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Introduction To Fourier Optics

by: Goodman, Joseph W.

Introduction To Fourier Optics

by: Goodman, Joseph W.

ISBN 13:
9780974707723
ISBN 10:
0974707724
Edition: 3rd
Format: Hardcover
Copyright: 12/10/2004
Publisher: W. H. Freeman

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Summary

Fourier analysis is a ubiquitous tool that has found application to diverse areas of physics and engineering. This book deals with its applications in optics, and in particular with its applications to diffraction, imaging, optical data processing, holography and optical communications.

Preface

vii

Introduction

(2)

Optics, Information, and Communication

(1)

The Book

(1)

Analysis of Two-Dimensional Signals and Systems

(28)

Fourier Analysis in Two Dimensions

(11)

Definition and Existence Conditions

(2)

The Fourier Transform as a Decomposition

(1)

Fourier Transform Theorems

(2)

Separable Functions

(1)

Functions with Circular Symmetry: Fourier-Bessel Transforms

(2)

Some Frequently Used Functions and Some Useful Fourier Transform Pairs

(3)

Spatial Frequency and Space-Frequency Localization

(3)

Linear Systems

(4)

Linearity and the Superposition Integral

(1)

Invariant Linear Systems: Transfer Functions

(2)

Two-Dimensional Sampling Theory

(9)

The Whittaker-Shannon Sampling Theorem

(4)

Space-Bandwidth Product

(5)

Foundations of Scalar Diffraction Theory

(32)

Historical Introduction

(4)

From a Vector to a Scalar Theory

(3)

Some Mathematical Preliminaries

(4)

The Helmholtz Equation

(1)

Green's Theorem

(1)

The Integral Theorem of Helmholtz and Kirchhoff

(3)

The Kirchhoff Formulation of Diffraction by a Planar Screen

(4)

Application of the Integral Theorem

(2)

The Kirchhoff Boundary Conditions

(1)

The Fresnel-Kirchhoff Diffraction Formula

(1)

The Rayleigh-Sommerfeld Formulation of Diffraction

(4)

Choice of Alternative Green's Functions

(2)

The Rayleigh-Sommerfeld Diffraction Formula

(1)

Comparison of the Kirchhoff and Rayleigh-Sommerfeld Theories

(2)

Further Discussion of the Huygens-Fresnel Principle

(1)

Generalization to Nonmonochromatic Waves

(1)

Diffraction at Boundaries

(1)

The Angular Spectrum of Plane Waves

(8)

The Angular Spectrum and Its Physical Interpretation

(2)

Propagation of the Angular Spectrum

(2)

Effects of a Diffracting Aperture on the Angular Spectrum

(1)

The Propagation Phenomenon as a Linear Spatial Filter

(3)

Fresnel and Fraunhofer Diffraction

(34)

Background

(3)

The Intensity of a Wave Field

(2)

The Huygens-Fresnel Principle in Rectangular Coordinates

(1)

The Fresnel Approximation

(8)

Positive vs. Negative Phases

(1)

Accuracy of the Fresnel Approximation

(4)

The Fresnel Approximation and the Angular Spectrum

(1)

Fresnel Diffraction between Confocal Spherical Surfaces

(1)

The Fraunhofer Approximation

(1)

Examples of Fraunhofer Diffraction Patterns

(9)

Rectangular Aperture

(1)

Circular Aperture

(2)

Thin Sinusoidal Amplitude Grating

(4)

Thin Sinusoidal Phase Grating

(2)

Examples of Fresnel Diffraction Calculations

(13)

Fresnel Diffraction by a Square Aperture

(4)

Fresnel Diffraction by a Sinusoidal Amplitude Grating---Talbot Images

(9)

Wave-Optics Analysis of Coherent Optical Systems

(30)

A Thin Lens as a Phase Transformation

(6)

The Thickness Function

(2)

The Paraxial Approximation

100

(1)

The Phase Transformation and Its Physical Meaning

100

(3)

Fourier Transforming Properties of Lenses

103

(5)

Input Placed against the Lens

104

(1)

Input Placed in Front of the Lens

105

(2)

Input Placed behind the Lens

107

(1)

Example of an Optical Fourier Transform

108

(1)

Image Formation: Monochromatic Illumination

108

(7)

The Impulse Response of a Positive Lens

109

(2)

Eliminating Quadratic Phase Factors: The Lens Law

111

(3)

The Relation between Object and Image

114

(1)

Analysis of Complex Coherent Optical Systems

115

(12)

An Operator Notation

115

(3)

Application of the Operator Approach to Some Optical Systems

118

(9)

Frequency Analysis of Optical Imaging Systems

127

(46)

Generalized Treatment of Imaging Systems

128

(7)

A Generalized Model

128

(1)

Effects of Diffraction on the Image

129

(2)

Polychromatic Illumination: The Coherent and Incoherent Cases

131

(4)

Frequency Response for Diffraction-Limited Coherent Imaging

135

(3)

The Amplitude Transfer Function

136

(1)

Examples of Amplitude Transfer Functions

137

(1)

Frequency Response for Diffraction-Limited Incoherent Imaging

138

(7)

The Optical Transfer Function

138

(2)

General Properties of the OTF

140

(1)

The OTF of an Aberration-Free System

141

(2)

Examples of Diffraction-Limited OTFs

143

(2)

Aberrations and Their Effects on Frequency Response

145

(9)

The Generalized Pupil Function

145

(2)

Effects of Aberrations on the Amplitude Transfer Function

147

(1)

Effects of Aberrations on the OTF

148

(1)

Example of a Simple Aberration: A Focusing Error

149

(3)

Apodization and Its Effects on Frequency Response

152

(2)

Comparison of Coherent and Incoherent Imaging

154

(8)

Frequency Spectrum of the Image Intensity

156

(2)

Two-Point Resolution

158

(2)

Other Effects

160

(2)

Resolution beyond the Classical Diffraction Limit

162

(11)

Underlying Mathematical Fundamentals

162

(1)

Intuitive Explanation of Bandwidth Extrapolation

163

(1)

An Extrapolation Method Based on the Sampling Theorem

164

(2)

An Iterative Extrapolation Method

166

(1)

Practical Limitations

167

(6)

Wavefront Modulation

173

(46)

Wavefront Modulation with Photographic Film

174

(12)

The Physical Processes of Exposure, Development, and Fixing

174

(1)

Definition of Terms

175

(3)

Film in an Incoherent Optical System

178

(1)

Film in a Coherent Optical System

179

(3)

The Modulation Transfer Function

182

(3)

Bleaching of Photographic Emulsions

185

(1)

Spatial Light Modulators

186

(26)

Properties of Liquid Crystals

187

(8)

Spatial Light Modulators Based on Liquid Crystals

195

(4)

Magneto-Optic Spatial Light Modulators

199

(3)

Deformable Mirror Spatial Light Modulators

202

(2)

Multiple Quantum Well Spatial Light Modulators

204

(4)

Acousto-Optic Spatial Light Modulators

208

(4)

Diffractive Optical Elements

212

(7)

Binary Optics

212

(4)

Other Types of Diffractive Optics

216

(1)

A Word of Caution

216

(3)

Analog Optical Information Processing

219

(78)

Historical Background

220

(6)

The Abbe-Porter Experiments

220

(2)

The Zernike Phase-Contrast Microscope

222

(2)

Improvement of Photographs: Marechal

224

(2)

The Emergence of a Communications Viewpoint

226

(1)

Application of Coherent Optics to More General Data Processing

226

(1)

Incoherent Image Processing Systems

226

(8)

Systems Based on Geometrical Optics

227

(5)

Systems That Incorporate the Effects of Diffraction

232

(2)

Coherent Optical Information Processing Systems

234

(5)

Coherent System Architectures

234

(3)

Constraints on Filter Realization

237

(2)

The VanderLugt Filter

239

(6)

Synthesis of the Frequency-Plane Mask

239

(3)

Processing the Input Data

242

(2)

Advantages of the VanderLugt Filter

244

(1)

The Joint Transform Correlator

245

(3)

Application to Character Recognition

248

(5)

The Matched Filter

248

(1)

A Character-Recognition Problem

249

(2)

Optical Synthesis of a Character-Recognition Machine

251

(1)

Sensitivity to Scale Size and Rotation

252

(1)

Optical Approaches to Invariant Pattern Recognition

253

(6)

Mellin Correlators

254

(2)

Circular Harmonic Correlation

256

(1)

Synthetic Discriminant Functions

257

(2)

Image Restoration

259

(6)

The Inverse Filter

259

(2)

The Wiener Filter, or the Least-Mean-Square-Error Filter

261

(1)

Filter Realization

262

(3)

Processing Synthetic-Aperture Radar (SAR) Data

265

(12)

Formation of the Synthetic Aperture

266

(1)

The Collected Data and the Recording Format

267

(2)

Focal Properties of the Film Transparency

269

(4)

Forming a Two-Dimensional Image

273

(1)

The Tilted Plane Processor

274

(3)

Acousto-Optic Signal Processing Systems

277

(7)

Bragg Cell Spectrum Analyzer

278

(2)

Space-Integrating Correlator

280

(1)

Time-Integrating Correlator

281

(2)

Other Acousto-Optic Signal Processing Architectures

283

(1)

Discrete Analog Optical Processors

284

(13)

Discrete Representation of Signals and Systems

284

(1)

A Serial Matrix-Vector Multiplier

285

(1)

A Parallel Incoherent Matrix-Vector Multiplier

286

(2)

An Outer Product Processor

288

(2)

Other Discrete Processing Architectures

290

(1)

Methods for Handling Bipolar and Complex Data

290

(7)

Holography

297

(102)

Historical Introduction

297

(1)

The Wavefront Reconstruction Problem

298

(5)

Recording Amplitude and Phase

298

(1)

The Recording Medium

299

(1)

Reconstruction of the Original Wavefront

300

(1)

Linearity of the Holographic Process

301

(1)

Image Formation by Holography

302

(1)

The Gabor Hologram

303

(3)

Origin of the Reference Wave

304

(1)

The Twin Images

305

(1)

Limitations of the Gabor Hologram

306

(1)

The Leith-Upatnieks Hologram

306

(10)

Recording the Hologram

307

(1)

Obtaining the Reconstructed Images

308

(2)

The Minimum Reference Angle

310

(1)

Holography of Three-Dimensional Scenes

311

(3)

Practical Problems in Holography

314

(2)

Image Locations and Magnification

316

(5)

Image Locations

316

(3)

Axial and Transverse Magnifications

319

(1)

An Example

320

(1)

Some Different Types of Holograms

321

(11)

Fresnel, Fraunhofer, Image, and Fourier Holograms

322

(1)

Transmission and Reflection Holograms

323

(2)

Holographic Stereograms

325

(1)

Rainbow Holograms

326

(3)

Multiplex Holograms

329

(2)

Embossed Holograms

331

(1)

Thick Holograms

332

(18)

Recording a Volume Holographic Grating

332

(2)

Reconstructing Wavefronts from a Volume Grating

334

(1)

Fringe Orientations for More Complex Recording Geometries

335

(2)

Gratings of Finite Size

337

(2)

Diffraction Efficiency---Coupled Mode Theory

339

(11)

Recording Materials

350

(5)

Silver Halide Emulsions

350

(1)

Photopolymer Films

351

(1)

Dichromated Gelatin

352

(1)

Photorefractive Materials

352

(3)

Computer-Generated Holograms

355

(12)

The Sampling Problem

356

(3)

The Computational Problem

359

(1)

The Representational Problem

359

(8)

Degradations of Holographic Images

367

(7)

Effects of Film MTF

368

(3)

Effects of Film Nonlinearities

371

(1)

Effects of Film-Grain Noise

372

(1)

Speckle Noise

373

(1)

Holography with Spatially Incoherent Light

374

(3)

Applications of Holography

377

(22)

Microscopy and High-Resolution Volume Imagery

377

(1)

Interferometry

378

(6)

Imaging through Distorting Media

384

(4)

Holographic Data Storage

388

(1)

Holographic Weights for Artificial Neural Networks

389

(4)

Other Applications

393

(6)

Fourier Optics in Optical Communications

399

(34)

Introduction

399

(1)

Fiber Bragg Gratings

400

(10)

Introduction to Optical Fibers

400

(3)

Recording Gratings in Optical Fibers

403

(1)

Effects of an FBG on Light Propagating in the Fiber

404

(3)

Applications of FBGs

407

(2)

Gratings Operated in Transmission

409

(1)

Ultrashort Pulse Shaping and Processing

410

(5)

Mapping of Temporal Frequencies to Spatial Frequencies

410

(2)

Pulse Shaping System

412

(1)

Applications of Spectral Pulse Shaping

413

(2)

Spectral Holography

415

(5)

Recording the Hologram

415

(2)

Reconstructing the Signals

417

(3)

Effects of Delay between the Reference Pulse and the Signal Waveform

420

(1)

Arrayed Waveguide Gratings

420

(13)

Component Parts of an Arrayed Waveguide Grating

421

(6)

Applications of AWGs

427

(6)

A Delta Functions and Fourier Transform Theorems

433

(8)

Delta Functions

433

(2)

Derivation of Fourier Transform Theorems

435

(6)

B Introduction to Paraxial Geometrical Optics

441

(14)

The Domain of Geometrical Optics

441

(2)

Refraction, Snell's Law, and the Paraxial Approximation

443

(1)

The Ray-Transfer Matrix

444

(3)

Conjugate Planes, Focal Planes, and Principal Planes

447

(4)

Entrance and Exit Pupils

451

(4)

C Polarization and Jones Matrices

455

(8)

Definition of the Jones Matrix

455

(2)

Examples of Simple Polarization Transformations

457

(2)

Reflective Polarization Devices

459

(4)

D The Grating Equation

463

(2)

Bibliography

465

(16)

Index

481

Amazon no longer offers textbook rentals. We do!

Introduction To Fourier Optics

Introduction To Fourier Optics

9780974707723

0974707724

Summary

Author Biography

Table of Contents

Supplemental Materials

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