statistical optics - goodman

f? OODMAN Statistical Optics The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and lntegral Calculus, Volume I Rlchard Courant Differential and lntegral Calculus, Volume I1 Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert . Methods of Mathematical Physics, Volume I1 D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & lrving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research (continued on inside back cover) 1 ISBN 0-47L-399Lb-7 (continued from back cover) Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1- Nuclear Structure Harold F. Dodge & Harry G. Romig Sampling Inspection Tables: Single and Double Sampling J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory- Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Regina C. ElandtJohnson & Norman L. Johnson Survlval Models and Data Analysis Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Joseph L. Fleiss Design and Analysis of Clinical Experiments Bernard Friedman Lectures on Applications-Oriented Mathematics Joseph Goodman Statistical Optics Phillip Griffiths & Joseph Harris Principles of Algebraic Geometry Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Marshall Hall Jr. Combinatorial Theory, Second Edition Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I-Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume 11-Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1-Power Series-Integration-Conformal Mapping-Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2-Special Functions-Integral Transforms-Asymptotics-Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3 Discrete Fourier Analysis- Cauchy Integrals-Construction of Conformal Maps Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra David C. Hoaglin, Frederick Mosteller & John W. Tukey Understanding Robust and Exploratory Data Analysis Harry Hochstadt Integral Equations Leslie Kish Survey Sampling Shoshichi Kobayashi & Katsumi Nomizu Foundations of Differential Geometry, Volume I Shoshichi Kobayashi & Katsumi Nomizu Foundations of Differential Geometry, Volume 2 Erwin 0. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Rupert G. Miller Jr. Survival Analysis Ali Hasan Nayfeh lntroduction to Perturbation Techniques Ali Hasan Nayfeh Perturbation Methods Ali Hasan Nayfeh & Dean T. Mook Nonlinear Oscillations Emanuel Parzen Modern Probability Theory & Its Applications P. M. Prenter Splines and Variational Methods Howard Raiffa & Robert Schlaifer Applied Statistical Decision Theory Walter Rudin Fourier Analysis on Groups Lawrence S. Schulman Techniques and Applications of Path Integration Shayle R. Searle Linear Models I. H. Segel Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems C. L. Siegel Topics in Complex Function Theory, Volume I- Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II- Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III- Abelian Functions and Modular Functions of Several Variables L. Spitzer Physical Processes in the Interstellar Medium J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems Giinter Wyszecki & W. S. Stiles Color Science: Concepts and Methods, Quant~tative Data and Formulae, Second Edition Richard Zallen The Physics of Amorphous Solids Arnold Zellner Introduction to Bayesian inference in Econometrics Statistical Optics JOSEPH W. GOODMAN Wiley Classics Library Edition Published 2000 A Wiley-Interscience Publication JOHN WILEY & SONS, INC. NewYork Chichester Weinheim Brisbane Singapore Toronto This text is printed on acid-free paper. @ Copyright O 1985 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Wiley Classics Library Edition published 2000. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-601 1, fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM. For ordering or customer information, please call 1 -800-CALL-WILEY. Library of Congress Cataloging in Publication Data: Library of Congress Catalog Card Number: 84- 13 160 ISBN 0-47 1-0 1502-4 ISBN 0-47 1-3991 6-7 (Classics Edition) Printed in the United States of America. 1098765432 1 To Hon Mai, who has provided rhe light. Preface Since the early 1960s it has gradually become accepted that a modern academic training in optics should include a heavy exposure to the concepts of Fourier analysis and linear systems theory. This book is based on the thesis that a similar stage has been reached with respect to the tools of probability and statistics and that some training in the area of statistical optics should be included as a standard part of any advanced optics curriculum. In writing this book I have attempted to fill the need for a suitable textbook in this area. The subjects covered in this book are very physical but tend to be obscured by mathematics. An author of a book on this subject is thus faced with the dilemma of how best to utilize the powerful mathematical tools available without losing sight of the underlying physics. Some compromises in mathematical rigor must be made, and to the largest extent possible, a repetitive emphasis of the physical meaning of mathematical quantities is needed. Since fringe formation is the most fundamental underlying physical phenomenon involved in most of these subjects, I have tried to stay as close as possible to fringes in dealing with the meaning of the mathematics. I would hope that the treatment used here would be particularly appealing to both optical and electrical engineers, and also useful for physicists. The treatment is suitable for both self-study and for formal presentation in the classroom. Many homework problems are included. The material contained in this book covers a great deal of ground. An outline is included in Chapter 1 and is not repeated here. The course on whch this text is based was taught over the 10 weeks of a single academic quarter, but there is sufficient material for a full 15-week semester, or perhaps even two academic quarters. The problem is then to decide what material to omit in a single-quarter version. If the material is to be covered in one quarter, it is essential that the students have previous exposure to probability theory and stochastic processes as well as a good grasp of Fourier methods. Under these conditions, my suggestion to the instructor is viii PREFACE to allow the students to study Chapters 1-3 on their own and to begin the lectures directly with optics in Chapter 4. Later sections that can be omitted or left to optional reading if time is short include Sections 5.6.4, 5.7, 6.1.3, 6.2, 6.3, 7.2.3, 7.5, 8.2.2, 8.6.1, 8.7.2, 8.8.3, 9.4, 9.5, and 9.6. It is perhaps worth mentioning that I have also occasionally used Chapters 2 and 3 as the basis for a full one-quarter course on the fundamentals of probability and stochastic processes. The book began in the form of rough notes for a course at Stanford University in 1968 and thus has been a long time in the making. In many respects it has been too long in the making (as my patient publisher will surely agree), for over a period of more than 15 years any field undergoes important changes. The challenge has thus been to treat the subject matter in a manner that does not become obsolete as time progresses. In an attempt to keep the information as up to date as possible, supplementary lists of recent references have been provided at the ends of various chapters. The transition from a rough set of notes to a more polished manuscript first began in the academic year 2973-1974, when I was fortunate enough to spend a sabbatical year at the Institute d'optique, in Orsay, France. The hospitality of my immediate host, Professor Serge Lowenthal, as well as the Institute's Director, Professor Andre Marechal, was impeccable. Not only did they provide me with all the surroundings needed for productivity, but they were kind enough to relieve me of duties normally accompanying a formal appointment. I am most grateful for their support and advice, without which this book would never have had a solid start. One benefit from the slowness with which the book progressed was the opportunity over many years to expose the material to a host of graduate students, who have an uncanny ability to spot the weak arguments and the outright errors in such a manuscript. To the students of my statistical optics courses at Stanford, therefore, I owe an enormous debt. The evolving notes were also used at a number of other universities, and I am grateful to both William Rhodes (Georgia Institute of Technology) and Timothy Strand (University of Southern California) for providing me with feedback that improved the presentation. The relationshp between author and publisher is often a distant one and sometimes not even pleasant. Nothing could be further from the truth in this case. Beatrice Shube, the editor at John Wiley & Sons who encouraged me to begin this book 15 years ago, has not only been exceedingly patient and understanding, but has also supplied much encouragement and has become a good personal friend. It has been the greatest of pleasures to work with her. 1 owe special debts to K C. Chn, of Beijing University, for his enormous inves tmen t of time in reading the manuscript and suggesting improvements, PREFACE ix and to Judith Clark, who typed the manuscript, including all the difficult mathematics, in an extremely professional way. Finally, 1 am unable to express adequate thanks to my wife, Hon Mai, and my daughter Michele, not only for their encouragement, but also for the many hours they accepted being without me while I labored at writing. Stan ford, California October 1984 Contents 1. Introduction 1.1 Deterministic versus Statistical Phenomena and Models 1.2 Statistical Phenomena in Optics 1.3 An Outline of the Book 2. Random Variables Definitions of Probability and Random Variables Distribution Functions and Density Functions Extension to Two or More Joint Random Variables St at is tical Averages 2.4.1 Moments of a Random Variable 2.4.2 Joint Moments of Random Variables 2.4.3 Characteristic Functions Transformations of Random Variables 2.5.1 General Transformation 2.5.2 Monotonic Functions 2.5.3 Multivariate Probability Transformations Sums of Real Random Variables 2.6.1 Two Methods for Finding p,(z) 2.6.2 Independent Random Variables 2.6.3 The Central Limit Theorem Gaussian Random Variables 2.7.1 Definitions 2.7.2 Special Properties of Gaussian Random Variables Complex-Valued Random Variables 2.8.1 General Descriptions 2.8.2 Complex Gaussian Random Variables [...]... and methods of analysis into the field of optics It is to the role of such concepts in optics that this book is devoted The field of statistical optics has a considerable hstory of its own Many fundamental statistical problems were solved in the late nineteenth century and applied to acoustics and optics by Lord Rayleigh The need for statistical methods in optics increased dramatically with the discovery... density function is expressible as -/ -, Mu(o)exp(-jou) dw 1 pu(u) = 2m O0 The characteristic function thus contains all information about the first-order statistical properties of the random variable U Under certain circumstances it is possible to obtain the characteristic function (and hence the probability density function by 2. 4-1 9) from knowledge of the n th-order moments for all n To demonstrate... a Thin Lens 7.1.3 Focal-Plane- to-Focal-Plane Coherence Relationships 7.1.4 Object-Image Coherence Relations for a Single Thin Lens 7.1.5 Relationship Between Mutual Intensities in the Exit Pupil and the Image 7.2 Methods for Calculating Image Intensity 7.2.1 Integration over the Source 7.2.2 Representation of the Source by an Incident Mutual Intensity Function 7.2.3 The Four-Dimensional Linear Systems... the time this book is completed 1.2 STATISTICAL PHENOMENA IN OPTICS Statistical phenomena are so plentiful in optics that there is no difficulty in compiling a long list of examples Because of the wide variety of these problems, it is difficult to find a general scheme for classifying them Here we attempt to identify several broad aspects of optics that require statistical treatment These aspects are... Fourier Transform A.3 Table of One-Dimensional Fourier Transforms A.4 Table of Two-Dimensional Fourier Transform Pairs Appendix B Random Phasor Sums Appendix C Fourth-Order Moment of the Spectrum of a Detected Speckle Image Index xvii 477 479 481 481 486 490 491 493 494 496 501 502 503 506 510 511 512 517 519 521 528 528 529 531 532 533 Statistical Optics Introduction Optics, as a field of science, is... Densities for Linearly Filtered Random Processes Autocorrelation Functions and the Wiener- Khinchin Theorem Cross-Correlation Functions and Cross-Spectral Densities The Gaussian Random Process 3.6.1 Definition 3.6.2 Linearly Filtered Gaussian Random Processes 3.6.3 Wide-Sense Stationarity and Strict Stationarity 3.6.4 Fourth-Order Moments The Poisson Impulse Process 3.7.1 Definitions 3.7.2 Derivation of Poisson... avoided is based on too narrow a view of the nature of statistical phenomena Experimental evidence indicates, and indeed the great majority of physicists believe, that the interaction of light and STATISTICAL PHENOMENA IN OPTICS 3 matter is fundamentally a statistical phenomenon, which cannot in principle be predicted with perfect precision in advance Thus statistical phenomena play a role of the greatest... Electromagnetic Wave Propagation Through the Inhomogeneous Atmosphere 8.4.4 The Log-Normal Distribution The Long-Exposure OTF 8.5.1 Long-Exposure OTF in Terms of the Wave Structure Function 8.5.2 N ear-Field Calculation of the Wave Structure Function Generalizations of the Theory 8.6.1 Extension to Longer Propagation Paths-Amplitude and Phase Filter Functions 8.6.2 Effects of Smooth Variations of the... plausibility For more rigorous treatment of the theory of probability, the reader may consult texts on statistics (e.g., Refs 2-1 and 2-2 ) In addition, there are many excellent engineering-oriented books that discuss the theory of random variables and random processes (e.g., Refs 2-3 through 2-8 ) 2.1 DEFINITIONS OF PROBABILITY AND RANDOM VARIABLES By a random experiment we mean an experiment with an outcome... Representation of a Monochromatic Signal by a Complex Signal 3.8 -2 Representation of a Nonmonochromatic Signal by a Complex Signal 3.8.3 Complex Envelopes or Time-Varying Phasors 3.8.4 The Analytic Signal as a Complex-Valued Random Process CONTENTS Xlll 3.9 The Complex Gaussian Random Process 3.10 The Karhunen-Loeve Expansion 4 Some First-Order Properties of Light Waves 4.1 Propagation of Light Waves . 1015 8-0 012, (212) 85 0-6 01 1, fax (212) 85 0-6 008, E-Mail: PERMREQ @ WILEY.COM. For ordering or customer information, please call 1 -8 00-CALL-WILEY Data: Library of Congress Catalog Card Number: 8 4- 13 160 ISBN 0-4 7 1-0 150 2-4 ISBN 0-4 7 1-3 991 6-7 (Classics Edition) Printed in the United States