9780974707723

Introduction To Fourier Optics

by
  • ISBN13:

    9780974707723

  • ISBN10:

    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.

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

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