Optical imaging and spectroscopy

This is the first text to present an integrated view of the optical and mathematical analysis tools necessary to understand computational optical system design. It presents the foundations of computational optical sensor design with a focus entirely on digital imaging and spectroscopy. It systematically covers:

Coded aperture and tomographic imaging

Sampling and transformations in optical systems, including wavelets and generalized sampling techniques essential to digital system analysis

Geometric, wave, and statistical models of optical fields

The basic function of modern optical detectors and focal plane arrays

Practical strategies for coherence measurement in imaging system design

The sampling theory of digital imaging and spectroscopy for both conventional and emerging compressive and generalized measurement strategies

Measurement code design

Linear and nonlinear signal estimation

The book concludes with a review of numerous design strategies in spectroscopy and imaging and clearly outlines the benefits and limits of each approach, including coded aperture and imaging spectroscopy, resonant and filter-based systems, and integrated design strategies to improve image resolution, depth of field, and field of view.

Optical Imaging and Spectroscopy is an indispensable textbook for advanced undergraduate and graduate courses in optical sensor design. In addition to its direct applicability to optical system design, unique perspectives on computational sensor design presented in the text will be of interest for sensor designers in radio and millimeter wave, X-ray, and acoustic systems.

Author Notes

David J. Brady, PHD, received a BA in physics and mathematics from Macalester College and MS and PhD degrees in applied physics from California Institute of Technology. Dr. Brady is a Professor of Electrical and Computer Engineering in the Pratt School of Engineering at Duke University, where he directs the Duke Imaging and Spectroscopy Program. Dr. Brady is the architect of numerous computational imaging and spectroscopy systems, including multimodal multiplex spectroscopy and coded aperture snapshot spectral imaging. His current work focuses on multiple aperture lens system design and optical coherence measurement. He is a Fellow of the Optical Society of America, SPIE, and IEEE.

Preface	p. xiii
Acknowledgments	p. xv
Acronyms	p. xvii
1 Past, Present, and Future	p. 1
1.1 Three Revolutions	p. 1
1.2 Computational Imaging	p. 3
1.3 Overview	p. 6
1.4 The Fourth Revolution	p. 8
Problems	p. 9
2 Geometric Imaging	p. 11
2.1 Visibility	p. 11
2.2 Optical Elements	p. 14
2.3 Focal Imaging	p. 22
2.4 Imaging Systems	p. 28
2.5 Pinhole and Coded Aperture Imaging	p. 31
2.6 Projection Tomography	p. 41
2.7 Reference Structure Tomography	p. 47
Problems	p. 50
3 Analysis	p. 55
3.1 Analytical Tools	p. 55
3.2 Fields and Transformations	p. 56
3.3 Fourier Analysis	p. 59
3.4 Transfer Functions and Filter	p. 64
3.5 The Fresnel Transformation	p. 67
3.6 The Whittaker-Shannon Sampling Theorem	p. 72
3.7 Discrete Analysis of Linear Transformations	p. 75
3.8 Multiscale Sampling	p. 79
3.9 B-Splines	p. 89
3.10 Wavelets	p. 96
Problems	p. 100
4 Wave Imaging	p. 103
4.1 Waves and Fields	p. 103
4.2 Wave Model for Optical Fields	p. 104
4.3 Wave Propagation	p. 106
4.4 Diffraction	p. 109
4.5 Wave Analysis of Optical Elements	p. 115
4.6 Wave Propagation Through Thin Lenses	p. 121
4.7 Fourier Analysis of Wave Imaging	p. 124
4.8 Holography	p. 130
Problems	p. 141
5 Detection	p. 147
5.1 The Optoelectronic Interface	p. 147
5.2 Quantum Mechanics of Optical Detection	p. 148
5.3 Optoelectronic Detectors	p. 153
5.3.1 Photoconductive Detectors	p. 153
5.3.2 Photodiodes	p. 159
5.4 Physical Characteristics of Optical Detectors	p. 162
5.5 Noise	p. 165
5.6 Charge-Coupled Devices	p. 170
5.7 Active Pixel Sensors	p. 176
5.8 Infrared Focal Plane Arrays	p. 178
Problems	p. 183
6 Coherence Imaging	p. 187
6.1 Coherence and Spectral Fields	p. 187
6.2 Coherence Propagation	p. 190
6.3 Measuring Coherence	p. 198
6.3.1 Measuring Temporal Coherence	p. 198
6.3.2 Spatial Interferometry	p. 201
6.3.3 Rotational Shear Interferometry	p. 204
6.3.4 Focal Interferometry	p. 209
6.4 Fourier Analysis of Coherence Imaging	p. 216
6.4.1 Planar Objects	p. 217
6.4.2 3D Objects	p. 219
6.4.3 The Defocus Transfer Function	p. 224
6.5 Optical Coherence Tomography	p. 227
6.6 Modal Analysis	p. 231
6.6.1 Modes and Fields	p. 231
6.6.2 Modes and Coherence Functions	p. 234
6.6.3 Modal Transformations	p. 236
6.6.4 Modes and Measurement	p. 243
6.7 Radiometry	p. 245
6.7.1 Generalized Radiance	p. 245
6.7.2 The Constant Radiance Theorem	p. 247
Problems	p. 248
7 Sampling	p. 253
7.1 Samples and Pixels	p. 253
7.2 Image Plane Sampling on Electronic Detector Arrays	p. 255
7.3 Color Imaging	p. 268
7.4 Practical Sampling Models	p. 272
7.5 Generalized Sampling	p. 276
7.5.1 Sampling Strategies and Spaces	p. 277
7.5.2 Linear Inference	p. 282
7.5.3 Nonlinear Inference and Group Testing	p. 284
7.5.4 Compressed Sensing	p. 288
Problems	p. 294
8 Coding and Inverse Problems	p. 299
8.1 Coding Taxonomy	p. 299
8.2 Pixel Coding	p. 304
8.2.1 Linear Estimators	p. 305
8.2.2 Hadamard Codes	p. 306
8.3 Convolutional Coding	p. 308
8.4 Implicit Coding	p. 310
8.5 Inverse Problems	p. 319
8.5.1 Convex Optimization	p. 320
8.5.2 Maximum Likelihood Methods	p. 329
Problems	p. 331
9 Spectroscopy	p. 333
9.1 Spectral Measurements	p. 333
9.2 Spatially Dispersive Spectroscopy	p. 337
9.3 Coded Aperture Spectroscopy	p. 341
9.4 Interferometric Spectroscopy	p. 349
9.5 Resonant Spectroscopy	p. 354
9.6 Spectroscopic Filters	p. 364
9.6.1 Volume Holographic Filters	p. 365
9.6.2 Thin-Film Filters	p. 371
9.7 Tunable Filters	p. 380
9.7.1 Liquid Crystal Tunable Filters	p. 381
9.7.2 Acoustooptic Tunable Filters	p. 386
9.8 2D Spectroscopy	p. 389
9.8.1 Coded Apertures and Digital Superresolution	p. 391
9.8.2 Echelle Spectroscopy	p. 393
9.8.3 Multiplex Holograms	p. 398
9.8.4 2D Filter Arrays	p. 401
Problems	p. 403
10 Computational Imaging	p. 407
10.1 Imaging Systems	p. 407
10.2 Depth of Field	p. 408
10.2.1 Optical Extended Depth of Field (EDOF)	p. 410
10.2.2 Digital EDOF	p. 416
10.3 Resolution	p. 424
10.3.1 Bandlimited Functions Sampled over Finite Support	p. 425
10.3.2 Anomalous Diffraction and Nonlinear Detection	p. 439
10.4 Multiaperture Imaging	p. 442
10.4.1 Aperture Scaling and Field of View	p. 443
10.4.2 Digital Superresolution	p. 450
10.4.3 Optical Projection Tomography	p. 459
10.5 Generalized Sampling Revisited	p. 465
10.6 Spectral Imaging	p. 472
10.6.1 Full Data Cube Spectral Imaging	p. 472
10.6.2 Coded Aperture Snapshot Spectral Imaging	p. 479
Problems	p. 487
References	p. 493
Index	p. 505

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Table of Contents