OPTICAL SIGNAL PROCESSING Edited by Joseph L. Horner Department of the Air Force Rome Air Development Center (AFSC) Hanscom AFB, Massachusetts ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers San Diego New York Berkeley Boston London Sydney Tokyo Toronto COPYRIGHT © 1987 BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY. RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, California 92101 United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD. 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging in Publication Data Optical signal processing. Includes index. 1. Image processing. 2. Optical data processing. I. Horner, Joseph L. (Joseph LeFevre) ΤΑΊ632.0674 Ί987 621.367 87-903 ISBN 0-12-355760-7 (alk. paper) PRINTED IN THE UNITED STATES OF AMERICA 87 88 89 90 9 8 7 6 5 4 3 2 1 List off Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin. Harrison H. Barrett (335), Optical Science Center, University of Arizona, Tuscon, Arizona 85721 H. Bartelt (97), University of Erlangen, Physikalisches Institut, Erwin- Rommel-Strabe 1, 8520 Erlangen, Federal Republic of Germany David Casasent (75, 389), Department of Electrical and Computer Engi- neering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 H. J. Caulfield (409), Center for Applied Optics, University of Alabama in Huntsville, Huntsville, Alabama 35899 J. N. Cederquist (525), Environmental Research Institute of Michigan, P.O. Box 8618, Ann Arbor, Michigan 48107 Roger L. East on, Jr. (335), Center for Imaging Science, Rochester Institute of Technology, Rochester, New York 14623 Nabil H. Farhat (129), The Moore School of Electrical Engineering, Uni- versity of Pennsylvania, 33rd & Walnut Streets, Philadelphia, Penn- sylvania 19104 Arthur D. Fisher (477), Optical Sciences Division, Naval Research Labora- tory, Washington, D.C. 20375 Mark O. Freeman (281), Department of Electrical and Computer Engineer- ing, University of Wisconsin, Madison, Wisconsin 53706 Michael Haney (191), The BDM Corporation, McLean, Virginia 22102 H. A. Haus (245), Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Insti- tute of Technology, Cambridge, Massachusetts 02139 E. P. Ippen (245), Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Insti- tute of Technology, Cambridge, Massachusetts 02139 K. P. Jackson (431), IBM, Watson Research Center, P.O. Box 218, York- town Heights, New York 10598 B. V. K. Vijaya Kumar (389), Department of Electrical and Computer Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 John N. Lee (165), Naval Research Laboratory, Washington, D.C. 20375-5000 xi xii LIST OF CONTRIBUTORS F. J. Leonberger (245), United Technologies Research Center, Silver Lane, East Hartford, Connecticut 06108 G. Michael Morris (23), The Institute of Optics, University of Rochester, Rochester, New York 14627 Dennis R. Pape (217), Photonic Systems Incorporated, 1900 South Harbor City Boulevard, Melbourne, Florida 32901 Demetri Psaltis (129, 191), Department of Electrical Engineering, Cali- fornia Institute of Technology, Pasadena, California 91125 Bahaa E. A. Saleh (281), Department of Electrical and Computer Engineer- ing, University of Wisconsin, Madison, Wisconsin 53706 H. J. Shaw (431), Edward L. Ginzton Laboratories, Stanford University, Stanford, California 94305 Cardinal Warde (477), Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massa- chusetts 02139 Francis T. S. Yu (3), Department of Electrical Engineering, The Pennsyl- vania State University, University Park, Pennsylvania 16802 David A. Zweig (23), The Perkin-Elmer Corporation, Danbury, Connecticut 06810 Preface It would be difficult to say just when the field of optical signal processing had its inception. Certainly the birth of the laser and the discovery of off- axis holography in the early 1960s got the field off to a running start. In the intervening years the field has seen several cycles of bloom and doom. Right now there seems to be a resurgence of interest and support for optical systems and devices as solutions to recurring technological problems. There have always been two basic characteristics of our field. First, it is a hybrid technology, and second, it has been a practical field, proposing solu- tions, as opposed to developing even deeper and more encompassing theories. It is a hybrid in that it has utilized the tools, theories, and techni- ques from many diverse disciplines—physics, mathematics, engineering, and chemistry. This is also reflected in our academic training: some of us come from the physical sciences and some from the engineering sciences. This book is in a sense a microcosm of all these facets. I have tried to get researchers from many different areas of optical signal processing to write synopses of their current work. It is also, by and large, a practical book, in which systems or algorithms that have been successfully tried and used are described. This book will be of special interest to workers and researchers in this field, students at a senior or graduate level, scientific administrators, and scientists and engineers in general. I would like to thank the contributors and dedicate this book to them; most of the contributors are colleagues and friends whom I have known since the late 1960s, as we have matured (rea lmeaning: grown old) together as the field has developed. I especially want to thank H. John Caulfield, Director of the Center for Applied Optics at the University of Alabama, Huntsville. Early on he encouraged and stimulated my interest in editing this book. I also thank my editors at Academic Press for their patience, help, and advice. We all hope this book will be a useful addition to a growing field, which is still in the process of realizing its full and rightful potential. Xlll OPTICAL SIGNAL PROCESSING 1.1 Color Image Processing FRANCIS Γ. S. YU DEPARTMENT OF ELECTRICAL ENGINEERING THE PENNSYLVANIA STATE UNIVERSITY UNIVERSITY PARK, PENNSYLVANIA 16802 I. Introduction 3 II. White-Light Optical Processing 4 HI. Source Encoding and Image Sampling 5 A. Source Encoding 6 B. Image Sampling 7 IV. Color Image Processing · 8 A. Color Image Deblurring 8 B. Color Image Subtraction 10 C. Color Image Correlation 12 D. Color Image Retrieval 15 E. Pseudocolor Imaging 16 F. Generation of Speech Spectrograms 19 V. Concluding Remarks 21 References 21 I. Introduction Although coherent optical processors can perform a variety of compli- cated image processings, coherent processing systems are usually plagued with annoying coherent artifact noise. These difficulties have prompted us to look at optical processing from a new standpoint and to consider whether it is necessary for all optical processing operations to be carried out by coherent sources. We have found that many optical processings can be carried out using partially coherent light or white-light sources (Lohmann [1], Rhodes [2], Leith and Roth [3], Yu [4], Stoner [5], and Morris and George [6]). The basic advantages of white-light optical processing are (1) it can suppress the coherent artifact noise; (2) the white-light sources are usually inexpensive; (3) the processing environmental factors are more relaxed, for instance, heavy optical benches and dust free rooms are not required; (4) the white-light system is relatively easy and economical to Copyright © 1987 by Academic Press, Inc. AH rights of reproduction in any form reserved. 4 FRANCIS T. S. YU operate; and (5) the white-light processor is particularly suitable for color image processing. II. White-Light Optical Processing An achromatic partially coherent processor that uses a white-light source [7] is shown in Fig. 1. The white-light optical processing system is similar to a coherent processing system except for the following: It uses an extended white-light source, a source-encoding mask, a signal-sampling grating, multi- spectral band filters, and achromatic transform lenses. For example, if we place an input object transparency s(x, y) in contact with a sampling phase grating, the complex wave field, for every wavelength λ, at the Fourier plane P would be (assuming a white-light point source) 2 E(p,q;\)=\ I s(x, y) exp(ip x) exp[-i(px + qy)] dx dy 0 = S(p-p q) (1) 09 where the integral is over the spatial domain of the input plane P (p,q) 1? denotes the angular spatial frequency coordinate system, p is the angular 0 spatial frequency of the sampling phase grating, and S(p q) is the Fourier 9 spectrum of s(x, y). If we write Eq. (1) in the form of a spatial coordinate system (α, β), we have E(a ß;\) = s(a-^p ß} (2) 9 09 where p = (2π/λ/)α, q = (2π/λ/)β, and / is the focal length of the achro- matic transform lens. Thus we see that the Fourier spectra would disperse into rainbow color along the a-axis, and each Fourier spectrum for a given wavelength λ is centered at a = (\//2π)ρ. 0 In complex spatial filtering, we assume that a set of narrow spectral band complex spatial filters is available. In practice, all the input objects are Fig. 1. White-light optical signal processor. 1.1 COLOR IMAGE PROCESSING 5 spatial frequency limited; the spatial bandwidth of each spectral band filter H(p„, q„) is therefore H( ,q )-[ . (3) Pn n 0f otherw se where p = (2π/λ /)α, q = (2π/λ /)β \ is the main wavelength of the n η n η 9 η filter, α = (λ„//2ττ)(ρ Η-Δρ) and α = (λ //2ττ)(/? -Δρ) are the upper 1 0 2 η 0 and lower spatial limits of H(p q ) and Δ/> is the spatial bandwidth of ny n 9 the input image s(x, y). Since the limiting wavelengths of each H(p,q ) are n n ρ + Δρ ρ -Δρ 0 0 λ, =λ„ — and A = A„——— (4) h Ρο-Δρ Ρο + Δρ its spectral bandwidth can be approximated by Δλ„ = λ —2 7Ä \2~ λ (5) η η /Γ-(ΔρΓ Po If we place this set of spectral band filters side by side and position them properly over the smeared Fourier spectra, the intensity distribution of the output light field can be shown to be J(x, γ)~Σ Δλ„ \s(x, y; λ„) * h(x, y; λ„)|2 (6) n = \ where Λ(χ, y\ λ ) is the spatial impulse response of H(p, q ) and * denotes η n n the convolution operation. Thus the proposed partially coherent processor is capable of processing the signal in complex wave fields. Since the output intensity is the sum of the mutually incoherent narrowband spectral irradi- ances, the annoying coherent artifact noise can be suppressed. It is also apparent that the white-light processor is capable of processing color images since the system uses all the visible wavelengths. III. Source Encoding and Image Sampling We now discuss a linear transform relationship between the spatial coherence (i.e., mutual intensity function) and the source encoding [8]. Since the spatial coherence depends on the image-processing operation, a more relaxed coherence requirement can be used for specific image- processing operations. Source encoding is to alleviate the stringent coher- ence requirement so that an extended source can be used. In other words, source encoding is capable of generating appropriate spatial coherence for a specific image-processing operation so that the available light power from the source can be more efficiently utilized. 6 FRANCIS T. S. YU A. SOURCE ENCODING We begin with Young's experiment under an extended-source illumina- tion [9], as shown in Fig. 2. First, we assume that a narrow slit is placed in the source plane P , behind an extended monochromatic source. To 0 maintain a high degree of coherence between the slits Qi and Q at plane 2 P , the slit size should be very narrow. If the separation between Qi and 2 Q is large, then a narrower slit size S, is required. Thus the slit width 2 should be \R w^ (7) 2K where R is the distance between planes P and P!, and 2h is the separation 0 0 between Qj and Q . Let us now consider two narrow slits S and S located 2 2 2 in source plane P . We assume that the separation between S! and S satisfies 0 2 the following path-length relation: r' -ri = (r -r ) + mA (8) 1 1 2 where the r\ and r are the distances from S to Qi and S to Q , respectively; 2 Y 2 2 m is an arbitrary integer; and λ is the wavelength of the extended source. Then the interference fringes due to each of the two source slits S! and S 2 should be in phase, and a brighter fringe pattern is seen at plane P. To 2 increase the intensity of the fringes further, one would simply increase the number of slits in appropriate locations in plane P so that the separation 0 between slits satisfies the fringe condition of Eq. (8). If the separation R is large, that is, if R » d and R »2h then the spacing d would be 09 P P Fig. 2. Source encoding. 1.1 COLOR IMAGE PROCESSING 7 Thus, by properly encoding an extended source, it is possible to maintain a high degree of coherence between Q and Q and at the same time to x 2 increase the intensity of the fringes. To encode an extended source, we would first search for a coherence function for a specific image-processing operation. With reference to the white-light optical processor shown in Fig. 1, the mutual intensity function at input plane P! can be written as [10] J(xi, x'i) = jj y(Xo)K(x , Xi)K*(x , xi) dx (10) 0 0 0 where the integration is over the source plane P , x , and x, are the 0 0 coordinate vectors of the source plane P and input plane P!, respectively, 0 γ(χ ) is the intensity distribution of the encoding mask, and X(x ,X!) is 0 0 the transmittance function between the source plane P and the input plane 0 P , which can be written as x Κίχ,,,χΟ-βχρ^ΐΓ^) (11) Substituting X(x ,X!) into Eq. (10), we have 0 J(x,-xl) = J j r(x )exp[/27r^(x -x' )J dx (12) 0 1 1 0 From this equation we see that the spatial coherence and source-encoding intensity form a Fourier transform pair, that is, 7(xo) = FT[/(x -x' )] (13) 1 1 and /(x -x;) = FT-1[5(x )] (14) 1 0 where FT denotes the Fourier transformation operation. Equations (13) and (14) are the well-known Van Cittert-Zernike theorem [11,12]. In other words, if a required coherence is provided, then a source-encoding transmit- tance can be obtained through the Fourier transformation. In practice, however, the source-encoding transmittance should be a positive real quan- tity that satisfies the physical realizability condition: 0^γ(χ )^1 (15) ο B. IMAGE SAMPLING There is, however, a temporal coherence requirement for partially coher- ent processing. If we restrict the Fourier spectra, due to wavelength spread, within a small fraction of the fringe spacing d of a narrow spectral band filter H (a, 0), then we have n vfHk «d (16) n