Introduction to Fourier optics

Goodman,J.W.Introduction to Fourier optics (3 ed. RSP,2005)(ISBN 0974707724)(600dpi)(509p) ......Page 3
Copyright ......Page 4
Contents xi  ......Page 10
Preface vii ......Page 7
1.1 Optics, Information, and Communication 1 ......Page 18
1.2 The Book 2 ......Page 19
2 Analysis of Two-Dimensional Signals and Systems 3 ......Page 20
2.1.1 Definition and Existence Conditions 4 ......Page 21
2.1.2 The Fourier Transform as a Decomposition 6 ......Page 23
2.1.3 Fourier Transform Theorems 7 ......Page 24
2.1.4 Separable Functions 9 ......Page 26
2.1.5 Functions with Circular Symmetry: Fourier-Bessel Transforms 10 ......Page 27
2.1.6 Some Frequently Used Functions and Some Useful Fourier Transform Pairs 12 ......Page 29
2.2 Spatial Frequency and Space-Frequency Localization 15 ......Page 32
2.3 Linear Systems 18 ......Page 35
2.3.1 Linearity and the Superposition Integral 19 ......Page 36
2.3.2 Invariant Linear Systems: Transfer Functions 20 ......Page 37
2.4.1 The Whittaker-Shannon Sampling Theorem 22 ......Page 39
2.4.2 Space-Bandwidth Product 26 ......Page 43
3.1 Historical Introduction 31 ......Page 48
3.2 From a Vector to a Scalar Theory 35 ......Page 52
3.3.1 The Helmholtz Equation 38 ......Page 55
3.3.3 The Integral Theorem of Helmholtz and Kirchhoff 39 ......Page 56
3.4.1 Application of the Integral Theorem 42 ......Page 59
3.4.2 The Kirchhoff Boundary Conditions 44 ......Page 61
3.4.3 The Fresnel-Kirchhoff Diffraction Formula 45 ......Page 62
3.5 The Rayleigh-Sommerfeld Formulation of Diffraction 46 ......Page 63
3.5.1 Choice of Alternative Green’s Functions 47 ......Page 64
3.5.2 The Rayleigh-Sommerfeld Diffraction Formula 49 ......Page 66
3.6 Comparison of the Kirchhoff and Rayleigh-Sommerfeld Theories 50 ......Page 67
3.7 Further Discussion of the Huygens-Fresnel Principle 52 ......Page 69
3.8 Generalization to Nonmonochromatic Waves 53 ......Page 70
3.9 Diffraction at Boundaries 54 ......Page 71
3.10.1 The Angular Spectrum and Its Physical Interpretation 55 ......Page 72
3.10.2 Propagation of the Angular Spectrum 57 ......Page 74
3.10.3 Effects of a Diffracting Aperture on the Angular Spectrum 59 ......Page 76
3.10.4 The Propagation Phenomenon as a Linear Spatial Filter 60 ......Page 77
4.1.1 The Intensity of a Wave Field 63 ......Page 80
4.1.2 The Huygens-Fresnel Principle in Rectangular Coordinates 65 ......Page 82
4.2 The Fresnel Approximation 66 ......Page 83
4.2.2 Accuracy of the Fresnel Approximation 68 ......Page 85
4.2.3 The Fresnel Approximation and the Angular Spectrum 72 ......Page 89
4.2.4 Fresnel Diffraction between Confocal Spherical Surfaces 73 ......Page 90
4.3 The Fraunhofer Approximation 74 ......Page 91
4.4 Examples of Fraunhofer Diffraction Patterns 75 ......Page 92
4.4.2 Circular Aperture 76 ......Page 93
4.4.3 Thin Sinusoidal Amplitude Grating 78 ......Page 95
4.4.4 Thin Sinusoidal Phase Grating 82 ......Page 99
4.5.1 Fresnel Diffraction by a Square Aperture 84 ......Page 101
4.5.2 Fresnel Diffraction by a Sinusoidal Amplitude Grating—Talbot Images 88 ......Page 105
5.1 A Thin Lens as a Phase Transformation 97 ......Page 114
5.1.1 The Thickness Function .98 ......Page 115
5.1.3 The Phase Transformation and Its Physical Meaning 100 ......Page 117
5.2 Fourier Transforming Properties of Lenses 103 ......Page 120
5.2.1 Input Placed against the Lens 104 ......Page 121
5.2.2 Input Placed in Front of the Lens 105 ......Page 122
5.2.3 Input Placed behind the Lens 107 ......Page 124
5.3 Image Formation: Monochromatic Illumination 108 ......Page 125
5.3.1 The Impulse Response of a Positive Lens 109 ......Page 126
5.3.2 Eliminating Quadratic Phase Factors: The Lens Law 111......Page 128
5.3.3 The Relation between Object and Image 114 ......Page 131
5.4.1 An Operator Notation 115 ......Page 132
5.4.2 Application of the Operator Approach to Some Optical Systems 118 ......Page 135
6 Frequency Analysis of Optical Imaging Systems 127 ......Page 144
6.1.1 A Generalized Model 128 ......Page 145
6.1.2 Effects of Diffraction on the Image 129 ......Page 146
6.1.3 Polychromatic Illumination: The Coherent and Incoherent Cases 131 ......Page 148
6.2 Frequency Response for Diffraction-Limited Coherent Imaging 135 ......Page 152
6.2.1 The Amplitude Transfer Function 136 ......Page 153
6.2.2 Examples of Amplitude Transfer Functions 137 ......Page 154
6.3.1 The Optical Transfer Function 138 ......Page 155
6.3.2 General Properties of the OTF 140 ......Page 157
6.3.3 The OTF of an Aberration-Free System 141 ......Page 158
6.3.4 Examples of Diffraction-Limited OTFs 143 ......Page 160
6.4.1 The Generalized Pupil Function 145 ......Page 162
6.4.2 Effects of Aberrations on the Amplitude Transfer Function 147 ......Page 164
6.4.3 Effects of Aberrations on the OTF 148 ......Page 165
6.4.4 Example of a Simple Aberration: A Focusing Error 149 ......Page 166
6.4.5 Apodization and Its Effects on Frequency Response 152 ......Page 169
6.5 Comparison of Coherent and Incoherent Imaging 154 ......Page 171
6.5.1 Frequency Spectrum of the Image Intensity 156 ......Page 173
6.5.2 Two-Point Resolution 158 ......Page 175
6.5.3 Other Effects 160 ......Page 177
6.6.1 Underlying Mathematical Fundamentals 162 ......Page 179
6.6.2 Intuitive Explanation of Bandwidth Extrapolation 163 ......Page 180
6.6.3 An Extrapolation Method Based on the Sampling Theorem 164 ......Page 181
6.6.4 An Iterative Extrapolation Method 166 ......Page 183
6.6.5 Practical Limitations 167 ......Page 184
7 Wavefront Modulation 173 ......Page 190
7.1.1 The Physical Processes of Exposure, Development, and Fixing 174 ......Page 191
7.1.2 Definition of Terms 175 ......Page 192
7.1.3 Film in an Incoherent Optical System 178 ......Page 195
7.1.4 Film in a Coherent Optical System 179 ......Page 196
7.1.5 The Modulation Transfer Function 182 ......Page 199
7.1.6 Bleaching of Photographic Emulsions 185 ......Page 202
7.2 Spatial Light Modulators 186 ......Page 203
7.2.1 Properties of Liquid Crystals 187 ......Page 204
7.2.2 Spatial Light Modulators Based on Liquid Crystals 195 ......Page 212
7.2.3 Magneto-Optic Spatial Light Modulators 199 ......Page 216
7.2.4 Deformable Mirror Spatial Light Modulators 202 ......Page 219
7.2.5 Multiple Quantum Well Spatial Light Modulators 204 ......Page 221
7.2.6 Acousto-Optic Spatial Light Modulators 208 ......Page 225
7.3.1 Binary Optics 212 ......Page 229
7.3.3 A Word of Caution 216 ......Page 233
8 Analog Optical Information Processing 219 ......Page 236
8.1.1 The Abbe-Porter Experiments 220 ......Page 237
8.1.2 The Zemike Phase-Contrast Microscope 222 ......Page 239
8.1.3 Improvement of Photographs: Marechal 224 ......Page 241
8.2 Incoherent Image Processing Systems 226 ......Page 243
8.2.1 Systems Based on Geometrical Optics 227 ......Page 244
8.2.2 Systems That Incorporate the Effects of Diffraction 232 ......Page 249
8.3.1 Coherent System Architectures 234 ......Page 251
8.3.2 Constraints on Filter Realization 237 ......Page 254
8.4.1 Synthesis of the Frequency-Plane Mask 239 ......Page 256
8.4.2 Processing the Input Data 242 ......Page 259
8.4.3 Advantages of the VanderLugt Filter 244 ......Page 261
8.5 The Joint Transform Correlator 245 ......Page 262
8.6.1 The Matched Filter 248 ......Page 265
8.6.2 A Character-Recognition Problem 249 ......Page 266
8.6.3 Optical Synthesis of a Character-Recognition Machine 251 ......Page 268
8.6.4 Sensitivity to Scale Size and Rotation 252 ......Page 269
8.7 Optical Approaches to Invariant Pattern Recognition 253 ......Page 270
8.7.1 Mellin Correlators 254 ......Page 271
8.7.2 Circular Harmonic Correlation 256 ......Page 273
8.7.3 Synthetic Discriminant Functions 257 ......Page 274
9.9.2 The Computational Problem 359 ......Page 276
8.8.2 The Wiener Filter, or the Least-Mean-Square-Error Filter 261 ......Page 278
8.8.3 Filter Realization 262 ......Page 279
8.9 Processing Synthetic-Aperture Radar (SAR) Data 265 ......Page 282
8.9.1 Formation of the Synthetic Aperture 266 ......Page 283
8.9.2 The Collected Data and the Recording Format 267 ......Page 284
8.9.3 Focal Properties of the Film Transparency 269 ......Page 286
8.9.4 Forming a Two-Dimensional Image 273 ......Page 290
8.9.5 The Tilted Plane Processor 274 ......Page 291
8.10 Acousto-Optic Signal Processing Systems 277 ......Page 294
8.10.1 Bragg Cell Spectrum Analyzer 278 ......Page 295
8.10.2 Space-Integrating Correlator 280 ......Page 297
8.10.3 Time-Integrating Correlator 281 ......Page 298
8.10.4 Other Acousto-Optic Signal Processing Architectures 283 ......Page 300
8.11.1 Discrete Representation of Signals and Systems 284 ......Page 301
8.11.2 A Serial Matrix-Vector Multiplier 285 ......Page 302
8.11.3 A Parallel Incoherent Matrix-Vector Multiplier 286 ......Page 303
8.11.4 An Outer Product Processor 288 ......Page 305
8.11.6 Methods for Handling Bipolar and Complex Data 290 ......Page 307
9.1 Historical Introduction 297 ......Page 314
9.2.1 Recording Amplitude and Phase 298 ......Page 315
9.2.2 The Recording Medium 299 ......Page 316
9.2.3 Reconstruction of the Original Wavefront 300 ......Page 317
9.2.4 Linearity of the Holographic Process 301 ......Page 318
9.2.5 Image Formation by Holography 302 ......Page 319
9.3 The Gabor Hologram 303 ......Page 320
9.3.1 Origin of the Reference Wave 304 ......Page 321
9.3.2 The Twin Images 305 ......Page 322
9.4 The Leith-Upatnieks Hologram 306 ......Page 323
9.4.1 Recording the Hologram 307 ......Page 324
9.4.2 Obtaining the Reconstructed Images 308 ......Page 325
9.4.3 The Minimum Reference Angle 310 ......Page 327
9.4.4 Holography of Three-Dimensional Scenes 311 ......Page 328
9.4.5 Practical Problems in Holography 314 ......Page 331
9.5.1 Image Locations 316 ......Page 333
9.5.2 Axial and Transverse Magnifications 319 ......Page 336
9.5.3 An Example 320 ......Page 337
9.6 Some Different Types of Holograms 321 ......Page 338
9.6.1 Fresnel, Fraunhofer, Image, and Fourier Holograms 322 ......Page 339
9.6.2 Transmission and Reflection Holograms 323 ......Page 340
9.6.3 Holographic Stereograms 325 ......Page 342
9.6.4 Rainbow Holograms 326 ......Page 343
9.6.5 Multiplex Holograms 329 ......Page 346
9.6.6 Embossed Holograms 331 ......Page 348
9.7.1 Recording a Volume Holographic Grating 332 ......Page 349
9.7.2 Reconstructing Wavefronts from a Volume Grating 334 ......Page 351
9.7.3 Fringe Orientations for More Complex Recording Geometries 335 ......Page 352
9.7.4 Gratings of Finite Size 337 ......Page 354
9.7.5 Diffraction Efficiency—Coupled Mode Theory 339 ......Page 356
9.8.1 Silver Halide Emulsions 350 ......Page 367
9.8.2 Photopolymer Films 351 ......Page 368
9.8.4 Photorefractive Materials 352 ......Page 369
9.9 Computer-Generated Holograms 355 ......Page 372
9.9.1 The Sampling Problem 356 ......Page 373
9.9.3 The Representational Problem 359 ......Page 376
9.10 Degradations of Holographic Images 367 ......Page 384
9.10.1 Effects of Film MTF 368 ......Page 385
9.10.2 Effects of Film Nonlinearities 371 ......Page 388
9.10.3 Effects of Film-Grain Noise 372 ......Page 389
9.10.4 Speckle Noise 373 ......Page 390
9.11 Holography with Spatially Incoherent Light 374 ......Page 391
9.12.1 Microscopy and High-Resolution Volume Imagery 377 ......Page 394
9.12.2 Interferometry 378 ......Page 395
9.12.3 Imaging through Distorting Media 384 ......Page 401
9.12.4 Holographic Data Storage 388 ......Page 405
9.12.5 Holographic Weights for Artificial Neural Networks 389 ......Page 406
9.12.6 Other Applications 393 ......Page 410
10.1 Introduction 399 ......Page 416
10.2.1 Introduction to Optical Fibers 400 ......Page 417
10.2.2 Recording Gratings in Optical Fibers 403 ......Page 420
10.2.3 Effects of an FBG on Light Propagating in the Fiber 404 ......Page 421
10.2.4 Applications of FBGs 407 ......Page 424
10.2.5 Gratings Operated in Transmission 409 ......Page 426
10.3.1 Mapping of Temporal Frequencies to Spatial Frequencies 410 ......Page 427
10.3.2 Pulse Shaping System 412 ......Page 429
10.3.3 Applications of Spectral Pulse Shaping 413 ......Page 430
10.4.1 Recording the Hologram 415 ......Page 432
10.4.2 Reconstructing the Signals 417 ......Page 434
10.5 Arrayed Waveguide Gratings 420 ......Page 437
10.5.1 Component Parts of an Arrayed Waveguide Grating 421 ......Page 438
10.5.2 Applications of AWGs 427 ......Page 444
A. 1 Delta Functions 433 ......Page 450
A.2 Derivation of Fourier Transform Theorems 435 ......Page 452
B.l The Domain of Geometrical Optics 441 ......Page 458
B.2 Refraction, Snell’s Law, and the Paraxial Approximation 443 ......Page 460
B.3 The Ray-Transfer Matrix 444 ......Page 461
B.4 Conjugate Planes, Focal Planes, and Principal Planes 447 ......Page 464
B.5 Entrance and Exit Pupils 451 ......Page 468
C.1 Definition of the Jones Matrix 455 ......Page 472
C.2 Examples of Simple Polarization Transformations 457 ......Page 474
C.3 Reflective Polarization Devices 459 ......Page 476
D Hie Grating Equation 463 ......Page 480
Bibliography 465 ......Page 482
Index 481 ......Page 498
cover......Page 1