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Spie Press Book

The New Physical Optics Notebook: Tutorials in Fourier Optics
Editor(s): George O. Reynolds; John B. DeVelis; George B. Parrent; Brian J. Thompson
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Book Description

Approaches the topic of physical optics with examples drawn from the physical processes described. Includes chapters on Fourier transforms, image formation, optical coherence, diffraction, interference, holography, interferometry, analog optical computing, synthetic aperture imaging, and others. Contains more than 600 photographs and line drawings and more than 650 references.

Book Details

Date Published: 1 January 1989
Pages: 572
ISBN: 9780819401304
Volume: PM01

Table of Contents
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Preface
Chapter 1. Huygens' Principle
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
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
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
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
Chapter 5. Formation in Terms of the Impulse Response
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
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
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
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
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
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
11.1 Introduction / 71
11.2 Elements of Classical Coherence Theory / 72
11.3 Review of the Theory of Partial Coherence / 75
11.3.1 Introduction / 75
11.3.2 Quasimonochromatic Approximation / 76
11.3.3 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
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 Amplitude Impulse Response / 99
12.6 Amplitude Transfer Function / 101
12.7 Conclusions / 101
References / 101
Chapter 13. Coherent Resolution
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
13.3.4 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 Examples
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
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
Chapter 16. Diffraction and Interference with Partially Coherent Light
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
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
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
181.4 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 / 169
18.3.1 Scanning Systems / 161
18.3.2 Fourier Spectrometers / 162
183.3 Holography and Interferometry / 162
183.4 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
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
Chapter 20. Photographic Films
20.1 Introduction / 178
20.2 Review of Photographic Films / 178
20.2.1 pertinent Him 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
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
22.1 Introduction / 220
22.2 Array Theorem / 221
22.3 Examples of Division of Wavefront Interferometry / 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
23.1 Introduction / 242
23.2 General Analysis / 242
23.3 Case I: Wavefront Preserving Interferometry for Holograms / 243
23.4 Case 11: Wavefront Measuring Interferometers / 243
23.4.1 Example 1: Twyman-Green Interferometer / 243
23.4.2 Example 2: Mach-Zehnder 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
23.5.2 Mathematical Analysis / 250
23.5.3 Applications of Michelson Interferometers / 251
23.5.4 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
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
24.6.1 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
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 Three-Dimensional 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
26.1 Introduction / 314
26.2 Basic objective and the Advantages of Holographic Interferometry / 314
26.2.1 Basic Objective / 314
26.2.2 Advantages / 315
26.3 Types of Holographic Interferometry / 315
26.4 Simple Holographic Interferometer Analysis / 315
26.4.1 Pure Linear Phase 315
26.4.2 Arbitrary Phase / 317
26.5 Double-Exposure Holographic Interferometry / 319
26.6 Differential or Time-lapse Double-Exposure Holographic Interferometry / 320
26.7 Single-Exposure (Real-Time) Holographic Interferometry / 321
26.7.1 Real-Time Recording Materials / 322
26 7.2 Aberration Balancing / 323
26.8 Multiple-Exposure or Time-Average Holographic Interferometry / 325
26.9 Multiple-Wavelength Holography for Contouring / 326
26.9.1 Two-Source Contouring / 326
26.9.2 Two-Frequency Method / 328
26 9 3 Index Mismatch Contouring / 329
26.10 Computer-Generated Holographic Interferometry / 329
26.11 Conclusions / 330
References / 331
Chapter 27. Applications of Holography
27.1 Introduction / 332
27.1.1 Early Developments / 1948-1962 / 332
27.1.2 The Modern Phase of Holography / 1962-Present / 334
27.2 Image Formation / 334
27.2.1 Optical Holography / 334
27.2.2 Nonoptical Holography / 349
27.3 Holographic Optical Elements / 354
27.3.1 Lenses / 355
27.3.2 Gratings / 355
27.3.3 Filters / 356
27.4 Conclusions / 358
27.5 Appendix: Miscellaneous Terminology / 359
27.5.1 Introduction / 359
27.5.2 Principal Properties of Holographic Systems / 360
27.6 Appendix: Interference Microscopy / 361
References / 363
Chapter 28. Communication Theory Techniques in Optics
28.1 Introduction / 371
28.2 Sampling Theorem / 371
28.2.1 Space Domain / 371
28.2.2 Frequency Domain / 372
28.2.3 Sampling Criteria and Space Bandwidth Product / 373
28.2.4 Two-Dimensional Sampling Theorem / 374
28.2.5 Examples / 374
28.3 Statistical Description of Random Samples / 375
28.3.1 Ensemble and Coordinate Averaging Descriptions of Random Processes / 375
28.3.2 Correlation Functions / 376
28.3.3 Spectral Density / 379
28.3.4 Examples of Statistical Techniques / 380
References / 385
Chapter 29. Analog Optical Computing: Experimental Fourier Analysis
29.1 Introduction / 387
29.2 Optical Fourier Transforms / 387
29.3 Slit Aperture / 388
29.4 Periodic Rectangular Apertures / 389
29.5 Optical Addition / 391
29.6 Optical Convolution / 392
29.7 Optical Spectrum Replication by Multiplication / 393
29.8 Appendix: Fourier Transform of a Rectangular Wave / 393
References / 395
Chapter 30. Analog Optical Computing: Fourier Synthesis Using Amplitude Filters
30.1 Generalized Optical System for Fourier Filtering / 396
30.2 Multiplication with Binary Filter Functions / 396
30.2.1 Halftone Removal / 397
30.2.2 Raster Removal / 398
30.2.3 Edge Enhancement / 398
30.2.4 Enhancement of a Periodic Signal in Additive Random Noise / 400
30.2.5 Filtering of Seismic Data / 401
30.3 Object Replication as an Example of Multiplication with a Periodic Binary Filter / 402
30.4 Optical Subtraction by Multiplication with a Periodic Amplitude Filter / 402
References / 407
Chapter 31. Analog Optical Computing: Fourier Synthesis Using Amplitude and/or Phase Filters
31.1 Optical Division / 408
31.2 Case I: Real Filters / 409
31.2.1 Example 1: Contrast Enhancement / 409
31.2.2 Example 2: The Cosine Experiment / 409
31.2.3 Example 3: Removal of Random Media Distortions / 410
31.3 Case II: Purely Imaginary Inverse Filters / 411
31.3.1 Example: Phase Correction of Human Cataracts / 411
31.4 Case III: Complex Inverse Filters / 414
31.4.1 Example 1: Correction of Defocused Images / 414
31.4.2 Example 2 Correction for Image Motion / 415
31.4.3 Example 3: Correction of Arbitrary Image Motion / 415
31.4.4 Example 4: Detection of Objects by Complex Inverse Filtering / 417
References / 420
Chapter 32. Analog Optical Computing: Additional Mathematical Operations
32.1 Fresnel Transform / 421
32.2 Mellin Transform / 422
32.3 Differentiation and Integration of Optical Signals / 424
32.3.1 Differentiation / 425
32.3.2 Integration / 427
References / 432
Chapter 33. Analog Optical Computing: Optical Correlation Techniques
33.1 Introduction / 433
33.2 Incoherent Light Correlation / 433
33.3 Coherent Light Correlation / 433
33.4 True One-Dimensional / Multichannel Correlation System / 436
33.4.1 Example 1: Two-Channel Correlation / 438
33.4.2 Example 2: Three-Channel Correlation / 439
33.4.3 Example 3: Matched Filtering / 439
33.4.4 Example 4: Ambiguity Function Processing / 442
References / 444
Chapter 34. Optically Modulated Imagery
34.1 Introduction / 445
34.2 The Concept of Carrier-Modulated Imaging / 445
34.3 Multiple Image Storage with Angularly Dependent Carriers / 446
34.4 Encoding Color Images on Black-and-White Film / 450
34.4.1 Sequential Exposures / 450
34.4.2 Simultaneous Exposures / 452
34.4.3 Image Brightness and Noise / 452
34.5 Phase-Modulated Images / 455
34.6 The Square-Array-Modulated Image Concept / 456
34.6.1 Example 1: Image Subtraction / 460
34.6.2 Example 2: Digital Encoding of Color / 462
34.6.3 Example 3: Square Array Digital Picture Storage of Wide Dynamic Range Data / 464
34.6.4 Viewing Considerations / 467
34.7 Image Holography: Three-Dimensional Image Modulation / 469
34.7.1 Example 1: Experimental Demonstration of High-Resolution Duplication Using Image Holography / 470
34.7.2 Example 2: Contact Printing Using Holography / 470
References / 473
Chapter 35. Phase Contrast
35.1 Introduction / 474
35.2 Phase Contrast Viewing Methods / 475
35.2.1 Zernike Techniques / 4 75
35.2.2 Dark Held Technique / 477
35.2.3 Oblique Illumination Techniques / 478
35.3 Phase Visualization by Defocus and Schlieren Techniques: Nonlinear Methods / 487
35.3.1 Defocus / 487
35.3.2 Schlieren Knife Edge / 488
35.4 Phase Contrast Imaging with Extended Linearity / 489
35.4.1 The Problem of Phase Redundancy / 489
35.4.2 Extended Linearity with Redundancy / 490
35.4.3 Extended Linearity without Redundancy / 496
35.5 Conclusions / 500
35.6 Appendix: Imaging with an Oblique Illumination Double-Sideband Phase Contrast System / 500
References / 502
Chapter 36. Partially Filled, Synthetic Aperture Imaging Systems: Incoherent Illumination
36.1 Introduction / 503
36.2 Nonlinearities of Partially Filled Synthetic Apertures Due to Degree of Coherence / 504
36.3 Aperture Synthesis with Incoherent Illumination / 505
363.1 Sequential Aperture Synthesis / 505
363.2 Simultaneous Aperture Syntheses / 506
36.4 Appendix: Derivations of the Alignment Tolerances Listed in Table 36.I for Small Segment Dislocations / 528
36.5 Appendix: Formulation of the Optical Synthetic Aperture Analysis / 532
References / 534
Chapter 37. Partially Filled / Synthetic Aperture Imaging Systems: Coherent Illumination
37.1 Aperture Synthesis with Coherent Illumination / 536
37.1.1 Partially Filled Apertures / 536
37.1.2 Homodyned Aperture Synthesis with Laser Illumination / 537
37.1.3 Dynamic Coherent Optical System / 541
37.2 Measurement of Gl2 (0) with an Optical Synthetic Aperture / 544
37.3 Super-Resolving Pupil Functions / 544
37.4 Conclusions / 547
References / 548
Chapter 38. Parametric Design of a Conceptual High-Resolution Optical Lithographic Printer
38.1 Introduction / 549
38.2 Background / 549
38.3 Proposed System and Critical Issues / 550
38.4 Optical Subsystem Considerations / 553
38.5 Exposure Subsystem Considerations / 555
38.6 Optical Lens Design Considerations / 557
38.7 Focusing and Alignment Considerations / 559
38.7.1 Focus / 559
38.7.2 Alignment / 560
38.8 Overview of the Proposed System / 560
38.9 Conclusions / 561
References / 562 Index / 564

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