°C): 55 to + 70, + 85, þ125, or + 150, depends on

construction

Temperature coefﬁcient: 20 to + 100 ppm/°C

V range: 100 to 8000 WV d.c.

Dissipation factor: (17) 3 10

4

Ceramic Disc

C range: 1 pF to 1 lF

Tolerance: 6 1to6 20%

V range: 100 to 7500 WV d.c.

Operating temperature (°C): 55 to + 150

Temperature coefﬁcient: 0 ppm/°C for NPO to 6 750ppm/°C for N750

Dissipation factor: 5 3 10

4

Film

Dielectric: Polyester Polycarbonate Polystyrene

C range (lF): 0.0001 to 12 (metalized) 0.0001 to 50 (metalized) 0.0001 to 1 (metalized)

V range (WV d.c.): 50 to 1600 50 to 600 50 to 600

Operating temperature (°C) 55 to + 125 55 to + 125 55 to + 85

Temperature coefﬁcient: +250 ppm/°CNonmonotonic,6 1% total 50 to 100 ppm/°C

Tolerances: 61to620% 61to610% 61to610%

Dissipation factor: 10

3

3 3 10

3

4

Electrolytic (polarized or unpolarized)

Aluminum (general purpose)

C range: 1–50 000 lF

Tolerance: 10 to +75%

V range: 3 to 450 WV d.c.

Maximum operating temperature (°C): 85

Direct current leakage: High

Low temperature stability: Low

Internal inductance limits high-frequency performance

Prone to leaking

Tantalum (foil and wet slug)

Electrolyte: Wet Dry

C range (lF): 15–2200 0.0047–1000

V range (WV d.c.): 3–300 2–150

Tolerance: 610% to 15 + 75% 610 to 640%

PASSIVE COMPONENTS 385

from 0.25 to 2 W with a maximum operating temperature of

125 °C. Resistance values are from 50 ohms to 200 k ohms,

depending on the model, and tolerances are 61%to65%.

Linearity is 60.25 % to 61.0 % and temperature coefﬁ-

cients are 620 ppm/°C. For the 10-turn models, turn-count-

ing dials are available.

Figure 6.25 Some common capacitor types.

Figure 6.24 Equivalent circuits: (a) resistor; (b) capacitor.

Table 6.6 Resistor coding

Color Signiﬁcant Digit Multiplier Tolerance

Black 0 1 —

Brown 1 10 —

Red 2 100 —

Orange 3 1 000 —

Yellow 4 10 000 —

Green 5 100 000 —

Blue 6 1 000 000 —

Violet 7 10 000 000 —

Gray 8 — —

White 9 — —

Gold — — 65%

Silver — — 610%

No color — — 620%

Table 6.6 Resistor coding

386 ELECTRONICS

Table 6.7 Capacitor coding

Color Signiﬁcant

Digits

Multiplier Capacitance

Tolerance (%)

d.c. Working

Voltage

Operating

Temperature (°C)

EIA/Vibration

Black 0 1 — — 55 to +70 10 to 55 Hz

Brown 1 10 61 100 — —

Red 2 100 62—55 to +85 —

Orange 3 1 000 — 300 — —

Yellow 4 10 000 — — 55 to +125 10 to 2000 Hz

Green 5 — 65 500 — —

Blue 6 — — — 55 to +150 —

Violet 7 — 67—— —

Gray 8 — — — — —

White 9 — 69 — — EIA

Gold — — 65 1000 — —

Silver — — 610 — —

Equivalences:

6

F ¼1 lF, 1 MFD.

9

F ¼0.001 lF, 1 gF, 1000 pF.

12

F ¼0.001 gF, 1 pF, 1 MMFD, 1 llF.

Table 6.7 Capacitor coding

PASSIVE COMPONENTS 387

Trimmers are used to compensate for the tolerance and

variation of ﬁxed components. They are not designed for

continuous adjustment, 200 cycles is their design life. The

resistance elements are carbon composition, cermet, or

wire. They can be single-turn or have multiturn lead screws

or worm gears.

6.2.3 Transmission Lines

The most common transmission lines are those with two

conductors. A number of common conﬁgurations are

shown in Figure 6.27. Common VHF ﬂat television antenna

ad-in cable is an example of a two-wire transmission line.

RG/U cables found in almost all laboratories are examples

Table 6.7 (cont.)

Six Dot or Six-Band Code

Five-Dot or Five-Band Code

A and B (when marked) temperature coefﬁcient A and B (when marked) temperature coefﬁcient

C ﬁrst signiﬁcant ﬁgure C ﬁrst signiﬁcant ﬁgure

D second signiﬁcant ﬁgure D second signiﬁcant ﬁgure

E decimal multiplier E decimal multiplier

F military code number

Temperature Characteristics

A B Temp. Coeff.

ppm/°C

Gray Black Gen. Purpose Black — NP0 0

Orange Orange N 1500 Brown — N030 30

Yellow Orange N 2200 Red — N080 80

Green Orange N 3300 Orange — N150 150

Blue Orange N 4700 Yellow — N220 220

Red Violet P100 Green — N330 330

Green Blue P030 Blue — N470 470

Gold Orange X5F Violet — N750 750

Brown Orange Z5F Gold — P100 +100

Gold Yellow X5P White —

Brown Yellow Z5P Gray —

Gold Blue X5S

Brown Blue Z5S

Gold Gray X5U

Brown Gray Z5U

388 ELECTRONICS

of coaxial transmission lines – such coaxial cable is also

used for UHF and satellite television leads. The wire-and-

plane conﬁguration is less common. The ribbon-and-plane

conﬁguration occurs very often in printed circuit boards

(PCBs), where the ribbon is the metal trace on one side

of the board and the plane is a continuous conducting sheet

on the opposite side, often called the ground plane. A trans-

mission line of this type is called a microstrip line. The

formulae for the characteristic impedance Z

of the geo-

metries in Figure 6.27 are given in Table 6.9.

The

properties of a transmission line are given in terms

of the series impedance Z and shunt admittance Y per unit

length:

Z ¼ R þ jxL

Y ¼ G þ jxC

ð6:30Þ

where j ¼

ﬃﬃﬃﬃﬃﬃﬃ

1

and G is the shunt cond uctance, which is the

reciprocal of the shunt resistance per unit length. The charac-

teristic impedance Z

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

Z=Y

. Voltage and current propa-

gate along a transmission line as waves. The properties of the

waves are determined by the propagation constant c and phase

velocity v

.Theyaregivenbyc ¼

ﬃﬃﬃﬃﬃﬃ

¼ a þ jb and v

x/b,wherex is the frequency of the wave. The wav elength in

the transmission line is k ¼ 2pv

/x ¼ 2p/b. The attenuation

of the wave is given by the factor e

a

per unit length. These

formulae are summarized in Table 6.10. For most practical

ransmission lines, the series resistance per unit length R is

small compared to the inductiv e reactance xL, and the shunt

conductance G is small compared to the reciprocal of the

capacitance reactance 1/xC. Under these conditions, Z

essentially

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

L=C

, a becomes [R/Z

þ GZ

]/2, and b

becomes x

ﬃﬃﬃﬃﬃﬃ

. The phase velocity is independent of

frequency and is the ratio of the speed of light in

Table 6.7 (cont.)

Capacitance

Color Digit (C and D) Multiplier (E) Nominal Capacitance

< 10 pF > 10 pF

Black 0 1 62.0 pF 620%

Brown 1 10 60.1 pF 61%

Red 2 100 — 62%

Orange 3 1 000 — 6 3%

Yellow 4 10 000 +100%, 0%

Green 5 — 60.5 pF 65%

Blue 6 — — —

Violet 7 — — —

Gray 8 0.01 60.2 pF +80%, to 20%

White 9 0.1 61.0 pF 610%

Nominal capacitance code is EIA-RS 198.MIL-SPEC code not the same. Five- and six-digit codes are both used for radial-lead and

axial-lead capacitors. Disc capacitors normally have typographical marking but may be color-coded.

N designates a negative temperature coefﬁcient; P designates a positive temperature coefﬁcient.

PASSIVE COMPONENTS 389

vacuum to the square root of the dielectric constant,

e, of the mat erial separating the conductors. For reason-

able values of con duc tor geomet ry, Z

lies approximately

between 50 and 500 ohms. The attenuation a is obtained

from the shunt conductance G and series resist ance R,

once Z

is known. For most dielectrics, G is very small

(for air, G can be taken equal to z ero) and R becomes the

dominant factor. Because of the skin effect, R increases

with frequency ( see Table 6.1). The properties of common

coax

ial cables are giv en in Table 6.11. Attenuation ratings

or RG/U cables as a function of frequency are given in Table

6.1

2. along with jacket information. As is to be expected, the

Table 6.8 Surface-mount (SMT) codes

SMT Resistor Tolerance Code

Letter Tolerance

D 60.5%

F 61.0%

G 62.0%

J 65.0%

SMT Capacitor Signiﬁcant Figure Code

Character Figures Character Figures Character Figures

A 1.0 N 3.3 a 2.5

B 1.1 P 3.6 b 3.5

C 1.2 Q 3.9 d 4.0

D 1.3 R 4.3 e 4.5

E 1.5 S 4.7 f 5.0

F 1.6 T 5.1 m 6.0

G 1.8 U 5.6 n 7.0

H 2.0 V 6.2 t 8.0

J 2.2 W 6.8 y 9.0

K 2.4 X 7.5

L 2.7 Y 8.2

M 3.0 Z 9.1

SMT Capacitor Code

Character Multiplier

110

2 100

3 1 000

4 10 000

5 100 000

6 1 000 000

7 10 000 000

8 100 000 000

9 0.1

390 ELECTRONICS

smaller cables show greater attenuation due to the neces-

sity of using a small-diameter inner conductor to maintain

a reasonable ratio of outer to inner conductor diameter.

The most common cable has a characteristic impedance

of 50 ohms. Twisted pairs of s ingle-conductor wire a re

used where immunity from noise is important. Unwanted

signals induc ed in both conductors can be canceled elec-

tronically by differential ampliﬁcation.

As a general rule, at least one end of a transmission line

should be terminated with a resistance equal to Z

to pre v ent

ringing and undesirable reﬂections if the line is used for

sending signals over distances greater than k/8. The trans-

mission of pulses with nanosecond rise times over distances

of a fe w centimeters on a printed circuit board, for example,

requires termination. In theory, termination of the source or

load end of the line is sufﬁcient. In practice, howe ver, it is

Figure 6.26 Some common types of variable resistors.

PASSIVE COMPONENTS 391

usually the load end that is ter minated. Because 50 ohms

cable is so common, electronic instruments designed to oper-

ate at high frequencies often have 50 ohms input and output

impedances to facilitate connections. Such low-impedance

instruments are not suitable for use in combination with

lower -frequenc y devices, which may be seriously over-

loaded by 50 ohms.

The velocity of propagation v

of an electrical signal

through a transmission line is 1=

ﬃﬃﬃﬃﬃﬃﬃ

¼ Z

=L ¼ 1=Z

For 50 ohms cable with a polyethylene or TeﬂonÔ

Table 6.9 Characteristic impedance of

transmission-line geometries

Geometry Z

(X)

Two-wire

138

ﬃﬃ

Coaxial

276

ﬃﬃ

Wire and plane

ﬃﬃ

Ribbon and plane

or Microstrip line

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

e þ 1:41

5:98h

0:8wþt

Twisted pair (AWG

24–28, 30 turns/f.)

110

Strip line

ﬃﬃ

0:67pwð0:8þtwÞ

e ¼1.0 for air and 5.0 for G-10 ﬁberglass epoxy circuit board.

Copper foil thickness is 0.001 in. for 1 oz cladding and 0.002 in.

for 2 oz cladding.

Table 6.10 General transmission-line properties

Quantity Symbol Relation to Fundamental

Parameters

Shunt admittance YG+ j x C

Series impedance ZR+ j x L

Characteristic impedance Z

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

Z=Y

Wavelength k 2 p/b

Propagation velocity v

ﬃﬃ

Attenuation constant a ½R=Z

+ GZ

=2

Propagation constant c

ﬃﬃﬃﬃﬃﬃ

¼ a þ jb

Figure 6.27 Fixed-geometry transmission-line conﬁgurations.

392 ELECTRONICS

Table 6.11 Properties of coaxial cable

Military RG

Number

Armor

O.D.

(in.)

Jacket

O.D.

(in.)

Jacket

Type

Dielectric

O.D. (in.)

Dielectric

Type

Center

Conductor

V.P.

(%) Capacitance

(pF/ft.)

Max. RMS

Operating

Voltage (V)

Nominal

Impedance

(X)

5B — 0.328 IIa .181 P 16 S 65.9 28.5 3 000 50

6A/U — 0.332 IIa .185 P 21 CW 65.9 20 2 700 75

7A/U — 0.405 I .285 P 7/21 C 65.9 29.5 5 000 52

8A/U — 0.405 IIa .285 P 7/21 C 65.9 29.5 5 000 52

9 — 0.420 II Gray .280 P 7/21 S 65.9 30 5 000 51

9A — 0.420 II Gray .280 P 7/21 S 65.9 30 5 000 51

9B/U — 0.420 IIa .280 P 7/21 S 65.9 30 5 000 50

10A/U 0.475 0.405 IIa .285 P 7/21 C 65.9 29.5 5 000 52

11A — 0.405 I .285 P 7/26 TC 65.9 20.5 5 000 75

11A/U — 0.405 IIa .285 P 7/26 TC 65.9 20.5 5 000 75

12A/U 0.475 0.405 IIa .285 P 7/26 TC 65.9 20.5 5 000 75

13 — 0.420 I .280 P 7/26 TC 65.9 20.5 5 000 74

13A/U — 0.420 IIa .280 P 7/26 T 65.9 20.5 5 000 74

14A/U — 0.545 IIa .370 P 10 C 65.9 29.5 7 000 52

17A — 0.870 IIa .680 P .188 C 65.9 29.5 11 000 52

17A/U — 0.870 IIa .680 P .188 C 65.9 29.5 11 000 52

18A/U 0.945 0.870 IIa .680 P .188 C 65.9 29.5 11 000 52

19A/U — 1.120 IIa .910 P .250 C 65.9 29.5 14 000 52

20A/U 1.195 1.120 IIa .910 P .250 C 65.9 29.5 14 000 52

21A — 0.332 IIa .185 P 16 N 65.9 29 2 700 53

22 — 0.405 I .285 P Two 7/.0152 C 65.9 16 1 000 95

22B/U — 0.420 IIa .285 P# Two 7/.0152 C 65.9 16 1 000 95

34B/U — 0.630 IIa .460 P 7/.0249 C 65.9 21.5 6 500 75

35B/U 0.945 0-870 IIa .680 P .1045 C 65.9 21 10 000 75

55B/U — 0.206 IIIa .116 P 20 S 65.9 28.5 1 900 53.5

57A/U — 0.625 IIa .472 P Two 7/21 C 65.9 16 3 900 95

58/U — 0.195 I .116 P 20 C 65.9 28.5 1 900 53.5

58A/U — 0.195 I .116 P 19/.0071 TC 65.9 30 1 900 50

58C/U — 0.195 IIa .116 P 19/.0071 TC 65.9 30 1 900 50

59/U — 0.242 I .146 P 22 CW 65.9 21.5 2 300 73

59B/U — 0.242 IIa .146 P .023 CW 65.9 21 2 300 75

62/U — 0.242 I .146 SSP 22 CW 84 13.5 750 93

62A/U — 0.242 IIa .146 SSP 22 CW 84 13.5 750 93

62B/U — 0.242 IIa .146 SSP 7/32 CW 84 13.5 750 93

63/U — 0.405 I .285 SSP 22 CW 84 10 1 000 125

PASSIVE COMPONENTS 393

Table 6.11 (cont.)

Military RG

Number

Armor

O.D.

(in.)

Jacket

O.D.

(in.)

Jacket

Type

Dielectric

O.D. (in.)

Dielectric

Type

Center

Conductor

V.P.

(%) Capacitance

(pF/ft.)

Max. RMS

Operating

Voltage (V)

Nominal

Impedance

(X)

63B/U — 0.405 IIa .285 SSP 22 CW 84 10 1 000 125

71A — < 0.250 I .146 SSP 22 CW 84 13.5 750 93

71B/U — 0.250 IIIa .146 SSP 22 CW 84 13.5 750 93

74A/U 0.615 0.545 IIa .370 P 10 C 65.9 29.5 7 000 52

79B/U 0.475 0.405 IIa .285 SSP 22 CW 84 10 1 000 125

87A/U — 0.425 V .280 TF 7/20 S 69.5 29.5 5 000 50

108A/U — 0.235 IIa .079 ea. P Two 7/28 TC 68 23.5 1 000 78

111A/U 0.490 0.420 IIa .285 P Two 7/.0152 C 65.9 16 1 000 95

114/U — 0.405 I .285 SSP 33 CW 88 6.5 1 000 185

114A/U — 0.405 IIa .285 SSP 33 CW 88 6.5 1 000 185

115 — 0.375 V .250 #IT 7/21 S 70 29.5 5 000 50

115A/U — 0.415 V .250 #IT 7/21 S 70 29.5 4 000 50

116/U 0.475 0.425 V .280 TF 7/20 S 69.5 29.5 5 000 50

122/U — 0.160 IIa .096 P 27/37 TC 65.9 29.5 1 900 50

140/U — 0.233 V .146 TF .025 SCW 69.5 21 2 300 75

141/U — 0.190 V .116 TF .0359 SCW 69.5 28.5 1 900 50

141A/U — 0.190 V .116 TF# .039 SCW 69.5 28.5 1 900 50

142/U — 0.206 V .116 TF# .0359 SCW 69.5 28.5 1 900 50

142/B — 0.195 IX .116 TF .039 SCW 69.5 28.5 1 900 50

143 — 0.325 V .185 TF .057 SCW 69.5 28.5 3 000 50

142A/U — 0.206 V .116 TF .039 SCW 69.5 28.5 1 900 50

143A/U — 0.325 V .185 TF .059 SCW 69.5 28.5 3 000 50

149/U — 0.405 I .285 P 7/26 TC 65.9 20.5 5 000 75

164/U — 0.870 IIa .680 P .1045 C 65.9 21 10 000 75

174/U — 0.100 I .060 P 7/.0063 CW 65.9 30 1 500 50

178B/U — 0.075 VII .034 TF 7/38 SCW 69.5 29.0 1 000 50

179B/U — 0.105 VII .063 TF# 7/38 SCW 69.5 19.5 1 200 75

180B/U — 0.145 VII .102 TF 7/38 SCW 69.5 15.0 1 500 95

187/U — 0.110 VII .063 TF 7/38 SCW 69.5 19.5 1 200 75

188/U — 0.110 VII .060 TF 7/.0067 SCW 69.5 29 1 200 50

195/U — 0.155 VII .102 TF 7/38 SCW 69.5 15 1 500 95

196/U — 0.080 VII .034 TF 7/38 SCW 69.5 29 1 000 50

209/U — 0.745 VI .500 SST 19/.0378 S 84 26.5 3 200 50

210/U — 0.242 V .146 SST 22 SCW 84 13.5 750 93

211A/U — 0.730 V .620 TF .190 C 69.5 29.0 7 000 50

394 ELECTRONICS

insulation, v

is of the order of 2 3 10

m/s, which gives a

delay of 5 ns /m. For delays up to a few hundre d nano-

seconds, high-quality, low-loss coaxial cable provides an

excellent delay line, because no distortion of the propa-

gated signal occurs w hen it is properly terminated. The

best cabl e to use for critical delay-line applications is

rigid or semirigid air-core coaxial cable. With air as the

dielectric, the shunt conductance is virtually zero. Semi-

rigid construction assures that the coaxial geometry is

maintained within tight tolerances, reducing distortion.

Such cable is practical for use at frequencies up to the

microwave region.

Table 6.11 (cont.)

Military RG

Number

Armor

O.D.

(in.)

Jacket

O.D.

(in.)

Jacket

Type

Dielectric

O.D. (in.)

Dielectric

Type

Center

Conductor

V. P.

(%) Capacitance

(pF/ft.)

Max. RMS

Operating

Voltage (V)

Nominal

Impedance

(X)

212/U — 0.332 IIa .185 P .0556 S 65.9 28.5 3 000 50

213/U — 0.405 IIa .285 P 7/.0296 C 65.9 29.5 5 000 50

214/U — 0.425 IIa .285 P 7/.0296 S 65.9 30 5 000 50

215/U 0.475 0.405 IIa .285 P 7/.0296 C 65.9 29.5 5 000 50

216/U — 0.425 IIa .285 P 7/26 TC 65.9 20.5 5 000 75

217/U — 0.545 IIa .370 P .106 C 65.9 29.5 7 000 50

218/U — 0.870 IIa .680 P .195 C 65.9 29.5 11 000 50

219/U 0.945 0.870 IIa .680 P .195 C 65.9 29.5 11 000 50

220/U — 1.120 IIa .910 P .260 C 65.9 29.5 14 000 50

221/U 1.195 1.120 IIa .910 P .260 C 65.9 29.5 14 000 50

222/U — 0.322 IIa .185 P .0556 N 65.9 29 2 700 50

223/U — 0.216 IIa .116 P .035 S 65.9 29.5 1 900 50

225/U — 0.430 V .285 TF 7/.0312 S 69.5 29.5 5 000 50

227/U 0.490 0.430 V .285 TF 7/.0312 5 69.5 29.5 5 000 50

228A/U 0.795 0.730 V .620 TF .190 C 69.5 29.0 7 000 50

264/U — 0.750 PU .176 P Four 19/27 C 69.5 40.0 N.A. 40

280/U — 0.480 IX .327 TT 9C 80 27 3 000 50

281/U — 0.750 VI .500 TT 19/.0378 S 80 27 3 200 50

301/U — 0.245 IX .185 TF 7/.0203 K 69.5 28.5 3 000 50

302/U — 0.206 IX .146 TF 22 SCW 69.5 21 2 300 75

303/U — 0.170 IX .116 TF .038 SCW 69.5 28.5 1 900 50

304/U — 0.280 IX .185 TF .059 SCW 69.5 28.5 3 000 50

307A/U — 0.270 IIIa .146 SSP 19/.0058 S 80.0 17 N.A. 75

316/U — 0.102 IX .060 TF 7/.0067 SCW 69.5 29 1 200 50

Designation listed at end of this table.

P: polyethylene; SSP: semisolid polyethylene; TF: Teﬂon; TT: Teﬂon tape; SST: semisolid Teﬂon.

Number of strands, gauge (B&S) or O.D., and material are speciﬁed. A single solid wire results in the lowest cable attenuation.

Stranding increases ﬂexibility. S: silvered copper; C: copper; TC: tinned copper; N: Nichrome; CW: Copperweld; SCW: silvered

Copperweld; K: Karma.

100% x (velocity of propagation)/(velocity in vacuum).

PASSIVE COMPONENTS 395

For longer delays, lumped-element delays are the most

practical. These delays consist of low-pass ﬁlter sections

connected in series. For frequencies below their corner

frequency, they act as delay lines. The number of sections

n required is related to the ratio of the delay time t

to the

rise time t

, and is given by n ¼ 1.5 t

. The incorporation

of multiple taps between the sections allows a choice of

delays with a single unit.

For a line le ngth less than a quarter wavelength, a

transmission line behaves like a capacitor or an inductor,

depending on whether the end of the line is an open

circuit or s hort circ uit. A line that is a n odd number

of quarter-wavelengths long behaves like a parallel res-

onant RLC circuit when short-circuited at one end, and

like a series resonant circuit when open-circuited.

The Qs of such resonant circuits are much higher than

attainable with lumped elements. There are, however, an

inﬁnite number of resonance s corresponding to frequen-

cies where:

=f ¼ð2n +1Þk=4

where n is an integer.

TABLE 6.12 Properties of coaxial cable

Attenuation ratings for RG/U cable

Nominal Attenuation [dB/(100 ft)]

Frequency (MHz): 1.0 10 50 100 200 400 1000 3000 5000 10 000

RG/U Type

5, 5A, 5B, 6, 6A, 212 0.26 0.83 1.9 2.7 4.1 5.9 9.8 23.0 32.0 56.0

7 0.18 0.64 1.6 2.4 3.5 5.2 9.0 18.0 25.0 43.0

8, 8A, 10, 10A, 213, 215 0.15 0.55 1.3 1.9 2.7 4.1 8.0 16.0 27.0 >100.0

9, 9A, 9B, 214 0.21 0.66 1.5 2.3 3.3 5.0 8.8 18.0 27.0 45.0

11, 11A, 12, 12A, 13, 13A, 216 0.19 0.66 1.6 2.3 3.3 4.8 7.8 16.5 26.5 > 100.0

14, 14A, 74, 74A, 217, 224 0.12 0.41 1.0 1.4 2.0 3.1 5.5 12.4 19.0 50.0

17, 17A, 18, 18A, 177, 218, 219 0.06 0.24 0.62 0.95 1.5 2.4 4.4 9.5 15.3 > 100.0

19, 19A, 20, 20A, 220, 221 0.04 0.17 0.45 0.69 1.12 1.85 3.6 7.7 11.5 > 100.0

21, 21A, 222 1.5 4.4 9.3 13.0 18.0 26.0 43.0 85.0 > 100.0 > 100.0

22, 22B, 111, 111A 0.24 0.80 2.0 3.0 4.5 6.8 12.0 25.0 > 100.0 > 100.0

29 0.32 1.20 2.95 4.4 6.5 9.6 16.2 30.0 44.0 > 100.0

34, 34A, 34B 0.08 0.32 0.85 1.4 2.1 3.3 5.8 16.0 28.0 > 100.0

35, 35A, 35B, 164 0.08 0.08 0.58 0.85 1.27 1.95 3.5 8.6 15.5 > 100.0 > 100.0

54, 54A 0.33 0.92 2.15 3.2 4.7 6.8 13.0 25.0 37.0 > 100.0

55, 55A, 55B, 223 0.03 0.30 1.2 3.2 4.8 7.0 10.0 16.5 30.5 46.0 > 100.0

57, 57A, 130, 131 0.18 0.65 1.6 2.4 3.5 5.4 9.8 21.0 > 100.0 > 100.0 > 100.0

58, 58B 0.33 1.25 3.15 4.6 6.9 10.5 17.5 37.5 60.0 > 100.0

58A, 58C 0.44 1.4 3.3 4.9 7.4 12.0 24.0 54.0 83.0 > 100.0

59, 59A, 59B 0.33 1.1 2.4 3.4 4.9 7.0 12.0 26.5 42.0 > 100.0

62, 62A, 71, 71A, 71B 0.25 0.85 1.9 2.7 3.8 5.3 8.7 18.5 30.0 83.0

62B 0.31 0.90 2.0 2.9 4.2 6.2 11.0 24.0 38.0 92.0

63, 63B, 79, 79B 0.19 0.52 1.1 1.5 2.3 3.4 5.8 12.0 20.5 44.0

87A, 116, 165, 166, 225, 227 0.18 0.60 1.4 2.1 3.0 4.5 7.6 15.0 21.5 36.5

94 0.15 0.60 1.6 2.2 3.3 5.0 7.0 16.0 25.0 60.0

94A, 226 0.15 0.55 1.2 1.7 2.5 3.5 6.6 15.0 23.0 50.0

396 ELECTRONICS

Jacket Type

Designation Material Temperature Limits (°C)

Type I Black polyvinyl chloride 40 to þ80

Type IIa Black polyvinyl chloride

(noncontaminating):

<1=4 in. 55 to þ80

>1=4 in. 40 to þ80

Type IIIa Black polyethylene 55 to þ85

Type IV Black synthetic rubber:

<1=2 in. 55 to þ80

>1=2 in. 40 to þ80

Type V Fiber glass 55 to þ250

Type VI Silicone rubber 55 to þ175

Type VII Polytetraﬂuoroethylene (Teﬂon) 55 to þ200

Type IX Fluorinated Ethylene Propylene (FEP) 55 to þ200

PU Polyurethane (Estane) 60 to þ180

Table 6.12 (cont.)

Nominal Attenuation [dB/(100 ft)]

Frequency (MHz): 1.0 10 50 100 200 400 1000 3000 5000 10 000

108, 108A 0.70 2.3 5.2 7.5 11.0 16.0 26.0 54.0 86.0 > 100.0

114, 114A 0.95 1.3 2.1 2.9 4.4 6.7 11.6 26.0 40.0 65.0

115, lISA, 235 0.17 0.60 1.4 2.0 2.9 4.2 7.0 13.0 20.0 33.0

117, 118, 211, 228 0.09 0.24 0.60 0.90 1.35 2.0 3.5 7.5 12.0 37.0

119, 120 0.12 0.43 1.0 1.5 2.2 3.3 5.5 12.0 17.5 54.0

122 0.40 1.7 4.5 7.0 11.0 16.5 29.0 57.0 87.0 > 100.0

125 0.17 0.50 1.1 1.6 2.3 3.5 6.0 13.5 23.0 > 100.0

140, 141, 141A 0.30 0.90 2.1 3.3 4.7 6.9 13.0 26.0 40.0 90.0

142, 142A, 142B 0.34 1.1 2.7 3.9 5.6 8.0 13.5 27.0 39.0 70.0

143, 143A 0.25 0.85 1.9 2.8 4.0 5.8 9.5 18.0 25.5 52.0

144 0.19 0.60 1.3 1.8 2.6 3.9 7.0 14.0 22.0 50.0

149, 150 0.24 0.88 2.3 3.5 5.4 8.5 16.0 38.0 65.0 > 100.0

161, 174 2.3 3.9 6.6 8.9 12.0 17.5 30.0 64.0 99.0 > 100.0

178, 178A, 196 2.6 5.6 10.5 14.0 19.0 28.0 46.0 85.0 > 100.0 > 100.0

179, 179A, 187 3.0 5.3 8.5 10.0 12.5 16.0 24.0 44.0 64.0 > 100.0

180, 180A, 195 2.4 3.3 4.6 5.7 7.6 10.8 17.0 35.0 50.0 88.0

188, 188A 3.1 6.0 9.6 11.4 14.2 16.7 31.0 60.0 82.0 > 100.0

209 0.08 0.27 0.68 1.0 1.6 2.5 4.4 9.5 15.0 48.0

281 0.09 0.32 0.78 1.1 1.7 2.5 4.5 9.0 13.0 24.0

PASSIVE COMPONENTS 397

Table 6.13 Common coaxial connector types

Size Classiﬁcation Connector Type Attachment Method Cable Size

Range (in.)

Maximum Frequency

(GHz)

RMS Working

Voltage (V)

Medium UHF Screw

0.5 500

Screw

Bayonet

Screw

;

1,000

1,500

7-mm precision Sexless Screw .141, .250, .325,

semirigid; RG 214/U, RG

142B/U

18 1,500

Miniature

BNC

MHV

TNC

Bayonet

Screw

;

500

5,000

500

SHV Bayonet 0.080 to 0.420 — 10,000 d.c.

Subminiature

SMB

SMC

SMA

Snap on

Screw

;

500

350

LEMO

Push on 0.100 to 0.195 4 1,500

Higher-voltage version of the BNC connector, not mateable with BNC connectors.

NIM high-voltage connector.

00 shell size. Manufactured in the United States as K-Loc by Kings Electronics Co.

Source: Reference 2.

Figure 6.28 Some coaxial connectors.

398 ELECTRONICS

6.2.4 Coaxial Connectors

Probably more time is spent with connectors than with any

other element of electronic hardware. When deciding on

the method of connecting various pieces of electronic

equipment, it is wise to be aware of the variety of connec-

tors available and choose a family of connectors best

suited to the task. In many cases, the choice of connector

is dictated by the connectors at the outputs and inputs of

existing equipment.

Figure 6.29(a) Procedure for stripping coaxial cables; Assembly procedure for BNC/MHV

ferrule-clamp connector.

PASSIVE COMPONENTS 399

The most common connector is currently the BNC. It is

a miniature bayonet type, but circuit density has increased

enormously with the extensive use of integrated circuits

and the BNC connector is now being replaced by a variety

of subminiature connectors – among which the LEMOÔ

has taken the lead for nuclear instrumentation. A list of

common coaxial connectors is given in Table 6.13.

addition to coaxial connector plugs, each series of con-

nectors has a wide variety of jacks and adaptors (generally

plug refers to the connector attached to the cable or wire,

while jack refers to the connector to which the plug mates).

Jacks for chassis mounting, bulkhead mounting, and

printed circuit-board mounting are available, as well as

hermetically seal ed jacks for making coaxial connections

Figure 6.29(b)

400 ELECTRONICS

through a vacuum wall. Tees and barrels allow o ne to

connect cables together and there are terminators that

can be attached directly to input or output jacks. In addi-

tion, each series has a certain number of interseries adap-

tors for connection of plugs or jacks to those of other

series. Some of the different connectors ar e shown in

Figure 6.28. It is advisable to reduce the number of adap-

tors

to a mini mum to maintain the transmission-line prop-

erties of the connections with a s few reﬂecti on-producing

discontinuities as possible.

A good connector should be easy to ﬁt to the proper

cable and should not introduce any discontinuities in

the transmission-line properties of the cable. Needless to

say, the characteristic impedance of the connector should

be identical to that of the cable. The connector should be a

strong mechanical ﬁt to the cable, and it should be easy to

connect and disconnect from mating connectors.

Any given connector type comes in a variety of styles to

accommodate different cable sizes. Conﬁgurations – such as

straight and right angle – are available, and often there are

different choices for the mechanical and electrical connec-

tions of the connector to the cable, the three most common

being a ferrule clamp and screw, crimp, and solder. The pro-

cedure for stripping coaxial cable by hand is shown in Figure

29(a). Shielded lead wire extractors are available for

moving insulated lead wire from braided shield. Similar

to a syringe, the extractor removes the lead wire from the

shield leaving the braid intact. Figure 6.29(b) shows the

sembly of a ferrule-clamp BNC/MHV connector.

Crimp-style connectors require the use of a special crimping

tool and die. They are stronger, less bulky, more uniform,

and electrically more robust than clamp and solder connec-

tors. Crimping avoids the swelling or melting of the cable

dielectric that can occur when solder-type connectors are

assembled. When attaching connectors to cable, it is highly

recommended that the manufacturer’s cable-cutting proce-

dures be followed so that the inner conductor, insulator,

outer conductor (braid or foil), and outer insulator are of

the proper length. In this way no discontinuities in the elec-

trical properties of the cable are introduced at the cable–

connector interface. Special cutting jigs are available to

assure the proper geometry when preparing the cable for

insertion into the connector.

Assembly instructions for several types of coaxial con-

nectors are given in the Chapter 6 Appendix.

6.2.5 Relays

A relay is an electrically actuated switch. Relay action can

be electromechanical or can be based on solid-state devi-

ces. A large number of contact conﬁgurations exist. Impor-

tant parameters are the operating voltage and power rating

of the relay, as well as the contact rating. The speed at

which mechanical relays operate is generally in the 10 to

100 ms range. General-purpose electromagnetic relays

operate at 6, 12, 24, 48, and 110 V d.c. and 6, 12, 24, 48,

110, and 220 V a.c. with coil power ratings of around 1 W

[see Figure 6.30(a)]. Such relays have contacts capable of

Figure 6.30 Mechanical relays: (a) medium-power relay;

(b) reed relay.

PASSIVE COMPONENTS 401

handling from 2 to 10 A. Sensitive mechanical relays use a

large number of turns of ﬁne wire on the electromagnet

coil. They operate with 28 V d.c. and require only 1 to 40

mW of coil power. Contacts are rated from 0.5 to 2 A.

A reed relay is a glass-encapsulated switch having

two ﬂexible thin metal strips , or ree ds, as contact ors.

The switch is placed inside an electromagnetic coil

[Figure 6.30(b)]. The relay contacts can be dry or mer-

cury-wetted.

Standard coil voltages are 6, 12,and24V

d.c., and the coil power is from 50 to 500 mW per reed-

switch capsule. Contacts are rated at 10 mA to 3 A,

depending on size. There is also a maximum open-cir-

cuit voltage that can be sustained by the opened con-

tacts. The low mass of the reeds makes operating times

of 0.2 to 2 ms possible. Small reed relays are made for

PCB mounting.

With inductive loads, the fast opening of relay contacts

can cause a large voltage to appear across them. Some

protective circuits for reducing this problem are illustrated

in Figure 6.31.

Solid-state

relays consi st of a solid-state switching ele-

ment dri v en by an appropriate ampliﬁer. Because the input

circuit is often optically isolated from the load, these relays

introduce little or no noise into the circuit that driv es them.

The load current determines the switching element. Field-

effect transistors (FETs) are used for lo w-level d.c., bipolar

junction transistors (BJTs) for intermediate d.c. currents, and

triacs and silicon-controlled rectiﬁers (SCRs) for large a.c.

and d.c. currents. Section 6.3 has a discussion of transistors

and

solid-state switches. Though there is no contact wear

with solid-state relays, their on resistance may be large com-

pared with electromechanical devices and they require care-

fully conditioned activating signals. They are much less

tolerant of overload than are electromechanical devices.

6.3 ACTIVE COMPONENTS

The overall properties of semiconductor diodes and tran-

sistors can be understood in terms of the properties of the

Figure 6.31 Contact-conditioning circuits for mechanical relays: (a) a.c. (for small loads

driven from the power line, R ¼ 100 ohms and C ¼ 0.05 lF); (b) d.c. (diodes, D, reduce the

peak voltage from the inductive load and should be able to handle the steady-state current

through the inductor).

402 ELECTRONICS

p–n junctions that form them. Without going into a dis-

cussion of solid-state physics, it is sufﬁcient to know that

p-type semiconductor material conducts electricity princi-

pally through the motion of positive charges (holes), while

n-type material owes its conductivity mainly to electrons.

Both p- and n-material can be produced from germanium

or silicon by the addition of impurity atoms – a procedure

called doping.

6.3.1 Diodes

Most semiconductor diodes consist of a p–n junction as

illustrated in Figure 6.32.Theschematicrepresent

ation is

shown next to the simpliﬁed drawing of the diode. The

diode is a unidirectio na l d evice: its d.c. current–voltage

(I–V) characteristics depend on the applied potential on

the anode with respect to the cathode. The I–V character-

istics of a typical small-signal silicon diode are drawn in

Figure 6.33. When the anode is p ositive with respect to

the

cathode (forward bias), the d iode conducts a large

current. When the polarity of the applied potential is

reversed (reverse bias), the current i s very small. If the

reverse voltage is increased beyond the peak reverse volt-

age (PRV), br eakd own occurs and the diode conducts

strongly again. Except in the ca se of specially desig ned

Zener diodes, this usually destroys t he diode. The for-

ward-bias voltage at which the diode begins to conduct

strongly is V

cutin

.Forgermaniumdiodes,V

cutin

is 0.2 V,

while for silicon diodes it is 0 .6 V. The I–V characteristics

shown in the g raph are accurately represented by the

formula:

¼ I

=gV

 1

ð6:31Þ

where I

¼ 10

9

A for silicon and 10

6

A for germanium.

is temperature-dependent, increasing at a rate of 11%/°C

for Ge and 8%/°C for Si. V

has the value 0.026 Vat 300 K

and is directly proportional to the absolute temperature,

and g is a unitless constant equal to one for germanium

and two for silicon.

Diodes can be separated into two types according

to the power they can dissipate. Power diodes are used

in high-current applications, for exam ple, as rectiﬁers in

power supplies. Importa nt speciﬁcations for power diodes

are t he maximum forward current, maximum PRV (peak

reverse voltage), and effective forward-bias resistan ce.

Low-power diode s or signal diodes are used to rectify

small signals, mix two frequencies to produce sum a nd

difference frequencies, and switch low voltages and cur-

rents. Besides the current and voltage ratings, the speed

with which diode s can be chan ged from the forward-bias

to the reverse-bia s condition and back is a factor i n hig h-

speed switching circuits. Switching speed is related to the

effective capacitance of the p–n junction. Typical

speciﬁcations for a power and signal diode are given in

Tables 6.14 and 6.15.

Man

y older diodes have a 1N-preﬁx designation.

The two ends of a diode are usually distinguished from

each other by a mark – the cathode end having a black

Figure 6.33 Typical current–voltage characteristics of a

small-signal silicon diode. Note change of vertical and

horizontal scales at the origin.

Figure 6.32 A diode and the corresponding symbol.

ACTIVE COMPONENTS 403

Maximum Ratings

4001 4002 4003 4004 4005 4006 4007

Peak reverse voltage (V) 50 100 200 400 600 800 1000

Non-repetitive peak reverse voltage (V) 50 100 200 400 600 800 1000

Average forward current (A) 1

Peak surge current (1 cycle) (A) 30

Operating temperature range (°C) 65 to +175

1.10

MIN.

.205 1.10

MIN.

.107

.024

DIA.

Table 6.15 Properties of 1N4001-1N4007 1-ampere silicon rectiﬁers

Maximum Ratings

Peak reverse voltage 75 V

Reverse current 25 nA

Average forward current 75 mA

Peak surge current (1 sec) 500 mA

Electrical Characteristics

Junction capacitance 4 pF

Reverse recovery time 4–8 ns

Table 6.14 Properties of the 1N914 fast-switching diode

band for glass-encapsulated diodes and a white band

for black plastic-encapsulated diodes. Power diodes can

dissipate large amounts of heat and are often constructed

for ease of mounting to a heat sink for efﬁcient heat dissipa-

tion. Some diode conﬁgurations are shown in Figure 6.34.

the case of the high-power diode, the cathode is a

stud that can be attached directly to a metal heat sink.

Generally, ﬁber or mica washers are used to isolate the

cathode electrically from the metal heat sink, and thermal

conductivity is enhanced with special silicone grease

404 ELECTRONICS

between the washers and heat sink. The mounting techni-

que is shown in Figure 6.35.

Because

the current through a diode is a nonlinear func-

tion of the voltage across it, the effective resistance

changes with diode voltage. This is shown in Figure

6.33, where the reciprocal of the slope of the curve passing

through

the origin and a point on the I–V characteristic

curve deﬁnes the static resistance at that point. The

dynamic resistance is the reciprocal of the slope of the

tangent to the curve at the point. The change in current

through a diode for small changes in voltage across it

requires knowledge of both static and dynamic resistance.

For the purposes of simpliﬁed circuit analysis, it is useful

to represent the I–V characteristic curve of a diode by a so-

called piecewise linear model. With this model, the for-

ward- and reverse-bias regions are represented by straight

lines with the transition occurring at the cutin voltage. The

piecewise linear curve is shown in Figure 6.36. The slope

the curve at voltages above V

cutin

is the reciprocal of the

average forward resistance. With this model it is a simple

matter to calculate the effect of the diode in a circuit, since

it behaves like a resistor in the forward-bias condition with

resistance R

, and in the reverse-bias condition it acts

essentially like an open circuit. A graphical representation

of this can be obtained by what is called load-line analysis.

Consider the circuit with an a.c. voltage source shown in

Figure 6.37 . The current through R

can be determined in

the following manner: given a value of V

, the voltage

across the diode, V

, and the current through it, I

, will be

determined by the intersection of the straight line with co-

ordinates (V

, 0) and (0, V

), as in Figure 6.38. Different

Figure 6.34 Diode case conﬁgurations: (a) glass-

encapsulated signal diode; (b) plastic-encapsulated

medium-power diode; (c) high-power diode.

Figure 6.35 Power-diode mount provides electrical insula-

tion with good heat dissipation.

Figure 6.36 Linearized current–voltage characteristic of a

diode.

Figure 6.37 Circuit for load-line analysis of a diode.

ACTIVE COMPONENTS 405

values of V

will give a family of parallel straight lines.

From the intersection points, one constructs a graph of V

as a function of V

. This dynamic curve, which is sho wn in

Figure 6.39, has much the same appearance as the original

tatic curve from which it is derived. If the input waveform

is drawn below the horizontal axis, the reﬂection of it on the

dynamic curve will give the output waveform as shown.

6.3.2 Transistors

Transistors are three-terminal devices. Any one of the

three terminals can be used as an input with a second

terminal as output and the third providing the common

connection between the input and output circuits.

Bipolar Junction Transistors (BJTs). These transis-

tors consist of an emitter, a base, and a collector. They are

designated npn or pnp, depending on the materials used for

the elements. As can be seen from Figure 6.40, a transistor is

o back-to-back diodes with the base element in common.

The major current ﬂow in a BJT transistor is from the emit-

ter to the collector across the base. Relatively little current

ﬂows through the base lead. The arrow on the emitter shows

the direction of the current ﬂow.

Some common BJT transistor case styles are shown in

Figure 6.41. To identify the leads of high frequency tran-

sistors,

manufacturers’ base diagrams should be consulted.

With plastic cases, there is a ﬂat on one side of the case to

help identify the leads. Leads are sometimes identiﬁed by

letters, or are in the following order – emitter, base, col-

lector – starting at the ﬂat or tab of sealed metal cans and

proceeding clockwise as viewed from the lead side of the

transistors. In power transistors, most of the power is dis-

sipated in the collector and the collector terminal is the one

with provision for attachment to a heat sink. Standard

transistor types have code designations beginning with

2N. Several manufacturers often make the same transis-

tors. Proprietary code designations are also used by man-

ufacturers to identify their products.

Since BJT transistors consist of two p-n junctions, a simple

ohmmeter test is a good way to verify that they are in working

condition once the transistor is isolated from the circuit. The

ohmmeter must provide at least 0.6 V, enough to forward-bias

a silicon p–n junction. The resistance between the emitter and

base should be low, of the order of a few hundred ohms or

less when the ohmmeter leads are attached so as to forward-

bias the junction. When the leads are reversed, the resistance

should be of the order of megohms. The same should be true

of the collector–base junction. The polarity of the ohmmeter

leads can be checked with a separate voltmeter.

In normal operation, the emitter–base junction of a tran-

sistor is forward-biased, while the base–collector junction is

reverse-biased. The three usual conﬁgurations, common

Figure 6.38 Graphical construction for determining

the dynamic transfer curve from the load line and the

static characteristic curve.

Figure 6.39 Graphical construction of output waveform

from input waveform and the dynamic transfer curve.

406 ELECTRONICS

emitter (CE), common base (CB), and common collector

(CC), are shown schematically in Figure 6.42.TheI–

characteristics of each conﬁguration consist of two sets of

curves, one for the input and the other for the output. The I–

V curves for a typical general-purpose transistor in the CE

conﬁguration, for example, are shown in Figure 6.43. There

are a set of curves rather than a single one for the input and

output circuits because the two circuits interact with each

other. When measuring the I–V characteristics of either the

input or output circuit, the condition of the other circuit

must also be speciﬁed. Figure 6.44 shows a circuit for meas-

ing the output characteristics of a CE conﬁguration.

For a ﬁxed series of I

values, set by adjusting V

,the

current into the collector I

is measured as a function of V

The variation in V

is obtained by changing V

. Transistor

operation can be understood in terms of the characteristic

curves. For a ﬁxed value of I

, I

increases rapidly with V

until a plateau is reached. I

increases thereafter much more

slowly with V

. In the plateau region, the value of I

depends on I

and is almost independent of V

.Thiscan

be made more quantitative by using load-line analysis. Two

points are sufﬁcient to establish the load line on the output

curves – they are points corresponding to I

¼0 where V

and to V

¼ 0 where I

¼ V

. The output curves

Figure 6.40 Bipolar junction transistors (BJTs) and the corresponding symbols.

Figure 6.41 Transistor case styles.

ACTIVE COMPONENTS 407

with a superimposed load line are shown in Figure 6.45.

The intersections of the load line with the characteristic

curves establish the operating voltages and currents. It is

possible to predict quantitatively how the current through

varies with input base current from these curves. For

linear operation, conditions are adjusted so that the tran-

sistor operates somewhere in the middle of the character-

istic output curves, where they are approximately spaced

equally and parallel for equal base-current increments.

Another way of analyzing transistor operation is by con-

structing an equiv alent circuit with passiv e elements and

sources. Such a circuit can then be analyzed by standard

methods. Because the equiv alent circuit contains only linear

Figure 6.42 (a) Common-emitter (CE), (b) common-base (CB), and (c) common-collector (CC)

conﬁgurations.

Figure 6.43 Current–voltage characteristics of a BJT transistor in the common-emitter (CE) conﬁguration:

(a) output circuit, and (b) input circuit.

Figure 6.44 Biasing circuit for the BJT common-

emitter (CE) conﬁguration.

408 ELECTRONICS

elements, it can represent the properties of the transistor only

within a small region of the characteristic curves about giv en

nominal v alues of the d.c., steady-state, or quiescent voltages

and currents. For this reason such a model is called a small-

signal model. A simpliﬁed low-frequency, small-signal cir-

cuit model of the BJT transistor in the CE conﬁguration

treats the output circuit as a controlled current source with

¼ bi

in parallel with output resistance r

.Herei

is the

base current and b, the ratio of collector current to base

current, is the current gain, a constant. The input circuit

can be modeled as a forward-biased diode with r

the diode

effective resistance. The cutin voltage of the diode is

assumed to be constant and for this reason does not appear

in the small-signal model. This is shown in Figure 6.43(a).

is necessary to keep in mind that the linear circuit is a

good representation of the transistor only for small excur-

sions of the input and output voltages and currents about

speciﬁed quiescent d.c. values. The equivalent circuit does

not show the biasing network necessary to establish the qui-

escent operating point. Practical circuits using separate power

supplies for biasing voltages are shown in Figure 6.47.

The

output signal is developed across the load resistor

, while capacitors C

and C

isolate the a.c. input and

output signals from the d.c. biasing levels.

Transistor data sheets give the values of the b, the cur-

rent gain, and r

, the input resistance, for different operat-

ing points. The parameters for the CB and CC

conﬁgurations can be calculated from those of the CE with

standard formulae.

By applying the standard methods of

circuit analysis to the equivalent circuit, the current, volt-

age, and power gains can be calculated, as well as the input

and output impedances under small-signal conditions. The

general properties of the three conﬁgurations are given in

the graphs of Figure 6.48. Because the charge carriers in

the p-

and n-materials that make up the transistor cannot

respond instantaneously to changes in voltage across the

junctions, the simple three-parameter (r

, b,r

) model is

approximately valid only at low frequencies. The response

of the transistor at high frequencies can be very different,

and equivalent-circuit models exist for the high-frequency

response. In these models, the effective capacitances

between the base-emitter, base-collector, and collector-

emitter are represented by capacitors C

, C

, and C

shown in Figure. 6.49 .

A BJT can also be operated as a switch. If the emitter–

base junction of a transistor is strongly forward-biased

(0.8 V for silicon), the total current through the transistor

will be limited by the external resistance in the circuit and

the voltage between emitter and collector will be of the

order of 0.2 V. In this condition, the transistor is said to be

saturated or on and the base current necessary to sustain

the current ﬂow from emitter to collector is I

, where I

is the total current in the collector circuit and b

is the large

signal current gain. If the emitter–base junction is reverse-

biased, no base current will ﬂow and no collector current

will ﬂow. Under this condition, the transistor acts as an

Figure 6.45 Relation between the static characteristic

curves and the load line.

Figure 6.46 Small-signal model of a BJT.

ACTIVE COMPONENTS 409

open circuit and is said to be cut off. In the saturated or the

cut-off condition, a transistor is similar to a closed or an

open switch. Transistor switches can operate at high fre-

quencies, unlike mechanical switches, but the saturated

resistance is never zero, and there is always at least a

0.2 V drop from the emitter to the collector.

The operating conditions for bipolar junction transistors

are summarized in Table 6.16. They determine whether a

transistor

is operating in the linear region (active), is satu-

rated,oriscut off. When reading the speciﬁcations for a

2N3904 transistor in Tables 6.16 and 6.17, the following

con

ventions are to be noted:

(1) Voltages between two terminals are speciﬁed by

either V or v with two or three subscripts. The ﬁrst

two subscripts indicate the terminals between which

the voltage occurs, and the third subscript, when

present, indicates the condition of the third ter-

minal. Thus, V

CBO

indicates a d.c. voltage between

collector and base with the emitter open. Subscripts

with repeated letters indicate power-supply voltages.

For example, V

is the power-supply voltage to the

collector, and V

is the power-supply voltage to the

base.

(2) By convention, all currents are taken to be positive

when they ﬂow into the leads of the transistor and

negative when they ﬂow out of the leads.

(3) Currents are speciﬁed by I or i with a subscript indicating

the terminal inv olv ed. I

is therefore a d.c. base current.

Transistors are destroyed if their maximum power capa-

bilities are exceeded, or if, when reverse-biasing the junc-

tions, the maximum reverse voltages are exceeded,

resulting in electrical breakdown. The maximum power

dissipation depends on temperature, and a transistor ﬁxed

to a heat sink can dissipate considerably more power than

one standing alone in free air. In pulse operation, the max-

imum steady-state power levels can be momentarily

exceeded without damage.

Field-Effect Transistors (FETs). The junction FET

or JFET is the simplest FET. It has three terminals – a

source, a gate, and a drain. An n-channel device is shown

in Figure 6.50. Current ﬂow is from source to drain with the

te re ve rse-bias ed with respect to the channel. Because of

this reverse bias, negligible current ﬂo ws into the gate. The

I–V charac teristics of a small-signal JFET are sho wn in

Figure 6.51. From the curves it can be seen that there is a

reg

ion where the drain current decreases with increasing

Figure 6.47 Practical transistor circuits using separate

power supplies for biasing voltages: (a) common emitter;

(b) common base; (c) common collector.

410 ELECTRONICS

rev erse bias from the gate to source, independent of the drain-

source voltage. This is the region where the transistor can be

operated as an ampliﬁer. About the region V

¼ 0, I

increases linearly with V

for ﬁx ed V

,withtheslope

equal to the reciprocal of the channel resistance R

channel

As V

becomes more negative, R

channel

increases. Transistor

operation in this region is that of a voltage-controlled r esi stor.

The FET can also be used as a switch, with the advantage

of no offset voltage from source to drain and almost perfect

electrical isolation of the gate signal from the output circuit.

Disadvantages are rather high on resistances (of the order

of hundreds of ohms) and low off resistances. Also, switch-

ing times are greater than for BJTs.

The simple structure of FETs results in low noise. As a

consequence, FETs are often used as the active elements in

low-level signal ampliﬁers. Field-effect transistors with

gates insulated by an oxide layer from the conducting

channel are called MOSFETs (metal oxide-semiconductor

Figure 6.48 Variation of the properties of the CE, CB, and CC transistor conﬁgurations with various input parameters:

(a) input resistance as a function of load resistance; (b) output resistance as a function of source resistance; (c) current

gain as a function of load resistance; (d) voltage gain as a function of load resistance.

ACTIVE COMPONENTS 411

FETs). The oxide gate insulation effectively blocks any

d.c. gate current ﬂow. The conducting channel in a MOS-

FET can be either p-doped (PMOS) or n-doped (NMOS).

Moreover PMOS and NMOS transistors can be of the

depletion mode or enhancement mode. For depletion-mode

transistors, the maximum drain current corresponds to

¼ 0. For both PMOS and NMOS enhancement-mode

transistors, there is no drain current at V

¼ 0. Only when

reaches the threshold value V

, will drain current ﬂow.

For NMOS enhancement V

is approximately þ2 V, for

PMOS enhancement V

is approximately 2 V. The con-

struction of PMOS and NMOS depletion-and enhance-

ment-mode transistors along with their schematic symbols

are shown in Figure 6.52. Typical characteristic output

curv

es are given in Figure 6.53.

epletion-mode MOSFETs are less common that

enhancement-mode devices because of their relatively low

transconductance (ratio of output current to input voltage).

Because of the higher mobility of electrons compared to

holes, NMOS transistors have properties that are superior

to PMOS transistors. The most common application of

PMOS transistors is in CMOS logic circuits (see Section

6.10). Low power consumption, ease of fabrication, and

gh packing densities have made MOSFETs extremely

common in large-scale (LSI) and very large-scale (VLSI)

integrated circuits.

Because of the gate insulation, static charge can accu-

mulate on the gate and voltage can build to levels sufﬁcient

to punch through the insulation. To avoid this, some MOS-

FET gates are protected with reverse-biased Zener diodes.

MOSFET devices are normally packaged in conducting

foam or with metal protecting rings that are removed just

prior to insertion into the circuit.

For switching high currents, the bipolar junction tran-

sistor was the device of choice until the development of the

power MOSFET and the insulated gate bipolar transistor

(IGBT). Because the BJT is current controlled and the

MOSFET is voltage controlled, the MOSFET has a num-

ber of signiﬁcant advantages at moderately high voltages

Figure 6.49 BJT showing: (a) Junction capacitances and (b) small-signal model with junction capacitances.

Table 6.16 2N3904 Transistor parameters

Condition of Transistor

Parameter Active Saturated Cut-Off

0.6 V 0.8 V < 0.0 V

510 V

(reverse bias)

0.6 V

(forward bias)

 V

(reverse bias)

510 V 0.2 V V

)

’ 0

V

’ 0

412 ELECTRONICS

and currents and especially at high switching speeds. The

current-carrying capacity of a small-signal MOSFET is

limited by the size of the conducting channel. One way

to increase current capacity is with a short and wide chan-

nel that has the form of a trench or groove. This is shown

in Figure 6.54 for an enhancement n-channel

power

Table 6.17 Properties of the 2N3904 N–P–N silicon transistor

Condition Parameter Value Conditions

Absolute Maximum Ratings V

CBO

60 V I

¼ 10 lA, I

¼ 0mA

25 °C in Free Air V

CEO

40 V I

¼ 1 mA, I

¼ 0 lA

(continuous) ¼ 200 mA V

EBO

6V I

¼ 10 lA, I

¼ 0mA

Maximum Power Dissipation ¼ 310 mW

‘‘On’’ Characteristics b

40 V

¼ 1V,I

¼ 100 lA

70 V

¼ 1V,I

¼ 1mA

0.65 to 0.85 V I

¼ 1 mA, I

¼ 10 mA

0.95 V I

¼ 5 mA, I

¼ 50 mA

0.2 I

¼ 1 mA, I

¼ 10 mA

0.3 I

¼ 5 mA, I

¼ 50 mA

Small Signal Characteristics r

1kX to 10 kX

b 100–400 V

¼ 10 V, I

¼ 1 mA,

25 kX to 1 MX

300 MHz V

¼ 20 V, I

¼ 10 mA

obo

4pF V

¼ 5V,I

¼ 0mA

ibo

8pF V

¼ 0.5 V, I

¼ 0mA

Saturation.

Frequency for b ¼ 1.

Common-base open-circuit output capacitance.

Common-base open-circuit input capacitance.

Figure 6.50 N-channel junction ﬁeld-effect transistor

(JFET): (a) Construction; (b) Symbol.

Figure 6.51 Current–voltage characteristics of a

small-signal, junction-ﬁeld-effect transistor (JFET).

ACTIVE COMPONENTS 413

Figure 6.52 MOSFET structures and schematic diagrams. (a) NMOS enhancement; (b) PMOS enhancement; (c) NMOS

depletion; (d) PMOS depletion.

414 ELECTRONICS

MOSFET. The materials are labeled p, n

, and n



indicat-

ing p-doped material, lightly n-doped material, and heavily

n-doped material. With the drain biased positive with

respect to the source and the gate at the source potential,

no current ﬂows between drain and source because the p–n

junctions are reverse biased. As the potential of the gate is

increased with respect to the source, an n-channel is

formed around the gate, resulting in a conduction path from

source to drain. The I–V static characteristics of a typical

n-channel enhancement power MOSFET, the VN66AFD, is

shown in Figure 6.55. The main characteristics to note are:

(1)

Drain current is essentially zero for V

less than 2 V.

This is the threshold voltage and varies from 0.5 to

2.5 V for power MOSFETs.

(2) Between V

¼ 2 V and V

¼ 4V, I

is a nonlinear

function of V

, increasing quadratically with V

.For

greater than 4 V, I

is a linear function of V

Figure 6.53 MOSFET output IV characteristics: (a) NMOS enhancement; (b) PMOS enhancement; (c) NMOS

depletion; (d) PMOS depletion.

ACTIVE COMPONENTS 415

(3) I

depends almost entirely on V

and is nearly inde-

pendent of V

Because the gate is insulated by an oxide layer from the

underlying p and n materials, there is no current ﬂow into

the gate under steady-state conditions. The input impe-

dance is essentially inﬁnite. However, because the gate

acts as one plate of a capacitor, with the oxide insulating

layer as the dielectric, current can ﬂow into the gate when

the voltage on the gate is changed. Typical gate capacitan-

ces are in the tens of picofarads. As a result, switching

times of nanoseconds are possible when the gate drive

voltage is derived from a low-impedance source.

The pow er MOSFET is an ideal voltage-controlled switch.

For the VN66AFD, the drain to source resistance, R

,varies

from 2 X at V

¼ 4Vand I

¼ 0.1 A to less than 1 X at

¼ 10 V and I

¼ 0.1 A. For V

¼ 2V, R

is of the

order of megohms. Power MOSFETs can be switched with

TTL or CMOS gates. Sample interface circuits using the

VN66AFD are shown in Figure 6.56(a) and (b). W ith 5 V

the gate of the MOSFET, the saturation drain current is

0.8 A. Higher drain currents can be achiev ed by increasing

the MOSFET gate voltage.

While power MOSFETs are mostly used in switching

applications, they can also be used as power ampliﬁers by

biasing them into the linear portion of the characteristic

curve. This is shown in Figure 6.56(c). With this arrange-

ment

the quiescent drain current is 0.675 A with V

8.6 V. An input voltage swing of 61 V results in a change

of current of 60.17 A about the quiescent value. While

Figure 6.54 Power MOSFET: (a) Construction; (b) Current

ﬂow.

Figure 6.55 VN66AFD power MOSFET output IV

characteristics and schematic diagram.

416 ELECTRONICS

Figure 6.56 Power MOSFET circuits: (a) CMOS to MOSFET; (b) TTL to MOSFET;

ACTIVE COMPONENTS 417

inefﬁcient, the circuit is simple and has less than 1% har-

monic distortion at 1 W.

Commercial applications for power MOSFETs are in

switch mode power supplies, motor controllers, lamp

drivers, and automotive ignition systems. While trench

and V power MOSFETs are common, there are other

MOSFET conﬁgurations based on laterally diffused

(LDMOS) geometries and pa rallel arra ys of MOSFETs

(HEXFETs). An important property of e nhancement

MOSFETs that allows them to be connected in parallel

is the drain-current negative-temperature coefﬁcient. This

means that as the temperature of the device increases, the

drain current will decrease. This is a consequence of

majority carrier conduction in the drain-source channel.

By contrast, the collector-current temperature coefﬁcient

in BJTs is positive; collector cur rent increases with tem-

perature, leading to the possibility of thermal runaway, in

which increasing temperature leads to increasing collec-

tor current that increases power dissipation and higher

temperatures, etc.

Power MOSFETS can operate at frequencies well in

excess of 100 kHz. While maximum voltages as high as

1000 V are available, most power MOSFETs are designed

for operation below 300 V. Current handling capabilities

extend to 100 A.

The IGBT i s a device t hat combines the high input

impedance of a power MOSFET with the high current

capabilities of a power BJT. The schematic symbol for

aIGBTisgiveninFigure 6.57(a) along with a simpliﬁed

uivalent circuit in Figure 6.57(b). The device is ‘‘on’’

henthebase(B)ofthep-n-p output transistor is neg-

ative with respect to the collector (C) by 0.6 to 0.8 V. The

total voltage drop from C to E is equal to the voltage drop

across the CB diode plus the drop acr os s t he input MOS-

FET. This latter voltage drop is a functi on of the gate-to -

source voltage, V

. The use of IGBTs is restricted to

switching applicat ions. In Table 6.18 the switching char-

cteristics of power M OSFETS, IGBTs, an d power BJTs

are compared.

The IGBT offers clear advantages over power MOS-

FETs at voltages above 300 V and at high currents and

speeds from 5 to 50 kHz. They are to b e preferred in

high-power applications with voltages greater than

1000 V provided the frequency requirements are less

than 20 kHz, the duty cycle is low, and variations in

load and line are small. A representative IGBT is the

IRGB860. It is available in TO-220AB, TO262, and

Pak packages. The maximum collector-to-emitter

voltage is 600 V and the maximum continuous collector

current is 28 A at 25 °C, falling to 19 A at 100 °C. The

maximum value of V

is 620 V. Exceeding this limit

subjects the device to permanent damage through

destruction of the insulating layer between gate and sub-

strate. When ‘‘on’’ (V

¼ 15 V and I

¼ 8A),V

approximately 2 V. Switching rise times are 20 to 30 ns

and fall times are 30 to 40 ns. Maximum power

Figure 6.57 IGBT: (a) schematic diagram; (b) internal

connections; (c) inductive load switching at high voltage.

418 ELECTRONICS

dissipation is 167 W a t 25 °C and 83 W at 100 °C. It is

worthnotingthatV

decreases with temperature so that

there is the possibility of thermal runaway in high-power

applications. This is not the case for power

MOSFETs. A circuit for switching an inductive load with

an IRGB860 is shown in Fig ure 6.57(c). T he diode sup-

presses

inductive voltage transients associated with

the switching of currents through the inductor. This pro-

tects the IGBT and results in cleaner switching wave-

forms.

Active Loads and Current Sources. Both BJT a nd

FET transistors can be used as resistors with static resis-

tances of kilohms and dy namic resista nces of te ns and

even hundreds of kilohms. Ac tive loads ar e commonly

used in integrated circuits w here resistors are difﬁcult

to fabricate. The high dynamic resistance (dv/di)ofBJTs

and FETs in their active region is also used for high out-

put-impedance current-source circ ui ts. Examples of BJT

current-source circuits are given in Figure 6.58.An

NMOS

depletion-mode transist or can also be converted

to a resistor by connecting the drain to the gate. The

nonlinear I–V character istics of this conﬁguration ca n

be found from t he output characteri stics of the transistor

with V

¼ V

6.3.3 Silicon-Controlled Rectiﬁers

The silicon -controlled rectiﬁer, SCR, is a switching

device with only two states – on and off.Intheon state,

the SCR has a low resistance, and some models are capa-

ble of passing over 100 A. In the off s tate, the resistance is

in the megohm range. The SCR has three terminals: an

anode,acathode,andagate. The transition from off to on

Table 6.18 Comparison of the properties of power MOSFET, IGBT and power BJT transistors

Input/Output Power MOSFET IGBT Power BJT

Input Power Very low Very low Moderate to high

Output Current High at low voltages,

low at high voltages

Very high, almost independent

of switching speed

Moderate, strong function

of switching speed

Switching Losses Very low Low to moderate Moderate to high

Figure 6.58 Current sources.

ACTIVE COMPONENTS 419

occur s when the voltage on the anode is positive wi th

respect to the cathode and a pulse of the corr ect polarity

and magnitude is applied to the gate. Once the SCR is on,

the gate loses all control over the functioning of the

device. The only way to turn it off is to reduce the

anode–cathode voltage to zero. If a sinusoidal voltage is

applied to the SCR anode, the device will be turned off

once each half cycle. By controlling the point in each

positive half cycle when the trigger pulse is applied, the

average current through the SCR can be varied over wide

limits (see Figure 6.59). This way of regulating the power

a load is very efﬁcient because very littl e power is

dissipated in the SCR. When the SCR is off,thereisno

current through it and the power dissipation is zero. When

the cur rent through the SCR is at a maximum, the voltage

across it is low, result ing in low power dissipation. Bilat-

eral triggering can be accomplished with a bilateral switch

or triac. A common application of this kind of power

control is the incandescent light dimmer. High-power

switching devices like the SCR and triac produce radio-

frequency in terference (rﬁ) during switching when there is

a voltage across them. Zero crossing switch ing avoids rﬁ

by timing the switching to tho se instants when there is no

voltage across the device. Silicon-controlled switches

(SCSs) a re similar to SCRs, but have the advantage of

being able to be turned off with a pulse.

6.3.4 Unijunction Transistors

The unijunction transistor (UJT) is a single bar of n-mate-

rial to the middle of which p-material is attached, forming

a p–n junction. This is shown schematically in Figure 6.60.

The

two ends of the bar are bases 1 and 2 (B1 and B2),

while the p-material is the emitter (E). When B2 is made

positive with respect to B1, there will be a potential gra-

dient along the bar and the potential at the point of attach-

ment of the emitter will be a ﬁxed fraction of the potential

across the bar. As long as the emitter is less positive than

the bar at its point of attachment, the emitter junction will

be reverse-biased and no current will ﬂow through it.

When the emitter potential is increased sufﬁciently to

forward-bias the junction, current will ﬂow in the E–B1

circuit and V

EB1

will fall. This is shown in the character-

istic curve (see Figure 6.61). A common application of

the

UJT is in relaxation oscillators where a capacitor is

charged through a resistor to the peak potential of the

UJT and then discharged. The UJT is also used in trigger

Figure 6.59 Current regulation with a silicon-controlled

rectiﬁer (SCR).

Figure 6.60 Unijunction transistor (UJT) and the

corresponding schematic symbol.

420 ELECTRONICS

circuits, pulse generators, and frequency dividers. The sta-

ble peak voltage, which is a ﬁxed fraction of the interbase

voltage, and high pulse-current capability make the UJT

very useful for SCR control circuits.

6.3.5 Thyratrons

For fast switching of high currents at high voltages, gas-

ﬁlled tubes called thyratrons are used. They are analogs

of SCRs and consist of a heated cathode, an anode, and a

grid sealed into a glass, gas-ﬁlled envelope. An arc can

be struck between the cathode and anod e, with the ini-

tiation of the arc controlled by the potential on the grid.

The grid is usually a cylindrical structure surrounding the

anode and cathode from which a bafﬂe or series of bafﬂes

with small holes extends between anode and cathode.

Since the anode and cathode are almos t completely

shielded from each other, only a small grid potential is

needed to overcome the ﬁeld at the cathode resulting

from the large anode potential. Once the arc has been

initiated, the grid loses control over the arc. Grid control

is re-established only when the anode potential falls

below the level nece ssary to sustain the a rc. Deute-

rium-ﬁlled thy ratrons can switch hundreds of a mperes

at tens of kilovolts in microseconds or less and are com-

monly used in the high-voltage discharge sources of

lasers. SCRs are often used to supply the trigger pulse

to the grid of the thyratron.

6.4 AMPLIFIERS AND PULSE

ELECTRONICS

6.4.1 Deﬁnition of Terms

In laboratory applications, ampliﬁers are used to transform

low-le v el signals to levels sufﬁ cient for observation and

recording, or for operation of electronic or electromechani-

cal devices. When choosing an ampliﬁer for a given task,

there are a number of considerations that require the deﬁni-

tion and explanation of several special terms. The goal is to

provide information for the experimentalist who must make

decisions regarding the use and speciﬁcations of ampliﬁers.

Ampliﬁers can be classiﬁed in a number of ways, among

them the following:

(1) By input and output variables

(2) By frequency domain

(3) By power levels.

Each of these classiﬁcations will be treated in turn, and

any given ampliﬁer will have its place somewhere within

each of the classiﬁcations. The two most common electri-

cal input and output variables are current and voltage.

There are therefore four different possible types of ampli-

ﬁer, corresponding to the two input-variable possibilities

and the two output-variable possibilities. These are listed

in Table 6.19. The gain of

an ampliﬁer is the ratio of the

output variable to the input variable. This is the equivalent

of the transfer function for the passive circuits already

considered. For voltage and current ampliﬁers, the gain

is unitless. For the transconductance and transresistance

ampliﬁers, however, their gains have units of siemens

(ohm

1

or sometimes mho) and ohm, respectively.

There are also ampliﬁers for which the input variable is

the time integral of the current or the charge. Such charge-

sensitive ampliﬁers have a voltage as an output, and the

Figure 6.61 Current–voltage characteristic curve for a

unijunction transistor showing the region of negative

resistance.

Table 6.19 Types of ampliﬁer

Input Variable Output Variable Ampliﬁer Type

Voltage Voltage Voltage

Voltage Current Transconductance

Current Voltage Transresistance

Current Current Current

AMPLIFIERS AND PULSE ELECTRONICS 421

gain is expressed in volts per coulomb or inverse farads.

Ampliﬁers with the time derivative of current as an input

variable are also possible.

The ampliﬁers in Table 6.19 have very different input

and

output properties. If the input is a current, the ampliﬁer

should have a low input impedance so as to affect the

source as little as possible. On the other hand, if the input

is a voltage the input impedance should be as large as

possible to avoid drawing current from the source and

changing the source output voltage. The opposite consid-

erations apply to the outputs of the ampliﬁers. If the output

is a current, it is desirable that the output be close to that of

an ideal current source – that is, a very high output impe-

dance. If the output is a voltage, the output impedance

should be low to approximate an ideal voltage source as

closely as possible. These considerations of input and

output impedance (see Table 6.20) are of fundamental

import

ance when matching an ampliﬁer to a detector or

transducer at the input and a load at the output. If the input

device is a current source, one should generally choose a

current, transresistance, or charge-sensitive ampliﬁer; if the

input device is a voltage source, a voltage or transconduc-

tance ampliﬁer is required. This assumes that ampliﬁcation

with minimum loading of the input circuit is desired. When

efﬁcient power transfer is desired, the impedances of the

source and load should match the input and output impe-

dances of the ampliﬁer as closely as possible.

Ampliﬁers can be divided into groups according to the

frequency domain in which they are designed to operate

(see Table 6.21). Consider the Bode plots of gain and phase

shift

shown in Figure 6.62 for a capacitance-coupled

verting (output 180° out of phase with input) ampliﬁer.

The curves can be understood qualitatively in the follow-

ing ways – at low frequencies the coupling capacitors

(capacitors in series with input and output to block d.c.

levels) reduce the low-frequency gain just like a high-pass

ﬁlter. At high frequencies the reduced gain of the active

devices (transistors) has the effect of shunt capacitances

across both the input and output circuits of the ampliﬁer,

resulting in properties similar to that of a low-pass ﬁlter.

The frequency difference between the corner frequencies

(3 dB points of the gain curve) is the bandwidth of the

ampliﬁer. Because the low corner frequency is usually

orders of magnitude smaller than the high corner frequency

(except in the case of tuned ampliﬁers that operate over a

very small frequency range), the bandwidth can be consid-

ered equal to the upper corner frequency. An often-used

ﬁgure of merit for ampliﬁers is the gain-bandwidth product

(GBWP), which is the midband gain times the bandwidth.

By this criterion, a low-gain, wide-bandwidth ampliﬁer is

equivalent to a high-gain, narrow-bandwidth ampliﬁer.

If it is possible for the output of an ampliﬁer to be

coupled back to the input (ca pacitan ce coupling is

always present to some degree because of stray capaci-

tances)insuchawayastobeinphasewiththesignalat

the i nput, a positive feedback or regenerative situat ion

will occur, giving rise to oscill ations and unstable behav-

ior. This is the origin of the familiar squawking and

whistling that occurs in public address systems when

the output from the loudspeakers ﬁnds its way back to

the microphone. The stability of an ampliﬁer against

such oscillations is expressed in terms of gain and phase

margins. If the value of the gain of an ampliﬁer (in dB) is

negative at frequencies for which the phase of the output

is equal to that of the inpu t, oscillations cannot occur.

Correspondingly, if the output is out of phase with the

Table 6.20 Ampliﬁer impedances

Ampliﬁer Type Input Impedance Output Impendance

Voltage High Low

Transconductance High High

Transresistance Low Low

Current Low High

Charge-sensitive Low Low

Table 6.21 Ampliﬁer frequency ranges

Ampliﬁer Type Frequency Range

d.c. 0 to 10 Hz

Audio 10 Hz to 10 kHz

r.f. 100 kHz to 1MHz

Video 30 to 1000 MHz

VHF 30 to 300 MHz

UHF 300 to 1000 MHz

Microwave 1000 MHz to 50 GHz

422 ELECTRONICS

input at all frequencies for which the gain is greater than

unity, oscillations cannot occur. The amount of negative

gain at zero phase is the gain margin; the phase differ-

ence a t 0 dB gain is the phase margin (see Figure 6.63).

The

larger these margins, the more stable the ampliﬁer.

Wide-band video ampliﬁers are particularly susceptible

to unstable behavior because even small stray capacitan-

ces are sufﬁcient to provide low-impedance paths from

the output to the input for high frequencies. Because of

the large power consumption in the pos itive feedba ck

(regenerative) mode, prolonged unstable operation of

an ampliﬁer can destroy it. This is especially true in

the case of fast-pulse ampliﬁers, which must have a very

large bandwidth in order to a ccurately amplify pulses

with short rise times. Compensation by the addition of

poles and zeros t o the transfer function can remedy this at

the expense of reduced b andwidth.

In classifying ampliﬁers by power rating, the distinctions

are rather arbitrary. Generally, preampliﬁers are designed to

operate with input voltage levels of millivolts and less, input

currents of microamperes and less, and input charge of

picocoulombs and less. Gain is not so important in pream-

pliﬁers as is ampliﬁer noise, which limits ultimate sensitiv-

ity. In some applications, a unit-gain preampliﬁer is used as

an impedance-matching device. Power ampliﬁers are

designed to furnish anywhere from a few to several hundred

watts to a matched load. Audio ampliﬁers are examples.

Intermediate between preampliﬁers and power ampliﬁers

are ampliﬁers that operate with input signal levels from

preampliﬁer outputs and produce outputs from a few to

several hundred milliwatts. Gains of such ampliﬁers are

high, and noise considerations are much less important than

overload recovery. Frequency- and gain-compensating cir-

cuits are often incorporated in such ampliﬁers.

Figure 6.62 Bode plots for a capacitance-coupled inverting ampliﬁer.

AMPLIFIERS AND PULSE ELECTRONICS 423

It has been assumed thus far that the output of an

ampliﬁer is a linear function of the input at any fre-

quency. Because the active elements (transistors) in

solid-state ampliﬁers have nonlinear characteristics, it

follows that ampliﬁers can only operate in a linear way

within a limited range of input conditions. For all ampli-

ﬁers, there is an input signal level beyond which the out-

put signal is severely distorted. Clipping of the output

waveform is an obvious form of distortion. Less obvious

distortions can be quantiﬁed by a Fourier analysis of the

output waveform for a sinusoidal input. The distortion in

the output can be described in terms of the coefﬁcients of

the harmonics. This harmonic distortion is important in

critical audio-ampliﬁer applications, but not generally in

the laboratory.

The properties of solid-state ampliﬁers may also be tem-

perature-dependent, and such factors as gain and distor-

tion, though acceptable at room temperature, may become

unacceptable at high or low temperatures.

6.4.2 General Transistor-Ampliﬁer

Operating Principles

The active elements in solid-st ate ampliﬁers can be n-p-n

or p- n- p bipolar junction transistors or ﬁeld-effect tran-

sistors. Field-effect transistors can be n-channel or

p-channel and can be operated in the depletion or the

enhancement mode. They can have gate structures in

direct contact with the conducting channel (JFETs) or

gates that are insulated from the c on duct ing channel by

an oxide layer (MOSFETs).

To use an inherently nonlinear transistor to make a

linear ampliﬁer requires ingenuity. Standard methods

involve operating the transistors over a limited range of

voltage and current where their nonlinear characteristics

can be approxim ated by linear functions, using comp en-

sating circuits to c ancel the nonlinearities with devices

that have opposite characteristics, o r applying negative

feedb ack.

Figure 6.63 Gain and phase margins.

424 ELECTRONICS

Transistors must be properly biased if they are to work

correctly. This means supplying, from external sources

such as batteries or d.c. power supply circuits, the correct

potential differences across the terminals and the correct

currents into them. Even in the absence of an external

signal, transistors dissipate power. The values of the d.c.

bias (or quiescent) voltages and currents deﬁne the operat-

ing point of the transistor. Signals from an outside source

or previous stage are then superimposed on the quiescent

values. As long as the signal does not represent too large a

deviation from these values, the transistor will operate

linearly. If the external signal is sufﬁciently large, however,

it can cut off the transistor (that is, reduce all the currents

through it to zero) or saturate it (that is, cause the transistor

to act as a short circuit).

Since the bias voltages and currents are d.c. and the

signal voltages and currents are a.c., it is possible to sep-

arate them. Capacitors or transformers can be used to cou-

ple a.c. signals without disturbing the quiescent d.c. values.

When capacitance coupling is used, the capacitors are

called blocking capacitors because they block d.c. voltages

and currents. Reasonably sized blocking capacitors usually

limit the low-frequency response of ampliﬁers to > 1 Hz

(capacitor lead inductance and stray shunt capacitances to

ground can also limit the high-frequency response). In

many applications, the poor transient response of the

high-pass circuits formed by the blocking capacitors can-

not be tolerated. Direct-coupled ampliﬁers – where the

bias levels of each transistor stage are designed to be com-

patible with the preceding and succeeding stages – provide

high gain to 0 Hz. Because of the need to match active

components and resistor ratios very precisely, such ampli-

ﬁers are often integrated-circuit (IC) ampliﬁers, where all

the elements of the circuit are manufactured simultane-

ously on a single chip. Direct-coupled designs are, in fact,

particularly suited to the IC manufacturing process, which

favors the production of transistors and diodes, but requires

quite special techniques for the production of resistors and

capacitors. Chopping is another method of achieving good

low-frequency response in ampliﬁers. With this method,

the input signal is chopped at a frequency much higher

than the highest characteristic frequency of the input sig-

nal. The resulting a.c. signal can be ampliﬁed by conven-

tional a.c.-coupled ampliﬁer stages. Rectiﬁcation of the

output of the ﬁnal stage restores the input waveform. The

advantages of chopper over direct-coupled ampliﬁers are

lower uncompensated input currents and voltages, and

comparative freedom from drifts with temperature. These

advantages have been largely offset by IC direct-coupled

ampliﬁer designs with FET input stages.

Ampliﬁer properties and speciﬁcations are best under-

stood by considering as an example the general-purpose

741 IC operational ampliﬁer. The name operational ampli-

ﬁer (op amp) was originally applied to ampliﬁers used in

analog-computer circuits which performed a wide variety

of mathematical operations. The term is now more gener-

ally applied to any high-gain, differential-input ampliﬁer.

Differential-input ampliﬁers have two input terminals

that are electrically isolated from ground and each

other. They are called the non-inverting (+) and inverting

() terminals. The output signal is proportional to the

difference between the signals at the two input terminals.

Single-ended inputs are those with one input terminal and a

ground terminal. Most operational ampliﬁer outputs are

single-ended – that is, the output is developed between a

single output terminal and ground. The ideal operational

ampliﬁer has the following characteristics:

 Inﬁnite input impedance

 Zero output impedance

 Inﬁnite voltage gain, 180° out of phase with the invert-

ing input terminal

 Inﬁnite bandwidth

 Zero output voltage for identical input voltages at the

two differential input terminals

 Properties independent of temperature, voltage levels,

and frequency.

Real operational ampliﬁers depart from the ideal.

Table

6.22 compares the properties of the common 741 IC opera-

tional

ampliﬁer and the premium OP07. The operational

ampliﬁer symbol is shown in Figure 6.64. The supply vol-

tages V

and V



are applied to the indicated terminals, not

to be confused with the signal input terminals. The output

is at the apex of the triangle and the terminals marked null

are for an external potentiometer to cancel the offset volt-

age in critical applications.

Common operational-ampliﬁer terms include:

Common-mode rejection ratio (CMRR). This is the ratio

of the differential gain A

to the common-mode gain

AMPLIFIERS AND PULSE ELECTRONICS 425

(often expressed in dB). The output of an opera-

tional ampliﬁer is A

times the differential voltage

plus A

times the common mode voltage. For arbi-

trary voltages v

and v

at the two ampliﬁer inputs, the

differential voltage is (v

– v

)/2 and the common

mode voltage is (v

þ v

)/2. For the 741, the 90 dB

value of the CMRR means that a 1 V signal at each

input terminal will result in a 32 lV output signal.

This is sho wn in the following calculation:

90 dB ¼ 20 log

;

¼ 10

4:5

¼ 3:2310

ð6:32Þ

Since the differential voltage is 0 V, the output voltage

will be the common-mode voltage multiplied by the

common-mode gain A

. For a common-mode voltage

of 1.0 V, the output voltage is then 1.0/(3.2 3 10

) ¼

32 3 10

6

Open-loop d.c. gain. This is the gain in the absence of a

connection from output to input – that is, in the

absence of any feedback. The gain of the ampliﬁer

in the presence of a feedback network is called the

closed-loop gain. With open-loop gains of the order

of 200,000 or more, it can be seen that the region of

linear operation applies to only very small input sig-

nals. At a gain of 200,000, an input signal of þ75 lV

is sufﬁcient to drive the output to þ15 V, the max-

imum possible level.

Frequency response. This is given in terms of either

the GBWP or the frequency at which the gain equals

0 dB (unit gain). The two methods give nearly the

same numbers for a single-pole transfer function.

For the 741, at 1 MHz the gain has fallen by over

ﬁve orders of magnitude from the d.c. value. It

should be kept in mind that these frequency-

response data are based on so-called small-signal

conditions, where the input is small enough so that

the output stages are operating well within their lin-

ear region.

Slew rate. This gives the time response of the ampliﬁer

to large input signals. For this speciﬁcation the

ampliﬁer is connected in a unit-gain (closed-loop)

conﬁguration with negative feedback, and an input

voltage step is applied. The slew rate is then taken as

the ratio of the amplitude of the input voltage to the

rise time for the output voltage waveform. For the

741, the slew rate is 0.5 V/ ls.

Input resistance. This is the resistance R

between the

input terminals with one terminal grounded.

Table 6.22 Comparison of Operational Ampliﬁer

Parameters

Electrical Properties 741 OP07

CMRR (dB) 90 120

Open-loop d.c. gain 200 000 500 000

GBWP (MHz) 1.5 0.6

Slew rate (V/ls) 0.5 0.3

Input resistance (MX)280

Output resistance (X)7560

Input offset

voltage (mV)

5 0.010

Input offset

current (nA)

20 0.3

Input bias

current (nA)

80 0.7

Input voltage

range (V)

613 613

Maximum peak-to-peak

output voltage swing (V)

28 25

Power-supply

rejection ratio (lV/V)

150 5

Power consumption (mW) 50 75

Typical characteristics at 25 °C with power-supply voltages

of 615 V:

Figure 6.64 Schematic symbol

for the operational ampliﬁer,

showing input, output, power

supply, and null terminals.

426 ELECTRONICS

Output resistance. This is the resistance R

(seen by the

load) between the output terminal and ground. It

determines whether the ampliﬁer approximates a

voltage or a current source.

Input offset voltage. This is the d.c. voltage V

that

must be applied across the input terminals to bring

the d.c. output to zero. For the 741 it is 0.8 mV and

can be compensated for. The 741 is not a good

choice for the ampliﬁcation of millivolt d.c. levels.

Input offset current (I

). This is the difference between

the currents into the input terminals necessary to

bring the output voltage to zero.

Input bias current (I

) This is the average of the currents

into the input terminals with the output voltage at zero.

It should be noted that these bias currents will ﬂo w

through circuit elements (generally resistors) attached

to the input terminals. If the resistances are not identical,

voltage differences will be developed across the input

terminals and ampliﬁed along with the input signal.

Input voltage range (V

). The maximum allowed input

voltage for which proper operation can be maintained.

Maximum peak-to-peak output voltage swing. The

maximum peak-to-peak output voltage that can be

obtained without clipping about a quiescent output

voltage of zero.

Power-supply rejection ratio. The change in input offset

voltage for a given change in power-supply voltage.

Operational ampliﬁers are particularly good in this

regard and do not require highly regulated power

supplies.

Temperature effects. The various offset and bias cur-

rents and voltages are temperature dependent. The

variations of these parameters with temperature are

speciﬁed by temperature coefﬁcients.

The 741 is internally compensated with a capacitor at

the high-gain second stage to produce a pole in the transfer

function at 6 Hz. This ensures stable operation under even

100% feedback conditions (of course, this gain in stability

reduces the high-frequency response of the ampliﬁer). Two

extra terminals are available for connection to an external

10 kX potentiometer, the wiper arm of which is connected

to the negative power supply. By adjusting the potentiom-

eter, the input offset voltage can be eliminated. Additional

features include short-circuit output protection and input

overload protection. Single ampliﬁers come in at least four

different packages: an 8 lead metal can, a 14 lead dual in-

line package (DIP), an 8 lead mini-DIP, and a 10 lead Flat

Pak. There is a commercial model – the 741C – that oper-

ates over a restricted temperature range, and a military

model – the 741A – that operates over an extended temper-

ature range. The 741 sells for about the price of a few

1/4 W composition resistors.

The OP07 is a premium grade operational ampliﬁer with

a very low input offset voltage, obtained by trimming thin-

ﬁlm resistors in the input circuit. The low offset voltages

usually eliminate the need for external null circuits. The

OP07 also has low input bias current and high open-loop

gain. It is a direct pin-for-pin replacement for the 741.

Some examples of more specialized operational ampliﬁers

are given in Table 6.23.

Because

of their high gain, wide bandwidth, and small

offsets, operational ampliﬁers with suitable feedback net-

works can perform a wide range of electronic functions.

There are many excellent texts devoted to operational-

ampliﬁer applications.

Here we give only a list of the

basic conﬁgurations. In all of these it is important to keep

in mind the following design rules:

(1) The offset-voltage temperature coefﬁcient must pro-

duce voltages much less than the input signal through-

out the anticipated temperature range. The offset

voltage can be eliminated with an external nulling

circuit at any given temperature, but variations with

temperature cannot be easily accommodated.

(2) The voltages created by the bias currents ﬂowing through

resistances attached to the input terminals must be less

than the signal voltage. For high output-impedance

Table 6.23 Some special operational ampliﬁers

Low offset voltage OP07

Low bias current (Harris) HA-5180

High voltage (Harris) HA-2640/45

Low power consumption (National) LF441

Single-power-supply

operation

(National) LM10

Wide bandwidth (National) LM318

(Burr-Brown) OPA606

Video preampliﬁer 733

AMPLIFIERS AND PULSE ELECTRONICS 427

sources this may create a problem, but it can be solved by

introducing an intermediate buf fer stage with a high

input impedance (so as not to load the source) and a

low output impedance (to minimize the ef fects of input

bias current). The temperature coefﬁ cient of the offset

current must produce of fset voltages much less than the

signal voltage over the anticipated temperature range. To

minimize bias-current effects, the resistances to ground

from both input terminals should be identical.

(3) Frequency response and compensation must prevent

the ampliﬁer from breaking into oscillation. The 741

is internally compensated. High-frequency ampliﬁers

lack internal compensation, but have extra terminals

for external compensation circuits.

(4) The maximum rate of change of a sinusoidal output

voltage V

sin xt is V

x. If this exceeds the slew rate

of the ampliﬁer, distortion will result. Slew rate is

directly related to frequency compensation, and high

slew rates are obtained with externally compensated

ampliﬁers using the minimum compensation capaci-

tance consistent with the particular conﬁguration. Data

sheets should be consulted.

6.4.3 Operational-Ampliﬁer

Circuit Analysis

If ideal behavior can be assumed (as is reasonable for circuits

where the open-loop gain is much larger than the closed-loop

gain), only the following two rules need be used to obtain the

transfer function of an operati onal-ampliﬁer circuit, as

shown schematically in Figure 6.65:

(1)

The voltage across the input terminals is zero.

(2) The currents int o the input terminals are zero (the invert-

ing terminal is sometimes called the summing point).

Applying these to the generalized circuit of Figure 6.65,

see that the voltage at the þinput is v

/(Z

þZ

), since

there is no current ﬂowing into the þ input and Z

, Z

form a

voltage di vider. From Rule 1, the voltage at the  input must

also equal v

/(Z

þ Z

). The current through Z

is then the

potential diff erence across it div ided by Z

,or:

 v

ðZ

þ Z



ð6:33Þ

This current must be equal in magnitude and opposite in

sign to the current from the output through the feedback

element Z

. This current, i

, is given by the potential differ-

ence across Z

divided by Z

¼ v

out

 v

ðZ

þ Z



¼ v

 v

ðZ

þ Z



ð6:34Þ

Solving for v

out

, we obtain:

 v

out

¼v

þ v

þ Z

Þð1 þ

Þð6:35Þ

Some useful conﬁgurations are illustrated in Figure 6.66.

e summer circuit [Figure 6.66(e)] is an elaboration of the

verting ampliﬁer , with the current into the summing point

coming from two external sources (v

and v

)canceledbythe

current from the feedback loop, v

out

.IfR

¼ R

¼ R,then

out

¼(R

/R)(v

þv

). If R

¼ R

,thenv

out

is equal to the

negati ve of the weighted sum of voltages v

and v

,thatis:

Figure 6.65 The general operational-ampliﬁer circuit.

Power supply and null terminals not shown.

428 ELECTRONICS

Figure 6.66 Operational-ampliﬁer conﬁgurations: (a) follower; (b) follower with gain; (c) inverting ampliﬁer; (d) subtractor;

(e) summer; (f) low-pass ﬁlter (integrator); (g) high-pass ﬁlter (differentiator); (h) logarithmic ampliﬁer; (i) precision rectiﬁer;

(j) clamp. The parameters are deﬁned in Figure 6.59.

AMPLIFIERS AND PULSE ELECTRONICS 429

Figure 6.66 (cont.)

430 ELECTRONICS

out

¼ ½ð

Þv

þð

Þv

ð6:36Þ

Any number of external signal sources can be summed

in this way.

A sinusoidal input to the low-pass ﬁlter [Figure 6.66(f)]

ves v

out

¼ðjxRCÞv

. For a nonsinusoidal input, the cur-

rent into the summing point from v

is v

/R, because the

in v erting input is at ground (rule 1). Often one speaks of the

inverting input being at virtual ground. Although there is

no direct connection from the inverting input to ground,

the condition in which both inputs are at the same poten-

tial results in the inverting input assuming a potential of

zero when the noninverting input is at g round potential.

The current through the fe edback capa citor of this circuit

is i

, and the voltage across the capacitor, v

out

is equal to

ð1=CÞ

dt.Sincei

and v

/R are equal in magnitude and

opposite in sign:

out

¼ð1=CÞ

dt ¼ð1=RCÞ

dt: ð6:37Þ

and the circuit acts as an integrator of the input voltage.

Integration times of several minutes or even hours are

possible with high quality, low-leakage capacitors and

operational ampliﬁers with small offset voltages and bias

currents.

For the high-pass ﬁlter [Figure 6.66(g)], v

out

RC(dv

/dt) and the circuit acts as a differentiator.

The integrator and differentiator circuits are simple

forms of active ﬁlters. More complex networks involving

only capacitors and resistors can be used to obtain poles in

the left half of the complex s-plane, which in the past were

only obtained with inductors in passive ﬁlter networks.

The operational ampliﬁer allows the use of reasonable

resistor and capacitor values even at frequencies as low

as a few hertz. An additional advantage is the high isola-

tion of input from output due to the low output impedance

of most operational-ampliﬁer circuits. The limitations of

active ﬁlters are directly related to the properties of the

operational ampliﬁer. Inputs and outputs are usually sin-

gle-ended and cannot be ﬂoated as passive ﬁlters can. The

input and output voltage ranges are limited, as is the output

current. Offset currents and voltages, bias currents, and

temperature drifts can all affect active ﬁlter performance.

A good introduction to active ﬁlters is the Active Filter

Cookbook by D. Lancaster.

The circuits in Figure 6.66(b) to (g) are examples of the

use

of operational ampliﬁers in analog computation. With

these circuits, the mathematical operations of addition,

subtraction, multiplication by a constant, integration, and

differentiation can be performed. Multiplication or divi-

sion of two voltages is accomplished by a logarithmic

ampliﬁer, an adder (for multiplication) or subtractor (for

division), and an exponential ampliﬁer.

Both the logarithmic and exponential ampliﬁers rely on

the exponential I–V characteristics of a p–n junction. When

this junction is the emitter–base junction of a transistor, the

collector current I

with zero collector–base voltage is:

¼ I

½expðqV

=gkTÞ1ð6:38Þ

where I

is a constant for all transistors of a given type, V

is the emitter–base voltage, q is the electron charge and g is

a constant, 1 for Ge and 2 for Si. Typically, I

is 10 to 15

nA for silicon planar transistors.

For I

> 10

8

A, the equation reduces to I

¼I

exp(qV

gkT). For the conﬁguration shown in Figure 6.66(h), i

¼ v

R ¼ I

exp(qv

out

/gkT)andv

out

¼ðgkT=qÞðln v

þ ln RI

Þ.

Since k, T, q, g, R, and I

are constants, v

out

will be propor-

tional to v

. Practical logarithmic ampliﬁers can operate

over three decades of input voltages. They do, however,

need temperature-compensating circuits that generally

require the use of matched pairs of transistors. In addition

to their arithmetic use, logarithmic ampliﬁers are fre-

quently used for transforming signal amplitudes that cover

orders of magnitude to a linear scale. Exponential (anti-

logarithmic) ampliﬁer circuits are logarithmic circuits with

the input and feedback circuit elements interchanged.

Logarithmic and exponential ampliﬁers are examples of

nonlinear circuits – the output is not linearly related to the

input. Operational ampliﬁers are used extensiv ely in non-

linear circuits. Because the cutin voltage of simple diodes

is a few tenths of a volt (0.2 V for Ge and 0.6 V for Si), they

cannot be used to rectify milli volt-level a.c. voltages. A

diode in the feedback loop of an operational ampliﬁer [see

Figure 6.66(i)] results in a rectiﬁer with a cutin volt age equal

the diode cutin voltage divided by the open-loop gain of

the ampliﬁer. With a slight modiﬁcation, the rectiﬁer circuit

canbeconvertedtoaclamp [see Figure 6.66(j)] in which the

AMPLIFIERS AND PULSE ELECTRONICS 431

output follows the input for voltages greater than a reference

voltage V

, but equals V

for input voltages less than V

Comparator circuits are used to compare an input signal

with a reference voltage level. The output is driven to V

or V



depending on whether the input is less than or

greater than the reference level [see Figure 6.67(a)]. Using

ampliﬁer in such a saturated mode is very poor practice

and practical comparators with internally clamped outputs

less than V



and V





are available. The LM311 is a

common example. The transition between the two output

states can be accelerated by the use of positive feedback

[Figure 6.67(b)]. Such a circuit is called a Sc

hmitt trigger

and ﬁnds wide application in signal conditioning when it is

necessary to convert a slowly changing input voltage into

an output waveform with a very steep edge. The price paid

for the fast transition is hysteresis – where the threshold

voltage for a positive transition of the output is different

from the threshold voltage for a negative transition. Hys-

teresis inhibits the output from oscillating between the two

output states when the input is very close to the threshold

level.

6.4.4 Instrumentation and

Isolation Ampliﬁers

Instrumentation ampliﬁers are used for amplifying low-le v el

signals in the presence of large common-mode voltages, as,

for example, in thermocouple and bridge circuits. The instru-

mentation ampliﬁer is dif ferent from the operational ampli-

ﬁer; the feedback network of the instrumentation ampliﬁer is

integral to it and a single external resistor sets the gain. The

output of the instrumentation ampliﬁer is usually single-

ended with respect to ground and is equal to the gain multi-

plied by the dif ferential input vol tage. Compared to an

operational ampliﬁer in the differential conﬁguration with

equiv alent gain, the instrumentation ampliﬁer has a higher

common-mode rejection ratio and higher input impedance.

Instrumentation ampliﬁers are often made up of three opera-

tional ampliﬁers, as shown in Figure 6.68. Ampliﬁers A1 and

together provide a differential gain of 1 þ 2R

and a

common-mode gain of unity. Ampliﬁe r A3 is a unit-gain dif-

ferential ampliﬁer. Ampliﬁers A1 and A2 operate as follo wers

with gain, and resistors R

do not af fect the input impedances.

Because ampliﬁer A3 is driven by the low output impedances

of Al and A2, the resistors R

can hav e rel ativ ely small values

in order to optimize CMRR and frequency response while

minimizing the ef fects of input of fset currents.

The three-ampliﬁer conﬁguration is limited to common-

mode voltages of 68 V in most applications. Typical high-

performance instrumentation ampliﬁers are the 1NA110

(Burr-Brown), LH0038 (National Semiconductor), and

AD624 (Analog Devices). Typical speciﬁcations for

high-performance ampliﬁers are given in Table 6.24.

Instrumentation

ampliﬁers cannot be used when the

common-mode voltage exceeds the power-supply voltage.

Figure 6.67 (a) Simple comparator (V

sat

and +V

sat

are the

minimum and maximum voltages the ampliﬁer can deliver;

is a constant reference voltage); (b) Schmitt trigger

(comparator with positive feedback).

432 ELECTRONICS

In these cases, an isolation ampliﬁer is required. Isolation

ampliﬁers are also useful when the input and output signals

of an ampliﬁer are referenced to different common voltage

levels. It is often necessary, for example, to impose a low-

voltage waveform on a d.c. high voltage. With an isolation

ampliﬁer, the modulation voltage can be derived from a

source referenced to ground and the ampliﬁer output can

be referenced to the d.c. high voltage. The internal con-

struction of the ampliﬁer isolates the high-voltage output

from the low-voltage input.

The basic isolation-ampliﬁer conﬁguration is shown in

Figure 6.69. For the above example, V

is the modulation

voltage referred to ground (V

¼ 0), and V

ISO

is the high

voltage modulated by V

. In cases where V

exceeds

610 V, the input common terminal is not grounded and

the common-mode voltage is referenced to the output com-

mon terminal. This effectively transfers V

across the

isolation barrier and allows for V

voltages up to the

maximum isolation rating of the ampliﬁer.

The isolation-mode rejection ratio (IMRR)andCMRR

are critical isolation-ampliﬁer parameters because of the

large common-mode and isolation voltages present. To cal-

culate the effect of common-mode and isolation voltages on

ampliﬁer performance, it is necessary to add the product of

IMRR and V

ISO

, and that of CMRR and V

to V

. Typical

values of IMRR and CMRR are 140 and 90 dB, respec-

tively. For an IMRR of 140 dB, a 1 kV isolation voltage

produces the equivalent of 0.1 mV at the input terminals

of the ampliﬁer. Other important parameters speciﬁc to iso-

lation ampliﬁers are the maximum isolation voltage, isola-

tion resistance, and isolation capacitance.

Figure 6.68 Three-ampliﬁer instrumentation ampliﬁer.

Table 6.24 Typical high-performance instrumentation

ampliﬁer speciﬁcations

1NA110 LH0038 AD624

Gain range 1–500 1–2000 1–1000

Gain nonlinearity (%) 0.001–0.01 0.001 0.001

Input impedance (X)53 10

5 3 10

CMRR (dB) 90110 120 130

Input offset-voltage

drift (lV/°C)

2 0.25 0.25

Input bias

current (nA)

0.050 50 50

Bandwidth (MHz) 2.5 2 25

Noise, referred to input

(nV/

ﬃﬃﬃﬃﬃﬃ

)

10 6 4

Figure 6.69 Isolation ampliﬁer.

AMPLIFIERS AND PULSE ELECTRONICS 433

Isolation between input and output is achieved with opti-

cal couplers or transformers. The latter are more expensive,

but have higher isolation voltage ratings and IMRR. An

additional advantage of the transformer-coupled ampliﬁers

is their built-in isolated power supply. The input and output

stages of the optically coupled ampliﬁers must have sepa-

rate power supplies. This means that the output-stage power

supplies must be ﬂoated at the isolation voltage. Burr-

Brown manufactures a full line of isolation ampliﬁers for

medical and industrial applications. The 3450 and 3656

series are transformer-coupled, while the 3650 and

150100 series are optically coupled. Prices range from tens

to hundreds of dollars, depending on speciﬁcations. Analog

Devices produces a premium transformer-coupled isolation

ampliﬁer, the AD295, as well as the less expensive AD202.

6.4.5 Stability and Oscillators

For circuits composed only of passi ve elements, the poles of

the transfer function will always lie on the left-hand side of

the complex s ¼ r þ jx plane, that is, will always be less

than zero. For circuits with acti v e elements, this is not nec-

essarily the case. If, for example, a fraction of the output

signal of an ampliﬁer is returned to the input in phase with

the original input signal, an unstable situation will result and

the output of the ampliﬁer will increase with time. Analysis

of such a circuit will show at least one pole to lie in the

positiv e half of the complex s-plane. Unwanted oscillations

in ampliﬁers are due to the regenerative coupling of a frac-

tion of the output signal back to the input (see Figure 6.70).

Stray

capacitances between input and output may be sufﬁ -

cient at high frequencies to couple the output signal back to

the input. This can be minimized by having the output and

input physically separated as far apart as possible. A copper

shield separating the output and input is often also effective,

and high-frequenc y circuits built on printed circuit boards

should have generous ground-plane areas.

While the lack of stability is undesirable in ampliﬁers,

sinusoidal oscillators depend on such instabilities for their

operation. Consider an ampliﬁer with gain A

(it can be any

one of the four already considered). If X

represents the

output signal (a current or voltage) and X

the input signal

(also a current or voltage), X

¼ A

. For a simple ampli-

ﬁer X

¼ X

(the source signal).

If a fraction b of the output is sent back to the input

in such a way as to cancel part of the source signal, the new

signal X

is X

 bX

, and the gain of the ampliﬁer with

feedback is the output signal divided by the source signal:

þ bX

1 þ bA

ð6:39Þ

For b > 0, the feedback signal acts to cancel the signal

from the source and A

< A

.Thisiscalledne gative or de gen-

erative feedback and is frequently used to stabilize ampliﬁer

gain and improve linearity and noise. For b < 0, the feedback

signal adds to the source signal at the input and A

> A

.This

is positive or r egenerative feedbac k and is sometimes used to

increase the gain of ampliﬁers at the expense of stability. If

¼1, A

¼ N and the ampliﬁer is unstable, with an

output that breaks into oscillation or saturates.

In practice, both A

and b are frequency dependent and

the response of such feedback ampliﬁers can be calculated.

If only stability criteria are desired, it is only necessary to

determine whether any poles of the transfer function lie in

the right half of the complex plane.

One will have an oscillator if bA

can be made equal to

1 for only a single frequency, by means of a frequency-

selective feedback network. There are a large number of

frequency-selective circuits based on LC and RC networks.

Quartz crystal oscillators are particularly stable and free of

temperature effects. These devices work by the application

of a potential difference across the faces of a quartz crystal

that becomes deformed and oscillates at a resonant fre-

quency determined by the size and orientation of the crys-

tal planes with respect to the electrodes. Crystal oscillators

Figure 6.70 Unwanted feedback from stray capacitance.

434 ELECTRONICS

with Q values of 10

to 10

at frequencies from tens of kHz

to over 100 MHz are commercially available in DIP and

SMT conﬁgurations.

6.4.6 Detecting and Processing Pulses

There is a large class of experiments, especially in nuclear

and particle physics, that deals with the detec tion an d

analysis of single events . With the advent of detectors

for low-energy photons, electrons, and ions, these techni-

ques have sp read to the ﬁelds of atomic and molecular

physics, chemistr y, and biology. Commercial inst rumen-

tation is widely available, but to s pecify and use the units

to best advantage a knowledge of the basic properties of

the detectors, ampliﬁers, and associated processing cir-

cuits is required.

Table 6.25 summarizes the properties of the more common

types

of detectors. The ﬁrst part of the table allo ws one to

estimate the output of a given detector for an arbitrary input.

A 5 MeV alpha particle depositing all its energy in a silicon

detector, for example, will create 1.4 3 10

electron–hole

pairs. W ith a suitable bias across the detector , the charge

can be collected in 0.1 to 10 ns. Similar considerations allow

one to calculate the outputs of other detectors. The detectors

can be represented electrically by the equiv alen t circuit of

Figure 6.71. The choice of preamp liﬁer, ampliﬁer , and shap-

ing

and analysis circuits now depends on the information to

be obtained from the pulse. Figure 6.72 sho ws the arrange-

ment

of three general categories of experiments – counting,

timing, and pulse-height analysis. Each one has different elec-

tronics requirements, but before considering these systems in

detail it is worthwhile to examine the circuits commonly

available for ampliﬁcation and shaping.

Preampliﬁers can be v oltage, current, or charge-sensiti v e.

Voltage preampliﬁers are not generally used, because the

voltage generated by most detectors depends on the capaci-

tance of the detector (Figure 6.73) that can change with bias

oltage and other circuit parameters. Current preampliﬁers

have lo w input impedances and are designed to conv ert the

fast current pulse from a photomultiplier or electron multi-

plier to a voltage pulse. Their sensiti vity is speciﬁed as out-

put millivolts per input milliampere. Char ge-sensiti v e

preampliﬁers are the most commonly used preampliﬁ ers

because their gain is independent of the capacitance of the

detector. Their sensitivity is speciﬁed in output milli v olts per

unit input charge or in equivalent output milliv olts per MeV

deposited in a giv en solid-state detector.

A schematic diagram of a combined detector and

charge-sensitive preampliﬁer is shown in Figure 6.73.

Neglecting

the effect of the coupling capacitor, the Laplace

transform of the output voltage v

(s) is:



ðsÞ¼



qðsÞ

1 þ 1=R

ð6:40Þ

Table 6.25 Particle Detectors

Particle

Detector

Output Signal Charge-

Collection

Time

Semiconductor:

1 electronhole pair=2:8eV deposited

1 electronhole pair=3:5eV deposited

0.110 ns

Photomultiplier 10

10

electrons/photoelectron 1 ns

Electron

multiplier

10

electrons/incident

electron

0.51ns

Microchannel

plate

10

electrons/incident

electron

0.1 ns

Scintillator:

Plastic

Alkali halide



1 photon/3keV deposited

0:110 ns

1 ls



Gas-ﬁlled tube 1 ion pair/25–35eV deposited 0.015 ls

For narrow depletion depth.

Figure 6.71 Equivalent circuit of a detector.

AMPLIFIERS AND PULSE ELECTRONICS 435

The function has a pole at s ¼1/R

; the Bode plot is

given in Figure 6.74. The high-frequency pole at x

is a

result of the preampliﬁer transfer function. The output wave-

form for a rectangular input pulse of duration s will be a tail

pulse of rise time s, amplitude q/C

, and decay time R

For very small values of s, the rise time of the output

pulse will be determined by the characteristics of the

ampliﬁer itself. Practical ampliﬁers use high-stability

NPO capacitors for C

with values from 0.1 to 5 pF; the

feedback resistor R

is made as large as is consistent with

the signal rate and leakage current. Noise in charge-

sensitive preampliﬁers is speciﬁed in terms of the energy

resolution FWHM in keV. This can be converted to an

equivalent charge noise with the factors in Table 6.25.

o test charge-sensitive preampliﬁers, the circui t of Fig-

e 6.75 can be used. An input step voltage applied to

Figure 6.72 Three categories of pulse experiments: (a) counting, (b) coincidence, and

436 ELECTRONICS

Figure 6.73 Combined detector and charge-sensitive preampliﬁer.

Figure 6.74 Bode plot for a charge-sensitive preampliﬁer.

Figure 6.75 Test circuit for charge-sensitive preampliﬁers.

AMPLIFIERS AND PULSE ELECTRONICS 437

the capacitor C

results in an amount of charge equal to

deposited on the input of the preampliﬁer. For

15

CwithC

¼ 10 pF, the amplitude of the input

voltage pulse must be 10 mV. The 50 ohm resistor in the

circuit is for te rmination purposes. The duration of the test

input current will be equal to the rise time of the voltage

input.

The output pulses from the preampliﬁer are generally

very different in shape from the input signals. This is the

case even with fast-current preampliﬁers. An important

function of the ampliﬁer and shaping circuits is to increase

the amplitude of the preampliﬁer output signal and change

its shape to minimize pulse overlap and optimize the sig-

nal-to-noise ratio. To minimize pulse overlap, the duration

of the pulses should be short compared with the average

time between them. In more quantitative terms, the rms

voltage level of the pulse train to be processed should

be much less than the required voltage resolution of the

system. If n is the pulse rate and v(t) is the functional form

of the pulse, then:

rms

¼ n

‘

vðt Þ

1=2

ð6:41Þ

For rectangular pulses of unit height and width s:

rms

¼ n

1=2

ð6:42Þ

The long-tail puls e from a charge-sensitive preampliﬁer

can be shortened with a differentiating circuit [Figure

6.7

6(a)]. The circuit reduces the fall time from R

RC. A disadvantage of simple differentiation is

undershoot, which appears on the trailing edge of the out-

put pulse. This can be substantially eliminated by modify-

ing the transfer function of the differentiating circuit to

include a zero that exactly cancels the pole in the pream-

pliﬁer transfer function [Figure 6.76(b)]. The Laplace

transfor

m of the transfer function of Figure 6.76(b) is:

s þ 1=R

s þðR

þ R

Þ=ðR

ð6:43Þ

If R

is set equal to R

from the preampliﬁer, under-

shoot can be eliminated. This technique of pole-zero com-

pensation is commonly used in pulse shaping.

For pulse-height analysis, a Gaussian waveform has the

best noise characteristics.

Such a shape can be obtained

from a tail pulse by a single differentiation and an inﬁnite

number of cascaded integrations with integration time con-

stants all equal to the differentiation constant. In practice,

four integrations give a shape very close to Gaussian.

Bipolar pulses can be obtained by double differentiation

of a tail pulse with an intermediate integration (Figure

6.77). An important property of the bipolar pulse is that

the

zero crossing always occurs at a ﬁxed time after its

start, determined by the time constant, and is independent

of pulse height. When used with zero-crossing discrimina-

tors, such pulses permit reliable timing to be accomplished

with long-decay-time pulses. Bipolar pulses, however,

have poorer noise characteristics than unipolar Gaussian

pulses.

Figure 6.76 Differentiating circuits: (a) without pole-zero

compensation; (b) with pole-zero compensation.

438 ELECTRONICS

An alternative to RC shaping is delay-line shaping. The

equivalent of unipolar and bipolar pulses can be obtained

with single- and double-delay-line circuits (Figure 6.78).

Adv

antages are the preservation of fast rise times, sharp

trailing-edge clipping, and greatly reduced base-line shifts.

These advantages are offset by the poor noise properties of

the pulses compared with RC shaping. Delay-line shaping

is mostly conﬁned to timing applications.

The shaping circuits discussed in the previous paragraph

are generally incorporated in the variable-gain main ampli-

ﬁer that follows the preampliﬁer. While noise is a consid-

eration with such ampliﬁers, it is not so critical as with

preampliﬁers because of the larger signal levels. Important

considerations are linearity and fast overload recovery. To

reduce baseline shifts from pulse pileup, main ampliﬁers

often incorporate a baseline restorer circuit. The principle

of operation is illustrated in Figure 6.79. A noninverting

pliﬁer with gain



HðsÞ is placed in the negative-feedback

loop of an ampliﬁer with gain



GðsÞ. The Laplace transform

of the transfer function for the system is:



GðsÞ

1 þ



GðsÞ



HðsÞ

ð6:44Þ

If both



GðsÞ and



HðsÞ are themselves transforms of

single-pole transfer functions, given by:



GðsÞ¼

1 þ T

and



HðsÞ¼

1 þ T

ð6:45Þ

where A and K are the mid-band gains of the ampliﬁers, the

overall transfer function is:

Að1 þ T

sÞ

AK þð1 þ T

sÞð1 þ T

sÞ

ð6:46Þ

At high frequencies (s >> 1) the transfer function reduces



GðsÞ, while for d.c. (s ¼ 0) the function is 1/K. The

overall effect of the circuit is to amplify high-frequency

pulses while attenuating low-frequency baseline shifts.

For counting applications, the principal considerations

are pulse rate and discriminator setting. The shaped pulses

from the ampliﬁer should be sufﬁciently short in duration

to avoid pileup and baseline shifts. A leading edge dis-

criminator can be used with a unipolar pulse. Since such

units are based on regenerative (positive-feedback) com-

parator circuits that have hysteresis, the decay of the input

pulse must not pass through the recovery voltage level

until the triggered state is attained. When bipolar pulses

are to be counted, zero-crossing discriminators should be

used.

Timing systems require that the leading-edge information

from the detector pulse be faithfully preserved. Timing

errors can arise from due time variations in the processed

pulses relative to the input pulse, long-term drift from com-

ponent aging, and noise. Wide-band current preampliﬁers

and fast timing ampliﬁers with short integrating and differ-

entiating shaping circuits or delay-line shaping should be

used. When using wide-band ampliﬁers, precautions should

Figure 6.77 Bipolar pulse shaping with CR–RC–CR circuits.

AMPLIFIERS AND PULSE ELECTRONICS 439

be taken to electrically terminate all connections properly

and avoid stray capacitances that can form positive-feed-

back paths and produce instability. When the detector signal

itself is of sufﬁcient amplitude – as it is for the output of a

photomultiplier tube used with a scintillation detector – a

timing signal can be taken directly from the detector without

further ampliﬁcation or shaping. Leading-edge and con-

stant-fraction discriminators are most commonly used for

timing. The constant-fraction discriminator provides the

Figure 6.78 (a) Unipolar and (b) bipolar pulse shaping with delay lines.

Figure 6.79 A baseline restorer circuit.

440 ELECTRONICS

better resolution times. With this discriminator, the input

signal is delayed and combined with a ﬁxed fraction of the

undelayed signal. A bipolar pulse with a zero crossing

independent of rise time and amplitude results can be used

to activate a zero-crossing detector.

In Figure 6.72(b), the delay inserted in the stop li

ne of the

system is to ensure that the stop pulse to the time-to-ampli-

tude conv erter (TAC) will always follow the start pulse. The

TA C conv erts the time difference between the start and stop

input pulses to a single pulse of an amplitude proportional to

the time dif ference. High quality, low-attenuation coaxial

cable makes an excellent delay line, and lumped-parameter

delay lines are also commercially av ailable. Timing informa-

tion is usually obtained by processing the output of the TA C

with a pulse-height analyzer (PHA). A more direct method is

with a time-to-digital con v erter that con v erts the time differ-

ence between the start and stop pulses to a digital word for

processing. Depending on detector characteristics, time res-

olution of pico-seconds can now be obtained.

Particle-spectroscopy experiments rely on the preservation

of the pulse-amplitude information from the detector because

the amplitude is a direct measure of the particle ener gy. Opti-

mum amplitude resolution is obtained by operating the pre-

ampliﬁer and ampliﬁer in their linear ranges, reducing

sources of noise and baseline shifts from pileup, and using

semi-Gaussian pulse shapes as inputs to the PHA. The func-

tion of the PHA is to con vert the pulse amplitude to a binary

number . This number can then be used to address a memory

location in a multichannel analyzer (MCA) or PC. The con-

tents of the memory location speciﬁed by the encoded pulse

height is then increased by one. Nonlinearities in the pream-

pliﬁer and ampliﬁer can be both dif ferential and integral,

illustrated in Figure 6.80.Thedif

fer ential nonlinearity is

the ratio of the slope of the ampliﬁer gain curve, at a speciﬁed

input level, to the slope, at a reference input le vel. The inte-

gral nonlinearity is the maximum vertical deviation of the

real gain curve from the ideal straight-line gain curve,

expressed as a percentage of maximum output. Such non-

linearities also occur in the circuits of the PHA and must be

taken into consideration for high-resolution work.

The manufacturers of pulse-processing equipment

include application notes and product guides with the cat-

alog descriptions of their instruments. These are generally

very helpful and should be read thoroughly before choos-

ing a system and selecting components.

6.5 POWER SUPPLIES

The design of regulated power supplies follows a standard

conﬁguration (see Figure 6.81). Raw a.c. from the outlet is

nverted, usually with a transformer, to the desired level.

This converted a.c. is rectiﬁed to produce unregulated d.c..

The unregulated d.c. then becomes the input to a regulator

circuit, whose output is the desired d.c. output voltage.

Figure 6.80 Ampliﬁer linearity.

Figure 6.81 Block diagram of a regulated power

supply.

POWER SUPPLIES 441

6.5.1 Power-Supply Speciﬁcations

Power supplies are speciﬁ ed by the maximum current, max-

imum voltage, and maximum power they can deli v er. It is

not always the case that maximum current can be delivered

ov er the complete voltage range of the supply, nor can the

maximum voltage be obtained at all current le v els. This

situation is illustrated in Figure 6.82. Maximum current

can

only be obtained ov er a limited range of voltage without

exceeding the power rating of the supply.

The change in output voltage per unit change in input

a.c. voltage is called the line regulation, while the change

in output voltage per unit change in load or output current

is called the load regulation. Both are generally speciﬁed

as a percentage. Many power supplies can be operated in a

constant-current mode where the output is a current essen-

tially independent of input and output voltage. Regulation

speciﬁcations then apply to the output current. Load reg-

ulation can be translated into an equivalent dynamic-out-

put resistance, since the relative change in load is the

negative of the relative change in current DR/R ¼DI/I:

load regulation ¼

DV=V

DR=R

¼

DV=V

DI=I

DV=DI

V=I

dynamic output

load

ð6:47Þ

As an example, if a ﬁlament power supply produces 3 A

at 5 V, and the load regulation is 0.1%, then the dynamic

output resistance is:

dynamic output

1 3 10

3

3 5V

¼ 1:67 3 10

3

X ð6:48Þ

Transient response and recovery time relate to the ability

of the power supply to recover from sudden changes in

load or line voltage at the stated operating point. If the line

and load ﬂuctuations are rapid, the power-supply regulat-

ing circuits may not be able to keep up with them and the

resulting regulation will be considerably worse than speci-

ﬁed. Generally, the better the regulation, the slower the

response to changes of line and load conditions. The reg-

ulation may also depend on the output power level, a point

worth noting in the speciﬁcations.

As well as maintaining a constant average d.c. leve l,

instantaneous values of the output voltage should not deviate

appreciably from the av erage. De viations come from ripple

at twice the line frequency for dissipati v e regulators, at the

switching frequency for switching regulators, and from reg-

ulating circuit transients. Speciﬁcati on of the rms ripple gi v es

an indication of the effecti v eness of the ﬁlter ing circuits. It

giv es no indication, howev er, of the presence of short-dura-

tion, large-amplitude voltage spikes at the output. A maxi-

mum peak-to-peak noise speciﬁcation is used to describe this

kind of instantaneous voltage deviation. As with regulation,

ripple and noise may depend upon the power level.

Even with a constant line voltage and constant load, the

output voltage can change if the temperature changes. This is

generally indicated by a temperatur e-coefﬁ cient speciﬁcation,

which gives the percentage change in output voltage per

degree change in temperature about a speciﬁed temperature.

For laboratory applications, this is usually not a critical spec-

iﬁcation. When working in extreme environments, howev er,

it may be signiﬁcant (for compact units that depend on

forced-air cooling or free-con vection cooling, adequate space

must be provided in the mounting to pre vent overheating).

Power supplies that convert a d.c. input voltage to a dif-

ferent d.c. output voltage are particularly useful when d.c.

rather than a.c. voltages are available. Voltage conversion

with these supplies is accomplished by changing the d.c.

input to a.c. at frequencies of 20 kHz and above, changing

Figure 6.82 Current, voltage, and power relations for a

power supply.

442 ELECTRONICS

the amplitude of the high-frequency a.c. with a transformer,

and rectifying and regulating the output of the transformer.

The ratio of the maximum output power to maximum input

power is the efﬁciency of conversion. d.c. to d.c. converters

have efﬁciencies that exceed 70 to 80% and are available in

a wide range of input and output voltages and powers. When

high voltage at low current is required, as, for example, for a

photomultiplier tube or electron multiplier, these units are

particularly convenient.

Though often not included in the speciﬁcation list, radio

frequency (rf) noi se can be an important consideration for

supplies used in the vicinity of sensitiv e wide-band ampli-

ﬁers and when trying to extract a weak signal from noise.

Some types of power supplies produce more r.f. noise than

others because of the design of the regulating circuit. Switch-

ing regulators with SCRs are particularly poor in this regard.

Other factors to consider in a power supply are bipolar

operation (can both the negative and positive terminals be

grounded to give positive and negative output voltages,

respectively?) and insulation from ground if the supply is

to be ﬂoated on another supply. Operation is simpliﬁed by

front-panel meters indicating both output voltage and cur-

rent, overload reset switches, and a convenient output ter-

minal conﬁguration and location.

A single output power supply can never be used to sup-

ply two voltages, one negative and one positive with

respect to ground. When it is necessary to have such vol-

tages as, for example, with operational-ampliﬁers, two

separate supplies must be used.

6.5.2 Regulator Circuits and Programmable

Power Supplies

A block diagram of a dissipative regulator circuit in a

power supply is illustrated in Figure 6.83. The sensing

res

istors R

and R

are across the output of the power

supply. A fraction R

/(R

þ R

) of the output voltage is

sent to a difference ampliﬁer, where it is compared with a

reference voltage, and the ampliﬁed difference used to con-

trol the pass element, a transistor in the common-collector

conﬁguration in this example. Depending on the output of

the difference ampliﬁer, the pass-element output voltage

will adjust itself to a value just sufﬁcient to sustain the

required input from the difference ampliﬁer. If, for some

reason, the output voltage rises, the output of the difference

ampliﬁer will decrease and the pass-element output will

decrease. The opposite occurs for a falling output. The

series dissipative regulator is inefﬁcient because the differ-

ence in voltage between the raw d.c. input and regulated

d.c. output falls across the pass element, which must then

dissipate power equal to the product of this voltage differ-

ence and the output current.

Figure 6.83 Block diagram of the regulator circuit in a power supply.

POWER SUPPLIES 443

More efﬁcient power supplies use circuits to control the

duty cycle of the pass element. In these circuits, the pass

element (a transistor, SCR, power MOSFET, IGBT, or

other solid-state device) acts as a switch and is either on

(no voltage drop across it) or off (no current through it).

The output voltage from such a regulator is:

out

¼ V

þ t

off

ð6:49Þ

where t

is the time for which the pass element is on and

off

is the time for which it is off in each cycle. The optimum

switching frequency for switching regulators is between 20

and 100 kHz. At these high frequencies, r.f.i. is present and

can cause problems with sensitive electronic circuits.

In practice, regulator circuits can be very complex, with

high-gain difference ampliﬁers or comparator preregulators,

multiple pass elements, overload and overvoltage protec-

tion, and temperature compensation. The above general

power-supply description, however, is sufﬁcient for an

understanding of remote programmable power supplies. If

and R

in Figure 6.83 are replaced by a potentiometer, a

change in its setting will result in a change in the regulated

output voltage. This is what occurs when one changes the

dial settings on the front panel of a variable power supply.

The internal potentiometer can clearly be replaced by an

external potentiometer (resistance programming) – or even

more directly – by an external voltage source (voltage pro-

gramming). The addition of such features requires very little

modiﬁcation to the basic power-supply regulator circuit, and

they are often available at no cost or as low-cost options.

Remote programming can be particularly useful in control

operations, where a digital code from a computer is changed

to a voltage by a digital-to-analog converter (DAC), and this

voltage is used to set the output of a power supply.

Overvoltage protection is an important feature in a

power supply. With such protection, one is assured that

no failure will result in a high voltage across the output

terminals of the supply. Crowbar circuits using SCR

switches are often used for overvoltage protection. Such

circuits short the output terminals of the supply when the

output voltage exceeds a preset value. The resulting short-

circuit current causes a fuse to blow or a circuit breaker to

open, shutting down the power supply until the fault that

caused the overvoltage is corrected. It is essential that the

protection circuit responds quickly to overload conditions

to avoid damage to the power supply. Response speed

should be included in the speciﬁcations.

Another built-in safety feature found on power supplies is

foldback current limiting. When the output current exceeds

a speciﬁed limit, it is automatically reduced by such circuits

to a low level and maintained there for a speciﬁed time

before being reset. Current-limiting circuits are triggered

by temperature-sensitive or power-dissipating elements.

In addition to variable output power supplies there are a

large number of ﬁxed-voltage power supplies on the market.

When working with logic circuits and operational ampliﬁer

circuits, only ﬁxed power-supply voltages are required.

Most ﬁxed-voltage supplies inc orporated in other units are

designed to operate from the a.c. line, although there are a

number of a.c.-to-d.c. converters. The least expensiv e conﬁg-

uration is the card power supply [Figure 6.84(a)]. All com-

nents are on a single printed circuit board with edge

contacts. The a.c. input must be brought to one set of contacts

and the d.c. output taken from another. For routine use, the

card supply should be mounted in a case or on a rack panel

with an on–off switch, a pilot light, a fuse, and output termi-

nals. This requires additional time and expense, which may

cancel the initial cost savings from purchasing such a supply.

Frame-mounted supplies [see Figure 6.84(b)] are similar

the card supplies in that all external connections,

switches, and output terminals are missing. The metal frame

facilitates mounting, however, and affords some protection

to the components. Rather than PCB contacts, frame sup-

plies usually have screw-type barrier connectors.

Fixed-voltage supplies also come in enclosed cases and

in encapsulated units suitable for direct connection to a

printed circuit board [see Figure 6.84(c)]. Many of the

so-called

ﬁxed-voltage supplies can be adjusted over a

5–10 % range about the nominal output voltage value.

Multiple ﬁxed-voltage units with two and even three vol-

tages are also common. It is often useful to have 615 V

and þ5 V available from a single power supply when both

linear and digital circuits are used together.

Manufacturers produce a wide range of supplies with dif-

ferent voltages, power ratings, and mechanical conﬁgura-

tions. It is therefore rarely worthwhile to construct a po wer

supply. A possible exception lies in the use of integrated-

circuit modules. There are two general types: ﬁxed and

variable output. The ﬁxed-output units are three-terminal

devices – unre gulated d.c. is applied across the input and

444 ELECTRONICS

common terminals, and regulated d.c. at the appropriate

voltage appears between the output and common terminals.

A representativ e unit of this type is the LM109 5 V, 1.5 A

monolithic regulator . The regulator combines on-chip thermal

shutdown with current limiting, an on-chip series pass

transistor, and a stable internal voltage reference. Further

details about the LM109 and its use in other applications

are available from the manufacturer.

The LM105 is an example of a variable-voltage integrated-

circuit re gulator. For this unit, the output is set by the ratio of

two external resistances. The maximum output voltage is

40 V, and the maximum output current is 20 mA. When an

external pass transistor is added to the basic regulator circuit,

the load current can be increased to 500 mA. The LM105 can

also be used as a switching regulator. Data and application

sheets should be consulted when using such regulators.

Useful power-supply circuits with integrated regulators

are illustrated in Figure 6.85. Fixed-voltage units are made

several manufacturers at several ﬁxed voltages from 4

to 20 V. Variable units are available for both positive and

negative voltages.

Though not strictly po wer supplies, integrated-circuit volt-

age references provide precise output voltages for d.c. input

voltages that can span a relati v ely wide range. Output vol-

tages are from 1 to 10 V with initial accuracies from 0.01 to

1.2%. Change in output voltage with temperature for these

units varies between 1 and 50 parts per million per degree

Celsius (ppm/°C). Output noise is exceptionally low, varying

from 1 to 50 lV peak-to-peak over a bandwidth of 0.1 to 10

Hz. Output currents are low, 5 to 100 mA.

6.5.3 Bridges

Bridges are used to measure the electrical properties of a

circuit element by comparison with a similar element. The

Wheatstone bridge, dev eloped in the early nineteenth century,

compares the potentials from two voltage di viders connected

in parallel across a voltage source, as shown in Figure 6.86(a).

aking the difference between the potentials at the

junction of R

and R

, V

out

¼ V

=½

ðR

þ R

ÞR

=ðR

þ R

Þ. When V

out

¼ 0, R

, the null condition. In the standard conﬁguration,

and R

are ﬁxed, R

is the resistance to be measured,

and R

is v a ried until a null or balanc e condition is achiev ed.

At null the relation between the resistances is independent of

. Null-type measurements require a means for v arying one

element of the bridge, and this is usually accomplished with a

system that incorporates feedback.

Bridges in most transducer applications are operated

off-null, or out of balance. For the simple bridge in Figure

Figure 6.84 Fixed-voltage power supplies; (a) card supply;

(b) frame supply; (c) enclosed case.

POWER SUPPLIES 445

6.86(b), three of the resistors are ﬁxed at value R while the

one to be measured, R

, deviates from R by xR, where x is a

unitless variable. The output voltage V

out

is given by:

out

¼ V



R þ R



¼

1 þ x=2



ð6:50Þ

For x=2<<1; V

out

V

ðx=4Þ.Asanexample,let

x ¼0.01, then V

out

¼V

ð0:01=4Þ, so that a 1% change

in R

gives a 0. 25% change in V

out

. The sensitivity of

the bridge, deﬁned as the change in output voltage for

a given change in input voltage, is 250 mV/V. Bridge

sensitivity can be doubled by adding a second identical

variable element opposite the ﬁrst, as shown in Figure

6.8

6(c). While the output of such a conﬁguration is

doubled,

the nonlinearity remains. The addition of two

more variable elements, R

¼ R(1 – x), with resistances

that change in opposite ways to the original elements,

results in a bridge with output equal to the fractional

change in resistance times the reference voltage. This is

shown in Figure 6.86(d). Bridges of this type are used with

two-element

strain gauges and piezo-resistive transducers.

The transducers are arranged so that there are complemen-

tary changes in resistance for sensors in adjacent bridge

arms.

Another way to linearize the output of a bridge circuit is

by inserting an operational ampliﬁer to null the bridge by

adding a voltage in series with the variable element R

that

is equal in magnitude and opposite in sign to the incre-

mental voltage across R

. This gives an output that is linear

in x for large values of x.

In bridge circuits that are operated out of balance, the

output is proportional to the reference voltage V

. A stable

reference voltage can be derived from an IC reference

source followed by an operational ampliﬁer stage. Ana-

log Devices and Maxim Integrated Products manufacture

signal-conditioning power supplies that have program-

mable outputs and include ampliﬁcation and ﬁltering. Be-

cause neither side of the bridge from which the voltage is

measured is at ground, instrumentation ampliﬁers are the

preferred devices for reading bridge outputs. These ampli-

ﬁers have the necessary differential inputs, high common-

mode rejection ratios, high input impedances, and resist-

ance programmable gain.

Figure 6.85 Examples of circuits with the LM109 ﬁxed-

voltage regulator and the LM105

variable-voltage regulator.

446 ELECTRONICS

6.6 DIGITAL ELECTRONICS

Digital systems are based on circuit elements (usually tran-

sistors) operated in such a way that they exist in only one

of two states. This is in contrast to analog systems, where

the outputs are continuous functions of the input variables.

Combinations of two-state, or binary, devices can perform

arithmetic and logic operations of arbitrary degrees of

complexity.

6.6.1 Binary Counting

With a binary system, it is usual to call the states 0 and 1.

Combinations of 0s and 1s can then be used for counting.

Some schemes are given in Table 6.26. Note that the lea

signiﬁcant bit (LSB) or column is 2

, the next 2

, and the

last or most signiﬁcant bit (MSB) is 2

. In other words, the

binary number system is merely a base 2 system, while

the decimal system is base 10. Other systems derived from

the binary system are the octal (base 8) and the hexadeci-

mal (base 16), as detailed in Table 6.26. In the binary

sys

tem, the number 2 does not appear, and in the octal

system 8 does not appear. The hexadecimal system substi-

tutes the letters A, B, C, D, E, and F for the decimal num-

bers 10, 11, 12, 13, 14, and 15, for which a single symbol

does not exist.

The state of the output of a logic device can be represented

by a voltage le v el or the presence or absence of a signal pulse

within a gi v en time window. A voltage-level system in which

the most positive voltage le v el corresponds to logical 1 is a

positive-logic system. One in which the least positi ve level

corresponds to logical 1 is a negative-logic system.

6.6.2 Elementary Functions

The basic logic gates, along with the corresponding rela-

tionships between input and output variables, are given in

Table 6.27 in truth-table form

along with the schematic

symbols.

Figure 6.86 (a) Wheatstone bridge; (b) off-null bridge with one variable

element; (b) off-null bridge with two variable elements; (c) off-null bridge with

two compensating variable elements; (d) off-null bridge with a compensati ng

variable element.

DIGITAL ELECTRONICS 447

6.6.3 Boolean Algebra

The rules for manipulating logic expressions based on

binary logic were formulated in the nineteenth century by

George Boole. The laws and identities are given in Table

6.2

8. Boolean algebra is useful for reducing complex truth

bles to the fewest possible gates. Consider, for example,

the three-variable (A, B, C), two-function (X, Y) truth table

at the top of Figure 6.87. The Boolean algebra expressions

r X and Y are obtained by identifying the states of each of

the variables (A, B, C) for which the function under con-

sideration (X or Y) is in the 1 state. For example, X ¼ 1

when A ¼ 0, B ¼ 0, and C ¼ 1. By convention, a bar over a

variable symbol indicates negation, so that if A ¼ 0,



A ¼ 1.

The coincidence of 1s at



B,andC to give X ¼ 1 requires

an AND operation, which is the ﬁrst term in the full expres-

sion for X in Figure 6.87. The other terms are derived from

e truth table in the same way, and they are all connected

together by OR operations. After simpliﬁcation by applica-

tion of the laws in Table 6.28, the expressions can be imple-

nted with elementary gates. The gates for the function X

are shown at the bottom of Figure 6.87.

Another

way of simplifying truth tables is by making a

logic map called a Karnaugh map. The map for the truth

table of Figure 6.87 is shown in Figure 6.88. The squares

corresponding

to the variables for which X and Y are 1 are

shaded. Contiguous shaded squares corresponding to 0 and

1 for a single variable, say C, with the other variables

constant, show that the value of the function is independent

of the state of C. In the map for Y, it can be seen that the

squares for



A  B are shaded for C and



C. It therefore fol-

lows that the state of Y is not dependent on the variable C

for these cases.

6.6.4 Arithmetic Units

After elementary gates, the next simplest logic units are

those that perform elementary binary arithmetic operations.

Some common arithmetic units are gi v en in Table 6.29.The

truth

table for the half adder follows the rules for binary

addition with C the low-order bit of the sum and D the

high-order bit. The full adder is an elaboration of the half

adder with an extra input. When adding two binary numbers

of more than one bit each, provision must be made for the

carry operation. This is the function of the C

n1

terminal,

that accepts the carry bit from the result of adding the pre-

ceding lower -order bits in the string (thus the designation

n1

). The results from the addition of the n-order bits

appear at terminals C

and S

.Thedigital comparator com-

pares the magnitude of the digital signals at input A

and B

and activates output C

, D

,orE

depending on whether A

, A

< B

,orA

¼ B

. Such elements can be connected

together to compare two n-bit binary numbers. The parity of

a binary number is deﬁned as odd (0) if there is an even

number of ls and ev en (1) if there is an odd number of 1s.

The parity code is often used to check for transmission errors

in bit strings. By sending a parity bit with an n-bit word

and testing the receiv ed word against the parity bit, single

bit errors can be detected. This is illustrated for a four-bit

word with the parity generator/chec ker in Table 6.29.

6.6.5 Data Units

For data acquisition and transmission, decoders, encoders,

multiplexers, and demultiplexers are commonly used. The

read-only memory (ROM) is a combination of decoder and

Table 6.26 Systems of numeration

Decimal Binary Octal Hexadecimal

0 0000 00 0

1 0001 01 1

2 0010 02 2

3 0011 03 3

4 0100 04 4

5 0101 05 5

6 0110 06 6

7 0111 07 7

8 1000 10 8

9 1001 11 9

10 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

MSB

1111

)

LSB

17 F

448 ELECTRONICS

Table 6.27 Logic gates

Name Symbol Truth Table Boolean Expression

ABY Y¼A+B

000

011

101

111

AND (coincidence)

ABY Y¼A  B

000

010

100

111

NOT (inverter)

Y ¼

NOR

ABY Y¼A þ B

001

010

100

110

NAND

ABY Y¼A  B

001

011

101

110

XOR (exclusive OR,

anticoincidence)

ABY Y¼ðB  AÞþðB  AÞ

000

011

101

110

XNOR (exclusive, NOR,

equivalence)

ABY Y¼ A  B þ A  B

001

010

100

111

DIGITAL ELECTRONICS 449

encoder and is frequently used to implement complex truth

tables. Programmable and erasable ROMs, called PROMs

and EPROMs, can have their internal logic modiﬁed for

the particular application of the user. Table 6.30 gives the

truth

tables and input–output terminal arrangements for

some simple data units.

6.6.6 Dynamic Systems

The logic units described so far are considered to be static

or combinatorial, because the output levels depend only on

the current input levels. The previous history of the signals

at the different inputs is irrelevant. With dynamic or

sequential systems, output signal levels depend on the his-

tory of the signal levels at the input terminals. The truth

tables for dynamic systems must specify the previous

states of the inputs and outputs in order for the state of a

particular output to be fully determined. Subscripts are

used to differentiate the time sequence of the output states.

Table 6.31 lists a number of ﬂip-ﬂops that

are the basic

building blocks in dynamic systems. Flip-ﬂops can be

strung together to make shift registers and counters. A shift



Q outputs

of each stage connected to the J and K inputs of the next

stage (see Figure 6.89). Data are entered serially in the ﬁrst

Table 6.28 Boolean Algebra

Laws Identities

Commutative A þ A ¼A

A þ B ¼B þ AA A ¼A

A  B ¼B  AAþ 1 ¼1

A  1 ¼A

Distributive A þ 0 ¼A

A  (B þC) ¼A  B þA CA 0 ¼0

De Morgan

A  B C ¼ A þB þ C

A þ B þC ¼ A  B C

Figure 6.87 Example of a truth table, the equivalent

Boolean algebraic expression, and implementation with

elementary gates.

Figure 6.88 Karnaugh map for the truth table of

Figure 6.87.

450 ELECTRONICS

Table 6.29 Arithmetic units

Name Symbol Truth Table

Half adder

A B Sum C D

0000 0 0

0101 0 1

1001 0 1

1110 1 0

Full adder

n-1

(sum) C

(carry)

000 0 0

010 1 0

100 1 0

110 0 1

001 1 0

011 0 1

101 0 1

111 1 1

Digital comparator

¼B

)

000 0 1

010 1 0

101 0 0

110 0 1

Parity generator/checker

ABCD P'

zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{

4bit word

Parity bit

PðP

=1Þ

PðP

=0Þ

DIGITAL ELECTRONICS 451

Table 6.30 Data units

Unit Symbol Truth Table

Decoder: Activates

one of 2

outputs

according to

an n-bit code.

CB A

CBAX

0 0 0100 0000 0

0 0 1010 0000 0

0 1 0001 0000 0

0 1 1000 1000 0

1 0 0000 0100 0

1 0 1000 0010 0

1 1 0000 0001 0

1 1 1000 0000 1

Encoder: n-bit

output code for

activation of one of

input lines.

DCBA

Input D C B A

00000

10001

20010

30011

40100

50101

60110

70111

81000

91001

Multiplexer: According

to an n-bit code, one

of 2

signal input lines

is connected to a

single output line.

8-to-1 line multiplexer

shown.

MUX

000A

001A

010A

011A

100A

101A

110A

111A

452 ELECTRONICS

unit, connected as a D ﬂip-ﬂop, and move from unit to unit

at each clock transition. Shift registers can be used as

counters, serial-to-parallel data converters using the paral-

lel outputs, and parallel-to-serial data converters using the

parallel inputs.

The basic serial or ripple binary counter is shown in

Figure 6.90. Three J/K ﬂip-ﬂops

can count to 2

in this

arrangement. In the shift-register conﬁguration, eight ﬂip-

ﬂops are needed to count to 2

Modulo-N counters with N 6¼ 2. These counters can be

made by decoding the counter outputs with gates and reset-

ting the ﬂip-ﬂops after N counts. Shift registers and coun-

ters are manufactured in a variety of conﬁgurations in

single 14- and 16-pin DIP and SMT packages.

6.6.7 Digital-to-Analog Conversion

Whenever it is necessary to connect a digital system to

an external device that operates in an analog mode, con-

verters are needed – either digital-to-analog (DAC) or

analog-to-digital (ADC). Of the two, the DAC is the

more fundamental, since many ADCs use DACs in their

construction.

A DAC produces an output current or voltage propor-

tional to the magnitude of the binary number at its input

terminals (see Figure 6.91). In one design, the binary

puts to a DAC activate FET analog switches that con-

nect the properly weighted current or voltage from a

reference source to the output. In the case of voltage

Table 6.30 (cont.)

Unit Symbol Truth Table

Demultiplexer: According

to an n-bit code, a single

input line is routed to

one of 2

output lines.

C B A Y Connected to

000X

001X

010X

011X

100X

101X

110X

111X

Read-only memory (ROM):

Combination of a

decoder and encoder

to convert an n-bit code

to an m-bit code, where

n and m are not

necessarily equal. 3-bit

input code (A

)

and 4-bit output code

) shown.

DIGITAL ELECTRONICS 453

Table 6.31 Flip-Flops

Unit Symbol Truth Table

R/S (reset-set) ﬂip-ﬂop:

Basic digital memory

unit.

R/ S

SRQQ

0101

1010

0 0 Indeterminate

1 1 Indeterminate

J/K ﬂip-ﬂop:An

elaboration

of the R/S avoiding

the indeterminate 1, 1

and 0, 0 states,

with separate preset (Pr)

and clear (Cr) inputs,

and a clock (Ck) input

that must be activated

for the outputs

to follow input

conditions.

J/ K

Upon the application of a Ck pulse

n+1

nþ1

0101

1010

Direct inputs

Pr Cr Q

0 0 Disallowed

0110

1001

1 1 Normal Clocked Operation

D (delay) ﬂip-ﬂop: Input

state appears at the

output

after a clock

pulse. Constructed

from a J/K ﬂip-ﬂop with

an inverter from J to K,

signal

applied to J.

Input

Upon the application of a Ck pulse

Input Q

001

110

T (toggle) ﬂip-ﬂop:

Output changes

state at each

clock transition.

Used as a binary

divider. Constructed

from a J/K ﬂip-ﬂop by

ﬁxing J and K at logic 1.

The subscript n + 1 designates the (n + 1)th state as distinct from the previous nth state. When R and S are 0, the output of Q remains

constant, equal to its previous value.

454 ELECTRONICS

DACs, an operational ampliﬁer in the summing mode

adds the weighted input voltages. Electric al speciﬁcations

to consider with a DAC are resolution, the number of

input bits or steps (an 8-bit DAC has 256 steps); linearity,

the maximum deviation from t he best straight line drawn

through the graph of output versus digital input; and

accuracy, the deviation of the output from that computed

on the basis of the digital input. Linearity primarily

depends on the resistors in the DAC circuit and the volt-

age drops across the internal transistor switches. For these

reasons, linearity is temperature dependent. Accuracy

depends on the factors a ffecting linearity and also on

the reference voltage, either inte rnal or extern al. In app li-

cations where speed of conversion is important, settling

time must be considered. This is the time necessary for

the analog output to stabilize to a level th a t is the

Figure 6.89 J/K ﬂip-ﬂops arranged as a 3-bit shift register.

Figure 6.90 J/K ﬂip-ﬂops arranged as an 8-bit binary ripple counter.

Figure 6.91 An 8-bit current digital-to-analog converter

(IDAC).

DIGITAL ELECTRONICS 455

equivalent of 61/2 of the least signiﬁcant bit of the binary

input. Other considerations are power-s upply sensitivity

and compatibility with input a nd output logic levels. If a

currentDACisusedinanapplication where the output

must be a voltage, a current-to-voltage converter is

needed. For low-voltage applications, this can be a resis-

tor. When higher voltages are required, the operational-

ampliﬁer circuits shown in Figure 6.92 can be used. The

characteristics

of the ampliﬁer should not degrade the

expected performance of the DAC with respect to linearity,

accuracy, and settling time.

A variation of the DAC is the multiplying DAC. Since

the output of a DAC is directly proportional to the binary

input and reference voltage, varying the reference voltage

has the effect of multiplying the output by a constant.

Digitally modulated waveforms can be easily produced

with such devices.

There is a larger variety of ADCs than DACs because

the complexity of analog-to-digital conversion lends itself

to a variety of techniques. Four ADC schemes are shown in

Figure 6.93. With the counter

ADC [see Figure 6.93(a)],

pulses from an oscillator or clock are routed to a counter

through control logic, which is activated by the output of a

comparator. The counter output goes to a DAC, the output

of which is compared to the input signal. When the DAC

output equals the input voltage, the comparator changes

state and disconnects the clock from the counter. The

binary number at the counter outputs is then proportional

to the analog input voltage.

The dual-slope ADC [see Figure 6.93(b)] converts volt-

age

to time by using the input voltage to charge a capa-

citor to a predetermined voltage and then discharging the

capacitor by connecting it to a reference voltage of the

opposite polarity. The input voltage is proportional to

the ratio of the charge to the discharge times, which is

recorded by a counter driven by a clock through control

logic. As long as the capacitor, clock, and reference volt-

age are stable during the conversion interval, the resolution

will depend only on the resolution of the capacitor circuit.

This method is the one most commonly used in digital

multimeters.

The successive-approximation ADC [see Figure 6.93(c)]

works

like the counter ADC except that a logic circuit,

rather than a clock and c ounter, drives the DAC. The logic

circuit starts by activating the most signiﬁcant bit of the

DAC. If the DAC output is greater than the input, the

logic c ircuit turns the MSB off and the next MSB on,

and the comparison is done again. The process of com-

parison continues to the LSB, after which the conversion

is complete. This method is fast a nd has high resolution.

Resolution, linearity, accuracy, and settling time are

important par ameter s used f or characterizing the opera-

tion of ADCs.

The fastest ADCs are ﬂash c onverters. These use 2

comparitors, a voltage divider with N resistors, and a

priority encoder to produce an N-bit binary output. The

speed of conversion depends primarily on the speed of

the comparitors. Eight-bit ADCs that can convert at a

rate of 10

samples per second (GSPS) are widely avail-

able. A simple 3-bit ﬂash converter circuit i s shown in

Figure 6.93(d) along with the truth table f or the priority

encoder

Figure 6.92 Conversion of the current output of an IDAC

to a voltage output: (a) inverting; (b) noninverting.

456 ELECTRONICS

Figure 6.93 Four analog-to-digital converters: (a) counter; (b) dual slope; (c) successive approximation; (d) ﬂash.

DIGITAL ELECTRONICS 457

Modular data-acquisition systems or data loggers with an

analog multiplexer (MUX) sample-and-hold (S/H) circuit,

and ADC are av ailable from many sources. A block diagram

of such a system is shown in Figure 6.94. Each of the trans-

ducer

-ampliﬁer-ﬁ lter circuits is connected to the sample-

and-hold circuit for a ﬁxed time thr ough the multiplex er.

The output of the sample-and-hold circuit is then digitally

encoded by the ADC. The frequency at which the various

inputs are sampled depends on the rate at which the signals

are varying. An important theorem of sampling theory states

that if a sampled signal contains no Fourier components of

higher than f

max

, the signal can be recovered with no distor-

tion, if sampled at a frequency of 2 f

max

6.6.8 Memories

Large-s cale integration (LSI) and very large-scale inte-

gration (VLSI) have made possible the production of

high-density, solid-state memories. The typical one-bit

memory cell is an R/S ﬂip-ﬂop with supplementary gates,

shown in Figure 6.95. When the ad

dress and write enable

lines are activated, the signal on the write line is registered

on the Q line. It will remain there as long as the write

enable line is not subsequently activated. To read the con-

tents of the memory cell, the address line has only to be

activated. Large-scale memories are composed of billions

of such elementary cells. Because the contents of any

single cell can be read by activating the appropriate

address line, such memories are called random-access

memories (RAMs). There are several different ways of

arranging the basic memory cells for addressing purposes.

For example , a 1024-bit RAM can be arranged as 1024

one-bit words or 256 four-bit words. The addressing

scheme in the ﬁrst case requires 10 address lines, one data

out line, and one data in line. For the 256 3 4 memory,

eight address lines are needed as well as four data in and

four data out lines. In addition to the address and data

lines, a read/not write (R=

W) line and a chip enable

Figure 6.94 Multiple-input data-acquisition system with an analog multiplexer (MUS), sample-and-hold (S/H) circuit, and

ADC.

Figure 6.95 Basic memory cell.

458 ELECTRONICS

(CE) line are needed. The sta te of the R=W li ne determines

whether data are to be read into or out of the memory; the

CE line is activated when reading or writing data.

Dynamic RAMs require an additional input, called the

refresh, to h old the contents o f the memory. Refreshing

is required continuously with the refresh sign al supplied

from a separate clock. Static RAMs require no such

refreshing. Solid-state RAMs may be volatile, meaning

that their contents are destroyed when the power is inter-

rupted. Battery backup can be provided for these memo-

ries in applications where the memory contents must be

retained in the event of a power failure. For modern mem-

ories based on MOS technology, external power sources

are not necessary to retain memory contents. Examples

are USB memory sticks and ﬂa sh memory cards used in

digital cameras and recorders.

Important parameters to consider for RAMs are power

dissipation, access time, and cycle time. The access time is

the time required after the activation of the address lines to

obtain valid data at the output. The cycle times are the

times required to complete a read- or write-data procedure.

The access and cycle times are related to the power dis-

sipation – generally, the lower the power dissipation, the

slower the memory.

Other considerations are po wer-supply voltages and input

and output signal levels. RAM must be able to accept data

from external devices and, in turn, produce output levels

capable of driving the circuits connected to its outputs.

ROMs are storage devices with permanent, unalterable

patterns of 0s and 1s in the individual cells. ROMs are used

extensively in computers for storage of the character-

generation bit patterns, lookup tables for routine code con-

versions, and control programs, such as those used in cal-

culators.

Programmable read-only memorys (PROMs) are ROMs

whose bit pattern can be altered. They are programmed

with a PROM programmer that permanently burns the

desired bit pattern into the PROM. The bit pattern can be

entered manually (memory location by memory location),

serially, or in blocks under the control of a computer con-

nected to the programmer.

Even more useful devices are erasable PROMS, or

EPROMS. These are programmed in the usual way, but

can also be erased and reprogrammed for other applica-

tions. Erasing is usually accomplished with ultraviolet

light in an EPROM eraser. This can take several minutes.

The EEPROM or electrically erasable PROM, can be very

quickly erased with electrical signals.

An example of the more common series of EPROMs is

the 2700 series, manufactured by INTEL, Advanced Micro

Devices, and others. Members of the series are the 2708,

2716, 2732, 2764, 27128, 27256, and 27512. The digits

following the 27 give the number of kilobits in the

EPROM. For example, the 2732 has 32 kilobits of memory

arranged in a 4096 3 8 pattern – that is, 4 kilobytes. A 12-

bit address (2

¼ 4096) is necessary to address 4 kilo-

bytes. The chip also has eight output pins – one pin each

for the þ5 V power, the ground, and the 25 V programming

voltage, and a chip-enable pin. The 2732 chip has 24 pins

and is programmed by entering 0s into the desired memory

locations since all the bits are 1s upon delivery or after

erasure. Programming is accomplished by applying þ25 V

to the OE/VPP programming-voltage pin, while the

address of the byte to be programmed is applied to the

appropriate address pins at the same time that the desired

8-bit pattern is placed on the output pins. When all voltage

levels are stable, a 50 ms TTL low-level pulse is applied to

the CE/PGM chip-enable pin.

Programmers for PROMs are designed to apply the

proper voltages in the required sequence to the PROMs.

Programmers in kit form cost less than $100. Fully

assembled programmers cost from $200 to $500 – the more

costly ones have the capability to program a wide variety of

EPROMs as well as copy and verify EPROM codes. The

programmers generally are controlled through the serial

port of a personal computer, and software is supplied with

the programmer and loaded into the computer. The PROMs

are useful in experimental work because they can be pro-

grammed to reproduce fairly complex truth tables, elimi-

nating the need for several different logic chips. The truth

table of Table 6.34, for example, can be fully implemented

wit

h a PROM having as few as 32 3 4 bits.

The implementation of truth tables with PROMs is inef-

ﬁcient because, in practice, only a limited number of var-

iable combinations are actually used. With a PROM, all

possible combinations of all the input variables are repre-

sented, resulting in a large bit count, most of which is never

used. Programmable array logic (PAL), programmable

logic arrays (PLAs), and ﬁeld programmable gate arrays

(FPGAs) permit the economical realization of logic

DIGITAL ELECTRONICS 459

expressions with a limited number of inputs and terms. The

units perform the functions of a custom IC. Of the three

devices, the PLAs and FPGAs are the most ﬂexible. Pro-

grammers for these devices are more complicated than

PROM programmers and cost, with software, several hun-

dred dollars for professional models and a few hundred

dollars for student models. XILINX, Altera, and Actel

are manufacturers of programmable logic devices. Cur-

rently FPGAs with as many as 10

gates are available for

a few tens of dollars. The two most used languages for

programming FPGAs are VHDL and Verilog. The acronym

VHDL stands for VHSIC Hardware Description Language,

and VHSIC refers to the Very High Speed Integrated Cir-

cuit program originally sponsored by the Department of

Defense for the development of high-speed integrated cir-

cuits. A working knowledge of VHDL is beyond the scope

of the average scientist, however it is quite practical to

implement rather complex codes using the very large vari-

ety of VHDL templates supplied by the manufacturers of

FPGAs. The software necessary to implement VHDL codes

is supplied by the manufacturer of the FPGAs and includes

all steps including logic checking and simulation for imple-

menting the code on an FPGA device. Communication with

the FPGA is through a USB link to a PC.

6.6.9 Logic and Function

To illustrate the ideas in the preceding sections on digital

logic, we now discuss a method for designing an interlock

circuit for a vacuum system.

High-vacuum systems often have a vacuum chamber

connected to a turbomolecular pump through a gate valve

(see Section 3.6.1). The turbo-pump has a high-pressure

outlet

connected to a mechanical rotary pump or dia-

phragm pump via a foreline and foreline valve. A bypass

roughing line with a roughing valve may be used for pre-

liminary evacuation of the chamber. Before this is done,

however, the foreline valve is closed. When the pressure in

the chamber is sufﬁciently low, the roughing line is closed,

the foreline valve is opened, and the chamber is turbo-

pumped through the gate valve.

To guard against accidents, it is worthwhile to have a

system of interlocks that activates valves in the proper se-

quence and turns the turbo-pump off in case of an accident.

The interlock system consists of sensors that continuously

sample the variables in the v acuum system, such as cooling-

water temperature, cooling-water pressure, foreline pressure,

vacuum-chamber pressure, and roughing-line pressure. The

security of the system depends on whether the physical

property sampled is above or below a predetermined thresh-

old. The second section of the interlock system is the logic,

which, with combinations of elementary gates, establishes

the relationships between the input variables from the sen-

sors and the output functions that control the various vac-

uum-system operations – such as the opening and closing of

the various valves and the application of voltage to the turbo-

pump. Because the output functions only assume one of two

values, the interlock system can be analyzed using either

Boolean algebra or Karnaugh maps. Examples of increasing

complexity are given below. A way of implementing the

system with a data selector is also discussed.

The simplest practical interlock system monitors the

cooling-water temperature and pressure, and turns off the

voltage to the turbo-pump if the water temperature is too

high, the water pressure is too low, or both. A truth table

relating the variables to the function is shown in Table

6.32. The letters and numbers in parentheses are logic

symbols

assigned to the variables (A, B), function (X),

and states of the variables (0, 1). The Boolean logic expres-

sion for the truth table is:

X ¼



A 



B ¼

A þ B ð6:51Þ

This is obtained by noting the condition under which

X is in the logical 1 state. Had there been more than one

occurrence of 1 for X, the expression would have

additional OR terms. The Boolean expression can be

implemented with the inverter-and-gate arrangement of

Table 6.32 Truth table

Variables Function

Water

Pressure (A)

Water Temperature (B) Diffusion Pump

Heater (X)

Low (1) Low (0) Off (0)

Low (1) High (1) Off (0)

High (0) Low (0) On (1)

High (0) High (1) Off (0)

460 ELECTRONICS

Figure 6.96. A bimetallic-switch temperature sensor can

provide the water-temperature variable, and a diaphragm-

type pressure sensor can provide the water-pressure varia-

ble. Power to the turbo-pump is controlled by a heavy-duty

relay actuated by a solid-state, optically isolated relay

driven by the output of the logic circuit. A practical circuit

is shown in Figure 6.97. It is assumed that logical 0 is less

than

0.8 V and logical 1 is greater than 2.4 V, consistent

with TTL logic. Optical isolators provide an effective inter-

face when controlling power circuits from logic circuits.

An optical isolator contains both an infrared-emitting

diode and a photodetector arranged in a single package,

so that the light from the diode is efﬁciently transmitted to

the detector through a transparent dielectric medium that

provides electrical isolation. The diode–detector pair is

shielded from ambient light by opaque encapsulating

material. Since only infrared radiation is used to commu-

nicate between diode and detector, there is no electrical

connection between the two. The communication is also

unidirectional, because the detector cannot provide a sig-

nal that can couple back to the diode. Typical applications

for isolators are elimination of common mode input signals

Figure 6.96 Gate arrangement corresponding to

Table 6.32.

Figure 6.97 Practical circuit for a vacuum-system interlock according to the truth table

of Table 6.29.

DIGITAL ELECTRONICS 461

and ground loops, level shifting between two circuits, logic

control of power circuits, and isolation of logic circuits

from noise. The last application commonly occurs when

using the output logic levels on a computer to control

external devices. Infrared-emitting diodes and photodetec-

tors are inherently nonlinear devices, but some isolators

are specially made for linear analog circuits. Photodiodes,

phototransistors, photo-Darlington transistor pairs, and

phototriacs are the detector units in isolators. Important

parameters to consider when choosing an isolator are the

isolation voltage, ratio of output current to light-emitting-

diode input current, and output power-handling capabil-

ities. Trans istor isolators have transfer ratios from 2 to

over 50%, while the Darlington transistor pairs have

ratios from 50 to 500 %. Iso lat ors wi th triac outputs

require i np ut trigger currents in the 10 to 30 mA ra nge

in order to switch 120 V a .c. at curre nts up to a few hun-

dred milliamperes. This is sufﬁcient to drive high-power

triacs, solenoids, small motors, and mechanical relays.

For proper isolator operation, the c haracteristics of the

output stage must be matched to the load. Data sheets

should be consulted. A common package for low-power

isolatorsisasix-pinDIP.

When switching transformer loads, solenoid valves,

contactors, lamp loads, and heaters, output current rating

should exceed the load rating by at least a factor of two.

Solid-state relays provide isolation, and an important

application of solid-state relays is the interface between

computers and power devices. OPTO 22 makes a line of

solid-state relays that can be turned on and off with stand-

ard TTL signal levels. The 120D10 can be used to switch up

to 10 A of a.c. current at 120 V, with a maximum voltage

drop of 1.6 V. The control circuit and switching circuits are

electrically isolated from each other up to 4 kV, and switch-

ing of the load occurs at zero voltage in the a.c. cycle,

thereby eliminating switching transients. Because of the iso-

lation between control signal and load, the circuit supplying

the control signal is protected from voltage spikes. The

relays are 1.2 in. high, 2.4 in. long and 1.8 in. wide.

A more useful interlock system using three variables and

two functions has the truth table of Table 6.33. The vari-

ables

monitored are water pressure and temperature and

turbo-pump foreline pressure. The functions are the turbo-

pump (on or off) and the gate valve (open or closed). The

Boolean expression is also given in the table, while the

Karnaugh map is shown in Figure 6.98 . In the map for Y,

the

1s are adjacent in the 10 column, so that Y is independ-

ent of the state of C.

As a ﬁnal example of logic design, consider incr easing

the number o f variables to ﬁve by includi ng the rough-

ing-line pressure and chambe r pre ssure and a dding the

roughing valve and foreline valve to the functions. With

ﬁve variables there will be 2

(or 32) combinations.

Table 6.33 Three-variable, two-function interlock

Truth Table

Variables Functions

Water

Pressure

(A)

Water

Temperature

(B)

Foreline

Pressure

(C)

Turbo-

Pump

(X)

Gate

Valve

(Y)

low (0) low (0) low (0) off (0) closed (0)

low (0) low (0) high (1) off (0) closed (0)

low (0) high (1) low (0) off (0) closed (0)

low (0) high (1) high (1) off (0) closed (0)

high (1) low (0) low (0) on (1) open (1)

high (1) low (0) high (1) off (0) open (1)

high (1) high (1) low (0) off (0) closed (0)

high (1) high (1) high (1) off (0) closed (0)

Boolean Expressions

X ¼ A 

B  C

Y ¼ A 

B  C þ A  B  C

Y ¼ A 

BðC þ CÞ

Y ¼ A 

Figure 6.98 Karnaugh map for the truth table of

Table 6.33.

462 ELECTRONICS

Systematic design of the interlock circuit will ensure that

none of them is left out. The truth table is given in Table

34. As an alternative to the Boolean expressions for

the

truth table o r a map, we can use a data selector to

establish the relationships among the variables and func-

tions. A 5-bit d ata selector has 5 input address lines , 1

output line, and 32 data lines. Depending on the 5-bit

input address, the state of the addressed input line is

transferred to the output line. Implementation of the

expression for Y is shown in Figure 6.99(a). A 4-bit data

Table 6.34 Five-variable, four-function interlock truth table

(A)

(B)

foreline

(C)

roughing

(D)

chamber

(E)

Turbo Pump

(X)

Gate Valve

(Y)

Roughing Valve

(R)

Foreline Valve

(W)

0 (low) 0 (low) 0 (low) 0 (low) 0 (low) 0 (off) 0 (closed) 0 (closed) 0 (closed)

0 0 0 0 1 (high) 0 0 0 0

0 0 0 1 (high) 0 0 0 0 0

000110 0 0 0

0 0 1 (high) 0 0 0 0 0 0

001010 0 0 0

001100 0 0 0

001110 0 0 0

0 1 (high) 0 0 0 1 (on) 1 (open) 0 1 (open)

0 1 0 0 1 0 0 1 (open) 0

010101 1 0 1

010110 0 1 0

011000 0 0 0

011010 0 1 0

011100 0 0 1

011110 0 1 0

1 (high) 0 0 0 0 0 0 0 0

100010 0 0 0

100100 0 0 0

100110 0 0 0

101000 0 0 0

101010 0 0 0

101100 0 0 0

101110 0 0 0

110000 0 0 0

110010 0 0 0

110100 0 0 0

110110 0 0 0

111000 0 0 0

111010 0 0 0

111100 0 0 0

111110 0 0 0

DIGITAL ELECTRONICS 463

selector [see Figure 6.99(b)] can also be used by employing

a foldback arrangement. Looking at the A, B, C, and D bits,

one sees that there are 16 pairs of combinations of A, B, C,

and D that are independent of whether E is 1 or 0. For each

of the 16 pairs, the function Y is independent of the state of

E, equals E, or equals

E. The 16 input lines of the 4-bit data

selector will each have 0, 1, E,or



E attached to them.

Even more complexity can be built into the circuit by

having time delays on the functions so that one valve is not

opening while the other is closing. Extra functions, such as

turning on and off and venting the mechanical pump, can

also be added. This systematic method of analysis ensures

that nothing is overlooked. By noting when two functions

change state upon the change of state of a variable, deci-

sions about sequencing can also be made.

6.6.10 Implementing Logic Functions

Implementing functions with transistor gates requires that

the 0 and 1 states be associated with voltage or current

levels. There are a large number of logic families, all of

which have internally consistent 0 and 1 levels, but which

are not necessarily compatible. The choice of a logic fam-

ily for the implementation of a given function depends on a

number of factors – among them are speed, power dissi-

pation, immunity to noise, number of available functions,

cost, and compatibility with external circuits and other

logic families. A summary of the properties of the most

common logic families is given in Table 6.35. As can be

seen

from the table, there is a tradeoff between speed and

power dissipation – the fastest logic dissipates the most

power per gate and the slowest dissipates the least. In an

effort to reduce power dissipation while maintaining

speed, nominal voltage levels have been reduced to 3.5

and as low as 2.5 V for some logic families from the nom-

inal TTL 5 V. Noise immunity is measured by noise mar-

gin, the meaning of which is illustrated in Figure 6.100.In

general,

logic families are not directly compatible – trans-

lator chips exist for interfamily conversion, and some sim-

ple conversion circuits are given in Figure 6.101. The

abbre

viations SSI, MSI, LSI, and VLSI stand for small-

scale integration, medium-scale integration, large-scale

integration, and very large-scale integration, and are used

to specify the number of gates on a chip. SSI is less than 12

gates per chip, MSI is between 12 and 100, LSI is more

than 100, and VLSI is more than 1000. Simple logic func-

tions employ SSI and MSI.

The most common logic family has been TTL (transistor-

transistor logic) and its variations, but CMOS logic (com-

plementary symmetry, metal-oxide semiconductor) has now

largely displaced TTL because of its low power consump-

tion and wide range of usable power-supply voltages.

Emitter-coupled logic (ECL) is only used when the highest

speeds are required. The ECL 10 000 series is a slower

version of the ECL II series and is not so sensitive to the

quality of the interconnections. With the II series, a circuit

Figure 6.99 Implementation of the Y-function of the truth

table of Table 6.34 with (a) a 5-bit data selector and (b) a 4-

bit

data selector using a fold back arrangement.

464 ELECTRONICS

board with a ground plane must be used and the intercon-

nections carefully laid out to minimize cross-coupling.

Important changes in the semiconductor electronics

industry in the last few years reﬂect new technologies as

well as new philosophies in electronics. Whole new fam-

ilies of logic have been born – based on CMOS, Schottky,

and gallium arsenide (GaAs) technologies. Portable elec-

tronic devices from laptop computers to cell phones and

personal digital assistants require high-speed and low-po wer

electronics. The inherently lo west-po wer technology is

Table 6.35 Logic families

Logic

Family

Propagation

Delay (ns)

Power Dissipation

(mW/gate)

0-Level (V) 1-Level (V) Noise Margin,

Low/High (V)

Fanout Power

Supply (V)

TTL:

54/74 10 10 0.2 3.9 0.3/0.7 10 +5

54/74LS 10 2 0.2 3.9 0.3/0.7 20 +5

54/74F 4 4 0.2 3.9 0.3/0.7 33 (50LS) +5

CMOS:

54/74C 30 0 0.2 4.8 0/7/0.6 >50 (10LS) +5

54/74HC 10 0 0.2 4.8 0.7/0.6 >50 (10LS) +5

54/74HCT 8 0.010 0.2 4.8 0.7/0.6 >50 (10LS) +5

4000 CD

= 5V 115 0.005 0.05 4.95 1.0 50 +5

= 15V 40 0.060 0.05 14.95 2.5 50 +15

ECL:

10,000 3 24 1.75 0.90 0.3/0.3 10 5.2

100,000 0.8 40 1.75 0.90 0.3/0.3 10 4.5

Figure 6.100 Illustration of ‘‘noise margin.’’ Noise margin for

1-state ¼ V

OHmin

-V

IHmin

, noise margin for 0-state ¼ V

ILmax

–V

OLmax

DIGITAL ELECTRONICS 465

Figure 6.101 TTL, CMOS, ECL, and discrete transistor interface circuits. (a) CMOS-TTL and TTL-CMOS (the value of R is

determined by rise time and loading considerations). From McMOS Integrated Circuits Data Book, Motor ola, Inc, 1973.

is determined by V

:0X for V

¼5V,

500 X for V

¼ 10 V, 1 k X for V

¼ 15 V); (c) ECL-TTL and TTL-ECL (from MECL System Design Handbook, 2nd edition, W.

R. Blood, Jr., and E. C. Tynan, Eds., Motorola Semiconductor Products, 1972. Copyright of Motorola, Inc. Use d with

permission.)

466 ELECTRONICS

CMOS, but it has suffered in the past from low speed. This

has largely been overcome with the HC and HCT logic

lines. Both are directly compatible with the older TTL

LS families, but offer greatly improved speed-to-power

ratios. Because TTL high levels can be as low as 2.2 V,

there can be difﬁculties driving HC devices from TTL out-

puts. This is overcome with the HCT family, which is

completely compatible with TTL over the full range of

TTL operating parameters. The HC logic has now replaced

the TTL LS family. The 4000 D series of CMOS can

operate with supply voltages from +5 to +15 V and is used

in conjunction with higher-voltage analog circuits.

FAST

[TM]

logic is based on Schottky technology and

approaches ECL 10 000 logic in speed, but with much

lower power consumption. FAST devices bear the desig-

nation 54/74F and have the advantage of TTL logic levels

while avoiding the smaller voltage swings and lower noise

margins of ECL.

FAST is a trademark of Fairchild Cam-

era and Instruments Corporation and is an acronym for

Fairchild Advanced Schottky TTL.

Because TTL is still used in some applications, a few

simple TTL circuits are given in Figure 6.102. The mechan-

al contact conditioner [Figure 6.102(a)] ensures that the

tput from a mechanical switch will be a single transition

rather than the series of voltage spikes normally resulting

from the mechanical bouncing of the contacts. Transistor-

transistor logic gates are either edge or level triggered. Edge

triggering refers to the transition between the 0 and 1 levels

(positive edge) or 1 and 0 levels (negative edge). Level

triggering occurs when the 0 or 1 is attained. Data sheets

specify the type of triggering each logic unit requires.

With most logic families, there is the tendency to gen-

erate current spikes during switching; this creates power-

supply noise. To reduce this noise, the power supply must

be decoupled with capacitors from the logic circuits. A

0.01 lF ceramic capacitor for each gate and an additional

0.1 lF capacitor for each 20 gates are generally sufﬁcient.

Counters and shift registers are especially sensitive to

power-supply noise and should be decoupled with a 0.1 lF

capacitor for every two devices. For optimum perform-

ance, unused inputs should be set to logic level 0 by direct

connection to ground or logic level 1 by connection to the

power-supply voltage through a 1 to 10 kX resistor.

Some additional features of TTL are three-state outputs

and open-collector outputs. A three-state output has the

standard 0 and 1 levels and also a high-impedance, inac-

tive state . In this state, the output assu mes the level of any

active output connected to it. The three-state outputs are

designed to be connected together in a common line or

bus structure so that when any single output is active, a ll

the others assume its level. The open-c oll ec tor output

requires a collector resistor to the power supply for oper-

ation. When connected together, open-collector outputs

allow one to implement an output AND function (often

incorrectly termed wired-OR) that is, when any output is

0, all become 0. Open-collector outputs have the disad-

vantageofreducedtransitionspeedandhighoutput

impedanc e in the 1 sta te. They are usuall y used as line

drivers.

6.7 DATA ACQUISITION

6.7.1 Data Rates

When designing an experiment, one important considera-

tion is the rate at which data are collected. It is usually

useful to think of an experiment in terms of sampling rate,

sampling time, and measurement precision. Consider a

spectroscopy experiment where the output of a monochro-

mator is incident on a photomultiplier tube – the output of

which are pulses of electrons that are recorded with a coun-

ter. The monochromator is stepped at a regular rate and

predetermined step size over the wavelength interval of

interest. The time spent at each step combined with the

number of steps determines the total number of counts

recorded. If the total number of signal counts in any interval

is C

and the number of noise counts is C

, the total number

of counts, C

,isC

þC

. The statistical uncertainty in C

ﬃﬃﬃﬃﬃﬃ

, and that in C

ﬃﬃﬃﬃﬃﬃﬃ

. The uncertainty in determin-

ing C

is therefore

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ C

, so the relative uncertainty is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ C

=ðC

 C

Þ. The counts increase linearly with

the time of measurement, but the relative uncertainty only

decreases as the inverse square root of the time of the meas-

urement. The data rate is the number of counts in a meas-

urement interval divided by the interval time.

Bits, bytes, wor ds, and characters are all used to specify

the amount of information. The number of bits necessary

to specify a given integer decimal D is given by N ¼

3.32 log

D. If N is a noninteger, it is rounded to the next

higher integer. If the decimal number is signed (that is, plus

DATA ACQUISITION 467

Figure 6.102 TTL signal-conditioning circuits: (a) mechanical-contact conditioner; (b) pulses from step inputs

(step duration must exceed output-pulse width); (c) edge triggering; (d) 60-Hz TTL square wave from the power line;

(e) TTL to LED.

468 ELECTRONICS

or minus), another bit is added. Eight bits make a byte, and

two bytes (16 bits) commonly, but not always, make a word.

A character is the equivalent of one word. If data are to

be transferred from the counter to a printer or other display

or storage device, the data acceptance rate of the device

must match the data output rate of the counter. Data rates

are often speciﬁed as a baud rate, which is the number of

times per second there is a transition on the signal line

from 0 to 1 or from 1 to 0.

For two devices to be compatible, a number of param-

eters must match. These include frequency response, volt-

age levels, timing, format, code, hand-shaking protocols,

and housekeeping procedures.

6.7.2 Voltage Levels and Timing

The most positive and most negative voltages correspond-

ing to the two logic states must match. For example, TTL 0

and 1 logic levels are þ3.2 and þ0.2 V, while ECL 0 and 1

levels are 0.75 and 1.55 V. Furthermore, the sign of the

logic must be identical – that is, positive or negative. Pos-

itive logic means that the more positive voltage level is

taken as a logical 1, and the more negative as logical 0.

The reverse is true for negative logic. If the signs do not

match and everything else is satisfactory, only inversion of

the input signal will be required.

Often a digital input or output circuit is compatible with

a logic family of which it is not a member. The 54/74C,

HC, and HCT families are TTL-compatible, for example,

which means that the voltage levels are compatible. The

sinking and sourcing capabilities may be very different,

however, for so-called compatible logic families. Sinking

has to do with the number of gates that can be attached to

the output of a single gate and still maintain reliable oper-

ation. With TTL logic, when an output is at logical 0 it

must be able to hold all inputs connected to it at logical 0.

Since this condition is a consequence of the input transis-

tors being in saturation, the output must be able to sink all

the saturation currents and still keep the inputs at their

required levels. A TTL output at logic level 1 attached to

a TTL input will turn off the input transistor, and very little

current will ﬂow in the input circuit. This is the sourcing

speciﬁcation. Fan-in and fan-out are directly related to the

sinking and sourcing capabilities of a gate. Fan-in is the

maximum number of logic inputs to a gate for reliable

operation, while fan-out is the number of logic outputs it

can drive reliably. These speciﬁcations should be carefully

considered when connecting two different logic families.

Timing is also important – the required rise and fall times,

as well as pulse widths, must be compatible. Timing dia-

grams show the relationship between signals and should be

consulted. Converter chips that change the signals from

one logic family directly to another are available.

6.7.3 Format

A serial format has all data on a single line in a sequential

pattern. This is economical as far as wiring is concerned,

but slower than a parallel format where there can be as

many data lines as bits, and all of the bits in a word are

transferred at the same time. This is the fastest way to

transmit data, but the least economical.

There are also parallel-serial formats where the data are

transmitted in sequential parallel codes. An eight-bit byte,

for example, could be transmitted with four lines as two

four-bit words. A synchronization code is necessary with

such an arrangement to be able to distinguish between the

beginning and end of a single byte string. It is possible

to convert from a serial code to a parallel code and vice

versa with converters that use shift registers. For serial-to-

parallel conversion, data are sent to the registers from

one end and then read from the outputs of each stage. For

parallel-to-serial conversion, data are put into each register

simultaneously and then extracted from the last register

sequentially, a bit at a time. Data transmission in one direc-

tion over a single line is called simplex, in two directions

over a single line is called half duplex, and in two directions

simultaneously, with a single line and two coding frequen-

cies or two separate lines, is full duplex. Data conversion

ICs called universal asynchronous receiver-transmitters

(UARTs) take a wide variety of data formats and convert

them to standard codes, one of which is ASCII (American

Standard Computer Information Interchange). The ASCII

computer code is given in Table 6.36.

major difﬁculty in setting up data-handling equipment is

the interface. The RS232C serial interface can handle data

rates to 20 kbps – it has a high input impedance (3 to 5 kX),

uses relatively high voltage (þ25 V), and is unbalanced and

therefore noise-susceptible. The pin assignments for the

DATA ACQUISITION 469

standard 25-pin connector used with this interface are giv en in

Figure 6.103. More adv anced interfaces such as the RS485

e balanced circuitry and can handle data rates well in excess

of 10 Mbps (megabits per second). There are computer inter-

faces designed to handle data rates to hundreds of Mbps.

Modems (modulator-demodulators) are devices for

converting a binary code to audio frequencies (300 to

3300 Hz) for transmission over telephone lines, and recon-

verting the audio frequencies to binary. They are separate

units to which both a telephone receiver and a data termi-

nal can be attached.

6.7.4 System Overhead

In all data-transmission schemes there are additional sig-

nals that are nec essary to assure that the data transfer

occurs correctly. These are sometimes called housekeep-

ing signals. In the c ase where such information is

exchanged back and forth between the sending unit and

the receiving uni t, they are called hand-shaking.These

additional signals contribute to what is called the system

overhead – that is, additional data c apacity which must

exist independent of the useful information transmitted.

When data are transferred at a regular rate between two

units, they must be kept in step. A sync bit is often used to

assure synchronization between the two units. When

data are transferred at a variable rate that depends on

other independent parameters of the system, they are

said to be asynchronous. In this case, the sending unit

must ale rt the receiving unit of t he c oming of data, and

the receiving unit then should give a ready to receive

signal, after which the data are transferred. When

data transfer is complete, an end of data signal is also

usually sent. Without these signals, there can be no reli-

able data transfer.

To ensure the reliability of data transfer and detect errors

in the transmission, an extra parity bit can be sent. One

scheme requires the parity bit to be 1 when the sum of the

data bits is even and 0 when the sum is odd (see Table

6.29). At the receiving unit, data bits are summed and

compared with the parity bit – if there is consistency, the

data are accepted; if not, they are rejected. A more

Table 6.36 ASCII computer code

00001111)b

00110011)b

YYYY01010101)b

0000NULDLESP0@P\ p

0001SOHDC1! 1AQaq

0010STXDC2$ 2BRbr

0011ETXDC3# 3CScs

0100EOTDC4$ 4DTdt

0101ENQNAK%5EUeu

0110ACKSYN&6FVfv

0111BELETB# 7GWgw

1000BS CAN( 8HXhx

1001HT EM ) 9I Yiy

1010LF SUB

:JZjz

1011VT ESC+ ; K[ k{

1100FF FS , <L\ l |

1101CR GS ¼M] m}

1110SO RS . >N^n~

1111SI US / ?O_oDEL

7-bit code gives 2

¼128 different words Columns 1 and 2 are machine commands such as carriage return (CR), line feed (LF), escape

(ESC), etc.

470 ELECTRONICS

elaborate way of ensuring integrity is to have the receiving

unit echo the received data back to the sender, where they

are compared with the original data. Any differences cause

the data to be rejected. This system minimizes transmis-

sion errors at the cost of additional complexity and lower

speed.

Returning to the example of the spectroscopy experi-

ment in Section 6.7.1, if the expected signal produces

counts per second and the background is 10 counts

per second, the statistical error after one second is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 10

=10

ﬃ 1%. If the counting interval is one sec-

ond, at least 13 bits are needed for the data alone. To be

safe, 16 bits should be used, with the extra bits reserved for

housekeeping functions. This data transfer rate of 2 bytes

per second is very modest. It is necessary, however, to

consider the true rate of data transfer. If the data are held

on the output lines of the counter for only 10 ms, the

effective rate is 200 bytes per second.

In order to reduce the timing requirements of the counter, a

latch can be used on the output lines to hold the data for a

predetermined amount of time regardless of the subsequent

status of the lines. The operation of a 4-bit latch based on four

D ﬂip-ﬂops (Table 6.31) is illustrated in Figure 6.104.Dataat

the

input lines to the latch (A

,andA

) are transferred

to the output lines (B

,andB

) when the control line

is activ ated. In the absence of a start signal on the control line,

the output levels cannot change even though the input levels

do. In this way, data can be held on the output lines for a time

sufﬁ cient for them to be processed by the subsequent data-

receiving unit. The timing relations among the various signals

are important for proper operation of the latch. The control

signal must arriv e when there are valid data on the input lines.

A data buffer serves a purpose similar to a latch. It holds

receiv ed data for processing by subsequent units or circuits.

Printers, which are inherently slow because they are mechan-

ical devices, often have data b uf fers that hold the input data

Figure 6.103 RS232C serial interface: 25-contact connector pin assignment.

DATA ACQUISITION 471

until the printing mechanisms can transfer them to paper.

The buf fer is then ready to accept another batch of data.

6.7.5 Analog Input Signals

The spectroscopy experiment discussed above could be

modiﬁed by using a detector with an output current propor-

tional to the incident light intensity, as in Figure 6.105.To

con

vert the current to a digital signal requires an ADC. The

resolution of the ADC is determined by the number of

output bits, and the analog signal must be compatible, both

in magnitude and in sign, with the input requirements of

the ADC. If the ADC accepts only a voltage with a max-

imum full-scale value of 1.0 V and the analog signal has a

current maximum of 10

8

A, conversion from current to

voltage can be made using an operational ampliﬁer with a

variable-gain element. Response and sampling times must

be considered. The analog input to the ADC must remain

constant long enough for the ADC to respond. This is

called the settling time. For times less than the settling

time, the ADC output will not be a valid representation

of the analog input.

Voltage-to-frequency converters provide an easy way to

convert analog signals into digital form. Consider the

AD537 converter manufactured by Analog Devices as an

example. Through the selection of two external resistors

and a capacitor, frequencies up to 100 kHz can be generated

with a maximum input current of 1.00 mA. The circuit for a

full-scale input of 1 V and a 10 kHz frequency maximum is

given in Figure 6.106. The combination of the 8.2 kX re

sis-

tor and 5 kX potentiometer sets the gain of the circuit. The

potentiometer is adjusted so that the output frequency is

10 kHz for a 1 V input. The 20 kX potentiometer nulls the

offset voltage of the input ampliﬁer. The linearity is

0.05 % of full scale at 25 °C, with a temperature coefﬁcient

of þ30 ppm of full scale per °C. To minimize noise, a

simple low-pass ﬁlter is used at the input. The 5 kX load

resistor, R

out

, allows the circuit to be reliably connected to

TTL logic. The circuit can be used to convert an analog

voltage to a digital word by connecting the output to a gated

counter. A four-digit decade counter gated for 1s will regis-

ter the input voltage to four signiﬁcant ﬁgures. A similar

circuit can be used to convert the output of an analog elec-

trometer to a digital format.

The circuit can also be used to integrate a varying analog

signal, as long as the signal variation occurs in a time that

is much longer than the reciprocal of the maximum fre-

quency. The area under the peaks in a gas chromatogram,

for example, can be recorded by connecting the output

from the chromatograph to a voltage-to-frequency con-

verter and using a counter to total the number of output

pulses. The scale factor depends on the maximum fre-

quency and full-scale input voltage.

Voltage-to-frequency converters can also be used for

frequency-to-voltage conversion. In this conﬁguration, the

input can be a TTL pulse train and the output is a voltage.

The circuit can be used as an FM demodulator, frequency

monitor, or motor speed controller. The AD537 voltage-to-

frequency converter, made by Analog Devices,

Figure 6.104 A 4-bit latch.

472 ELECTRONICS

Figure 6.105 Example of a light-measuring system using an ADC with a

sample-and-hold circuit at the input.

Figure 6.106 Voltage-to-frequency conversion circuit. A 1.00 V input gives

a 10 kHz output frequency.

DATA ACQUISITION 473

accommodates positive or negative input voltages and

negative currents. It operates from a single 5 to 36 V supply

and has a maximum full-scale frequency output of

100 kHz.

For the systems under consideration, the output current

must not be changing faster than the ADC can respond.

When the analog signal is changing too rapidly, a sample-

and-hold, S/H, circuit can be used ahead of the ADC.

Important parameters of a S/H circuit are the sampling

time and the output decay time. S/H circuits use a capacitor

as a memory element, with the sampling time proportional

to the capacitance. Because of leakage, capacitors cannot

permanently maintain their voltage – fast sampling circuits

with small capacitors maintain their output voltages for

much less time than slower circuits. The decay time is

the time for the output to fall to a ﬁxed fraction of the

original value. A ﬁgure of merit for S/H circuits is the ratio

of sampling time to decay time. For the simple S/H circuit

shown in Figure 6.107, a control signal closes the MOS-

FET

switch, and the 1 lF capacitor is charged with a time

constant R

C, where R

is the on resistance of the switch.

Typical values of R

are 10

to 10

X, giving a time con-

stant of 10

4

to 10

2

s for the sampling time. The decay

time depends on capacitor leakage, the off resistance of the

MOSFET, and the bias currents of the operational ampli-

ﬁer. When high-quality capacitors with polyethylene, pol-

ystyrene, polycarbonate, or Teﬂon dielectrics are used,

most of the decay will be due to current through the switch

(~10

9

A) and bias currents (10

9

to 10

8

A for an average,

low bias-current operational ampliﬁer). In this example,

the decay will be of the order of 2 to 20 mV/s. Special

MOSFET switches and operational ampliﬁers with

picoampere bias currents can reduce these decay times

even further.

6.7.6 Multiple Signal Sources: Data Loggers

A multiple-transducer, data-acquisition system is a

straightforward extension of the s ingle-transducer sys-

tem already described. Figure 6.108 shows one po ssible

rrangement. Such systems are useful when it is neces-

sary to monitor and recor d several d ifferent signa ls at

virtually the same time. If the transducers all have analog

outputs, the most convenient arrangement is an analog

multiplexer. The function of the multiplexer is to alter-

nately connect each of the analog signal lines to an ADC

circuit a nd the recordin g instrument. The switching

between the various signal lines is accomplished by sep-

arate control li nes. Multiplexing reduces the number of

circuit components at the expense of more complex con-

trol and synchronization circuits. With the system in

Figure 6.108, the data rate can be as much as four times

that

of a simple system.

6.7.7 Standardized Data-Acquisition

Systems

A number of companies manufacture complete data-

acquisition units speciﬁcally designed for the laboratory.

As long as the input signals are compatible and the data

rates are within the limits of the unit, they provide a fast

and efﬁcient means of constructing a data-acquisition

system. Data acquisition from multiple sensors is a com-

mon industrial situation and there are several kinds of

industrial data loggers. These, however, are designed for

reliability rather than ﬂexibility and are generally not

suited to laboratory data acquisition, where many different

kinds of transducers are used. There are two standardized

laboratory data-acquisition systems, nuclear instrumenta-

tion module NIM and CAMAC.

The NIM system consists of individual electronic units

that ﬁt into a mounting frame or bin, which has a central

power supply. The NIM bin is capable of powering several

individual units, depending on their size. The bin power

supply provides 624 V, 612 V, and usually 66V. Each

full-size bin has 12 slots in which instrument module units

Figure 6.107 A sample-and-hold circuit using a capacitor

as a memory element.

474 ELECTRONICS

can be placed. Units can occupy anywhere from one to six

slots. The bin power supplies and individual units have

been designed so that a bin can accept the full comple-

ment of modules without becoming overloaded. A short

list of standard NIM modules is given in Table 6.37. Inter-

conne

ctions between modules are made with coaxial

cable. In older units, B NC connections are common;

newer units use higher-density, LEM O- typ e connectors.

Input and output speciﬁcations are standardi ze d so th at

NIM modules can be connected together without compat-

ibility concerns. The NIM logic level speciﬁcations are

given in Table 6.38.

Originally

the NIM standard voltages were 612 V and

624 V. As the use of integrated circuits increased, a 66V

voltage was included in the standard. Modules operating from

612 V and 624 V supplies, howe v er , are still the most ﬂex-

ible, because all bins have these voltages. Where 66V is

required for a module in a 612/624 V bin, it is best to derive

it from within the module using the av ailable 612 V. Use of

Figure 6.108 A multiple-transducer data-acquisition system using a multiplexer.

Table 6.37 Modules available in NIM

Power supplies

Preampliﬁers, ampliﬁers

Discriminators

Coincidence units

Delays

Signal generators, pulse generators

Counters/timers

Gates

DACs and ADCs

Analog adders, subtractors, dividers, multipliers

Time to amplitude converters (TACs)

Signal averagers

Multichannel analyzers

Table 6.38 NIM Logic Levels

Output (must deliver) Input (must accept)

Digital Data

Logic 1 þ 4toþ 12 V þ 3toþ 12 V

Logic 0 þ 1to2V þ 1.5 to 2V

Fast Logic (50 X impedance)

Logic 1 14 to –18 mA 12 to 36 mA

Logic 0 1toþ 1mA 4toþ 20 mA

DATA ACQUISITION 475

high-current, 6 V modules in a 612/624 V bin should be

av oided because the regulation of the 612 V and 624 V sup-

plies will be degraded by the high current in the common

return line. Precise reference voltages should be produced in

the modules themselves, since the bin voltages hav e relatively

wide tolerances, 624.0 (þ0.7%), 612.0 (þ1.0%), and 66.0

(þ3.0%). The NIM po wer-connector pin assignments and

other details are given in Figure 6.109. The NIM standard

gic levels are not compatible directly with common logic

families such as TTL or ECL. The po wer-suppl y voltages are

also different from common logic supplies (þ5V) and opera-

tional-ampliﬁer supplies (þ15V). Some con version circuits

between NIM, ECL, and TTL le vels are gi ven in Figure 6.110.

uclear instrumentation module systems are limited

in complexity to hard-wired interconnections between mod-

ules. This becomes cumbersome when there are several

modules that must be linked together. To circumvent the

limitations of NIM systems, the CAMAC system was devel-

oped. This system retains the use of individual modules that

can be plugged into a central power supply unit – in this

Figure 6.109 NIM connector pin assignment (GP ¼ guide pin, GGP ¼ ground guide pin, GS-1 ¼ guide socket, GGS ¼

ground guide socket).

476 ELECTRONICS

Figure 6.110 (a) TTL-NIM conversion circuit, (b) Slow NIM-TTL conversion circuit, (c) Slow

NIM-TTL with a 4-input NAND gate, (d) Fast NIM to MECL III, (e) MECL III to fast NIM. (fast

NIM levels 17 mA, 0.200 V maximum high, 0.600 V minimum low; MECL threshold

–1.45 V. (From R. F. Nagel, NIM Fast Logic Modules Utilizing MECL III Integrated Circuits,

DATA ACQUISITION 477

case, a crate. The CAMAC crate, however, has a large

number of additional lines besides those for the power.

The additional lines form the data bus. The bus has 24

read and 24 write lines, 4 station sub-address lines, and 5

station function lines – each station has its own identiﬁca-

tion line and look-at-me (LAM) line. Common to all sta-

tions are two timing lines, three status lines, and three

control lines. These lines are connected to the control unit

(crate controller). Also connected to the controller are the

lines from the computer, generally divided into a set of

data bits and address bits. The controller interprets the

signals from the computer and sends appropriate signals

to the individual CAMAC units or stations. This is shown

schematically in Figure 6.111, with the line designations

ven in Table 6.39. With each of the units under digital

control,

it is possible, through the use of a computer con-

nected to the crate controller, to have systems capable of

extremely complex logic and control functions. Data can

be collected by the computer and stored, displayed, and

manipulated with a degree of complexity limited only by

the programming language used by the computer.

The CAMAC system offers hardware and software

compatibility among individual units. P rogramming

can be a formidable task because the information trans-

ferred between the crate controller and the computer is

a binary machine-language code that has no relation to

Figure 6.111 The CAMAC bus.

478 ELECTRONICS

the high-level languages used for scientiﬁc calculations.

An alternative is to write the codes in a high-level lan-

guage, such as FORTRAN, and at appropriate points in

the program call a machine-language subroutine that con-

verts the FORTRAN variables to the bit code necessary for

control of the crate modules. When done in this way,

machine-language programming can be relatively simple.

A CAMAC system can represent a considerable invest-

ment in money and in the time necessary to learn the

required programming techniques. The need for a com-

puter to run the system properly – and the computer

peripherals such as terminals, printers, and mass storage

units – are additional expenses. The advantage of the

CAMAC system is the complete ﬂexibility that it provides.

As in NIM systems, the individual modules are not costly

because there is no need for internal power supplies or

complex logic circuits. There are now several manufac-

turers offering lines of CAMAC crates, controllers, and

individual function modules. There are also NIM–

CAMAC adapters that permit one to run certain NIM mod-

ules under CAMAC control.

6.7.8 Control Systems

Control theory establishes a framework that enables one to

optimize an active system for accuracy, stability, transient

response, resistance to external perturbations, and internal

component changes. The method of analysis uses the Lap-

lace transform formalism in a way that is similar to that used

in circuit theory (see Section 6.1.5). Control theory is an

tablished engineering subject and there are many excel-

lent texts available. The purpose of this section is to give a

brief introduction to the subject and provide general infor-

mation on the analysis of systems and the proper conﬁgu-

rations for accomplishing given tasks.

All control systems, whether electrical, mechanical,

hydraulic, pneumatic, optical, thermal, acoustical, or elec-

tromechanical can be represented in terms of one of the

two block diagrams shown in Figure 6.112.

e ﬁrst system is open loop where the re is no signal

path from the output back to the input. An example is the

burner on the top of a stove. Once the position of the

burner switch or valve is set, there is no further control

over the burner output. The second system is closed loop,

in which a portion of the sampled output is sent back to

the input and compared with the input signal. An exam-

ple of a closed-loo p sys tem is the oven of a stove. The

temperature is s et by an external input and this input is

compared to a signal proportional to the temperature of

the oven. If the oven temperature exceeds the set

Table 6.39 CAMAC line designations

Line Code

(no. of lines used)

Command Function

N(1) Station number Selects station

A(4) Subaddress Selects section of station

F(5) Function Deﬁnes function

S(2) Strobe Controls phase of

operation

R(24) Read Parallel data to module

W(24) Write Parallel data from module

L(1) Look-at-me Request for service

B(1) Busy Operation in progress

X(1) Command

accepted

Module ready

Q(1) Response Status

Z(1) Initialize Sets module

I(1) Inhibit Disables module

C(1) Clear Clears registers

P(5) Extra lines

þ24V

þ6V



Power

Figure 6.112 Control system block diagram:

(a) open loop, (b) closed loop.

DATA ACQUISITION 479

temperature, the oven heat source is turned off; if the

oven temperature is less than the set temperature, the

source is turned on.

The standard method for testing an open-loop system is

to apply s ignals at the inputs of each stage, starting with

the last and proceeding to the ﬁrst – verifying the input

and output signals at each po int. This sequential testing

method cannot be used for a closed-loop system because

the input to each stage is related to the output of the

overa ll system.

All closed-loop systems have an input, an output, a sum-

ming or comparison unit, a controller, the working unit that

is controlled, a measuring or sampling unit, and a feedback

path. Once mathematical models for each of the units in the

system are developed and combined appropriately, the over-

all performance of the system can be evaluated and opti-

mized by varying the parameters of the model.

Each unit of a control system can be characterized by a

transfer or gain function. These functions describe how the

input to the unit is transformed by it and converted to the

output. The individual transfer functions themselves are,

in general, the solutions of ordinary, linear differential

equations that are most easily expressed in terms of Laplace

transforms (see Section 6.1.5). The full representation of

e system in terms of Laplace transforms is particularly

easy to assess with respect to stability, accuracy, and tran-

sient response.

Consider the general system shown in Figure 6.113 con-

sisting

of an input variable r(t), output variable c(t), and

transfer functions g

ðtÞ, g

ðtÞ and bðtÞ. The Laplace trans-

forms of these functions are



RðsÞ,



CðsÞ,



ðsÞ,



ðsÞ, and



BðsÞ respectively. The transfer function for the overall

system is:

gðtÞ¼

ðtÞg

ðtÞ

1 þ bg

ðtÞg

ðtÞ

ð6:52Þ

with the equivalent Laplace transform:



GðsÞ¼



ðsÞ



ðsÞ

1 þ



BðsÞ



ðsÞ



ðsÞ

ð6:53Þ



GðsÞ can be written as the ratio of two polynomials in s:



GðsÞ¼

PðsÞ

QðsÞ

ð6:54Þ

The roots of P(s) give the zeros of the transfer function,

and the roots of Q(s) give the poles of the transfer function.

The system is stable if the poles of the transfer function lie

in the left half of the complex s-plane.

System Response

(i) Sensitivity. Sensitivity S is a measure of the fractional

change in



GðsÞwith a fractional change in any part of the

system represented by the variable b. The smaller the S,

the less sensitive the system is to changes in any element of

the system:

S ¼



GðsÞ=



GðsÞ

Db=b

ð6:55Þ

As examples, S will be calculated for variations in the con-

troller transfer function



ðsÞand for the feedback,



BðsÞ:

Case 1: Relative change in



ðsÞ;

S ¼

1 þ



BðsÞ



ðsÞ



ðsÞ

ð6:56Þ

Case 2: Relative change in



BðsÞ;

S ¼



BðsÞ



ðsÞ



ðsÞ

1 þ



BðsÞ



ðsÞ



ðsÞ

ð6:57Þ

Figure 6.113 Block diagram of a generalized closed-loop

control system with schematic representations of the

transfer functions and their Laplace transforms.

480 ELECTRONICS

For Case 1, S is small when



BðsÞ,



ðsÞ, and



ðsÞ are

large. For Case 2, S is small only if



BðsÞ,



ðsÞ, and



ðsÞ

are small, so a system cannot simultaneously be made

insensitive to changes in the transfer function of the con-

trolled unit and transfer function of the feedback element.

The solution is to use a high-quality feedback element that

remains stable over a wide variety of conditions and to

increase the transfer functions of the other system elements

in order to stabilize the overall system with regard to their

changes.

(ii) Steady-state accuracy. The steady-state accuracy of a

system e

ðtÞ is the difference between the input signal rðtÞ

and the closed-loop signal from the output bcðtÞ taken in

the limit as t ! ‘. In terms of Laplace transforms, the

difference between the input signal and the closed-loop

signal from the output is:



RðsÞ



BðsÞ½1 þ



BðsÞ



ðsÞ



ðsÞ

: ð6:58Þ

In s-space, the limit as t ! ‘ is obtained by multiplying:



RðsÞ



BðsÞ½1 þ



BðsÞ



ðsÞ



ðsÞ

ð6:59Þ

by s and taking the limit as s ! 0:



¼ lim

s!0



RðsÞ



BðsÞ½1 þ



BðsÞ



ðsÞ



ðsÞ

: ð6: 60Þ

To evaluate



, it is necessary to specify the signal



RðsÞ.

For a unit step input



RðsÞ¼1=s (see Table 6.2) so that



¼ lim

s!0



RðsÞ



BðsÞ½1 þ



BðsÞ



ðsÞ



ðsÞ

: ð6: 61Þ

For simpliﬁcation assume a unity feedback system so

that



BðsÞ¼1. If then



ðsÞ



ðsÞ is of the form

FðsÞ=s

QðsÞ, where FðsÞ and QðsÞ are polynomials in s

and N > 1,



will approach zero and the output will

approach the input.

(iii) Proportional, Integral, and Differential (PID)

Control. The most general type of controller is one that

provides an output that is the sum of three terms – one

proportional to the difference between the reference sig-

nal and controlled signal, one proportional to the time

integral of the difference, and one proportional to the time

differen tial of the difference. These PID controllers use

operational ampliﬁers conﬁgured as direct gain elements,

integrators, and differentiators to attain these functions.

The Laplace transforms of the three functions give a

transfer function that has a form that depends on the

details of the operational-ampliﬁer circuits. As an exam-

ple, consider the circuit in Figure 6.114.Ithasthetransfer

nction:



GðsÞ¼

Kð1 þ sR

ð1 þ sR

ð6:62Þ

for R

þ R

¼ C



GðsÞcan be rewritten as the sum

of three terms:



GðsÞ¼K 1 þ

þ R



1 þ sR



ð6:63Þ

where the ﬁrst term is the P, the second the I and the last the

D. The unit represented by the transfer function



HðsÞ has

been added to limit the frequency response and increase

the overall stability of the system. Commercial PID con-

trollers allow one to adjust the absolute as well as the

relative weights of each of the terms to attain the optimum

overall system response. This generally means a response

that has the maximum bandwidth consistent with a phase

margin of approximately 60°.

Figure 6.114 PID controller circuit.

DATA ACQUISITION 481

6.7.9 Personal Computer (PC)

Control of Experiments

Computer operation of experiments is best suited to rou-

tine measurements on systems with a high degree of

reliability – the latter condition is not always met for

ordinary laboratory experiments. It is not worthwhile

to add a computer to an experiment that is intended to

make a limited number of specialized measurements.

Though it may be tedious, it is often much more efﬁcient

to take measurements by hand rather than purchase spe-

cialized measuring instruments, a computer or a com-

puter interface, and software, connect them together,

write the necessary software, and place the system i nto

operation. On the other hand, routine measurements in

an experiment that continually produces large amounts

of data are well suited to computer operation. Before

considering computer control it is important to com-

pletely understand the experiment. Special attention

should be given to the range of variables to be measured

and controlled, the response time of the system, and the

accuracy and precision of the quantities that are meas-

ured and controlled.

Two classes of computer-based measurement and con -

trol systems will be discussed. The ﬁrst is based on the

IEEE 488 or GPIB bus and requires measuring and control

instruments compatible with the bus as well as the com-

puter, interface circuit, and software. The second type of

system is based on an interface circuit that either ﬁts into

one of the computer expansion slots, or resides in a sep -

arate chassis an d is connected to the computer through a

standard data transmission link like the RS232 serial inter-

face. With the IEEE 488 system, sensors and transducers

are connected to individua l instruments, which, in turn,

are connected to the IEEE 488 bus. In the second type of

system, by contrast, sensors and transducers are directly

connected to the interface board via screw terminals or

coaxial connectors. In both systems, software is needed

for the host computer.

It is possible to purchase an IEEE 488 interface card

for a PC that will effectively control up to 12 IEEE 488-

compatible instruments, provided that there are no

restrictive timing or synchronization requirements.

Within the IEEE 488 system, all signal conditioning

and digital-to-analog conversion is done within the indi-

vidual instruments attached to the bus. The IEEE 488 bus

is separa te from the bus structure of the cont rol com-

puter, and communi cation is enti rely through th e inter-

face. Adapters for converting from the IEEE 488 bus to

the RS 2 32C interface are readily available. IEEE 488

data paths are 8 bits (1 byte) wide, and a complete data

transmission consists of two serial 8-bit bytes. Each unit

connected to the bus is autonomous, with its own power

supply.

Connections to the bus are throug h standard 24-pin

connectors (see Fig ure 6.115 ) arranged so that they

can

be stacked one on top of the other and connected

in a d aisy-chain con ﬁguration. There can be up to 15

interconnected devices on a single bus, but the total

transmission path length cannot exceed 20 m. Instru-

ments con nected to the bus are designated as talkers,

listeners, and controllers. A tape reader is a talker, for

example, while a signal generator is a listener. Some

instruments may be able to talk and listen, or even (like

a variable-range frequency counter) talk, listen, and

control. The bus itself is passive, and all the circuitry

enabling an instrument to talk, listen, or control is con-

tained within the instrument itself. Simple systems built

around the bus need not even use a controller, but can

have just one talker and one listener, as long as the

instruments have the built-in interface circuitry that

allows their functions to be assigned under so me form

of local control. The more usual conﬁguration with a

personal computer uses interface messages to assign

the function of talker or listener to instruments on

the bus.

For PC-based IEEE 488 systems, there is variation

among the software offered by the different manufac-

turers. Three criteria for choosing sof tware are ease of

use, ﬂexibility, and speed. Software that is easy to use is

generally slow and difﬁcult to adapt to special tasks. For

specialized applications ,softwaremusthavemany

options and a variety of functions. This re quires that

the experimenter spend additional time organizing and

assembling the ﬁnal progra m. If progr ams are to be fast

they must be written in assembly language – a time-con-

suming task.

A simple PC-controlled experiment for measuring the

dielectric constant of a liquid as a function of temperature

482 ELECTRONICS

is shown in Figure 6.116. In this experiment, a digital

impedance bridge, lock-in ampliﬁer, and digital voltmeter

are connected to a computer via an IEEE 488 bus. The

dielectric constant and conductivity of the liquid are cal-

culated from the measurement of the capacitance and

resistance of a liquid-ﬁlled cell. Measurements are made

over a range of temperatures, and a platinum resistance

thermometer is used to measure the thermostat tempera-

ture. Programming the IEEE 488 bus usually requires pro-

ﬁciency in a high-level language such as BASIC and

complete knowledge of the operation of each instrument

on the bus and its device-dependent commands. For the

system in Figure 6.116, timing is not a consideration and

the

measurement sequence can follow the simple ﬂow

chart in Figure 6.117.

Implementing the ﬂow chart with the IEEE 488 bus

requires knowledge of the characteristics of the instru-

ments on the bus. The thermomete r is a talker,andthe

digital voltmeter is a listener when its ranges are being

set, and a talker when sending the voltage readings to the

computer. To begin, the address of each instrument is set

with switches on their back panels. The instruments

are wired in daisy-chain fashion to the computer with

ribbon cable and the IEEE 488 piggyback plugs. Sufﬁ-

cient time must be provided in the program for instrument

readings to stabilize. This is done with wait loops inserted

in the program (see Figure 6.118). The input and output

ta formats for each instrument must also be accommo-

dated in the program so that the commands and data

from the computer a re correctly read by the instruments,

and the data from the instruments correctly read and

Figure 6.115 IEEE 488 interface-bus connector pin assignment. Logic levels are TTL-

compatible negative logic (‘‘1’’, 0 to 0.4 V; ‘‘0’’, 2.5 to 5.0 V).

Figure 6.116 A personal-computer-controlled IEEE 488

temperature-measuring system.

DATA ACQUISITION 483

stored by the computer. Even for this relatively simple

system, the BASIC program requires several lines of

code. For more complex s ystems with special timing

requirements, simple BASIC pr ogra ms may be too s low

or too inﬂexible. When this is the case, systems with

separate software packages are required. Such systems

are offered by Keithley Instruments and National Instru-

ments, among others.

Data acquisition and control systems based on I/O mod-

ules and boards that connect directly to a personal com-

puter are justiﬁed when there are a large number of

standard sensors and the cost of separate IEEE 488 instru-

ments is too great. For an I/O board system, it is necessary

to consider the number of input channels, the number of

output channels, input and common-mode signal levels,

sampling rates, measurement precision, and computer

and software requirements.

Interface boards can be programmed directly in BASIC

once the addresses of all the I/O ports are known. As with

all dynamic systems, timing is crucial, and routines must

be written to allow time for ADC conversions and data

storage. Interpreted BASIC programs are slow, while com-

piled BASIC has a considerable speed advantage. Opti-

mum speed and ease of programming are usually

accomplished with software supplied by the manufacturers

speciﬁcally for their interface boards. Such software

Figure 6.117 Flow chart for

measurement sequence in

system of Figure 6.116

Figure 6.118 IEEE-488 BASIC program example.

484 ELECTRONICS

has machine language subroutines for initializing the

ports and reading and writing data. These routines are

designed to be easy to use and can generally be called

from within a BASIC program. The more sophisticated

manufacturer-supplied software is menu driven, with true

foreground – background computer operation and graphic

data display with full interfacing to standard spreadsheet

packages. Since much more time is spent with software

than hardware, it is important that the programming mate-

rials supplied by the manufacturer be clear, easy to use,

and well documented.

A typical small, commercial, data-acquisition interface

circuit is shown in Figure 6.119(a). The details of analog

input

circuits are shown in Figure 6.119(b). In this exam-

ple,

there are four single-ended or two differential analog

inputs, each connected to a S/H circuit and analog multi-

plexer. The output of the multiplexer is connected to a

unit-gain instrumentation ampliﬁer, a programmable-gain

ampliﬁer, and a second S/H circuit. The output of the

second S/H is connected to a 12-bit ADC through a

signal-conditioning network. The ADC output goes

to the internal interface bus. Boards of this type plug

directly into the expansion slot of a personal computer.

Connections to the input circuits are made through the

screw terminals on the board.

Sample and hold circuits capture the analog input sig-

nals and hold for a time sufﬁcient for the ADC to convert

the analog signal to a binary output. The operation of the

S/H has already been discussed. Of particular importance

are the acquisition time, the aperture time, the decay time,

and the slew rate (the maximum large-signal change that

the S/H circuit can produce).

Input circuits can typically accommodate full-scale

input voltages from 20 mV to 10 V. The number of samples

per second is from 5000 to 10 000. With a 12-bit ADC, the

system has a maximum resolution of 1 part in 4000, or

0.025%. In practice, this resolution cannot be realized for

low-level input signals because of ampliﬁer zero and gain

drifts, noise, common-mode error signals, and ADC non-

linearities. These must all be taken into account and an

error budget established when assessing the ﬁnal accuracy

of the system.

Important analog output speciﬁcations for instrument

control are the resolution and the settling time required

to achieve the quoted resolution. Since the analog output

voltages are the input signals to other devices, output volt-

age and current ranges are important. The digital input and

output ports are usually 8-bits wide and operate with TTL

levels.

The primary concern when connecting sensors to a data-

acquisition system is elimination of noise. Noise can be

generated on the signal lines from magnetic ﬁelds, electric

ﬁelds, thermal gradients, friction, and improper grounding.

These noise sources can be controlled by proper choice of

input and output impedances and of lead-wire composi-

tion, length, shielding, and placement.

High output-impedance, current-source transducers are

less sensitive to magnetically induced noise than low

output-impedance, voltage-source transducers. It is impor-

tant to distinguish between ground and common (or return)

lines in transducer circuits. Ground lines do not normally

carry current, but return lines do. Return lines carry the

signal currents that complete the transducer circuit. Opera-

tional ampliﬁers normally have a single output terminal

and terminals for positive and negative power-supply vol-

tages. There is no separate common terminal, and the return

current must ﬂow in the power-supply lines. For this rea-

son, it is important to bypass the power-supply leads with

large, high-frequency ceramic disk capacitors located as

close to the ampliﬁer as possible.

When a return line is connected to ground at more than

one point in the circuit, it is possible to develop a voltage

across the line due to small dif ferences in ground potentials

and the ﬁnite resistance of the return line. Grounding the

signal return line at a single point in the circuit changes a

single-ended transducer conﬁguration to differential,andany

difference in ground potentials appears as a common-mode

voltage. When it is impossible to avoid multiple grounds in a

system, an isolator can be used between the transducer and

the input to the data-acquisition circuit. Because there is no

galvanic connection across an isolator, potential differences

between grounds cannot result in current ﬂo w.

Return lines should have the lowest possible inductance

and should overlap the signal lines as much as possible.

Shielded, twisted-pair cable is generally best for trans-

ducer connections. The shielding does not carry a current

and serves to reduce electric and magnetic noise pickup.

With twisted-pair cable, pickup is induced equally in both

wires and can be canceled by an ampliﬁer with a differ-

ential input. Twisted-pair cables in several sizes and

DATA ACQUISITION 485

Figure 6.119 (a) Data-acquisition interface; (b) analog input circuits.

486 ELECTRONICS

conﬁgurations are available from Belden and Alpha.

Cable-length guidelines are given in Table 6.40. In coaxial

cable,

the outer conductor is the return line.

A s maller source of noise is static discharges when

insulators of dissimilar material s rub against each other.

This is called triboelectric induction and can be elimina-

ted with special low-noise cable that has graphite lubri-

cant between dielectric surfaces. The ultimate obstacle to

complete noise elimination comes from thermoelectric

effects when junctions of dissimilar m etals are a t differ-

ent temperatures. Typical values are 0.1 lV/°C. Thermo-

electric solder (70% cadmium, 30% tin) can be used

for low-level circui ts, and precautions should be taken

to keep all circuit elements and devices at the same

temperature. Carbon and metal-ﬁlm resistors produce

larger thermoelectric voltages than precision wire-wound

resistors.

Once the sources of noise in the system have been

reduced to acceptable levels, input ﬁltering can be used

to improve the signal-to-noise ratio. Filtering cannot, how-

ever, eliminate the effects of improper wiring.

Example of Sensor and Control Electronics. In

this example, a silicon substrate inside an ultrahigh vac-

uum chamber is heated to a predetermined temperature

and then maintained at that temperature while an electron

gun directs electrons at the surface and a mass spectrom-

eter monitors the masses of the atoms and molecules emit-

ted from the surface. An ion gauge monitors the pressure

in the experimental chamber. The data from the experi-

ment are count rates as a function of mass spectrometer

setting. The rates are recorded and stored for subsequent

analysis. A schemati c representation of the system is given

in Figure 6.120. The system is a mixed digital and analog

syst

em with a computer supplying control and data-acquis-

ition functions, and the heater and thermocouple circuits

operating with analog signals. D/A and A/D circuits pro-

vide the translation between the digital and analog

domains.

It is most convenient to divide the overall system into

subsystems and determine the operating conditions for

each of them. In the example, the subsystems are:

 Substrate/heater

 Thermocouple temperature monitor

 DMM

 Picoammeter current monitor

 Mass spectrometer

 Electron gun

 Ion gauge

The substrate/heater and thermocouple temperature

monitor form the temperature control system that both

sends and receives signals to and from the computer. The

electron gun receives signals from the computer while the

DMM and ion gauge send signals. The mass spectrometer

both receives and sends signals. The signals it receives set

the mass range and scanning rate. The signals it sends are

pulses from the detector.

There are a number of manufacturers of computer inter-

face boards that are speciﬁcally designed for the control and

monitoring of experiments – among them are National

Instruments (manufacturer of LabVIEW), Hewlett-Packard

(Agilent), Keithley Instruments, and Datel. All have cata-

logs that describe their products in detail and provide very

useful information on the general conﬁguration of data-

acquisition and control systems. The purpose here is to

provide a plan of organization and guidelines.

The ﬁrst task is to deﬁne the operating parameters for

each of the subsystems. For the substrate/heater, this

means deﬁning the input power necessary to obtain the

required temperature of the silicon substrate. Once the

power is known, it is possible to deﬁne the power-supply

requirements and its programming input requirements. For

this example, the heater is a coil of tungsten wire that has a

resistance of 3 X at room temperature. The required max-

imum power was determined to be 81 W (27 Vat 3 A). This

is supplied by a 300 W power supply with a range of 0 to

30 V at 0 to 10 A. The power supply is voltage program-

mable with variable gain, so that an input voltage from 0 to

Table 6.40 Instrumentation cable-length guidelines

Signal Bandwidth Accuracy Maximum Cable Length

Source (Hz) (%) (ft.) (m)

4 to 20 mA <10 0.5 1000–5000 300–500

61to610 V <10 0.5 50–300 15–90

610 mV to 61 V <10 0.5 5–100 1.5–30

Shielded twisted pairs.

DATA ACQUISITION 487

10 V will vary the output from 0 to 30 V when the internal

gain of the power supply is set to three. The outputs of D/A

cards used for power-supply control are generally 0 to 1

and 0 to 10 V. When this is not sufﬁcient to drive the

output of the power supply to the required maximum

level, an intermediate gain stage will be required. The

supply that is used is current limiting. For this application,

the current-limiting control is set so that 3 A are available at

all voltage settings. This prevents excessive current draw

when the ﬁlament is cold – a necessary precaution for tung-

sten that has a temperature coefﬁcient between 4.5 and 8.9 3

3

per °C.

Because the programming voltage to the heater power

supply is in the range 0 to 10 V, a computer interface card

with a DAC is used that has a maximum analo g outpu t

voltage of 10 V. The input to the card is a 12-bit code

giving a maximum possible resolution of one part in

4096 or 0.025% at 30 V output. At 27 V, the resolut ion

is 0.0225% slightly exceeding the maximum available

resolution. The the rmocouple is a type K NiCr/NiAl,

with a working temperatur e range of 200to1300°C.

It is non-magnetic and compatible with the ultrahigh vac-

uum environment in which it is located. The thermocou-

ple wires are crimped to a copper lug that is ﬁxed to a stud

Figure 6.120 System for controlling the temperature of a silicon substrate while moni-

toring the atoms and molecules emitted from the surface under electron bombardment.

488 ELECTRONICS

on the stage holding the silicon substrate. The wires are

connected to the leads of a UHV thermocouple electrical

feedthrough. The leads on the atmospheric pressure side of

the feedthrough are connec ted to the signal conditioner/

isolator unit that converts the output of the thermocouple

to an analog voltage that is changed to a temperature by the

software that interprets the outpu t from the interface card.

A block diagram of the substrate temperature control sys-

tem is shown in Figure 6.121. In this ﬁgure, the individual

functi

ons are represented by blocks. The Laplace trans-

form of the transfer function for each block is indicated

(see discussion of Laplace transforms in Section 6.1.5).

The

transforms are obtained from consideration of the

differential equations that relate the output of each func-

tion to the input. The compensator is a proportional/inte-

gral type with constants K

and K

adjusted to attain the

optimum response and stability of the circuit (see Section

6.7.8). One detail to b e noted is that the output power of

the

ﬁlament ampliﬁer must be linearly related to the differ-

ence between the set temperat ure T

and the output temper-

ature T

for a Laplace transf orm analysis to be used.

Determination of Block Parameters. The time

response of the D/A, ampliﬁer, ﬁlament, thermocouple,

ampliﬁer/ﬁlter, and A/D are obtained from the speciﬁca-

tions of the individual elements. The constants K

and K

were chosen so that the input to the A/D in the thermo-

couple circuit is 0 V at approximately 100 °C and 4 V at

1000 °C. For the system under consideration:

¼ 1.2 3 10

5

¼ 5 3 10

5

¼ 1 3 10

3

¼ 1 3 10

3

¼ 0.3535 V

¼ 86.67 s

¼ 0.25 s

¼ 1.2 3 10

5

The remaining parameters – thermal resistance, R

and heat capacity C

, are characteristic of the experimen-

tal arrangement and ar e determined experimentally fr om

heating and cooling curves and a measurement of the

maximum temperature at maximum power input. The

assumption is made that the heat loss from the s ubstrate

to the surroundings is proportional to the temperature

difference between the subs trate and s urroundings

 T

). The initial slope of the heating curve dT

=dt

as a function of time for a constant heat input) when

the substrate is at the temperature of the surroundings

Figure 6.121 Block diagram of the silicon substrate-temperature-control system.

DATA ACQUISITION 489

and the heat loss is zero is dT

=dt ¼ C

dQ=dt,whereC

is the heat capacity of the substrate and dQ=dt is the rate

at which heat is added to the substrate. Knowing dQ=dt,

the input power, and dT

=dt, C

can be calculated. R

correspondingly determined from the asymptotic temper-

ature of the substrate for a constant power input. Assuming

heat loss proportional to (T

 T

), the thermal resistance

of the system R

is given by (T

 T

)/input power. The

values of C

and R

can be checked by a cooling-curve

measurement. With the substrate initially at T

> T

and

no heat input, the time for the temperature to fall to e

1

 T

)isR

¼ 300 s. This is consistent with the

values for R

and C

of 5.6 K/W and 54 J/K.

Because the time constant for the substrate and load is

at least two orders of magnitude larger that any other

time constant in the system, it is possible to simplify

the circuit to the one shown in Figure 6.122(a),where

the

overall transfer function of the D/A, ampliﬁer,

ﬁlament, and feedback transfe r function a re all set equal

to one. In Figure 6.122(b) , the substrate, load, and sum-

ing junction are replaced by a single transfer function

/(1 þ ss),whereR

is the effective thermal loa d equal

to R

þ T

.Inthiscase,s ¼ R

¼ 30 0 s, T

is the

temperature of the surroundings, and Q

is the power

input to the substrate at the set temperature T

. It should

be noted that the value of R

will change with the temper-

ature of the surroundings and the set temperature of t he

substrate. To maintain the substrate at 500 K, the system

requires a heat input of 36 W, giving a value of 13.9 K/W

for R

. T he overall transfer function for Figure 6.122(b),



ðsÞ=



ðsÞ,is



ðsÞ=



ðsÞ¼

13:9ðK

s þ K

300s

þð13:9K

þ 1Þs þ 13:9K

as þ 1

21:6bs

þð0:072b þ aÞ s þ1

ð6:65Þ

where a ¼K

and b ¼1/K

. The response and stabi lity

of the system are op timiz ed by the appropriate choice of

and K

. Figure 6.123 shows the frequency dependence

of the system transfer function for different values of a

and b. This can be done empirical ly or by using standard

Figure 6.122 (a) Simpliﬁed block diagram of the silicon substrate-temperature-control system; (b) block diagram with

load and substrate transfer functions combined.

490 ELECTRONICS

control analysis methods – some of which are discussed

in Section 6.7.8 and in more detail in the references at

the

end of the chapter. Programs such as Mathematica

and Matlab

have special packages for control analysis

and design.

A DMM card is used to monitor the voltage across the

leads of the heater and compare the results with the pro-

grammed voltage. The DMM is speciﬁed to have a reso-

lution of 5 1/2 digits 61 in the next to least signiﬁcant

digit. When set on the 10 V range, the card can resolve

1 mV (0.01%) – more than adequate for verifying the out-

put voltage of the power supply considering that the max-

imum resolution of the DAC is only 0.025 %.

The AT-MIO-16X interface board from National Instru-

ments is supplied with software and connectors. It can be

installed in any available 16-bit expansion slot on a PC. It

has 16 single-ended and 8 differential analog input chan-

nels of 16 bits each, and a maximum sampling rate of 100

kilo-samples/s. Gains of 1, 2, 5, 10, 20, 50, and 100 are

software-selectable. The output of the ion gauge is con-

nected to one of the analog input channels. There are

two analog output channels driven by 16-bit DACs. The

two channels are used to control the electron-gun power

supply and mass spectrometer. The maximum update rate

is 100 kilo-samples/s and the output software-selectable

voltage ranges are 0 to 10 V unipolar, and 610 V bipolar.

The board also has eight digital TTL-compatible I/O lines

and three independent 16-bit counter/timers. One of the

counters is used to register the output counts from the mass

spectrometer. A standard GPIB interface board is used

to monitor the output of the picoammeter that registers

the current from the electron gun that is collected by the

silicon substrate.

6.8 EXTRACTION OF SIGNAL

FROM NOISE

6.8.1 Signal-to-Noise Ratio

With many experiments, an important consideration is the

minimum detectable signal that can be recovered. This

depends on the signal-to-noise ratio

(SNR or S/N) rather

than the absolute value of the signal. In counting experi-

ments, where the minimum signal is one event, the uncer-

tainty associated with C

signal counts is

ﬃﬃﬃﬃﬃ

so that the

relative uncertainty is

ﬃﬃﬃﬃﬃ

or 1=

ﬃﬃﬃﬃﬃ

. In principle,

one could attain arbitrarily high precision by counting

for long times, but this is often not practical because of

instabilities in the experimental system.

With analog systems, where the signal is a voltage, cur-

rent, or charge, the SNR depends on the source resistance

and capacitance, shot noise, 1/f or ﬂicker noise, and ampli-

ﬁer noise. In this discussion, we assume that sources of

noise such as r.f.i. do not exist. The noise will be assumed

to be conﬁned to the source and preampliﬁer and to repre-

sent the theoretical limit for such a combination.

Consider a detector that is a source of voltage with out-

put impedance R

, connected to an ampliﬁer with a gain A

as shown in Figure 6.124. Johnson noise is associated with

the random motion of electrons in R

. Its rms value over a

frequency bandwidth Df in Hz is:

Johnson

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

4kTR

ð6:66Þ

where k is Boltzman’s constant (1.38 3 10

23

J/K), and T

is the absolute temperature of the resistor. Johnson noise is

frequency independent – that is, the rms noise per unit

bandwidth (noise density) is the same at all frequencies.

For this reason, Johnson noise is often called white noise.

For the purposes of circuit analysis, the noise from R

can

be represented by a voltage source giving a voltage v

Johnson

in series with a noiseless resistor R. The noise current from

this source is i

Johnson

¼ v

Johnson

/R.

Figure 6.123 Frequency dependence of steady-state

transfer functions for a range of system parameter values.

See text for deﬁnition of a and b.

EXTRACTION OF SIGNAL FROM NOISE 491

Shot noise has its origin in the discrete nature of the

electronic charge. The shot current noise accompanying

a current i is

shot

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2qiDf

ð6:67Þ

where q is the electronic charge in coulombs. Like Johnson

noise, shot noise is frequency independent.

Flicker or 1/f noise tends to dominate Johnson and shot

noise below 100 Hz. The frequency dependence of this

noise is of the form 1/f

, where n is usually between 0.9

and 1.35. Flicker noise imposes an important limitation on

the SNR at low frequencies. For this reason, measurements

should, if at all possible, be made at frequencies where

white noise dominates.

6.8.2 Optimizing the Signal-to-Noise Ratio

An ideal ampliﬁer of gain A

can represent a real ampliﬁer

with current and voltage noise generators at the input ter-

minals. It is usually assumed that the noise sources are

frequency independent. Consider the system in Figure

6.125, where v

and i

represent the rms voltage and cur-

rent noise per Hz

1/2

. The SNR is then the output voltage

due to the signal alone divided by the total output voltage,

including noise:

SNR ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

4kTR

þ v

þði

ﬃﬃﬃﬃﬃﬃ

ð6:68Þ

From this formula it is clear that the SNR can be

improved by reducing R

, Df, and T. When characterizing

noise in an ampliﬁer, the noise ﬁgure (NF) is often used:

NFðdBÞ¼20 log

input voltage SNR without amplifier

output SNR from amplifier

ð6:69Þ

An ideal ampliﬁer will have the same SNR at both the

input and output terminals. The smallest possible NF is 0,

and an NF of 3 dB means that the ampliﬁer has reduced the

SNR by 1=

ﬃﬃﬃ

at its output terminals from what it was at

the input terminals. Exceedingly good commercial ampli-

ﬁers can have NFs as low as 0.05 dB over a limited range of

frequency and source resistance. To evaluate the impor-

tance of the NF it is necessary to know the input signal

level, source resistance, and frequency bandwidth. If the

SNR is 10

at the input terminals of an ampliﬁer, for

example, an ampliﬁer with a NF of 20 dB will reduce it

to 10

at the output terminals. This may still be entirely

satisfactory for the intended application. Manufacturers of

preampliﬁers and ampliﬁers often supply contour plots of

constant NF in frequency source-resistance space.

For optimum SNR, it is important to match the source

resistance to the ampliﬁer. The optimum value of the

source resistor R

is v

. This results in a minimum

NF given by:

min

¼ 10 log 1 þ

4kTR



ð6:70Þ

where R

is the optimum value of the source resistance.

The source resistance is generally a property of the source.

To transform the source’s intrinsic resistance R

to the

optimum resistance R

, a transformer is used (never an

additional series or shunt resistor). If the ratio of secondary

to primary turns is a then a

¼ R

. Although it was

stated that the maximum SNR occurs when R

¼ 0, in

Figure 6.124 Voltage source v

with output impedance R

connected to an ampliﬁer of gain A

Figure 6.125 Real ampliﬁer and signal source v

with noise

sources represented by voltage and current sources v

and i

492 ELECTRONICS

practice all sources have ﬁnite resistance and the SNR can

be optimized by transformer matching. Photomultiplier

tubes, photodiodes, and electron multipliers are best rep-

resented (see Figure 6.126) as noiseless constant-

current

sources in parallel with shot-noise and Johnson-

noise sources resulting from the addition of a load resistor,

, to the circuit. In this case the SNR is optimized by

using as large a value of R

as possible and an ampliﬁer

with high input impedance and low v

and i

. Ampliﬁers

with FET input stages are the best choice. Maximum prac-

tical values of R

are limited by the capacitance C of the

input circuit (including cables) and the input impedance of

the ampliﬁer. There is no beneﬁt in having R

greater than

the input impedance of the ampliﬁer or so large that the

time constant R

C requires working at low frequencies

where 1/f noise dominates. The justiﬁcation for using large

values of R

comes from the fact that the voltage signal

from a current source is proportional to R

, while the

Johnson noise is proportional to

ﬃﬃﬃﬃﬃﬃ

An alternative way of specifying ampliﬁer performance

is with the equivalent noise temperature T

deﬁned as the

necessary increase in temperature of the source resistor to

produce the observed noise at the ampliﬁer output – the

ampliﬁer being considered noiseless for this purpose:

¼ Tð10

NF=10

1Þ, ð6:71Þ

where T is the absolute temperature of the source resistor.

Using the example of the ampliﬁer with an NF of 3 dB and

a source resistor at T ¼ 300 K:

¼ 300 Kð10

0:3

 1Þ¼300 K ð6:72Þ

In this case, the ampliﬁer introduces an amount of noise

equal to the noise from the source resistor.

6.8.3 The Lock-In Ampliﬁer and Gated

Integrator or Boxcar

The proper matching of a signal source to an ampliﬁer is

the ﬁrst step to be taken in the recovery of a signal accom-

panied by noise. Once this has been done correctly, a

number of signal-enhancing techniques can be used to

extract the signal.

Because of the difﬁculty in making d.c. measurements

due to zero drifts, ampliﬁer instabilities, and ﬂicker noi se,

the signal of interest should, if at all possible, be at a

frequency sufﬁciently high that the dominant noise is

white noise. A d.c. or low-frequency signal can be con-

verted to a higher frequency by chopping the signal at the

higher frequency. It is essential to choose a chopper fre-

quency far from the power-line frequency and its harmon-

ics. Frequencies near known noise frequencies should be

avoided.

Signal-enhancing techniques are mainly bas ed on

bandwidth reduction. Because the white-noise power

per unit bandwidth is constant, reducing the bandwidth

will proportionally reduce t he noise power. Of course, as

the bandwidth goes to zero, the noise and signal power

both go to zero as well. Common bandwidth-narrowing

circuits are the resonant ﬁlter and low-pass ﬁlter. For

resonant ﬁlters, t he width of the re sonance is given in

terms of Q, which is approximately equal to f

/Df,where

is the frequency to which the ﬁlter is tuned and Df is the

ﬁlter bandwidth. Practical values of Q for el ectronic res-

onant ﬁlters vary from 10 to 100. A simple detection

system might take the form shown in Figure 6.127.The

rectiﬁ

er converts the a.c. signal back to d.c., so it can

be recorded on a chart recorder or read from a meter.

With this arrangement, the noise passed by the ﬁlter is

rectiﬁed along with the signal and adds to the recorded

d.c. level.

The effective bandwidth can be substantially narrowed if,

in the above arrangement, the ordinary rectiﬁer is replaced

by a synchronous rectiﬁer. This kind of rectiﬁer acts as a

switch that is opened and closed in synchronization with the

chopper. Because the phase relations for each of the noise

components are random (a characteristic of white noise),

Figure 6.126 Representation of noise sources in a detector.

EXTRACTION OF SIGNAL FROM NOISE 493

they will tend to cancel each other when averaged – a low-

pass ﬁlter at the output of the rectiﬁer can be used to do the

averaging. The RC time constant of the ﬁlter is related to the

effecti ve pass band of the system Df by:

Df ¼

4RC

ð6:73Þ

for a single-section, low-pass ﬁlter, and

Df ¼

4nRC

ð6:74Þ

for n concatenated low-pass ﬁlters – each with time con-

stant RC. Quite small values of Df are possible with such a

system. The only limitation is the length of time necessary

for the measurement. If Df is the pass band, the measure-

ment time is approximately 1/Df so that it is necessary for

the source signal to remain stable over times comparable to

1/Df. The chopping frequency is normally chosen to be 10

times the highest component frequency to be recovered in

the source signal.

The system described above is often called a lock-in

ampliﬁer or phase-sensitive detector. The details of the

operation of such devices are well documented.

As far

as signal enhancement is concerned, however, the formulae

given above are sufﬁcient for estimating the beneﬁts of

such devices. It is well to remember that the SNR is propor-

tional to 1=

ﬃﬃﬃﬃﬃﬃ

, so that narrowing the pass band by a factor

of four increases SNR by a factor of two, but increases the

time of measurement by a factor of four.

When the signal to be detected has the form of a repet-

itive low-duty-cycle train of pulses, the lock-in ampliﬁer

may not be the best method for signal enhancement. The

duty cycle is the fraction of time during which the signal of

interest is present. With low duty cycles, signal informa-

tion is available for only a fraction of the total time, while

noise is always present. With timing and gating circuits, it

is possible to connect the signal line to an RC integrating

circuit only during those times when the signal is present.

The time constant of the integrator is then chosen to be

very much larger than the period of the pulse train. The

time required for the capacitor to charge to 99% of the ﬁnal

voltage level is 4.6RC, so that ﬁve time constants after the

ﬁrst gate opening the capacitor should be charged to within

1% of the ﬁnal steady-state value – provided the signal is

continuously present. If the signal is present for a fraction c

of the time, the time constant of the integrator must be

increased to 5RC/c. With this system, known as a gated

or boxcar integrator, the SNR is increased only by increas-

ing the time of the measurement. The effective bandwidth

of the instrument is c/4RC. Table 6.41 compares the impor-

tant

parameters associated with lock-in ampliﬁers and

gated integrators.

6.8.4 Signal Averaging

With a repetitive signal, merely averaging the signal over

many cycles can improve the SNR. Let SNR

represent the

SNR in one cycle, and N the number of cycles over which

one averages. The SNR improvement is proportional to

ﬃﬃﬃﬃ

. If each cycle lasts for a time s, the time T necessary

to arrive at a speciﬁed SNR is given by:

T ¼

SNR



s ð6:75Þ

Figure 6.127 Simple detection and signal-enhancement system.

494 ELECTRONICS

Lock-in ampliﬁers and gated integrators are inherently

superior to simple signal averaging because of the band-

narrowing functions they perform. The bandwidth

improvement is only an advantage, however, when the

highest frequency component in the signal to be recovered

permits a long integrating time.

6.8.5 Waveform Recovery

When it is necessary to know the variation of a signal with

time, waveform recovery techniques are needed. The gated

integrator can be converted to an instrument for waveform

recovery by the inclusion of variable delay and variable

gate-width functions. A separate RC network is required

for each delay time in such a scheme. A schematic repre-

sentation of such a system is shown in Figure 6.128. Each

separate

delay corresponds to a different part of the wave-

form. The duty cycle for each gate opening is s/T ¼ c,so

that the effective bandwidth is c/4RC. An integration time

of 5RC/c is needed for the charge on each capacitor to

reach a steady-state value. If the waveform has been

divided into n parts, the total time of measurement is

5nRC/c.

Digital schemes for recovering waveforms use ADCs to

convert the analog signal level to a digital number, which is

then recorded in the appropriate time channel with the aid

of delay and gating signals. With such instruments, called

digital signal analyzers, SNRs are only limited by the

length of time of the measurement. The long-term stability

of the various components, however, limits the use of very

long measuring times. If the absolute value of the waveform

is needed, one must record the number of cycles processed

by the instrument. Data rates are limited by the conversion

speed of the ADC that encodes the amplitude information.

An advantage of digital signal analysis is the increased

versatility in data manipulation and the production of per-

manent records on paper, magnetic, or semiconductor

media. Such data are then available for computer analysis.

Instruments related to the digital waveform recorders

are transient recorders and memory oscilloscopes. While

these offer no gain in SNR over that in the original signal,

they do provide outputs that are a record of a single wave-

form. An inefﬁcient, but commonly used, method of SNR

enhancement with these instruments is the separate record-

ing of many waveforms and subsequent digital averaging

by a computer.

Table 6.41 Comparison of lock-in ampliﬁer and gated integrator

Parameter Lock-in Ampliﬁer Gated Integrator

Duty cycle, c > 0.50 < 0.50

Bandwidth, Df 1/8RC c/4RC

Minimum measurement time 5RC 5RC/c

Highest recoverable signal frequency f

max

1/20pRC for chopping frequency > pRC/2 c/20 pRC for repetition frequency > pRC/2

Design notes 1. Determine f

max

, the highest frequency

component of the signal to be recovered.

1. Required measurement time is 5RC/c.

2. Choose f

, the chopping frequency,

where f

¼10f

max

2. Bandwidth is c/4RC.

3. Choose low-pass ﬁlter constants 1/RC ¼

2pf, so as to pass frequency f

max

3. Preferred to a lock-in ampliﬁer for signal

repletion rate < 10 Hz and low duty

cycle.

4. The bandwidth Df is 1/8RC, and a tuned

ampliﬁer with a Q of 10 is sufﬁcient to

pass all frequency components of the

signal to f

max

EXTRACTION OF SIGNAL FROM NOISE 495

6.8.6 Coincidence and Time-Correlation

Techniques

There are a few general principles that govern all time-

correlation measurements, which will be discussed in suf-

ﬁcient detail to be useful in assembling and optimizing the

operating parameters of experiments where time is a

parameter.

Correlated events are related in time, and this time rela-

tion can be established either with respect to an external

clock or to the events themselves. Random or uncorrelated

events bear no ﬁxed time relation to each other but, on the

other hand, their very randomness allows them to be quan-

tiﬁed. Consider the passing of cars on a busy street. It is

possible to calculate the probability P



ðnÞ that n cars pass

within a given time interval in terms of the average number

of cars



n in the interval where P

n

ðnÞ, the Poisson distribu-

tion, is given by:

n

ðnÞ¼



: ð6:76Þ

If 100 cars pass a ﬁxed position on a highway in an hour,

for example, then the average number of cars per minute

is 100/60. The probability that two cars pass in a minute

isgivenby0:6

=2e

0:6

¼ 0:10. The probability that three

times the average number of cars pass per unit time is

0.02. P



ðnÞ and the integral of P



ðnÞ for



n ¼ 1 are shown

in Figure 6.129. It is worthwhile to note that only a

single

parameter, the average value



n, is sufﬁcient to

deﬁne the function. The function is also not symmetric

about



This example of passing cars has imp lications for

counting experiments. Consider again the particle-count-

ing experiment shown in Figure 6.72(a).Itconsistsofa

detector

, preampliﬁer, ampliﬁer/shaper, discriminator,

and c ount er. The detector converts the energy of an

incoming particle to an electrical signal that is ampliﬁed

by the preampli ﬁer to a level sufﬁcient to be ampliﬁed

and shaped by the ampliﬁer. T he discriminator converts

the signal from the ampliﬁer to a standard electronic

pulse of ﬁxed amplitude and time duration, provided that

the amplitude of the signal from the ampliﬁer exceeds a

set thresho ld. Th e coun te r rec ords the number of puls es

from the disc rimina tor for a predet ermine d period of

time. The factors that affect themeasurementarecount-

ing rate, sign al d urati on, a nd processing times.

Figure 6.128 Relation between gate width s, delay time t, and single-cycle time T in

waveform recovery. The duty cycle c is given by s/T.

496 ELECTRONICS

In counting experiments, the instantaneous rate at

which particles arrive at the detector can be signiﬁcantly

different from the average rate . I n orde r to assess the rate

at which the s ystem ca n accept data, it is ne cessary to

know how the signals from the detector, preampliﬁer,

ampliﬁer, and discriminator all vary with time. If signals

are arriving randomly at an average rate of 1 kHz at the

detector, for example, the average time between the start

of each signal is 1 0

3

s. If we consider a time interval of

3

s, the average number of signals arriving in that

interval is one. If as many as three pulses can be regis-

teredinthe10

3

s, then 99% of all pulses will be counted

(see Figure 6.129). To register the thr ee randomly dis-

trib

uted pulses in the 10

3

s interval, another factor of

three in time resolution is required, with the result that

the system must have the capability of registering events

at a 10 kHz uniform rate, in order to be able to register

randomly arriving events at a 1 kHz average rate with 99%

efﬁciency. For 99.9% efﬁciency, the required system band-

width increases to 100 kHz. Provided that the discriminator

and counter are capable of handling the rates, it is then

necessary to be sure that the duration of all of the electronic

signals are consistent with the required time resolution. For

1 kHz, 10 kHz and 100 kHz bandwidths, this means that the

signal durations must be no longer than 0.1, 0.01, and

0.001 ms, respectively. An excellent discussion of the

application of statistics to physics experiments is given

by Melissinos.

The processing times of the electronic units must also be

taken into consideration. There are propagation dela ys

associated with the active devices in the ele ctronics cir-

cuits and delays associated with the actual registering of

events by the counter. The manufacturers of counters spec-

ify proce ssing delays in terms of maximum count rate.

A 10 MHz counter may only count at a 10 MHz rate if

the input signals arrive at a uniform rate. For randomly

arriving signals with a 10 MHz average rate, a system with

a 100 MHz bandwidth is required, to record 99% of the

incoming events.

The result that is sought in counting experiments is a

rate (number of events per unit time). For convenience, we

divide the total time of the measurement T into n equal

time intervals, each of duration T/n. If there are N

counts

registered in interval i, then the mean or average rate is

given by:

i¼1

T=n

ð6:77Þ

where N

is the total number of counts registered during

the course of the experiment. To assess the uncertainty in

the overall measured rate, we assume that the individual

rate measurements are statistically distributed about the

average value. In other words, they ari se from statistical

ﬂuctuations in the a rrival times of the events and not

from uncertainti es introduced by the measuring instru-

ments. When the rate measurement is statistically dis-

tributed about the mean, the distribution of events can

be described by the Poisson distribution, P



ðnÞ.The

uncertaintyintherateisgivenbythestandarddeviation

andisequaltothesquarerootoftheaveragerate

ﬃﬃﬃ



Most signiﬁcant is the relative uncertainty:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

N= t

ð6:78Þ

The relative uncertainty decreases as the number of counts

per counting interval increases. For a ﬁxed experimental

arrangement, increasing the time of the measurement

increases the number of counts. As can be seen from the

formula, the relative uncertainty can be made arbitrarily

small by lengthening the measurement time. Improvement

Figure 6.129 Poisson distribution and cumulative Poisson

distribution for

n ¼1.

EXTRACTION OF SIGNAL FROM NOISE 497

in relative uncertainty, however, is proportional to the

reciprocal of the square root of the measurement time.

To reduce the relative uncertainty by a factor of two, it is

necessary to increase the measurement time by a factor of

four. One soon reaches a point where the fractional

improvement in relative uncertainty requires a prohibi-

tively long measurement time.

Coincidence experiments require explicit knowledge of

the time correlation between two events. Consider the

example of electron impact ionization of an atom in which

a single incident electron strikes a target atom or molecule

and ejects an electron from it. Because the scattered and

ejected electrons arise from the same event, there is a time

correlation between their arrival times at the detectors.

In a two-detector coincidence experiment, of

which Figure 6.72(b) is an example, pulses from the

two

detectors are ampliﬁed andthensenttodiscrimina-

tors – the outputs of w hich are standard rectangular

pulses of constant amplitude and duration. The outputs

from the two discriminators are then sent to the start and

stop inputs of a time-to-amplitude converter or TAC.

Even though a single event is responsible for ejected

and scattered e lectrons, the two electrons will not arrive

at the detectors simultaneously because of differences in

path lengths and electron velocities. Electronic propa-

gation delays and cable delays also contribute to the

start and stop signals not arriving at the inputs of the

TAC simultaneously – sometimes the start signal arrives

ﬁrst, sometimes the stop signal is ﬁrst. I f the signal to the

start input arrives after the signal to the stop,thatpairof

events will not result in a TAC output. The result can be

a 50% reduction in the nu mber of recorded coinciden-

ces. To overcome this limitation, a time delay is inserted

in the stop line between the discriminator and the TAC.

This delay can be a length of coaxial cable (typical

delays are of the order of 1 ns/ft. – see Table 6.11), a

lumped

delay line, or an electronic delay circuit. The

purpose of the delay is to insure that the stop signal

always arrives at the stop input of the TAC after the start

signal. A perfect coincidence will be recorded at a time

difference approximately equal to the de lay time. When

a time window twice the length of the delay time is used,

perfect coincidence will lie at the center of the time

window, and it is possible to make an accurate assess-

ment of the ba ckground by considering the regions to

either side of the perfect coincidence region. An exam-

ple of a time spectrum is shown in Figure 6 .130.

alternative to the TAC and PHA/ADC (see Section

6.4.6) is the time-to-digital converter (TDC) – a unit that

combines the functions of the TAC and PHA/ADC. These

units have start and stop inputs and an output that provides

a binary number with a value that is directly proportional

to the time difference between the stop and start signals.

The TDC can be connected to an MCA or PC with the

appropriate digital interface.

By storing the binary outputs of a PHA/ADC or a TDC

in the form of a histogram in the memory of a MCA or PC,

analyses can be performed on the data taking full account

of the limitations of the individual components of the

measuring system. For the preampliﬁers and discrimina-

tors, time resolution is the principal consideration. For the

TAC, resolution and processing time can be critical. The

PHA/ADC or TDC provide the link between the analog

circuits of the preampliﬁers and discriminators and the

digital input of the MCA or PC. The conversion from

analog to digital by a PHA/ADC or TDC is not perfectly

linear and the deviations from linearity need to be taken

into consideration in precise work.

To assess the precision of a coincidence measurement,

it is necessary to consider, not just the event under

Figure 6.130 Coincidence time spectrum.

498 ELECTRONICS

consideration, but also all other events arriving at th e two

detectors. While the events under study are correlated in

time and result in a peak in the time spectrum centered

approximately at the dela y time, the re are also back-

ground events that be ar no ﬁxed time relation to each

other. If the average ra te of the backgroun d events in

each detector is R

and R

, t hen the rate that two such

events will be recorded within time Ds is given by: R

where:

¼ R

Ds ð6:79Þ

Let the rate of the event under study be R

. It will be

proportional to the probability of occurrence of the event

, the source function S, and the acceptances and efﬁcien-

cies of the detectors d

and d

¼ p

ð6:80Þ

For the background, each of the rates R

and R

will be

proportional to the source function, the probability for

single events p

and p

, and the properties of the individual

detectors:

¼ Sp

ð6:81Þ

Combining the two expressions for R

and R

¼ S

Ds ð6:82Þ

Comparing the expressions for the background rate and

the signal rate, one sees that the background increases as

the square of the source function while the signal rate is

proportional to the source function. The signal-to-back-

ground rate R

is then:

SDs

ð6:83Þ

It is important to note that the signal is always accompa-

nied by back grou nd. We now consider the signal and

background after accumulating counts over a time T.

For this, it is informative to refer to the t ime spectrum

in Figure 6.130. The total number of counts within an

rival time difference Ds is N

and t his number is the

sum of the signal counts N

¼ R

T a nd the ba ck gr oun d

counts N

¼ R

T :

¼ N

þ N

ð6:84Þ

The determination of the background counts must come

from an independent measurement, typically made in a

region of the time spectrum outside of the signal region,

yet representative of the background within the signal

region. The uncertainty in the determination of the signal

counts dN

is given by the square root of the uncertainties

in the total counts and the background counts:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ N

ð6:85Þ

The essential quantity is the relative uncertainty in the

signal counts dN

. This is given by:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ N

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 2N

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

T þ 2R

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ 2=R

ð6:86Þ

Expressing R

in terms of R

results in the following

formula:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 2ðÞDs

ð6:87Þ

There are a number of conclusions to be drawn from the

above formula. The relative uncertainty can be reduced to

an arbitrarily small value by increasing T, but because the

relative uncertainly is proportional to 1=

ﬃﬃﬃﬃ

, a reduction in

relative uncertainly by a factor of two requires a factor of

four increase in collection time. Reducing Ds can also

reduce the relative uncertainty. It is understood that Ds is

the smallest time window that includes the entire signal.

Using the fastest possible detectors, preampliﬁers, and dis-

criminators and minimizing time dispersion in the section

of the experiment ahead of the detectors all help to

decrease Ds.

The signal and background rates are not independent,

but are coupled through the source function S.Asa

EXTRACTION OF SIGNAL FROM NOISE 499

consequence, the relative uncertainty in the signal

decreases with the signal-to-background rate R

, a some-

what unanticipated result. Dividing dN

by its value

at R

¼ 1 gives a reduced relative uncertainty

½

equal to

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 2ðÞ=3

. To review this

result, consider a case where there is one signal count

and one background count in the time window Ds. The

signal-to background ratio is 1, and the relative uncertainty

in the signal is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2 þ 1

=1 ¼ 1:7. By increasing the source

strength by a factor of ten, the signal will be increased by a

factor of 10 and the background by a factor of 100. The

signal-to-background ratio is now 0.1, but the relative

uncertainty in the signal is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

110 þ 100

=10 ¼ 1:45 – a

clear improvement over the larger signal-to-background

case.

Another method for reducing t he relative uncertainty

is to increase the precision of the measurement of back-

ground. The above formulae are based on an independ-

ent measurement of background over a time window Ds

that is equivalent to the time window within which the

signal appears. If a larger time w indow for the back-

ground is used, the uncertainty in the background deter-

mination can be correspondingly reduced. Le t a time

window of width Ds

be used for the determination

of background, where Ds=Ds

¼ q <1. If the rate at

which counts are accumulated in time window Ds

, the background counts to be sub tracted from

the total counts in time window dN

/ N

become

T ¼ qN

. The uncertainty in the number o f b ack-

ground counts t o be subtracted from the total of signal

plus background is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

. The relative uncertainty

of the signal is then:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ 2q

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ 2qN

ð6:88Þ

The expression for the reduced relative uncertainty is

then:

½

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ 2qðÞ

ð6:89Þ

The single coincidence measurement can be expanded to a

multiple detector arrangement if it is necessary to measure

coincidence rates as a function of more than one parame-

ter. This is a much more efﬁcient way of collecting data

than having two detectors that are scanned over the range of

the parameters. Depending on the signal and background

rates, detector outputs can be multiplexed and a detector

encoding circuit can be used to identify those detectors

responsible for each coincidence signal. If detectors are

multiplexed, it is essential to recognize that the overall

count rate is the sum of the rates for all of the detectors.

This can be an important consideration when rates become

comparable to the reciprocal of system dead time.

It is often the case that signal rates are limited by the

processing electronics. Consider a coincidence time spec-

trum of 100 channels covering 100 ns with a coincidence

time window of 10 ns. Assume a signal rate of 1 Hz and a

background rate of 1 Hz within the 10 ns window. This

background rate implies an uncorrelated event rate of 10

kHz in each of the detectors. To register 99% of the incom-

ing events, the dead time of the system can be no larger

than 10 ls. The dead time limitation can be substantially

reduced with a preprocessing circuit that only accepts

events falling within 100 ns of each other (the width of

the time spectrum). One way to accomplish this is with a

circuit that incorporates delays and gates to only pass sig-

nals that fall within a 100 ns time window. With this circuit

the number of background events that need to be processed

each second is reduced from 10, 000 to 10, and dead times

as long as 10 ms can be accommodated while maintaining

a collection efﬁciency of 99%. This can be considered to

be an extension of the multiparameter processing in which

the parameter is the time difference between processed

events. Goruganthu et al. discuss a preprocessing circuit.

6.9 GROUNDS AND GROUNDING

6.9.1 Electrical Grounds and Safety

A battery or power supply produces a potential difference

between its two output terminals. Only by deﬁning the

potential of one of the terminals in an absolute way can

the potential of the other terminal be given an absolute

value. By convention, the electrical potential of the earth

is deﬁned to be zero. When one output terminal of a battery

or power supply is connected to the earth, the absolute

potential of the other terminal is then equal to the potential

500 ELECTRONICS

difference. Because the surface of the earth is a fairly good

conductor of electricity, all points will be at nearly the

same potential. A good connection to the earth via a copper

rod buried in the ground is the most convenient way of

establishing zero potential. Since such connections are not

always readily available in the laboratory, one often uses

connections to metal water pipes that go underground, to

deﬁne zero potential.

Most connections to the a.c. line are now made with

three-prong plugs and three-conductor wire. The wire is

usually color coded in North America – black correspond-

ing to the high-voltage or hot side of the line, white to the

low-voltage or neutral, and green to the earth or ground.

The terminals on a.c. plugs and receptacles are also coded –

the hot terminal is brass, the neutral terminal is chrome-

plated, and the ground terminal is dyed green. Switches

and fuses for use with a.c. lines should always be placed in

the hot line, otherwise the full line voltage will be present

at the input even with an open switch or a blown fuse.

The three-wire system is designed for safety. Consider a

piece of electrical equipment with a metal case operating

from the a.c. line. Normal practice requires that the case be

connected to the green ground wire of the line cord. Should

the hot wire come in contact with the case, a very large

current would ﬂow in the hot line and blow a fuse or open a

circuit breaker. If the case is not connected to ground, it

will assume the potential of the hot line and could give an

electric shock to anyone touching it. Of course, if the case

were not a conductor, there would be no danger even if the

hot line made a connection to it. There are a large number

of appliances and hand power tools with so-called double

insulated cases that do not require a separate ground con-

nection for safety purposes. Ground-fault (circuit) inter-

rupters (GFI or GFCI) are safety devices that are

incorporated in a.c. power outlets where there is a danger

of operators of electrical equipment attached to the outlet

touching electrical ground while using the equipment. The

GFI senses any current ﬂowing directly to ground and

switches off all power to the equipment to minimize elec-

trical shock. Ground-fault interrupter electrical outlets are

standard in humid environments outdoors and in bath-

rooms and underground installations.

From this discussion it should be clear that fuses and

circuit breakers are important safety elements in electrical

circuits. Fuses are generally of either the standard quick-

response type or the slow-blow type. The former will open

whenever its maximum rated current is exceeded, even

momentarily, while the slow-blow fuse is designed to sus-

tain momentary current surges in excess of the maximum

rated continuous value. The two types are not interchange-

able, even though they may have identical maximum con-

tinuous current ratings. Circuit breakers are generally of

the electromagnetic-relay or the bimetallic-strip type.

They can be reset after opening from an overload.

It is sometimes necessary to ﬂoat or remove all ground

connections from a piece of electrical equipment. This is

necessary when a signal between two points in a circuit,

neither of which is at ground, is to be measured, ampliﬁed,

or processed in some way. Power supplies are ﬂoated when

it is necessary to produce a well-deﬁned potential difference

with reference to a nonzero potential. An example is the

ﬁlament heater supply of a high-voltage electron gun with

the ﬁlament at a high negative potential. The heater supply

is connected across the ﬁlament with one lead at the high

negative potential. In this conﬁguration, neither heater sup-

ply lead is at ground potential. Floating introduces the pos-

sibility of additional noise and electrical breakdown within

the circuit with a resulting destruction of components. There

are safety hazards associated with ﬂoated circuits.

At this point it is worthwhile to make the distinction

between d.c. and a.c. grounds. A d.c. ground connection

is a direct low-resistance connection to ground, while an

a.c. ground connection is one that does not permit d.c.

currents to ﬂow while offering low impedance to a.c. cur-

rents. In

Figure 6.131, power supply 1 has the negative

terminal

and case (G terminal ) at d.c. ground. Power

Figure 6.131 Power supply 2 ﬂoating on power supply 1.

The V2

,V2



, and G terminals of supply 2 are assumed to

have no direct d.c. connection to ground.

GROUNDS AND GROUNDING 501

supply 2 is ﬂoating on power supply 1 and, in the absence

of any external connections, no current will ﬂow through

the terminals of the supplies. Since high-quality power

supplies generally have very low output impedances, the

a.c. impedances of the terminals marked V1

,V2



, and

with respect to ground are low, although the potentials

at the terminals are not zero. It is good to keep in mind that

the impedances to ground are frequency-dependent

because of the characteristics of the output circuits. At high

frequencies, the impedances may become large due to the

frequency characteristics of the output circuit. As a result,

transient voltage spikes may not be effectively shunted to

ground and may adversely affect the circuits to which the

power supplies are connected. A remedy is the use of good

high-frequency capacitors of an adequate voltage rating

between the terminals V1

and V2

and ground.

Figure 6.132 illustrates a typical line-operated power

supply

connected to an a.c. outlet via a three-wire line

cord. Under normal operation, either the negative or the

positive output terminal is connected to the ground termi-

nal, depending on whether a positive or a negative voltage

with respect to ground is desired. When ﬂoating the power

supply, the ground connection is removed and the potential

at which the supply is to be ﬂoated is applied to either the

positive or negative output terminal. This may be satisfac-

tory for levels of as much as a few hundred volts, but has its

hazards because the internal circuitry is ﬂoating, while the

case is at ground through the green wire in the three-wire

line plug. Potentials at least equal to the ﬂoating potential

plus the potential difference at the output terminals now

exist at the terminals of several components in the internal

circuit. Components are often mechanically ﬁxed to the

grounded chassis. The electrical insulation between the

components and the chassis, as well as that between

the primary and secondary of the power transformer, must

be sufﬁcient to sustain the d.c. voltage difference. In the

event of electrical breakdown, components will be des-

troyed and the shafts of the controls may attain a potential

that is equal to the ﬂoating potential and thus present a

shock hazard. The maximum potential for ﬂoating line-

powered equipment in this way is generally 600 V.

When ﬂoating line-operat ed equipment at voltages

above the rated maximum voltages, it is necessary to

completely remove the ground connection to the case .

The easiest method is to use a two-terminal to three-

terminal a.c. line-plug converter and not connect the third

terminal to ground at the a.c. outlet. If the case of t he

instrument is then electrically isolated from all conduct-

ing surfaces by placing it in a P lexiglasÔ enclosure, it

can b e electrically ﬂoated at the desired potential without

risk of electr ical breakdown be twe en the components of

the circuit and the case. With the case at a nonzero poten-

tial, there is a shock hazard associated with cont act ing it

and the controls so that ac cess must be provided via aux-

iliary insulated knobs and shafts. A further potential

problem is the possibility of electrical breakdown

between the primary and secondary windings of the

power transformer. At the primary, the peak voltage val-

ues are +155 V, corresponding to the normal peak values

of the a.c. line voltage. The secondary voltage, however,

will have a d.c. compone nt equal to the ﬂoating voltage

superimposed on the normal a.c . value. If the resulting

Figure 6.132 Mounting a line-operated power supply so that both output terminals are

independent of the a.c. line ground.

502 ELECTRONICS

d.c. plus peak a.c. secondary voltage exceeds the voltage

rating of the tr an sform er insul ation, electrical breakdown

can occur, d estroying the transformer and possibly the

rest of the circuit. Isolation transformers are commonly

used to solve this problem. These transformers have a 1:1

turns ratio and high-voltage insulation between the pri-

mary and secondary windings. T he primar y is connected

to the a.c. line, while the secondary is connect ed to the

primary of the input transformer of the instrument to be

ﬂoated. In this way, the ﬂoating voltage appears across

the isolation-transformer windings. The case and controls

are still at the ﬂoating potential, and precautions similar

to those in the former situation must be observed. When

specifying an isolation transformer, the power-handling

capacity in watts or k ilovolt-amperes (KVA) as well as

the maximum isolation voltage must be considered.

A substitute for an isolation transformer is two high-

voltage ﬁlament transformers of the same turns ratio, con-

nected back to back. Such transformers are often used in

oscilloscope power supplies. This will produce the neces-

sary 1:1 overall voltage ratiowith isolation. Often such trans-

formers are more readily available and less expensive than

high-voltage, high-power, single-isolation transformers.

When ﬂoating instruments that are not directly powered

from the a.c. line, the external power supply (whether it is a

battery or line-operated supply) must be ﬂoated, too. The

precautions that apply to the ﬂoating of line-operated instru-

ments apply here also. Table 6.42 summarizes the important

nsiderations involved when ﬂoating power supplies.

6.9.2 Electrical Pickup: Capacitive Effects

It is often necessary to detect and measure electrical signals

in the millivolt and even microvolt range. If the signals are

accompanied by noise that is generated by external sources,

the signals can be so degraded as to render the measure-

ment useless. The elimination of external noise sources –

or, if this is not possible, the elimination of their effects – is

an important element in the design and construction of

electronic measuring, control, and detection systems.

Consider a wire at a potential V

in the vicinity of a

second wire that is insulated from all conducting surfaces

[see Figure 6.133(a)]. Coulomb forces between the

cha

rges on the surfaces of the wires will cause p olari za-

tion of the free charges in wire 2. Because wire 2 is

Table 6.42 Floating power supplies

(A) Normal Operation

(1) Input-line cord connected to three-terminal a.c. outlet

(2) Chassis at ground potential

(3)  or + output terminal to grounded center terminal for a

+or output voltage

(B) Low-voltage ﬂoating operation

(1) Input-line cord to three-terminal a.c. outlet

(2) Chassis at ground potential

(3) + or  terminal to ﬂoating potential

(4) Grounded output terminal unconnected

(1) Input-line cord attached to 3-2 plug adaptor with ground

terminal unconnected

(2) Chassis at ﬂoating potential

(3) + or – output terminal connected to chassis output

terminal (at ﬂoating potential)

(4) Case and chassis isolated from all conductors

(5) Insulating shafts and knobs on all switches and dials

(D) High-voltage ﬂoating operation

(1) a.c. input from isolation transformer

(2) Instrument case at ﬂoating potential

(3) Case and chassis electrically isolated from all conducting

surfaces

(4) Insulated shafts and knobs on all switches and controls

Figure 6.133 (a) Capacitive coupling between two wires;

(b) the equivalent electrical circuit with the effect of wire 1

on wire 2 represented by C.

GROUNDS AND GROUNDING 503

electrically isolated, it will remain e lectrically neutral. If

wire 2 is n ow connecte d to ground throug h a resistance R,

a current will momentarily ﬂow due to the presence of the

positive charges on wire attracting negative charge to

wire 2 from the ground . The equivalent circuit is shown

in Figure 6.133(b). Typical values of the coupling capaci-

tance

are 1 to 100 pF. Two twisted #22 polyethylene-

insulated wires, for example, will have a c apacitance of

20 pF/ft. The center-wire-to-shield capacitance of RG/58

coaxial cable is 33 pF/ft. If we assume that V

is varying

sinusoidally at frequency x, the rms potential across R

is given by:

1rms

R þ 1=xC

¼ v

1rms

xRC

1 þ xRC

ð6:90Þ

(the voltage-divider formula). Thus the rms potential

across R increases with R, x, and C.

In the average laboratory, there are many sources of a.c.

voltage that can couple capacitatively to signal lines –

open-line sockets, lighting ﬁxtures, and line cords are a

few examples. An estimate of the capacitance C

min

neces-

sary to induce a 1 mV rms voltage across 1 MX from a

power-line source can easily be made by setting V

1rms

equal to 120 V, x ¼ 2pf ¼ 188 rad/s, and neglecting

xRC with respect to 1:

min

1 3 10

3

1:2 3 10

V 3 1:88 3 10

1

3 10

¼ 0:044 pF

ð6:91Þ

a value easily attained. Such induced voltages can be sub-

stantially reduced by the use of shielding. If a grounded

shield is placed around wire 2, the situation illustrated in

Figure 6.134 will occur. The conducting shield around

wire

2 will have a current induced in it when connected

to ground, due to the potential on wire 1. This current,

however, ﬂows through a low-resistance connection. In

addition, and most important, any charge on the shield will

reside on the surface, and the interior will be ﬁeld-free.

In practice, common coaxial braided shield is about 90%

effective against capacitatively coupled voltages from

external sources. Foil shields are even more effective.

6.9.3 Electrical Pickup: Inductive Effects

A c hanging magnetic ﬁeld can induce a current in any

loop it cuts. The magnitude of th e induced current

depends on the area of t he loop and the time rate of

change of the magnetic ﬁeld. High-resistance circuits

are not greatly affected by such inductive effects, but

they are important in low-resistance circuits, such as the

input circuits of curren t and pu lse ampliﬁers. Co mmon

sources of magnetic-ﬁeld pickup are transformers,

inductors, and wires carrying large a.c. currents. Effec-

tive shielding against low-frequency magnetic ﬁelds is

accomplished with ferromagnetic enclosures that con-

centrate the stray magnetic ﬁelds within the shield

material. The usual practice is to enclose the source

of the magnetic ﬁelds within such shields. Higher-fre-

quency magnetic ﬁelds are best shielded with copper

enclosures. Ed dy currents induced in the copper pro-

duce counter magnetic ﬁelds. A rapidly changing cur-

rent is a source of time-varying magnetic ﬁelds that can

themselves induce currents in other circuits. Fast rise

time pulses in the low-impedance output circuits of

pulse ampliﬁers can generate rapidly changing mag-

netic ﬁelds that can in turn induce u nwanted currents

in nearby low-impedance input circuits. Once again, the

most effective shielding is h igh conductivity copper

sheet or foil.

Figure 6.134 Shielding to prevent capacitive coupling.

504 ELECTRONICS

6.9.4 Electromagnetic Interference and r.f.i.

The high-frequency ﬂuctuation of current or charge in a

conductor results in the radiation of part o f the energy in

the conductor in the form of an electromagnet ic wave.

Such a wave propagates through space at the speed of

light and, when not carrying useful information, is called

radio-frequency interference (r.f.i.). Sources of such

radiation are automobile ignition systems, microwave

ovens, electrical discharges, electric motors, electrome-

chanical switches and relays , and electronic switches

such as thyratrons, rectiﬁers, SCRs, and triacs. Power sup-

plies with switching regulators are often sources of r.f.i.

This interference can be reduced by the use of zero-

crossing switching regulators in which the switching only

occurs when the voltage across the switch is zero. The

most effective shield against r.f.i. is a grounded enclosure

of a conducting material, such as copper or aluminum. On

the surfaces of such a shield, the electric component of any

incident electromagnetic wave is zero and further propa-

gation is not possible. Conducting screens, rather than

solid sheet, are often used for r.f.i. shielding because of

the savings in weight. When using such a screen, it is impor-

tant that the mesh size be small compared to the wave-

length of the highest-frequency component of the r.f.i.

Standards have now been established for r.f.i. emission

from certain classes of electrical and electronic equipment.

Sensitive, high-frequency-measuring equipment must have

good immunity to r.f.i. and additional r.f.i. shielding can be

often purchased as an option for equipment that must oper-

ate in especially noisy environments.

6.9.5 Power-Line-Coupled Noise

Consider the case illustrated in Figure 6.135,wherea

single supply line powers three circuits. If circuit 1 sud-

denly requires a large amount of current, circuits 2 and 3

may be affected because of the resistance and inductance

of the power-supply line. A large current drawn by circuit

1 can caus e a momentary voltage dr op at circuits 2 a nd 3

that can be propa ga ted as noi se t hroughout t he circuit.

The greater the time rate of change o f the current pulse

through circuit 1, the larger the effect on the other

circuits. This probl em is very common with logic circuit s,

particularly TTL circuits, that h ave saturating out put

stages. If a number of gates switch simultaneously, very

large transient current spikes can appear on the power

line. These transients are then interpreted as a change in

logic level by other gates, and transitions occur that are

entirely spurious. Standard practice is to use low-resist-

ance, low-inductance power-supply lines to the logic

gates and decouple the gates f rom the power supply with

high-frequency capacitors from the power-supply termi-

nal of the gate to ground. For TTL, ever y group of 20

gates must be decoupled from the power supply with a 0.1

lF capacitor, and every group of 100 gates must be

decoupled wit h an a dditional 0.1 lF tantal um capacitor

with good high-frequency characteristics.

Similar situations arise with switched, high-current

devices such as temperature-controlled furnaces operated

directly from the a.c. line. Large current transients may

affect all equipment plugged into the same line. The only

remedy here is to operate the high-current device from a

completely separate line circuit.

As an example, consider a series of logic gates to be

connected to a power supply by 1 ft. of #22 wire, which has

a resistance of 16 X/1000 ft. and an inductance of 640 lH/

1000 ft. If a few gates switch simultaneously, resulting in a

current spike of 10 mA with a rise time t

of 10 ns, the

momentary voltage drop along the line will be approxi-

mately iZ, where Z is

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ x

. In this case:

Z ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

16 3 10

3

XðÞ

þ 2p 3 3:3 3 10

1

3 6:4 3 10

7

HðÞ

ð6:92Þ

Figure 6.135 Current ﬂow in three circuits on a common

power line.

GROUNDS AND GROUNDING 505

where x ¼ (2p/3)t

has been used in the estimate of the

inductive reactance of the wire. The voltage drop is then:

3

A 3 133 X ¼ 1:3V ð6:93Þ

For the TTL logic, this drop could be enough to cause

some marginally substandard gates to change state

momentarily.

6.9.6 Ground Loops

Instrument terminals are connected to ground in order to

have the potentials of those terminals be at 0 V for refer-

ence purposes, assuming that every ground connection is

made directly to the zero potential of the earth. This is

often not the case, since most ground connections are

through the third wire of the a.c. line. Since this line has

ﬁnite resistance, currents ﬂowing in it will cause potential

drops and, depending on the point on the line where a

ground connection is made, the potential can be substan-

tially different from 0 V. When the 0 V references of two

instruments that are connected together differ, there is

danger of introducing noise into the system. The problem

is made all the worse by the fact that the reference points

can change their potentials with respect to each other in a

way independent of other system parameters. The solution

to this problem is to have only a single ground point in the

system and connect all the zero reference points and

shields to it. This means removing the ground connections

in the power-line cords of all line-operated instruments,

and isolating all shields and cases from conducting surfa-

ces that may be connected to ground at points other than

the single system ground. All connections to this single

system ground should be made as short as possible, with

the lowest-resistance conductors available. By having the

0 V reference potential connection and shield connection

at the same point in the system, no currents can be induced

in the reference line.

To illustrate these ideas, two different ways of connect-

ing a system composed of a signal source, ampliﬁer, and

recorder are shown in Figure 6.136. In the top arrangement

each

case is separately grounded and also connected to the

other cases through the outer conductor of the coaxial

cable between them. If the three grounds are at different

Figure 6.136 System grounding: (a) multiple grounds; (b) single ground to eliminate

ground loops.

506 ELECTRONICS

potentials, currents will ﬂow through the coaxial outer

shields connecting the devices together. Since the refer-

ence-potential line is the shield, it will take on different

potentials at different points in the circuit. As these poten-

tials change, the signal levels will change – the result being

seen as noise on the signal line.

In the second ar rangement , the common reference line

and the instrument shields are all attached to ground at a

single point – the reference ground. No gro und l oo ps c an

exist, and the reference line remains at the same potential

everywhere in the system. Clearly this is a su perior

arrangement. The imple mentation may be difﬁcult, how-

ever, since it is necess ary to connect all the cases and

shields separately to a single ground point. If all the

instrumentsaremountedinasinglerack,eachmustbe

electrically isolated from the conducting rack structure.

The coaxial-shield connections must al so be isolated

from the cases, an d the ground conn ectio n in the a. c. l ine

cord must be removed from each of the instruments. It is

not always necess ary to t ake such precautions with all

stages o f a system – it may be sufﬁcient to eliminate

ground loops from the most sensitive element to which

the signal source is connected.

It is worthwhile to understand the origins of ground

loop and shielding problems in order to be able to s ol ve

them when they arise. An ext ensive treatment is given by

Morrison.

The problem of ground loops also occurs when meas-

urements must be made across two electrical terminals,

neither of which is at ground potential.

Bridge measure-

ments are a common example of this. For ﬂoating meas-

urements, instruments that have the reference input

terminal electrically separate from the ground or common

terminal must be used, otherwise the ﬂoating potential

(common-mode potential) will be short-circuited.

In Figure 6.137, v

is the source voltage to be measured,

is the common-mode voltage, Z

is the input impedance

of the measuring system, and Z

is the impedance from the

common of the measuring circuit to the low terminal –

normally 10

to 10

X in parallel with 10

to 10

pF. The

presence of v

results in currents i

,andi

ﬂowing

through Z

and Z

. This presents no difﬁculties so long as

the resistance of the lines is zero; if the resistances are ﬁnite,

the common-mode currents will result in potential differ-

ences at the low input terminal and add to the error of the

measurement. Generally, Z

<< Z

and the critical parameter

is the ratio of the resistance of the low signal line to Z

. This

ratio is frequency-dependent, because Z

is complex. If the

source and instrument grounds are not at the same potential,

the difference will add to v

The common-mode rejection ratio (CMRR) is a quan-

tity for specifying how well an instrument rejects a com-

mon-mode voltage superimposed on the voltage to be

measured (the normal mode voltage):

CMRRðdBÞ¼20 log

, ð6:94Þ

where v

is the portion of the common-mode voltage that

appears as a normal-mode voltage, and therefore a source of

error. Meters that can be ﬂoated have CMRRs from 80 to

120 dB at d.c. and 60 to 100 dB at line frequency. When

higher values are required, special voltmeters having an

additional guard terminal must be used. This terminal,

when connected to the low terminal of the source by a low-

resistance connection, shunts the common-mode current

from the measuring terminals. Such meters offer CMRR

values of 160 dB at d.c. and 140 dB at line frequency. For

a meter with a CMRR of 160 dB, a 10 V common-mode

signal will result in a 0.1 lV normal-mode voltage.

Figure 6.137 Measurement of v

across two terminals,

both of which are not at ground. Current ﬂow through Z

the impedance from the low terminal of the measuring

instrument to ground, will result in an error voltage.

GROUNDS AND GROUNDING 507

6.10 HARDWARE AND

CONSTRUCTION

It is almost always better to purchase a piece of electronic

equipment than to design and construct it. This is certainly

the case for power supplies, ampliﬁers, signal generators,

and similar equipment that is mass-produced by a large

number of companies in a wide variety of models.

When one does, however, decide to construct a piece of

electronic equipment because of cost or the unavailability

of commercial units, there are a number of well-deﬁned

steps to follow:

(1) Design of the circuit

(2) Selection of components

(3) Construction and testing of a breadboard model

(4) Construction of the ﬁnal circuit

(5) Mounting

(6) Final testing.

Except for the simplest circuits, one is well advised to

use proven designs that can be found in manufacturers’

application books and in books and articles on circuit

design. A few such publications are given in the list of

references.

There are, in addition, well-established tech-

niques that are used by electronic engineers (but not often

included in textbook examples of circuit design) that can

make the difference between a circuit that works and one

that does not. These include bandwidth limiting, power-

supply decoupling, and signal conditioning.

6.10.1 Circuit Diagrams

Two kinds of circuit diagrams are the block diagram and

the schematic wiring diagram. The block diagram shows

the logical layout of the circuit by grouping all elements

necessary for a single function into a single rectangle.

Although simple, such diagrams are very useful in under-

standing the general operation of a circuit. The block dia-

gram is much like the ﬂowchart of a computer program.

The schematic wiring diagram shows all the compo-

nents of the circuit and the connections between them.

Figure 6.138 lists symbols used in schematic diagrams.

The

more complete the schematic, the more useful it is

for troubleshooting. A schematic will have the values

and ratings of all the components, as well as numbers

and color codes when necessary. Good schematics include

the values of voltages at critical points in the circuit and

drawings of waveforms where appropriate. One generally

reads schematic diagrams starting at the upper left with the

input and proceeding to the lower right to the output.

A useful addition to the schematic diagram is the chassis

layout diagram, which shows the physical location of all

parts. For ease of drawing, components that appear next to

each other on the schematic may be far away from each

other on the actual chassis or circuit board.

W ith increasing use of integrated circuits, it is more and

more difﬁcult to identify the functions of dif ferent elements

in a schematic. This is because the integrated circuits are

often only represented by rectangles with pin numbers. To

identify their function, it is necessary to consult a manufac-

turer’s catalog. Abbre viations common with ICs are gi v en in

Table 6.43 along with representati ve package outlines. Sche-

matic

diagrams also help identify speciﬁc components. If

there is an operational ampliﬁer on a circuit board with a

balance control near it for nulling purposes, it is useful to

know where the ampliﬁer is in the circuit and the nature of

the input and output before proceeding with adjustments.

The location of damaged components can be useful infor-

mation when deciding on the probable cause of the damage

and other components that may also have been af fected.

6.10.2 Component Selection and

Construction Techniques

When selecting components, the considerations that an elec-

tronic engineer ﬁnds important may be dif ferent from those

of a laboratory scientist building only a single example of a

circuit. It is always wise to overspecify components – that is,

to use components of higher ratings and better quality than

a critical cost-effective analysis of the circuit would show

to be necessary. Usually the cost of components is a small

fraction of total project cost when time is considered.

Once the circuit design has been decided upon and the

components assembled, a breadboard model can be con-

structed. This may seem an unnecessary and time-

consuming step, but care at this stage will save a great deal

508 ELECTRONICS

Figure 6.138 Symbols for schematic circuit diagrams.

HARDWARE AND CONSTRUCTION 509

of time later. The breadboard circuit should be constructed

from a complete, detailed schematic circuit diagram.

There are a number of prototype circuit boards and aids

for making breadboard models. Prototype boards use sock-

ets to which components and wires can be connected in a

temporary way . The spacing of the sockets is usually on .1 in.

centers to accommodate the usual 14- and 16-pin dual

in-line integrated circuits. The sockets accommodate only

a limited range of solid-wire sizes. Outside of this range, the

wire is either not held securely or the socket is bent out of

shape. Prototype boards of thi s type are satisfactory for low-

frequency circuits and logic circuits using TTL and CMOS.

For sensitive high-frequenc y circuits and ECL logic, stray

capacitance between sockets is a problem, and such circuits

must be built on a circuit board with a ground plane if they

are to work properly.

At this stage it is necessary that the

breadboard circuit follo w the schematic in ev ery detail. The

mechanical layout should be neat, with interconnections

between components as short as possible. This simpliﬁes

troubleshooting and avoids pickup problems.

Interfaces to external power, and input and output cir-

cuits, present some difﬁculty when working with bread-

boards. Dangling wires and alligator-clip connections

invite short or open circuits and damaged components.

Whenever possible, the breadboard should be mounted on

a larger structure with terminals and connectors to which

semi-permanent power-supply and signal connections can

be made (see Figure 6.139). Connections from these termi-

ls to the breadboard can then be made with short lengths

of hookup wire.

The breadboard circuit should be fully tested before

proceeding to the ﬁnal construction stage. During testing

the circuit should be operated with the same input and

output connections the ﬁnal circuit will have.

Once the breadboard circuit is functioning properly, the

ﬁnal circuit can be constructed. Depending on the complex-

ity of the circuit, there are a number of construction techni-

ques available. In general, all components are mounted on

circuit boards with the boards ﬁtted into a case or attached to

a panel. The power supply can be incorporated into the

circuit, or power-supply voltages can be brought in from

the outside-through connectors. For simple low-frequency

circuits involving only a few components and a moderate

number of connections, perforated circuit board and push-in

terminals can be used [see Figure 6.140(a)]. To avoid bend-

ing

the terminals when they are inserted in the board, an

insertion tool matched to the terminal should be used. All

connections are individually made and soldered for such

circuits. Whenev er possible, activ e components such as

ICs and transistors should be used with sockets, and all

soldering done with the components removed from the sock-

ets. Perforated circuit board with printed circuit wiring is

also a conv enient medium for making ﬁnal circuits [see

Figure 6.140(b)]. With this type of circuit board, all solder-

ing

is done on the board and there is no need for separate

terminals. To facilitate bringing power to the components,

Figure 6.139 Circuit breadboard mounted to chassis on standoffs to allow proper con-

nection of power supply, input and output leads.

510 ELECTRONICS

power-supply and ground-bu s structures are often part of

such boards. For more complex circuits, custom-printed cir-

cuit boards (see Section 6.10.3)orWireWrap

boards (see

Section 6.10.4) can be used.

The

circuit board containing all the electrical compo-

nents and a power supply, if required, is typically mounted

on a standard 19 in. aluminum rack panel on standoffs.

When there is a need for more than two or three circuit

boards, the means of mounting and of making the inter-

connections must be considered more carefully. For multi-

ple circuit boards, card-cage mounting – using guides and

edge connectors, as shown in Figure 6.141, is a common

technique.

Interconnections between boards are made

between the edge connectors on the rear panel of the chas-

sis. A variation of this method uses a motherboard, to

which all the connections from the other boards are

brought. In this method, the edge connectors provide

power to the separate boards and help to mechanically

retain the boards in the chassis. Signal leads are brought

to the motherboard via multiple-pin connectors and ﬂat

multiple-conductor cable, using mass termination hard-

ware for increased reliability. A variation of the mother-

board conﬁguration includes the edge connectors on the

motherboard. An on–off switch, pilot light, and fuse are

put on the front panel, as well as input and output con-

nectors and controls. When labeling the panel, it is wise

to indicate schematically the electronic functions per-

formed by each section of the circuit with standard

symbols. Labels can be applied with the silk-screen

Figure 6.140 Perforated circuit boards for use with (a) pin

connections and (b) direct solder connections.

Figure 6.141 Circuit boards mounted in a

card cage showing interconnections and

guide slots.

HARDWARE AND CONSTRUCTION 511

technique or dry transfer letters, India ink, or embossed

pressure-sensitive tape. A protective cover should be

placed over the circuit (see Figure 6.142).

Construction

can be simple. A portable electric drill

or drill press is necessary for drilling proper-sized holes

in panels and covers. A list o f electronic-circuit c on-

struction tools is given in Table 6.43 and a list of useful

rdware is given in Table 6.44. Flathead screws should

e used on exterior surfaces, and lock washers should be

used under nuts. Standard .062 in. circuit board can be

cut easily with a hacksaw and drilled with standard high-

speed drills. A nibbling tool is u seful for making irreg-

ular-shaped holes in sheet metal, and a set of chassis

punches fro m 1/2 to 1 1/2 in. speeds up work and makes

accurate holes in sheet metal. A tapered hand reamer is

very useful for enlarging holes in sh eet metal and circuit-

board material.

Figure 6.142 Mounting of a circuit board on a rack panel.

Table 6.43 Electronic-circuit construction tools

Nutdrivers

Sheet-metal nibblers

Universal electrician’s tool

Needle-nose pliers

Slip-joint pliers

½-in tapered reamer

Wire cutters

Wire strippers

Soldering gun, pencil

Knife

Single-edge razor blades

Solder sucker

Solder wick

Heat gun

Clip-on heat sinks

Chassis punches

5=8,3=4,1ð1=8Þ,1ð1=4Þin:Þð

Circuit-board holder

Note: These tools supplement those listed in Table 1.1.

Table 6.44 Hardware and electronic equipment

Hardware

Screws (ﬂathead and roundhead), nuts, ﬂat washers, lock

washers (4–40, 6–32, 10–24)

Solder lugs and terminals

Binding posts

Grommets

Standoffs

Cable clamps

Line cord

Hookup wire

Spaghetti (ﬂexible thin insulating tubing) in assorted sizes

Shrink tubing in assorted sizes

Eyelets

Fuse holders

Indicator lamps

Switches

Electronic Equipment

Signal sources:

Signal generator

Pulse generator

Logic pulse source

VOM/DVM

Oscilloscope

Logic probe

Logic clips

Test leads for VOM and DVM

Oscilloscope probes:

3 1 probe for low frequencies

3 10 compensated probe for frequencies above 10 MHz

Radio-frequency probe for demodulating r.f. signals

512 ELECTRONICS

6.10.3 Printed Circuit Boards

The use of PCBs in laboratory electronics is justiﬁ ed when

sev eral identical boards are needed or when the proper func-

tioning of the circuit requires the kind of controlled geome-

try that printed circuit boards offer. Emitter-coupled logic

(ECL) circuits require microstrip line geometries for inter-

connections and precise placement of components to achiev e

fast rise times while at the same time avoiding crosstalk

between circuit elements. Sensitiv e lo w-l e v el ampliﬁer cir-

cuits require precise lead placement to eliminate noise

pickup. Printed circuit boards consist of an insulated sub-

strate covered with a metal (usually copper) foil. Some of the

common rigid substrates used for copper -clad boards are

listed in Table 6.45 along with their codes. Nonrigid boards

or ﬂe

x-boards are used to ﬁt into irregular conﬁned spaces.

Commercial production of PCBs begins with copper-

clad laminated boards, usually epoxy-impregnated ﬁber-

glass .062 in. thick, from which copper is removed by

chemical etching to form the pattern of traces, pads, and

busses that are the electrical connections and mounting

areas for the individual electronic components and connec-

tors. To increase circuit density, patterns can be formed on

both sides of the board with electrical connections between

the layers made by plated holes or vias. Sandwiches of up

to four boards (eight layers) are common, and current man-

ufacturing capabilities permit as many as 40 layers. After

fabrication of the board pattern, holes are drilled for com-

ponent leads, vias, and fasteners – a thin layer of solder

(solder plate) is ﬂowed over the copper and through the vias

to protect from oxidation and increase the ease of compo-

nent soldering. Solder mask – a thin, tough, insulating ﬁlm

– is placed over the board, leaving only the solder terminals

and pads uncovered. The mask protects the traces, acts as

an insulator to prevent short circuits, and prevents solder

bridges from occurring when components are soldered to

the board. Component outlines and descriptive information

are printed on the board using a silk-screen technique.

The circuit patterns are photographically transferred

to the boards using photo-plots and photo-resists. The

photo-plots are the equivalent of a photographic negative

and contain all of the detail at the required precision of the

ﬁnal circuit board. In the past, photo-plots were made by

hand with opaque tape and precut pads and pad arrays, but

this has been commercially superseded by CAD/CAM

(computer aided design/computer aided manufacture)

programs that are now widely available for PCs. These

programs have two parts – schematic capture and board

layout. Simulation software is often available within the

layout programs to verify the functioning of the circuits for

a variety of input signals. Printed circuit boards produced

with CAD/CAM software have a number of advantages,

even at the single board prototype level:

 Uniform electrical and mechanical properties as a result of

using standard materials and automated fabrication meth-

ods based on standard electronic and mechanical engineer-

ing con v entions that are built into the CAD/CAM programs

 Error checking in the schematic-capture routines

 Linking the output of the schematic-capture program to

circuit-analysis programs for evaluation of the circuit

Table 6.45 Circuit-board subtrates

Type of board material Designation Application

Paper-base phenolic XXXP Hot punching

XXXPC Room-temperature punching

Paper-base phenolic FR-2 Flame-resistant

Paper-base epoxy resin FR-3 Flame-resistant

Glass-fabric-base epoxy resin FR-4 General-purpose ﬂame-resistant

FR-5 Temperature and ﬂame-resistant

G-10 General purpose

G-11 Temperature-resistant

Glass-fabric-base polytetraﬂuoroethylene resin GT and GX Controlled dielectric constant

Note: Standard thicknesses, including the copper clad ding, range from 1/32 (0.031) to 1/4 (0.250) in., with 1/16 (0.062) in. the most common.

HARDWARE AND CONSTRUCTION 513

 Electronic recording and transmission of the photo-plot

(Gerber), drill, solder mask, silk-screen, and outline ﬁles

 Competitive pricing and fast turnaround.

These advantages have to be weighed against the incon-

venience of modifying printed circuit boards that are only

meant to be prototypes, and having to acquire and learn the

CAD/CAM software. Manufacturers of schematic-capture

and PCB-layout programs are listed at the end of this chap-

ter. Trial versions of their software products are generally

available and many offer student and educational institution

discounts. A number of PCB fabricators make available

layout programs that are easy to use for relatively simple

circuits. Procedures for producing commercial PCBs using

schematic-capture and board-layout programs are detailed

in the following two sections.

Schematic Capture. A schematic diagram of the cir-

cuit is laid out on the computer using components from the

program library. Components not in the library can

sometimes be obtained from the manufacturer of the com-

ponent. The library entry contains mechanical and electrical

information about the component, as well as the numbering

and designation of the pins and/or terminals. Layout is

accomplished by arranging the components on the com-

puter screen with the mouse or by specifying coordinates

and then interconnecting the pins of the components. Each

connection is a node. From the schematic arrangement, a

netlist is made. This is a list of all the components along

with their electrical parameters and the nodes to which they

are connected. The netlist is the basis of various error-

checking routines to verify that inputs and outputs are not

grounded and that no component is shorted.

Board Layout. The netlist from the schematic-capture

program is the input to the board-layout program. Layout

starts by deﬁning the size and shape of the board and the

number and designation of layers. For a two-sided board,

one side (the top) is the component side and the other (the

bottom) is the wiring side – even though there will gener-

ally be wiring on both sides.

Componentsareplacedontheboardfromastackofout-

line drawings (rat nest) with connections speciﬁed by the

netlist. The components with their accompanying wires are

initially arranged within the board area according to a few

simple rules: separate input and outputs by as large a distance

as possible; make po wer-supply and ground connections as

short as possible; minimize the number of crossed traces; and

horizontal and vertical routing of traces. Final routing of the

connections is done manually for small, uncomplicated

boards with only a few components. Autorouting routines

are useful for complex boards, but hand routing may still

be necessary in certain circumstances. For small boards, it

is possible to skip the schematic-capture part of the procedure

and go directly to the board-layout routine. In this case, parts

are placed manually and interconnections made individ ually.

When parts are available in the program library, this can be

an efﬁcient method for board layout, but all automatic error

checking is lost with manual parts placement. Table 6.47 lists

impo

rtant PCB layout considerations.

The PCB manufacturer requires computer ﬁles to fabri-

cate the boards. These ﬁles are routinely transferred elec-

tronically over the Internet. The ﬁles specify the board

layout, board size and shape, hole pattern, solder-

Table 6.46 PCB construction considerations

(1) Board size, shape material [ 1=16 in: G10 is most common

with 1 oz./ft.

(35 lm) copper cladding]

(2) External connections

(a) Solder or wrapped to terminals

(b) Plugs

(3) Mounting

(a) Screws

(b) Guide slots and edge connector

(4) Component layout

(a) Mechanical stress

(b) Thermal stress

(5) Lead layout

(a) 1=16 or 0.050 in. preferred width; no sharp corners

(b) 0.015 in. minimum lead clearance, larger in the vicinity

of solder connections

(i) Insulated wire bridges for few crossovers

(ii) Double-sided board and plated-through holes for

many crossovers

514 ELECTRONICS

mask pattern, and silk-screen labels and outlines. It is essen-

tial that the ﬁles follow precisely the format required by the

manufacturer. There is one Gerber ﬁle and one aperture ﬁle

per layer. The Gerber ﬁle speciﬁes the interconnections and

the aperture ﬁle gives the widths of the traces. If solder mask

and silk-screen printing are used, each requires a Gerber ﬁle

and aperture ﬁle per layer . Holes are speciﬁ ed by a drill ﬁle

and a drill list ﬁle. For laboratory purposes, the FR-4 grade

board is the current standard. The copper-foil cladding is

usually cathode-quality, electrolytic copper. The most com-

mon thickness is 1.0 oz./ft.

(35 lm). Turn-around time for

double-sided boards is generally three to ﬁv e days. A rectan-

gular , double-sided board, 3 in. by 5 in, costs less than $100.

Per board prices fall substantially for two or more boards.

Components are ﬁxed to PCBs by soldering. For large,

complex, multilayer boards, the PCB manufacturer will

often have the capacity to automatically locate parts on

the board and solder them in place using wave soldering

for through-hole components and reﬂow methods for

surface-mount components. For surface-mount parts a sol-

der-paste mask is used. This mask has openings corre-

sponding to the solder pads. It is placed on the board,

properly aligned in relation to the pads, and solder paste

is squeezed over it. When the mask is removed, solder

paste covers only the pads, the components can then be

placed in position ready for soldering. When hand solder-

ing, through-hole wire lead components are held in place

on the board by inserting the leads through the appropriate

holes in the board and bending them outward at 45°. The

board can then be turned over for soldering the leads to the

pads. After soldering, the leads are clipped short with ﬂush

cutting pliers, see Figure 6.143. Soldering surface mount

components

is more difﬁcult and takes some practice.

When the pads on the board have a solder reﬂow ﬁnish,

soldering is easier than if solder has to be added. With

reﬂow ﬁnish pads, ﬂux is ﬁrst applied to the pads from a

ﬂux pen or syringe and the component placed in position

with leads aligned with the pads. The component is then

tacked in position by heating opposite corner pins with a

ﬁne-tip, well-tinned soldering iron from which all excess

solder has been removed. Each pin is then heated in

sequence to melt the solder and form a high conductivity

joint. It is wise to repeat this procedure a second time to

insure the secure soldering of all the pins. The board can be

examined under a strong light source to check for solder

bridges. Bridges can be removed with solder braid.

For boards without a solder plate ﬁnish, surface mount

components can be soldered in place using the same gen-

eral technique, but with a thin coating of solder on the iron

tip. As the tip is wiped over the component leads solder

Figure 6.143 Pliers used as a heat sink. A heat sink is required when

soldering to the leads of heat-sensitive components.

HARDWARE AND CONSTRUCTION 515

is transferred from the tip to the leads and pads making

effective solder joints. With this technique, solder bridges

are more likely and careful inspection is required.

To solder surface-mount resistors and capacitors, solder

must ﬂow over the circuit-board pad and component

contact. This is illustrated in Figure 6.144. To solder sur-

ace-mount transistors and ICs with coarse-pitch leads to

circuit-board pads it is necessary that solder ﬂow between

the component contacts and pads. Fine solder, and ﬁne-tip-

ped soldering iron, a low-po wer binocular microscope, and

steady hands are required for these component s. Solder ﬂux

dispensed from a pen or syringe with a ﬁne tip can be applied

to the pads and the component contacts set down on top of

the ﬂux. The contact is then heated with a ﬁne-tip soldering

iron and ﬁne wire solder applied until the solder melts and

wets the component contact and circuit-board pad.

Although commercial production of PCBs from master

artwork has been replaced by fabrication directly from com-

puter ﬁles, it is still possible to make a PCB from hand-drawn

artwork with kits that are available from electronics suppliers.

The kits consist of circuit boards and sensitizers or presensi-

tized boards, dev eloper, ferric chloride etchant, and trays and

brushes. The ﬁrst step is creation of the artwork master , a

precise representation of the ﬁnal traces that will appear on

the board. The master is produced using drafting techniques.

To increase speed and accuracy of manual drafting, PCB dry-

transfer drafting tapes, socket-hole patterns, and terminal

pads are av ailable. The tools needed are a T-square, triangles,

an X-ActoÔ knife to cut the tape to length, and tweezers for

removing the dry transfers from the backing sheet. To avoid

dimensional changes with temperature and humidity, the art-

workcanbepreparedonMylarÔ drafting ﬁlm rather than

ordinary paper. The pattern on the master photographic neg-

ativ e is transferred to the circuit board by the use of a photo-

resist sensitizer. Boards can be purchased presensitized, or

unsensitized blanks can be coated with a photoresist that is in

aerosol or liquid form. A ne gative resist, after exposure to UV

light, is unaffected by a subsequent developer solution,

whereas UV-exposed, positive resist is dissolved by dev el-

oper. If the master artwork is a positive (that is, the desired

foil pattern is represented by opaque areas on a transparent

background), a positive resist is required. The sensitized

Figure 6.144 Soldering surface-mount (SMT) components.

516 ELECTRONICS

board is exposed to strong light through the full-size master .

The board is then placed in a glass tray containing de veloper.

Areas on the board exposed to the light will be dissolved,

while those areas protected by the artwork will remain.

After full development, the board is rinsed, dried, and placed

in an etching solution. It is also possible to laser print or

photocopy circuit designs directly onto specially coated trans-

fer paper – available from JDR Microdevices – that is then

ironed on to a blank PC board, which is then ready for etching.

Sev eral electronics suppliers sell resist pens that are used to

draw PCB artwork directly on bare circuit board. Ferric chlor-

ide is the most common etchant. It works best when gently

heated and agitated. Full etching can take up to one hour per

board and should always be done in a glass tray. When etching

is complete, the board is rinsed and all etchant residues

removed with steel wool or a solvent. A more complete

description of the procedure is giv en in the 1999 edition of

the ARRL Handbook for Radio Amateurs. The photoresists

have limited shelf life, and the etchant is corrosiv e.

Transistor and integrated circuit packages for PCB

mounting come in a wide variety of forms. Table 6.47 gives

the

designation of some common packages with represen-

tative diagrams.

A technique related to PCBs and based on thick-ﬁlm tech-

nology is used to pr oduce high-density circuit patterns on

alumina (Al

) substrates. A screen with 200 to 300 lines/

in. transfers the desired circuit pattern with a special ink

containing suspended metal particles and a binder. When

the inked substrate is ﬁred, the metal particles fuse to each

other and the substrate, producing a tightly bonded con-

ducting pattern. Components are then soldered to the

appropriate pads on the substrate with microsoldering irons

or solder paste and carefully controlled hot air. Thick-ﬁlm,

rather than discrete, resistors are often used with this tech-

nique because they can be produced by the same printing

technique by using a different ink. Small, high-capacitance

chip capacitors replace the more conventional disc and

tubular capacitors. With the thick-ﬁlm technique, it is often

quite easy to incorporate ICs and discrete components on

the same substrate to produce a self-contained hybrid cir-

cuit. Such a circuit can be hermetically sealed and has the

appearance of a large IC. The advantages of such circuits

are small size, excellent electrical properties, and good

mechanical strength. There are a number of companies that

produce hybrid circuits starting from schematic diagrams.

Because of its specialized nature, thick-ﬁlm work is best

left to such ﬁrms.

Solder for electrical and electronic work is an alloy of tin

and lead and is speciﬁed by the ratio in weight % tin to lead.

Thus 40/60 solder is 40% tin and 60% lead by weight. An

Table 6.47 Transistor and integrated circuit packages

Transistor

TO-3 Round Can on Diamond Base

TO-5 Round Can

TO-220 Rectangle with Heat Sink

Through Hole IC

DIP Dual In-Line Package

PDIP Plastic Dual In-Line Package

SIL Single In-Line

SIM Single In-Line Module

SIP Single In-Line Package

VIL Vertical In-Line

ZIP Zig-Zag In-Line Package

Surface Mount IC

PSMC Plastic Surface Mount

Component

QSOP Quarter Size Small Outline

Package

SOIC Small Outline IC

SOL Small Outline Large

SOP Small Outline Package

SOT Small Outline Transistor

SSOP Small Shrink Outline Package

TQFP Thin Quad Flat-Pack

TSOP Thin Small Outline Package

TSSOP Thin Shrink Small Outline

Package

IC Modules

BGA Ball Grid Array

DIMM Dual In-Line Memory Module

JLCC J-Lead Chip Carrier

LCCC Leadless Ceramic Chip Carrier

LDCC Leaded Ceramic Chip Carrier

PGA Pin Grid Array

PLCC Plastic J-Lead Chip Carrier

SIMM Single In-Line Memory

Module

HARDWARE AND CONSTRUCTION 517

Table 6.47 (cont.). All dimensions in mm

12 3

456

SEATING

PLANE

.95

.90

.05

2.0

1.3

.65

2.10

.32

.14

1.25

3-Lead SOT, Small Outline Transistor

TO-3

9 Lead SIP

14 Lead PDIP

TO-220

TO-5

TO-29

6.6

5.1

3.8 MIN

8.5

9.4

4.8

12.8

1.3

Transistor

Through Hole IC

Surface Mount Transistor

9.6

2.54

22.2

2.54

3.0

5.8

19.3

6.6

3.5

0º –15º

4.9

0.46

2.54

16.5

14.73

25.4

12.4

30.2

7.4

19.5

11.5

2.2

1.0

φ4

518 ELECTRONICS

TOP VIEW

PIN #1 I.D.

SIDE VIEW

END VIEW

SEATING

PLANE

4.4

6.4

7.8

.25

.65

.10

1.0

.15

.25

1.0

0.10

1.20

.60

24 Lead TSSOP, Thin Shrink Small Outline Package

Surface Mount IC

SEATING

PLANE

PIN (1) IDENTIFIER

1.27

1.15

9.9

9.0

1.15

.51

2.7

4.4

.89 R

3.9

.74

PLCC, Plastic Leaded Chip Carrier

Pin #1

Indicator

44.3

24.2

20.3

1.8

1.5

1.02

45° Chamfer

4.3

2.0

.22

10.5

44.8

1.27

68 Lead Plastic Flatpack

Seating Plane

44 Lead QFP, Quad Flatpack

.30

12.4

10.0

2.35

.15

1.2

0.80

.05

Table 6.47 (cont.)

HARDWARE AND CONSTRUCTION 519

Front View

1 80

Back View

118.1

17.8

1.27

1.04

1 Mbit

32-lead PLCC

(550 x 450 MILS)

Side View

8.4

1.27

80 Pad Single In-line Leadless Memory Module (SIMM)

.56

2.54

3.18

78.7

16.5

5.1

30 Lead In-line Leaded Memory Package (SIP)

Seating

Plane

detail X

pin 1 index

mark location

index

12345678910 111213

seating plane

2.54

0.46

2.54

33.5

19.2

2.58

1.27

3.30

120 Pin

CPGA: Ceramic Pin Grid Array

IC Modules

100 BGA, Ball Grid Array

0.8

0.5

7.2

SIDE VIEW

BOTTOM VIEW

1.4

Table 6.47 (cont.)

520 ELECTRONICS

eutectic alloy with the sharp melting point of 183 °C(361°F)

is formed when the mixture is 63/37. As one departs from this

ratio, the melting point becomes less sharp, extending over a

larger temperature range. Solder wire can be purchased in

diameters from .015 in. (28 gauge) to .062 in. (16 gauge).

Fluxes, whose purpose it is to dissolve the oxides on the

surfaces of the metals to be joined, are almost always used in

soldering. Rosin ﬂuxes are commonly used for electrical and

electronic work. Under no circumstances should acid ﬂuxes

be used. These are extremely corrosi ve and can se verely dam-

age components, insulation, and the circuit board itself. Fluxes

come in paste and liquid form and are conv enien tly packaged

in pens and syringes for surface-mount component work.

There are three types of rosin ﬂuxes: R (low activity), RMA

(mild acti vity), and RA (activ e). The R type is normally used.

There are now ﬂuxes that can be removed by rinsing with

water and also no-clean ﬂuxes that do not have to be removed

after soldering. Solder wire for electronic use generally has

ﬂux incorporated in it, though pure ﬂux is also av ailable.

The solder should be maintained at 35 to 65 °C(60to

120 °F) above its melting point for a time sufﬁcient to

completely wet the surfaces to be joined. Too little heat

will result in insufﬁcient wetting of the surfaces and a so-

called cold-solder joint, which is mechanically and electri-

cally unsatisfactory. Too much heat can destroy compo-

nents, melt plastic insulation, and burn the circuit board.

When soldering heat-sensitive components, a heat sink can

be used near the component to protect it. This can be in the

form of a pair of long-nose pliers or special tweezers, which

are clamped on the lead between the source of heat and

component to be protected (see Figure 6.143). To ensure a

goo

d joint, the tip of the soldering iron should have a thin

bright coat of molten solder covering it, for thermal contact.

With time, this coating becomes contaminated with oxides

and should be renewed by wiping the surface and reapply-

ing fresh solder. This is called tinning the iron. The prop-

erly tinned hot tip is then brought in contact with the

surfaces to be soldered, and only when they have reached

the temperature necessary to melt the solder should solder

be applied to them. A common mistake is to melt the solder

on the surface of the iron and hope it will ﬂow onto the

surfaces to be soldered. Since the molten solder ﬂows

toward the hottest point, this method leads to wasted solder

and cold-solder joints. Poor solder joints also result from

insufﬁcient heat and from contaminated surfaces that resist

being wetted by the solder even in the presence of ﬂux.

When soldering is complete, the ﬂux should be removed

with a commercial ﬂux solvent or isopropyl alcohol.

Increasing recognition of the toxic properties of lead and

organic ﬂuxes and solvents has resulted in the availability of

lead-free solders combined with noncontaminating ﬂuxes or

water-soluble ﬂuxes in a variety of formulations. The lead-

free solders are mostly tin with copper, silver, bismuth, and

antimony added, to enhance to varying degrees mechanical

strength, electrical conductivity, thermal properties, and

wetting and ﬂow. Many of these solders are compatible with

lead–tin solder. Noncontaminating ﬂuxes can remain on the

circuit after soldering while water-soluble ﬂuxes can be

removed with a deionized water rinse.

Soldering irons are generally of two types, the soldering

gun [Figure 6.145(a)] and the single-element soldering pen-

l [Figure 6.145(b)]. Guns come in single- and dual-watt

dels from 100 to 325 W. They have the advantage of

being able to be turned on and off quickly, but are generally

too powerful, heavy, and bulky for PCB work. Soldering

pencils come in wattages from 12 to 75 W with a large

variety of tip shapes. Thermostatic control and stands with

tip-cleaning sponges are often used with them. For best

results, soldering-iron tips should be cleaned and tinned

regularly, and the heating elements should be checked for

good electrical, mechanical, and thermal contact to the tips.

It is often necessary to remove a component from a PCB

and replace it. One method that does not require desoldering

the old component is shown in Figure 6.146. This technique

does

not work with ICs and multilead components, where

desoldering from the board is necessary . Three common

desoldering methods are solder wick, solder aspiration, and

heat and pull. Solder wick is copper braid coated with rosin

ﬂux that withdraws solder from a joint by capillary action

when placed on top of the molten solder to be removed.

Generally, more heat is required to remov e a component than

to solder it in place initially . Braid is sold in widths from

.030 in. to .210 in. The ﬁne braid is most useful for removing

solder bridges between the leads of ﬁne-pitched, surface-

mount components. Solder can also be removed by using a

sucking tool to aspirate the solder after melting it with a

soldering iron. The tool can be a rubber bulb with a heat-

resistant nonmetallic tip, or a triggered spring-loaded syringe.

Special heat-and-pull soldering irons are needed to remov e

multilead components, such as ICs. These irons have tips

HARDWARE AND CONSTRUCTION 521

shaped to heat all leads simultaneously. These tips often do not

heat up evenly, resulting in nonuniform heating of the compo-

nent leads. If the component is lifted before all leads are free,

the circuit-board traces can be damaged. After removal of the

component, the holes must be cleaned of residual solder

before proceeding with the insertion of another component.

Solder removal by heating followed by shaking or blowing

should be avoided. It results in solder splashes that can cause

short circuits. Surface-mount components can be removed in a

variety of ways. The simplest is to use solder braid to remove

as much solder from each of the leads as possible and then

heat each lead until the solder is melted and pry it away from

its pad with a ﬁne dental pick. When this is done to all the

pads, the component can be removed from the board. This

method results in the bending of all the component leads and

may lift the pads from the board. Printed circuit-board tracks

that hav e been damaged by overheating or mechanical stresses

can be removed with a knife and replaced with ne w sections

soldered directly to undamaged foil. When pads become

detached from the substrate, they can be replaced with new

ones anchored to the board with swaged eyelets.

An alternative removal method uses a length of music

wire that is inserted behind the leads of the surface-mount

component. As each pin is heated the wire is slid under it to

free it from the pad. This is done for each of the leads until

the component is freed from the board. Because the force

on the wire is parallel to the surface of the circuit board, the

chance of lifting pads and traces is reduced.

When a large number of surface-mount components are

to be soldered, a hot-air rework station gives faster and more

uniform and reliable results that hand soldering with a ﬁne-

tip iron. Such rework stations consist of a source of hot air, a

hand piece or holder, and a set of nozzles. The openings in

the nozzles match the position and size of the contacts of the

surface-mount component to be soldered. With these units,

the temperature, air-ﬂow rates, and duration of air ﬂow can

be separately controlled. The surface-mount components

are placed on the circuit-board pads, which have been coated

with solder paste. The appropriate nozzle is inserted into the

hand piece and the air-ﬂow rate, temperature and ﬂow dura-

tion selected. The nozzle is placed over the component and

the heated air turned on. All contacts are heated simultane-

ously to the temperature at which the solder ﬂows and the

component contacts are bonded to the circuit-board pads. In

a few seconds all connections are made. The procedure is

repeated for all of the components. The more advanced units

allow for programming of air ﬂow, air temperature and

heating cycle. Control over lead temperature and heating

time means that there is no damage to the component nor

to the circuit board. The rework station can also be used to

Figure 6.145 (a) Soldering gun; (b) single-element

soldering pencil.

Figure 6.146 Replacing a component on a printed circuit

board.

522 ELECTRONICS

remove surface-mount components from circuit boards by

heating the contacts with the correct size nozzle and remov-

ing the component once the solder holding the contacts

becomes molten. Some rework stations incorporate vacuum

tweezers into the hot-air nozzles to assist in the removal of

the components. Because of the small size of surface-mount

resistors and capacitors, and the ﬁne pitch of surface-mount

IC contacts, a low-power binocular microscope is very use-

ful for assessing the quality of the solder joints and inspect-

ing for solder bridges between contacts.

In the preceding discussion of PCBs, low-frequency

applications have been assumed. If the board is made for

high-frequency applications, a great deal more care is

required in component placement and lead geometry. For

fast logic circuits using ECL ICs, microstrip line geome-

tries are recommended.

6.10.4 Wire Wrap

Boards

Boards, made by the Gardner–Den ver Company under the

trade name Wire WrapÔ, have sockets spaced at intervals

corresponding to the spacing of the leads on inte grated cir-

cuits. The sockets have long, square cross-section posts, so

that when the socket is swaged into a substrate material the

post extends on the back-side. The length of the post deter-

mines how many separate connections are to be made to it.

Three- and four-layer length posts are the most common (see

Figure 6.147). A special wrapping tool is used to

make

connections to the pins. The tool can be manual,

line-operated, battery-operated, or air-operated. The hand

tool is entirely adequate for circuits with up to 10 ICs. As

the wire is wrapped around the post, the high pressures gen-

erated between the wire and the sharp corners of the post

form a cold weld, which has good electrical and mechanical

properties. The advantages of such a system are:

(1) No solder connections to cause heat damage to com-

ponents and circuit board

(2) Electrical components that plug into sockets and are

easily removed for replacement or testing

(3) Higher component density than obtainable with double-

sided circuit boards, because wire crossings are possi-

ble without short circuits

(4) Ease of removing and remaking connections (an

unwrapping tool that is a companion to the wrapping

tool allows one to remove connections – however, if the

connection that one wants to remove is not the highest

of a stack, one must remove the upper ones to get to it).

(5) No artwork, photographic reproduction, masking, or

etching required

(6) Reliability

(7) Speed of fabrication

In practice, one uses single-conductor wire specially made

for wrapping. The three most common gauges are AWG 30

(0.25 mm), 28 (0.32 mm), and 26 (0.40 mm). Different wrap,

unwrap, and insulation-stripping tools are used for each

gauge. One can obtain the wire in rolls or in precut and

prestripped lengths. If one uses rolls, it is necessary to have

a wire stripper to remove 1 in. of insulation at either end of

the length of wire to be wrapped. Thermal strippers ensure

that the conductor will not be nicked when stripped, but

special mechanical strippers that do an adequate job can also

be obtained inexpensively.

The usual Wire WrapÔ board consists of a matrix of

sockets with spacing corresponding to the spacing of the

terminals on the normal 14- or 16-pin DIP IC. After the

placement of ICs on the board has been decided upon, a

Wire WrapÔ list is made, which indicates the pins between

which connections are to be made. Each pin is identiﬁed by

a letter plus number code identifying the column and row of

the pin [see Figure 6.148(b)]. Once the list is complete, all

the

wrapping can be done at one time. It is common for

Wire WrapÔ boards to have a ground plane and a power-

Figure 6.147 Wire Wrap

post.

HARDWARE AND CONSTRUCTION 523

supply voltage plane or bus. The Wire WrapÔ posts can be

connected to these planes at intervals of 14 to 16 pins. A

solder bridge can sometimes be made between the appro-

priate pin and the exposed ground plane. Connections to the

plane from outside the board can be made with a screw-

and-lug connection to tie points on the board. Signal con-

nections are usually via ribbon connectors to DIP sockets.

Discrete components are used with mounting plat-

forms or, if sufﬁcient space is available, they can be

wrapped directly to t he posts. The platforms have pins

that ﬁt the socket holes in the board, and the discrete

components are soldered to the posts or forked terminals

on the top of the platform (see Figure 6.149). When a

circuit

with only a few ICs must be constructed, an inex-

pensive method is to use individual Wire WrapÔ sockets

and glue them to perforated circuit board with 0.100 in.

hole-spacing. This is much less expensive than commer-

cial boards and entirely adequate for low-frequency

applications. A disadvantage of Wire Wrap Ô boards is

their high initial cost, but they can be reused.

Initial veriﬁcation of the connections on a board is

done by removing all components, attaching the ground

and power-supply leads, and measuring the voltage at each

pin. They should all be consistent with the W ire WrapÔ list.

6.10.5 Wires and Cables

There are many types of electrical wires used in the labo-

ratory. Selection of the correct type is important for cor-

rectly functioning equipment. Wire should be selected

according to its voltage and current rating for routine low-

frequency operation. For applications involving high fre-

quencies and low signal levels, more care must be taken.

The use of multiple-conductor cables can simplify wiring,

Figure 6.148 (a) A Wire Wrap

board; (b) example of a

wrap list.

Figure 6.149 Platform for mounting discrete components.

The platform plugs into the Wire Wrap

board.

Table 6.48 Current-carrying capacities of copper-

insulated wire

B&S Gauge Diameter (in.) Allowable

Current

(A)

Resistance

per 100 ft.

(X)

8 0.128 50 0.628

10 0.102 30 0.999

12 0.081 25 1.588

14 0.064 20 2.525

16 0.051 10 4.016

18 0.040 5 6.385

20 0.032 3.2 10.15

22 0.025 2.0 16.14

24 0.020 1.25 25.67

26 0.016 0.80 40.81

28 0.013 0.53 64.90

30 0.010 0.31 103.2

For rubber-insulated wires the allowable current should be

reduced by 30%.

At 20 °C (68 °F).

524 ELECTRONICS

and some knowledge of the kinds of multiple conductor

conﬁgurations is useful. Table 6.48 lists the diameter, allow-

le current, and resistance per 100 feet of B&S-gauge

insulated copper wire. Table 6.49 lists the electrical proper-

es of common thermoplastics used for insulation.

The most common wire is a.c. line cord, the type used for

connection to the a.c. outlet. Twin-conductor zip cord should be

avoided in laboratory applications because of its limited resist-

ance to mechanical stresses. Three-conductor color-coded line

cord is best suited for the laboratory . The double insulation of

Table 6.49 Electrical properties of thermoplastics

Material Trade Name Volume

Resistivity

(X cm)

Dielectric

Strength

(V/mil)

Power Factor

at 60 Hz

Characteristics

ABS Lustran 10

–10

300–450 .003–.007 Tough, average overall electrical

properties

Acetals Delrin 10

500 .004–.005 Strong, good electrical properties to

125 °C

Acrylics Lucite, Plexiglas,

Perspex

>10

450–480 .04–.05 Resistant to arcing

Fluorocarbons:

CTFE KEL-F 10

450 .015 Excellent electrical properties, some

cold ﬂow

FEP Teﬂon FEP >10

500 .0002 Properties similar to TFE, good to

400 °F

TFE Teﬂon TFE >10

400 <.0001 One of the best electrical materials

to 300 to 500 °F, cold ﬂow

Polyamides Nylon 10

–10

300–400 .04–.6 Good general electrical properties,

absorbs water

Polyamide-imides

and polyimides

Vespel, Kapton 10

–10

400 .002–.003 Operating temperatures from 400

to 700 °F, excellent electrical

properties

Polycarbonates Lexan 10

410 .0001–.0005 Good electrical, excellent

mechanical properties, low water

absorption

Polyethylene and

Polypropylenes

—10

–10

450–1000 .0001–.006 Good electrical, weak mechanical

and thermal properties

Polyethylene

terephthalates

Mylar >10

500–710 .0003 Tough, excellent dielectric

properties

PVC Saran 10

–10

300–1100 .01–.15 Low cost, general purpose, average

electrical properties

mil ¼.001 in.

HARDWARE AND CONSTRUCTION 525

the wires provides extra mechanical and electrical protection.

The standard code is black for hot, white for neutral, and green

for ground, and should be observed at both the plug and the

chassis end of the cord. T o minimize damage to the line cord at

the chassis end, strain relief and mechanical protection of the

insulation should be provided. This is often accomplished with

a single strain-relief grommet or combination plastic grommet

and clamp, as in Figure 6.150. An alternativ e to direct con-

nection

of an a.c. line with plug to a chassis is an a.c. r eceptacle

or power entry module. These accept standard a.c. line cords

with male connectors on the a.c. outlet end and female con-

nectors that mate to the receptacle or module. The receptacles

and modules may contain on–off switches, fuses, pilot lights,

and r .f.i ﬁlters. Some examples are sho wn in Figure 6.151.

Line

cord is almost always stranded to enhance ﬂexibil ity.

If the wire is to be used in high-current-carrying applications,

care should be taken not to cut the strands when stripping,

since that will limit the current carrying capacity of the wire

and cause heating at the stripped end. Sometimes the indi-

vidual strands are insulated with varnish. When making elec-

trical connections with wire of this kind, the insulation must

be removed with ﬁne emery paper or steel wool.

Another type of wire used for a.c. lines is the solid-con-

ductor #12 or #14 gauge wire for po wer distribution. The most

common are two- and three-conductor Romex, which is PVC-

insulated, and two-conductor BX, which has a metal-armored

outer covering. Both types can be routed within walls in either

metal or PVC conduit. Because of the heavy gauge of the

conductors, connections are made to screw terminals or with

wir e nuts when splices are invo lved. The installation of a.c.

lines requires a professional electrician who knows the con-

ventions, regulations (codes), and procedures for fusing and

connection to existing po wer lines.

For electronic circuits where the voltages are less than

a few hundred volts and the curre nts are a few amperes,

hookup wire is u sed. This can be solid conductor or

multistranded. The solid-conductor wire is easier to

use when making connections because it does not fray,

but it lacks the ﬂexibility of multistranded wire. Hookup

wire is generally tinned – that is, coated with a tin–lead

alloy to enhance solderability. The insulation is usually

PVC, polyethylene, or TeﬂonÔ.

When stripping wire, care should be taken to avoid

nicking the conductor of solid wire and cutting strands

of multistranded wire. There are a large variety of wire

strippers on the market (see Figure 6.152), but none is

foolproof

and all require a certain amount of skill if the

conductor is to remain undamaged. Thermal strippers that

melt the insulation locally before it is withdrawn from the

wire work very well, but are not portable. For TeﬂonÔ-

insulated wire, thermal strippers are very useful because

the slippery material is difﬁcult to grip.

When working with stranded wire, it is recommended

that the ends be tinned. It should be remembered, however,

that solder will render multistrand wire rigid, so tinning

should be conﬁned to a short length at the end. For coding

purposes, the insulation of hookup wire comes in many

Figure 6.150 Mounting line cord at the chassis to relieve

strain on the electrical connections.

Figure 6.151 A.c receptacle/power line modules:

(a) simple; (b) on–off switch incorporated;

526 ELECTRONICS

colors and combinations of colors. Color coding is a very

useful way to avoid wiring errors and makes subsequent

troubleshooting easier.

Test-prod wire is highly ﬂexible multistrand wire with

rubber insulation rated at a few thousand volts. Such wire

comes with red or black insulation and is used with multi-

meters and in high-voltage circuitry.

For voltages from a few kilovolts to several tens

of kilovolts, special high-voltage cable must be used.

The most common jacket materials are silicone rubber,

TeﬂonÔ, and KaptonÔ. Silicone-rubber insulation is very

ﬂexible, but has only modest dielectric breakdown strength

and volume resistivity, so that high-voltage cables made

with it have large diameters. KaptonÔ, a polyimide, has

Figure 6.152 Wire strippers.

HARDWARE AND CONSTRUCTION 527

high breakdown strength and volume resistivity, and cables

made with it are relatively small in diameter. Stiffness is

the principal disadvantage of KaptonÔ. The properties of

TeﬂonÔ are intermediate between those of silicone rubber

and KaptonÔ, and it is usually the best compromise. Typ-

ical properties of high-voltage TeﬂonÔ cable are given in

Table 6.50. One source of high-voltage cable is the ignition

cables

used in automobiles. The silicone-rubber-insulated

stainless-steel or copper stranded-conductor type found in

high-performance cars can be used to 50 kV. The more

common carbon-ﬁlament conductor cable used to mini-

mize r.f.i. is not suitable.

Magnet wir e is varnish-insulated, solid-conductor wire

used for winding electromagnets, transformers, and induc-

tors. The thin insulation means that a large number of turns

can be packed into a given volume. To make electrical con-

nections with such wire, the varnish must be removed with

emery paper, steel wool, or special solvents. Magnet wire is

not a suitable substitute for hookup wire. When using it for

electromagnets, one should be aware of the possible buildup

of heat around the inner windings, which can degrade the

insulation and create short circuits. The varnish insulation is

rated for voltage break-down and heat resistance.

For high-current electromagnets, rectangular cross-

section wire is used, because the high surface-area-to-

volume ratio facilitates convection cooling. In applications

that require conduction cooling, hollow-core wire is used,

through which cooling water can be circulated.

In addition to two- and three-conductor line cord, there

are many other multiconductor, round-cable conﬁgurations.

The conductors can be solid or stranded. The wires are

color-coded for identiﬁcation. For low-level, low-frequency

signals, the wires can be enclosed in a single shield, as is

done for microphone cable. Conﬁgurations where there is

individual shielding of single wires also are available.

Shielding can be in the form of a braid or a foil – if it is

foil, a drain wire is also included, which is electrically

connected to the shield and to which connections can be

made. For high-frequency applications there is coaxial

cable and 300 X, parallel-conductor cable with transmis-

sion-line properties. These are discussed in the sections

on coaxial cable and connectors (Sections 6.2.3 and 6.2.4).

Flat

multiconductor cable is very useful when a large

number of wires are needed, as with computer and data inter-

faces. There are many different arrangements of the wires

within such cable. The most common consists of round par-

allel conductors. There are also ﬂat conductors and alternat-

ing round and ﬂat conductors. Flat conductors minimize

interconductor capacitance and interference among signals.

Twisted pairs of wires are used for transmission lines because

constant impedance can be maintained and the wires are

ﬂexible and easy to route. An alternating twisted pair–straight

geometry is often used for data transmission. The great

advantage of ﬂat cable is that mass termination insulation

displacement connectors can be used. These connectors are

designed so that the cable is clamped and electrical contact is

made to each of the wires in a single operation with a special

tool. No stripping, soldering, or crimping is required. The

reliability of such connections is e xcellent.

6.10.6 Connectors

Probably the best-kno wn connector combination is

the binding post and banana plug or tip plug (see Fig-

e 6.153). A wide variety of conductors and conductor

rminations can be made to binding posts in a rapid, reli-

able semipermanent manner. Binding posts have the disad-

vantage of being bulky and highly susceptible to the pickup

and radiation of electromagnetic energy. When mounting

binding posts on a chassis, the mounting hole should be

made large enough to accommodate the shoulders on the

insulating sleeves. In this way, the central conductor is kept

well away from the chassis. The standard spacing between

posts is 0.75 in. This corresponds to the spacing of twin-

conductor banana plugs (see Figure 6.154), which are quite

mmon and useful, especially when it is necessary to

Table 6.50 Typical high-voltage Teﬂon-insulated cable

d.c. Voltage

Rating

(kV)

Conductor Cable Diameter (in.)

10 19/36

0.077

15 0.097

20 0.117

25 0.137

40 0.197

50 0.237

a.c. voltage rating is typically 20–25% of d.c.

19 strands of #36 wire.

528 ELECTRONICS

connect coaxial cable to binding posts. The twin plug usu-

ally has one terminal marked ground, to which the shield of

coaxial cable is attached.

Alligator clips (see Figure 6.155), although useful with

test

leads, should not be used in any permanent or even

semipermanent installation. The type of clip into which

Figure 6.153 (a) Binding post; (b) banana plug.

Figure 6.155 Alligator clip with insulated plastic cover.

Figure 6.154 Twin-conductor banana plug.

HARDWARE AND CONSTRUCTION 529

one inserts a banana plug is more useful than a clip requiring

solder or screw connections. Flexible insulating sleev es that

ﬁt over the clips prev ent short circuits and are always used

when the clip is at the end of a test lead.

Phone plugs (see Figure 6.156) come in several different

izes and provide one means for the termination and con-

nection of coaxial cable carrying low-frequency signals.

Because this type of plug is polarized (that is, the connec-

tions can only be made in one way), it is sometimes used for

low-voltage, low-current d.c. power-supply connections.

There are many variations on the basic plug–jack design.

There are plugs that can accommodate three or more sepa-

rate connections, and there are jacks that remain shorted

until the insertion of the plug.

Insulated barrier strips (see Figure 6.157) with screw

terminals

are a good way of making semipermanent con-

nections for d.c. applications, and are often found on the

rear panels of power supplies.

For terminating the ends of wires, there are a variety of

terminal connectors that can be attached to the wire by sol-

dering or crimping (see Figure 6.158). The terminal used

should

be of the correct size with respect to both the wire

Figure 6.156 Phone plug.

530 ELECTRONICS

used and the opening at the end. Quick-connect, friction-type,

push-on terminals are very useful in d.c. applications, when

the connection must be repeatedly made and broken. Such

terminals are often also found on mechanical relays, circuit

breakers, and mechanical switches. Crimp connectors are

color-coded according to the wire-size range they can accom-

modate. It is important to use the proper crimp-tool opening –

color-codedonmanytools–toavoidtoolooseacrimp(too

large a hole) or a severed wire (too small a hole). Three

diff erent typ es of crimping tool are show n in Figure 6.159.

en soldering connectors, only enough heat should

be used to make a good joint, since too much heat will melt

the insulation. Some type of third hand is helpful in this

regard – a small vice or an alligator clip at the end of a heavy

piece of solid copper wire anchored to a metal base.

A very large part of the electronics-har dware indus-

try is devoted to the manufac ture of connectors. For

laboratory applications, only a few of the most com-

mon ones will be described, and some guidelines for

connector s election will be given. Electrical c ontacts

between the wires and connector pins can be made by

soldering or crimping. For some connectors, the pins

must be re moved to make the electrica l connection

and then i nserted into the connector block. Removal

of the pin then requires a special tool. A common

power connector using crimped sockets and pins is

shown in Figure 6.160. High -density conn ectors using

rimped t erminals and integral holding latches are

shown in Figure 6.16 1.

D-connectors

derive their name from the cross-sectional

shape of the connector body (see Figure 6.162). The usual

232C interface uses a 25-pin, subminiature D-connector.

The connector can have up to 50 contacts and connection is

made in a variety of ways: by soldering the conductors into

a hollow recess at the back of the contact (solder pot); with

crimp pins and sockets; and with ribbon-cable mass termi-

nation contacts. Such connectors can be attached directly

to a panel with the correct cutout. When ﬁtted with a shell

(either plastic or metal) and a cable clamp, they become

plugs. Locking accessories are also available for securing

the plug to the mating jack, and the D-shape assures cor-

rect mating. Double-density connectors of this type are

also made, and there exist a wide variety of conﬁgurations

with high-voltage, high-current, and coaxial contacts, in

addition to the standard single pins. Because pins are very

closely spaced, shrink tubing is routinely used over the

solder connections. This tubing comes in a variety of sizes,

materials, and shrink ratios. When used to insulate solder

connections, the tubing serves a strain-relief as well as an

insulating function. It is important to choose the correct

Figure 6.158 Wire terminals.

Figure 6.157 Barrier strip.

HARDWARE AND CONSTRUCTION 531

diameter tubing for the application. If the tubing is too

small in diameter, it will split upon being shrunk over

the enclosed wire or connector – if the diameter is too

large, it will not ﬁt tightly. Heating should be done with

a heat gun rather than a soldering iron.

Threaded circular connectors (see Figure 6.163)are

sed on designs originally used by the military for aircraft.

They employ separate removable pins and a threaded mat-

ing collar to make a mechanically secure union between

male and female connectors. There is a broad range of sizes,

styles, and pin arrangements, and for this reason these con-

nectors are used on a variety of laboratory electronic equip-

ment. There are various ways of retaining the pins in the

insulator block. Some of them require special insertion and

removal tools, while others use a second backup block held

in place inside the connector.

Nuclear instrumentation module (NIM) and CAMAC

equipment are examples of the connection of a modular elec-

tronic unit to a main chassis. The basic connector is a rec-

tangular insulator block, which holds contact pins maintained

in place by one-way spring action. Wires are crimped to the

Figure 6.159 Crimping tools.

Figure 6.160 Multiple contact connector, crimp terminals,

insertion/extraction tool.

532 ELECTRONICS

pins that are then inserted into the block. An extraction tool is

required for pin removal. When the connector has a large

number of pins, considerable force is required for mating

and threaded screw jacks are often used. Extra pins can be

purchased separately and shrouds are av ailable to con v ert the

connector to a plug.

No high-voltage connector is entirely satisfactory, and

forthisreasontheyshouldbeavoidedandpermanent

connections with ceramic feedthroughs or standoffs

made whe never possible. Reynolds/Teledyne manufac-

tures a wide range of single-conductor, multiple-conduc-

tor an d co-axial high-voltage wire and c onnector s with

voltage ratings to 70 kV. European-type phenolic spark-

plug connectors ma ke acceptable connectors when used

with ignition cable; a drilled-out Teﬂon Ô-insulated r.f.

coaxial connector can a lso be used. These are illustrated

in Figure 6.16 4.

6.11 TROUBLESHOOTING

6.11.1 General Procedures

There are a number of steps that can be taken when a piece

of electronic equipment fails to operate properly. These

depend on the complexity of the equipment and the avail-

ability of test equipment and diagrams.

The worst symptoms are usually the easiest to treat. An

experienced TV repairman once noted that 95% of all

Figure 6.162 (a) D-connector; (b) pin and socket crimp

contacts; (c) pin and socket extraction with tool;

(d) ribbon-cable connections.

Figure 6.161 Multiple conductor connector and crimped

terminal.

TROUBLESHOOTING 533

malfunctions in TV sets could be found and corrected in

less than one half hour. For the other 5% the best solution

was to sell the customer a new set. This also applies to

laboratory equipment. With increasing use of highly reli-

able integrated circuits and resistance and capacitance

modules, the most unreliable elements of a circuit are

the mechanical parts (such as switches, dials, and fans)

and especially the connectors. When an ampliﬁer or power

supply no longer works, one’s ﬁrst impulse should not be

to take out screwdriver and wrench and begin disassem-

bling the chassis, but to be sure that it is plugged in, that the

on–off switch is functioning, that all fuses are intact, that

the cooling fans are operating, and that the air ﬁlters are

clean and not blocked. Switch contacts can be cleaned with

spray cleaners made for the purpose. If these measures

produce no results, the various dial and switch settings of

the instrument should be checked. Often what is viewed as

a malfunction is merely an incorrect setting, causing the

instrument to operate in an unexpected mode.

If these simple actions are not effective, the next course

of action depends on the complexity of the equipment and

the availability of circuit diagrams. To repair a complex

circuit without circuit diagrams is almost impossible. If

diagrams are not at hand, the manufacturer should be

contacted for the necessary diagrams and troubleshooting

procedures. Often these are available online, so a web

search is a good way to begin.

There are, of course, certain visual checks that one can

perform without knowledge of the circuit. Charred resis-

tors and an overheated circuit board are readily apparent,

as are loose and dangling wires. One difﬁculty with merely

replacing a damaged component, however, is that only the

symptom may be treated. The charred resistor may be the

result of a failure in another component.

Troubleshooting is most effective and efﬁcient when a

complete set of circuit diagrams, schematic drawings,

chassis diagrams, and functional block diagrams are avail-

able. These are often accompanied by a troubleshooting

guide, which lists the most frequently encountered mal-

functions, the symptoms, and the remedies. The area in

which the malfunction is occurring can often be localized

by studying the functional block diagram of the unit. As an

example, consider a counter-timer that responds normally

to input signals but gives erratic readings when counting

for preset time intervals, and erratic times when in the

preset-counts mode. In this case, the gating circuit and

Figure 6.164 High-voltage connectors made

from a spark-plug and r.f. connector.

Figure 6.163 Threaded military-type connector.

534 ELECTRONICS

the time base are obviously suspect. One should begin by

looking at that part of the circuit.

Good schematic diagrams include waveforms and volt-

age levels at all critical points in the circuit. These should

be checked ﬁrst. Well-designed circuit boards often have

the d.c. voltage levels printed directly at the appropriate

test points and components identiﬁed by a printed letter-

and-number code that corresponds to an identical code on

the schematic diagram.

A common difﬁculty is gaining access to components and

connections in the restricted space between boards in a

multiple circuit-board assembly. Extender boards (see

Figure 6.165)arecircuitboardsarrangedinsuchawaythat

ey mate to the circuit-board connector at one end and the

circuit board itself at the other end. The extender board is of

sufﬁcient length to place the board in a position where the

components and circuit interconnections are easily accessi-

ble. Signal injection is a common method for isolating a

circuit fault. With this technique, an appropriate signal is

injected at the input of the suspected circuit element, and the

output is monitored. This works well for linear circuits, such

as ampliﬁers, but becomes quite complex for digital circuits,

where it may be necessary to stimulate several input termi-

nals and monitor several output terminals simultaneously –

and often in synchronization with a clock signal. Logic

pulsers, probes, and clips, are useful for small-scale testing.

They are shown in Figure 6.166. For more complex circuits,

is necessary to capture the signals and store them for

subsequent analysis. There are logic analyzers made expres-

sly for this purpose. They are expensive, however, but

worthwhile in situations where a large amount of digital

circuit troubleshooting is done – more the domain of the

electronic technician than the experimental scientist. Often

it is much more economical to replace all the suspected ICs

in a given section (especially if they are easily removable

and in sockets) than to test each one individually.

Some common sources of faults in electronic equipment

are:

(1) Electrolytic capacitors in general

(2) Pass transistors in the output circuit of power supplies

(3) Input transistors in the input circuits of ampliﬁers and

preampliﬁers

(4) Mechanical switches and potentiometers.

Repeated failure of input transistors in low-level pream-

pliﬁer circuits can often be cured by placing two diodes,

such as lN914s, across the input, as shown in Figure 6.167.

long as the input signal does not exceed a few tenths of

a volt, both diodes remain nonconducting, allowing the

unattenuated signal to pass. Should the signal exceed

0.6 V – positive or negative – one or the other diode will

conduct, shunting the signal to ground and protecting the

input from excessive voltage levels.

6.11.2 Identifying Parts

One can often localize the malfunction to a circuit compo-

nent, but may not know enough about the component to be

Figur e 6.165 Use of the extender board for trou-

bleshooting.

TROUBLESHOOTING 535

able to replace it. The parts list may gi v e the equipment

manufacturer’s component code rather than the standard

code of the component manufacturer . When this is the case,

it is necessary to identify the component from the code

printed on it. Most ICs, transistors, and other components

have a four-digit date code gi ving the date of manufacture.

The ﬁrst two digits are the year, and the next two are the

week of the year. Thus, 9812 is the 12th week (last week in

April) in 1998. The other codes are the manufacturer’s com-

ponent designation. To help identify the manufacturer, a list

of logos can be found at the follo wing web sites: http://

www.icmaster.com/LogosA-M.asp and http://www.icmaster.

com/LogosN-Z.asp. The site http://www.elektronikforum.de/

ic-id has links to icmaster and others. Semiconductor

manufacturer homepages and data sheets are given at http//

www.bgs.nu/sdw/p.html. A list of the preﬁx codes of

semiconductor manufacturers is gi v en in Table 6.51.Once

the

manufacturer is known, the appropriate data book or web

Figure 6.166 Logic pulser, probe, clip, and test prod.

536 ELECTRONICS

site can be consulted. One should replace components with

caution, paying attention to the package type and temper -

ature range. The three standard ranges are commercial (0 to

70 °C), industrial (25 to þ85 °C), and military (55 to

þ125 °C). Sometimes specially selected or matched compo-

nents are used. Replacement with off-the-shelf units may not

work in this case.

Cited References

1. H. W. Bode, Network Analysis and Feedback Ampliﬁer

Design, Van Nostrand, Princeton, NJ, 1945.

2. Electr. Design, 24, 63, 1976.

3. J. Millman and C. C. Halkias, Integrated Electronics:

Analog and Digital Circuits and Systems, McGraw-Hill,

New York, 1972, pp. 244–245.

4. J. G. Tobey, G. E. Huelsman, and L. P. Graeme, Operational

Ampliﬁers, Design and Application, McGraw-Hill, New

York, 1971; J. Graeme, Designing with Operational

Ampliﬁers, McGraw-Hill, New York, 1977.

5. E. Fairstein and J. Hahn, Nuclear pulse ampliﬁers –

fundamentals and design practice, Nucleonics, 23(7 ),

56, 1965; Nucleonics, 23(9), 81, 1965; Nucleonics, 23(11),

50, 1965; Nucleonics 24(1), 54, 1966; Nucleonics, 24(3) ,

68, 1966.

6. Voltage Regulator Handbook, National Semiconductor

Corporation, Santa Clara, CA, 1975.

7. FAST Data Manual , Signetics Corp., Sunnyvale, CA, 1984.

8. Standard Nuclear Instrument Modules, adopted by AEC

Committee on Nuclear Instrument Modules, US

Government Publication TID-20893 (Rev. 3).

9. P. H. Garrett, Analog I/O Design, Reston Publishing Co.,

Reston, VA, 1981.

10. S. Letzter and N. Webster, IEEE Spectrum, August, 67–75,

1970.

11. John C. Fisher, Lock in the Devil, Educe Him, or Take Him

for the Last Ride in a Boxcar? Tek Talk, Princeton Applied

Research, 6, No. 1.

12. A. C. Melissinos, Experiments in Modern Physics,

Academic Press, New York, 1966, Chapter 10.

13. R. R. Goruganthu, M. A. Coplan, J. H. Moore and J. A.

Tossell, J. Chem. Phys., 89, 25, 1988.

14. R. Morrison, Grounding and Shielding Techniques in

Instrumentation, John Wiley & Sons, Inc., New York, 1967.

15. Floating Measurements and Guarding, Application Note

123, Hewlett-Packard, Palo Alto, CA, 1970.

16. S. Weber (Ed.), Circuits for Electronics Engineers,

Electronics Book Series, McGraw-Hill, New York, 1977; W.

Figure 6.167 Use of protection diodes at a low-level input.

Table 6.51 Semiconductor integrated-circuit code preﬁxes

Company Preﬁx

Analog Devices AD

Advanced Micro Devices Am

General Instrument AY, GIC, GP

Intel C, I

RCA CA, CD, CDP

TRW CA, TDC, MPY, CMP, DAC,

MAT, OP

Precision Monolithics PM, REF, SSS

National Semiconductor DM, LF, LFT, LH, LM, NH

Fairchild F, A, lL, Unx

Ferranti FSS, ZLD

GE GEL

Harris HA

Motorola HEP, MC, MCC, MCM, MFC,

MM, MWM

Intersil ICH, ICL, ICM, IM

ITT ITT, MIC

Siliconix L, LD

Fugitsu MB

Mostek MK

Plessy MN, SL, SP

Signetics N, NE, S, SE, SP

Raytheon R, RAY, RC, RM

Texas Instruments SN, TMS

Sprague ULN, ULS

Westinghouse WC, WM

Hewlett-Packard 5082-nnnn

Vishay Si

x ¼number; n ¼letter.

REFERENCES 537

Furlow (Ed.), Circuit Design Idea Handbook,Cahner’s

Books, Boston, 1974; Electronics Circuit Designer’s

Casebook, Electronics, New York; Signetics Analog

Manual, Applications, Speciﬁcations, Signetics Corporation,

Sunnyvale, CA; Linear Applications Handbook, Vols. 1 and

2, National Semiconductor Corporation, Santa Clara, CA.

17. W. R. Blood, Jr., MECL Applications Handbook, 2nd edn.,

Motorola Semiconductor Products, Phoenix, AZ, 1972.

18. D. Lindsey, The Design and Drafting of Printed Circuits,

2nd edn., Bishop Graphics, Westlake Village, CA, 1984.

19. D. H. Sheingold (Ed.), Transducer Interfacing Handbook,

Analog Devices, Norwood, MA, 1980.

General References

CAMAC and IEEE-488 (GPIB or HP-IB)

CAMAC: A Modular Instrumentation System for Data

Handling, ESONE Committee, Report EUR 4100, 1972,

Chapters 4– 6.

CAMAC Tutorial Issue, IEEE Trans. Nucl. Sci., NS-20 (2), April

1973.

D. Horelick and R. S. Larsen, CAMAC: ‘‘A Modular Standard,’’

IEEE Spectrum, April 50, 1976.

HP-IB General Information, Hewlett-Packard Publication No.

5952–0058.

IEEE Standard 488, available from the IEEE Standards Ofﬁce,

345 E. 47th St., New York, NY 10017.

Speciﬁcations for the CAMAC Serial Highway and Serial Crate

Contr oller Type 62, Report EUR 6100e, Commission of the

European Communities, Greel, Belgium, 1976, Chapter 14.

Circuit Theory

P. Grivet, The Physics of Transmission Lines at High and Very

High Frequencies, Academic Press, New York, 1970.

H. V. Malmstadt, C. G. Enke, and S. R. Crouch with G. Horlick,

Electronic Measurements for Scientists, Benjamin, Menlo

Park, CA, 1974.

J. Millman and A. Grabel, Microelectronics, 2nd edn., McGraw-

Hill, New York, 1987.

C. J. Savant, Jr., Fundamentals of the Laplace Transform,

McGraw-Hill, New York, 1962.

A. I. Zverev, Handbook of Filter Synthesis, John Wiley & Sons,

Inc., New York, 1967.

Printed Circuit-Board Software

Schematic Capture and Board Layout

Electronics Workbench

908 Niagra Falls Boulevard, Suite 068

North Tonawanda, New York

14120-2060

800-263-5552

FAX: 416-977-1818

http://www.electronicsworkbench.com

PADS Software Inc.

165 Forest Street

Marlborough MA 01752

508-485-4300

FAX: 508-485-7171

http://www.pads.com

Ivex Design International

15232 NW Greenbrier Parkway

Beaverton, OR 97006

503-531-3555

FAX: 503-629-4907

WinDraft, WinBoard, IvexView, IvexSpice

Cadence Design Systems

2655 Seely Road

San Jose, CA 95134

1-800-746-6223

FAX: 408-943-0513

http://www.cadence.com

Mentor Graphics Corporation

8005 S.W. Boeckman Road

Wilsonville, OR 97070

1-800-547-3000

http://www.mentor.com/pcb/

P-CAD

12348 High Bluff Drive

San Diego, CA 92130

858-350-3000

FAX: 858-350-3001

http://www.pcad.com

Protel Technologies, Inc.

5252 North Edgewood Drive

Suite 175

538 ELECTRONICS

Provo, UT 84604

1-800-544-4186

FAX: 801-224-0558

http://www.protel.com

Printed Circuit-Board Fabricators

Golden Gate Graphics

South Bay Circuits

Advanced Circuits

21100 East 33rd drive

Aurora CO 80011

http://www.advanced circuits.com

Control Analysis and Design

R. C. Dorf, Modern Control Systems, 6th edn., Addison-Wesley,

New York, 1992.

T. E. Fortmann and K. L. Hitz, An Introduction to Linear Control

Systems, Marcel Dekker, New York, 1977.

G. F. Franklin, D. J. Powell, and A. Emami-Naeini, Feedback

Contr ol of Dynamic Systems, 2nd edn., Addison-Wesley,

New York, 1991.

B. C. Kuo, Automatic Control Systems, 6th edn., Prentice-Hall,

New Jersey, 1990.

K. Ogata, Modern Control Engineering, 2nd edn., Prentice-Hall,

New Jersey, 1991.

C. L. Phillips and R. D. Harbor, Feedback Control Systems, 2nd

edn., Prentice-Hall, New Jersey, 1991.

Components

M. Grossman, Focus on r.f. Connectors, Electr. Design, 24(11),

60, 1976.

C. A. Harper, To compare electrical insulators, Electr. Design,

24(11), 72, 1976.

Handbook of Components for Electronics, C. A. Harper (Ed).,

McGraw-Hill, New York, 1977.

T. H. Jones, Electronic Components Handbook, Reston Publish-

ing, Reston, VA, 1978; Selecting capacitors properly, electr.

design, 13, 66, 1977.

Data Books

D.A.T.A. Books, D.A.T.A., San Diego, CA, Volumes

include Optoelectronics, Digital IC, Linear IC,

Transistor, Diode, Thyristor, Power Semiconductor,

Interface IC.

MECL System Design Handbook, W. R. Book, Jr., and E. C.

Tynan, Jr. (Eds.), 2nd edn., Motorola Semiconductor Products,

Pheonix, A2, 1972.

Motorola Semiconductor Data Library: Vo l . 1, EIA Type

Numbers to 1N5000 and 2N5000; Vo l . 2 , Discrete

Products, EI A Type Numb ers 1N5000 and U p, 2N5000 and

Up, 3N ... and 4N ...; Vol . 3 , Disc rete Products , Motorola

Non-Registered Type Numbers; Vo l . 4 , MECL Integrated

Circuits.

National Semiconductor Data Books: Linear, TTL, CMOS,

MOSFET, Memory, Discrete, National Semiconductor

Corporation, Santa Clara, CA.

Optoelectronics Designer’s Catalog, Hewlett-Packard, 1984.

Signetics Data Manual; Logic, Memories, Interface, Analog,

Microprocessor, Military, Signetics, Sunnyvale, CA.

The TTL Data Book for Design Engineers, 1st edn., Texas

Instruments, Dallas, TX, 1973.

Voltage Regulator Handbook, National Semiconductor

Corporation, Santa Clara, CA.

Handbooks

J. C. Whitaker (Ed.), The Electronics Handbook (The Electrical

Engineering Handbook Series), CRC Press/IEEE Press, Boca

Raton, FL, 1996.

ARRL Handbook, 83rd edn., American Radio Relay League,

Newington, CT, 2006.

L. J. Giacoletto (Ed.), Electronics Designers’ Handbook,

2nd edn., McGraw-Hill, New York, 1977.

T. D. S. Hamilton, Handbook of Linear Integrated Electronics for

Research, McGraw-Hill, New York, 1977.

ITT Engineering Staff, Reference Data for Radio Engineers, 6th

edn., Sams, Indianapolis, 1979.

K. Henney (Ed.), Radio Engineering Handbook, McGraw-Hill,

New York, 1959.

Master Catalogs

Electronic Design’s Gold Book: Master Catalog and Directory of

Suppliers to Electronics Manufacturer.

REFERENCES 539

Electronic Engineers Master, United Technical Publications,

Garden City, NJ.

Noise

S. Letzter and N. Webster, Noise in ampliﬁers, IEEE Spectrum,

August, 67–75, 1970.

A. V. D. Ziel, Noise in solid-state devices and lasers, Proc. IEEE,

58(8), 1178, 1970.

Particle and Radiation Detection

L. J. Herbst (Ed.), Electronics for Nuclear Particle Analysis ,

Oxford University Press, London, 1970.

Electro-Optics Handbook: A Compendium of Useful

Information and Technical Data, RCA Defense

Electronics Products, Aerospace Systems Division, Burling-

ton, MA, 1968.

Glenn F. Knoll, Radiation Detection and Measurement,

John Wiley & Sons, Inc., New York, 1979.

Optoelectronics Designer’s Catalog, Hewlett-Packard, Palo Alto,

CA, 1980.

Modular Pulse-Processing Electronics, ORTEC, 801 South

Illinois Avenue, Oak Ridge, TN 37831–0895, 2001.

Practical Electronics

Design Techniques for Electronics Engineers, Electronics Book

Series, McGraw-Hill, New York, 1977.

P. Horowitz and W. Hill, The Art of Electronics, 2nd edn.,

Cambridge University Press, Cambridge, 1989.

D. Lancaster, CMOS Cookbook, Sams, Indianapolis, 1977.

D. Lancaster, TTL Cookbook, Sams, Indianapolis, 1974.

Trade Publications

Digital Design, Benwill, Boston: computers, peripherals,

systems; monthly.

Electronic Component News, Chilton Col, P.O. Box 2010,

Radnor, PA 19089; monthly.

Electronic Design, Hyden Publishing Co., Inc., a subsidiary

of VNU, 10 Mulholland Dr., Hasbrouck Heights,

NJ 07604.

Electronic Engineering Times, CMP Publications, Manhasset,

N.Y.; biweekly tabloid.

Instrument and Apparatus News (IAN), Chilton, Radnor, Pa.:

instruments, industrial controls, digital systems; monthly.

Troubleshooting

R. E. Gasperini, Digital Trouble Shooting, Hayden, Rochelle

Part, NJ, 1976.

Techniques of Digital Trouble Shooting, Hewlett-Packard

Application Note 163–1.

Electronic Measurements

Low Level Measurements: Precision D.C. Current, Voltage, and

Resistance Measurements, 5th edn., Keithley Instruments,

Cleveland, OH, 1998.

540 ELECTRONICS

APPENDIX 541

542 ELECTRONICS

APPENDIX 543

544 ELECTRONICS

APPENDIX 545

546 ELECTRONICS

DETECTORS

Phenomena that are studied experimentally often manifest

themselves as sources of electromagnetic radiation or par-

ticles. To be useful, the radiation or particles that are

involved in the experiment must be detected. In this chap-

ter we will consider the operating characteristics, selection

criteria, and performance of various types of radiation

and particle detectors. We will focus primarily on detectors

of optical radiation, from X-rays to far infrared, and on

charged-particle detectors. For a discussion of detectors

of high-energy photons, such as c rays, and elementary

particles, such as neutrons, neutrinos, and the many

particles involved in high-energy nuclear physics, we

refer the reader to the more specialized treatises on these

subjects.

1–4

7.1 OPTICAL DETECTORS

Optical detectors of various kinds detect electromagnetic

radiation from the X-ray to the far-infrared region of the

electromagnetic spectrum. In common with other branches

of electronics, the development of optical detectors has

occurred by a series of advances through the use of gas-

ﬁlled tubes and vacuum tubes to various semiconductor

devices. Gas-ﬁlled and vacuum-tube devices still retain

some niche electronics applications, such as high-voltage

switching, microwave power ampliﬁcation, and special-

ized audio. Gas-ﬁlled photodetectors, which offer some

degree of signal ampliﬁcation in low-cost consumer ap-

plications, have essentially disappeared. Vacuum-tube

photodetectors, especially photomultiplier tubes, remain in

wide-spread use for detection of radiation below about 1 lm.

This is especially true for low-light-level signal detection

(photon counting), and in applications where a large detector

area is required (as in scintillation counters). The designer

of an optical system is confronted with a broad range of

detector types: vacuum-tube, semiconductor, and thermal.

The last category includes thermopiles, pyroelectric detec-

tors, Golay cells, and bolometers, each with its own advan-

tages and disadvantages.

The choice of detector for a given application will

almost invariably involve a choice from among the numer-

ous commercially available devices in each of these cate-

gories. The construction of optical detectors is rarely

undertaken in the laboratory except by the specialist. The

choice of detector will be governed by factors such as:

(1) The wavelength region of the radiation to be detected

(2) The intensity of the radiation to be detected

(3) The time response required to resolve high-speed

events

(4) The detector surface area required

(5) The environmental conditions in which the detector is

to be used

(6) The cost

(7) The electronics to be used in conjunction with the

detector.

The choice of a detector for a particular experiment

should not be an exercise performed in isolation. The other

components of the experimental system may inﬂuence it,

and vice versa. This is particularly true if very weak radi-

ation is to be detected. In such a situation, action should be

taken to maximize the light signal actually reaching the

detector; this will involve a careful choice of optical com-

ponents to be placed between source and detector – for

547

CHAPTER

example, suitable light collection and focusing optics. If

the light from the source must pass through a dispersing

element (monochromator, etalon, etc.) before reaching the

detector, then the choices of dispersing element and detec-

tor are likely to be interrelated. Some dispersing elements

have high resolution (see Section 4.7), but low light

throughput;

others the reverse. Still others have high

throughput and resolution, but can only be scanned in a

restricted way, if at all. In a given experimental situa-

tion, the various requirements of resolution, light through-

put, scanability, and available detector sensitivities must

be offset one against another in arriving at a sensible

compromise.

Detectors can be classiﬁed as photon detectors or ther-

mal detectors. In photon detectors, individual incident

photons interact with electrons within the detector mate-

rial. This leads to detectors based on photoemission, where

the absorption of a photon frees an electron from a mate-

rial; photoconductivity, where absorption of photons

increases the number of charge carriers in a material or

changes their mobility; the photovoltaic effect, where

absorption of a photon leads to the generation of a potential

difference across a junction between two materials; the

photon-drag effect, where absorbed photons transfer their

momentum to free carriers in a heavily doped semiconduc-

tor; and photochemical detectors, such as the photographic

plate.

In thermal detectors, the absorption of photons leads to

a temperature change of the detector material, which may

be manifest as a change in resistance of the material, as in

the bolometer; the development of a potential difference

across a junction between two different conductors, as in

the thermopile; or a change of internal dipole moment

polarizability in a temperature-sensitive ferroelectric crys-

tal, as in a pyroelectric detector. With the exception of the

last, thermal detectors have slow time response when com-

pared to photon detectors. They do, however, respond uni-

formly at all wavelengths (in principle).

Photon detectors can be further classiﬁed by the spectral

region to which they are sensitive. Most photoemissive

detectors operate from the soft X-ray region through

to about 1.2 lm and rapidly become insensitive beyond

1 lm. New semiconductor photocathodes, however, are

becoming available that are sensitive out to 1.7 lm. Photo-

diodes operated in a ‘‘Geiger’’ mode provide single photon

detection capability from about 250 nm to 1.8 lm. Photo-

conductive and photovoltaic detectors based on different

materials are used right from the visible into the very far

infrared, at least to 1000 lm. Photographic ﬁlms, which

are also photon detectors, generally respond best in the

visible, although ﬁlms marginally sensitive out to about

1.2 lm are available. Films with appropriate ﬂuorescent

coatings respond, to ultraviolet light.

This brief survey is not intended to be exhaustive. Many

other detection mechanisms have been described, but not

all are commonly used or are commercially available. For

more information and details about detectors in general

than will be found here, the reader should consult Refer-

ences 5–16, and the catalogs of manufacturers.

7.2 NOISE IN OPTICAL DETECTION

PROCESS

The issue of noise becomes of great importance when an

optical detector is used for detection of a weak signal.

Noise is the randomly ﬂuctuating voltage or current pro-

duced by the detector and its associated electronics, which

interferes with the ability of the system to see the signal

being looked for. There are several sources of noise, and an

understanding of their origin and magnitude is very impor-

tant in designing a detection system that has the ability to

see the desired signal. A noise voltage or current ﬂuctuates

both positively and negatively about zero on a timescale

that is determined by the frequency response of the system

generating the noise. Consequently, if the noise is charac-

terized by a current i

, the aver age noise current is <i

> ¼ 0.

The noise must therefore be characterized by its mean

square value, averaged over a sufﬁ cien tly long time <i

This is often called the noise power, although strictly

speaking, the noise power is <i

>R, where R is an effective

resistance through which the noise current ﬂows. There are

several important sources of noise, which deserve separate

consideration.

7.2.1 Shot Noise

Shot noise, also called photon noise,orquantum noise,is

inescapable. This is noise associated with the signal being

548 DETECTORS

detected. If a light signal being detected gives an average

detected current of < i

>, then the shot noise is:

¼ 2e<i

>Df ð7:1Þ

where e is the magnitude of the electronic charge, and Df is

the frequency bandwidth being detected. Filtering the out-

put signal and reducing the operating bandwidth will

reduce this noise. Shot noise arises because of the discrete

nature of the charge carriers produced in the detection

process. A given detected current examined microscopi-

cally reveals itself to be a sequence of current impulses,

which, although arriving at an average rate over time, ﬂuc-

tuate in a random way. The individual current impulses

have a characteristic time duration, determined by the time

response of the detector. If each current impulse was in-

ﬁnitely narrow – as d function – then the frequency spec-

trum of the noise would be ﬂat or white over all

frequencies. In reality, the shot noise spectrum is ﬂat over

frequencies up to a maximum value determined by the

time response of the detector. If the detector has a time

constant s, determined by resistance and capacitance, then

its 10% to 90% rise time is t

¼ 2.197s. The bandwidth Df

is related to s by:

Df ¼

2ps

ð7:2Þ

7.2.2 Johnson Noise

Johnson noise, also called thermal noise or Nyquist noise,

is associated with the effective resistance of the detector

circuit. For a resistance R it is described by a noise power:

4kTDf

ð7:3Þ

where k is Boltzmann’s constant, and T is the absolute

temperature. Johnson noise arises because of the black-

body radiation associated with an enclosure at absolute

temperature T. A resistor at temperature T acts as an an-

tenna for the electric ﬁelds of the local blackbody radia-

tion. If the resistor did not reradiate its detected ﬁelds, then

it would not remain in thermal equilibrium. Consequently,

it generates a noise current.

7.2.3 Generation-Recombination (gr) Noise

Generation-recombination (gr) noise is most important

in lightly doped semiconductors. It results from the ran-

dom recombination of electrons and holes in the material.

The noise power for gr noise can be written as:

4<i



Nð1 þ 4p

ð7:4Þ

where s is the characteristic time constant for recombina-

tion in the semiconductor, and



N is the average number of

carriers.

7.2.4 1/f Noise

1/f noise, also called ﬂicker noise, current noise or excess

noise, is still not well understood. It contributes at low

frequencies, and has been shown to continue to increase

down to frequencies as low as 10

–4

Hz. 1/f noise power can

be written as:

1=f

K< i>

ð7:5Þ

where K is a constant for a particular device, <i> is the

average (d.c.) current through the device, a lies between

0.5 and 2, and n ;1. Because 1/f noise dominates at low

frequencies, measurements at very low frequencies should

be avoided whenever possible. In experiments where light

emission results from some form of stimulation, for exam-

ple in ﬂuorescence or light scattering, it is generally possi-

ble to periodically excite the phenomenon and move the

detection to a frequency synchronous with the excitation.

Good examples involve lock-in detection, boxcar averag-

ing, or digital signal averaging (see Chapter 6 for more

details).

Thermal noise and shot noise have so-called white

spectra – they contribute equal noise signals in a given

detection bandwidth at any frequency. Current noise gen-

erally shows a 1/f frequency dependence. As shown in

Figure 7.1, gr noise contributes at frequencies up to a value

the order of the reciprocal of the carrier lifetime, and

then falls off rapidly with increasing frequency.

NOISE IN OPTICAL DETECTION PROCESS 549

7.3 FIGURES OF MERIT FOR

DETECTORS

Before discussing individually the characteristics of com-

monly used and commercially available detectors, the vari-

ous ﬁgures of merit used by manufacturers to specify their

products will be described. These are the noise-equivalent

power (NEP), detectivity (D

), responsivity (R), quantum

efﬁ cienc y (g), and time constant (s), which allo w such ques-

tions to be answered as: What is the minimum light intensity

falling on the detector that will gi v e rise to a signal voltage

equal to the noise voltage from the detector? What signal

will be obtained for unit irradiance? How does the electrical

signal from the detector vary with the wavelength of the light

falling on it? What is the modulation frequency response

of the detector or its ability to respond to short light pulses?

7.3.1 Noise-Equivalent Power

The noise-equivalent power (NEP) is the rms value of the

sinusoidally modulated radiant po wer falling upon a detector,

that giv es an rms signal voltage equal to the rms noise voltage

from the detector . The NEP is usually speciﬁ ed in terms of a

blackbody source at 500 K, the reference bandwidth for the

detection of signal and noise (usually 1 or 5 Hz), and the

modulation frequency of the radiation (usually 90, 400, 800

or 900 Hz). For example, a noise-equiv alent power written

NEP (500 K, 900, 1) implies a blackbody source at 500 K, a

900Hz modulation frequency, and a 1 Hz detection band-

width. Thus, if a radiant intensity I (W/m

) falls on a detector

of sensitive area A (m

), and if signal and noise voltages V

and V

are measured with bandwidth Df (Hz) (small enough

so that the noise voltage frequency spectrum is ﬂat within it),

then the NEP measured is:

NEP ¼

ﬃﬃﬃﬃﬃﬃ

WHz

1=2

ð7:6Þ

7.3.2 Detectivity

At one time, detectivity was deﬁned as the reciprocal of the

NEP. Most detectors exhibit an NEP that is proportional to

the square root of the detector area; so a detector-area-

independent detectivity D

is now used, speciﬁed by:



ﬃﬃﬃ

NEP

ð7:7Þ

is speciﬁed in the same way as NEP: for example,

(500 K, 900, 1). To specify the variations in response

of a detector with wavelength, the spectral detectivity is

used. Thus, the symbol D

( k, 900, 1) would specify the

response of the detector to radiation of wavelength k,

Figure 7.1 Schematic frequency dependence of noise in semiconductor detectors; i

the noise current.

550 DETECTORS

modulated at 900 Hz and detected with a 1 Hz bandwidth.

The units of D

are cm Hz

1/2

–1

. Curves of D*(k) for

various detectors are shown in Figure 7.2.

or a thermal detector of absorptivity and emissivity e,

at absolute temperature T

, completely enclosed by an

environment at temperature T

, the photon-noise-limited

detectivity can be shown to be:



4:0 3 10

1=2

ðT

þ T

1=2

cm Hz

1=2

1

ð7:8Þ

For a photon detector, the limiting spectral detecti vity is:



ðkÞ¼

gðmÞ

2hmp

1=2

‘

gðm

Þv

=kT

ðe

=kT

 1Þ

1=2

ð7:9Þ

where g(m) is the quantum efﬁciency of the photoemissive

surface (the average number of free electrons produced for

each incident photon absorbed), k ¼ c

/m, and m

is the

lowest frequency to which the detector is sensitive. Spec-

tral detectivities predicted by Equation (7.9) are descibed

Kruse, McGlauchlin, and McQuistan.

7.3.3 Responsivity

The responsivity R (A/W) of a detector speciﬁes its

response to unit irradiance:

<¼i

=P ð7:10Þ

A similar ﬁgure of merit, usually used to characterize pho-

toemissive detectors, is the radiant sensitivity S, which is

the current per unit area of the photoemissive surface pro-

duced by unit irradiance:

S ¼

ð7:11Þ

Figure 7.2 Variation of the Detectivity (D

) as a function of wavelength for a comprehensive set of

different detectors.

FIGURES OF MERIT FOR DETECTORS 551

where i

is the total current from the detector and P the

total radiant power falling on it. Some curves showing the

spectral variation of radiant sensitivity for different photo-

emissive surfaces are given in Figure 7.3.

7.3.4 Quantum Efﬁciency

For a photon detector, the quantum efﬁciency is

de ﬁned as:

g ¼

number of electrons or electronhole pairs produced

number of photons absorbed

ð7:12Þ

It is easy to show that the quantum efﬁciency of a photon

detector and its responsivity are related according to:

<¼

ð7:13Þ

where e is the magnitude of the electronic charge.

Figure 7.3 Wavelength dependence of the radiant sensitivity of several commercially

available photocathode materials. (From Handbook of Lasers, R. J. Pressley (Ed.), CRC

Press, Cleveland, 1971; by permission of the CRC Press.)

552 DETECTORS

7.3.5 Frequency Response and

Time Constant

The frequency response of a detector is the variation of

responsivity or radiant sensitivity as a function of the mod-

ulation frequency of the incident radiation. The signal

from the detector should be a.c.-coupled; otherwise the

generated d.c. signal that is produced as the detector begins

to fail to respond to the modulation will also be detected.

The frequency variation of R and the time constant s of the

detector are generally related according to:

<ðf Þ¼

<ð0Þ

ð1 þ 4p

1=2

ð7:14Þ

like a low-passs ﬁlter, as shown in Figure 7.4.

Thus

the responsivity has decayed to a value of

<ð0Þ=

ﬃﬃﬃ

at a frequency 1/2ps. The time constant s is a

simple measure of the ability of the detector to respond

to a sharply rising or falling optical signal.

A very important parameter that determines the fre-

quency response of a detector is its capacitance. For driv-

ing a 50 ohm load, for example, a capacitance of 1 pF will

limit time constant to 50 ps. With the exception of photo-

multiplier tubes (PMTs) there is a direct relationship

between detector size and time constant. Photomultiplier

tubes with a sensitive area of 2000 mm

can respond as

quickly as 1–2 ns. However, for semiconductor detectors

there is no escaping the size/time-constant relationship.

For example, a semiconductor with a 1 mm sensitive area

will have a limiting time response of 1 ns and a bandwidth

of 160 MHz. On the other hand, a small size photodiode

with a diameter of 25 lm and designed for direct coupling

to optical ﬁber will have a bandwidth out to 20 GHz.

7.3.6 Signal-to-Noise Ratio

The random ﬂuctuations in the output voltage or current

from a detector set a lower limit to the radiant power that

can be detected, given the detector temperature and

operating conditions, source modulation frequency, and

electronic-detection-system bandwidth. The signal-to-

noise ratio (S/N ratio) is the ratio of electrical power pro-

duced by the detected light to the noise power, which can

be written in a simple form as:

ð7:15Þ

where i

is the current produced by the detected light, and

is the noise current. Angular brackets <  > indicate

time averaging. Noise can often be reduced by operating

the detector in an appropriate way. In a practical detection

system, the detector must be coupled to various forms of

electronic processing systems, pre-ampliﬁers, ampliﬁers,

ﬁlters, lock-in detectors, and so on. This electronic system

necessarily creates additional noise; in a well-designed

system this is kept to a minimum.

It will be seen in the following sections that there are

various ways to reduce, and even essentially eliminate,

detector noise. Photon noise, however, which arises from

the signal itself cannot be eliminated. Thus, the ultimate

performance of any detector is photon-limited. The

photon-noise limit is different for thermal detectors, which

are sensitive to total absorbed radiation, and photon detec-

tors, which respond, at least in a microscopic way, to the

absorption of individual quanta.

The signal-to-noise (S/N) performance of a detector in a

given situation can usually be calculated from the detector

characteristics speciﬁed by the manufacture and the cha-

racteristics of the electronic system that the detector will

drive. Speciﬁcally important are the dark-noise level, the

noise ﬁgure [especially for devices with internal gain such

as avalanche photodiodes (APDs)], the quantum efﬁciency

(or responsivity) of the detector, and the input impedance

of the following electronics and its noise characteristics.

Figure 7.4 Typical frequency dependence of

detector responsivity R.

FIGURES OF MERIT FOR DETECTORS 553

Davis

has provided several examples of how to calcu-

late detector noise performance in various situations.

If the detector manufacturer speciﬁes D* or NEP, and

not all do, signal-to-noise calculations can be simpliﬁed.

Frequently the dark-noise current will be speciﬁed, usually

in units of nA or pA. Noise generally increases with the

square root of the bandwidth used. For example, a detector

with a bandwidth of 100 MHz and a dark current of 5 nA

has a dark noise of 0.5 pA/

ﬃﬃﬃﬃﬃﬃ

7.4 PHOTOEMISSIVE DETECTORS

Photoemissive detectors include vacuum photodiodes,

photomultiplier tubes, microchannel plates, and photo-

channeltrons. These are all p hoton detectors that utilize

the photoelectric effect. When radiation of frequency m

falls upon a metal surface, e lectrons are emitted if the

photon energy hm is greater than the work function /

characteristic of the material being irradiated. A simpli-

ﬁed energy-level diagram illustrating this effect for a

metal–vacuum interface is shown in Figure 7.5(a).Formost

etals, /; is in a range from 4–5 eV (1 eV [ 1.24 lm)

although for the alkali metals it is lower, for example,

2.4 eV for sodium and 1.8 eV for cesium. Pure metals,

alloys, (particularly beryllium–copper) and cesium iodide

are used as phot oemissive surfaces in ultraviolet an d

vacuum-ultraviolet detectors. Lower work functions, and

consequently sensit ivities that can be extended into the

infrared, can be obtained with special semiconductor

materials. Figure 7.5(b) shows a schematic energy-level

diag

ram of a semiconductor–vacuum interface. In this

case the work function is deﬁned as / ¼ E

vac

– E

, where

is the energy of the Fermi level. In a pure semiconduc-

tor, the Fermi level is in the middle of the band gap, as

illustrated in Figure 7.5(b).Inap-ty

pe doped semiconduc-

tor, E

moves down toward the top of the valence band,

while in n-type material it moves up toward the bottom of

the conduction band. Consequently, /; is not so useful a

measure of the minimum photon energy for photoemission

as it is for a metal. The electron afﬁnity v is a more useful

measure of this minimum energy for a semiconductor.

Except at absolute zero, photons with energy hv > v cause

photoemission. Photons with energy hm > E

lead to the

production of carriers in the conduction band: this leads to

intrinsic photoconductivity, which is the operative detec-

tion mechanism in various infrared detectors, such as InSb.

7.4.1 Vacuum Photodiodes

Once electrons are liberated from a photoemissive surface

(a photocathode), they can be accelerated to an electrode

(the anode), positively biased with respect to the cathode,

and generate a signal current. If the acceleration of photo-

electrons is directly from cathode to anode through a vac-

uum, the device is a vacuum photodiode. Because the

Figure 7.5 Band structure of: (a) a metal–vacuum

interface and (b) a pure semiconductor–vacuum

interface (/ ¼ work function; v ¼ electron afﬁnity;

¼ band-gap energy; E

¼ Fermi level).

554 DETECTORS

electrons in such a device take a very direct path from anode

to cathode and can be accelerated by high voltages – up to

several kilovolts in a small device – vacuum photodiodes

have the fastest response of all photoemissive detectors.

Rise times of 100 ps or less can be achieved. External con-

nections and electronics are generally the limiting factors in

obtaining short rise times from such devices. Vacuum pho-

todiodes, however, are not very sensitive, since, at most, one

electron can be obtained for each photon absorbed at the

photocathode.

If the space between photocathode and anode is ﬁlled

with a noble gas, photoelectrons will collide with gas

atoms and ionize them, yielding secondary electrons.

Thus, an electron multiplication effect occurs. However,

because the mobility of the electrons moving from cathode

to anode through the gas is slow, these devices have a long

response time, typically about 1 ms. Gas-ﬁlled photocells

are no longer competitive with solid-state detectors and

have disappeared from use.

7.4.2 Photomultipliers

If photoelectrons are accelerated in vacuo from the pho-

tocathode and allowed to strike a series of secondary

electron-emitting surfaces, called dynodes, held at progres-

sively more positive voltages, a considerable electron mul-

tiplication can be achieved and a substantial current can be

collected at the anode. Such devices are called photomul-

tipliers. Practical gains of 10

(anode electrons per photo-

electron) can be achieved from these devices for short light

pulses. Continuous gains must be held lower, to perhaps

. This limit is imposed primarily by the ability of the

ﬁnal dynodes in the chain to withstand the thermal loading

produced by continuous electron impact, and by the time

needed for the dynodes to be recharged when large cur-

rents are drawn from the anode. Because of their very high

gain, photomultipliers can generate substantial signals

when only a single photon is detected: for example, an

anode pulse of 2 ns duration containing 10

secondary

photoelectrons produced from a single photoelectron will

generate a voltage pulse of 4 V across 50 ohms. This,

coupled with their low noise, makes photomultipliers very

effective single-photon detectors. Photomultiplier D

values

can range up to 10

cm Hz

1/2

–1

. Only the dark-adapted

human eye, which can detect bursts of about 10 photons in

the blue, comes close to this sensitivity.

The time-response characteristics of photomultiplier

tubes depend to a considerable degree on their internal

dynode arrangement. The response of a given device can

be speciﬁed in terms of the output signal at the anode that

results from a single photoelectron emission at the photo-

cathode. This is illustrated in Figure 7.6. Because electrons

passing

through the dynode structure can generally take

slightly different paths, secondary electrons arrive at the

anode at different times. The anode pulse has a character-

istic width called the transit-time spread, which usually

ranges from 0.1 to 20 ns. The time interval between

Figure 7.6 Typical anode pulse produced by a single photoelectron emission at

the cathode of a photomultiplier tube. t is the time following photoemission. The

transit-time T, the transit-time speed DT, and the peak anode current i

all ﬂuctuate

from pulse to pulse.

PHOTOEMISSIVE DETECTORS 555

photoemission at the cathode and the appearance of an

anode pulse is called the transit time, and is usually a

few tens of nanoseconds. The transit time and transit-time

spread also ﬂuctuate slightly from one single-photoelec-

tron-produced anode pulse to the next. Although this is a

ﬁne point, it may be something to worry about in precision-

timing experiments. The principle suppliers of photomul-

tiplier tubes are Hamamatsu, Burle Industries

(now

merged with Photonis), Electron Tubes, Phillips

(Amperex), Photek, and Sens-Tek.

There are s even main types of dyn ode structure in

common usage in photomultiplier tubes; these are illus-

trated in Figure 7.7 . The circular cage stru cture [Figure

7.7

(a)] (use d, for example, in the H amamatsu 1P28 pho-

tomultiplier tube) is compact and can be designed for

good electron-collection efﬁciency and small transit-

time spread. This dynode structure works well with opaque

photocathodes, but is not very suitable for high-ampliﬁcation

requirements, where a larger number of dynodes is re-

quired. The box-and-grid [Figure 7.7(b)] and Venetian-

blind structures [Figure 7.7(c)] (used, for example, in the

Hamamatsu Models R464 and R1513, respectively) offer

very good electron-collection efﬁciency. Because they col-

lect multiplied electrons independent of their path through

the dynode structure, a wide range of secondary-electron

trajectories is possible, leading to a large transit-time

spread and slow response. Typical response times of these

types of tube are 10–20 ns. Venetian-blind tubes can easily

be extended to many dynode stages and have a very stable

gain in the presence of small power-supply ﬂuctuations.

These tubes also have an optically opaque dynode struc-

ture providing very low dark-current noise when operated

under appropriate conditions.

The focused dynode structure [Figure 7.7(d)] (used, for

example, in the Hamamatsu R331, R2059, and the old

Phillips 56 AVP and other 56-series tubes

) is designed

so that electrons follow paths of similar length through the

dynode structure. To accomplish this, electrons that devi-

ate too much from a speciﬁed range of trajectories are not

collected at the next dynode. These types of tube offer

short response times, typically 1–2 ns; some recently

developed tubes are even faster.

The mesh type of dynode structure [Figure 7.7(e)] has a

series of crossed ﬁne-mesh dynodes arranged in close

proximity. The structure allows compact construction,

high immunity to magnetic ﬁelds, as well as uniformity

of response and good pulse linearity. Versions of this type

with special anodes provide position-sensitive perform-

ance. In this type of device the output signal from a series

of anodes provides direct information on the location of

illumination on the photocathode surface.

The metal-channel dynode structure [Figure 7.7(g)] pro-

vides a very compact dynode structure and fast response

becomes of the closeness between each stage of dynodes.

This structure also allows position-sensitive detection.

Good examples of this type of tube are in the Hamamatsu

R5900 series. These types of tube can tolerate quite large

magnetic ﬁelds. The Hamamatsu R5946 tube has been

shown to operate satisfactorily in ﬁelds of 4kG.

Closely rela ted to thes e f unda men tal photomult iplier

dynode structures is the micro channel plate (MCP) [Fig-

ure 7.7(f)]. Instead o f traditional dynodes, photoelectrons

enter a bundle of capillary tubes fused together in an

array. Each tube has a resistive coating on its inner sur-

face that acts as a continuo us electron multiplier. Each

capillary individually can be referred to as a channel

electron multiplier (CEM) [or channeltron (a trademark

of Burle Industries)]. In these capillaries electrons make

multiple reﬂections from the tube walls generating sec-

ondary electrons. MCPs have fast time response, good

immunity from external magnetic ﬁelds, and position-

sensitive capability when provided with multiple anodes.

These devices are available commercially from Burle

(Photonis), DelM ar Ventures, El-M ul, Hamamatsu, Pho-

tek, TecTra, and Topag. CEMs a re primarily used for

particle detection (see later).

Other types of multiplier structures, not shown in Figure

7.7, are also available. Traveling-wave phototubes and var-

ious

types of crossed-ﬁeld photomultiplier have very short

response times, down to 0.1 ns.

7.4.3 Photocathode and Dynode Materials

The performance of a photomultiplier depends not only

on its internal structure, but also on the photoemissi v e mate-

rial of its photocathode and the secondary-electron-emitting

material of its dynodes. The selection of a photodiode or

photomultiplier for a particular spectral response depends

on an appropriate selection of photocathode material. The

wavelength dependence of various commercially available

556 DETECTORS

Figure 7.7 Schematic diagram of the internal structure of various types of

photomultiplier tube; (a) circular cage; (b) box and grid; (c) Venetian blind;

(d) focused dynode; (e) mesh type; (f) microchannel electron multiplier;

(g) metal-channel dynode structure. D ¼ dynode; PC ¼ photocathode.

PHOTOEMISSIVE DETECTORS 557

photocathode materials is shown in Figure 7.3;someradiant

sensitiviti es and quantum ef ﬁ ciencies are giv en in Table 7.1.

Figure 7.8 sho ws the radiant sensiti vities and quantum efﬁ-

cien

cies of some new negative electron af ﬁ nity (NEA) pho-

tocathode materials. Practical quantum efﬁciencies for

photoemissiv e materials range up to about 0.4. The short-

wavelength cutoff of a given material depends on its work

function. This cutoff is not sharp because, except at absolute

zero, there are always a few electrons high up in the con-

duction band available for photoexcitation by low-energy

photons. Some few of these electrons, because of their ther-

mal excitation, will be emitted without any photostimulation.

This contributes the major part of the dark current observed

from the photocathode. Materials that have low work func-

tions, and are consequently more red- and infrared-sensitiv e,

have higher – often much higher – dark currents than mate-

rials that are optimized for visible and ultraviolet sensiti vity.

Such photocathodes are best operated cooled. Unless a pho-

totube is to be used primarily for detecting long-wavelength

radiation, we recommend selecting a photocathode with the

shortest possible wav elength response.

Photocathodes are available in both opaque and semitrans-

parent forms, depending on the model of phototube. In the

semitransparent form the photoelectrons are ejected from the

thin photoemissiv e layer on the side opposite to the incident

light. In both types the photocathode has to perform two

important functions: it must absorb incident photons and

allow the emitted photoelectrons to escape. The latter ev ent

is inhibited if photons are absorbed too deep in a thick photo-

emissi ve layer , or if the photoelectrons suffer energy loss from

scattering in the layer . If the emitted photoelectron has too

much energy, it can excite a further electron across the band

gap. This pair-production phenomenon inhibits the release of

photoelectrons from the photoemissive layer, and accounts for

the ultraviolet cutoff characteristics of the different materials

show n in Figure 7.3. W ith reference to Figure 7.5(b), it can be

own that for pair production to occur , the incident photon

energy must be greate r than 2E

. For materials where v < E

photoelectrons have their best chance of escaping, and the

photocathode its highest quantum efﬁcienc y.

Because semitransparent photocathodes allow photons

to penetrate sufﬁciently for photoelectrons to escape on the

far side of the layer, they are deposited as semiconductor

layers on the insulating glass substrate of the entrance

window. These photocathodes are less tolerant of relatively

high light levels than are opaque photocathodes, which can

be deposited on a conductive substrate. A conductive sub-

strate preserves ﬁeld distribution within the PMT even at

relatively large cathode currents. When an opaque photo-

cathode is used, photons pass through the entrance window

of the PMT and strike the photocathode, which is mounted

separately, as shown schematically in Figure 7.7(a). Photo-

electrons

are emitted on the same side of the photocathode

as photons are absorbed.

Practical photoemissive materials fall into two main

categories: classical photoemitters and NEA materials.

Classical photoemitters generally involve an alkali metal

or metals, a group V element, such as phosphorus, arsenic,

Figure 7.7 (cont.)

558 DETECTORS

antimony, or bismuth, and sometimes silver and/or oxygen.

Examples are the Ag-O-Cs (S1) photoemitter, which has

the highest quantum efﬁciency beyond about 800 nm of

any classical photoemitter, and Na

KSbCs, the so-called

tri-alkali (S-20) cathode.

Negative electron afﬁnity photoemitters have only been

developed within the last 15 years. These materials gen-

erally utilize a photoconductiv e single-crystal semiconductor

substrate, with a very thin surface coating of cesium and

usually a small amount of oxygen. The cesium (oxide)

layer lowers the electron afﬁnity below the value it would

have in the pure semiconductor, achieving an effectively

negative value. Examples of such NEA photoemitters are

GaAs (CsO) and InP (CsO). Negative electron afﬁnity

emitters can offer very high quantum efﬁciency and

extended infrared response. For example, GaAs (CsO)

has higher quantum efﬁciency in the near infrared then an

S-1 photocathode. Other new NEA photocathodes include

InP/InGaAsP (sensitive to 1.4 lm) and InP/InGaAs (sensi-

tive to 1.7 lm). Commercial photomultipliers with NEA

photocathodes are available from Burle Industries and

Hamamatsu, that offer response out to 1.7 lminatube

cooled to 100 °C. Development of NEA photoemitters is

continuing

, and the experimentalist seeking long-

wavelength response would be well advised to follow the

literature and check for the introduction of new commercial

tubes. For further details about NEA materials, the inter-

ested reader should consult the article by Zwicker.

Table 7.1 Characteristics of photoemissive surfaces

Cathode Radiant Sensitivity (mA/W) 1.06 lm Peak Quantum

Efﬁciency (%)

kpeak

(lm) Cathode Dark

Current

(A/cm

)

515 nm 694 nm

S-1 Cs-O-Ag 0.6 2 0.4 0.08 800 9 3 1

–12

S-10 Cs-O-Ag-Bi

20 2.7 0 5 470 4 3 10

16

Sb on MnO

39 0.2 0 13 440 10

16

(tri-alkali) 53 20 0 18 470 9 3 10

16

S-22 (bi-alkali) 42 0 0 26 390 2 3 10

15

GaAs

d–g

48 28 0 14 560

16

GaAsP

60 30 0 19 400 3 3 10

15

InGaAs(Cs)

d,f

7 2.6 0.1 15 380 2 3 10

14

InP/InGaAs

d,e,f

3 3 11(1.5 lm) 1.55 lm

4 3 10

14

InP/InGaAsP

d,f

3 3 10(1.3 lm) 1.3 lm

4 3 10

15

S-25 (ERMA)

53 26 0 25 430 1 3 10

15

Cs-Te (solar blind) — — — 15 254 2.5 3 10

17

Note: Table shows typical values, but these can vary greatly from one manufacturer to another. We recommend that manufacturers’ data

sheets be consulted for more details.

At room temperature.

Cathode designated S-3 is similar.

Several types of CsSb photocathodes exist where the CsSb is deposited on different opaque and semitransparent substrates and various

window materials are used.These photocathodes have the designations S-4, 5, 13, 17, and 19 as well as S-11.

NEA photoemitters.

Available from Burle Industries.

Available from Hamamatsu Corporation.

Sensitive out to 1.7 lm. Exact spectral characteristics will depend on thickness of photoemitter and whether it is used in transmission

or not.

Sensitive out to 1.4 lm. Exact spectral characteristics will depend on thickness of photoemitter and whether it is used in transmission

or not.

Extended-red S-20.

PHOTOEMISSIVE DETECTORS 559

The performance of the dynode material in photomulti-

plier tubes is speciﬁed in terms of the secondary-emission

ratio d, as a function of energy. For a phototube with n

dynodes the gain is d

. In the past, the most common

dynode materials were CsSb, AgMgO, and BeCuO. The

last is also used as the primary photoemitter in windowless

photomultipliers that are operated in vacuo for the

detection of vacuum-ultraviolet radiation. BeCuO can be

reactivated after exposure to air. The above materials

have d-values of 3–4. Newer NEA dynode materials have

much higher d-values; in particular, that of GaP can range

up to 40 for an incident-electron energy of 800 eV. With

such high d-values, a photomultiplier tube needs fewer

dynodes for a given gain, but with larger interdynode

accelerating voltages. Such tubes are compact and provide

fast time response. In very many commercial photo

multipliers, at least the ﬁrst dynode is now often made

of GaP. This offers improved characterization of the single-

Figure 7.8 Quantum efﬁciencies and radiant sensitivities of near-infrared semiconductor

photocathode materials.

560 DETECTORS

photo-electron response of the tube, which is important in

designing a system for optimum signal-to-noise ratio.

7.4.4 Practical Operating Considerations

for Photomultiplier Tubes

Complete photomultiplier assemblies are available, in

which the tube, mounting base, dynode chain and output

connector are pre-packaged. Suppliers include C&L

Instruments, Hamamatsu, OE Technologies, and Products

for Research, For the experimentalist who desires more

control over tube operation, the following sections should

be useful. (Note also that Hamamatsu have published a

comprehensive guide to photomultiplier use.

)

Dynode Chains. The accelerating voltages are supplied

to the dynodes of a photomultiplier by a resistive voltage

div ider called a dynode chain. The relative resistance v alues

Figure 7.9 Dynode chains for Phillips 56-series photomultiplier tubes: (a) chain for high gain and fast time response;

(b) chain for high linearity (R

and R

adjusted for optimum performance). PC ¼ photocathode; g1,g2 ¼ grids;

acc ¼ accelerator grid; D1–D14 ¼ dynodes. Resistance values are in ohms, capacitance values in lF. For very low-level

light detection, all resistances can be scaled upward to reduce overall chain current.

PHOTOEMISSIVE DETECTORS 561

in the chain determine the distribution of voltages applied to

the dynodes. The total chain resistance R determines the

chain current at a given total photocathode–anode applied

voltage. Some phototubes are supplied with an integral

dynode chain, but most are not. Adequate dynode-chain

designs are generally supplied by the manufacturer with

each tube. Alternative designs intended for certain types of

response, such as maximum gain for short pulses or highest

linearity, can frequently be found by consulting the literature.

Two examples of such dynode-chain designs for use with

Phillips 56-series tubes are giv en in Figure 7.9. The total

dyn

ode-chain resistance is chosen so that the chain current

is at least 100 times greater than the average d.c. anode

current to be drawn from the tube. This current is speciﬁed

for each tube and may range as high as 1 mA for high-gain

tubes. The operation of photomultiplier tubes at such high

average currents for very long is not recommended. Long-

term d.c. anode currents should be kept between 1 and 10 lA

for most tubes.

There are several interesting features of the dynode

chains shown in Figure 7.9. The photocathode is generally

operated

at negative potential with the anode near ground.

This makes it easy to couple the output signal to other

electronics. The tube can be operated with the cathode

grounded, but in this case the signal from the anode, which

is now at high positive potential, must be coupled through

high-voltage capacitors or an insulated transformer, as

shown in Figure 7.10. The photocathode is also often con-

nected

to a conducting shield, which is either a painted

coat of colloidal graphite (Aquadag) on the outside of

the tube envelope, or a metal foil wrapped around the tube

envelope. If the photocathode is at negative potential,

appropriate insulation must be used around the tube if

the tube is in close proximity to any grounded metal parts

inside its housing.

Many photomultiplier tubes have one or more focusing

electrodes between the photocathode and the ﬁrst dynode.

The voltage on these electrodes can be adjusted to opti-

mize the collection of photoelectrons from the photoca-

thode. The last three or four dynodes are decoupled with

high-voltage, high-frequency capacitors (disk ceramics

work well in this application). These capacitors prevent

depression of the dynode-chain voltage on the last few

dynodes when a large pulse of electrons passes through

the tube (the secondary-electron current drawn from each

dynode must be supplied by the dynode chain). For high-

frequency applications the inclusion of small damping

resistors (typically between 50 X and 1 kX) between the

decoupling capacitors and the dynodes is recommended. The

resistor R

, the anode resistor, determines the actual voltage

that will be produced by a given anode current, since the

photomultiplier serves as a current source. R

should not

be so large that the voltage dev eloped across it is signiﬁc ant

compared with the voltage between the anode and the last

dynode. A value of R

between 1 and 10 MX is usual. In

high-frequency applications, such as single-photon count-

ing, the signal from R

should be coupled out through a

50 X coaxial cable terminated in 50 X. In many cases, the

effective value of the anode load is set by the input impe-

dance of the electronics to which the tube is connected. In

Figure 7.10 Anode signal coupling methods for a

photomultiplier operated with the anode at high

positive potential: (a) capacitor coupling for fast-risetime,

short-pulse operation (the component sizes are typical;

the capacitors should be high-frequency, high-voltage

types); (b) transformer coupling for lower-frequency,

modulated operation (the high-voltage winding on the

transformer should be sufﬁciently well insulated for

isolation from the core; the size of R

will depend on

various factors, such as transformer primary impedance

and operating frequency).

562 DETECTORS

such applications the cable connection to the anode should

be shielded as close to the anode as possible, even going so

far as to insert R

under the grounded screen of the coaxial

cable. Some high-frequency tubes are supplied with an

integral coaxial connector on the anode. In any case, the

aim is to reduce parasitic inductance and capacitance asso-

ciated with the anode connection. For example, even with a

50 X load, a parasitic capacitance greater than 20 pF will

limit the response time of the tube to 1 ns.

The actual response-time behavior of the photomultiplier

can be determined by observing its single-photo-electron

response. This is done by looking at the anode pulses with

a fast oscilloscope, which generally requires that the 50 X

coaxial cable from the anode be terminated in 50 X.The

photocathode should not need to be illuminated for this to

be done; sufﬁcient noise pulses will usually be observed.

The pulses should appear as in Figure 7.6. If they have

o much of an exponential tail they are probably

limited by the anode resistor and parasitic capacitance.

These anode pulses reﬂect the time distribution and number

of secondary electrons reaching the anode following single

(or multiple) photoelectron emissions from the photoca-

thode. If the height distribution of anode pulses is measured,

a distribution such as is shown in Figure 7.11 will probably

seen.

Mounting Photomultiplier Tubes. Photomultiplier

tubes are generally mounted by clamping their plastic

socket inside a cylindrical tube housing. The housing

should be light-tight: a photomultiplier should never be

exposed to ambient lighting when its high-voltage dynode

chain is on, for the resultant large secondary-electron

current will disintegrate the last dynodes and may strip

the photocathode layer itself. If the total power

dissipation of the dynode chain is low, the whole dynode

chain may be mounted directly on the tube socket. If space

is not at a premium, the dynode chain can be remote from

the tube base and connected to it with high-voltage-

insulated wire. The damping resistors, decoupling cap-

acitors, and anode resistor should, however, be kept in

Figure 7.11 Schematic photomultiplier anode pulse-height distribution likely to

be observed in practice. The best signal-to-noise ratio would be obtained in a

photon-counting experiment by collecting only anode pulses in a height range

roughly indicated by the shaded region AB.

PHOTOEMISSIVE DETECTORS 563

close proximity to the tube. The photomultiplier should be

mounted so there is no optical path from its base to its

photocathode.

Photomultipliers are fragile and should be mounted so

they are not subject to stress. This is particularly important

if a tube is to be cooled. In practice, this means that the

tube should be grasped at only one point in its mount.

Rugged (and expensive) photomultipliers that can with-

stand severe vibrations and accelerations are available

from ADIT and Hamamatsu.

Noise in Photomultiplier Tubes. Noise in photo-

multipliers comes from several sources:

(1) Thermionic emission from the photocathode

(2) Thermionic emission from dynodes

(3) Field emission from dynodes (and photocathode) at

high interdynode voltages

(4) Radioactive materials in the tube envelope (for example,

K in glass)

(5) Electrons striking the tube envelope and causing

ﬂuorescence

(6) Electrons striking the dynodes and causing ﬂuorescence

(7) Electrons colliding with residual atoms of vapor in the

tube (cesium for example) and causing ﬂuorescence

(8) Cosmic rays.

Noise from photomultipliers is always greater after

they have been exposed to light (without high voltage

applied). They gradually become quieter after operation

under dark conditions for an extended period.

Noise from thermionic emission can be reduced consid-

erably by cooling the tube (particularly for S-1 tubes).

A factor of 10–1000 reduction in noise can be obtained

by cooling to about 20 °C. S-1 tubes need to be cooled

to low temperatures, but temperatures below about 70 °C

are not recommended. Too much cooling has a marginal

effect on reducing thermionic emission – which will

already be negligible for most tubes at 20 °C – and may

have deleterious effects. At low temperatures, the conduc-

tivity of the photocathode layer falls, which causes it to no

longer be an equipotential. The resultant distorted ﬁeld

distribution between cathode and dynodes will increase

the possibility of noise from sources such as item (5) above.

Two convenient designs of photomultiplier-tube coolers are

shown in Figure 7.12. In the design shown in Figure

7.1

2(a), a copper or aluminum cylinder encloses the tube

(wi

thout touching it). This tube is in thermal contact with a

chamber containing Dry Ice (or liquid nitrogen). Conden-

sation on the face of the photomultiplier tube is minimized,

since moisture preferentially condenses and freezes on the

much colder metal tube. In the second design, shown in

Figure 7.12(b), cold nitrogen gas boiled off from a liquid-

trogen Dewar ﬂows through a copper tube surrounding

the photomultiplier, and ﬁnally sprays over its photoca-

thode surface to minimize water-vapor condensation. The

rate of supply of cold nitrogen gas can be adjusted to pro-

vide a range of temperatures.

Photomultiplier-tube coolers are available from Amherst

Scientiﬁc, Electron Tubes, Hamamatsu, and Products for

Research.

When noise from ﬁeld emission is a problem with cer-

tain high-voltage, high-gain tubes, one solution is to

reduce the voltage. In single-photon-counting experi-

ments, larger than normal anode pulses may result from

ﬁeld emission and can be rejected with an appropriate

window discriminator.

Noise from radioactive envelope materials should gen-

erally be negligible. Noise from electrons striking the tube

envelope can be reduced by a shield around the tube held

at photocathode potential. Noise from electrons striking

the dynodes and causing ﬂuorescence causes the fewest

problems in Venetian-blind tubes, which have little or no

direct optical path from dynodes to photocathode. Noise

from gas in the tube can be a problem in old tubes, which

frequently become gassy; solution: buy a new tube. Noise

from cosmic rays is usually unimportant; it can be reduced

by shielding.

Of all these sources of noise, thermionic emission

from the photocathode is generally by far the most impor-

tant. For a given photocathode material the total noise

will depend on the photocathode area. Most manufac-

turers will list the dark current observed at the anode.

The values in Table 7.1 have been derived from man-

ufacturers’

anode dark currents corrected for tube gain

and photocathode area. Under comparable conditions,

tubes with a small photocathode area, like the old S-20

ITT FW-130 with a photocathode diameter of 0.25 cm,

are less noisy than tubes with large photocathodes, like

the 46 mm photocathode of the S-20 Hamamatsu R550.

In many experiments a large photocathode area is

564 DETECTORS

unnecessary – light coming through a monochromator slit

illuminates a very small area. The effective photocathode

area, and consequently its thermionic noise, can be reduced

by wrapping a magnetic coil around the photocathode,

which prevents electrons other than those from the center

of the photocathode from reaching the ﬁrst dynode. Under

circumstances where photomultipliers must be operated

in close proximity to magnetic ﬁelds, magnetic shields to

Figure 7.12 Photomultiplier-tube coolers: (a) using Dry Ice reservoir in thermal contact

with a metal tube close to, but electrically insulated from, the photocathode; (b) using

cold nitr ogen gas cir culated around tube and sprayed onto photocathode surface

(a thermistor monitors temperature and allows control of the rate of supply of cold gas).

PHOTOEMISSIVE DETECTORS 565

enclose the tube are available from Ad-Vance Magnetics,

Amuneal, Magnetic Shield Corp. (Perfection Mica), Mu

Shield, and Products for Research.

In the anode pulse-height distributions shown in Figure

7.11, small anode pulses are much more likely to corre-

spond

to noise than are pulses in the middle of the distri-

bution. In photon-counting experiments these small pulses

should be rejected with a discriminator. Awindow discrim-

inator provides simultaneous rejection of these pulses and

those which are much larger than average.

Ultraviolet and Vacuum-Ultraviolet Detection

with Photodiodes and Photomultipliers.

For

detection of radiation down to about 105 nm, phototubes

with windows of LiF are available, as are tubes with

windows of MgF

or sapphire. Windowless phototubes or

CEMs are used for detection of even shorter wavelengths.

For detection of radiation down to 58 nm or beyond,

conventional photomultiplier tubes sensitive to visible

light (S-11) can be used if the outer surface is coated with

a layer of sodium salicylate – or if a sodium-salicylate-

coated disk is placed close to the photocathode. Sodium

salicylate ﬂuoresces in the visible with almost

unity quantum efﬁ ciency and converts incident vacuum-

ultraviolet radiation to a wavelength where a conv entional

tube can detect it. The response of the sodium salicylate is

also fast, so that 1 ns ultraviolet detection is possible. To

prepare a sodium-salicylate-coated windo w, a solution of

sodium salicylate in reagent-grade methanol (80 g/L) is

atomized and sprayed onto the windo w, at a distance of

about 10 cm from the atomizer. Commercial nasal sprays

and air brushes pressurized with dry nitrogen are suitable

for this purpose. The atomizer should be far enough from

the windo w that no large drops can be deposited. The

method works better if the window is kept warm (50–

70 °C). Spraying should be continued until the density of

the sodium salicylate layer reaches about 20 g/m

,which

can be determined by weighing.

7.5 PHOTOCONDUCTIVE

DETECTORS

Photoconductive detectors can operate through either

intrinsic or extrinsic photoconductivity. The physics of

intrinsic photoconductivity is illustrated in Figure 7.13(a).

Photons

with energy hm > E

excite electrons across the

band gap. The electron–hole pair that is thereby created for

each absorbed photon leads to an increase in conductivity

(mostly from the electrons.) Semiconductors with small

band gaps respond to long-wavelength infrared radiation

but must be cooled accordingly; otherwise thermally

Figure 7.13 Mechanism for: (a) intrinsic photoconductivity; (b) extrinsic

photoconductivity.

566 DETECTORS

excited electrons swamp any small photoconductivity

effects. Table 7.2 lists commonly available intrinsic photo-

conducti

ve detectors together with their usual operating

temperature and the limit of their long-wavelength

response k

, together with some representative ﬁgures for

detectivities and time constants. Note that silicon and ger-

manium are also operated in both photovoltaic and ava-

lanche modes (see Section 7.6).

a semiconductor is doped with an appropriate mate-

rial, impurity levels are produced between the valence and

conduction bands, as shown in Figure 7.13(b). Impurity

vels that are able to accept an electron excited from the

conduction band are called acceptor levels,whereas

impurity levels that can have an electron excited from

them into the conduction band are called donor levels.

Thus, in Figure 7.13(b) photons with energy hm > E

excite

an electron to the impurity level, leaving a hole in the

valence band and thereby giving rise to p-type extrinsic

photoconductivity. Photons with energy hm > E

will excite

an electron into the conduction band, giving n-type extrin-

sic photoconductivity. For example, gold-doped germa-

nium has an acceptor level 0.15 eV above the valence

band and is an extrinsic p-type photoconductor, as is cop-

per-doped germanium, which has an acceptor level 0.041

eV above the valence band. These used to be the two most

commonly used extrinsic photoconductive detectors,

responding out to about 9 lm and 30 lm, respectively,

but they have been largely superseded by mercury cad-

mium telluride (MCT) detectors. Curves showing the var-

iation of their D

with wavelength are given in Figure 7.14.

Table 7.3 lists the operating characteristics of some extrin-

sic

photoconductive detectors. Detectors listed with oper-

ating temperatures below 28 K will in practice frequently

be operated at 4 K, since liquid helium is a safe, available

coolant, although its use involves more complicated tech-

nology than the use of liquid nitrogen. Only long wave-

length response gallium-doped germanium detectors are

currently commercially available, although other extrinsic

Table 7.2 Intrinsic photoconductive detectors

Semiconductor T (K) E

(eV) k

(lm) D

(max) s

(cm Hz

1/2

1

)

CdS 295 2.4 0.52 3.5 3 10

’50 ms

CdSe 295 1.8 0.69 2.1 3 10

’10 ms

295

1.12 1.1 <2 3 10

—

295

0.67 1.8 10

10 ns

PbS 295 0.42 2.5 <2 3 20

—

195 0.35 3.0 <5 3 10

—

77 0.32 3.3 <8 3 10

—

PbSe 295 0.25 4.2 1 < 10

–53 10

1 ls

195 0.23 5.4 1.5–4 310

3050 ls

77 0.21 5.8 <3 3 10

50 ls

InSb

77 ’0.23 5.5–7.0 <3 3 10

0.11 ls

77 <0.1 1225 10

10

>1 ns

Increased sensitivity can be obtained by cooling.

Detectors with time constants from 50 ps upward and various detectivities are available.

Detectors operated in a photovoltaic mode with time constants from 120 ps upward and various detectivities are available.

Detectors with time constants ranging from about 100 ls to 10 ms and varying detectivities are available.

More commonly operated in a photovoltaic mode.

Wavelength range depends on stoichiometry

Silicon detectors are available from many suppliers.

Ge detectors are available from Jobin Yvon and Judson. PbS and PbSe detectors

are available from Cal Sensors, Hamamatsu, Judson and New England Photoconductor, InSb detectors are available from Hamamatsu,

InfraRed Associates, Judson, and Kolmar Technologies. MCT detectors are available from Boston Electronics, Hamamatsu, InfraRed

Associates, Judson, and Kolmar Technologies.

PHOTOCONDUCTIVE DETECTORS 567

detectors are still custom made in specialized research

laboratories.

All photoconductive detectors, whether intrinsic or extrin-

sic, are operated in essentially the same way, although there

are wide differences in packaging geometry. These differ-

ences arise from dif fering operating temperatures and speed-

of-response considerations. A schematic diagram showing

the main construction features of a liquid-nitrogen-cooled

photoconductive or photovoltaic detector is giv en in

Figure 7.15. Uncooled detectors can be of much simpler

cons

truction – for example, in a transistor or ﬂat solar-cell

package.

One feature of the cooled detector design shown in Figure

7.15 is worthy of note. The ﬁeld of view of the detector is

generally

restricted by an aperture, which is kept at the

temperature of the detection element. This shields the

detector from ambient infrared radiation, which peaks at

9.6 lm. For detection of low-level narrow-band infrared

radiation the inﬂuence of background radiation can be

further reduced by incorporating a cooled narrow-band

ﬁlter in front of the detector element. The ﬁlter will only

radiate beyond the cutoff wavelength of the detector, and

thus restricts transmitted ambient radiation to a narrow

band. Liquid-helium-cooled detectors generally have a

double Dewar; an outer one for liquid nitrogen surrounds

the inner, for liquid helium. Liquid-nitrogen-cooled detec-

tors, such as HgCdTe, are recommended in preference to

liquid-helium-cooled detectors, such as Ge:Cu, whenever

Figure 7.14 D

(k) as a function of wavelength for various

photoconductive detectors. (Courtesy of Hughes Aircraft

Company.)

Table 7.3 Extrinsic photoconductive detectors

Semiconductor Impurity T (K) k (lm) D

(or NEP) s

Ge:Au

p-type 77 8.3 3 3 10

10

30 ns

Ge:Hg

p-type <28 14 1–2 3 10

> 0.3 ns

Ge:Cd p-type <21 21 2–3 3 10

10 ns

Ge:Cu

p-type <15 30 1–3 3 10

>0.4 ns

Ge:Zn

a,b

p-type <12 38 12 3 10

10 ns

Ge:Be p-type <3 115 2 3 10

>1 ls

Ge:In p-type 4 111 — <1 ls

Ge:Ga p-type 4 >200 8 3 10

13

(NEP) <1 ls

Si:Ga p-type 4 17 109–10

>1 ls

Si:As n-type <20 23 1–3.5 310

0.1 ls

Sometimes also contain silicon.

Sometimes also contain antimony.

568 DETECTORS

there is a choice. Some miniature-package commercial

detectors can be cooled with Joule–Thompson refrigeration

units driven with compressed gas, which eliminates the

need for externally supplied liquiﬁed-gas coolant. Thermo-

electrically cooled (Peltier effect) infrared detector pack-

ages are available from Cal Sensors, Hamamatsu, Marlow,

and New England Photoconductor, for the operation of

MCT, PbS, or PbSe detectors down to temperatures of

193 K. Further details of the operating principles behind

these and other refrigeration techniques used with infrared

detectors are given by Hudson and Hudson.

Figure 7.16 shows a basic biasing circuit commonly

used for operating photoconductive detectors. R

is the

detector dark resistance. It is easy to see that the change

in voltage, DV, that appears across the load resistor R

for a

small change DR in the resistance of the detector is:

DV ¼

V

ðR

þ R

ð7:16Þ

This is at a maximum when R

¼ R

. Thus it is common

practice to bias the detector with a load resistance equal to

the detector’s dark resistance. The bias voltage is selected

to give a bias current through the detector that gives

optimum detectivity. This bias current will generally be

speciﬁed by the manufacturer. Figure 7.17 shows a simple

op-amp

circuit for use with a photoconductive detector.

To obtain a fast response from a photoconductive

detector, great care must be taken to minimize the stray

capacitance C

in the input circuit to the preampliﬁer.

Otherwise, the time constant of the detector will be

limited by R

. The ultimate limits to the speed of an

actual detector are set by its internal capacitance C

and

Figure 7.15 Radiation-shielded liquid-nitrogen-cooled photoconductive or

photovoltaic infrared detector assembly.

Figure 7.16 Simple biasing circuit for operating a

photoconductive detector with modulated radiation.

Figure 7.17 Simple op-amp circuit for operating a

photoconductive detector.

PHOTOCONDUCTIVE DETECTORS 569

the majority-carrier lifetime. Many comme rcial detectors

are manufactured so that the stray capacitance of the

detector and its connection leads is very small. This

is generally true of high-speed commercial detectors

packaged in all-metal Dewars with integral coaxial bias

connections. Metal Dewar packages are preferable to

glass ones: although the latter are cheaper, they are very

fragile.

If a detector is not speciﬁcally packaged to minimi ze

stray inductance, it is possible to reduce the stray capaci-

tance of the detector package and improve its speed of

response by the technique of ‘‘bootstrap ping,’’ which is

illustrated in Figure 7.18. All bias leads to the detector

d the leads to the preampliﬁer are double-shielded.

The preampliﬁer should ideally have a high input impe-

dance, a low input capacitance, a wide bandwidth, and

50 ohm output imp edance. Such p reampliﬁers can be

constructed, or bought from detector suppliers or Perry

Ampliﬁer. The inner shield is not grounded, but is con-

nected directly to the low-impedance output of the unit-

gain preampliﬁer. Thus the inner shield is ‘‘bootstrap-

ped’’ to the signal voltage and stray capacitance is effec-

tively eliminated. By this means the speed of response of

a detector can be improved substantially, say from 1 ls

down to 50 ns. An alternative way to improve the speed

of response, at the expense of signal (but not detectivity),

is to reduce the value of the load resistor.

A few photoconductive detectors are worthy of brief extra

comment. Silicon and germanium are much more commonly

used for photodiodes, frequently in an avalanche mode. These

devices are discussed in Section 7.6. Lead sulﬁde detectors

ve high impedance, 0.5 to 100 MX, and slow response, but

are the most sensitive detectors in the spectral region between

2and3lm and can be used uncooled. D

(k) curves for

these detectors are shown in Figure 7.19. They are available

from

Cal Sensors, Hamamatsu, Judson, and New England

Photoconductor. Lead selenide is sensitive to longer wave-

lengths than lead sulﬁde, but InAs operated in a photovoltaic

mode is to be preferred in this spectral region (3–4 lm).

InSb operated in a photov oltaic mode is probably the detector

of choice between 4 and 5.3 lm. Beyond about 5 lm,

HgCdTe (MCT) is the detector of choice and is to be pre-

ferred to detectors such as Ge:Hg and Ge:Cu, which must be

operated below liquid-nitrogen temperature. MCT detectors

Figure 7.18 Arrangement for ‘‘bootstrapping’’ an infrared

detector to minimize effects of parasitic capacitance.

Figure 7.19 D

as a function of wavelength for various

lead-salt photoconductive detectors. (Courtesy of Hughes

Aircraft Company.)

570 DETECTORS

can be operated in either a photoconductive or photov oltaic

mode. HgCdTe comes in different stochiometries, generally

represented as Hg

1–x

Te. Different stoichiometries have

diff erent spectral responses. By varying its composition,

HgCdTe exceeds in performance all other 77 K detectors

between 6 and 12 lm. Sometimes these detectors also

contain zinc and are designated HgCdZnTe. Thermoelec-

trically cooled MCT detectors have higher detectivity at

shorter wavelengths than MCT detectors operated at

77 K, as s hown in Figure 7. 20. HgCdTe detectors are

avai

lable from Boston Electronics, Hamamatsu, InfraRed

Associates, Judson, and Kolmar Technologies. For fur-

ther details of the above detectors, t he reader should con-

sult References 5, 7, 12, and 26 . Supplie rs of other

detectors

are listed in Reference 25.

The

use of extrinsic photoconductivity for the detec-

tion of far-infrared radiation requires the introduction of

appropriate dopi ng materi al into a semiconduc tor in order

to generate an acceptor or donor impurity level extremely

close to the valence or conduction bands, respectively.

Well-characterized impurity levels have been generated

in germanium in this way using gallium,

indium,

boron,

or beryllium doping. The long-wavelength sensi-

tivity limit is restricted to about 120 lm, but can be

extended to 200 lm in Ge:Ga by stressing the crystal.

Ge:Ga detectors are available from QMC Instruments.

Longer-wavelength-sensitive, extrinsic photoconductivity

can be observed in appropriately doped InSb in a magnetic

ﬁeld. Bulk InSb can be used more efﬁciently for infrared

detection in a different photoconductive mode entirely.

Figure 7.20 D

as a function of wavelength for room temperature, thermoelectrically

cooled, and liquid nitrogen cooled (77 K) mercury cadmium telluride photovoltaic

detectors manufactured by Judson.

PHOTOCONDUCTIVE DETECTORS 571

Even at the low temperature at which far-infrared photo-

conductive detectors operate (< 4 K), there are carriers in

the conduction band. These free electrons can absorb far-

infrared radiation efﬁciently and move into higher-energy

states within the conduction band. This change in energy

results in a change of mobility of these free electrons,

which can be detected as a change in conductivity, using

a circuit such as the one shown previously in Figure 7.17.

Som

e typical wavelength response curves are shown in

Figure 7.21. These hot

-carrier-effect photoconductive

detectors or hot-electron bolomoters can be used success-

fully over a wavelength range extending from 50 to 10

lm;

they have detectivities up to about 1 3 10

cm Hz

1/2

–1

and response times down to 1 ls. They are frequently oper-

ated in a large magnetic ﬁeld (several hundred kA/m or

more). These detectors are av ailable from QMC Instruments.

Magnetically tuned detectors are also available from QMC

Instruments. These detectors are tuned in wavelength

response by operating them in a magnetic ﬁeld.

31,32

7.6 PHOTOVOLTAIC DETECTORS

(PHOTODIODES)

In a photovoltaic detector photoexcitation of electron–hole

pairs occurs near a junction, when radiation of energy

greater than the band gap is incident on the junction region.

Extrinsic photoexcitation is rarely used in photovoltaic

photodetectors. The internal energy barrier of the junction

causes the electron and hole to separate, creating a poten-

tial difference across the junction. This effect is illustrated

for a p–n junction in Figure 7.22.

ther types of structure are also used, such as p–i–n,

Schottky-barrier (a metal deposited onto a semiconductor

surface), and heterojunction (a junction between two differ-

ent semiconductors). The p–n and p–i–n structures are the

most commonly used. All these devices are commonly

called photodiodes. The characteristics of some important

photodiodes are listed in Table 7.4. Important photodiodes

Figure 7.21 Responsivity as a function of wavelength of a hot-carrier InSb

photoconductive detector operated at two different temperatures and various

magnetic ﬁeld strengths. The number on each curve is the magnetic ﬁeld strength in

units of 10

A/m.

572 DETECTORS

Table 7.4 Photovoltaic detectors (photodiodes)

Semiconductor T Wavelength D

(max) s Suppliers

(K) Range (lm)

Si 300 0.2–1.1 <2 3 10

——

GaAlAs 300 0.8–0.93 10

–14

(NEP) 1ls (1)

Ge 300 0.4–1.8 10

0.3 ns (2)

InGaAs 300 1–2.5 8

4 ns (2)

InAs 300 1–3.8 <4 3 10

5 ns–1 ls (3)

InAs 77 1–3.2 4 3 10

0.7 ls (3)

InSb 300 1–7 1.5 3 10

0.1 ls (4)

InSb 77 1–5.6 <2 3 10

>25 ns (5)

HgCdTe 77 1–25

–10

>1.6 ns

(6)

(1) Very sensitive, narrow spectral response detectors. Available from Advanced Photonix, Anadigics, and Opto-Diode;

(2) Available from Electro-Optical Systems, Fermionics, Hamamatsu, Judson, and Perkin-Elmer Optoelectronics (formerly

EG&G Optoelectronics) and Newport; (3) Electro-Optical Systems, Judson, and Melles Griot and Judson;

(4) Electro-Optical Systems, Hamamatsu, InfraRed Associates, and Kolmar Technologies; (5) Electro-Optical Systems, Kolmar

Technologies; Technologies; (6) Boston Electronics, Infrared Associates, Judson, Hamamatsu, Kolmar Technologies, Newport/Oriel.

A very wide range of silicon photoconductive and photovoltaic detectors are available with NEP ﬁgures down to 10

–16

WHz

1/2

and

time constants down to 6 ps. Reference 25 contains a list of suppliers.

Range varies from one supplier to another.

Figure 7.22 Photoexcitation at a p–n junction.

PHOTOVOLTAIC DETECTORS 573

include silicon for detection of radiation between 0.1 and

1.1 lm, germanium for use between 0.4 and 1.8 lm, and

indium (gallium) arsenide between 1 and 3.8 lm. Respon-

sivity variations with wavelength for photodiodes that are

most important for near-infrared (communications) applica-

tions are shown in Figure 7.23. Other important photodio-

des

include indium antimonide between 1 and 7 lm, and

mercury–cadmium telluride between 1 and 20 lm. Some

typical curves of D

(k) are shown in Figure 7.24. These

spectral response regions are not all necessarily covered by

a detector operating at the same temperature, for example,

InSb responds to 7 lm at 300 K, but to wavelengths no longer

than 5.6 lm at 77 K. The wavelength response of HgCdTe

detectors depends also on the stoichiometric composition

of the crystal.

The maximum wavelength of response of

1–x

Te can be estimated from its band gap E

and the

operating temperature T. E

is approximated by the

formula:

eVðÞ¼0:302 þ 1:93x  0:81x

þ 0:832x

þ5:35 1 2xðÞ10

4

T ð7:17Þ

All these photodiodes have very high quantum efﬁ-

ciency, deﬁned in this case as the ratio of photons absorbed

to mobile electron–hole pairs produced in the junction

region. Values in excess of 90% have been observed in

the case of silicon.

When a photodiode detector is illuminated with radia-

tion of energy greater than the band gap, it will generate a

voltage and can be operated in the very simple circuit

illustrated in Figure 7.25(a). It is much better, however,

generate a photodiode detector in a reverse-biased

mode, as shown in Figure 7.25(b), where positive voltage

applied to the n-type side of the junction and negative to

the p-type. In this case, the observed photosignal is seen as

a change in current through the load resistor. The differ-

ence between the two modes of operation can be easily

seen from Figure 7.26, which shows the I–V characteristics

a photodiode in the dark and in the presence of increas-

ing levels of illumination. At a given level of illumination

the photodiode can generate either an open-circuit voltage

or a short-circuit current I

. A photodiode responds

much more linearly to changes in light intensity and has

greater detectivity when operated in the reverse-biased

mode. Ideal operation is obtained when the diode is oper-

ated in the current mode with an operational ampliﬁer that

effectively holds the photodiode voltage at zero – its opti-

mum bias point. Two simple practical circuits which can

be used to operate a photodiode in this way are shown in

Figures 7.27 and 7.28.

In Figure 7.28, the bias voltage V

is not necessary, but

for many photodiodes will improve the speed of response,

albeit at the expense of an increase in noise. Integrated

packages incorporating a photodiode and operational

ampliﬁer are available from Centronic (especially UV

detectors), Hamamatsu, New Focus, Newport Corporation,

Opto Diode, OSI Optoelectronics, Perkin–Elmer Opto-

electronics, and Thorlabs. The p–i–n structure is most

commonly used in these devices because its performance,

in terms of quantum efﬁciency (number of useful carriers

generated per photon absorbed) and frequency response,

can be readily optimized. These devices have very low

noise and fast response. In practice, the limiting sensitivity

that can be obtained with them will be determined by the

noise of the associated ampliﬁer circuitry.

7.6.1 Avalanche Photodiodes

Ava lanche photo diodes (APDs)areavailablecommer-

cially for operation from about 250 nm to 1800 nm.

Figure 7.23 Responsivity of important near- infrared

photodiodes.

574 DETECTORS

Silicon APDs operate between 300 to 1100 nm, germa-

niumAPDsbetween800and1600nm,andInGaAs

APDs from 900 to 1 700 nm. Although they are more

costly than Si or Ge APDs, InGaAs APDs generally have

higher noise and have a faster response time f or a given

active area. If the reverse-bias voltage on a photodiode is

increased, photoinduced charge c arriers can acquire suf-

ﬁcient energy transversing the junction region to pro-

duce additional electron–h ole pairs. Such a photo diode

exhibits current gain and is called an avalanche

Figure 7.24 D

as a function of wavelength for various photovoltaic detectors.

(Courtesy of Hughes Aircraft Company.)

PHOTOVOLTAIC DETECTORS 575

photodiode (APD). It is, in so me respects, the so lid-state

analog of the photomultiplier. Avalanche p hotodiodes

are noisier than p–i–n photodiodes, but because they

have internal gain, the practical sensitivity that can be

achieved with them is greater. For detection of weak

light signals, particularly short pulses, the signal-to-

noise ratio will not be dominated by the associated elec-

tronics. A good discussion of the design, fabrication,

Figure 7.25 Photovoltaic detector operated in:

(a) open-circuit mode; (b) reverse-biased mode.

Figure 7.26 I–V characteristics of a photodiode in the

dark and with increasing levels of illumination.

Figure 7.27 Simple op-amp circuit for reverse-

bias operation of a photodiode. If the d.c. bias is

not included, then the detector is held at zero

voltage and is operated in a ‘‘current-mode.’’

Figure 7.28 Op-amp circuit for reverse-bias

operation of a photodiode.

576 DETECTORS

and operating characteristics of various photodiode

detectors has been given by Gowar.

Avalanche photo-

diodes are available from Advanced Photonix, L aser

Components DG, OSI Optoelectronics, Paciﬁc Silic on

Sensor, Perkin–Elmer Optoelectronics, and Sensors

Unlimited.

7.6.2 Geiger Mode Avalanche

Photodetectors

If an APD with a very low dark current is operated in

the Geiger mod e,

35–38

where the reverse-bias voltage V

is set greater than the diode breakdown voltage V

then a single photon can trigger a substantial circuit

pulse. In other words, the current or voltage pulse they

produce from t he detection of a single photon is above

their noise levels. The internal gain of the APD can

reach 10

–10

. To prevent the diode from permanent

damage it must be operated with a ‘‘que nching’’ current,

which reduces the bias voltage to stop the avalanche

process. Otherwise the diode will conduct a l arge current

when it is biased above the breakdown voltage. It is

desirable to reduce the dark current by cooling the

APD. APDs operated in this way are true ‘‘single

photon’’ detectors, and can replace PMTs in many pho-

ton-counting applications.

Photodiodes using silcon, InGaAs/InP, InGaAs/Si and

HgCdTe have all been successfuly used in Geiger mode.

Complete Geiger-mode APD modules are available from

Perkin–Elmer Optoelectronics. Dark counts below 1 count

per second (CPS) have been reported for Perkin–Elmer

SLiK silicon APDs cooled to 20 °C, and dark counts belo w

250 cps are typically achievable with a cooled PerkinElmer

0.5 mm C30902S APD.

Anexampleofanoperatingarrangementforan

InGaAs-cooled Geiger-mode APD is shown in Figure

7.2

9. For operation in Geiger mode, the r everse bias is

Figure 7.29 Arrangement for operating a Geiger-mode APD.

PHOTOVOLTAIC DETECTORS 577

held just below the breakdown voltage (20–40 V). The

bias voltage is brieﬂy gated above th e breakdown value

synchronously with the excitation process that i s

expected to gene rat e sin gle photons. Avalanche d oes

not generally occur unless an actual photon is detected.

The avalanche pr oc ess gene rate s a signiﬁcant cur rent

pulse with peak current 1 mA. When the gat ing voltage

app lied to the APD is removed, the avalanche is quenched

because the APD is now below b reakd own, an d the cur-

rent pulse terminates.

7.7 DETECTOR ARRAYS

Arrays of individual photodetector elements, based on

photodiode, photoconductive, pyroelectric, microbolome-

ters, CMOS, and CCD elements, are widely available for

use in both the visible and the infrared. Such arrays are

useful in a variety of applications, such as spectral analy-

sis, image analysis, and position sensing.

7.7.1 Reticons

Multiple element linear arrays, often called ‘‘reticons,’’

are widely used in spectrographs. Light from the diffrac-

tion grating in such a n instrument falls on such an

array instead of on an exit slit. Arrays based on sili-

con, InGaAs, HgCdTe, PbS, and PbSe are available from

various manufacturers, including Advanced Photonix (Si),

Cal-Sensors (PbS, PbSe), Fermionics (HgCdTe, InGaAs),

Hamamatsu (Si, InGaAs), Kodak (Si), Perkin–Elmer Opto-

electronics (Si), SensArray Infrared (PbS and PbSe), and

Sensors Unlimited (Goodrich)(InGaAs). Silicon-based reti-

cons are linear CCD (charge coupled device) arrays. The

number of pixels in a linear detector can be as large as

10, 200, although 1024 or 2048 element arrays are most

common. Linear arrays can also be used for position

sensing.

7.7.2 Quadrant Detectors

Quadrant detectors (quads) are particularly useful in

laser-beam tracking and similar operations. These detec-

tors have four contiguous active elements with very little

inactive area between them, as shown in Figure 7.30(a) .

a light beam is centered on the detector, all four ele-

ments provide the same signal. By the use of a circuit,

such as the one shown in Figure 7.30(b), simultaneous

dis

play of the X and Y displacements of the bea m

from the center of the array can be obta ined. If the

signals from the four quadrants are A, B, C, and D in

the circuit shown i n Figure 7.30(b), then the relative

position

of the center of a circular illumination spot

can be calculated as:

x ¼

ðB þ DÞðA þ CÞ

A þ B þ C þ D

ð7:18Þ

y ¼

ðA þ BÞðC þ DÞ

A þ B þ C þ D

ð7:19Þ

The displacements x and y are fractions, which would have

to be calibrated by moving the beam centroid by a known

distance in a particular application.

Silicon quadrant detectors are available from Advanced

Photonix, Electro-Optical Components, OSI Optoelectronics,

and Silicon Sensors. Ge and InAs quad detectors are available

from Judson. Infrared HgCdTe quad detectors are av ailable

from Judson and Raytheon Vision Systems (formerly Santa

Barbara Research Center). In some simple situations, small

one-dimensional deﬂections of a light spot can be measured

by focusing the light spot on the edge of a razor blade, and

measuring the amount of light reaching a photodetector

placed beyond the sharp edge, as shown in Figure 7.31.

7.7.3 Lateral Effect Photodetectors

Lateral effect photodetectors (LEP) also provide output

signals that allow determination of the position of the

centroid of an incident light spot on the surface of the

LEP. They are therefore useful in experiments in which a

laser beam is deﬂected, and the deﬂection needs to be

detected, or they can be used in general laser-beam track-

ing applications. The LEP, in its simplest form, consists of

a surface resistive layer on top of a p–n junction substrate,

and has two lateral electrodes. When a light ray is received,

the resulting photo-induced currents diffuse separately

along the junction faces and recombine at a distance from

their origin of separation. The analytical solution of the

diffusion equation, representing the potential on the sur-

face of the LEP on the two sides, varies approximately

578 DETECTORS

linearly with respect to the incident position of the light

and the received power. The dependence on the received

power can be eliminated by normalizing with respect to the

total received power.

Normally, the fabrication of a two-dimensional LEP can

be divided into: (1) Wallmark dual-axis, (2) duo-lateral, and

(3) tetra-lateral structures.

Most commercial LEPs use the

duo-lateral type, shown schematically in Figure 7.32, since it

rovides the best linearity. Most of f-the-shelf LEPs hav e a

0.1% linearity error near the center region and the error

increases to 1% when approaching the edges. These devices

can detect the movement of a small light spot with micro-

meter or smaller precision. Lateral ef fect photodetectors with

preampliﬁers are available from Electro-Optical Systems

(EOS), On-Trak, and Paciﬁc Sensor . LEP bundles, including

post-ampliﬁcation circuits, are available from Hamamatsu,

Figure 7.30 (a) Schematic diagram showing the construction of a quadrant

detector; (b) a circuit suitable for providing X and Y beam-deﬂection readouts

in a beam-centering or beam-tracking application.

DETECTOR ARRAYS 579

Newfocus, and Thorlabs. In contrast to quadrant detectors,

LEPs are superior for their large linear region and small

internal resistance. The latter results in a short response

time, but a larger noise equivalent power. This implies that

quadrant detectors are better in applications that involve

weak received power, such as feedback sensors in remote

sensing applications. LEPs, on the other hand, are advanta-

geous as local kinematic sensors.

7.7.4 Imaging Arrays

Two-dimensional arrays of photodetector generally show

up in imaging systems. Complementary Metal-Oxide-

Semiconductor (CMOS) or CCD arrays based on silicon

are common in visible and near-infrared digital camera

systems. These array detectors can be thought of as equiva-

lent to an array of ‘ ‘pho ton-buckets.’’ The number of photons

detected at each array element produces a corresponding

number of electron–hole pairs. The electrons at each pixel

are trapped in a potential well, equiv alent to a small capacitor ,

and then read out sequentially by moving these electrons from

well to well.

InGaAs arrays provide performance between

0.9 lmand2.2lm. Infrared cameras for operation beyond

10 lm use arrays of microbolometers (see later). A compre-

hensiv e list of suppliers of array detectors in dif ferent spectral

regionsisavailable.

In consumer digital cameras, CCD and CMOS arrays are

the standard image detectors. Such cameras generally con-

tain all the electronics to read out the signals from the array

elements and store them in digital format, including color

and grayscale. The most common image format from such

cameras is .jpeg. The number of available pixels in such

cameras continues to increase, and formats with more than

16 million pixels are already available. Typical formats are:

1216 3 912 (1 megapixel), 1600 3 1200 (2 megapixel),

2240 3 1680 (4 megapixel), and 4064 3 2704 (11.1 mega-

pixel). The actual number of pixels in these arrays is larger

than the number speciﬁed by the resolution, because some

dark array elements are used for reading out the image. It is

worth noting that the effective resolution of a good-quality

ﬁlm camera is at least 20 million pixels, detemined by the

‘‘grain’’ size in the ﬁlm. The image stored by such cameras

is a single ‘‘frame,’’ captured as the average illumination of

each pixel over the exposure time chosen. Color is gener-

ally captured by having a ﬁlter array placed in front of the

pixels. The ﬁlter array usually has alternating rows of red/

green and blue/green ﬁlters, a so-called ‘‘Bayer pattern.’’

The image is processed using the signals from adjacent

pixels to provide a best estimate of the color at each pixel,

a process called demosaicing.

Advanced digital cameras

use Foveon X3 technology (Foveon, Inc., 2820 San Tomas

Expressway, Santa Clara, CA 95051), in which the active

pixel elements are embedded in a silicon matrix at different

depths. Because blue, green, and red light penetrates differ-

ent distances into silicon, the camera acts as though it has

three sequential blue, green, and red imaging arrays. The

quantum efﬁciency, sensitivity, maximum frame rate, satu-

ration light level, and dynamic range of CCD and CMOS

Figure 7.31 Schematic arrangement for measuring the

deﬂection of a focused light beam by using a knife edge.

Figure 7.32 Schematic construction of duo-lateral lateral

effect photodetector (LEP).

580 DETECTORS

imagers vary and manufacturers’ data sheets should be con-

sulted. Of the two, CCD imagers are generally more sensi-

tive, and have lower noise than CMOS imagers; CMOS

imagers on the other hand use less power and are less

expensive. As CCD imagers cannot be gated electronically,

if short exposures are required, then a mechanical shutter is

needed. Infrared imaging arrays with response from 0.5–14

lm, based on InSb and HgCdTe, are available from Ray-

theon Vision Systems; HgCdTe imaging arrays are avail-

able from Sofradir.

The experimentalist who wishes to work with CCD or

CMOS imaging arrays that are not already integrated into a

complete camera system should consult the suppliers of such

devices, such as K odak or Sony. This is a specialized endeavor.

If it is desired to have complete control of image capture as a

digital ﬁle directly into a computer , then a digital camera with

compatibility with a framegrabber card is needed. Framegrab-

ber cards usually utilize a special interface standard called

Cameralink, which is used by all major scientiﬁc camera man-

ufacturers. It allows for data rates in excess of 2 Gb/s. Scien-

tiﬁc cameras differ from consumer ones in that they provide

uncompressed frames at high frame rates, such as 210 fps in

the case of the Imperx IPX-210. These uncompressed frames

allow for adva nced image analysis in Labvie w, Matlab, and

other image-processing applications.

The primary manufac-

turers of framegrabbers are Imperx and National Instruments,

while cameras can be acquired from Imperx, Dalsa, Pulnix,

and Flir. It is worth noting that some cameras have now

come on the market that use a gigabit Ethernet standard

to transmit frames, the Imperx IPX-2M30H-GC

(1920 3 1080 30 fps color) being one example.

7.7.5 Image Intensiﬁers

In some applications, for example in astronomy or

night vision, it is desirable to obtain an image that can

be viewed by the human eye, or with a digital camera,

when the light levels available are extremely low. Low-

light-level imaging can be carried out with an image inten-

siﬁer. Image intensiﬁers work by using weak visible or

near infrared light to liberate photoelectrons from a GaAs

photocathode, which has a high quantum efﬁciency to

about 920 nm. The photoelectrons are accelerated onto a

microchannel plate, where secondary electron ampli-

ﬁcation increases their number. The ampliﬁed electron

stream then falls onto a phosphor screen where the image

is rendered visible. Figure 7.33 shows the principle of oper-

atio

n. As image intensiﬁers have evolved, photocathode

materials and the electron multiplication stages have

improved. The earliest image intensiﬁers were called gen-

eration 0, G0, which used S1 photocathodes, G1 tubes used

an improved S-20 photocathode. G2 and G3 tubes used a

MCP for electron multiplication, typical ampliﬁcation

gains can be as high as 10

. G2 tubes use an S-25 photo-

cathode with typical peak sensitivity of 50 lA/W. G3 tubes

use GaAs or GaAsP photocathodes with typical sensitivity

of 200 lA/W. Nowadays only G2 and G3 tubes should be

considered for use. Manufacturers of image-intensiﬁer

Figure 7.33 Operating arrangement of a microchannel plate image intensiﬁer.

DETECTOR ARRAYS 581

tubes include Electrophysics Corporation, Hamamatsu,

ITT Night Vision, Photek, Photonis, and Thales.

7.8 SIGNAL-TO-NOISE RATIO

CALCULATIONS

7.8.1 Photomultipliers

In many applications using photomultiplier tubes, the

anode pulses are integrated to give a ﬂuctuating analog

current. The shot noise originating at the photocathode

is, from Equation (7.1):

¼ 2eð<i

> þ <i

>ÞDf ð7:20Þ

where <i

> is the average photocathode current produced

by a light source and <i

> is the average photocathode

dark current. This noise is multiplied by the ampliﬁcation of

the electron number by interaction with the N dynodes of

the tube. If each dynode has a secondary emission mul-

tiplication efﬁciency d the overall gain of the tube is G:

G ¼ d

ð7:21Þ

Because of statistical ﬂuctuations in the secondary

emission process and, in addition, because electrons can

originate thermionically from the dynodes, the noise at the

anode is further increased by a noise factor F. The overall

noise appearing at the anode is:

¼ 2eG

F <i

> þ <i

>ðÞDf ð7:22Þ

For d ¼ 4, and a 14 stage tube, G ¼ 2.6 3 10

, and

typically F ’ dðd  1Þ¼1:08.

A photomultiplier is a current source: to convert this

current to a detected voltage the ampliﬁed photoelectron

current passes through an anode resistor of value R. This

anode resistor may be part of the photomultiplier circuit, or

may be provided in whole or in part by the input impe-

dance of a following ampliﬁer stage. The Johnson noise

from the resistor is:

4kTDf

ð7:23Þ

To optimize detection of a signal, it is common practice

to amplitude modulate the signal at some angular fre-

quency x

so as to permit synchronous detection at this

frequency (see Section 6.8). The optical power reaching

the photocathode can be represented in this case as:

P ¼ P

1 þ m sin x

tðÞð7:24Þ

where m is a modulation parameter.

The average photocathode current is:

> ¼

egP

ð7:25Þ

and:

ðtÞ¼<i

>1þ m sin x

tðÞð7:26Þ

At the anode, the time-varying part of this current is:

tðÞ¼<i

>Gm sin x

t: ð7:27Þ

The signal-to-noise ratio (S/N) at the input to the following

electronics is therefore:

þ <i

2eG

Fð<i

> þ <i

>ÞDf þ 4kTD f =R

ð7:28Þ

The noise from the photomultipler tube is usually sufﬁ-

ciently large that the Johnson noise can be neglected. If

it is assumed that <i

>  <i

>, then for m ¼ 1 and S/N ¼ 1

we have, from Equations (7.25) and (7.28):

ðP

min

2hm

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

F<i

>Df

ð7:29Þ

Example: Typical values for a good photomultiplier will

be g ¼ 0:2, F ’ 1, <i

> ’ 10

15

A. For a 530 nm source,

Equation (7.29) gives (P

)

min

¼ 3 3 10

–16

7.8.2 Direct Detection with p–i–n

Photodiodes

The shot noise from a p–i–n photodiode is:

¼ 2e <i

> þ i

ðÞDf ð7:30Þ

582 DETECTORS

where <i

> is the average signal current, and i

is the dark

current (usually speciﬁed, for a low-noise photodiode, in

units of nA or pA).

The average signal current is, in a similar way to Equa-

tion (7.25),

> ¼

egP

ð7:31Þ

where g is the quantum efﬁciency, which is much larger

than for a photomultiplier: values of 0.7–0.8 are common.

For the simple equivalent current of the detector shown in

Figure 7.34, there is an additional Johnson noise contribu-

tion of magnitude:

4kTDf

ð7:32Þ

The overall S/N ratio for direct detection of an unmodu-

lated signal is:

þ <i

ðegP

=hmÞ

2eRðegP

=hm þ i

ÞDf þ 4kTDf

ð7:33Þ

This S/N ratio would be reduced by a factor m

/2 for a

modulated signal (cf. Equation 7.28). If shot noise domi-

nates over dark current and Johnson noise, then the shot-

noise-limited S/N ratio is:

2hmDf

ð7:34Þ

In a practical application using a photodiode there will

be additional stages of electronic ampliﬁcation that add

noise. It is common to characterize the effect of an elec-

tronic circuit on the noise by its noise ﬁgure, F

The noise ﬁgure can be deﬁned conveniently as:

noise power at output of circuit

noise power at the input 3 amplifier power gain

ð7:35Þ

For input Johnson noise the mean-square, ampliﬁed, out-

put noise current is:

AJN

4kTGDf

ð7:36Þ

where G is the power gain of the ampliﬁer within the

frequency band being considered. The actual output

mean-square noise current is:

actual

4kTGF

ð7:37Þ

It is as if the ampliﬁer were noiseless with the input John-

son noise increased by the noise ﬁgure.

The noise ﬁgure is frequently quoted in dB, a noise

ﬁgure of 3dB would represent a doubling of the out-

put noise over the value expected from a noiseless

ampliﬁer. The term noise temperature T

is also used,

deﬁned by:

¼ 1 þ

ambient

ð7:38Þ

Figure 7.34 Equivalent circuit of a p–i–n photodetector.

S/N RATIO CALCULATIONS 583

Example: We illuminate an InGaAs photodiode with a

responsivity of 0.8 A/W at 1.3 lm with a power of 10 lW.

The system bandwidth is 100 MHz, the dark current is

5 nA (equivalent to 0.5 pA Hz

–1/2

). We assume that the

ampliﬁcation electronics has a noise ﬁgure of 6 dB (rel-

ative to a 50 ohm input). We note the following:

Received power P

¼ 10

–3

3 10 mW ¼ 10 lW

Signal current <i

> ¼ 8 lA

Dark current <i

> ¼ 5 nA (in this case dominated by <i

Signal power ¼ (<i

R ¼ 3.2 nW

Shot noise power ¼ 2e(<i

>+<i

>) dfR ¼ 1.28 3

–14

Johnson noise power ¼ 4kTdf ¼ 4(1.38 3 10

–22

)

(300)(10

) ¼ 1.66 pW

Effective Johnson noise power including noise Figure ¼

0.6

3 1.66 pW ¼ 6.6 pW.

In this case the Johnson noise is dominant, the effective

S/N ratio is:

3:2 3 10

9

6:6 3 10

12

¼ 485

7.8.3 Direct Detection with APDs

In an APD there is a multiplication of the number

of charge carriers by a factor M. This m ultiplication

can result from secondary ionizations produced by

both electron s an d holes. It is desirable that one or other

of these charge carrier s s hould have a signiﬁcantly

greater secondary ionization coefﬁcient

than the

other.

The current in an APD incre ases by the factor

M, but the associated shot noise increases further,

because i n a given avalanche process M will ﬂuctuate,

taking values M, M 6 1, M 6 2, etc. The mean-square

noise current thereby increases, not by a f actor M

,but

by a fa ctor FM

,whereF is called the noise factor.In

silicon APDs, F typically lies in the range 2–20. There-

fore, the shot noise becomes:

¼ 2eFM

> þ i

ðÞDf ð7:39Þ

Both photo- and dark-generated carriers contribute to

the shot noise. The overall S/N ratio is modiﬁed from

Equation (7.33) and becomes:

þ <i

ðegP

=hmÞ

2eRFM

ðegP

=hm þ i

ÞDf þ 4kTDf

ð7:40Þ

Equation 7.40 shows that the S/N ratio improves with

increasing multiplication as the Johnson noise contribution

becomes less important until the avalanche shot noise

becomes dominant. The avalanche-limited S/N ratio is:

2FhmDf

ð7:41Þ

a reduction of the signal-to-noise ratio from the quantum-

limited value by the noise factor.

The NEP can be computed for both p–i–n photodiodes

and APDs by setting S/N ¼ 1 in equations like (7.33) and

(7.40) and thereby the minimum input power for S/N ¼ 1

is determined. For P

¼ P

min

, we expect the dark current to

be larger than the signal current, so Equation 7.40 becomes:

ðMegP

=hmÞ

ð2eFM

þ 4kT=RÞDf

ð7:42Þ

For S/N ¼ 1 and a 1 Hz bandwidth, P

¼ P

min

¼ NEP,

which gives, for an APD:

NEPðWHz

1=2

Þ¼

Meg

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2eFM

þ 4kT=R

ð7:43Þ

The equivalent result for a p–i–n diode can be obtained by

setting M ¼ F ¼ 1.

Example. For an InGaAs APD with F ¼ 10, M ¼ 100,

R ¼ 50 X, i

¼ 2 nA, and responsivity 0.8 A/W, the

quantum efﬁciency is:

g ¼

0:8ð6:626 3 10

34

Þð3 3 10

ð1:6 3 10

19

Þð1:55 3 10

6

¼ 0:64

From Equation 7.43 the NEP is:

NEP WHz

1=2



ð2 3 1:6 3 10

19

3 10

3 2 3 10

9

þ 4 3 1:38 3 10

22

3 300=50Þ

1=2

0:8 3 100

¼ 4:7 3 10

13

WHz

1=2

Note that in this case the thermal noise is dominant.

584 DETECTORS

7.8.4 Photon Counting

For the detection of very low light levels where photomul-

tipliers or Geiger-mode APDs can be used, the technique

of photon counting is the most sensitive technique. Sup-

pose that the signal to be detected corresponds to a photon

ﬂux at the detector of N

per second. This corresponds to a

detected count rate of N

¼ gN

per second. Along with

this goes a dark count rate of N

per second. If the detected

counts are integrated for T seconds the total number of

counts is:

¼ðN

þ N

ÞT ð7:44Þ

Since the number of counts observed in a given integra-

tion interval ﬂuctuates statistically, then, for a Poissonian

distribution, the standard deviation of the number of counts

observed is N

ﬃﬃﬃﬃﬃﬃ

. Thus the counts recorded during

‘‘signal’’ intervals can be written as:

¼ðN

þ N

ÞT 6

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðN

þ N

ÞT

ð7:45Þ

If the dark counts alone are integrated over the same time

interval T the total number of counts can be written as:

¼ N

T 6

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ð7:46Þ

The signal-to-noise ratio of the photon-counting process

is determined by the difference between N

and N

, taking

into account their respective standard deviations. It can be

characterized as:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðN

þ 2N

ÞT

ð7:47Þ

This signal-to-noise ratio can be continuously improved

by extending the integration time. The ‘‘signal’’ and

‘‘dark’’ counting intervals can be alternated by chopping

or ‘‘gating.’’

Example. Consider a dark count rate of 100 /s and a

signal count rate of 1 /s. A signal-to-noise ratio of 10 will

be achieved when T=

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

201T

¼ 10, i.e. after an integration

period of about 6 hours. It should be noted that if the count

rates are too high, so that some counts are missed – so

called ‘‘pile-up’’ effects,

then these calculations are

slightly modiﬁed.

7.9 PARTICLE AND IONIZING

RADIATION DETECTORS

For charged-particle energies up to a few tens of keV there

are two detection schemes in wide use. The particles can

be collected at a metal surface and the resultant electrical

current measured directly, or they can be detected by col-

lecting the slower secondary electrons that are ejected

from a metal surface by impact of the primary particle.

Charged particles can also be detected with photographic

emulsions, scintillators, and various solid-state devices.

Emulsions have largely been supplanted by the methods

mentioned above, and solid-state devices are only suitable

for the detection of high-energy particles (above 30 keV).

Table 7.5 lists the properties of common particle detectors.

e collector for the direct detection of a current of

charged particles is called a Faraday cup. Typical designs

are illustrated in Figure 7.35. These simple collectors are

nnected directly to a current-measuring device and are

useful at currents down to the detection limits of modern

electrometers – about 10

–14

A. A properly-designed Faraday

cup does not permit secondary electrons to escape. For a

positiv e-ion collector, the loss of a secondary electron

appears to the current-measuring instrument as an additional

ion, while for an electron collector the loss of each secondary

cancels the effect of an incident primary electron. To prevent

the escape of secondary electrons, the depth of a Faraday cup

should be at least ﬁv e times its diameter. A suppressor

Table 7.5 Particle detectors

Particle

Detector

Output Signal

Level

Charge-Collection

Time

Ge 2.8 eV/electron–hole pair 0.1–10 ns

Si 3.5 eV/electron–hole pair 0.1–10 ns

Electron

multiplier

–10

electrons/

incident electron

0.5–1 ns

Microchannel

plate

–10

electroncs/

incident photon

0.1 ns

Scintillator:

Plastic ~1 photon/3keV 0.1–10 ns

Alkali halide ~1 photon/3keV 1 ls

Gas-ﬁlled tube 25–35 eV/ion pair 0.01–5 ls

For narrow depletion depth.

PARTICLE AND IONIZING RADIATION DETECTORS 585

aperture or grid biased to about 30 V in front of a Faraday

cup effecti v ely pre v ents the escape of most secondaries.

A grounded grid in front of the suppressor as illustrated

in Figure 7.35(b) prevents ﬁeld penetration from the sup-

pressor

in the direction of the incident current source.

When a particle beam must be aligned and sharply

focused, a concentric pair of collectors [Figure 7.35(c)]

is useful. With this arrangement the beam-focusing ele-

ments

are adjusted to maximize the ratio of current to

the inner cup in relation to the current to the outer cup.

Charged-particle currents of less than 10

–14

A can be

detected with an electron multiplier, which is like a photo-

multiplier without the photocathode. As illustrated in

Figure 7.36 , these devices have an internal dynode struc-

ture.

Secondary electrons produced by impact of a particle

on the ﬁrst dynode are accelerated towards the second

dynode through a potential drop of 100–300 V. The impact

of these electrons results in a number of secondaries that

are in turn accelerated into the third dynode, and so on. The

secondary emission coefﬁcient of the dynodes is typically

about three electrons per incident particle; the impact of a

single particle on a multiplier with n electrodes results in a

pulse of about 3

electrons.

Electron multipliers are available with 10 to 20 dynodes

to provide gains of 10

to 10

. The dispersion in time of the

shower of electrons from the last dynode is on the order of

Figure 7.36 An electron multiplier. Electrical connections

shown are appropriate for detecting positive ions. Grids at

the entrance of the multiplier prevent the escape of

secondary electrons.

Figure 7.35 Faraday cup designs. Design (b) has a grid

biased to suppress secondary electron emission. Design (c)

has a double cup for aligning and focusing a beam.

586 DETECTORS

10 ns. The corresponding current through a 50 ohm meas-

uring resistor ranges from 800 lV to 800 mV, which is

easily detected with modern pulse-counting electronics.

Furthermore, if time resolution is not required, the output

current from an electron multiplier can be measured

directly with an electrometer.

The electrodes of an electron multiplier are fabricated

of a material that has a high work function – typically a

Be–Cu alloy that has been ‘‘activated’’ by some proprietary

process. The high work function is desirable because it

inhibits thermionic emission that would result in noise

pulses at the multiplier output. On the other hand, incident

particles must have energies in excess of a few hundred eV

to assure efﬁcient secondary emission. When working with

lower-energy particles, it is necessary to provide an accel-

eration stage at the multiplier input. For incident particles

with energies greater than 300 eV, the detection efﬁciency of

an electron multiplier can exceed 90%.

For the detection of positive ions, an electron multiplier is

usually operated with the ﬁrst dynode at a high negative

potential and the last dynode near ground potential, as in

Figure 7.36. This arrangement provides acceleration of inci-

nt ions. For electrons or negative ions, the cathode is

usually biased positive by a few hundred volts and the last

dynode is at a high positive potential relative to ground, as in

Figure 7.37. In this latter conﬁguration, it is only convenient

operate in a pulse-counting mode, since the detection

electronics must be electrically insulated from the measur-

ing resistor. Ordinarily, the multiplier output is coupled to

the pulse-counting electronics via a high-voltage disk

ceramic capacitor of about 100 pF. A problem sometimes

encountered with this arrangement is that sparking between

dynodes or across dynode resistors gives rise to large high-

frequency transients that are transmitted through the cou-

pling capacitor and damage the electronics. This problem

can be cured by coupling the output of the multiplier to the

electronics through a transformer that will attenuate large

pulses because of saturation of the ferrite core material. A

suitable transformer can be produced by making a 10-turn

biﬁlar winding of well-insulated wire on a ferrite core (e.g.

Ferroxcube), as illustrated in Figure 7.38.

The number of

turns and their position must be carefully adjusted to assure

a proper impedance match between the multiplier and the

electronics.

The output current from an electron multiplier is limited

by the current available from the resistive voltage divider

Figure 7.37 A channel electron multiplier. Electrical connections shown are for the

detection of electrons.

PARTICLE AND IONIZING RADIATION DETECTORS 587

that establishes the potential of the dynodes. To ensure that

the gain of a multiplier is not reduced because of depletion

of the dynode charge, the maximum output current should

be at least an order of magnitude less than the current

drawn by the dynode resistor chain. For CEMs, the output

current should be an order of magnitude less than the cur-

rent from the high-voltage supply through the (typically

ohm) resistance of the channel.

An important variant of the electron multiplier uses a

continuous dynode as illustrated in Figure 7.3 7.Theseare

channe

l electron multipliers (CEM) or channeltrons.

They are glass tubes with semiconducting i nner surf aces.

The end-to-end resistance is about 10

ohm. In operation,

a potential of about 3 kV across the CEM yields a gain of

about 10

. Channel electron multipliers have the advant-

age of small size (about 50 mm long), low cost, and

ruggedness. Recently, monolithic ceramic CEMs have

become available from OptoTechn ik. These consist of a

ceramic block with an interior serpentine channel. Many

con ﬁgurations a re avai labl e, w ith entrance apertures as

small as a few mm

to more than 1 cm

. The overall

volume ranges from 1 to 5 cm

. The monolithic ceramic

CEMs are very robust. They have found wide use in

rocket-borne instruments, where force s at l aunch can

exceed 30 G.

The gain of a CEM is determined, n ot by the absolute

size, but rather by the ratio of the length of the channel to

the diameter. This ratio is about 50 for a conventional

CEM. Very small CEMs are available in close-packed

arrays. Each channel is a few micrometers in diameter

and a few mm long. The arrays, known as microchannel

plates or MCPs, are available i n sizes up to 10 cm on a

side. Bec ause the length-to-diameter ratio is only about

20, microchannel plates are usually stacked in pairs to

provide easily detected charge pulses. Owing to the small

size of the channel, the c harge cloud through a chann el is

temporally much more compact than in a full-size CEM.

The charge cloud is delivered in about 1 ns. With lead-

ing-edge discrimination it has been possible to time the

arrival of a charged particle at the detector with a reso-

lution of a few hundred p icoseconds.

Microchannel plates are used as position-sensitive

detectors of electrons and ions at energies up to at least

10 keV. A particle striking the front of the plate triggers

an electro n avalanc he in only one channel. The position

of the charge cloud emitted at the output of a channel can

Figure 7.38 A coupling transformer between an electron multiplier and a sensitive pulse

ampliﬁer. Properly constructed, a transformer will faithfully transmit signal pulses while

attenuating large noise pulses.

588 DETECTORS

be loc ated with an accuracy approaching the diamet er of

the channel . Bo th one -dime nsion al and two-dimensional

position information can be extracted. A number of meth-

ods have been developed to obtain position information.

The most straightforward scheme is to provide an array of

collectors each with its own pulse ampliﬁer and counter.

This is the most robust method, but expensive and

impractical if the full resolution of the microchannel plate

is to be realized – a standard 2.5 cm round MCP can

potentially provide more than 10

pixels. Many posi-

tion-sensitive detectors employ a resistive strip anode

across the ba ck o f a stacked pair of MCPs. The arrival

of a charge pulse at a point on the anode is detected

simultaneously as a pulse at each end or eac h c orne r of

the anode, a nd the position is determined from the ratio of

the pulse heights.

7.9.1 Solid-State Detectors

A solid-state detector (SSD) converts particle energy to

charge that is then collected and ampliﬁed. Silicon detec-

tors convert every 3.6 eV of particle kinetic energy to a

single electron–hol e pair. The energy resolution of a SSD

depends on the charge generated by the incident particle,

the noise generated by the d et ector, an d the electronic

circuits to which the output of the detector is connected.

Resolution is also affected by the charge generat ion

mechanism within the detector. Charge generation falls

within a purely statistical process and one determine d b y

a constant energy loss per electron–hole pair creation.

There is also the variable energy loss in the thin window

of the detecto r and the efﬁciency of charge collection as a

function of the geometry of the e le ctron –ho le p air pro-

duction. The arrangement of an SSD with FET ampliﬁer

followedbyashapingampliﬁerandpulse-heightana-

lyzer is shown in Figure 7.39.

The SSD is essen tia lly a reverse-biased diode wit h the

bias

voltage applied through a high resistance R

in series

with the voltage supply. The FET is used in the common

source (CS) conﬁguration as a transconductance ampli-

ﬁer (see also Chapter 6). There is a large gate bias resistor

from the gate to ground. The shaping ampliﬁer

increases the amplitude of the signal from the FET output

and also transforms the output pulse into one with an

approximate Gaussian shape with rise-time s

and f all -

time s

.Normallys

and s

are set equal to a single time s.

The response of the shaping ampliﬁer as a function of

frequenc y x is given by:

AðxÞ¼A

ðx=sÞ

1 þðx=sÞ

ð7:48Þ

where A

is the mid-band gain of the ampliﬁer.

Figure 7.39 A solid-state detector with an FET ampliﬁer followed by a pulse-shaping

ampliﬁer and a pulse-height analyzer.

PARTICLE AND IONIZING RADIATION DETECTORS 589

The SSD can be modeled as a current source i

parallel with a c apacitance C

that represents the effec-

tive capacitance of the SSD and the h igh voltage bias

resistor R

,asshowninFigure 7.40.Thecurrentsource

represents the leakage c urrent of the detector. The

small-signal model for the FET, shown in Figure 7.41,

includes the capacitance of the

gate-channel junction C

and the voltage-controlled c urrent source, g

,where

is the transconductance of the JFET and v

is the

gate-source signal voltage. Current ﬂowing in the

reverse-biased gate-channel junction is represented by

the current source i

. There are various contributions to

both shot and Johnson noise in the arrangement shown in

Figure 7.41.Theseare:

(1)

Shot noise from the reverse-bias leakage current of the

SSD <i

SN1

¼ 2ei

(2) Johnson noise from the series bias resistor <i

JN1

4kTDf =R

(3) Shot noise from the JFET gate current <i

SN2

2ei

(4) Johnson noise from the gate bias resistor <i

JN2

4kTDf =R

(5) Johnson noise from the channel resistance < i

JN3

(4kTdfcg

), where for a long channel device c ¼ 2/3.

The current noise can be converted to voltage noise at the

gate of the FET by multiplying by the input impedance

of the FET. This impedance is dominated by C

and C

Because the noise sources are incoherent they are added in

quadrature. The total noise voltage is then:

> ¼



2ei

þ 2ei

4kT



þ 4kTcg



Df ð7:49Þ

where C

¼ C

+ C

. When this expression is integrated

over the response function of the shaping ampliﬁer, the

noise voltage referred to the input of the FET is:

> ¼

ði

þ i

Þþ

kTs



2cg

ð7:50Þ

Figure 7.41 Small-signal equivalent circuit of an FET.

Figure 7.40 Equivalent circuit of a solid-state detector.

590 DETECTORS

The equivalent noise charge (ENC)

is obtained by multi-

plying this expression by C

, with the result:

ENC ¼

ði

þ i

Þþ

kTs



kTC

2cg

ð7:51Þ

As an example, let us evaluate this expression using the

experimental parameters of the Canberra fully depleted

passivated implanted planar silicon (PIPS) solid-state

detector, model FD 150-16-500 RM. The parameters of

the 2SK152 low-noise n-channel JFET are used to evaluate

the noise contribution from the JFET. A time constant of

–6

s was used for the shaping parameter. Below is a list

of the magnitudes of the parameters:

s ¼ 10

–6

¼ 166 nA

¼ 5nA

T ¼ 300 K

¼ 50 pF, C

¼ 15 pF, C

¼ 65 pF

¼ 108 ohm

¼ 30 mA/V

Additional Considerations. In order to transfer the

maximum energy from the detector to the JFET, the input

impedance of the JFET should be matched to the output

impedance of the SSD. This means that a transistor with

¼ C

should be chosen and stray capacitance

eliminated. The ratio of energy transferred to theoretical

maximum energy transfer is given by 4 x/(1 + x)

, where x

is the ratio of detector to gate capacitance, C

. The

choice of the shaping constant s is an important factor in

the ENC, but it is also important to recognize that s ﬁxes

the maximum count rate. For s ¼ 10

–6

s, the maximum

asynchronous count rate that can be accommodated with

90% efﬁciency is 100 kHz. The temperatures of the

SSD and JFET can be controlled. In this analysis the

temperature of the SSD and JFET are assumed equal,

however it is possible to independently cool one or the

other. The leakage current of the Canberra PIPS detector

is a strong function of temperature and is given by

¼ 63  10

9

 2

T92ðÞ=5

ð7:52Þ

7.9.2 Scintillation Counters

Scintillation counters allow the detecti on of ionizing radi-

ation (X-rays, c-rays), and energetic particles (protons,

neutrons, muons, pions, etc.) by conversion of their

energy into visible light. A typical s cintillation counter

uses a ﬂuorescent solid or liquid that converts a nonioniz-

ing photon or energetic particle into a ﬂash of visible

light. The visible light is generally detected with a photo-

multiplier with a large-area photocathode placed in close

proximity to the scintillation m aterial. Scintill ators are

often made of plastics impregnated with a ﬂuorescent

dye. The intensity of the light ﬂash produced by detection

of an energetic photon or particle is correlated with the

energy of the detected photon or particle, so the energy

spectrum of the detected radiation or particles can be

determined from the ﬂash intensity. This is often carried

out using a multichannel analyzer, an instrument that

sorts detected electric pulses into a histogram that shows

their height distribution. Scintillators are characterized

by their efﬁciency; an efﬁciency of 0.1 corresponds t o

the production of one visible or UV photon from the

detection of a particle or photon of energy 25 eV.

Also

of importance are the absorption and emission spectra,

signal linearity, and the rise and fall times of the scinti-

lation pulse . The se pul ses can be as short as 1 n s for a

modern plastic scintillator. Further inform ation about

scintillation counters can be obtained from the specialist

literature.

51–54

7.9.3 X-Ray Detectors

X-rays can be detected with scintillators, for example

organic scintillators, single crystals of bismuth germanate

(BGO), or single crystals of sodium-activated cesium

iodide [CsI(Na)], but are generally detected with silicon

or germanium photodiodes. Such detectors are available

from Amptek, Canberra, and Hamamatsu.

7.10 THERMAL DETECTORS

Thermal detectors, in principle, have a detectivity that

is independent of wavelength from the vacuum ultraviolet

THERMAL DETECTORS 591

upward, as shown in Figu re 7.42. The absorbing

properties of the ‘‘black’’ su rface of t he detector will,

however, show some wavelength dependence, and the

necessity for a protective window on some detecto r

eleme nts may limit the useful spectral bandwidth of the

device. Most commonly available thermal detectors,

although by no means as sen sitive as various types of

photon detectors, a chieve spectral respons e very far

into the infrared – to the microwave region, in fact –

while con v eniently operating at room temperature. The oper-

ating characteristics of some commercially available thermal

detectors are given in Table 7.6. Each of these detectors is

iscussedbrieﬂybelow.Putley

giv es a more detailed

discussion.

Figure 7.42 Typical D

(k) curves for various thermal detectors assuming total

absorption of incident radiation. The operating temperature, modulation frequency,

and typical useful wavelength range are shown for each detector. In each case, the

detector is assumed to a view a hemispherical surround at a temperature of 300 K.

592 DETECTORS

7.10.1 Thermopiles

Thermopiles, although they are one of the earl iest forms

of infrared detector, are still widely used. Their operation

is based on the Seebeck effect, where heat ing the junc-

tion between two dissimilar conductors generates a

potential difference across the junction. An ideal device

should have a large Seebe ck coefﬁcient, low resistance

(to minimize ohmic heating), and a low thermal conduc-

tivity (to minimize heat loss between the hot and cold

junctions of the thermopile). These devices are usually

operated with a n equal number of hot (irradiated) a nd

cold (dar k) junctions, the l atter serving as a ref erence

to compensate for d rifts in ambient temperature. Both

metal (copper–constantan, bismuth–silver, antimony–

bismuth) an d sem iconduct or ju nctions are used as the

active elements. The junctions can take the form of

evaporated ﬁlms, which improves the robustness of the

devices and reduces their time constant, although this is

still slow (0.1 ms at best). Because a thermopile has very

low outpu t impeda nce, and generates low voltages, it

must be used with a specially designed low-noise ampli-

ﬁer, or with a step-up transformer, as shown in Figure

43. Such transformers can be conveniently built in the

labo

ratory by winding the primary and secondary coils

on a small ferrite torus.

Although thermopiles, along with other thermal detec-

tors, do not have absolutely ﬂat spectral response over

unlimited wavelength regions, they can be remarkably ﬂat

within restricted regions – in the visible or from 1 to 10

lm, for example. In addition, such detectors with calibra-

tions traceable to NIST are available. Thus they are invalu-

able in the absolute calibration (both for radiant sensitivity

and for spectral response) of light sources, detectors, and

spectrometers. Thermopiles are available from Boston

Electronics, The Eppley Laboratory, Hamamatsu, Laser Probe,

Perkin–Elmer Optoelectronics, Scientech, and Thorlabs.

7.10.2 Pyroelectric Detectors

Pyroelectric detectors utilize the change in surface charge

that results when certain asymmetric crystals (ones that can

possess an internal electric dipole moment) are heated. The

crystalline material is fabricated as the dielectric in a small

capacitor, and the change in charge is measured when the

element is irradiated. Thus, these devices are inherently a.c.

Table 7.6 Characteristics of commercially available thermal detectors

Device D

(cm Hz

1/2

1

) Time Constant Suppliers

Thermopile (1–4) 3 10

20 ls–60 ms Boston Electronics, Eppley Hamamatsu,

Laser Probe, Newport,

Perkin–Elmer Optoelectronics–Scientech, Thorlabs

Pyroelectric 10

–10

>100 ps Perkin–Elmer Optoelectronics, Hamamatsu,

Scientech Laser Probe, SensArray, Spiricon,

Scitec Instruments

Bolometer 2.5–10

1 ms Eltec Eltec, Electro-Optical Components

QMC Instruments SensArray Sofrdir

Golay Cell <10

10

NEP (W Hz

1/2

) ’10 ms QMC Instruments, Microtech Instruments

Figure 7.43 Operating circuit for a thermopile

using a dark junction (or junctions) and a differential

ampliﬁer for compensation.

THERMAL DETECTORS 593

detectors. If the chopping frequency of the input radiation

is slow compared to the thermal relaxation time of the

crystal, the crystal remains close to thermal equilibrium

and the current response is small. When the chopping

period becomes shorter than the thermal relaxation time,

much greater heating and current response results. The

responsivity of the detector in this case can be written as:

R ¼

pðTÞ

ðA=WÞð7:53Þ

where p(T) is the pyroelectric coefﬁcient at temperature T,

d is the spacing of the capacitor electrodes, and q and C

are the density and speciﬁc heat of the crystal, respectively.

The equivalent circuit of a pyroelectric detector is a

current source in parallel with a capacitance, which can

range from a few to several hundred picofarads. For opti-

mum performance, the resultant high impedance must be

matched to a low-input-impedance, low-output-impedance

ampliﬁer. Two examples of such circuits are given in

Figure 7.44. Pyroelectric detectors are available from

DIAS

Infrared GmbH, Hamamatsu, Laser Probe, Perkin–

Elmer Optoelectronics, Scientech, Scitec Instruments, and

SensArray.

Frequently pyroelectric detector packages contain two

pyroelectric elements connected with reverse polarity so

that the detector only responds to the difference in illumi-

nation between the two elements. This is a useful way to

reduce the effect of background radiation. For faster

response the capacitance of the detector must be shunted

with a small resistor (though this reduces the detectivity).

Pyroelectric detectors are robust and have frequency

responses extending from a few hertz to 100 GHz or so.

Their detectivities are comparable with those of thermo-

piles, and they also have a ﬂat spectral response. They can

replace the thermopile in many applications as a conven-

ient, room temperature, wide-spectral-sensitivity detector

of infrared and visible light. Pyroelectric detector arrays

are available from Electro-Optical Components, Scitec,

SensArray, Spectum Detector, and Spiricon.

Pyroelectric detectors are widely used for the detection

of very short-duration infrared laser pulses. High-energy

pulses, however, generate acoustic waves in the detector

crystal giving rise to spurious signals. These acoustic sig-

nals are more of a problem in the observation of long laser

pulses (> 100 ns) than they are with short pulses. Pyro-

electric detectors are much more sensitive than photon-

drag detectors

for this purpose.

Photon-drag detectors operate by utilizing the momen-

tum transfer between photons and photo-produced carriers

in a material, creating an electromotive force. They are

fast, but relatively insensitive with typical NEP of 4 3

–3

WHz

1/2

. They are mainly used for detecting intense

pulses from 10 lm carbon dioxide lasers.

7.10.3 Bolometers

The resistance of a solid changes with temperature accord-

ing to a relation of the form:

RTðÞ¼R

1 þ c T  T

ðÞ½ð7: 54Þ

Figure 7.44 Two examples of operating circuits for pyroelectric detectors.

594 DETECTORS

where c is the temperature coefﬁcient of resistance, typi-

cally about 0.05/K for a metal, and R

is the resistance

at temperature T

A bolometer is constructed from a material with a large

temperature coefﬁcient of resistance. Absorbed radiation

heats the bolometer element and changes its resistance.

Bolometers utilize metal, semiconductor, or almost super-

conducting elements. Metal bolometers utilize ﬁne wires

(platinum or nickel) or metal ﬁlms. The mass of the

element must be kept small in order to maximize its temper-

ature rise. Even so, the response time is fairly long (> 1 ms).

Semiconductor bolometer elements (thermistors) have

larger absolute values of c and have largely replaced metals

except where very long-term stability is required.

Bolometer elements can be operated in several ways; a

simple bias circuit for a single element is shown in Figure

7.45(a). However, it is usual to operate the elements in

pairs

in a bridge circuit, as shown in Figure 7.45(b) (see

also Chapter 6). One element is irradiated, while the sec-

ond

serves as a reference and compensates for changes in

ambient temperature.

Thermistors have a negative I–V characteristic above a

certain current and will exhibit destructive thermal run-

away unless operated with a bias resistor. It is usually best

to operate the thermistor at currents below the negative-

resistance part of its I–V characteristic. Bolometers can

operate to wavelengths up to 1000 lm, usually limited

by the transmission of their entrance window. These devi-

ces are available from B.F. Goodrich (acquired Barnes

Engineering from the EDO Corporation), Infrared Labo-

ratories, and Sofradir.

Microbolometers, generally used in thermal imaging

applications in the 8–16 lm spectral region, use a grid of

vanadium oxide or amorphous silicon on top of a silicon

grid. Infrared radiation heats the vanadium oxide, or amor-

phous silicon, and changes its electrical resistance. The

array of resistance changes is read out and provides a

thermal image of an object. They operate at room temper-

ature and do not require cooling.

Microbolometer arrays are typically 640 3 480, 320 3

240, or 160 3 120 pixels. Arrays are available from

NEC, Honeywell, and ULIS-IR. Complete camera systems

are available from BAE, CDIP, FLIR, Fluke Test Instru-

ments, Infrared Solutions, InfraredVision Technologies

Corporation (L-3 Communications), ISG Thermal Sys-

tems, Jenoptik, Land Infrared, Raytek, and Thermoteknix.

7.10.4 The Golay Cell

In a Golay cell (named for its Inventor, M.J.E. Golay),

radiation is absorbed by a metal ﬁlm that forms one side

of a small sealed chamber containing xenon (used

because of its low thermal conductivity). Another wall

of the chamber is a ﬂexible membrane, which moves

as the xenon is heated. The motion of the membrane

Figure 7.45 Operating circuits for thermistor

bolometers: (a) simple bias circuit; (b) bridge

circuit using compensating shielded thermistor,

with device construction shown.

THERMAL DETECTORS 595

is used to change the amount of light reﬂected to a photo-

detector. The operating principle and essential design

features of a modern Golay cell are shown in Figur e

46. Although these detectors are fragile, they are quite

sensiti

ve and are still used for far-infrared spectroscopy.

Golay cells are available from QMC Instruments and

Microtech Instruments.

7.11 ELECTRONICS TO BE USED

WITH DETECTORS

The primary signal from a photodetector may be a time-

varying current, as, for example, in the case of a photo-

multiplier, or a time-varying voltage, as, for example, in

the case o f a photodiode us ed in photovoltaic mode. In

general, the primary signal from the photodetector will be

proce ssed using electronics that follows the detector. This

is most often a current or voltage ampliﬁer, or a current to

voltage converter (transimpedance) ampliﬁer. When a

detector is being selected, it is often time-saving to buy

a detect or–ampliﬁer integrated combination that

will provide a n electrical signal in a useful format fo r

analysis. Manufacturers’ data sheets should be consulted

for recommend ed operational circuits. A few issues are

important in designing or specifying circuits to be used in

conjunction with the detector. For optimum power trans-

fer, the output impedance of the detector should be

matched to th e input impedance of the followi ng circuit.

For example, if a photomultiplier is used with a 50 X

anode resistor, th en the input impedance of the following

circuitry should also be 50 ohm for optimum high-speed

perfo rmance. Ma ny volta ge ampliﬁers have a very large

input impedance, so if the input to the ampliﬁer is con-

nected to a detector with output impeda nce R, the input

impedance of the circuit will become R. For high -speed

detector operation the signal from the detector may be

connected by 50 X coaxial cable to the input of the fol-

lowing electronics. The input impedance of these elec-

tronics should also be 50 X. The choice of input and

output impedance will a ffect the noise of the entire detec-

tor/ampliﬁer combination. If the no ise ﬁgure of the elec-

tronics is known, then the overall noise performance can

be determined, using the methods discussed in Section

8. If the detector/electronics combination has an

nknown noise ﬁgure then this will have to be determined

experimentally. This is a specialized endeavor, but many

manufacturers, such as Agilent, Maxim, National Instru-

ments, and Rohde and Schwarz have application notes

available to explain h ow thi s is done.

Figure 7.46 Schematic design of the Golay detector. The top half of the line grid is

illuminated by the LED and imaged back on the lower half of the grid by the ﬂexible

mirror and meniscus lens. Any radiation-induced deformation of the ﬂexible

mirror moves the image of the line grid and changes the illumination reaching the

photodiode.

596 DETECTORS

7.12 DETECTOR CALIBRATION

In certain cases, the data supplied by a detector manufacturer

on parameters such as D

(k)ors will only indicate a range of

values within which the detector’s characteristics will fall, or

the data may not be sufﬁciently reliable. If necessary, more

accurate detector calibration can be carried out.

To determine D

(k) for a detector, its response must be

measured with a source giving a known irradiance E

(k)

at the detector. This can be done either with a calibrated

source such as a blackbody, or by comparison with another

detector , such as a thermopile, which has a calibrated

response. To determine the temporal response function of

a detector operated in a giv en conﬁguration, all that is nec-

essary is to irradiate the detector with a very short light pulse

and record the output pulse shape on a fast oscilloscope that

has its input appropriately terminated. For response func-

tions below about 1 ns, a sampling oscilloscope should

be used in conjunction with repetiti ve short-light-pulse irra-

diation of the detector . For detectors with response faster

than about 1 ns, sufﬁ ciently short light pulses can be

obtained from a mode-locked Nd:YAG, Nd:glass, ruby, or

dye laser. Pulses from mode-locked argon or CO

lasers may

not be short enough to calibrate a very fast detector . To obtain

short light pulses outside con v eniently available wav elength

regions, nonlinear harmonic generation or mixing schemes

can be used, but the dif ﬁ cultie s of such techniques can be

sev ere. To determine the time response of a detector that

responds slo wer than 1–2 ns, any pulsed light source of much

shorter duration than the detector response can be used.

Short-duration ( ’ 10 ns) ﬂashlamps are available from

Perkin–Elmer Optoelectronics and Xenon Corporation.

Very-short-duration, low-energy, pulsed light sources

are easily made in the laboratory. A very simple design

is shown in Figure 7.47. A high-voltage discharge between

two

electrodes spaced by a few millimeters or less in a

high-pressure gas is used. Hydrogen works very well,

and even air at atmospheric pressure is satisfactory. To

obtain a short-duration ﬂash, only the self-capacitance C

of the electrodes must be allowed to discharge. To accom-

plish this, a small charging resistor must be placed very

close to the high-voltage electrode; a larger series charging

resistor can be placed farther from the electrode. The tips

from ballpoint pens make excellent electrodes in this

application. The ﬂash duration is proportional to L/p,

where L is the electrode spacing and p the gas pressure.

The breakdown voltage is proportional to L and also

approximately to p: the capacitance of the electrode gap

is proportional to L, so the ﬂash energy

is propor-

tional to L

. Thus, for short-duration, high-energy

ﬂashes, p should be high. The repetition frequency of the

lamp, which is most easily operated in a free-running

mode, will depend on the charging time constant.

Endnotes

The ﬁrst dynode often has a larger d value than the others, but

we will assume that d is an average value.

The secondary ionization coefﬁcient is the number of secondary

electron–hole pairs produced per unit length by a speciﬁc charge

carrier (electron or hole) in trav eling through the material.

Cited References

1 R. K. Bock and A. Vasilescu, The Particle Detector

Briefbook, Springer, New York, 1998.

2 C. Enss, Cryogenic Particle Detection, Topics in Applied

Physics, Vol. 99, Springer, New York, 2005.

3 R. C. Fernow Introduction To Experimental Particle

Physics, Cambridge University Press, Cambridge, 1989.

Figure 7.47 Simple design for high-pressure,

nanosecond-duration pulsed light source. Generally

R >> r, where r ranges from 1 k ohm to 1 M ohm.

DETECTOR CALIBRATION 597

4 K. Kleinknecht Detectors For Particle Radiation, 2nd

revised edn., Cambridge University Press, Cambridge, 1998.

5 P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan,

Elements of Infrared Technology, John Wiley & Sons, Inc.,

New York, 1962.

6 C. C. Davis, Lasers and Electro-Optics, Cambridge

University Press, Cambridge, 1996.

7 R. D. Hudson, Jr., and J. W. Hudson (Eds.), Infrared

Detectors, Benchmark Papers in Optics, Vol. 2, Dowden,

Hutchinson and Ross, Stroudsburg, PA, 1975.

8 D. Wood, Optoelectronic Semiconductor Devices, Prentice-

Hall, New York, 1994.

9 R. J. Keyes (ed.), Optical and Infrared Detectors, Topics in

Applied Physics, Vol. 19 Springer, Berlin, 1977.

10 R. H. Kingston, Detection of Optical and Infrared

Radiation, Springer Series in Optical Sciences, Vol. 10,

Springer, Berlin, 1978.

11 D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation

Principles and Applications, Cambridge University Press,

Cambridge, 2007.

12 P. Capper and C. T. Elliott (Eds.), Infrared Detectors and

Emitters: Materials and Devices, Kluwer, Dordrecht,

2001.

13 M. Henini and M. Razeghi (Eds.), Handbook of Infra-red

Detection Technologies, Elsevier, Amsterdam, 2002.

14 G. Knoll, Radiation Detection and Measurement, 3rd

revised edn., John Wiley & Sons, Ltd, Chichester, 2000.

15 G. H. Rieke, Detection of Light: From the Ultraviolet to the

Submillimeter, 2nd edn., Cambridge University Press,

Cambridge, 2003.

16 J. D. Vincent, Fundamentals of Infrared Detector Operation

and Testing, Wiley-Interscience, New York, 1989.

17 RCA photomultiplier tube types formerly manufactured by

RCA are supplied by Burle Industries (now merged with

Photonis).

18 Phillips photomultipler tubes were formerly available from

Amperex, but many of these tube types are now

manufactured by Photonis. These tubes are also available

from Richardson Electronics.

19 L. Brocco, D. Casadei, G. Castellini, et al., Behavior in

strong magnetic ﬁeld of the photomultiplers for the

TOF system of the AMS-02 space experiment, Proceedings

of ICRC 2001: 2193, Copernicus Gesellschaft, 2001.

20 Static crossed-ﬁeld photomultipliers used to be available

from ITT. See also V. J. Koester, Improved timing resolution

in time-correlated photon-counting with a static crossed-

ﬁeld photomultiplier, Anal. Chem., 51, 458–459, 1979.

21 I. Prochazka, A. L. Migdall, A. Pauchard, et al. (Eds.),

Photon Counting Applications, Quantum Optics, and

Quantum Cryptography, Proceedings of SPIE – 6583, May

10, 2007.

22 H. R. Zwicker, in Optical and Infrared Detectors,R.S.

Keyes (Ed.), Topics in Applied Physics, Vol. 19, Springer,

Berlin, 1977, 149–196.

23 Photomultiplier Tubes: Basics and Applications

, 2nd edn.,

Hamamatsu

Photonics, Hamamatsu City, Japan, 1999.

24 ‘‘Window’’ discriminators are available from EG&G and

LeCroy.

25 Laser Focus Buyers Guide, published annually by Pennwell

Publishing Co., 1421 South Sheridan, Tulsa, OK 74112

01460, lists a large number of suppliers of a wide range of

optical detectors as does the The Photonics Buyers’ Guide,

published annually by Photonics Spectra, Laurin Publishing

Co., Berkshire Common, P.O. Box 4949, Pittsﬁeld, MA

01202–4949.

26 D. Long, in Optical and Infrared Detectors, R. J. Keyes

(Ed.), Topics in Applied Physics, Vol. 19, 101–147,

Springer, Berlin, 1977.

27 W. J. Moore and H. Shenker , Infrared Phys., 5, 99–106, 1965.

28 F. J. Low, J. Opt. Soc. Am., 51, 1300–1304, 1961. See also

B. T. Draine and A. J. Sievers, High responsivity, low-noise

germanium bolometer for far infrared, Opt. Commun., 16,

425–429, 1976.

29 H. Shenker, W. J. Moore, and E. M. Swiggard, J. Appl.

Phys., 35, 2965–2970, 1964.

30 E. H. Putley, Appl. Opt., 4, 649–656, 1965.

31 M. A. C. S. Brown and M. F. Kimmitt, Infrared Phys., 5, 93–

97, 1965.

32 P. Norton, Opto-Elect. Rev., 10(3), 159–174, 2002.

33 G. L. Hansen, J. L. Schmit, and T. N. Casselman, J. Appl.

Phys., 53, 7099–7101, 1982.

34 J. Gowar, Optical Communication Systems, 2nd edn.,

Prentice-Hall, Englewood Cliffs, NJ, 1993.

35 H. Dautet, P. Deschamps, B. Dion, et al., Appl. Opt., 32(21),

3894–3900, 1993.

36 S. Cova, A. Lacaita, F . Zappa, and P. Lovati, in Advances in

Fluorescence Sensing Technology II, J. Lakowicz (Ed.),

Proc. SPIE 2388, paper 09, SPIE Conf. Photonics West, San

Jose, CA, USA, Feb. 6–7, 56–66, 1995.

37 A. Lacaita, F. Zappa, S. Cov a, and P. Lov ati, App. Opt., 35,

2986–2996, 1996.

38 S. Cova, M. Ghioni, A. Lacaita, C. Samori, and

F. Zappa, Appl. Opt. 35, 1956–1976, 1996.

39 T. Nesheim, Single photon detection using avalanche

photodiode, M.Sc. Thesis, Norwegian University of Science

and Technology, Trondheim, Norway, 1999.

40 H. J. Woltring, IEEE Transactions on Electron Devices,

(8), 581–590, 1975.

598 DETECTORS

41 A. J. Theuwissen (Ed.), Solid-State Imaging with Charge-

Coupled Devices (Solid-State Science and Technology

Library), Kluwer, Dordrecht, 2002.

42 T. V. Wilson, K. Nice, and G. Gurevich, How digital

cameras work. November 29, 2006 http://www.

howstuffworks.com/digital-camera.htm (June 02, 2007).

43 T. Klinger, Image Processing with Lab VIEW and IMAQ

Vision, Prentice-Hall, Englewood Cliffs, NJ, 2003.

44 R. J. McIntyre, IEEE Trans. Electr on. Devices, ED-13, 164–

169, 1966.

45 Hamamatsu Photon Counting Application Note. http://

sales.hamamatsu.com/assets/applications/ETD/

PhotonCounting_TPHO9001E04.pdf

46 C. C. Davis and T. A. King, J. Phys. A. 3, 101–109,

1970.

47 J. Milman and H. Taub, Pulse, Digital, and Switching

Waveforms, Chap. 3, McGraw-Hill, New York, 1965;

C. N. Winningstad, IRE Trans. Nucl. Sci, NS43, 26, 1959;

C. L. Ruthroff, Proc IRE, 47, 1337, 1959.

48 L. J. Richter and W. Ho, Rev. Sci. Instrum., 57, 1469, 1986;

R. M. Tromp, M. Copel, M. C. Reuter, Rev. Sci. Instrum., 62,

2679, 1991.

49 P. Horowitz and W. Hill, The Art of Electronics, 2nd edn.,

Cambridge Universtiy Press, Cambridge, 1989.

50 V. Radeka, in Annual Review of Nuclear and Particle

Science, Vol. 38, J. D. Jackson (Ed.), 1988, pp. 217–278.

51 R. L. Heath, R. Hofstadter and E. B. Hughes, Nucl. Instr.

Meth., 162, 431–476, 1979.

52 J. B. Birks, Theory and Practice of Scintillation Counting,

Pergamon Press, New York, 1964.

53 R. K. Bock and A. Vasilescu, The Particle Detector

Briefbook, Springer, Berlin, 1998.

54 G. Knoll, Radiation Detection and Measurement, 3rd

revised edn., John Wiley & Sons, Ltd, Chichester, 2000.

55 E. H. Putley, in Optical and Infrared Detectors, R. J. Keyes

(Ed.), Topics in Applied Physics, Vol. 19, Springer, Berlin,

1977.

56 A. F. Gibson, M. F. Kimmitt, and A. C Walker, Appl.

Phys. Lett., 17, 75–77, 1970. See also R. Kesselring, A. W.

Kalin, and F. K. Kneubuhl, Infrared Phys., 33, 423–436,

1992.

57 M. J. E. Golay, Rev. Sci. Instrum., 18, 357–362, 1947.

General References

D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation

Principles and Applications, Cambridge University Press,

Cambridge, 2007.

R. K. Bock and A. Vasilescu, The Particle Detector Briefbook,

Springer, Berlin, 1998.

P. Capper and C. T. Elliott (Eds.), Infrared Detectors and

Emitters: Materials and Devices, Kluwer, Dordrecht, 2001.

C. C. Davis, Lasers and Electro-Optics, Cambridge University

Press, Cambridge, 1996.

C. F. G. Delaney and E. C. Finch, Radiation Detectors, Oxford

Science Publications, Clarendon Press, Oxford, 1992.

C. Enss, Cryogenic Particle Detection, Topics in Applied

Physics, Vol. 99, Springer, Berlin, 2005.

R. C. Fernow, Introduction To Experimental Particle Physics,

Cambridge University Press, Cambridge, 1989.

M. Henini and M. Razeghi (Eds.), Handbook of Infra-Red

Detection Technologies, Elsevier, Amsterdam, 2002.

R. D. Hudson, Jr., and J. W. Hudson (Eds.), Infrared Detectors,

Benchmark Papers in Optics, Vol. 2, Dowden, Hutchinson and

Ross, Stroudsburg, PA, 1975.

K. Kleinknecht, Detectors For Particle Radiation 2nd revised

edn., Cambridge University Press, Cambridge, 1998.

R. H. Kingston, Detection of Optical and Infrared Radiation,

Springer Series in Optical Sciences, Vol. 10, Springer , Berlin,

1978.

G. Knoll, Radiation Detection and Measurement, 3rd revised

edn., John Wiley & Sons, Inc., New York, 2000.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements

of Infrared Technology , John W iley & Sons, Inc., New York,

1962.

R. J. Keyes (Ed.), Topics in Applied Physics, Optical and

Infrared Detectors, Springer, Berlin, 1977.

G. H. Rieke, Detection of Light: From the Ultraviolet to the

Submillimeter, 2nd edn., Cambridge University Press,

Cambridge, 2003.

J. D. Vincent, Fundamentals of Infrared Detector Operation and

Testing, Wiley-Interscience, New York, 1989.

D. Wood, Optoelectronic Semiconductor Devices, Prentice-Hall,

New York, 1994.

REFERENCES 599

MEASUREMENT AND CONTROL OF TEMPERATURE

There are two levels of concern with temperature in

scientiﬁc experiments. One is the control of temperature

to achieve some secondary (but essential) aim in the appa-

ratus. Examples are the use of a cold trap in a vacuum line,

and the use of heaters and coolants in a distillation column.

For such needs, the temperature needs only to be known

and kept constant to within a few kelvins. In the second

case, the measurement of the dependence of physical

parameters on temperature is a primary aim of the experi-

ment. A physicist learns about the nature of a material by

measuring such properties as density or heat capacity as a

function of temperature. An organic chemist studies the

kinetics of a chemical reaction by measuring its rate of

reaction as a function of temperature. For these experi-

ments, the temperature must be varied over a range and

controlled at any point in that range, at resolutions better

than 1 K.

Sometimes the temperature must be known accurately.

That is, the measurement must be closely calibrated to the

International Temperature Scale. Accurate measurements

are necessary if the new data are to be used with other

measurements on the system under study. If measurements

of the density of water are to be combined with measure-

ments of its kinematic viscosity to calculate its shear vis-

cosity as a function of temperature, then the temperature

must be measured with the same accuracy in both the

density measurements and the kinematic viscosity meas-

urements. The accuracy also matters if measurements in

one laboratory are to be compared to measurements in

another laboratory of that same quantity (e.g., the shear

viscosity as a function of temperature).

For some purposes, the precision is more important than

the accuracy. Such is the case when it is the derivative of a

property with respect to temperature that is of interest.

Then the changes in temperature need to be measured with

very ﬁne resolution, but the accuracy, the exact temper-

ature on the international scale, is not as important. A

physicist wishing to test a theoretical prediction for the

thermal expansion (the change of volume with tempera-

ture) of a superconducting solid will be more concerned

with precision than with accuracy, even though he or she

will have some requirements on the accuracy.

In this chapter we will describe how to measure and

control the temperature for simple needs, usually meaning

a resolution of 1 K. We will also describe more precise and

accurate methods for temperature measurement and control,

methods that achieve a resolution of 1 mK and better. Since

we must be able to measure the temperature in order to

control it, we will ﬁrst discuss thermometry. For both meas-

urement and control, we will focus on the temperature range

from 10 K to about 1800 K, and on methods that are prac-

tical for most laboratories. We will brieﬂy discuss thermom-

etry at very low and very high temperatures.

8.1 THE MEASUREMENT OF

TEMPERATURE

A thermometer can be constructed from a system with a

measurable property that depends strongly on temperature.

We will discuss here the ‘‘working’’ thermometers useful

By Sandra C. Greer, The University of Maryland, College Park, MD

and Mills College, Oakland, CA.

600

CHAPTER

in most laboratories, as opposed to special ‘‘standard’’

thermometers, such as gas thermometers, used in calibra-

tion laboratories.

1–4

8.1.1 Expansion Thermometers

Expansion thermometers use as the thermometric property

the volume of the thermometric system. For example, the

common mercury thermometer uses the change in volume

(as reﬂected in the change in length) of a column of mer-

cury conﬁned to a cylindrical capillary tube. There exist

expansion thermometers using the thermal expansion of a

metal that have industrial applications.

We will limit our-

selves to the liquid-in-glass thermometers used in scien-

tiﬁc research.

5,6

Liquid-in-glass thermometers date to the

seventeenth century

and are still common in research lab-

oratories. They do not lend themselves readily to computer

automation of the measurement process, but they are use-

ful for approximate measurements that do not need to be

automated, or as laboratory standards for the calibration of

other thermometers.

Such thermometers are limited in range by the freezing

and boiling points of the liquids used and by the softening

point of the glass in which the liquid is contained. Mercury

has been the most common thermometer ﬂuid because of

its nearly linear coefﬁcient of thermal expansion, but

organic liquids are also used and are safer. Design consid-

erations also include the choice of the glass and the relative

dimensions of the parts of the thermometer. Thermometers

can be designed for high sensitivity in a particular range by

including in the liquid column a section of larger diameter,

a contraction chamber, so that the liquid expands in that

volume before it reaches the range of interest (see Figure

8.1). Mercury thermometers can operate in the range 235–

923

K. Organic liquids have the disadvantages that they do

not have very linear thermal expansions and they must be

dyed to be visible, but they are still useful: toluene (183 to

373 K), ethanol (163 to 373 K), pentane (73 to 293 K).

Thermometers made with mercury and with organic

liquids are available with resolutions as good as 0.02 K

(Brooklyn Thermometer).

There are a number of difﬁculties in obtaining high

accuracy and precision with liquid-in-glass thermometers.

Good thermal contact between the thermometer and the

system of interest is difﬁcult to achieve for systems other

than ﬂuids. The thermometer can be sensitive to pressure

changes. If the thermometer is heated to its highest temper-

atures, it will require days to return to its original calibra-

tion because of hysteresis in the glass.

Mercury thermometers designed to be accurate and sta-

ble to about 0.01 K over temperature ranges of 3 to 5 K are

commercially available (Brooklyn Thermometer, Omega

Engineering) and make good, cheap working temperature

standards. Mount the mercury thermometer in a stirred

bath, the temperature of which is under control (Section

8.2), along with any other thermometers that you want to

Figure 8.1 Mercury-in-glass thermometer. The auxiliary scale

is designed to allow calibration at the ice point. The contraction

chamber permits high sensitivity (a small capillary diameter)

without having a very long stem. The immersion line indicates

the depth to which the thermometer was immersed in the

calibration bath. The expansion chamber prevents the buildup

of pressure and avoids breakage on overheating.

MEASUREMENT OF TEMPERATURE 601MEASUREMENT OF TEMPERATURE 601

calibrate against the mercury thermometer. Be careful in

reading the meniscus position to avoid parallax error; a

telescope makes this easier. Use the thermometer at the

same immersion depth at which it was originally cali-

brated; a difference in immersion depth will necessitate

stem corrections. Tap the thermometer before each meas-

urement to avoid sticking of the mercury column to the

stem wall. Monitor the stability of the thermometer by

regularly measuring the ice point (Section 8.1.9).

ﬁnal hint: if the liquid in a thermometer becomes

separated, it can be rejoined by cooling the thermometer

bulb with dry ice shavings until all the liquid is back in the

bulb. Never heat a liquid-in-glass thermometer to expand

the liquid to the full length of the capillary tube in an effort

to rejoin the liquid: the thermometer will break.

8.1.2 Thermocouples

7–10

Thermocouples use as the thermometric property the volt-

age that develops between two junctions of two different

metals when the junctions are at different temperatures.

Thermocouple thermometers have been used since about

1885,

and still have uses ranging from hand-held digital

thermometers to sophisticated calorimeters.

When there exists a difference in electron density

between two points in a metallic conductor, a voltage

develops between those two points. Such a difference in

electron density can arise even in a conductor made of a

homogeneous metal, because the electron density varies

when the temperature varies. Thus, a temperature gradient

across any metallic material causes a voltage to develop

across that material. If we try to measure this voltage by

attaching leads made of the same metal, then the voltage

difference will also develop in the leads and the effects will

cancel. If the leads are of a different metal, as shown in

Figure 8.2(a), then the difference in the thermally induced

ltages between the two metals will cause a net voltage

between the junctions: the Seebeck effect.

This thermo-

electric voltage, or ‘‘thermal emf,’’ depends upon the par-

ticular choice of metals and upon the difference in

temperature between the junctions, but depends only

slightly on the pressure. The Seebeck effect is a bulk prop-

erty of metals in a temperature gradient. It is not a property

of the junctions themselves: it is not a ‘‘contact potential,’’

and treating it as such can lead to mistakes in the use of

thermocouples.

A related property is the Peltier effect:

when a current is passed through a circuit such as Figure

8.2(a), by replacing the voltmeter with a battery, then one

junction

will be heated and the other junction will be

cooled. The Peltier effect can be used to construct electri-

cal heating and cooling devices.

The connection of two wires of two different metals at

junctions at two different temperatures,asinFigure 8.2(a),

Figure 8.2 Thermocouple conﬁgurations. Lines of different

thicknesses represent wires of different metals or alloys. T

and T

are two different temperatures. V is a voltmeter.

602 MEASUREMENT AND CONTROL OF TEMPERATURE602 MEASUREMENT AND CONTROL OF TEMPERATURE

is called a thermocouple. The voltage developed across the

thermocouple is a measure of the difference in tempera-

ture, (T

– T

). Thus, the measurement of the temperature

with a thermocouple requires only a voltmeter of sufﬁcient

resolution. The relationship between the thermoelectric

voltage and the temperature difference, while nearly a

direct proportionality, cannot be predicted, but must be

measured for a given pair of metals. The nature of the

Seebeck effect leads to several principles useful in the

design of such thermocouple thermometers:

2,16

(1) The law of homogeneous metals: a thermocouple

requires two different metals. If the two wires are of

the same material, then no net thermal voltage will

develop, even in the presence of a temperature gra-

dient. Therefore, voltmeter lead wires, as shown in

Figure 8.2(b), will not contribute to the measured volt-

age

if they are made of the same metal, and if their

ends (at T

and at the voltmeter) are at the same tem-

peratures so that they are under the same temperature

gradient. On the other hand, inhomogeneities due to

strains or impurities in a metal conductor will be, in

effect, regions of a different metal, and will, in the

presence of a temperature gradient, act as ‘‘mini-

thermocouples,’’ generating spurious thermal voltages

and leading to inaccuracies in the thermometry.

(2) The law of intermediate metals: a thermocouple

requires two different temperatures. If there is no dif-

ference in temperature between the ends of a pair of

wires, then no net thermal voltage will develop

between them, even if the wires are of different metals.

That is, in Figure 8.2(a),ifT

¼ T

, no voltage devel-

ops. A consequence of this law is that another wire

may be inserted into the thermocouple circuit, so long

as both ends of that wire are at a common temperature,

that need not be either of the temperatures involved in

the actual thermocouple (T

or T

). This means that

thermocouple junctions may be made with any kind of

solder or any other method of attachment, so long as

each junction is itself all at the same temperature.

(3) The law of successive metals: if thermocouples are

made of pairs of metal A with metal B, metal B with

metal C, and metal A with metal C, then the voltages

developed by each of the thermocouples between a

given pair of junction temperatures will be related as

¼ V

+ V

. This equation allows the calculation

of tables of thermocouple voltages for any pair of

metals A and C if the tables are already available for

A and C with respect to a reference metal B.

(4) The law of successive temperatures: if a given thermo-

couple develops a voltage V

between T

and T

and a

voltage V

between T

and T

, then it will develop a

voltage V

¼ V

+ V

between T

and T

. It follows that

only the junction temperatures matter: intermediate

temperatures along homogeneous wires do not matter.

It also follows that if thermocouple tables are available

in which voltages are given for each temperature T

with respect to a reference temperature T

, then vol-

tages may be calculated with respect to a different

reference temperature T

if the voltage V

is known.

Thermocouple junctions may be placed in series in order

to amplify the voltage signal. Such a thermopile is shown

in Figure 8.2(c), where there are three identical thermo-

couples

in series, producing a voltage three times that of a

single thermocouple (since voltages in series add).

There are a great many possible thermocouple pairs,

since any two metals or alloys can form a thermocouple.

The choice of a particular pair will depend upon its sensi-

tivity in the temperature range of interest and upon such

considerations as corrosion resistance. Several thermocou-

ple pairs have come into common use; their properties are

well known, and good-quality wire is readily available

(Omega Engineering; Watlow).

Table 8.1 gives the most common thermocouple types

and

their properties. Types C, D, and G are all various

combinations of alloys of tungsten and rhenium, and are

useful at high temperatures because these metals do not

readily vaporize. Types R and S are of platinum with

platinum–rhodium alloy and have low sensitivity, but have

high stability and accuracy. Types K, N, and E all use

nickel alloys. Type K has a wide range of usefulness,

low thermal conductivity, and good resistance to oxidation,

but cannot be used in a reducing atmosphere above 1100 K

and shows instability in the calibration due to a phase

transition in Chromel at 570 K. Type N is a more stable

substitute for Type K. Type E is common in low-temperature

applications because the thermal conductivities of the

materials are low, and thus the wires do not carry

heat into the apparatus. Types E, J, and T all use the

MEASUREMENT OF TEMPERATURE 603MEASUREMENT OF TEMPERATURE 603

copper–nickel alloy Constantan. Type J has the advantage

of high sensitivity and the disadvantage that iron is readily

oxidized. Type T, probably used most often, has the advant-

age that one material is copper, from which the voltmeter

leads are also likely to be made, so that the chance of

extraneous thermal voltages is reduced. On the other hand,

copper oxidizes above 620 K and has a very high thermal

conductivity (see Table 8.5 below). The last two Chromel

ermocouples in Table 8.1, one with gold–iron alloy and

e with copper–iron alloy, are used at cryogenic temper-

atures, along with types E, K, and T (Section 8.1.5). Ther-

couples made of wires from two different elemental

metals (gold, silver, platinum, etc.) can be used for cases

requiring very high stability and precision.

4,17

The construction of reliable thermocouple thermo-

meters requires care. Use good-quality, annealed thermo-

couple wire. Each wire can be individually tested for

homogeneity by connecting its ends to a voltmeter and

passing the wire slowly through liquid nitrogen; wires that

do not show any measurable thermoelectric voltage are

suitable for use. Use the largest-diameter wire that you

can tolerate: large wire is more likely to be homogeneous

and is less susceptible to strains. Make the junctions

mechanically sound and electrically and thermally contin-

uous. In principle, thermocouple wires can be twisted or

clamped to make a junction.

In practice, better results are

obtained if they are soldered or welded (see Section 1.4).

or work below 443 K, Type T can be joined with ordinary

tin–lead solder, using a rosin ﬂux. All can be soldered with

low melting tin–silver solder. For work at higher temper-

atures and for better mechanical strength, all can be brazed

with a high-melting silver alloy (Section 1.4.6). All but

ype T can be spot-welded. All can be welded with a torch,

using a reducing ﬂame of oxygen with either natural gas or

acetylene to melt the two wires together into a ﬁrm bead.

Ready-made thermocouples, thermopiles, and thermopile

arrays can be purchased from Omega Engineering,

SensArray, InstruLab, Watlow, et al.

Make good thermal contact between the junctions and

the points at which the temperatures are to be measured.

Junctions can be mechanically attached to solids using a

thermally conducting grease, or bonded with a thermally

conducting adhesive (Cotronics, Omega Engineering,

Wakeﬁeld). Thermocouples are often placed in protective

metal or ceramic sheaths (thermowells),

but such

arrangements increase the response time. Protect the wires

from mechanical stresses. The wires can be electrically

insulated with Teﬂon (to 553 K) or Kapton (to 700 K);

ﬁberglass or ceramic is required for higher temperatures.

Avoid air drafts and temperature gradients in the vicinity of

a thermocouple circuit.

A thermocouple or thermopile produces a low-level d.c.

voltage (10–100 lV) that requires particular care in meas-

urement (see Keithley handbook

and application notes).

A digital voltmeter of appropriate sensitivity sufﬁces for

the measurement of the thermocouple voltage (Keithley,

Agilent). Follow appropriate procedures for shielding and

grounding in the measurement circuitry (Section 6.9).

Commercial

thermocouple ampliﬁers are available for $2

to $20 (Analog Devices, Linear Technology). Sometimes

(e.g., for control purposes) it is desirable to linearize the

output signal, and such circuits are also available (Analog

Devices).

Thermocouples measure the temperature differences

between junctions. This property can be used to advantage

Table 8.1 Properties of common thermocouples

Type

Materials Useful

Range

(K)

Sensitivity

(lVK

1

)

20 K 300 K

C, D, G Tungsten/Rhenium 32–2600 — 20

R, S Platinum/PtRh 220–1800 — 6

K Chromel

/Alumel

10–1500 4.1 41

N Nicrosil/Nisil

10–1500 3 26

E Chromel

/Constantan

10–700 8.5 61

J Iron/Constantan

60–1000 — 52

T Copper/Constantan

20–700 4.6 41

Chromel

/AuFe 10–1000 15 20

Chromel

/CuFe 10–300 >11

The type designation is that of the Instrument Society of

America

Chromel is an alloy of nickel with 10% chromium

Alumel is an alloy of nickel with 2% aluminum, 2%

manganese, and 1% silicon

Constantan is an alloy of copper with 43% nickel

Nicrosil is a alloy of nickel, chromium, and silicon; Nisil is an

alloy of nickel, magnesium, and silicon.

604 MEASUREMENT AND CONTROL OF TEMPERATURE604 MEASUREMENT AND CONTROL OF TEMPERATURE

when a difference is just what is required, as in some

temperature-control circuits. If, instead, an absolute tem-

perature measurement is required, then one junction (the

reference junction) must be kept at a constant, known tem-

perature. For example, let T

in Figure 8.2 be the reference

junction of known T

. Then the absolute temperature at T

is obtained by combining the known T

and the difference

– T

) as obtained from the thermocouple voltage (see

below). A simple (but inconvenient) way to do this is to

keep the reference junction at 273.15 K by immersing it in

a slurry of ice and water (see Section 8.1.9). The reference

temperature can also be established with commercially

available ﬁxed point cells that are made from Peltier devi-

ces (Hart Scientiﬁc, Omega Engineering; $1200).

Two less-expensive methods are either to make an iso-

thermal block, or to use an electronic compensation circuit.

An isothermal block consists of a material of high thermal

conductivity (Table 8.5) onto which the reference junction

and

an independent thermometer are mounted with good

thermal contact, and then surrounded by thermal insulation

(Table 8.5). Then the independent thermometer is used to

measure

the reference temperature. This is useful, even

though it requires an independent thermometer, because

that thermometer only needs to function near room temper-

ature, but then permits thermocouple measurements of

temperatures far from room temperature.

An electronic compensation circuit or ‘‘electronic ice

point’’ is an electronic circuit that measures the temper-

ature at the reference junction and then adds a voltage to

the thermocouple circuit that compensates for the fact that

the reference junction is not actually at 273.15 K. These

‘‘cold junction compensation’’ circuits can be made from

components, or purchased. Analog Devices and Linear

Technology make integrated circuits (AD594, AD595,

LT1025) that include both compensator and ampliﬁer for

$15–$40, and Omega makes complete devices for $200–

$600. For the best thermocouple measurements of temper-

ature, reference junctions made from ice baths or other

ﬁxed-point baths (Sections 8.1.9; 8.2.1) permit more accu-

rate

measurements (60.01 K) than do these isothermal

blocks and electronic ice points (60.4 to 61 K).

In order to convert the thermocouple voltage to a tem-

perature, it is n ecessary to use conversion table s or to

calibrate directly. The National Institute of Standards and

Technology has published extensive tables of thermo-

couple voltages. A calibration using the tables is likely

to be accurate only to a few degrees, due to variations

among wires. For more accurate measurements, the ther-

mocouple must be compared with a standard thermometer

(usually a platinum resistance thermometer; see Section

8.1

.3 below) over the temperature ran

ge of interest. Voltage-

temperature points either from the tables or from a direct

calibration can be ﬁtted by a polynomial:

T ¼ a

þ a

V þ a

þ ð8:1 Þ

where T is the temperature, V is the voltage, and enough

terms are included to describe the data. The calibration

determines the accuracy of the temperature measurement

on the International Temperature Scale (Section 8.1.9). The

ecision of temperature measurements with thermocouples

is considerably better than the accuracy: temperature differ-

ences can be resolved to 1 mK, using thermopiles and sen-

sitive ampliﬁers/voltmeters.

The advantages of thermocouples as thermometers are:

they are simple, rugged, and inexpensive; thermopiles can

have resolutions of 1 mK; they can be used over a very

broad range of temperature (see Table 8.1); they are small;

they

respond quickly. The disadvantages are: the voltage

signals are small and hard to measure; accuracy is hard to

attain and maintain; a reference junction is necessary for

absolute temperature measurements; they are very sensi-

tive to magnetic ﬁelds.

8.1.3 Resistance Thermometers

Resistance thermometers use as the thermometric property

the dependence of electrical resistance on temperature.

There are two main kinds of resistance temperature detec-

tors (RTDs): conducting metal RTDs and semiconductor

RTDs. Metal RTDs have been in use since the late nine-

teenth century,

whereas semiconductor RTDs came into

use only in the twentieth century. Resistance temperature

detectors are invaluable in modern thermometry because

they are small and stable, and provide an easily measured

electrical quantity.

Metal Resistance Thermometers.

Metal resist-

ance thermometers consist of wire coils or thin ﬁlms of

electrically conducting metals or alloys, together with the

MEASUREMENT OF TEMPERATURE 605MEASUREMENT OF TEMPERATURE 605

instrumentation needed to measure the electrical resist-

ance. As the temperature increases, the increase in kinetic

energy of the metal atoms leads to an increase in the elec-

trical resistivity. The larger the initial resistance, the larger

the change of resistance with temperature, and thus the

greater the sensitivity.

While a number of metals can be used for thermometry

(Table 8.2), platinum is most commonly used because it is

resistant

to corrosion and its electrical resistance has a

nearly linearly increase with temperature of 0.4%/K.

Indeed, the platinum resistance thermometer (PRT) is the

standard device for the International Temperature Scale of

1990 between 13.8033 K and 961.78 K (see Section

8.1.9).

Some typical platinum resistance thermometers

are shown in Figure 8.3. Usually, PRTs have resistances of

or 100 X at room temperature, but thin-ﬁlm PRTs can

have resistances of 1000 to 2000 X. The resistance as a

function of temperature behaves as (see Figure 8.4):

R ¼ R

þ R

T þ R

þ ð8:2Þ

where the T

term is important for measurements with a

resolution of millikelvins. With care in the resistor construc-

tion and in the measurement circuitry, a resolution of 0.1 mK

can be achiev ed over a very broad range of temperatures

with platinum resistance thermometers (see Figure 8.4 and

Table 8.2), available from suppliers such as Barnant, Hart,

Lake

Shore Cryotronics, Minco, Omega Engineering, and

Table 8.2 Properties of common resistance thermometers

Materials Resistivity

(Xm) 3 10

at 273 K

Temperature Coefﬁcient

of Resistance

1

) 3 10

Useful Range (K) Sensitivity

(mK)

20 K 300 K

Platinum 11 3.9 20–1000 10 0.1

Nickel 59 6.0 213–423 — —

Copper 1.7 3.9 173–373 — —

Ruthenium oxide — — 0.04–40 5

—

Rhodium–iron

— 0.5–300 0.05 5

Approximate resolution under typical conditions.

Not for use in magnetic ﬁeld.

At 4.2 K.

Figure 8.3 Platinum resistance thermometers: (a) standard,

high-resolution model made by Minco Products, Inc., in which

the platinum is wound as a wire coil on a ceramic base. Two

leads (A) pass through the lid and attach to one end of the coil

(B) at C. At the other end, two leads are again attached (E) and

pass through the center of the base to the lid at F. The

assembly is then enclosed in a inert atmosphere. This PRT is

3/8’’ long; (b) Film RTD such as those made by Omega

Engineering, Inc. They can be very small, 1/8’’ or less in length.

606 MEASUREMENT AND CONTROL OF TEMPERATURE606 MEASUREMENT AND CONTROL OF TEMPERATURE

Rosemount. Thin, surface-mount foil resistance thermome-

ters made from platinum are also available (Minco).

Resistance thermometers are also made of other metals

(see Table 8.2). Nickel has a high sensitivity to temperature

change,

but the dependence of resistance on temperature is

nonlinear, making its use over a large temperature range

more difﬁcult.

22–24

Copper has a low resistivity, so a longer

wire is required to achieve a useful resistance, but its resist-

ance is fairly linear in temperature.

25,26

Copper and nickel

thermometers are made by Thermometrics. The other

materials in Table 8.2 are used for cryogenic thermometry

and

will be discussed below in Section 8.1.5. New materi-

als,

such as niobium thin ﬁlms, are under development for

resistance thermometry.

Semiconductor Resistance Thermometers.

Thermistors

12,16

are small beads of semiconducting mate-

rial (metal oxides), the resistance of which depends on

temperature (Table 8.3). While electrons ﬂow freely in a

metal,

in a semiconductor, the electrons must ﬁrst be

excited into a conducting state; the electrons will thus ﬂow

more freely and the resistance will decrease as the temper-

ature increases. The term ‘‘negative temperature coefﬁ-

cient’’ or ‘‘NTC’’ is used. The resistance of a thermistor

decreases at a rate of about 4%/K; a thermistor is 10 times

more sensitive than a PRT. A thermistor differs from a

metal resistance thermometer in that its electrical resist-

ance is much more sensitive to temperature change, its

resistance decreases as temperature increases, and its

resistance is not linear in its temperature dependence

(see Figure 8.4). There exist thermistors that have positive

temperature

coefﬁcients of resistance, for which the resist-

ance increases with temperature as for metals; they are not

useful for thermometry, but are used for circuit protection

devices.

The Steinhart–Hart equation provides a good empirical

description for a thermistor (see Figure 8.4):

28,29

1=T ¼ A þ Bðln RÞþCðln RÞ

þ ð8:3Þ

where A, B,andC are empirical constants and where

higher-order terms of odd power may be required for a

broad temperature range or for high resolutio n. If a

linearized resistance is required, then linearizing cir-

cuits can be made

12,16

or bought. For example, t he YSI

Figure 8.4 The left ordinate gives the resistance as a function

of temperature T for a thermistor (solid line) which has a room

temperature resistance of about 4 kX, and for a platinum

resistance thermometer, PRT, (dotted line) which has a room

temperature resistance of about 100 X. Note that the scales

differ by a factor of 1000. The right ordinate gives the

thermoelectric voltage referenced to 273 K of a Type T

copper/constantan thermocouple (dashed line) as a function

of temperature.

Table 8.3 Properties of common semiconductor

thermometers

Type Materials Useful

Range

(K)

Sensitivity

(mK)

20 K 300 K

Semiconductor Thermistor 77–600 — 0.01

Germanium

1–30 0.5 —

Carbon 0.04–300 1 10

Carbon-in-glass 1–100 0.75 —

Diode Silicon

0.01–300 20 15

Gallium arsenide

0.01–300 15 100

Approximate resolution under typical conditions

Not for use in magnetic ﬁeld

MEASUREMENT OF TEMPERATURE 607MEASUREMENT OF TEMPERATURE 607

model 4800 linearizes thermistor output to 60.1 K from

273 K to 373 K ($75). (YSI and Betatherm are now

subdivisions of Measurement Specialties.) L inearizing

circuits for thermistors are also available from O mega

Engineering.

Typical thermistor resistances are 1 to 10 kX. Thermis-

tors can readily resolve a millikelvin and can be made to

resolve a microkelvin. Thermistors can be very small

(1 mm), and very stable with time and temperature

cycling.

Their disadvantage is that their resistance rap-

idly decreases with increasing temperature and thus their

usefulness decreases above about 373 K, but thermistors

designed for use up to 573 K are available (Measurement

Specialties, Adsem).

Interchangeable thermistors (matched as well as 60.1 K

over 50 K), ultrastable thermistors (changing <0.01 K in

100 months at 298 K), and thin surface-mount thermistors

are also available (Measurement Specialties 46000 series;

Thermometrics). Thermistor-based thermometers have

been developed for measurements in radio-frequency-ﬁeld

environments.

Measurement Systems For Resistance

Thermometry.

Complete resistance thermometry

systems are commercially available for lower resolution

(0.01 to 1 K) measurements (Anton Paar, Barnant, Hart

Scientiﬁc, Omega Engineering, Techne, Yokogawa, Newport

Instruments) and for higher resolution measurements

to 1 mK (Anton Paar, Guildline Instruments, Hart Scien-

tiﬁc, Instrulab), or to 0.25 mK (Hart Scientiﬁc). Neverthe-

less, it is useful to understand the considerations in

constructing the resistance-measuring equipment so

that one may take advantage of equipment one already

has, or make a thermometer for a special need, such

as for very high resolution in a particular temperature

range.

Resistance thermometry requires the measurement of

electrical resistance, usually by putting a known current

through the resistance thermometer and then measuring

the voltage developed across it. The ﬁrst consideration

for a resistance thermometer is the stability over time of

the resistor itself (RTD or thermistor). The stability

requirements depend on the resolution required and deter-

mine the price. As discussed above, thermistors and RTDs

have been developed that drift less than a few mK per year.

Mechanical stresses caused by mounting (e.g., use of hard

adhesives) can, however, cause signiﬁcant drifts in resist-

ance thermometers.

Thesecondconsiderationforaresistancethermome-

ter is its self-heating.

When a current ﬂows through a

resistor, there occurs Joule heating of I

R,whereI is the

current and R is the resistance. The current in the thermo-

metric resistor must be sufﬁciently low that the resist or

itself is not heated above the temperature of its surround-

ings. The dissipation factor of the resistor speciﬁes the

self-heating. For example, a typical dissipation factor for

athermistoris4lW/mK. This means that a current

resulting in 4 lW o f power will heat the thermistor by 1

mK. To obtain a resolution of 1 mK with a 4 k X

thermistor, the current is thus limited to 3 3 10

5

For a 25 X PRT, the current limit is about 3 mA for a

resolution of 1 mK.

The third consideration is the possibility of thermal emfs

in the thermometer circuit. These are the very effects that

make thermocouple thermometers possible (Section 8.1.2),

ut as extraneous voltages they can interfere with resistance

thermometry when the resistance is determined by measur-

ing a d.c. voltage. Thermal emfs may be evaluated by

reversing the current in the resistance circuit: the effect will

add for one current direction and subtract for the other. If

such effects are present, they may be corrected by averaging

the two readings or by using an a.c. resistance-measuring

method.

The fourth consideration is the effect of the resistor

leads. If the resistance of the lead wires enters into the

resistance measurement, then that resistance and its

temperature dependence can cause an error in the thermom-

etry. Lead effects can be minimized by using short wires

of large diameter. They can be eliminated by using four-

wire measurement techniques, in which two wires carry

the current through the resistor and two other wires are

used to measure the voltage across it.

If the voltage is

measured with a high-impedance device, then no signiﬁ-

cant current is carried in the voltage leads, no signiﬁcant

voltage drop occurs across those leads, and there is no lead

error.

The design of precision resistance-measuring circuits is

an art that changes as technology advances. We will not

discuss the details of such designs here, but refer the reader

to the literature

1,12,14,16

and to the manufacturers of

608 MEASUREMENT AND CONTROL OF TEMPERATURE608 MEASUREMENT AND CONTROL OF TEMPERATURE

resistance instruments (Guildline, Lake Shore Cryotronics,

Stanford Research; $2500–$8000), and of digital multi-

meters (Agilent, BK Precision, Keithley; $700–$4500).

Figure 8.5 shows a simple circuit that requires only a

digital

voltmeter, a battery, and a standard resistor for the

assembly of a resistance thermometer with a resolution of

1 mK. A 1.5 V silver oxide battery is a cheap, readily

available, and stable source of a 1.5 V voltage. The ther-

mometer resistance R

will indicate the temperature. For a

4kX thermistor, a standard resistor R

of about 50 kX is

required to keep the current below the level of self-heating.

The standard resistor must be stable with time and temper-

ature (even though it will remain at room temperature);

Vishay makes such stable resistors. R

equals V

/I, where

is the voltage drop across R

and I is the current through

. The current I is the same in R

, thus I equals V

where V

is the voltage drop across the standard resistor

and R

is its resistance. Thus:

¼ R

ðV

Þð8:4Þ

If R

is known, then only V

and V

need to be measured to

obtain R

. Actually, R

need not be known exactly, since it

is a constant. The ratio V

can be used as the thermo-

metric variable when the thermometer is calibrated, and

Equation (8.3) can be written with this ratio replacing R.I

order to measure temperature to 1 mK, the voltages across

the thermistor and resistor of 0.1 to 1 V need to be meas-

ured to six signiﬁcant ﬁgures; some voltmeters can directly

measure the ratio V

8.1.4 Semiconductor Thermometers

12,16

The thermistors discussed above are made from semicon-

ductors and in that sense, thermistors are semiconductor

(resistance) thermometers. Semiconducting elements such

as germanium are also used to make resistance thermom-

eters (see Section 8.1.5 below on cryogenic thermometry).

different category of semicondu ctor thermometers

uses a junction semiconductor (diode or transistor), and

take s as the thermometric property the temperature

dependence of the c urrent–voltage c haracteristics of the

junction itself. These devices produce currents or voltages

that are linear (within 61 K) in temperature. Typical sen-

sitivities are 1 lAK

1

and 10 mV K

1

, leading to typical

temperature resolutions of 0.1 to 1 K over a typical range

of 223–423 K.

The diodes or transistors can be com-

bined into more complex circuits that amplify and linea-

rize or even digitize the signals. Such integrated circuit

(IC) devices can re quire just a d.c. supply voltage to pro-

duce a temperature tran sducer. These IC thermometers are

cheap and simple and easily automated. They can be used

as the independent thermometers in the thermocouple

reference junction circuits discussed above,

or wher-

ever a meas urement of 61 K is required. They are not

yet capable of reﬁned temperature measurements. For

measurements of the output voltages or currents at th ese

resolutions, digital multimeters sufﬁce (Agilent, BK Pre-

cision, Keithley).

Integrated-circuit thermometers that use diodes include

the LM95233–LM95235 series and the LM35 (National

Semiconductor). Other diode thermometers that are widely

used in cryogenic thermometry will be discussed below in

Section 8.1.5. Integrated-circuit thermometers that use

ansistors include the AD590

and the AD7416–AD7418

series of 10-bit temperature-to-digital converters (Analog

Devices). Costs are only $1 to $7. Other suppliers are

Andigilog and Adsem. Data sheets for IC thermometers

are readily found on the Internet.

Some IC temperature sensors (e.g., AD22100, Analog

Devices) operate on the temperature dependence of the

resistance of a thin metal ﬁlm, but they are packaged in

Figure 8.5 A simple resistance thermometry circuit: a series

arrangement of a thermistor or a platinum resistance

thermometer (R

), a standard resistor (R

), and a battery (B).

MEASUREMENT OF TEMPERATURE 609MEASUREMENT OF TEMPERATURE 609

integrated circuits with voltage outputs that are nearly

linear in temperature (+22.5 mV K

1

) and that allow a

resolution of about 0.1 K. Thus they are ‘‘IC resistance

thermometers.’’

8.1.5 Temperatures Very Low: Cryogenic

Thermometry

Cryogenic temperatures can be taken as those below 90 K,

the boiling point of oxygen. The lowest temperatures so far

measured are in the 100 pK range.

Cryogenic experi-

ments require fastidious attention to the control of the ﬂow

of heat into the apparatus (cryostat), and there is a consid-

erable literature on these techniques.

35–41

Some of the

thermometers discussed above can be used at low temper-

atures, and some special methods have been developed for

use at low temperatures.

Thermocouples can be used at low temperatu res,

above about 10 K (for example, copper–constantan,

Table 8.1). The thermocouple leads must be thermally

anchored

at each stage of the cryostat in order to avoid

thermal emfs. See Section 8.1.2 for suppliers of thermo-

couples.

Resistance t hermometers are also valuable at

low temperatures:

platinum, nick el,

copper, ruthe-

nium oxide,

rhodium–iron, constantan, and manganin

(Table 8.2). Platinum resistance thermometers lose sen-

siti

vity below abou t 2 0 K. Rhodium–iron resistors are

fairly linear in the dependence of resistance on temper-

ature, but have some dependence of the resistance on

magnetic ﬁeld (magnetoresistance). Manganin and con-

stantan h ave very low thermal expansions and temper-

ature coefﬁcients of resistance at room temperature

(Table 8.5) and are often used to make stable resistors,

ut, at temperatures below about 200 K, their resistances

begin to decrease with temperature and then they can be

used as thermometer elements. Lake Shore Cryotronics

makes the Cernox (zirconium oxynitride) t hin-ﬁlm

resistance thermometer, which has low magnetoresist-

ance. Carbon resistors were traditional in cryogenic

thermometry, but they are unstable on temperature

cycling, exhibit magnetoresistance, and are now hard

to obtain. Carbon-in-glass resistors are more stable and

more available. There are semiconductor thermometers

available for low temperatures;

41,44

Table 8.3 gives

typical ranges and sensitivities for silicon diodes and

gallium arsenide diodes. Lake Shore Cryotronics, Sci-

entiﬁc Instruments, Inc., and Minco are sources of the

above thermometers for low temperatures.

In addition to the thermometers that are low-temperature

adaptations of thermometric devices used at higher tem-

peratures, there are thermometric devices that are used

only at low temperatures. The details of these technologies

are outside the scope of this chapter, but an introduction

will be provided, and the same will be done for high tem-

perature thermometers in the next section. The thermom-

eter types and their operating principles will be listed, with

references for further information.

Thermometers speciﬁc to cryogenic temperatures can

be divided into primary thermometers, which give

directly the thermodynamic temperature, and secondary

thermometers, which require calibration against a primary

thermometer.

Each technique requires its own particular

measurement system external to the cryostat. The primary

thermometers are based on several different principles:

(1) Gas thermometers use the pressure of a gas (helium)

under conditions such that the ideal gas law PV = nRT

is applicable. For known, ﬁxed volume V, number of

moles of gas n, and gas constant R, the measurement of

the pressure allows the temperature to be computed.

Gas thermometry requires careful design, but can be

used in the range 4.2 to 100 K.

2,46

Gas thermometry, as

well as vapor pressure and melting-curve thermometry

(below), requires means of measuring pressure.

36,40,41

(2) Vapor-pressure thermometers use the pressure of a

gas under conditions such that liquid and vapor

coexist.

40–42,46

For a given pressure, the temperature

is thermodynamically determined. Equations for these

vapor pressure curves are known and allow the calcu-

lation of the temperature. The useful temperature

range is determined by the gas chosen: oxygen (54–

90 K), nitrogen (63–84 K), neon (24–40 K), hydrogen

(14–20 K),

He and

He (0.3–5 K).

(3) Helium melting-curve thermometers use the pressure

of a gas under conditions such that solid and liquid

coexist.

36,41,42,46–48

Again, the temperature is deter-

mined by a pressure measurement. The useful range

is from 1 to 230 mK for

He.

(4) Noise thermometers are based on the temperature

dependence of the noise (ﬂuctuations) in the Brownian

610 MEASUREMENT AND CONTROL OF TEMPERATURE610 MEASUREMENT AND CONTROL OF TEMPERATURE

motion of conducting electrons, which results in a

noise in the voltage across a resistor.

1,36,41,49,50

The

noise in the voltage is measured to determine the tem-

perature, but these voltages are at the lV level and are

hard to measure. Noise thermometers have useful sig-

nals only below 1 K. Noise and nuclear orientation

thermometers (below) are not sold commercially, but

must be ‘‘home-made.’’

(5) Nuclear orientation thermometers depend on the occu-

pation of nuclear energy levels as a function of temper-

ature.

2,36,42

The energy levels are split by a magnetic

ﬁeld. At low temperatures, only the lowest state is

occupied. At high temperatures, all states are occu-

pied. At intermediate temperatures, the occupied

levels emit c-rays anisotropically, and the c-ray

emission rate parallel to the magnetic ﬁeld is a meas-

ure of temperature. The materials usually used are

Co and

Mn. The useful range is 0.003 to 0.03 K.

(6) Coulomb blockade thermometers use the temperature

dependence of the conductance of a tunnel junction

array in the range 20 mK to 30 K.

Secondary thermometers speciﬁc to low temperatures

are:

(1) Magnetic thermometers are based on the temperature

dependence of the paramagnetic susceptibility.

1,42

The

most widely used material is cerium magnesium nitrate

(CMN), used from a 10 mK to 4.2 K.

Magnetic and

NMR thermometers (below) must be home-made.

(2) NMR thermometers use the temperature dependence

of the nuclear magnetic resonance.

36,41

An NMR ther-

mometer made from platinum wire has been used from

0.5 mK to 30 K.

(3) Capacitance thermometers depend on the temperature

dependence of capacitors made of layered glass

and ceramic, and operate between 1.4 K and 290 K

(Lake Shore Cryogenics).

They are not reproducible

through heating/cooling cycles, but are useful as rela-

tive or control thermometers.

8.1.6 Temperatures Very High

As for low temperature thermometers, some ‘‘room tem-

perature’’ devices can also operate into the higher range

of temperatures. Thermocouples are used up to 2600 K

(Section 8.1.2; Table 8.1). Metal resistance thermometers

are

also of value: platinum is useful up to about 1300 K

(Section 8.1.3; Table 8.2).

Research

at high temperatures often requires a method

that does not involve contact between the probe and the

system of interest. Pyrometers rely on thermal radiation

(which includes ultraviolet, visible, and infrared wave-

lengths, 7 to 20 lm) and operate in the range 373 K to

4000 K.

3,53

For example, astronomers use thermal radia-

tion to measure the temperatures of bodies such as the Sun

(6000 K). The total radiation intensity per unit surface

area, per unit time, of a body is M(T) ¼ e/U T

,whereU

is the known Stefan–Boltzmann constant and e is the emis-

sivity of the body.

If the radiating body is a ‘‘blackbody,’’

then e ¼ 1 and the pyrometer is a primary thermometer.

The emissivity e depends on wavelength for nonblackbod-

ies. In practice, the conditions needed for primary, black-

body pyrometry are rarely met (or needed) outside of

standards laboratories.

A practical pyrometer requires an optical detector to

collect the radiation, together with a detector/transducer

system to convert the radiation intensity to an electrical

signal and/or read-out.

1,54

Some devices use ﬁber optics to

collect the radiation and delivery it to the detector. Ther-

mal detectors convert the collected radiation into heat that

can then be measured by thermocouples, resistance ther-

mometers (bolometers), or pyroelectric devices.

Photon

detectors (photovoltaic, photoemissive, or photoconduc-

tive) convert the radiation directly into an electrical signal.

Pyrometers with 1% accuracy can be constructed in the

laboratory,

but there are good commercial products

available and making one’s own pyrometer is not likely

to be necessary. Commercial pyrometers of the ‘‘broad-

band’’ type operate over a span of wavelengths (0.3 to

20 lm),usethetotalemissivity,andareusedupto1300K

with 1% accuracy (Omega Engineering). Narrow-band

pyrometers, such as infrared pyrometers, operate over a

wav elength of about 1 lm,andcanmeasureupto3300K

with 0.2 to 2% accuracy. The Omega Engineering web-

site has a lengthy discussion of the design and calibration

of radiation thermometers. The costs, depending on the

resolution and on the level of the instrumentation, range

from $100 to $5000 (Omega Engineering, Land Infrared).

Sears sells a Craftsman hand-held infrared thermometer

for the range 255 to 800 K at 2% accuracy for $80.

MEASUREMENT OF TEMPERATURE 611MEASUREMENT OF TEMPERATURE 611

8.1.7 New, Evolving, and Specialized

Thermometry

Fluorescence (or phosphor) thermometry uses the temper-

ature dependence of ﬂuorescent intensity: a ‘‘reporter’’

molecule that will ﬂuoresce is embedded in the system

of interest; it is excited by light (usually a laser), and then

the ‘‘after-glow’’ intensity is measured to determine the

temperature. This technique is useful from 200 to 3000 K,

at 5% accuracy. Such devices are not available commer-

cially, but can be of value in the laboratory.

3,56

For exam-

ple, ﬂuorescence thermometry has been used to measure

temperatures on nanoscale devices.

The temperature dependence of the infrared absorption

spectrum of a molecule (e.g., H

O) can be used to measure

temperature, so-called ‘‘molecular thermometers.’’

This

is another method of thermometry that can be used at the

nanoscale.

8.1.8 Comparison of Main Categories of

Thermometers

Liquid-in-glass thermometers are cheap and easy to use,

but are limited in range, in precision (0.01 K), and in

means of automation. Thermocouples are cheap, are useful

over a wide range, have good precision (mK), and can be

automated; however, spurious voltages can cause prob-

lems. Platinum resistance thermometers offer broad range

and very good precision (0.1 mK), at higher cost. Thermis-

tors allow extremely high precision (1 lK), but for limited

range in temperature. Resistance thermometers are readily

automated. Integrated circuit thermometers offer simple,

easily automated temperature measurement when a low

resolution of 0.1 to 1 K is all that is required.

8.1.9 Thermometer Calibration

Ideally, the working scientist would like to have temper-

ature measurements that are on the fundamental, thermo-

dynamic temperature scale. Primary measurements on the

thermodynamic scale are usually made only in standards

laboratories with very expensive and very complex ther-

mometers, such as ideal-gas thermometers. The exceptions

are cryogenics laboratories, where primary thermometers

are often integrated into the apparatus. The thermody-

namic temperature is generally conveyed to the working

laboratory by means of the International Temperature

Scale, which was last deﬁned in 1990 (ITS-90). The ITS

approximates the thermodynamic temperature scale as

closely as is technically and practically possible by deﬁn-

ing the temperatures for a set of ﬁxed points and by spec-

ifying the means for interpolation between those ﬁxed

points. Fixed points are temperatures that can always be

reproduced, and are usually the temperatures at which

phase transitions occur. The ITS is maintained in the

United States at the National Institute of Standards and

Technology (NIST).

Differences between the thermody-

namic temperature scale and ITS-90 are 0.020 K at 373 K

and 0.150 K at 903 K.

Other laboratories may send a thermometer (usually a

platinum resistance thermometer) to NIST for calibration

on the ITS-90, and then use that working standard to cal-

ibrate still other thermometers. Such a calibration can cost

$1000 or more. Most companies that make and sell ther-

mometers maintain such secondary standards, with which

they can perform calibrations ‘‘traceable to the National

Institute of Standards and Technology’’ (Guildline, Hart

Scientiﬁc).

For most scientiﬁc laboratories, the best procedure is to

acquire a thermometer calibrated to the accuracy needed

for that laboratory, either by purchasing a calibrated ther-

mometer or by sending a thermometer to a calibration

laboratory (NIST or a commercial service). Once cali-

brated, that ‘‘working standard’’ thermometer should be

regularly checked for shifts or drifts in its calibration by

measuring a ﬁxed point. The most reliable and available

such ﬁxed point is the triple point of water (where ice,

liquid water, and water vapor coexist), which can be re-

produced to better than 1 mK. Water-triple-point cells are

commercially available (Hart), but triple-point measure-

ments are difﬁcult. It is easier to use the ice point, the

freezing point of water, as a ﬁxed point. The temperature

at which ice and water coexist at one atmosphere of pres-

sure is 273.15 K and can be reproduced in most laborato-

ries to 0.002 K. First, distilled water is degassed by several

cycles of freezing it, evacuating the gas above it, and then

remelting it. The ice point can then be achieved by mixing

distilled, degassed water with small pieces of ice made

from distilled, degassed water, and then continuously

612 MEASUREMENT AND CONTROL OF TEMPERATURE612 MEASUREMENT AND CONTROL OF TEMPERATURE

stirring that slurry while the temperature measurement is

made on the thermometer immersed in the slurry.

A variety of thermometric standard reference materials,

are sold by NIST including calibrated thermometers and

ﬁxed-point cells, covering the range from 14 to 2040 K.

Many ﬁxed-point cells are available commercially (Hart

Scientiﬁc).

Other thermometers can be compared to the working

standard by placing both in a temperature-controlled envi-

ronment (see Section 8.2), close together and under the

same

conditions at which the working standard was

calibrated. The temperature is then varied over the range

of interest, and measurements are made on the working

standard and on the thermometer under calibration. The

temperature is taken from the working standard, and an

appropriate equation (see above) is ﬁtted to the thermo-

metric property of the second thermometer as a function of

temperature. Keep in mind E. B. Wilson’s admonition

that,

‘‘An experimenter of experience would as soon

use calibrations carried out by others as he [or she] would

use a stranger’s toothbrush.’’

8.2 THE CONTROL OF

TEMPERATURE

We will ﬁrst consider cases for which the temperature is

to be controlled at a single ﬁxed value. Usually such

cases require only rough control, to a degree or two.

For example, we may want a trap in a vacuum system

that will condense one vapor, but not others. Precise con-

trol at ﬁxed temperatures would be required for ther-

mometer calibrations using ﬁxed points (see Section

1.9). We will also consider the control of temperature

ver a range within which any value may be selected. We

will discuss how to ac hieve such control at various levels

of precision.

8.2.1 Temperature Control at

Fixed Temperatures

Control at ﬁxed tempera tures is mo st easily achieved at

points of phase equilibri um.

1,2

For example, the point at

which the solid, liquid, and gas phases of a pure substance

coexist(thetriplepoint)hasacompletelydetermined

pressure and a completely determined temperature. Triple

points thus make excellent temperature reference

points, with accuracies of about 1 mK. As discussed in

Section 8.1.9, several triple points are used to deﬁne

e International Temperature Scale. They are not appro-

priate for temperature control in most laboratories, how-

ever, since triple points can be difﬁcult to achieve and to

maintain.

The temperatures of vaporization, sublimation, and

melting of pure substances are fully determined when

the pressure is ﬁxed. These phase transitions are readily

achieved and maintained, and are therefore very useful for

temperature control. The eutectic temperature, the temper-

ature of a two-component mixture at which a liquid sol-

ution and both pure solids coexist at a ﬁxed pressure, can

also serve as a temperature control point. For all these

phase equilibria, the accuracy and stability of the temper-

ature depend on the accuracy and stability of the pressure,

and on the purity of the materials used.

Melting-point baths are easily made and are therefore in

common use. The making of an ice-point bath is discussed

in Section 8.1.9. Melting-point baths using organic liquids

aqueous solutions, with temperatures ranging from 113

to 286 K, can be prepared.

62–64

These slush baths are made

by cooling the organic liquid with either dry ice or liquid

nitrogen until the bath liquid begins to freeze and a slush of

solid and liquid is formed. The slush should be contained

in a Dewar ﬂask and frequently stirred. Care must be taken

in using liquid nitrogen, which can condense air and pos-

sibly create explosive mixtures.

Some useful phase-transition baths are given in Table

8.4. Coyne gives a table of melting-points for aqueous

solutions.

8.2.2 Temperature Control at

Variable Temperatures

Control at variable temperatures requires that the temper-

ature be measured by a control thermometer and compared

with the desired temperature (the set point T

). The differ-

ence in temperature from the set point indicates whether

the system needs to be heated or cooled. If the control

thermometer provides an electrical signal, then that signal

can be used to drive a heater or a cooler, and thus to control

the temperature.

CONTROL OF TEMPERATURE 613CONTROL OF TEMPERATURE 613

Figure 8.6 shows the main elements of such a thermo-

stat. The thermostat will include the control thermometer,

from which an electrical signal goes to the signal condi-

tioner, where the signal is compared with the signal

expected at the set point, conditioned further in ways to

be described below, and then ampliﬁed to drive the thermo-

stat heater or cooler. Although it is possible to control a

cooling device such as Peltier junction,

it is usually eas-

ier to control a heating element. Thus, the thermostat may

include a cooler operating at a constant power to cool the

system to a temperature below the set point, from which

the set point is reached by means of the control heater. At

higher temperatures, the thermostat may require an auxil-

iary heater, operating at constant power, to raise the tem-

perature to near the set point, from which temperature the

control heater achieves the set point. The thermostat will

also include a measurement thermometer, independent of

the control thermometer.

The thermal circuit may be modeled in analogy to an

electrical circuit.

67–71

The ﬂow of heat is analogous to a

ﬂow of electrical current. There is associated with each

element a thermal resistance, R. For a wall of thickness

d, area A, and thermal conductivity k, R is given by:

R ¼ d = Ak ð 8 :5Þ

Table 8.5 gives values of the thermal conductivity for var-

ious

materials used in thermostat construction. In analogy

with Ohm’s law for current ﬂow, the heat ﬂow J induced by

a temperature difference DT across the wall is:

J ¼ DT=R ð8:6Þ

The thermal capacitance C of a thermostat element is its

speciﬁc heat, values of which are also given in Table 8.5.

The thermal

time constant for an element is RC.

The analysis of such thermal circuits can, in principle, be

made in the same way as that for electrical circuits.

68,69,71

If the required level of temperature control is not high

(60.1 K or more), then the controller can simply turn the

control heater on or off, depending on whether the thermo-

stat is too hot or too cold. This on–off control will, of

course, produce large oscillations around the set point.

For better temperature control, the controller must have

a more sophisticated feedback loop (see Section

6.7.9).

12,69,71,72

First, the thermostat will require a constant ‘‘back-

ground’’ heating. Most of the background heating should

be done by the auxiliary heater rather than by the control

heater, but the control heater could have a level P

background power. Second, the controller will provide to

the heater a power P

proportional to the deviation from

the desired set point:

¼ GðT

 TÞð8:7Þ

Table 8.4 Fixed temperatures from phase transitions

Temperature System

Phase

Transition

Precision

(K)

(K) (°C)

356 183 67% tin, 33% lead Eutectic 2

273 100.0 Water Vaporization 0.1

302.92 29.77 Gallium Melting 0.05

286 13 p-Xylene Melting 1

273 0.0 Water Melting 0.002

263 10 Diethylene glycol Melting 1

252 21 23% sodium

chloride/77% water

Eutectic 2

243 30 Bromobenzene Melting 1

232 41 Acetonitrile Melting 1

221 52 Benzyl acetate Melting 1

210 63 Chloroform Melting 1

200 73 Trichloroethylene Melting 1

195 78 Carbon dioxide Sublimation 1

189 84 Ethyl acetate Melting 1

182 91 Heptane Melting 1

175 98 Methanol Melting 1

166 107 Isooctane Melting 1

157 116 Ethanol Melting 1

147 126 Methylcyclohexane Melting 1

142 131 Pentane Melting 1

132 141 1,5-Hexadiene Melting 1

113 160 Isopentane Melting 1

77 196 Nitrogen Vaporization 1

See references 1,21,62,63.

Percentages are given as weight per cent.

The precision/accuracy is that to be expected without

extraordinary attention to purity and pressure control.

614 MEASUREMENT AND CONTROL OF TEMPERATURE614 MEASUREMENT AND CONTROL OF TEMPERATURE

Table 8.5 Properties of thermostat materials at 298 K

Conductor Thermal Conductivity

(W cm

1

)

Speciﬁc Heat

(J g

1

)

Density

(g cm

3

)

Emissivity (polished)

Aluminum 2.4 0.90 2.7 0.05

Brass 1.2 0.38 8.5 0.03

Constantan 0.22 0.4 8 —

Copper 4.0 0.39 8.9 0.02

Manganin 0.21 0.41 8.5 —

Nickel 0.91 0.44 8.9 0.05

Platinum 0.69 0.13 21.5 0.04

Stainless steel 0.14 0.4 7.8 0.1

Insulator Thermal Conductivity

(W cm

1

)

Speciﬁc Heat

(J g

1

)

Density

(g cm

3

)

Useful Temperature

Range (K)

Air (1 atm) 0.00025 1.0 0.0012 —

Alumina 0.06

1.0 4.0 3 to 2200

Bakelite 0.0023 1.6 1.3 3 to 390

Fiberglass 0.00002–0.004 0.8 0.06 3 to 1100

Macor 0.0017 0.75 2.5 3 to 1300

Magnesia 0.07 1.2 3.6 3 to 2700

Nylon 0.0024 1.7 1.1 3 to 420

Pyrex 0.001 0.8 2.2 3 to 1100

Styrofoam 0.00003–0.0003 1.3 0.05 3 to 350

Teﬂon TFE 0.004 1.0 2.1 3 to 350

At about 1200 °C.

Figure 8.6 The elements of a thermostat. The controller uses the signal from the

control thermometer to drive the control heater. The thermostat can also include an

auxiliary heater (H), a cooling element (C),and a measurement thermometer (T).

CONTROL OF TEMPERATURE 615CONTROL OF TEMPERATURE 615

where G is the proportional gain and T is the current

temperature. As G is increased, a critical value will be

reached at which temperature oscillations will occur; i.e.,

the control will revert to the on–off mode. The total heater

power P is then:

P ¼ P

þ GðT

 TÞð8:8Þ

Third, the need for background power is likely to

change, since the heat losses to the environment will

change as the temperature of the thermostat is varied and

as the temperature of the environment changes. The con-

troller can adjust for this changing requirement by provid-

ing to the heater a power related to the integral over time of

the deviation from the set point. The total heater power

then becomes:

P ¼ P

þ GðT

 TÞþR

ðT

 TÞdt ð8:9Þ

This integral control is also called reset control, and R is the

reset constant. The combination of proportional control and

integral control is called two-term control or PI control.

Sometimes another control term, proportional to the

derivative of the temperature with time, is included:

P ¼ P

þ GðT

 TÞþR

ðT

 TÞdt þ DðdT=dtÞ

ð8:10Þ

The derivative term alters the response when there are fast

changes in temperature. Control using proportional, inte-

gral, and derivative terms is called three-term control or

PID control. Laboratory thermostats rarely change tem-

perature rapidly, and derivative control is not usually needed.

Detailed analysis of a thermostat and its controller is

rarely possible, because the parameters R and C are not

well known, because the thermal resistances at interfaces

(e.g., between the heater and the thermostat) are very

hard to assess, and because effects due to radiation and

convection enter. Nonetheless, the study of model circuits

has led to some generalizations about thermostat design

that are of practical use:

68,69,72

(1) Heat distribution should be maximized. This is done

by using materials of high conductivity and by distrib-

uting the heaters. For ﬂuid baths (see below), the heat

is distributed by stirring.

(2) The bath or block should have a long time constant

with respect to the exchange of heat with the environ-

ment. Conductive and convective losses are reduced by

using insulating materials or by enclosing the thermo-

stat in a vacuum. Radiation can be reduced by using

reﬂective materials.

(3) The heater should have a short time constant for trans-

mitting heat to the bath. Therefore it should be of high-

conductivity material and should be in good contact

with the block or bath ﬂuid.

(4) The control thermometer should have a very short time

constant for response to the bath or block temperature.

Therefore it should be small and should be in good

contact with the block or ﬂuid.

(5) The proportional gain should be set at about half the

value at which oscillations begin.

(6) The reset constant should equal the thermal resistance

between the thermostat bath or block and the environ-

ment, multiplied by the thermal capacitance of the bath

or block.

The control loops implementing Equations (8.9) or

(8.10) can be done by either analog

73–76

or digital cir-

cuits.

66,77–80

The thermometers discussed in Section 8.1

are inherently analog, but most are easily digitized (i.e.,

digital voltmeter that reads a resistance or a correspond-

ing voltage). It is advantageous to have thermometers that

produce outputs linear in temperature for control circuits.

Analog Devices has a number of linearized IC thermom-

eters and IC controllers that operate at levels of 60.1

to 61 K. For example, the Analog Devices TMP01 is a

sensor and comparator with ‘‘a control signal from one of

two outputs when the device is either above or below a

speciﬁc temperature range’’ (Analog Devices webpage).

Other complete temperature-control instruments that oper-

ate on signals from analog thermometers are commercially

av ailable. Simple on–off or proportional controllers designed

to control to 0.1 to 2.0 K cost $40–$1000 (Minco, Omega

Engineering, Cole-Parmer). Instruments are av ailable with

proportional control (Omega Engineering, Cole-Parmer) or

with full PID control: Lake Shore Cryotronics, 61mK;

Wavelength Electronics, 63 mK; both around $2000.

For digital control circuits, the analog thermometer sig-

nal is converted to a digital signal, operated on by a com-

puter program, then converted back to an analog heater

616 MEASUREMENT AND CONTROL OF TEMPERATURE616 MEASUREMENT AND CONTROL OF TEMPERATURE

power.

66,78–80

A digital control system can treat thermom-

eter output in the software, by using ﬁts to Equations

(8.1)–(8.3), rather than by using hardware linearization.

Such

a digital controller is especially convenient as a part

of a computerized data-collection system, to change the

temperature at programmed time or temperature intervals.

Commercial digital controllers include those from Wave-

length Electronics, and some that are intended for cryo-

genic temperatures, but that are useful to about 450 K, with

resolutions as good as 61 mK (Scientiﬁc Instruments,

Inc.; Lake Shore Cryotronics).

Stirred Liquid Baths. Stirred liquid baths, in which

the temperature of a working liquid is controlled, are the

most common type of thermostat because they are simple,

versatile, and inexpensive. Three kinds of liquid bath devices

are available commerically. First, there are controller–

stirrer devices that can be inserted into tanks of water to

control within 610 to 100 mK, from room temperature to

363 K, for a few hundred dollars (Omega Engineering,

VWR, Cole-Parmer). Second, there are complete bath sys-

tems that are designed to circulate a ﬂuid to an external

experimental assembly; the control is 60.01 to 0.1 K and

they can have cooling capacity, so that a typical range is 253

to 473 K, and some are programmable through an RS-232

interface (Neslab, Brookﬁeld, Thermo Fisher Scientiﬁc,

Lauda, Hart, J-Kem Scientiﬁc). Third, there are complete

bath systems that are designed for an experimental as-

sembly to be inserted within their enclosed tanks. The

suppliers of the circulating baths also make the enclosed

baths. Hart Scientiﬁc and Guildline make precision

enclosed ﬂuid baths stable at levels of 60.7 mK to 61 mK.

Often the researcher decides to construct a ﬂuid bath: to

save money, to achieve better control, or to provide a par-

ticular conﬁguration. In fact, there is no commercial bath

with control to 61 mK or better and with a port through

which the experimenter can view the experiment. If you

need such a bath (for example, for phase-separation stud-

ies), you must make it.

Figure 8.7 shows a typical ﬂuid

bath, designed to control to 61 mK or better. The bath

vessel can be any large container; 36 L cylindrical Pyrex

jars are available that can be used over a large temperature

range and that are transparent. Radiative heat losses can be

reduced with a layer of aluminum foil, or reﬂective plastic

(such as is used for camping blankets) placed next to the

vessel. Fiberglass batting, as is used to insulate buildings,

is easily wrapped around the vessel to insulate it. Styro-

foam sheets about 3 in. thick can be cut to ﬁt around the

vessel. Styrofoam can also be formed in situ if a mold is

placed around the vessel (Read Plastics, 800-638-6651).

The bath is supported on three sections of glass or plastic

tubing that are ﬁlled with insulation. Much of the heat loss

or gain of the bath is through its top, so it is important that

the top be well insulated. An insulated lid, cut to allow

the various components to be inserted, is one solution.

Figure 8.7 shows instead an insulating layer of hollow

3/4

in. O.D. polypropylene balls; the balls insulate while

allowing easy access to the bath, but can be used only

below about 400 K (Cole-Parmer, VWR).

The choice of a liquid for the bath depends on temper-

ature range, cost, and convenience. Table 8.6 gives the

properties

of some common bath liquids. Sometimes an

oil will be preferred because the electrical conductivity

of aqueous solutions makes electrical connections within

the bath awkward and unsafe. Silicone oils can be ordered

with a rust inhibitor added, but those inhibitors turn brown

and make the bath opaque.

The control heater, as discussed above, should be made

from material of high thermal conductivity. A commercial

heater with a copper sheath and with a power of about 150

to 250 W is satisfactory (Omega Engineering). An ordi-

nary 60 W light bulb is an easy and cheap control heater:

a power cord is soldered to the bulb and the connections

electrically insulated with a silicone adhesive sealant. The

background heater need not respond quickly, and can

therefore be a glass or stainless-steel immersion heater

(Omega Engineering); its power will depend on the tem-

perature range, the heat capacity of the bath, and the heat

losses of the bath. The background heater can be driven by

a manually variable transformer (Variac).

There are several ways of providing a cooling element to

the bath. Figure 8.7 shows a coil of copper tubing, through

ich cold liquid is circulated from an external source. That

source can be a commercial refrigerated bath or circulating

chiller (Neslab, Cole-Parmer). Cold liquid can also be

obtained by inserting a commercial immersion cooler into

a container of ﬂuid (e.g., diethylene glycol) and pumping

that liquid through the bath cooling coil (Neslab, Thermo

Fisher, Cole-Parmer). An immersion cooler could be

inserted directly into the stirred liquid bath, but these coolers

CONTROL OF TEMPERATURE 617CONTROL OF TEMPERATURE 617

Figure 8.7 A stirred liquid thermostat. The bath elements are: C, a coil through which

cold liquid ﬂows; H

, a commercial blade heater serving as a background heater; H

60 W light bulb serving as the control heater; I, styrofoam insulation; J, polypropylene

balls serving as the top insulation; L, the bath liquid; P, plastic pipes supporting the

vessel; S, the stirrer; V, a Pyrex jar serving as the bath vessel; and W, the workspace.

The control thermometer and the measurement thermometer are not shown.

618 MEASUREMENT AND CONTROL OF TEMPERATURE618 MEASUREMENT AND CONTROL OF TEMPERATURE

are not designed to work at elevated temperatures and such a

practice will eventually damage them.

The bath stirrer is an ordinary laboratory stirrer of 1/20

or 1/10 hp. The shaft is of stainless steel to reduce heat

transfer from the motor. Stirrers can transmit electrical

noise, which can interfere with the controller and ther-

mometers, so it may be necessary to provide the stirrer

with an electrical shield.

The conﬁguration of the bath elements is crucial. Figure

8.7 shows the heaters placed near the stirrers, so that the

heat

is readily distributed. The cooling coil is itself some-

what distributed. The point is to arrange the elements so

that the stirrer will prevent temperature gradients.

Safety precautions are in order. The possibility that

the bath will overheat can be precluded by installing a

device that will turn off all power if a set temperature is

exceeded. Omega Engineering, Cole-Parmer, Guildline, and

Instruments for Research and Industry sell such devices for

$85–$300, but cheaper (<$10) thermal switches are avail-

able from Newark Electronics. A pan made of sheet metal or

plywood, sealed at the joints and placed under the bath, will

contain the bath liquid should the vessel break. Above 200

K, the bath liquids may fume and require the installation of

a fume hood. Of course, one should never put hands or tools

into a ﬂuid bath when any of its components are powered.

Enclosure Thermostats.

Enclosure thermostats

control the temperature of an experimental block or stage

held in an environment of vacuum or of stagnant gas. Such

thermostats are used rather than stirred liquid thermostats if

state-of-the-art temperature control (6 0.01 mK) is required,

if the temperature range needed is above or below that of

available bath liquids, or if the experimental apparatus can-

not be immersed in a stirred liquid. For example, optical

Table 8.6 Properties of bath liquids at 298 K

Liquid Useful Temperature

Range

Viscosity

(cP)

Thermal

Conductivity

(W cm

1

)

Density

(g cm

3

)

Speciﬁc Heat

(J g

1

)

Price

($/L)

°C (K)

Silicone oils:

200 40 to 180 233 to 450 1 0.001 0.96 1.7 20

510 50 to 180 223 to 450 50 0.001 0.62 1.7 20

550 40 to 200 233 to 470 100 0.001 1.1 1.7 20

710 10 to 230 263 to 500 500 0.001 1.1 1.7 50

Hydrocarbon oils:

74971 25 to 160 298 to 430 ~10 ~0.001 0.8 2 20

74972 25 to 150 298 to 420 ~10 ~0.001 0.8 2 20

74974 25 to 110 298 to 380 ~10 ~0.001 0.8 2 20

Water 5 to 90 278 to 360 1.0 0.0060 1.0 4.2 0

Ethylene glycol:

100% 11 to 180 260 to 450 32 0.0026 1.1 2.4 10

50 wt% water 33 to 105 240 to 380 3.7 — 1.1 3.4 5

Ethanol:

100% 117 to 60 160 to 330 1.0 0.0017 0.79 2.5 4

50 wt% water 30 to 75 240 to 350 2.4 — 0.92 4.0 2

Methanol:

100% 90 to 60 180 to 330 0.55 0.0014 0.80 2.6 5

50 wt% water 50 to 65 220 to 340 1.8 — 0.92 3.6 2

Dow Corning Corp

Precision Scientiﬁc, Inc.

CONTROL OF TEMPERATURE 619CONTROL OF TEMPERATURE 619

experiments are difﬁcult in stirred baths because bubbles

and debris get into the optical path. For many experiments,

the vibrations that are inevitable in a stirred bath cannot be

tolerated. Much of the work on enclosure thermostats is in

the literature on cryogenics (‘‘cryostats’’)

35,36,39,40

and on

calorimetry.

83–85

In an enclosure thermostat, sometimes called an ‘‘onion’’

thermostat, the temperature is controlled by means of con-

centric layers that are in sequence thermally insulating,

thermally conducting, and thermally controlled.

75,86

The

insulating layers are usually vacuum regions. The conduct-

ing layers are made of metal. A controlled (conducting)

layer has a heater and a thermometer, connected to a con-

troller (see above). The innermost conducting layer is the

experimental stage or block. The result is that the alternat-

ing layers of conductors and insulators attenuate thermal

gradients and ﬂuctuations, making them smaller and smaller

as the central experimental stage is neared. There are two

design concepts for such a thermostat. The ﬁrst maximizes

the heat capacities of the layers in order to reduce the ther-

mal gradients.

The disadvantage of this approach is that

the time constants are very long, and the changes in temper-

ature are very slow. The second design concept maximizes

the number of stages in order to attenuate gradients; this

approach has the advantage of short time constants, but is

limited by practical size considerations.

The only commercially available enclosure thermostats

are cryostats for low-temperature regimes,

so it is useful

to discuss designs for higher temperatures and for more

general purposes. Figure 8.8 shows a conﬁguration for a

simple

enclosure that will control temperature to 1 mK or

better. There are four conducting layers and three insulat-

ing layers (all vacuum) in this thermostat. This thermostat

can operate only at temperatures above that of its outer-

most layer. Thus that outer layer must be provided with a

means of achieving the required temperature, usually

about 0.5 K below the temperature at the experimental

stage. For temperatures between room temperature and

about 20 K above room temperature, the outer layer can

be left at room temperature. For temperatures below room

temperature, the outer layer can be immersed in a cold bath

or can have copper tubing soldered around it, through

which cold liquid can be circulated. For example, to oper-

ate between 77 and 127 K, the vacuum container could be

immersed in liquid nitrogen. Likewise, for temperatures

more than 20 K above room temperature, a hot bath or

hot circulating liquid can be used.

For some designs, it may be possible to use thermo-

electric coolers (TEC or Peltier devices)

66,77,79

or minia-

ture refrigerators to provide cooling below ambient. Recall

that for a Peltier device, a current through metal junctions

induces a temperature difference. A TEC device has the

advantage that it can be either a heater or a cooler,

Figure 8.8 A simple enclosure thermostat. The thermostat is

made of seven layers. The outer layer (L

) is a vacuum

container made of thermally conducting metal and held at a

temperature slightly below the desired set point. The lid is

sealed with the O-ring seal at O, and the can is evacuated by

means of valve V. Layers L

, and L

are insulating vacuum

layers. Layer L

is a thermally conducting controlled layer,

wound with heater H and ﬁtted with a control thermometer

(not shown). Layer L

is a conducting layer. L

is the experimental

stage or block. Supports (S) are made of an insulator such

as nylon. Wires (W) to the thermometers, heaters, and

experimental transducers enter through the feedthrough (F)

and are thermally anchored on each successive stage.

620 MEASUREMENT AND CONTROL OF TEMPERATURE620 MEASUREMENT AND CONTROL OF TEMPERATURE

depending on the direction of the current through it; it has

the disadvantage that in the cooling mode, the heat

removed from the system must be disposed of by some

kind of heat exchanger (ﬂowing air or water). One TEC

can pump up to 125 W, and they can be cascaded for

increased cooling. Devices cost $10 to $100 (Marlow, Mel-

cor, Ferro Tec). The Ferro Tec webpage has an introduc-

tion and design guide. Miniature refrigerators operate on

the principle of Joule–Thomson cooling. They require

ﬂowing gas as the heat exchanger and, depending on the

choice of gas, can operate at temperatures between 83 and

303 K, with a cooling capacity of 0.5 to 10 W/cm

per

stage and control of 60.1 K (MMR Technologies, starting

at $1690).

Of course, the choice of solders, insulating materials,

etc., will depend on the temperature range of operation.

Copper is the best choice for conducting layers (see Table

8.5), but aluminum is not bad and is much lighter. Isolation

between

stages can be further increased if radiative losses

are reduced by having conducting stages of low emissivity

(Table 8.5).

While Figure 8.8 shows an evacuated thermostat, it is

often

convenient for the insulating layer to be air. In fact,

the thermal conductivity of air is not signiﬁcantly

decreased as the pressure decreases until the pressure rea-

ches about 10

4

torr. Thus air at 1 atm is just as good an

insulator as an evacuated space, unless low pressures can

be achieved. At low temperatures, a disadvantage of air is

that water can condense from it, but the air can be dried or

dry nitrogen can be used. A disadvantage of a vacuum is

that vibrations from the vacuum pump are transmitted to

the thermostat.

The heater in Figure 8.8 is a wire, wound symmetrically

and

biﬁlarly (to reduce inductive effects) on the outside of

the controlled layer. The heater is shown as simply glued to

the outside of the layer, but better thermal contact is

obtained if the wire is glued into grooves machined into

the metal. Manganin wire is good for heaters because it has

a high electrical resistivity that does not change signiﬁ-

cantly with temperature (MWS Wire Industries). Foil heat-

ers that can be glued on where needed are often useful for

the end plates (Omega Engineering, Minco). It is important

that the heater power be distributed as evenly as possible

over the controlled layer. The total heater power must be

calculated from the estimated heat losses for the thermo-

stat. A thermostat like that in Figure 8.8, 18 cm high and 18

in diameter and operating between 273 and 313 K,

requires a heater of 315 X, operated at 0–15 V.

Since the heat distribution is entirely passive, attention

must be given to all unsymmetrical heat losses that could

lead to temperature gradients. All support pieces connecting

one layer to another must be of an insulating material (such

as nylon or glass) and should present a minimum cross-

section for heat transfer. All wires entering the thermostat

should be of the smallest possible diameter. All wires must

be thermally anchored at each stage: they must be wrapped

around the stage in good thermal contact with it, so that they

will come to the temperature of that stage. Since windows in

a thermostat easily cause gradients, they must be kept small

and measures taken to compensate for losses through them.

Cryostats or dewars for low temperatures are often

designed and constructed by scientists,

36,39

but are also

commercially available (Cryomech, Advanced Research

Systems, Janis).

Cited References

1. T. J. Quinn, Temperature, 2nd edn., Academic Press,

New York, 1990.

2. J. F. Schooley, Thermometry, CRC Press, Inc., Boca Raton,

FL, 1986.

3. P. R. N. Childs, J. R. Greenwood, and C. A. Long, Rev. Sci.

Instrum., 71, 2959–2978, 2000.

4. J. Fischer and B. Fellmuth, Rep. Prog. Phys., 68, 1043–

1094, 2005.

5. J. A. Wise, Liquid-in-Glass Thermometry, US Government

Printing Ofﬁce, Washington, DC, 1976.

6. Handbook of Temperature Measurement: Resistance and

Liquid-in-Glass Thermometry, Vol. 2, R. E. Bentley (Ed.),

Springer, Singapore, 1998.

7. D. D. Pollack, Thermocouples: Theory and Properties,

Chemical Rubber Co., Boca Raton, FL, 1991.

8. T. W. Kerlin, Practical Thermocouple Thermometry,

Instrument Society of America, Research Triangle Park,

NC, 1999.

9. Manual on the Use of Thermocouples in Temperature

Measurement, 4th edn., American Society for Testing

Materials International, West Conshohocken, PA, 1993.

10. Handbook of Temperature Measurement: Theory and

Practice of Thermometric Thermometry, Vol. 3,

R. E. Bentley (Ed.), Springer, Singapore, 1998.

REFERENCES 621

11. D. D. Pollack, Thermoelectricity: Theory, Thermometry,

Tool; ASTM Special Publication 852, American Society for

Testing and Materials, Philadelphia, 1985.

12. T. D. McGee, Principles and Methods of Temperature

Measurement, John Wiley & Sons, Inc., New York, 1988.

13. T. J. Seebeck, Ab. K. Akad. Wiss. Berlin 265, 1822–1823,

1821.

14. J. V. Nicholas and D. R. White, Traceable Temperatures:

An Introduction to Temperature Measurement and

Calibration, 2nd edn., John Wiley & Sons, Inc., New York,

2001.

15. J. C. A. Peltier, Ann. Chim. Phys., 56, 371, 1834.

16. L. Michalski, K. Eckersdorf, J. Kucharski, and J. McGhee,

Temperature Measurement, 2nd edn., John Wiley & Sons,

Inc., New York, 2001.

17. N. P. Moiseeva, Meas. Tech., 47, 915–919, 2004.

18. Low Level Measurements Handbook: Precision DC

Current, Voltage, and Resistance Measurements, 6th edn.,

Keithley Instruments, Cleveland, OH, 2007.

19. H. L. Callendar, Phil. Trans. Royal Soc. London, 178, 161–

230, 1887.

20. J. L. Riddle, G. T. Furukawa, and H. H. Plumb, Platinum

Resistance Thermometry, NBS Monograph 126,US

Government Printing Ofﬁce, Washington, DC, 1973.

21. H. Preston-Thomas, Metrologia, 27, 3–10 (1990).

22. G. A. Lushchaev, V. A. Karchkov, E. I. Fandeev, and

I. K. Sologyan, Measurement Techn., 24, 475–479,

1981.

23. A. A. Khan, A. R. M. Alamoud, and M. A. Al-Turaigi, Intl.

J. Elec., 67, 931–936, 1989.

24. O. B. Verbeke, J. Spinnewijn, and H. Strauven, Rev. Sci.

Instrum., 58, 654–656, 1987.

25. E. A. Tombasov, Z. P. Chepurnaya, and V. V. Yakunin,

Measurement Techn., 34, 935–938, 1991.

26. T. M. Dauphinee and H. Preston-Thomas, Rev. Sci. Instrum.,

25, 884–886, 1954.

27. O. Bourgeois, E. Andre

, C. Macovei, and J. Chaussy, Rev.

Sci. Instrum., 77, 126 108/126 101–126 108/126 103, 2006.

28. J. S. Steinhart and S. R. Hart, Deep-Sea Res., 15, 497–503,

1968.

29. H. J. Hoge, Rev. Sci. Instrum .,

59,

975–979, 1988.

30. T. J. Edwards, Rev. Sci. Instrum., 54, 613–617, 1983.

31. J. Schuderer, T. Schmid, G. Urban, T. Samaras, and

N. Kuster, Phys. Med. Biol., 49, N83–N92, 2004.

32. J. J. Connelly, in Handbook of Temperature Measurement:

Resistance and Liquid-in-Glass Thermometry, Vol. 2, R. E.

Bentley (Ed.), Springer, Singapore, 1998, pp. 55–82.

33. M. J. Pertijs and J. H. Huijsing, Precision Temperature

Sensors in CMOS Technology, Springer, Dordrecht, 2006.

34. J. T. Tuoriniemi and T. A. Knuuttila, Physica B, 280, 474–

478, 2000.

35. A. C. Rose-Innes, Low Temperature Techniques, The

English Universities Press, Inc., London, 1964.

36. R. C. Richardson and E. N. Smith (Eds.), Experimental

Techniques in Condensed Matter Physics at Low

Temperatures, Addison Wesley, Reading, MA, 1998.

37. F. Pobell, Matter and Methods at Low Temperatures, 3rd

edn., Springer, New York, 2007.

38. A. Kent, Experimental Low-Temperature Physics, AIP

Press, New York, 1993.

39. J. Ekin, Experimental Techniques: Cryostat Design,

Material Properties and Superconductor Critical-Current

Testing, Oxford University Press, Oxford, 2006.

40. G. K. White and P. J. Meeson, Experimental Techniques in

Low-Temperature Physics, 4th edn., Clarendon Press,

Oxford, 2002.

41. D. S. Betts, An Introduction to Millikelvin Technology,

Cambridge University Press, Cambridge, 1989.

42. G. Schuster, D. Hechtﬁscher, and B. Fellmuth, Rept Prog.

Phys., 57, 187–230, 1994.

43. R. Sahul, V. Tasovski, and T. S. Sudarshan, Sens. Actuat. A:

Physical, 125, 358–362, 2006.

44. Y. Hu, in Experimental Techniques in Condensed Matter

Physics at Low Temperatures, R. C. Richardson, R. P. Feyn-

man, and E. N. Smith (Eds.), Westview Press, New York,

1998, pp. 308–320.

45. E. L. Ziercher, K. I. Blum, and Y. Hu, in Experimental

Techniques in Condensed Matter Physics at Low

Temperatures, R. C. Richardson, R. P. Feynman, and E. N.

Smith (Eds.), Westview Publisher, New York, 1998.

46. F. Pavese and G. Molinar, Modern Gas-Based

Temperature and Pressure Measurements,PlenumPress,

New York, 1982.

47. W. Ni, J. S. Xia, E. D. Adams, P. S. Haskins, and

J. E. McKisson, J. Low Temp. Phys., 101, 305–310, 1995.

48. E. Pentii, J. Tuoriniemi, A. Salmela, and A. Sebedash, Rev.

Sci. Instrum., 146, 71–83, 2007.

49. R. J. Soulen, W. E. Fogle, and J. H. Colwell, J

. Low Temp.

Phys., 94, 385–487, 1994.

50. L. Spietz, R. J. Schoelkopf, and P. Pari, Appl. Phys. Lett.,

89, 183123/1–183123/3 (2006).

51. J. P. Kauppinen, K. T. Loberg, A. J. Manninen, and J. P.

Pekola, Rev. Sci. Instrum., 69, 4166–4175, 1998.

52. C. Buchal, J. Hanssen, R. M. Mueller, and F. Pobell, Rev.

Sci. Instrum., 49, 1360–1361, 1978.

53. D. P. DeWitt and G. D. Nutter, Theory and Practice of

Radiation Thermometry, Wiley Interscience, New York,

1988.

622 MEASUREMENT AND CONTROL OF TEMPERATURE

54. M. J. Ballico, in Handbook of Temperature Measurement:

Temperature and Humidity Measurement, Vol. 2, R. E.

Bentley (Eds.), Springer, Singapore, 1998, pp. 67–98.

55. P. Poulsen and S. K. Ault, Rev. Sci. Instrum., 77, 094901/1–

094901/6, 2006.

56. K. T. V. Grattan and Z. Y. Zhang, Fiber Optic Fluorescence

Thermometry, Chapman and Hall, London, 1995.

57. T. Jigami, M. Kobayashi, Y. Taguchi, and Y. Nagasaka, Intl.

J. Thermophys., 28, 968–979, 2007.

58. G. A. Marcus and H. A. Schwettman, J. Phys. Chem. B,

111, 3048–3054, 2007.

59. J. Lee, N. A. Kotov, Nano Today, 2, 48–51, 2007.

60. B. W. Mangum, G. T. Furukawa, K. G. Kreider, et al.

J. Res. Natl. Inst. Stand. Tech., 106, 105–149, 2001.

61. E. B. Wilson, An Introduction to Scientiﬁc Research,

McGraw-Hill, New York, 1952.

62. R. E. Rondeau, J. Chem. Eng. Data, 11, 124, 1966.

63. A. M. Phipps and D. N. Hume, J. Chem. Ed., 45, 664, 1968.

64. G. S. Coyne, The Laboratory Companion: A Practical

Guide to Materials, Equipment, and Technique, 2nd edn.,

Wiley-Interscience, New York, 2005.

65. J. Tapping, in Handbook of Temperature Measurement:

Temperature and Humidity Measurement, Vol. 1, R. E.

Bentley (Ed.), Springer, Singapore, 1998, pp. 203–214.

66. A.W. Sloman, P. Buggs, J. Malloy, and D. Stewart, Meas.

Sci. Tech., 7, 1653–1664, 1996.

67. E. D. West, in Treatise in Analytical Chemistry,I.M.

Kolthoff and P. J. Elving (Eds.), John Wiley & Sons, Inc.,

New York, 1967.

68. M. Kutz, Temperature Control, John Wiley & Sons, Inc.,

New York, 1968.

69. M. V. Swaay, J. Chem. Ed. 46, A515–A518, 1969.

70. W. K. Roots, Fundamentals of Temperature Control,

Academic Press, New York, 1969.

71. E. M. Forgan, Cryogenics, 14, 207–214, 1974.

72. J. R. Leigh, Temperature Measurement and Control, Peter

Peregrinus Ltd., London, 1988.

73. D. Sarid and D. S. Cannell, Rev. Sci. Instrum., 45,1082–

1088, 1974.

74. L. Bruschi, R. Storti, and G. Torzo,

Rev. Sci. Instrum., 56,

427–429,

1985.

75. P. K. M. Unni, M. K. Gunasekaran, and A. Kumar, Rev. Sci.

Instrum., 74, 231–242, 2003.

76. B. J. Thysse, J. Chem. Phys., 74, 4678–4692, 1981.

77. X. Zhu, E. Krochmann, and J. Chen, Rev. Sci. Instrum., 63,

1999–2003, 1992.

78. R. B. Strem, B. K. Das, and S. C. Greer, Rev. Sci. Instrum.,

52, 1705–1708, 1981.

79. A. Kojima, C. Ishii, K. Tozaki, et al. Rev. Sci. Instrum., 68,

2301–2304, 1997.

80. P. Cofrancesco, U. Rufﬁna, M. Villa, P. Grossi, and

R. Scattolini, Rev. Sci. Instrum., 62, 1311–1316, 1991.

81. H. Ogasawara, Rev. Sci. Instrum., 57, 3048–3052, 1986.

82. E. C. Harrigan, Calibration enclosures, in Handbook of

Temperature Measurement: Resistance and Liquid-in-Glass

Thermometry, Vol. 2, R. E. Bentley (Ed.), Springer,

Singapore, 1998, pp. 145–160.

83. Experimental Thermodynamics, Vol. 1, J. P. McCullough

and D. W. Scott (eds.), Butterworth’s, London, 1969.

84. D. C. Ginnings, Precision Measurement and Calibration:

Selected NBS Papers on Heat, US Government Printing

Ofﬁce, Washington, DC, 1970.

85. J. L. Hemmerich, J.-C. Loos, A. Miller, and P. Milverton,

Rev. Sci. Instrum., 67, 3877–3884, 1996.

86. T. M. Sporton, J. Phys. E. Sci. Instrum., 5, 317–321, 1972.

General References

American Society for Testing Materials International, Manual on

the Use of Thermocouples in Temperature Measurement, West

Conshohocken, PA, 1993.

R. E. Bentley, Handbook of Temperature Measurement, Springer-

Verlag, Singapore, 1998.

Peter R. N. Childs, Practical Temperature Measurements,

Butterworth-Heinemann, Oxford, 2001.

Jack W. Ekin, Experimental Techniques for Low-Temperature

Measurements: Cryostat Design, Material Properties, and

Superconductor Critical Current Testing, Oxford University

Press, Oxford, 2006.

Thomas D. McGee, Principles and Methods of Temperature

Measurement, John Wiley & Sons, Inc., New York, 1988.

L. Michalski, K. Eckersdorf, J. Kucharski, and J. McGhee,

Temperature Measurement, 2nd edn., John Wiley & Sons, Inc.,

New York, 2001.

National Institute of Standards and Technology, Gaithersburg,

MD, Thermometry Group Website.

J. V. Nicholas and D. R. White, Traceable Temperatures: An

Introduction to Temperature Measurement and Calibration,

2nd edn., John Wiley & Sons, Inc., New York, 2001.

Frank Pobell, Matter and Methods at Low Temperatures,

Springer, Berlin, 1996.

Daniel D. Pollack, Thermocouples: Theory and Properties, CRC

Press, Boca Raton, FL 1991.

Robert C. Richardson and Eric N. Smith (Eds.), Experimental

Techniques in Condensed Matter Physics at Low

Temperatures, Addison-Wesley, Reading, MA, 1998.

REFERENCES 623

T. J. Quinn, Temperature, 2nd edn., Academic, New York, 1990.

J. F. Schooley (Ed.), Temperature: Its Measurement and Control

in Science and Industry, Vol. 5, American Institute of Physics,

New York, 1982. See also other volumes in this series.

J. F. Schooley, Thermometry, CRC Press, Boca Raton, FL, 1986.

J. F. Swindells (Ed.), Precision Measurement and Calibration,

Selected NBS Papers on Temperature, NBS Special

Publication 300, Vol. 2, US Government Printing Ofﬁce,

Washington, DC, 1968.

Temperatures.com, a website with information and resources on

thermometry.

J. A. Wise, Liquid-in-Glass Thermometry, NBS Monograph

150, US Government Printing Ofﬁce, Washington, DC,

1976.

624 MEASUREMENT AND CONTROL OF TEMPERATURE

INDEX

Note: Figures and Tables are indicated by italic page numbers

1/f noise 492, 549

Abbe diagram (glass chart) 169

Abbe V number 168

aberrations, imaging system 169,

191, 161, 503, 561

charged-particle optics 333–336

and exact ray tracing 171

ABS thermoplastic 525

a.c. line

ground connection 501

three-wire system 501, 525

a.c. line cord 526

mounting at chassis end 526

a.c. line receptacles 18, 526

circuit diagram symbol(s) 509

accuracy of temperature

measurement 600

achromat lens 169, 189

achromatic doublets (lenses) 169,

169, 191

acoustic absorber 229

acousto-optic modulators 238, 288

acrylic plastics 24

jointing of 24

in optical components 193, 241

properties 20, 233, 234, 241, 525

thermoforming of 24

in vacuum systems 117

active electronic components 363,

402–421

circuit diagram symbol(s) 509

active ﬁlters 381, 431

adhesives 34

in vacuum systems 117

admittance 366

Ahrens polarizer

208, 209

Airy function 301

alexandrite lasers 264

aligned section (in drawing) 43

alkali-ion source 344

alligator clips 529

alloy steels 18, 19, 20

alumina ceramics 24

as electrical insulators 130, 356

properties 20, 24, 356, 615

in vacuum systems 116, 130

aluminum and alloys 22, 356

properties 19, 141, 220, 615

in vacuum systems 117, 139,140

aluminum coatings on mirrors 245

aluminum plate, vibration-isolated

optical table 229

American Standard Pipe Thread 37

speciﬁcations 73

American Standard threaded

fasteners 26

speciﬁcations 71

Amici prisms 199

ampliﬁers 421–435

classiﬁcations 421, 422

frequency ranges 422

impedances 422

stability 434

types 421