A comprehensive cross section of phase-space optics
This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques. Phase-Space Optics: Fundamentals and Applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to:
- Describe optical phenomena using Wigner and ambiguity functions
- Perform phase-space rotations using ray transformation matrices
- Influence the trade-off between pupil size and depth of field
- Analyze and design optical signals using the Radon-Wigner transform
- Accomplish superresolution by squeezing phase space
- Interpret the intimate relationship between radiometry and coherence
- Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect
- Develop discrete models, sampling criteria, and interpolation formulae
- Work with ultrafast processes and complex space-time structures
Author(s): Markus Testorf, Bryan Hennelly, Jorge Ojeda-Castaneda
Edition: 1
Publisher: McGraw-Hill Professional
Year: 2009
Language: English
Pages: 412
Contents......Page 6
Preface......Page 14
1.1 Introduction......Page 20
1.2 Elementary Description of Optical Signals and Systems......Page 21
1.2.2 Mutual Coherence Function and Cross-Spectral Density......Page 22
1.2.3 Some Basic Examples of Optical Signals......Page 23
1.3.1 Definitions......Page 24
1.3.2 Some Basic Examples Again......Page 26
1.3.3 Gaussian Light......Page 28
1.3.4 Local Frequency Spectrum......Page 30
1.4.3 Radiometric Quantities......Page 31
1.4.4 Instantaneous Frequency......Page 33
1.5.1 Fractional Fourier Transformation......Page 34
1.5.3 Generalized Marginals—Radon Transform......Page 35
1.6.1 First-Order Optical Systems—Ray Transformation Matrix......Page 37
1.6.2 Phase-Space Rotators—More Rotations in Phase Space......Page 38
1.6.3 More General Systems—Ray-Spread Function......Page 40
1.6.4 Geometric-Optical Systems......Page 41
1.6.5 Transport Equations......Page 42
1.7 Wigner Distribution Moments in First-Order Optical Systems......Page 43
1.7.1 Moment Invariants......Page 44
1.7.2 Moment Invariants for Phase-Space Rotators......Page 45
1.7.3 Symplectic Moment Matrix—The Bilinear ABCD Law......Page 47
1.8 Coherent Signals and the Cohen Class......Page 48
1.8.1 Multicomponent Signals—Auto-Terms and Cross-Terms......Page 49
1.8.2 One-Dimensional Case and Some Basic Cohen Kernels......Page 51
1.8.3 Rotation of the Kernel......Page 52
1.8.4 Rotated Version of the Smoothed Interferogram......Page 54
References......Page 59
2.1 Introduction......Page 64
2.2.1 General Formulation......Page 66
2.2.2 Application to Simple Objects......Page 67
2.3.1 Propagation in Free Space......Page 68
2.3.2 Transmission through a Thin Object......Page 69
2.3.3 Propagation in a Paraxial Optical System......Page 70
2.4 The AF in Isoplanatic (Space-Invariant) Imaging......Page 71
2.5.1 Derivation of the Zernike-Van Cittert Theorem from the Propagation of the AF......Page 72
2.5.3 The Pupil-AF as a Generalization of the OTF......Page 73
2.6 Phase-Space Tomography......Page 74
2.7 Another Possible Approach to AF Reconstruction......Page 75
2.8.1 Fresnel Diffraction Images as In-Line Holograms......Page 77
2.8.2 Application to Phase Retrieval and X-Ray Holotomography......Page 78
References......Page 79
3.1 Introduction......Page 82
3.2.1 Canonical Integral Transforms and Ray Transformation Matrix Formalism......Page 83
3.2.2 Modified Iwasawa Decomposition of Ray Transformation Matrix......Page 85
3.3.1 Matrix and Operator Description......Page 86
3.3.3 Fractional Fourier Transform......Page 88
3.3.4 Gyrator......Page 92
3.4 Properties of the Phase-Space Rotators......Page 93
3.4.1 Some Useful Relations for Phase-Space Rotators......Page 94
3.4.2 Similarity to the Fractional Fourier Transform......Page 95
3.4.5 Scaling Theorem......Page 96
3.4.6 Phase-Space Rotations of Selected Functions......Page 97
3.5.1 Some Relations for the Eigenfunctions......Page 99
3.5.2 Mode Presentation on Orbital Poincaré Sphere......Page 101
3.6 Optical Setups for Basic Phase-Space Rotators......Page 103
3.6.1 Flexible Optical Setups for Fractional FT and Gyrator......Page 104
3.6.2 Flexible Optical Setup for Image Rotator......Page 106
3.7.1 Generalized Convolution......Page 107
3.7.2 Pattern Recognition......Page 109
3.7.4 Signal Encryption......Page 113
3.7.5 Mode Converters......Page 114
3.7.6 Beam Characterization......Page 115
3.7.7 Gouy Phase Accumulation......Page 119
3.8 Conclusions......Page 120
References......Page 121
4.1 Introduction......Page 126
4.2.1 Definition and Basic Properties......Page 127
4.2.2 Optical Implementation of the RWT: The Radon-Wigner Display......Page 136
4.3.1 Analysis of Diffraction Phenomena......Page 141
4.3.2 Inverting RWT: Phase-Space Tomographic Reconstruction of Optical Fields......Page 153
4.3.3 Merit Functions of Imaging Systems in Terms of the RWT......Page 157
4.4.1 Optimization of Optical Systems: Achromatic Design......Page 170
4.4.2 Controlling the Axial Response: Synthesis of Pupil Masks by RWT Inversion......Page 175
4.4.3 Signal Processing through RWT......Page 176
References......Page 181
5.1 Introduction......Page 184
5.2 The Product-Space Representation and Product Spectrum Representation......Page 185
5.3 Optical Imaging Systems......Page 189
5.4 Bilinear Optical Systems......Page 192
5.5 Noncoherent Imaging Systems......Page 195
5.6 Tolerance to Focus Errors and to Spherical Aberration......Page 197
5.7 Phase Conjugate Plates......Page 202
References......Page 208
6.1 Introduction......Page 212
6.2 General Definitions......Page 214
6.3 Description of SR......Page 216
6.3.1 Code Division Multiplexing......Page 219
6.3.2 Time Multiplexing......Page 220
6.3.3 Polarization Multiplexing......Page 221
6.3.5 Gray-Level Multiplexing......Page 222
6.3.6 Description in the Phase-Space Domain......Page 224
6.4 Conclusions......Page 232
References......Page 233
7.1 Introduction......Page 236
7.2 Conventional Radiometry......Page 237
7.4 Mutual Coherence Function......Page 240
7.5 Stationary Phase Approximation......Page 243
7.6 Radiometry and Wave Optics......Page 245
7.7.1 Blackbody Radiation......Page 250
7.7.2 Noncoherent Source......Page 251
7.7.3 Coherent Wave Fields......Page 252
7.7.4 Quasi-Homogeneous Wave Field......Page 253
References......Page 254
8.1 Introduction......Page 256
8.2 Small-Wavelength Limit in the Position Representation I: Geometrical Optics......Page 257
8.2.1 The Eikonal and Geometrical Optics......Page 258
8.2.2 Choosing z as the Parameter......Page 261
8.2.3 Ray-Optical Phase Space and the Lagrange Manifold......Page 262
8.3.2 The Transport Equation and Its Solution......Page 264
8.3.3 The Field Estimate and Its Problems at Caustics......Page 266
8.4 Flux Lines versus Rays......Page 268
8.5 Analogy with Quantum Mechanics......Page 269
8.5.1 Semiclassical Mechanics......Page 270
8.5.2 Bohmian Mechanics and the Hydrodynamic Model......Page 272
8.6.1 The Helmholtz Equation in the Momentum Representation......Page 273
8.6.2 Asymptotic Treatment and Ray Equations......Page 275
8.6.3 Transport Equation in the Momentum Representation......Page 277
8.6.4 Field Estimate......Page 278
8.7 Maslov's Canonical Operator Method......Page 279
8.8.1 Parabasal Gaussian Beams......Page 280
8.8.2 Sums of Gaussian Beams......Page 283
8.9.1 Derivation of the Estimate......Page 285
8.9.2 Insensitivity to γ......Page 288
8.9.3 Phase-Space Interpretation......Page 289
8.10 A Simple Example......Page 290
References......Page 294
9.1 Introduction......Page 298
9.2 Phase-Space Optics Minimum Tool Kit......Page 299
9.3 Self-Imaging of Paraxial Wavefronts......Page 303
9.4 The Talbot Effect......Page 304
9.5 The "Walk-off" Effect......Page 308
9.6 The Fractional Talbot Effect......Page 309
9.7 Matrix Formulation of the Fractional Talbot Effect......Page 314
9.8 Point Source Illumination......Page 317
9.9 Another Path to Self-Imaging......Page 320
9.10 Self-Imaging and Incoherent Illumination......Page 321
9.11 Summary......Page 324
References......Page 325
10.1 Introduction......Page 328
10.2.1 The Wigner Distribution Function and Properties......Page 331
10.2.3 The Phase-Space Diagram......Page 333
10.2.4 Harmonics and Chirps and Convolutions......Page 335
10.2.5 The Comb Function and Rect Function......Page 337
10.3.1 Band-limitedness in Fourier Domain......Page 340
10.3.2 Band-limitedness and the LCT......Page 341
10.3.3 Finite Space-Bandwidth Product—Compact Support in x and k......Page 343
10.4.1 Nyquist-Shannon Sampling......Page 344
10.4.2 Generalized Sampling......Page 347
10.5 Simulating an Optical System: Sampling at the Input and Output......Page 348
References......Page 351
11.1 Introduction......Page 356
11.2.1 Representation of Pulsed Fields......Page 357
11.2.2 Pulse Ensembles and Correlation Functions......Page 359
11.2.3 The Time-Frequency Phase Space......Page 362
11.2.4 Phase-Space Representation of Paraxial Optical Systems......Page 368
11.2.5 Temporal Paraxiality and the Chronocyclic Phase Space......Page 372
11.3.1 Measurement Strategies......Page 376
11.3.2 Pulse Characterization Apparatuses as Linear Systems......Page 377
11.3.3 Phase-Space Methods......Page 380
11.3.4 Interferometric or Direct Techniques......Page 388
11.4 Conclusions......Page 397
References......Page 398
B......Page 404
D......Page 405
G......Page 406
M......Page 407
P......Page 408
R......Page 409
S......Page 410
W......Page 411
Z......Page 412
