Introduction To Fourier Optics

by Goodman, Joseph W.

• ISBN13: 9780974707723
• ISBN10: 0974707724
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-12-10
• Publisher: W. H. Freeman

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.

Author Biography

Joseph W. Goodman held the William Ayer Chair in Electrical Engineering at Stanford, and also served in several administrative posts, including Chair of the Department of Electrical Engineering, and Senior Associate Dean of Engineering for Faculty Affairs. He is now the William Ayer Professor Emeritus. His work has been recognized by a variety of awards and honors, including the F.E. Terman Award of the American Society for Engineering Education, the Dennis Gabor Award of the International Society for Optical Engineering (SPIE), the Max Born Award, the Esther Beller Hoffman Award, the Ives Medal from the Optical Society of America, and the Education Medal of the Institute of Electrical and Electronics Engineers. He is a member of the National Academy of Engineering and has served as president of the Optical Society of America and the International Commission for Optics.

Table of Contents

Preface	vii
Introduction	1	(2)
Optics, Information, and Communication	1	(1)
The Book	2	(1)
Analysis of Two-Dimensional Signals and Systems	3	(28)
Fourier Analysis in Two Dimensions	4	(11)
Definition and Existence Conditions	4	(2)
The Fourier Transform as a Decomposition	6	(1)
Fourier Transform Theorems	7	(2)
Separable Functions	9	(1)
Functions with Circular Symmetry: Fourier-Bessel Transforms	10	(2)
Some Frequently Used Functions and Some Useful Fourier Transform Pairs	12	(3)
Spatial Frequency and Space-Frequency Localization	15	(3)
Linear Systems	18	(4)
Linearity and the Superposition Integral	19	(1)
Invariant Linear Systems: Transfer Functions	20	(2)
Two-Dimensional Sampling Theory	22	(9)
The Whittaker-Shannon Sampling Theorem	22	(4)
Space-Bandwidth Product	26	(5)
Foundations of Scalar Diffraction Theory	31	(32)
Historical Introduction	31	(4)
From a Vector to a Scalar Theory	35	(3)
Some Mathematical Preliminaries	38	(4)
The Helmholtz Equation	38	(1)
Green's Theorem	39	(1)
The Integral Theorem of Helmholtz and Kirchhoff	39	(3)
The Kirchhoff Formulation of Diffraction by a Planar Screen	42	(4)
Application of the Integral Theorem	42	(2)
The Kirchhoff Boundary Conditions	44	(1)
The Fresnel-Kirchhoff Diffraction Formula	45	(1)
The Rayleigh-Sommerfeld Formulation of Diffraction	46	(4)
Choice of Alternative Green's Functions	47	(2)
The Rayleigh-Sommerfeld Diffraction Formula	49	(1)
Comparison of the Kirchhoff and Rayleigh-Sommerfeld Theories	50	(2)
Further Discussion of the Huygens-Fresnel Principle	52	(1)
Generalization to Nonmonochromatic Waves	53	(1)
Diffraction at Boundaries	54	(1)
The Angular Spectrum of Plane Waves	55	(8)
The Angular Spectrum and Its Physical Interpretation	55	(2)
Propagation of the Angular Spectrum	57	(2)
Effects of a Diffracting Aperture on the Angular Spectrum	59	(1)
The Propagation Phenomenon as a Linear Spatial Filter	60	(3)
Fresnel and Fraunhofer Diffraction	63	(34)
Background	63	(3)
The Intensity of a Wave Field	63	(2)
The Huygens-Fresnel Principle in Rectangular Coordinates	65	(1)
The Fresnel Approximation	66	(8)
Positive vs. Negative Phases	68	(1)
Accuracy of the Fresnel Approximation	68	(4)
The Fresnel Approximation and the Angular Spectrum	72	(1)
Fresnel Diffraction between Confocal Spherical Surfaces	73	(1)
The Fraunhofer Approximation	74	(1)
Examples of Fraunhofer Diffraction Patterns	75	(9)
Rectangular Aperture	76	(1)
Circular Aperture	76	(2)
Thin Sinusoidal Amplitude Grating	78	(4)
Thin Sinusoidal Phase Grating	82	(2)
Examples of Fresnel Diffraction Calculations	84	(13)
Fresnel Diffraction by a Square Aperture	84	(4)
Fresnel Diffraction by a Sinusoidal Amplitude Grating---Talbot Images	88	(9)
Wave-Optics Analysis of Coherent Optical Systems	97	(30)
A Thin Lens as a Phase Transformation	97	(6)
The Thickness Function	98	(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