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Introduction to Fourier Optics 2nd-Goodman
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Introduction to Fourier Optics 2nd-Goodman
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Introduction
to
Fourier Optics
SECOND EDITION
Joseph
W.
Goodman
Stanford University
THE McGRAW-HILL COMPANIES,
INC.
New York St. Louis San Francisco Auckland Bogot6 Caracas Lisbon
London Madrid Mexico City Milan Montreal New Delhi
San Juan Singapore Sydney Tokyo Toronto
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ABOUT
THE
AUTHOR
JOSEPH
W.
GOODMAN
received the A.B. degree in Engineering and Applied
Physics from Harvard University and the M.S and
Ph.D. degrees in Electrical Engi
-
neering from Stanford University. He has been a member of the Stanford faculty since
1967, and served as the Chairman of the Department of Electrical Engineering from
1988 through 1996.
Dr. Goodman's contributions to optics have been recognized in many ways. He has
served as President of the International Commission for Optics and of the Optical So
-
ciety of America (OSA). He received the F.E. Terman award of the American Society
for Engineering Education
(1971), the Max Born Award of the OSA for contributions
to physical optics
(1983), the Dennis Gabor Award of the International Society for Op
-
tical Engineering (SPIE, 1987), the Education Medal of the Institute of Electrical and
Electronics Engineers (IEEE,
1987), the Frederic Ives Medal of the OSA for overall
distinction in optics
(1990), and the Esther Hoffman Beller Medal of the OSA for con
-
tributions to optics education (1995). He is a Fellow of the OSA, the SPIE, and the
IEEE. In 1987 he was elected to the National Academy of Engineering.
In addition to
Introduction to Fourier Optics,
Dr.
Goodman is the author of
Statis
-
tical Optics
(J.
Wiley
&
Sons, 1985) and the editor of
International Trends in Optics
(Academic Press, 1991). He has authored more than 200 scientific and technical articles
in professional journals and books.
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CONTENTS
Preface
1
Introduction
1.
Optics, Information, and Communication
1.2
The Book
2
Analysis of Two
-
Dimensional Signals and Systems
2.1
Fourier Analysis in Two Dimensions
2.1.1 Dejinition and Existence Conditions
/
2.1.2 The Fourier
Transform as a Decomposition
/
2.1.3 Fourier Transform
Theorems
/
2.1.4 Separable Functions
/
2.1.5 Functions with
Circular Symmetry: Fourier
-
Bessel Transforms
/
2.1.6 Some
Frequently Used Functions
and Some Useful Fourier Transform
Pairs
2.2
Local Spatial Frequency and Space
-
Frequency Localization
2.3
Linear Systems
2.3.1 Lineurity and the Superposition Integral
/
2.3.2 Invuriunt
Linear Systems: Transfer Functions
2.4
Two
-
Dimensional Sampling Theory
2.4.1 The Whittaker
-
Shannon Sampling Theorem
/
2.4.2 Spacse-
Bandwidth Producf
Problems
-
Chapter
2
3
Foundations of Scalar Diffraction Theory
3.1 Historical Introduction
3.2
From
a
Vector to a Scalar Theory
3.3
Some Mathematical Preliminaries
3.3.1 The Helmholtz Equation
/
3.3.2 Green
:s
Theorem
/
3.3.3 The Intrgrul Theorem oj Helmholtz and Kirchhofl
3.4
The Kirchhoff Formulation of Diffraction by
a
Planar
Screen
3.4.1 Applicution cfrhr Integral Theorem
/
3.4.2 The Kirchhoff
Boundary Conditiorzs
/
3.4.3
The L'resnel-Kirchhoff D;ffrclction
Formula
3.5
The Rayleigh-Somrnerfeld Formulation of Diffraction
3.5.1 Choice of Alternative Green
:s
Furzction.~
/
3.5.2 The
Kuylc.igh-Sornmerfeld 1)iffruc.tion Fornzulu
xvii
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xii
Contents
3.6
Comparison of the Kirchhoff and Rayleigh
-
Sommerfeld
Theories
3.7
Further Discussion of the Huygens
-
Fresnel Principle
3.8
Generalization to Nonmonochromatic Waves
3.9
Diffraction at Boundaries
3.10
The Angular Spectrum of Plane Waves
3.10.1
The Angular Spectrum and Its Physical Interpretation
/
3.10.2
Propagation of the Angular Spectrum
/
3.10.3
Effects
of a Diffracting Aperture on the Angular Spectrum
/
3.10.4
The Propagation Phenomenon as a Linear Spatial Filter
Problems
-
Chapter
3
4
Fresnel and Fraunhofer Diffraction
4.1
Background
4.1.
I
The Intensity of a Wave Field
/
4.1.2
The Huygens
-
Fresnel
Principle in Rectangular Coordinates
4.2
The Fresnel Approximation
4.2.1
Positive vs. Negative Phases
/
4.2.2
Accuracy of the
Fresnel Approximation
/
4.2.3
The Fresnel Approximation and
the Angular Spectrum
/
4.2.4
Fresnel Diffraction Between
Confocal Spherical
Sur$aces
4.3
The Fraunhofer Approximation
4.4
Examples of Fraunhofer Diffraction Patterns
4.4.1
Rectangular Aperture
/
4.4.2
Circular Aperture
/
4.4.3
Thin Sinusoidal Amplitude Grating
/
4.4.4
Thin
Sinusoidal Phase Grating
4.5
Examples of Fresnel Diffraction Calculations
4.5.1
Fresnel Diffraction
by
a Square Aperture
/
4.5.2
Fresnel Diffraction by a Sinusoidal Amplitude
Grating
-
Talbot Images
Problems
-
-
Chapter
4
5
Wave
-
Optics Analysis of Coherent Optical Systems
5.1
A Thin Lens as a Phase Transformation
5.1.
I
The Thickness Function
/
5.1.2
The Paraxial
Approximation
/
5.1.3
The Phase Transformation and
Its Physical Meaning
5.2
Fourier Transforming Properties of Lenses
5.2.1
Input Placed Against the Lens
/
5.2.2
Input Placed in Front
of the Lens
/
5.2.3
Input Placed Behind the Lens
/
5.2.4
Example
of an Optical Fourier Transform
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Contents
5.3
Image Formation: Monochromatic Illumination
5.3.1 The Impulse Response of a Positive Lens
/
5.3.2 Eliminating
Quadratic Phase Factors: The Lens Law
/
5.3.3 The Relation
Between Object and Image
5.4
Analysis of Complex Coherent Optical Systems
5.4.
I
An Operator Notation
/
5.4.2 Application of the Operator
Approach to Some Optical Systems
Problems
-
-
Chapter
5
6
Frequency Analysis of Optical Imaging Systems
6.1
Generalized Treatment of Imaging Systems
6.1.1 A Generalized Model
/
6.1.2 Effects of Diffraction on the
Image
/
6.1.3 Polychromatic Illumination: The Coherent and
Incoherent Cases
6.2
Frequency Response for Diffraction
-
Limited Coherent
Imaging
6.2.1 The Amplitude Transfer Function
/
6.2.2 Examples of
Amplitude Transfer Functions
6.3
Frequency Response for Diffraction
-
Limited Incoherent
Imaging
6.3.1 The Optical Transfer Function
/
6.3.2 General Properties
of the OTF
/
6.3.3 The OTF of an Aberration
-
Free System
/
6.3.4 Examples of Diffraction
-
Limited OTFs
6.4
Aberrations and Their Effects on Frequency Response
6.4.1 The Generalized Pupil Function
/
6.4.2 EfSects of
Aberrations on the Amplitude Transfer Function
/
6.4.3 Effects
of Aberrations on the OTF
/
6.4.4 Example of a Simple
Aberration: A Focusing Error
/
6.4.5 Apodization and Its
Effects on Frequency Response
6.5
Comparison of Coherent and Incoherent Imaging
6.5.1 Frequency Spectrum of the Image Intensity
/
6.5.2
Two
-
Point Resolution
/
6.5.3 Other Effects
6.6
Resolution Beyond the Classical Diffraction Limit
6.6.1 Underlying Mathematical Fundamentals
/
6.6.2 Intuitive
Explanation of Bandwidth Extrapolation
/
6.6.3 An Extrapolation
Method Based on the Sampling Theorem
/
6.6.4 An Iterative
Extrapolation Method
/
6.6.5 Practical Limitations
Problems
-
-
Chapter
6
7
Wavefront Modulation
7.1
Wavefront Modulation with Photographic Film
7.1.1 The Physical Processes of Exposure, Development, and
Fixing
/
7.1.2 Dejinition of Terms
/
7.1.3 Film in an Incoherent
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