Table Of ContentT H E N E W
PHYSICAL OPTICS NOTEBOOK:
TUTORIALS IN FOURIER OPTICS
T H E N E W
PHYSICAL OPTICS NOTEBOOK:
TUTORIALS IN FOURIER OPTICS
George 0. Reynolds
Honeywell Electro-Optics Division
John B. DeVelis
Merrimack College
George B. Parrent, Jr.
Innovative Imaging Systems
Brian J. Thompson
University of Rochester
Copublished by
SPIE—The International Society for Optical Engineering
and
American Institute of Physics
SPIE OPTICAL ENGIN EE RING PRESS
Library of Congress Cataloging-in-Publication Data
The New physical optics notebook.
Rev. ed. of. Physical optics notebook / George B.
Parrent, Brian J. Thompson.
Includes bibliographies and index.
1. Optics, Physical. I. Reynolds, George O.
H. Parrent, George B. Physical optics notebook.
QC395.2.N48 1989 535'.2 88-34527
ISBN 0-8194-0130-7
Library of Congress Catalog Card No. 88-34527
Composition: Carrie Binschus
Design: Matt Treat
Printing: Union Printing Company
Copublished by
SPIE—The International Society for Optical Engineering
P.O. Box 10
Bellingham, Washington 98227
and
American Institute of Physics
335 East 45th Street
New York, New York 10017
Copyright © 1989 The Society of Photo-Optical Instrumentation Engineers
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PRINTED IN THE UNITED STATES OF AMERICA
Third printing 1998
Table of Contents
Preface, xv
Chapter 1 Huygens' Principle i
1.1 Light as a Wave Disturbance, 1
1.2 Wave Propagation, 2
1.2.1 Far-Field Approximation, 6
1.2.2 Fraunhofer Condition, 6
References, 7
Chapter 2 Fourier Transforms 8
2.1 Introduction, 8
2.2 Diffraction Problems, 9
2.2.1 Slit Aperture, 9
2.2.2 Rectangular Aperture, 10
2.2.3 Circular Aperture, 11
2.2.4 Delta Function, 12
2.3 Conclusion, 13
Chapter 3 Array Theorem 14
3.1 Introduction, 14
3.2 The Array Theorem, 14
3.3 Applications of Array Theorem, 16
3.3.1 Two Beam Interference, 16
3.3.2 One Dimensional Array, 17
3.4 Some Examples, 18
3.5 Appendix: The Convolution Theorem, 21
Reference, 22
Chapter 4 Image Formation: The Impulse Response 23
4.1 Introduction, 23
4.2 Impulse Response, 23
4.2.1 Linearity, 24
4.2.2 Stationarity, 24
4.3 Image of a Point Object, 26
4.4 Conclusions, 28
4.5 Appendix: The Relationship to Geometrical Optics, 29
V
Chapter 5 Image Formation in Terms of the Impulse Response 30
5.1 Introduction, 30
5.2 Impulse Response for a Cylindrical Lens, 30
5.3 Image of a Bar, 31
5.4 Image of Two Bars, 33
5.5 Image of Three Bars, 35
5.6 Experimental Illustrations, 35
Reference, 36
Chapter 6 Resolution in Terms of the Impulse Response 38
6.1 Introduction, 38
6.2 Two-Point Resolution, 38
6.3 Image of Two Points: One Dimensional, 39
63.1 Rayleigh Criterion, 40
63.2 Sparrow Criterion, 40
6.4 Image of Two Points: Two Dimensional, 42
6.5 Conclusions, 43
Chapter 7 Image Formation: The Transfer Function 44
7.1 Introduction, 44
7.2 Image of a Cosinusoidal Intensity Distribution, 44
7.3 Periodic Real Object, 46
7.4 The Transfer Function and the Aperture Function, 47
7.5 Conclusion, 48
Chapter 8 image Formation in Terms of the Transfer Function 49
8.1 Introduction, 49
8.2 The Transfer Function, 49
8.3 Image of a Ronchi Ruling, 51
8.4 Defocused Lens, 54
8.5 Appendix: Fourier Transform of a Dirac Comb, 54
Chapter 9 Fresnel Diffraction 57
9.1 Introduction, 57
9.2 Fresnel Diffraction: Near Field, 57
9.3 Fresnel's Integrals, 60
9.4 Fresnel Diffraction by a Rectangular Aperture, 60
9.5 Fresnel Diffraction by a Straight Edge, 62
9.6 Fresnel Diffraction by a Circular Aperture, 62
Chapter 10 Heuristic Introduction to Partially Coherent Light 64
10.1 Introduction, 64
10.2 Partially Coherent Light, 65
10.2.1 Experiment 1, 65
10.2.2 Experiment 2, 69
10.2.3 Experiment 3, 70
10.3 Conclusions, 70
Chapter 11 Elementary Theory of Optical Coherence: Part I 71
11.1 Introduction, 71
11.2 Elements of Classical Coherence Theory, 72
11.3 Review of the Theory of Partial Coherence, 75
M
11.3.1 Introduction, 75
11.3.2 Quasimonochromatic Approximation, 76
11.33 Coherence Volume, 82
11.3.4 Solution of the Coupled-Wave Equations, 84
11.3.5 The Imaging Problem: Coherent and Incoherent
Limits, 86
References, 93
Chapter 12 Image Formation with Coherent Light 94
12.1 Introduction, 94
12.2 The Measurement of Intensity, 94
12.3 Addition of Optical Fields, 95
12.4 The Imaging Problem, 97
12.4.1 Incoherent Fields, 98
12.4.2 Coherent Fields, 98
12.5 The Amplitude Impulse Response, 99
12.6 The Amplitude Transfer Function, 101
12.7 Conclusions, 101
References, 101
Chapter 13 Coherent Imaging. Resolution 102
13.1 Introduction, 102
13.2 Image of a Two-Point Object, 102
13.3 One-Dimensional System, 104
13.3.1 Incoherent Limit, 104
13.3.2 Rayleigh Criterion, 104
13.3.3 Sparrow Criterion, 104
133.4 Coherent Limit, 105
13.4 Discussion: One-Dimensional System, 105
13.5 Two-Dimensional System, 107
13.5.1 Incoherent Limit, 107
13.5.2 Rayleigh Criterion, 107
13.5.3 Sparrow Criterion, 107
13.5.4 Coherent Limit, 108
13.6 Discussion: Two-Dimensional System, 108
13.7 Conclusions, 108
References, 109
Chapter 14 Coherent Imaging: Examples 110
14.1 Introduction, 110
14.2 Image of an Edge Object, 110
14.3 Image of a Slit Object, 114
14.4 Reflected Light Imaging, 116
14.5 Conclusions, 117
References, 117
Chapter 15 Coherence Theory Solution to the Pinhole Camera 118
15.1 Introduction, 118
15.2 Pinhole Camera with Incoherent Illumination, 120
15.3 Pinhole Camera with Coherent Illumination, 127
15.4 Conclusions, 128
15.5 Appendix: Transfer Function of the Pinhole Camera, 128
References, 130
vii
Chapter 16 Diffraction and Interference with Partially Coherent Light 131
16.1 Introduction, 131
16.2 Diffraction with Partially Coherent Light, 131
16.3 One-Dimensional Apertures, 134
16.4 Two-Dimensional Apertures, 135
16.5 Multiple-Beam Interference with Partially Coherent Light, 135
16.6 Analysis of a Partially Coherently Illuminated Array, 136
References, 137
Chapter 17 Elementary Theory of Optical Coherence: Part II 138
17.1 Examples of Spatial Coherence Effects in Optical
Instruments, 138
17.1.1 Apparent Transfer Functions, 138
17.1.2 The Microdensitometer, 141
17.1.3 The Microscope, 145
17.1.4 The Contact Printer, 148
References, 150
Chapter 18 Elementary Theory of Optical Coherence: Part III 152
18.1 An Empirical Approach for Use in Optical Instrument
Design, 152
18.1.1 Coherence Nomograph, 152
18.1.2 Microcamera, 153
18.1.3 Projection Printers, 155
18.1.4 Viewers, 156
18.2 Coherent Imaging Systems, 156
18.2.1 Phase Contrast Microscope, 157
18.2.2 Holographic Systems, 158
18.2.3 Speckle Photography and Interferometry, 159
18.2.4 Aberration Balancing, 159
18.2.5 Image Processing, 159
18.3 Temporal Coherence Considerations in Optical System
Design, 160
18.3.1 Scanning Systems, 161
18.3.2 Fourier Spectrometers, 162
18.3.3 Holography and Interferometry, 162
18.3.4 Laser Contact Printing, 163
18.3.5 Speckle Effects in Fiber Optic Communication
Systems, 164
18.4 Summary, 165
References, 165
Chapter 19 Selected Criteria for Image Analysis 168
19.1 Introduction, 168
19.2 Image Formation, 169
19.3 Image Quality Criteria, 171
19.3.1 Fidelity Defect and Fidelity, 172
19.3.2 Relative Structural Content, 173
19.3.3 Correlation Quantity, 173
19.4 Discussion, 174
19.4.1 Application to Photographic Images, 175
19.4.2 Application to Photographic Lenses, 176
References, 177
viii
Chapter 20 Photographic Films 178
20.1 Introduction, 178
20.2 Review of Photographic Films, 178
20.2.1 Pertinent Film Parameter Measurements, 179
20.2.2 Achievable System Performance, 195
20.3 Appendix: Derivation of the Relationship Between
(S/N)D and (S/N)E 195
,
References, 197
Chapter 21 Sources of Coherent Noise and Their Reduction 199
21.1 Introduction, 199
21.2 System Noise Considerations in Coherent Optical Systems, 199
21.2.1 Effects of Film Nonlinearities and Linear
Processing, 200
21.2.2 Phase Image Noise, 202
21.2.3 Cleanliness of Optical Components, 203
21.3 Speckle Noise Reduction Techniques, 204
21.3.1 Speckle and Holographic Systems, 204
21.3.2 Depth-of-Focus Noise in Holographic Systems, 205
21.3.3 Speckle in Coherent Imaging Systems, 206
21.3.4 Speckle Reduction by Control of Temporal
Coherence, 209
21.3.5 Speckle Reduction by Control of Spatial
Coherence, 209
21.3.6 Speckle Reduction by Time-Averaging, 212
21.4 Design Considerations for Coherent Optical Systems, 215
References, 218
Chapter 22 Division of Wavefront Interferometry 220
22.1 Introduction, 220
22.2 Array Theorem, 221
22.3 Examples of Division of Wavefront Inerferometry, 222
22.3.1 Example 1: Two Slits, 222
22.3.2 Phase Measurement with a Two-Slit
Interferometer, 228
22.3.3 Example 2: Three-Slit Array, 230
22.3.4 Phase Measurement with a Three-Slit
Interferometer, 231
22.3.5 Example 3: Multiple-Slit Array, 234
22.3.6 Example 4: Infinite Grating, 238
22.3.7 Spectral Resolvability of a Diffraction Grating, 239
References, 241
Chapter 23 Division of Amplitude Interferometry 242
23.1 Introduction, 242
23.2 General Analysis, 242
23.3 Case I: Wavefront Preserving Interferometry for Holograms, 243
23.4 Case II: Wavefront Measuring Interferometers, 243
23.4.1 Example 1: Tuyman-Green Interferometer, 243
23.4.2 Example 2: Mach-Zebnder Interferometer, 246
23.4.3 Example 3: Watson Interference Microscope, 247
23.5 Case III: Michelson Interferometer with Variable Delay, 248
23.5.1 General Discussion, 248
ix
23.5.2 Mathematical Analysis, 250
23.5.3 Applications of Michelson Interferometers, 251
235.4 Asymmetric Sources, 254
23.6 Case IV: Shearing Interferometry, 255
23.61 General Discussion, 255
23.62 Theory for Linear Shearing Interferometry, 257
References, 263
Chapter 24 Multiple-Beam Interference 264E
24.1 Introduction, 264
24.2 Analysis, 265
24.3 Visibility of the Fringes of an N-Beam
Interferometer, 269
24.4 Additional Characteristics of Multiple-Beam
Interferometers, 270
24.5 Chromatic Resolving Power of a Multiple-Beam
Interferometer, 274
24.6 Fabry-Perot Interferometry, 275
24.61 Example 1: Spectroscopic Measurements, 275
24.62 Example 2: Laser Cavities, 277
24.63 Example 3: Tunable Filters, 280
24.64 Example 4: Interference Filters, 283
24.65 Example 5: Bistable Devices for Optical Switching, 290
References, 292
Chapter 25 Introduction to Holography 293
25.1 Introduction, 293
25.2 Reconstruction of a Two-Beam Interferogram, 293
25.3 Reconstruction of Ideal Two-Beam Interferograms, 295
25.4 Basic Description of a Two-Beam Hologram, 295
25.5 Formation and Reconstruction of a Fourier Transform
Hologram, 296
25.6 Other Comments on Fourier Transform Holograms, 298
25.7 Types of Holograms, 299
25.8 Simplified Three-Dimensional Holography, 300
25.8.1 Two Point Object, 300
25.8.2 Continuum of Point Sources, 302
25.8.3 Comments on TbreeDimensional Holography, 303
25.9 Fresnel and Fraunhofer Holography, 305
25.9.1 Hologram Formation, 305
25.9.2 Hologram Reconstruction, 306
25.10 Space Bandwidth Product of a Fresnel Hologram, 311
References, 313
Chapter 26 Holographic Interferometry 314E
26.1 Introduction, 314
26.2 Basic Objective and the Advantages of Holographic
Interferometry, 314
262.1 Basic Objective, 314
26.2.2 Advantages, 315
26.3 Types of Holographic Interferometry, 315
26.4 Simple Holographic Interferometer Analysis, 315
