T 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. 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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