Theory of remote image formation

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
Acknowledgements......Page 18
1.1 Remote image-formation systems......Page 19
1.2 The history of image formation......Page 22
1.3 Radar and sonar systems......Page 26
1.4 Imaging by projections......Page 32
1.5 Passband and complex baseband waveforms......Page 34
1.6 Temporal and spatial coherence......Page 36
1.7 Monodirectional waves......Page 38
Monochromatic monodirectional waves......Page 39
Time-varying monodirectional waves......Page 40
1.8 Wavefront diffraction......Page 41
Space-varying monochromatic waves......Page 42
Vector-valued waves......Page 43
1.9 Deterministic and random models......Page 44
2.1 The one-dimensional Fourier transform......Page 47
2.2 Transforms of some useful functions......Page 52
2.3 The dirichlet functions......Page 56
2.4 Passband signals and passband filters......Page 61
2.5 Baseband and passband sampling......Page 63
2.6 Signal space......Page 66
2.7 The matched filter......Page 72
2.8 Resolution and apodization......Page 77
Problems......Page 79
Notes......Page 84
3.1 The two-dimensional Fourier transform......Page 85
3.2 Transforms of some useful functions......Page 89
3.3 Circularly symmetric functions......Page 98
3.4 The projection-slice theorem......Page 103
3.5 Hankel transforms......Page 106
3.6 Two-dimensional pulse arrays......Page 108
3.7 Sampling in two dimensions......Page 110
3.8 Two-dimensional signals and filters......Page 118
3.9 Resolution and apodization......Page 120
Problems......Page 121
Notes......Page 127
4 Optical imaging systems......Page 129
4.1 Scalar diffraction......Page 130
4.2 The Huygens–Fresnel principle......Page 133
4.3 Fresnel and Fraunhofer approximations......Page 136
Fresnel approximation......Page 137
Fraunhofer approximation......Page 138
4.4 The geometrical optics approximation......Page 139
4.5 The ideal lens......Page 141
Lens as an imager......Page 143
Lens as a Fourier transformer......Page 147
Lens construction......Page 149
4.6 Noncoherent imaging......Page 150
4.7 Optical filtering......Page 154
4.8 Phase-contrast imaging......Page 157
4.9 Wavefront reconstruction......Page 159
Problems......Page 164
Notes......Page 169
5 Antenna systems......Page 171
5.1 Aperture and pattern......Page 172
5.2 Reciprocity......Page 179
5.3 Antenna arrays......Page 181
Steered arrays......Page 186
The Butler array......Page 187
5.4 Focused antennas and arrays......Page 190
5.5 Nondiffracting beams......Page 191
5.6 Interferometry......Page 192
5.7 Vector diffraction......Page 194
5.8 Scanning antenna patterns......Page 197
5.9 Wideband radiation patterns......Page 198
Problems......Page 199
Notes......Page 203
6.1 Theory of the ambiguity function......Page 204
6.2 Properties of the ambiguity function......Page 211
6.3 Shape and resolution parameters......Page 214
6.4 Ambiguity function of a pulse train......Page 217
6.5 Ambiguity function of a Costas pulse......Page 221
6.6 The cross-ambiguity function......Page 226
6.7 The sample cross-ambiguity function......Page 228
Problems......Page 232
Notes......Page 237
7.1 The received signal......Page 239
Polarization......Page 243
Delay and doppler......Page 244
7.2 The imaging equation......Page 246
7.3 Imaging resolution......Page 249
7.4 Focusing and motion compensation......Page 251
7.5 Structure of typical imaging systems......Page 255
7.6 Computing the cross-ambiguity function......Page 260
7.7 Dual aperture imaging......Page 265
Problems......Page 267
Notes......Page 270
8.1 The three-dimensional Fourier transform......Page 272
8.2 Transforms of some useful functions......Page 274
8.3 Diffraction by three-dimensional objects......Page 280
8.4 Observation from diffraction data......Page 283
8.5 X-ray diffraction by arrays......Page 285
8.6 Diffraction imaging......Page 290
8.7 Model formation from diffraction data......Page 291
8.8 Diffraction from fiber arrays......Page 296
8.9 Diffraction from excited arrays......Page 298
Problems......Page 300
Notes......Page 303
9 Construction and reconstruction of images......Page 305
9.1 Deconvolution and deblurring......Page 306
The Wiener filter......Page 308
The clean algorithm......Page 310
9.2 Deconvolution of nonnegative images......Page 311
9.3 Blind image deconvolution......Page 314
Conditions for blind image deconvolution......Page 315
An algorithm for blind image deconvolution......Page 318
Conditions for phase retrieval......Page 320
Algorithms for phase retrieval......Page 323
9.5 Optical imaging from point events......Page 325
9.6 Coded aperture imaging......Page 329
Problems......Page 334
Notes......Page 336
10 Tomography......Page 339
10.1 Projection tomography......Page 340
Parallel beam inversion......Page 342
Fan-beam inversion......Page 346
Data limitations......Page 347
Fourier representation......Page 348
Algebraic reconstruction......Page 349
Modal-based imaging......Page 352
10.3 Merging of multiple images......Page 353
10.4 Diffraction tomography......Page 355
10.5 Diffusion tomography......Page 361
10.6 Coherent and noncoherent radar tomography......Page 364
10.7 Emission tomography from magnetic excitation......Page 367
10.8 Emission tomography from decay events......Page 370
10.9 Coherence tomography......Page 371
Problems......Page 373
Notes......Page 377
11 Likelihood and information methods......Page 379
11.1 Likelihood functions and decision rules......Page 380
Likelihood of waveforms......Page 383
11.2 The maximum-likelihood principle......Page 385
11.3 Alternating maximization......Page 386
Variance estimation......Page 387
Covariance estimation......Page 391
11.4 Other principles of inference......Page 394
11.5 Nonnegativity constraints and discrimination......Page 397
11.6 Likelihood methods in blind image deconvolution......Page 403
11.7 Likelihood methods in photon imaging......Page 405
11.8 Radar imaging of diffuse reflectors......Page 408
11.9 Regularization......Page 413
11.10 Notions of equivalence......Page 415
11.11 The Dempster–Laird–Rubin method......Page 418
Problems......Page 420
Notes......Page 424
12.1 The radar range equation......Page 426
12.2 Coherent detection of pulses in noise......Page 428
12.3 The Neyman–Pearson theorem......Page 432
12.4 Rayleigh and ricean probability distributions......Page 437
12.5 Noncoherent detection of pulses in noise......Page 441
12.6 Detection under unknown parameters......Page 443
Compound hypotheses......Page 445
12.7 Clutter......Page 449
12.8 Detection of moving objects......Page 452
12.9 Coherent estimation of pulse parameters......Page 456
12.10 Noncoherent estimation of pulse parameters......Page 461
Problems......Page 468
Notes......Page 472
13 Passive and baseband surveillance systems......Page 473
13.1 Radio astronomy......Page 474
13.2 Estimation of direction......Page 479
13.3 Passive location of emitters......Page 484
13.4 Magnetic anomaly detection......Page 488
13.5 Estimation of differential parameters......Page 491
13.6 Detection of unknown waveforms......Page 493
13.7 Lidar surveillance......Page 494
Problems......Page 495
Notes......Page 497
14 Data combination and tracking......Page 499
14.1 Noncoherent integration......Page 500
14.2 Sequential detection......Page 503
14.3 Multitarget sorting......Page 504
14.4 The assignment problem......Page 508
14.5 Multilateration......Page 513
Problems......Page 515
Notes......Page 516
15 Phase noise and phase distortion......Page 517
15.1 Quadratic-phase errors......Page 518
15.2 Phase noise and coherence......Page 521
15.3 Phase noise and the Fourier transform......Page 523
15.4 Phase noise and the matched filter......Page 524
15.5 Phase noise and the ambiguity function......Page 527
15.7 Array errors......Page 529
Notes......Page 530
References......Page 531
Index......Page 547