# Experimental studies on microwave detection and imaging of targets in clutter using correlation techniques

код для вставкиСкачатьINFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zed) Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Experimental Studies on Microwave Detection and Imaging of Targets in Clutter Using Correlation Techniques by Tsz K. Chan A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 1998 Approved by. Chairperson of Supervisory Committee) Program Authorized to Offer Degree__ Date. £ . (iff R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission . UMI Number: 9836149 Copyright 199 8 by Chan, Tsz King All rights reserved. UMI Microform 9836149 Copyright 1998, by UMI Company. AH rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. © Copyright 1998 Tsz K. Chan R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. In presenting this dissertation in partial fulfillment of the requirements for the Doctoral degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this dissertation is allowable only for scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright Law. Requests for copying or reproduction of this dissertation may be referred to University Microfilms, 1490 Eisenhower Place, P.O. Box 975, Ann Arbor, M I 48106, to whom the author has granted “ the right to reproduce and sell (a) copies o f the manuscript in microfilm and/or (b) printed copies of the manuscript made from microfilm.” Signature. Date r L /ie . ; R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. University of Washington Abstract Experimental Studies on Microwave Detection and Imaging of Targets in Clutter Using Correlation Techniques by Tsz K. Chan Chairperson of Supervisory Committee Professor Yasuo Kuga Department o f Electrical Engineering Recently, the detection and imaging o f targets in the presence of strong clutter has become an increasingly important research area in environmental science. The major momentum behind of the proliferation of this research discipline is the growing public awareness of environmental issues such as the detection of abandoned land mines and imaging of terrain and vegetation features. Since remote sensing for these environmental missions routinely requires electromagnetic (EM) radiation probing through natural stratified media and since most existing sensing tools (such as radars and their variants) are prone to passive interference (such as scattering of incident EM energy) from the media themselves, the call for an effective subsurface sensing tool for these detection and imaging applications has become an increasingly urgent task faced by radar engineers. This dissertation details a three-year-long research effort performed at the University of Washington. Specifically, this research focuses on the applications of a novel corre lation phenomenon in various target detection and imaging problems in environmental science. The technique examined in this dissertation makes uses of the complex angular correlation function (ACF) and/or frequency correlation function (FCF) measurement to R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. achieve enhanced visibility contrast for targets embedded in strong-clutter environment. Experimental research is conducted at both millimeter-wave (75-110 GHz) and X-band (7-13 GHz) frequencies. The results clearly demonstrate the relative effectiveness of this correlation technique over conventional techniques in various detection and imaging ap plications. Finally, a list of research topics is appended at the end of this dissertation to define the framework for the scope and depth o f further investigation on this topic. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. TABLE OF CONTENTS List of Figures iv List of Tables Chapter 1: xiii Introduction 1.1 Environmental applications of radars 1 ................................................................. 3 ................................................... 4 1.3 Synthetic aperture radar as an imaging t o o l ....................................................... 6 1.2 Ground-penetrating radar as a detection tool Chapter 2: Angular Memory Effect 12 2.1 Angular memory effect in the 0 - p la n e ................................................................ 12 2.2 Angular memory effect in the c j-p la n e ................................................................ 16 2.3 Correlation peaks and second-order Kirchhoff approximation ..................... 23 2.4 Applications of angular correlation fu n c tio n ...................................................... 26 2.5 Other forms of correlation fu n c tio n s.................................................................... 27 Chapter 3: 3.1 Correlation Technique in Target Detection Target detection at millimeter-wave freq u en cies................................................ 28 29 3.1.1 Experimental s e tu p .................................................................................... 32 3.1.2 Experimental r e s u l t s ................................................................................. 36 3.2 Target detection at X-band frequencies ............................................................. 37 3.2.1 Experimental s e tu p .................................................................................... 37 3.2.2 Experimental r e s u l t s ................................................................................. 41 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 3.3 Summary of target detection using correlation technique Chapter 4: 4.1 43 Correlation Technique in TargetImaging 44 3-D imaging using circular S A R ......................................................................... 46 4.2 Circular SAR processing a lg o r i th m ................................................................... 49 4.3 Generalized ambiguity function of circular S A R ............................................ 53 4.3.1 Analytic fo rm u latio n ................................................................................ 53 4.3.2 Numerical calcu latio n s............................................................................. 59 4.3.3 Experimental r e s u l t s ................................................................................ 64 4.4 Experimental studies on 3-D imaging using circularS A R ............................. 64 4 .4 .1 Experiment A: Confocal reconstruction of layers of spheres . . . . 4.5 4.6 4.4.2 Experiment B: Confocal reconstruction of a single s p h e r e ...... 4.4.3 Experiment C: Confocal reconstruction of a model helicopter Clutter suppression using correlation im a g in g ........................................... 69 ... 73 73 4.5.1 Conventional SAR p ro c e ss in g ............................................................... 77 4.5.2 Frequency-correlation SAR p ro c e s s in g ............................................... 77 4.5.3 Angular-correlation SAR processing...................................................... 78 4.5.4 Experimental comparison ...................................................................... 87 Summary of target imaging using correlation technique.................................. 95 Chapter 5: 5.1 67 Conclusion 100 S u m m a r y ....................................................................................................................100 5.2 Further studies ..........................................................................................................103 Bibliography Appendix A: 105 System Calibration 109 ii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Appendix B: Chirp radar 114 B .l Case A: Infinite pulse d u ratio n ................................................................................115 B.2 Case B: Finite pulse duration..................................................................................118 Appendix C: Determination of reference slant range 123 C .l Analytic fo rm u la tio n ...............................................................................................123 C.2 Experimental results .........................................................................................124 C.2.1 Experiment A: Single sphere along x - a x i s ........................................... 125 C.2.2 Experiment B: Single sphere along y - a x i s ........................................... 125 Appendix D: MATLAB codes for circular SAR processing 130 D .l Main p ro g ram ............................................................................................................130 D.2 Other su b ro u tin e s.....................................................................................................130 iii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. LIST OF FIGURES 1.1 The simplified block diagram of a typical ground-penetrating radar. . . . . 5 1.2 The operation of an airborne SAR system. The cross-range resolution (along the x-axis) is given by the antenna size and down-range resolution (along the y - axis) is given by the measurement bandwidth (or pulsewidth) of the system............................................................................................................. 1.3 7 Fourier-transform relationship between near-field and far-field variations: broad near-field variation transforms to narrow far-field variation, (a) Pencil beam pattern resulting from a broad circular near-field pattern, (b) Fan beam pattern resulting from a rectangular near-field pattern. Sidelobes of these beams are not shown in this figure....................................................... 2.1 9 The scattering geometry of angular memory effect in 0-plane. The neces sary condition for strong angular correlation is governed by the generalized Snell’s law: s in d\ —s in Oi = s in 6's —s in Qs ..................................................... 2.2 13 Plot of Eq. 2.2 on the sin(0|) —sin(0^) plane. The angular memory line and scan line intercept at the reference point (sin( 0i),s in ( 0 ,)) and are, by definition, perpendicular to each other. 2.3 ............................................................ 15 Field equivalence under reciprocity condition, (a) the original scattering situation: an a-polarized transmitter transmitting at 0T and a ^-polarized receiver receiving at Or . (b) the reciprocal version of the original scattering geometry: a /^-polarized transmitter transmitting at Or and an a-polarized receiver receiving at Or........................................................................................... iv R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 17 2.4 The scattering geometry of angular memory effect in the <p-plane. At con stant ^-incidence, the resulting “plane” of incidence traces out a conical surface in 3-D space................................................................................................ 2.5 19 The signature of 0 -plane ACF as a function of reference angles (o t . <ps ) . “i” stands for reference incident angle <&, “s” stands for reference scattered angle cps. x - and y-axes represent <z>- and o s, respectively, in degrees. 2.6 . . 22 (a) Comparison between experimental and analytical ACF signatures across the narrow contours in Fig. 2.5 for the case (0 t,0 s) = (0°, 180°), and (b) Comparison between experimental and analytical ACF signatures across the wide contours in Fig. 2.5 for the case (&, 0 S) = (0°, 180°)..........................24 2.7 The three major components in the second-order Kirchhoff Approximation: (a) first-order scattering: single bounce, (b) second-order scattering: iden tical doubly-bounced signals resulting from identical propagation paths, (c) second-order scattering: identical doubly-bounced signals resulting from time-reversed propagation paths............................................................................. 3.1 25 A far view of the millimeter-wave system used in the experiments. System specifications of this advanced vector scattereometer are fully documented in [23]......................................................................................................................... 3.2 30 A close view of the same system shown in Fig. 3.1. In this figure, the trans mitting antenna (on the left hand side) is covered with a servo-mechanical polarizer. The receiving antenna (on the right hand side) is designed to receive both copolarized and cross-polarized scattered signals............................31 3.3 ACF magnitude of the selected natural media at millimeter-wave frequen cies (95-100 GHz) for (0j,0s) = (20°, —20°), along (solid line) and per pendicular to (dotted line) angular memory line: (a) fine sand, (b) rough sand, (c) gravel, and (d) rock..................................................................................... 34 v R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 3.4 Target detection with spatial and angular scans with (9i: 9S) = (20°, —20°). Spot size of the footprint « 30A............................................................................ 3.5 35 (a) ACF magnitude as a function of footprint: (9i,9s) — (2 0 °,—20°) and {O'^Q's) = (10°. —10°). (b) RCS as a function of footprint: (O'^d’s) = (6i, 9S) = (20°, —20°). It is clear from this comparison that ACF technique results in higher target visibility contrast than RCS technique............................ 36 3.6 The top view of the X-band bistatic target detection system. In the course of the experiments, the system scans over the composite target-soil medium contained in the sand box....................................................................................... 3.7 39 Frequency dependence of the dielectric parameters o f the soil medium used in the experiment: (a) attenuation constant, (b) relative permittivity constant, (c) ACF magnitude along (solid line) and perpendicular to (dotted line) the angular memory line for {9U9S) = (2 0 °,-2 0 °) and (d) ACF magnitude along (solid line) and perpendicular to (dotted line) the angular memory line for (9i, 6s) = (20°. —4 0 ° )................................................................... 40 3.8 Object buried at 6 cm below the surface with (9Z,9S) = (30°,—30°): (a) radar cross section as a function of footprint. (0-,0^) = (30°,—30°), (b) ACF magnitude as a function of footprint. {9\,9's) = (50°,—50°). Object placed above the surface with (9i,9s) = (30°,—30°); (c) radar cross section as a function of footprint. (9'i ,9's) = (30°,-30°), (d) ACF magnitude as a function of footprint. (9^,9^) = (50°,—50°).............................................................. 42 4.1 (a) The geometry of spotlight-mode linear SAR. (b) Altitude ambiguity caused by propagation paths of equal lengths (dx = d?)........................................ 45 4.2 (a) The geometry of spotlight-mode circular SAR. (b) Altitude ambiguity resolved by propagation paths of different lengths(dx^ d2).................................. 47 vi R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . 4.3 Different window functions are used at different data-acquisition positions in order to capture the “clean” responses from target located at the focal point............................................................................................................................ 4.4 Geometry of a circular SAR system. Focal point r Q being located at (x0, ~ h 0).................................................................................................................... 4.5 51 55 Magnitude variations of the generalized ambiguity function x (T ,r0) pro jected along the x - , y -, and 2-axes. Bandwidth: 7-13 GHz. Sweep time = 4 s. Depth h 0 of the focal plane = 1 m below the flight track. Depression angle 6dp = 45°. r c = (0, —h0)......................................................... 4.6 61 Pixel resolution (in terms of wavelength) along the x —, y—, and 2 -axes as a function of depression angles 6dp for circular SAR system. Bandwidth: 7-13 GHz. Sweep time = 4 s. rQ= (0, —h), where h — a x tan(0dp). . . 4.7 62 Pixel resolution (in terms of wavelength) along the x - , y- , and 2-axes as a function of depression angles Qdp for linear SAR system. Bandwidth: 7-13 GHz. Sweep time = 4 s. r 0 = (0, —h ), where h = a x ta n (9dP). ■ ■ 63 4.8 2-D circular SAR image of a conducting sphere in free space. The sphere was located at a distance of 15 cm (or 5A at a center frequency of 10 GHz). 65 4.9 1-D extraction of data points along the x-axis that contains the bright image in Fig. 4.8. The 3dB peak width of the generalized ambiguity function of circular SAR system is approximately 0.25A................................. 66 4.10 Schematic for 3-D confocal imaging of layers of metallic spheres using circular SAR. Bandwidth: 7-13 GHz.................................................................. vii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. 68 4.11 Experimental result for the imaging experiment shown in Fig. 4.10: (a) no sphere, corresponding to “layer (a)” in Fig. 4.10, (b) one sphere, cor responding to “layer (b)” in Fig. 4.10, (c) three spheres, corresponding to “ layer (c)” in Fig. 4.10 and (d) no sphere, corresponding to “layer (d)” in Fig. 4.10...................................................................................................................... 70 4 .12 Schematic for 3-D confocal imaging of a metal sphere suspended in free space using circular SAR. Bandwidth: 7 -1 3 ........ G H z...................................... 71 4.13 Experimental result for the imaging experiment shown in Fig. 4.12. The image is displayed as a stack of uniformly spaced (vertically) contours. The apparent dark line that connects the top and bottom contour layers is produced by the PLOT3 routine in MATLAB and has nothing to do with the actual image......................................................................................................... 72 4.14 Schematic for 3-D confocal imaging o f a palm-sized model helicopter suspended in free space using circular SAR. Bandwidth: 7-13 GHz. . . . 74 4.15 Experimental result for the imaging experiment shown in Fig. 4.14. The image is displayed as distributed clusters o f dots for enhanced visibility about its details. Note that the comer structures at the helicopter tail result in the corresponding strong reflection in the image. On the other hand, the longitudinal dimension of the image agrees with the actual length of the h elico p ter............................................................................................................ 75 4.16 Schematic of bandwidth partitioning in the frequency-correlation SAR for (a) 4 partitions and (b) 8 partitions........................................................................ 79 4.17 Schematic of angle partitioning in the angular-correlation SAR for (a) 3°, (b) 30°, (c) 45°, (d) 90°, (e) 120° and (f) 150°. Angles are not drawn to scale............................................................................................................................. viii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 81 4.18 Conventional SAR image of a 63 mm conducting sphere on top of absorber material....................................................................................................................... 83 4.19 Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with a decorrelation angle of 2°. The bright annular ring results from the highly-correlated terms in the summation mechanism in Eq. 4.41....................................................................... 84 4.20 Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with a decorrelation angle of 20°. Note that the previous bright annular image in Fig. 4.19 has dimmed significantly as a result of using large decorrelation angle (i.e. 20 °) in this case.............................................................................................................................. 85 4.21 Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with multiple decorrelation angles of 20°, 40° and 60°. Note that the previous annular image in Fig. 4.20 has disappeared almost completely. This image demonstrates the importance of using large number of large decorrelation angles in angular-correlation SAR processing in low-clutter environment......................... 86 4.22 Experiment A: a schematic for microwave imaging in medium-clutter en vironment using different kinds of SAR processing methods. The size of spheres (diameter = 25 mm) is much larger than the size (mean diameter ss 3 mm) of the gravel particles............................................................................ 88 4.23 Experiment A: conventional SAR processing continues to produce faithful image of the scene in medium-clutter environment. The two spheres are indicated unambiguously by the bright dots in the Figure.....................................89 R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 4.24 Experiment A: frequency-correlation SAR processing results in an im age strikingly similar to that produced by conventional SAR processing. This mage demonstrates that the benefit of applying frequency correlation technique is not obvious in not only low-clutter environment, but also medium-clutter environment................................................................................... 91 4.25 Experiment A: angular-correlation SAR processing results in an image strikingly similar to that produced by conventional SAR processing. This image demonstrates that the benefit of applying angular correlation tech nique is not obvious in not only low-clutter environment, but also mediumclutter environment.................................................................................................. 92 4.26 Experiment B: a schematic for microwave imaging in heavy-clutter envi ronment using different kinds of SAR processing methods. The size of spheres (diameter = 25 mm) is about the same as that (mean diameter ~ 30 mm) of the gravel particles.............................................................................. 93 4.27 Experiment B: a top view of Fig. 4.26.............................................................. 94 4.28 Experiment B: conventional SAR processing failstodisplay thecorrect image of spheres in heavy-clutter environment.Sphere size = 25 mm, mean gravel particle size s; 30 mm, bandwidth = 7-13 GHz............................. 96 4.29 Experiment B: frequency-correlation SAR processing results in an im age strikingly similar to that produced by conventional SAR processing. Again, frequency-correlation SAR processing fails to display the correct image of spheres in heavy-clutter environment. Sphere size = 25 mm, mean gravel particle size « 30 mm, bandwidth = 7-13 GHz. This im age demonstrates that in heavy-clutter environment, frequency-correlation SAR processing may not be an effective means for clutter suppression. . . x R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 97 4.30 Experiment B: angular-correlation SAR processing results in an image that correctly accounts for the presence of the spheres. In fact, it is the only means among other SAR processing schemes examined in this investiga tion that brings clutter level down to a reasonably low level, leading to clear visibility of spheres in the presence of strong clutter. Sphere size = 25 mm, mean gravel particle size ~ 30 mm, bandwidth = 7-13 GHz. This images demonstrates that in the presence of strong clutter, angular corre lation SAR processing is an effective tool of achieving a higher degree of clutter suppression compared with the conventional SAR technique, resulting in a higher target-to-clutter ratio........................................................... 98 A. 1 ACF signature measurement of a large tilted metal flat plate. The way the antennas are moved describes an angular memory line for (Oi,d3) = (30°. —30°) on the s i n ^ - s i n ^ plane. As expected, the correlation level approaches to 1 over a wide range of variable incident angles 6\ B .l 110 Frequency-time plot of transmitted pulse, received pulse, and the de chirped pulse. The net effect of this chirping/de-chirping process is to compression of a T-long pulse into a 1/B -long pulse, allowing fine spa tial resolution................................................................................................................ 116 B.2 Delay-time characteristic o f a de-chirping filter matched to the transmitted chirp pulse, assuming linear FM modulation......................................................... 117 B.3 Plot of Eq. B.22 with sweeping time T = 4 s and chirp bandwidth B = 6 GHz. The 3dB width of the de-chirped signal is about 1.057I B ...................... 122 C .l Experimental determination of reference slant range. Ideally, the center of rotation should be the same as the center of illumination (except for the obvious altitude difference)....................................................................................... 127 xi R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. C.2 Experimental setup for determination of reference slant range in which a 63 mm conducting sphere, located at an altitude o f h below the circular SAR flight track, was placed at a distance of 15 cm along the ar-axis relative to the center of rotation. Three independent reflection measurements were made to solve for variables p, (f> and h ................................................................ 128 C.3 The relative locations of the calculated center of illumination and the ideal center of illumination. The negligible spatial discrepancy verifies the superb construction accuracy of the circular SAR system used in this experimental research................................................................................................. 129 D. 1 The structural components of CORRSAR.M....................................................... 131 D.2 MATLAB code of CORRSAR.M............................................................................ 132 D.3 MATLAB code of CORRSAR.M, continued from Fig. D.2 .......................... 133 D.4 MATLAB code of CORRSAR.M, continued from Fig. D.3 .......................... 134 D.5 MATLAB code of CORRSAR.M, continued from Fig. D.4 .......................... 135 D .6 MATLAB code of GETDATA.M D.7 MATLAB code of V O L S IZ E .M ............................................................................ 137 D .8 MATLAB code of F C U S G R ID .M .........................................................................138 D.9 MATLAB code of L E N S G R ID .M .........................................................................139 .........................................................................136 D. 10 MATLAB code of R A D E X .M ............................................................................... 140 D . l l MATLAB code of S C R E E N IN F O .M .................................................................. 141 D.12 MATLAB code of K A ISE R .M ............................................................................... 142 D.13 MATLAB code of GATING.M ............................................................................... 143 D. 14 MATLAB code of C H O P B A N D .M ...................................................................144 D. 15 MATLAB code of F R E Q _A C F.M ...................................................................... 145 D.16 MATLAB code of T IM E _ A C F .M .........................................................................146 D.17 MATLAB code of N O R M A L .M ............................................................................147 XII R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. LIST OF TABLES 3 .1 Dimension and absorption characteristics of the four natural media used in the millimeter-wave experiments 4.1 ................................................................. 32 Specification comparison between linear SAR and circular S A R ................. 48 xiii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. ACKNOWLEDGMENTS To come to the pleasure you have not you must go by a way in which you enjoy not. - St. John o f the Cross (1542-1591) Before I express my wholehearted appreciation to a number of individuals in this section, I would like to take up some space here to share with you, my dear readers, something invaluable I learned about experimental research succinctly summarized by St. John of the Cross’s counsel on one’s pilgrimage centuries ago. Experimental research such as the one outlined in this dissertation, by its very timeconsuming nature, is an endeavor no less demanding than any other research areas. In the course of my 5-year training in the Ph.D. program at the University o f Washington, I have the privilege of sailing through a number o f “dark nights” (both physically in laboratory and psychologically in mind) during my sojourn over “research plateau” (a term coined by Prof. Ishimaru) where I hardly foresaw further breakthroughs ahead. The reason why I consider it a privilege (as opposed to agony!) to experience dark nights is that although the dark nights are both unpleasant and inevitable along any non-trivial research path, they contain the necessary nutritious ingredients for a research novice to grow from being dependent to being independent in capability, from being naive to being experienced in skills, and from being arbitrary to being thoughtful in conclusion making. O f tremendous benefits to him during dark nights, such novice therefore should ask and continue to ask even though there seems to be no answer, seek and continue to seek even though there seems to be no solution, and knock and continue to knock even though the door seems to remain shut. Very often at a certain point along this long journey of work in patience xiv R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. and steadfastness, however, a kind o f elegant inspirtation suddenly sparks, lighting up all previous dark nights in much the same way as the sun’s radiance breaks into the dark at daybreak. After all, perseverance is the lead to an once hidden answer, the map for an once overwhelming labyrinth and the key to an once shut door. I wish to express my deepest appreciation to all members, present and past, of the Electromagnetics and Remote Sensing Laboratory (ERSL) at the University o f Washington. In particular, special thanks must first go to Professor Kuga for his guidance and financial support. Throughout my years in the program, he has been the single most influential mentor to me who constantly enriched and expanded my research interests with his new insights and unparallelel experimental expertise. On many occasions, in particular, his heuristic approach to technical problems and broad readership of technical literature have been such a great help to me - much like a lighthouse to the ships wandering in the sea at night, saving me from stumbling over many potential “research potholes” invisible to a naive researcher like me. These potholes are diverse in nature and include from re-inventing the wheel, searching randomly in the dark, to majoring in minor ideas while missing the whole picture altogether. In short, he has been a timely “rescue” to me on a number of occasions that could have infectiously eclipsed my research impetus and progress in the future. In physical chemistry, a catalyst is a substance that speeds up a chemical reaction by providing an alternative reaction path of lower activation (start-up) energy. By the same token, if Professor Kuga’s guidance and my work are considered as reaction components, Professor Ishimaru’s insightful counsel is definitely the catalyst responsible for many exothermic “research reactions” over the years in the past. While his legendary counsel is inseparable from his being an authoritative figure in the field, his smile and kind advice are also inseparable from his being a great nurturing advisor to young researchers - feeding them with encouragement, implanting them with sound research philosophy and finally xv R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . letting them grow as mature and independent minds of various personal styles. His artistic way of doing research and bird’s eye view of entangling technical issues have constantly surprised me by joy. To me, his office has always been synonymous with “powerhouse” a place where one could regain personal and technical momentum to walk through curtains of uncertainties with calmness and confidence. Furthermore, I want to acknowledge the contributions by many undergraduate students who unreservedly dedicated their time and talent to my research. They not only helped me identify and solve a wide range of technical issues “behind the scene”, but also accepted and carried on uncomplainingly many of my demanding requests. I truly owed them a lot. Over the years, there had been many helpful students who facilitated my work in one way or another. Of particular significance to my research among these talented individuals are (1) Canh Kha, (2) Kenneth Pinyan and (3) Hatim Saleem. Mr. Kha is a professional whom I enjoyed chatting and working with him very much. He was always a good source of humor which I benefited most, especially in times of research obstacles. On the other hand, Mr. Pinyan is an all-rounder specializing in a wide spectrum of skills, ranging from heavy-duty work like metal machining to Iight-duty work like computer programming. In fact, this research will remain largely incomplete without the circular SAR system that he constructed with intense dedication over months of hard work. Last but not least, Mr. Saleem is another gifted individual whom I owed a lot. His uncomplaining work attitude and inquisitive personality have enabled greatly my research, making my work to proceed in the smoothest possible extent. Finally, I would like to express my gratitude to the following fellow classmates, both former and present, for their friendship and support. Their presence is truly essential to the my research life at ERSL: Jun-Ho Cha, Chi-Te Chen, Todd Elson, Leibing Huang, Bertin Koala, Charlie Le, Seung-Woo Lee, Qin Li, Chien-Min Lin, Jun Liu, Garfield Mellema, Katsuhiro Ono, Kyung Pak, Christopher Penwell, Phillip Phu, John Rockway, xvi R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Lynn Sengers, Geoffrey Wang, Ji-hae Yea, Cynthia Young, Guifii Zhang, and Hui Zhao. This alphabetically sorted list is by no means exhaustive and I deeply apologize to those whom I miss. Before I close this section, I must reserve a unique space for our ERSL’s program coordinator: Ms. Noel Henry. From the date I joined this group till now, she has been a great helper to many of us in the group. Her office is a truly wonderful place for at least 3 good reasons. First, it is the place where students can obtain accurate information such as submission deadlines, reimbursement policy, and travel arrangements. The way she organizes information enables her to handle all these repetitive requests with grace and meekness, even at the peak of busy periods. Secondly, it is the place where faculty can rely on for accurate information when it comes to the time for financial and research issues - anything from proposal deadlines, contact information, to budget handling. Finally, perhaps the most important reason of all, it is the place where both students and faculty can seek emotional support and replenishment - her advice, help, smile, humor and encouragement all add up to make her office a uniquely helpful place for us to stop by. I am truly thankful for her unconditional dedication to everyone of us. xvii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. DEDICATION This dissertation is unreservedly dedicated to my parents, Lap Chan and Miu-King Lam-Chan, for their unconditional love and unselfish sacrifice to me since my childhood. Without their emotional support and care over years, this dissertation would not have been a reality. Even though they do not understand even one single equation or plot in this work at their education level, they understand and make me understand the transforming power of enduring love. The following verses (from I Corinthians 13) are reverently presented to honor their love for me: Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails. xviii R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Chapter 1 INTRODUCTION Since its introduction in early 40’s, radar, an acronym name for “fladio Detection And hanging” , has been in extensive use in a wide range of applications. Simply stated, a radar system consists of a directive antenna which serves as an interfacing device between the region under surveillance and the internal transmitter/receiver electronic circuitry system. A radar operates by radiating a sequence of bursts of electromagnetic energy into the region illuminated by the antenna beam. If there is a reflective target within the illuminated volume, it will absorb a fraction of the incident energy and scatter the rest of the energy in other directions. Most radars deployed for remote-sensing applications operate at the frequency range of 0.1-10 GHz. At these frequencies, electromagnetic radiation exhibits long penetration depth into most natural media such as clouds, light rain, vegetation and snow. In the case of a monostatic radar, only the portion of the scattered energy observed in backscattering direction is received. Assumming point scatterer and freespace propagation, the relationship between the received power PR and the transmitted power Pt is given by the well-known radar equation [21, 25] Pr PT C iG a A2 { A -K fR \p f .... K } where G\ is antenna gain of the transmitter (a measure of how spatially directive the transmitting antenna emits power, Go the antenna gain of the receiver (a measure o f how spatially directive the receiving antenna receives power), A the wavelength in free space at the operating frequency, R i the range from the transmitting antenna to the scatter, Ro the range from the scatter to the receiving antenna, and finally, a the radar cross section R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 2 (RCS) of the illuminated target. From Eq. 1.1, it is important to note that the received power PR decreases rapidly as ranges (R \ and Ro) increase (i.e. received power oc 1/distance4). As a result, for longrange surveillance applications it is necessary to have a powerful transmitting antenna that is capable of sending high-power (on the order of 106 watts) microwave radiation into free space. Note that Eq. 1.1 expresses the return power from a point target while neglecting propagation, polarization and other system losses. Modifications for Eq. 1.1 become necessary in practical systems to account for scattering by distributed targets such as clouds, rough surfaces and canopy layers. Note also that in the case of monostatic radar systems, it is the part of the energy backscattered to the radar antenna that constitutes the observed echo, from which one can deduce the following parameters useful for target identification and characterization [3, 25]: • range, • radial velocity, • angular direction, • size, and • shape. The history of radar development spanned over half of a century, with applications ex tending from military surveillance to environmental sensing. A short list of this eventful evolution process is presented chronologically below [21 ]: • Early radars 1. 1922 - Continuous-wave (CW) radar 2. 1934 - Pulse radar R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 3 3. 1940 - Airborne radar 4. 1946 - Imaging radar • Imaging radars 1. 1952 - Side-Looking Airborne Radar (SLAR) 2 . 1966 - Extensive mapping by SLAR 3. 1952 - “Dopper Beam Sharpening” system 4. 1958 - Synthetic Aperture Radar (SAR) • Space radars 1. 1973 - Skylab scattereometer (non-imaging) 2 . 1978 - Seasat SAR and scattereometer 3. 1981 - Shuttle Imaging Radar (SIR-A) 4. 1983 - Shuttle Space Lab (European) SAR 5. 1984 - Shuttle Imaging Radar (SER-B) 6 . 1990 - Shuttle Imaging Radar (SIR-C) 7. 1993 - Earth Observing System (EOS) SAR I.I Environmental applications o f radars During the past 50 years of research and development, radar technology has witnessed significant growth in capability, variety, and functionality. Presently its applications are diverse and penetrate deep into many aspects of our daily life, ranging from military surveillance and weapon control to civilian navigation for air/sea traffic safety, law en forcement, weather forecasting [2], and remote sensing of geological media [12, 28, 30]. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 4 Although radar continues to be an indispensable remote-sensing tool for modem mili tary and civilian applications, it is the evolution from these applications to environmental applications, which calls for superb subsurface sensing capability, that has been injecting momentum to much of the radar research in recent years [22]. Examples of these envi ronmental applications include detection of trenches, landfill debris, grave sites, chemical spills, nuclear waste, underground utility lines, abandoned active land mines, as well as imaging of terrain and vegetation regions. As a result of the significant impact of these critical issues to our environment, the call for an effective subsurface sensing tool for these detection and imaging applications has become an increasingly urgent task faced by radar engineers. Depending upon the functions it performs, a remote-sensing radar could be categorized either as a (1) detection radar and (2) imaging radar. From an application point of view, detection radars usually deal with those issues where spatial resolutions for revealing details of targets are of secondary priority. However, imaging radars deal with those issues where fine spatial resolutions are necessary for accurate target identification. In subsequent sections of this chapter, working principles of ( 1) ground-penetrating radar (GPR) as a detection tool and (2) synthetic aperture radar (SAR) as an imaging tool will be addressed. 1.2 Ground-penetrating radar as a detection tool GPR was invented in the early 70’s for detecting engineering and environmental targets in the upper 10 m ground layer of the earth [22]. When used in practice, GPR’s operate in close vicinity of the soil-air interface. Essentially, a GPR is similar to a time-domain reflectometer which transmits high-power transient pulses into the ground and receives the reflected transient echoes from the region under surveillance, as shown in Fig. 1.1. With reference to Fig. 1.1, a GPR system is usually towed continuously by a vehicle over the ground at uniformly spaced intervals. The distance between consecutive intervals R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 5 transient source transient receiver signal processing an tennas ground surface \ \ i i * i i i / i buried target Figure 1.1: The sim plified block diagram o f a typical ground-penetrating radar. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 6 is called the trace spacing and is usually less than 0.3 m. Each time the antennas traveled over one of these intervals, the GPR performs the following sequence of operations [22]: 1) the transient source emits a pulse into the ground, 2) the transient receiver is then turned on to wait for the radar echo from the ground, and 3) after a brief period of time (usually less than 1 p s) the receiver is turned off. The time-domain information that is recorded while the receiver is turned on is called a trace. Such a trace can be used to determine the a) size, b) shape, and c) depths of targets buried under the illumination spot on the ground surface. By mapping these recorded time-domain traces for each interval into their space-domain equivalent via a knowledge of certain medium parameters (e.g. dielectric constant), a two-dimensional RCS plot of the area under ground can be constructed. Finally, it is important to realize that simple as the concepts of GPR’s are, however, reliable detection and clear image construction are often undermined by practical imple mentation challenges, which include careful antenna design to avoid mutual coupling and rejection to interference due to scattering by random rough surfaces. 1.3 Synthetic aperture radar as an imaging tool In contrast to the small-scale illumination area achievable by GPR’s, SAR’s are used for surveillance over a large-scale illumination area [11, 18, 31], as shown in Fig. 1.2. In practical environmental imaging applications, SAR technology makes use of airborne or spacebome radars for terrain mapping. To understand the operation of SAR, one may begin with an examination at how a radar of given shape directs its power in space [21], From antenna theory, it is a well-known fact that near-field variation and far-field variation bear a Fourier-transform relationship. This succinct Fourier relationship is a direct result of applying far-field approximation in the Green’s function formulation for antenna radiation [13]. In view of this result, a radar of wide aperture (i.e. broad nearfield antenna pattern) produces a narrow far-field antenna pattern, and vice versa. In Fig. 1.3 two common types of radar are illustrated. In Fig. 1.3(a), the near-field antenna R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 7 v # - & ►y (down-range) / / pixel footprint x (cross-range) Figure 1.2: The operation o f an airborne SAR system. The cross-range resolution (along the x -a x is) is given by the antenna size and down-range resolution (along the y -a x is) is given by the measurement bandwidth (or pulsewidth) o f the system. R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 8 pattern exhibits circular symmetry over a broad circular aperture. As a result, the radar produces a sharp far-field antenna beam that bears a circular symmetry similar to that of the antenna aperture. Because of its obvious shape, the beam so produced is known as a pencil beam. In Fig. 1.3(b), on the other hand, a radar with a rectangular aperture produces a far-field antenna beam that exhibits an elongated elliptical shape, with the narrow near-field variation along the shorter dimension o f the rectangle being transformed to a broad far-field variation, and the broad near-field variation along the longer dimension of the rectangle being transformed to a narrow far-field variation. The resulting beam is commonly known as a fa n beam. SAR can produce high-resolution images based on the generation of an effective long antenna (hence producing sharp a far-field antenna beam) by signal (Doppler) processing means rather than by the actual size of a long physical antenna. With reference to Fig. 1.2, the cross-range and down-range resolutions of an image pixel are determined by the boresight beamwidth (and hence the antenna aperture size L) and transmitted pulsewidth, respectively. In a theoretical case, it can be shown that the cross-range resolution (Aar) and down-range resolution (A y) can be expressed as [5] A* = ! (1.2) ± y = 02 B R sin c. 9n (1-3) where B represents the measurement bandwidth o f the SAR system, c the speed of light in free space, and 9 is the depression angle measured from the horizon. It is important to note that the high quality of SAR imaging, however, does not happen by accident or without cost. In practice, a successful SAR system requires demanding system specifications and regular verification/monitoring of performance over time. Flight path irregularity, phase errors due to oscillator instability, requirement of high-speed data recording media for data surface scattering, are acquisition, and strong speckles due torandom volume and but a few practical and costly issues that have to be dealt with in SAR applications [25]. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (b) Figure 1.3: Fourier-transform relationship between near-field and far-field variations: broad near-field variation transforms to narrow far-field variation, (a) Pencil beam pattern resulting from a broad circular near-field pattern, (b) Fan beam pattern resulting from a rectangular near-field pattern. Sidelobes o f these beams are not shown in this figure. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 10 From the discussion above it is apparent that the usefulness of GPR’s can be severely limited by interference due to random scattering from ground surfaces. Likewise, the quality of SAR images can be adversely impaired by speckles as a result of random scattering from terrain and vegetation media. In this regard, optimum detection and imaging using G PR’s or SAR’s therefore demand suppression of clutter return produced by random multiple scattering. In subsequent sections of Chapter 2, a heuristic account of achieving clutter suppression using a correlation phenomenon will be presented. Constructed in light of a scattering phenomenon known as memory effect, this technique makes uses of the complex angular correlation function (ACF) and/or frequency correlation function (FCF) measurement to achieve enhanced visibility contrast for targets embedded in clutter. Among numerous environmental applications of these correlation techniques are, for instance, detection of abandoned active land mines and topographical imaging of natural terrains. To make the presentation of this work as logically smooth as possible, this dissertation is organized in a chronological sequence for those critical research studies that surfaced in this research effort. Chapter 2 presents the concept of memory effect of scattering by random media. Counter-intuitive as this correlation phenomenon seems to be, it is emphasized that the only necessary condition for this effect is random scattering, may it be single or multiple scattering. In addition, the rationale behind applications of this phenomenon in detection and imaging problems is discussed, and a way of quantifying the memory strength using ACF is introduced. In chapter 3, experimental studies on subsurface target detection using ACF measure ment are presented. To demonstrate the effectiveness of this correlation technique over the traditional technique based on RCS acquisition, a comparison between the detection results using ACF and RCS measurement is made. It is shown that in detection situations where the main clutter source comes from random scattering, ACF technique generally works better than traditional RCS technique, resulting in higher target visibility in strong-clutter R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. II environment. As an extension of applications of this ACF technique in other areas, the subject of SAR imaging is explored in Chapter 4. The chapter presents a chronological account on the development of a novel three-dimensional (3—D) SAR confocal imaging system. Specifically, the concept of circular SAR is presented, together with analytic derivation and calculations of the system’s generalized ambiguity function [25]. In addition, experimental studies on the 3-D confocal imaging capability of circular SAR are presented. In parallel to the organization of Chapter 3, a comparison between imaging results using correlation and traditional techniques is made. It is shown that in imaging situations where the main clutter source comes from random scattering, correlation-SAR processing generally works better than traditional SAR processing, resulting in higher target visibility in strong-clutter environment. Finally, concluding remarks, together with a list of topics proposed for further research in this area are given in Chapter 5. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Chapter 2 ANGULAR MEMORY EFFECT When a wave is incident upon a two-dimensional (2-D ) rough surface, it undergoes variable degrees of absorption, scattering, and depolarization. Depending upon surface roughness and dielectric parameters, the resulting co-polarized and cross-polarized scat tered waves are in general in all directions and exhibit completely random phase fluc tuations. At first glance, it is intuitive to assume that these scattered waves contain no statistically coherent information (such as the incidence direction) of the original incident waves. 2.1 Angular memory effect in the 6-plane In a series of theoretical and experimental studies on wave transmission in diffusive me dia [7, 8] during the late 80’s, however, condensed-matter physicists found that such intuition is only a partial truth. The new findings, long overlooked by classical studies, show that the direction of incident waves can be deduced from diffused field measurement by virtue of a phenomenon known as the angular memory effect. Basically, this effect describes how the changes in the direction of the incident wave are “remembered” , or cor related, by the diffused scattered waves when a certain relationship between incident and scattering angles is satisfied. Simply stated, this relationship, as shown in Fig. 2.1, depicts the existence of strong correlation between scattered waves when the difference between the transverse incident wave vectors is equal to the difference between the transverse scattered wave vectors [16, 19]. Mathematically, angular memory effect can be characterized by ACF. Denoting the R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 13 2(0.) Es(0s;0i) n random rough surface Figure 2.1: The scattering geometry o f angular memory effect in 0-plane. The necessary condition for strong angular correlation is governed by the generalized Snell’s law: s in # ’ - sin # , = s in # ’ - s in # s R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 14 unprimed E s(9i, 0S) the reference scattered wave observed at 9S due to an incidence at 0* and the primed E a{9'i.9's) the variable scattered wave observed at 9's due to an incidence at 0-, the ACF T(9'i: 9's-, 9i, 9S) is defined as Q's, 9ii9S) =< E s(0i;0s)E s'(0;,0;) > (2.1) where the angle brackets denote an ensemble average measurement over a large number of independent realizations, signifying the statistical nature of scattering involved. The asterisk mark appearing within the angle brackets refers to complex conjugation. All the experimental results included in this dissertation assume TM -, or p-polarization. The reason for this choice of polarization is that EM energy can be most efficiently coupled into a given scattering medium with minimal scattering at Brewster-angle incidence, which exists only for TM polarization. With reference to Fig. 2 .1, the condition for strong angular correlation is reiterated here as sin 0, —sin 0* = sin 9S —sin 0S (2.2) where (0 i,0 s) and (0-.0^) refer to the reference and variable antenna angles, respectively, in which ACF is to be measured. On the sin(0’) — sin(0’) plane in Fig. 2.2, Eq. 2.2 represents a straight line passing through the point (sin(0;),sin(0s)) with a slope of +1. Previous theoretical work suggests that along this line there exists a high, non-uniform level of correlation but rapid bilateral decorrelation away from the line [16]. Because of its association with high angular correlation, this particular line is appropriately known as the angular memory line corresponding to antenna angles (0*. 9S. On the other hand, the line that passes through the same reference point (sin(0j), sin(0s)) but with a slope o f -1 (i.e. perpendicular to the angular memory line), is called the scan line. In general, there exist along the angular memory line two points, A ( s i n ^ ) , s in ^ ^ ) ) and B (sin(0^2).sin(0j2)), where the strongest correlation occurs. At point A where (sin(0'1), sin( 03!)) = (sin(0t), sin(0s)), the variable scattered wave coincides with the ref erence scattered wave. Therefore, Eq. 2.1 reduces to an autocorrelation operation and thus R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 15 sin(6s)-axis sin(0i)-axis / / / / / &^ (sin(-es),sin(-0i)) -O <y* S y S / #<$> y 0. y y / / / / / / (sin(0i),sin(es)) '- • • V <s> Figure 2.2: Plot o f Eq. 2.2 on the sin (0t ) - s i n ( 0 3) plane. T he angular memory line and scan line intercept at the reference point (sin (# i), sin (0 s )) and are, by definition, perpendicular to each other. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 16 attains a maximum. Because of this self-correlation operation, the ACF measurement is actually identical to RCS (intensity) measurement. At point B where (sin(#-2) ,s in ( ^ 2)) = (sin(—0S), s in (—0 J ), however, the variable and reference scattered waves are related by reciprocity relationship [28], which in turn establishes (ignoring polarization depen dence for the time being) the equivalence between the variable scattered wave observed at 0's2 = —Oi due to an incidence at 0'i2 = —0S and the reference scattered wave observed at 0S due to an incidence at 0,. Consequently, in this case Eq. 2.1 again reduces to another autocorrelation operation and thus attains a maximum. Before proceeding to the next section, a few remarks concerning the second type of field equivalence (the one established under reciprocity condition) are given here. First, reciprocity condition requires not only reciprocal antenna positions, but also reciprocal polarizations [28]. This scenario is illustrated in Fig. 2.3. Second, it is difficult in practice to obtain exact time-reversed propagation paths Pi and P>, where Pi is defined to be incidence-at- 07'-and-scattering-at- 0 R and P2 to be incidence-at-0fl-and-scattering-at9t , as shown in Fig. 2.3(a) and (b). Therefore, the resulting level of correlation will be lower compared with that resulting from the first kind of field equivalence (the one established from autocorrelaton condition). 2.2 A ngular m em ory effect in the o-plane In previous section, it is emphasized that angular memory effect is an inherent property of random scattering and becomes apparent as long as a certain phase matching condition (the generalized Snell’s law given in Eq. 2.2) is fulfilled. Although developed for scattering in the plane of incidence (the 2-D 0-plane), satisfaction of this phase matching condition can be extended to 0—plane. In fact, This independence of angular memory effect on coordinate planes makes surveillance platforms based on this correlation technique both flexible and practical to implement. First-order Kirchhoff approximation (KA1) is used in the following analysis to demon- R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 17 (a) a-polarized transmitter transmitting at &r P-polarized receiver receiving at 0R original (b) a-polarized receiver receiving at 0t P-polarized transmitter transmitting at 0R reciprocal version Figure 2.3: Field equivalence under reciprocity condition, (a) the original scattering situation: an a polarized transmitter transmitting at Or and a /3-polarized receiver receiving at O r . (b) the reciprocal version o f the original scattering geometry: a ^-polarized transmitter transmitting at Or and an a-polarized receiver receiving at 6 t - R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 18 strate angular memory effect in the o-plane. It is assumed that the single-bounce scattering mechanism takes place only in the upper infinite hemisphere, as shown in Fig. 2.4 Denote the umprimed reference incident and scattering wave vectors by the reference transverse wave numbers Ki and K s and the primed variable incident and scattering wave vectors by the variable transverse wave numbers K x and K s , one has sin 6i cos (bii Ki = k sin Q{ sin d>iy —cos OiZ Ki — k cos OiZ (2.3) sin 93 cos 0 sx Ks — k sin 0Ssin d>sy co s9sz ks + k cos 6sz (2.4) sin 6'i cos o ’iX k sin 6'i sin 0 xy — cos 9\z k x — k cos OiZ (2.5) sin 9S cos o sx k sin 6S sin 0 sy cos 6 'sz ks + k cos 9sz ( 2 .6 ) where Ki = k(sm0iCos<piX -f- sinfl, sinewy), ks — A:(sin0s cosd>si: + s in 0 s sind»sy), k / = A:(sin 0- cos + sin 0- sin d^y), and = A;(sin 6's cos <p’sx -F sin 0’s sin <p’sy ) . In addition, R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. 19 z X Figure 2.4: The scattering geometry of angular memory effect in the <jhplane. At constant ^-incidence, the resulting “plane” o f incidence traces out a conical surface in 3 -D space. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 20 it can be shown that the correlation between the reference scattered field represented by K s and the variable scattered field represented by K s is proportional to the exp(— where ud = w c = I17-17!" (2-7^ where V — TcJ— «7 and v — kJ — k~'. Obviously, maximum angular correlation results when U2 = 0.This requires |(«7 - k ~) - (a; - « " ') | =0 (2.8) Note that Eq. 2.8 necessarily reduces to Eq. 2.2 in the plane of incidence. The details of this reduction are presented in the following analysis. With k~ — k (sin 9i cos O ii 4 sin 9{ s in &{/) TcJ = k(sin 9S cos psx 4- sin 9S sin o sy) Ki = k(sin9i cosO ii 4 s i n ^ sin (pty) k^ ’ — k(sin 9S cos p'sx 4 sin 9S sin o sy) obtained previously, Eq. 2.8 can be expanded as 0 — ^i) (^5 )J” = |[(A;sin9S cos o s — Arsing cosOj) — (A:sin9S co so s — Arsing co s0 J]£ ’ 4 [(A: sin 9S sin o s — k sin 0; sin ©;) — (A: sin 9's sin o s — k sin 9\ sin 4>i)\y[ = \A x 4 B y \2 = A2 + B 2 (2.9) where A = ( k s m 9 s cos<ps — Arsing cosd>i) — (ksin9'acos(p's — k s in 9[ cos (pj and B = (A: sin 9S sin <ps — k sin 0* sin (pi) — (k sin 9's sin <p's —k sin 9\ sin 0 ’). The condition that A 2 4 B 2 = 0 requires both A = 0 and 5 = 0. That is, (k sin 9s cos (ps — k sin 9i cos (pi) — (k sin 9S cos (ps — k sin 0* cos ©’) = 0 (2.10) (A:sin0s sin<?)s — A rsin^sinipi) - (Arsin^sintpg — A :s in ^ s in 0 |) = 0 (2.11) R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 21 In the plane of incidence where tpi = <t>\ — 0° and ®s - <ps = 180°, Eq. 2.10 and Eq. 2.11 result in sin 9{ — sin 0£ = sin 9S —sin 6S (2.12) which is exactly Eq. 2.2, the condition for strong angular correlation in the emplane. Next, another special case of significance to practical implementation is considered. In this case, the surveillance platform moves along a horizontal circular orbit at a fixed angle 6 from the 2-axis. Therefore, 9{ = 9\ = 6S = 6's = 9. As a result, Eq. 2.9 becomes [(cos <ps —cos (pi) — (cos©^ —co so £)]2 + [(sin<f»s —sintpi) —(sin o s —sin©’)]2 - 0. (2.13) Given a fixed pair of (o£. ©s), Eq. 2.13 is a function of two variables: o\ and o s. Assigning angular dependence to Eq. 2.13 as r(6-, <PS : 6 i , o s ) — [(cosos —coso,) — (cosol —cos©’)]2 + [(sinos —sinOj) — (sin o l —sinO j)]2. (2.14) a plot of r(o [. ol; ®i, 6 S) for various combinations of (®i: o s) is shown in Fig. 2.5. As evident in the figure, the signature of r(o [, o s; o *. o s), depending on the choice of reference angles {®i,®s), can vary from straight lines to elongated contours. In the case of (oi-Os) = (0°.0°), the transmitting and receiving antennas are positioned in specular configuration. In general, maximum angular correlation results as long as the two antennas lie in the same plane of incidence, independent of the orientation o f the plane relative to x - or y-axis. This independence of orientation is manifested by the straight line strips in the figure. In the case of (o,, o s) = (0°, 180°) (or (0°, —180°)), however, the transmitting and receiving antennas sire positioned in backscattering (monostatic) configuration. For maximum correlation it is necessary that the variable antenna configuration coincides with the reference antenna configuration. As this coincidence takes place only at a point on the ( plane, the resulting maximum correlation occurs at a point where (<p£, ®s) = (0[, <ps). This unique ACF signature is qualitatively demonstrated experimentally (using gravel particles asthe random medium with particle dimension rj A) and analytically (assuming R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. -200 0 200 Figure 2.5: The signature o f ©-plane ACF as a function o f reference angles (4>i.0s )• “i” stands for reference incident angle <f>i, “s" stands for reference scattered angle <bs . x - and y —axes represent o[ and (t)s , respectively, in degrees. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 23 first-order random surface scattering) using KA1. The results are shown in Fig. 2.6. Note that the apparent underestimation by K A l (demonstrated by the relatively slow decorrelation from the correlation maximum) implies that the actual scattering mechanism could well be beyond first-order in nature. The insufficiency of KAl formulation can be remedied by including second-order scattering effects, as explained in the next section. 2.3 Correlation peaks and second-order Kirchhoff approximation Analytically, the correlation peaks discussed in Chapter 2.1 can be described by different components of second-order scattering. Recent studies on scattering by high-slope 2 -D random rough surfaces based on the second-order Kirchhoff approximation (KA2) [1] indicate that for the case of reference antenna positions located in the backward direction, which is the case deployed in this research and in most practical applications, the firstorder scattering component in KA2, as shown in Fig. 2.7, gives rise to a broad response along the angular memory line when single scattering dominates but two peaks when multiple scattering dominates as a result of the second-order ladder and cyclic scattering components in KA2, as shown in Fig. 2.7. Specifically, the ladder term gives rise to the correlation peak at point A in Fig. 2.2 where the autocorrelation condition is satisfied, whereas the cyclic term gives rise to the correlation peak at point B in the same figure where the reciprocity condition is satisfied [16]. Furthermore, it can be shown that the lateral width of ACF is on the order of 1ID , where D is the illumination spot size expressed in wavelengths, and is independent of surface roughness [1]. This theoretical prediction is found to be in good agreement with experimental observations on millimeterwave scattering from random rough surfaces [4]. In summary, given a reference pair of antenna angles (0*, 03) there exists high correlation along the angular memory line defined by Eq. refsnell, with correlation peaks located at (sin (^),sin (0 j)) = (sin(0i), sin(0s)) and (sin(0'),sin(0j)) = (sin(—0S), sin (—0*)), but low correlation elsewhere on the sin(0j) — sin(0[,) plane. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 24 (a) ACF signature across the narrower contours for phi.= 0 °, phig = 180° KAl Lfo Experiment 02 -20 -15 -10 •5 0 5 transmitter angle phi. (primed) in degrees 10 15 20 15 20 (b) ACF signature across the wider contours for phi.= 0 °, phig = 180° KAl ••= 0.6 u_ o Experiment •20 -15 -10 •5 0 5 transmitter angle phi. (primed) in degrees 10 Figure 2.6: (a) Comparison between experimental and analytical ACF signatures across the narrow contours in Fig. 2.5 for the case (<f>i,<t>s ) = ( 0 ° ,1 8 0 ° ), and (b) Comparison between experimental and analytical ACF signatures across the wide contours in Fig. 2.5 for the case (0 t, <j>3) = (0 ° ,1 8 0 ° ). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 25 E, first-order Kirchhoff scattering: single bounce second-order Kirchhoff scattering: double bounce (ladder term) second-order Kirchhoff scattering: double bounce (cyclic term) Figure 2.7: The three major com ponents in the second-order Kirchhoff Approximation: (a) first-order scattering: single bounce, (b) second-order scattering: identical doubly-bounced signals resulting from identical propagation paths, (c) second-order scattering: identical doubly-bounced signals resulting from time-reversed propagation paths. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 26 2.4 Applications o f angular correlation function Recall from discussion in previous sections that while strong angular correlation exists along the angular memory line, rapid decorrelation occurs across the angular memory line (i.e. along the scan line). It is important to realize that the achievement of this low level of ACF (clutter) does not come from signal processing means or novel hardware design. Rather, it is merely a direct result when random scattering is the dominant scattering mechanism, which is commonplace in many practical remote-sensing problems [12]. In contrast to random scattering produced by clutter, scattering by most discrete manmade targets (such as land mines), however, is usually characterized by single or double bounces from well-defined (and hence deterministic) scattering centers with slowly varying angular memory signature over a wide range o f angles on the sin(0j) —sin(6^) plane. As a result, the rapid decorrelation off the angular memory line due to clutter scattering does not find its counterpart in the case of scattering by these man-made targets. Thus, if ACF measurement is performed at a point far away from the angular memory line, low correlation will result if the illuminated region covers a region where there is no target, but high correlation otherwise. Numerically, the following argument may provide useful insights to ACF’s relative effectiveness over the traditional RCS technique: in obtaining ensemble average over in dependent measurement samples of scattering by clutter, addition of complex ACF (com plex numbers with magnitude and phase) could result in a low correlation level for the ACF detection technique, addition of scalar RCS (non-negative numbers with magnitude only) does not necessarily result in a low speckle level for RCS detection technique. In principle, the target visibility using ACF contrast should therefore be higher than that using RCS contrast. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 27 2.5 Other forms o f correlation functions Given the definition o f ACF as a correlation function that measures the similarity be tween two variables in angular domain, it is possible to devise other forms of correlation functions defined in domains other than angular domain. Depending upon the nature of applications, one form of correlation may be more effective than another. For instance, in considering the polarization similarity between two scattered fields, one could form polarization correlation function that makes use of the Poincard’s parameters commonly used in polarization characterization [15]. The resulting polarization-correlation technique may be more suitable than angle-correlation technique in detecting and imaging polarized targets such as submarine’s periscope surfacing out of the sea. On the other hand, fre quency correlation function [1], which considers similarity of frequency content between two scattered fields, could be more effective than other forms of correlation functions in detection and imaging applications where clutter exhibits high frequency-dependence, which is a rather common characteristic for naturally occurring random volume media. In the next chapter, the rationale for using ACF technique in clutter-suppressed detection ap plications will be exemplified. In Chapter 4. on the other hand, the development of various correlation techniques in clutter-suppressed imaging applications will be presented. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Chapter 3 CORRELATION TECHNIQUE IN TARGET DETECTION While related studies were conducted in the past to demonstrate ACF signature and its use in detection of a target embedded in numerical clutter [4, 29], it is important to evaluate the effectiveness of ACF technique in actual remote-sensing settings. For this reason, the application of this detection technique in realistic clutter environment is presented in this chapter. To achieve this, realistic clutter is simulated by using natural media such as 1) fine sand, 2) rough sand, 3) gravel, and 4) rock, in which the combined scattering of both surface and volume media behaves as strong interfering source to the detection radar system. In practical remote sensing applications, sensing radars usually operate at low frequen cies (e.g. 0.1-1 GHz) as pointed out in Chapter 1. This requirement is necessary in order for deeper energy penetration into natural media such as canopy layer or soil medium with high moisture content. If one were to simulate this frequency requirement in laboratory, he or she would have to construct forbiddenly large-scale experimental setup consisting of, for example, heavy antennas, long supporting booms, large observation bench and so forth. As a result of this inherent construction difficulty in low-frequency scattering studies, a compromise must be made in laboratory studies in which the operating frequencies are ‘reasonably’ scaled-up (or equivalently, wavelengths being scaled-down), thus reducing the dimension of experimental setup necessary for observing wave phenomena. Adopting this scale-up strategy, application of ACF detection technique at millimeterwave frequencies (75-110 GHz, or wavelength A = 3 mm at a center frequency of 100 GHz) is considered. In this regard, experimental equipment can be maintained at a man R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 29 ageable size in laboratory settings so that the existence of angular memory effect for different media can be confirmed quickly with our existing facilities documented in [23] and [24], Next, the application of ACF technique in detection at X-band frequencies (7-13 GHz, or wavelength A = 3 cm at a center frequency of 10 GHz) is investigated. At a scale-down factor of 10 from millimeter-wave frequencies, the results at X-band frequencies should demonstrate accurately enough the effectiveness of this correlation technique at ever lower frequencies (e.g. UHF to L-band) in actual remote sensing applications. 3.1 Target detection at millimeter-wave frequencies Millimeter-wave (75-110 GHz) experiments are performed to study the ACF signature of a number of natural scattering media selected in this investigation. The experiments involve the use of a previously constructed bistatic radar system [23], which is shown in Fig. 3.1 and Fig. 3.2. The system is calibrated using a large flat conducting plate as the known target. Such system calibration is necessary to ensure that both the magnitude and frequency responses are corrected and compensated for measurement accessories before any measurement is made. The relevant details of this crucial procedure can be found in [4] and is briefly repeated here in Appendix A for readers’ convenience. In the course of the experiments, the selected media under examination are kept dry in order to maintain minimal absorption loss. The detailed dimension and absorption char acteristics of these four media at millimeter-wave frequencies are tabulated in Table 3.1. Note that the average size, which is usually expressed in terms of wavelength A (= 3 mm at a center frequency of 100 GHz), of media particles ranges from submillimeter to tens of millimeters. Besides, it is worthwhile to observe from this table that certain relationship exists between attenuation and particle dimension. On one extreme, for small entities such as fine and rough sand particles, attenuation due to multiple scattering (as characterized by scattering cross section os in transport theory [12]) is fairly small. On R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 30 Figure 3.1: A far view o f the millimeter-wave system used in the experiments. System specifications o f this advanced vector scattereometer are fully documented in [23]. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 31 Figure 3.2: A close view o f the same system shown in Fig. 3.1. In this figure, the transmitting antenna (on the left hand side) is covered with a servo-mechanical polarizer. The receiving antenna (on the right hand side) is designed to receive both copolarized and cross-polarized scattered signals. R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 32 the other extreme, for large entities such as rock particles, the major scattering mechanism is mainly first-order in nature. The resulting single-bounce scattering does not contribute strongly to the overall scattering loss, and thus exhibit low attenuation. At Mie resonance region where the particle size is comparable with A, however, attenuation due to multi ple scattering becomes exceedingly high, as shown in the case of gravel particles whose dimension is on the same order of A. Both surface and volume scattering are significant in this particular case. As a result, gravel medium exhibits the highest attenuation among the selection. Table 3 .1: Dimension and absorption characteristics o f the four natural media used in the millimeter-wave experiments Medium Attenuation Skin Depth Shape M ajor Axis M inor Axis fine sand 3.14 dB/cm 1.38 cm m sphere 0.09 mm 0.09 mm rough sand 3.70 dB/cm 1.17 cm ~ sphere 0.99 mm 0.99 mm gravel 6.21 dB/cm 0.70 cm « ellipsoid 8.34 mm 4.59 mm rock 3.74 dB/cm 1.16 cm ss ellipsoid 26.82 mm 14.52 mm 3.1.1 Experimental setup At a Fixed reference transmitter angle o f 0l = 20° and a fixed reference receiver angle of 9S = 40°, the TM co-polarized ACF signature along and perpendicular to the angular memory line for each of the selected media is measured and the result is shown in Fig. 3.3. The shape of ACF for the media demonstrates a pattern strikingly similar to that for two-dimensional conducting random rough surfaces [4]: along the angular memory line the correlation peaks occur at the autocorrelation and reciprocity points, with rapid decorrelation occurring along the scan line. It is important to note that within the angular resolution of measurement, the angular width of angular memory line is also the R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 33 same for all four selected media and does not depend on the roughness characteristics of the medium of interest, as consistent with theoretical predictions based on KA2 [16]. Thus, it is appropriate to infer that angular memory effect is a quite “universal” scattering phenomenon in that its occurrence does not depend on the mechanisms that lead to random scattering, but rather on random scattering itself. The above observation of “universality” is important for practical reasons since it suggests that the existence of angular memory effect in a wide range of actual remote sensing applications wherever random scattering exists. This existence of angular memory effect makes ACF technique applicable for improved measurement in a wide range of detection issues. To study the applicability of ACF measurement in detection o f a target buried in a natural scattering medium, a long conducting cylinder of diameter a = 3 mm is buried under a rough sand medium at a depth of d = 6 mm. With (0{,0S) = (20°, —20°) and = (3 0 °,—30°) (note that the point {0\,9's) = (3 0 °,—30°) is far away from the angular memory line corresponding to (9i: 9S) — (20°. —20°), as a requirement from the discussion in Section 2.4), the correlation measurement then proceeds with two different types of scan, namely, angular scan and spatial scan, as shown in Fig. 3.4. While angular scan involves moving the antennas in the plane of incidence (i.e. the 0-plane) from 0° to 40°, spatial scan allows the antenna footprint to scan continuously over the sand-air interface (i.e. along a straight line). The footprint (spot size « 90 mm) is moved over a distance of 200 mm, with 100 mm from either side of the cylinder, in increments of 2 mm during the experiment. In other words, at each of these 101 footprint locations, ACF is measured as a function of frequency. Because of the stationary nature of the problem, only frequency samples (but not spatial samples) are available for ensemble averaging. With a measurement bandwidth of 35 GHz and a decorrelation bandwidth of 1 GHz, about 35 independent frequency samples are available to each single look of correlation measurement. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 34 X 10'4 (a) fine sand X 10“* 4 4 <D3 3 (b) rough sand E U. Lt_ <, c. o o o 0 0 10 20 30 40 50 0 60 10 x 10 -3 (c) gravel x10-3 2 2 031.5 1.5 c» 1 cn . cn I 30 40 50 60 50 60 (d) rock ea 1 E E LL. L i_ O <c. 05 o <c, ' 0 0 20 incident angle in degrees incident angle in degrees 10 20 30 40 incident angle in degrees 50 60 0.5 0 0 10 20 30 40 incident angle in degrees Figure 3.3: ACF magnitude o f the selected natural m edia at millimeter-wave frequencies (9 5 -1 0 0 GHz) for (0 i , 9 s ) = (20°, —2 0 °), along (solid line) and perpendicular to (dotted line) angular memory line: (a) fine sand, (b) rough sand, (c) gravel, and (d) rock. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 35 antennae angular scan spatial scan footprint rough sand cylinder Figure 3.4: Target detection with spatial and angular scans with (6 i , 6 s ) = (2 0 ° , - 2 0 ° ) . Spot size o f the footprint « 30A. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 36 x lO ’3 (a) Detecton using A C F x 10*3 1a 1.8 1.6 1 .6 (b) Detection u sin g R C S 1.2 I 0.6 0.6 0.4 0.4 02 0.2 -100 Figure 3.5: 0.8 •so SO 10O • 10O sam pling distance in mm (a) ACF magnitude as a function o f footprint: 50 •SO sam pling d ista n c e in mm sampling (0 i , 8 3) = 100 ( 2 0 ° ,- 2 0 ° ) and (0 [ , 0 S) = ( 1 0 ° ,- 1 0 ° ) . (b) RCS as a function o f footprint: (0t , 0 s ) = (6t , 0 s ) = (2 0 °, - 2 0 ° ) . It is clear from this comparison that ACF technique results in higher target visibility contrast than RCS technique. 3.1.2 Experimental results In Fig. 3.5(a), the target visibility in terms of ACF magnitude is plotted as a function of footprint locations x expressed in millimeters, with the object buried at approximately x = 0 mm. It is clear from the Figure that the magnitude of ACF attains a reasonably low level at regions where the buried object is absent. This low level o f magnitude signifies the fact that angular correlation due to incoherent scattering by natural media, when measured across the angular memory line, is quite insignificant. On the other hand, as the footprint approaches the region where the object is buried directly underneath, however, the magnitude of ACF rises rapidly. This increase in correlation level can be explained by observing that in coherent scattering by those deterministic objects with well-defined scattering centers, the scattered fields exhibit high degree of coherent information and therefore, the correlation between the fields maintains at a high level. As target visibility depends only on the target-to-clutter ratio, an unambiguous decision R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 37 can be made about the absence/presence of the buried target based on the above rapid Iow-to-high transition of correlation level. When compared with ACF, the traditional RCS approach produces a weaker visibility contrast with the results shown in Fig. 3.5(b). As evident from the figure, RCS plot shows only a slowly varying profile of intensity, making it difficult to discriminate the target from the noisy surrounding medium. To summarize, it is demonstrated that in target detection applications where the clutter sources (including surface and volume scattering) primarily exhibit random scattering, the proposed ACF technique is superior to the traditional RCS technique, resulting in higher target visibility contrast. 3.2 Target detection at X-band frequencies As illustrated in the previous section on millimeter-wave scattering, the proposed ACF technique is shown to be more effective than the traditional RCS technique in terms of target-to-clutter ratio. In practical subsurface remote sensing applications, millimeter- wave radiation, however, has limited usefulness because of its significant attenuation in common geophysical media [25]. For ground penetration applications, UHF (0.3-1 GHz) to L-band (1-2 GHz) is a more realistic frequency band o f choice since radiation in these frequency bands can penetrate deep into geophysical media such as moist soil/vegetation layers or canopies. In this section, the results of a scaled-down (from the UHF- and L-bands) experimental investigation are presented. The details of this investigation are described in the following sections. 3.2.1 Experimental setup A bistatic far-field scattereometer operating at X-band frequencies is constructed to inves tigate the angular memory effect of scattering by a natural medium. The whole assembly is shown in Fig. 3.6. It consists of two rigid booms, with each of them supporting an antenna radiating at TM polarization. The reason for using this particular choice of polarization is R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 38 that EM energy can be most efficiently coupled (with minimal scattering) into a scattering medium at Brewster-angle incidence, which exists only for TM polarization. To allow for bistatic scanning capability, the two booms are controlled by independent stepping motors and can move freely in the plane of incidence (i.e. the 0-plane). Since the whole bistatic radar assembly sits on a horizontal translation stage driven by a stepping motor, the resulting system can perform not only angular-scan measurement, but also spatial-scan measurement, similar to the millimeter-wave system described in Section 3.1.1. The natural medium under examination is typical garden soil housed in a container with dimensions of approximately 1 m x 1 m x 1 m. The soil is kept dry and exhibits a slightly rough soil-air interface. The attenuation constant a and relative permittivity er of the medium are determined using transmission measurement. The dependence of a and er on frequency is shown in Figs. 3.7(a) and (b). From the measurement the relative permittivity and attenuation constant of the medium are found to have mean values of 3.13 and 0.50 dB/cm, respectively, over frequencies. To verify the existence of angular memory effect for this particular scattering medium, ACF is measured along and perpendicular to the angular memory line for two antenna configurations: (0i,6s) = (2 0 °,—20°) and (0i,0s) = (2 0 °,—40°). As mentioned in Chapter 2.1, correlation peaks occur at angle pairs where autocorrelation condition or reciprocity condition is satisfied. For the case of (0*, 0S) = (20°. —20°), the autocorrelation and reciprocity peaks coalesce together into a single peak, as shown in Fig. 3.7(c). For the case of (0t,0s) = (20°,—40°), on the other hand, the autocorrelation peak occurs at (Pile's) = (20°,—40°) and the reciprocity peak at (0,-,0s) = ( —40°,20°), as shown in Fig. 3.7(d). As evident from the figures, the angular memory effect of the soil medium used in this investigation at X-band frequencies is very similar to its counterpart at millimeterwave frequencies shown in Fig. 3.3. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 39 Figure 3.6: The top view o f the X-band bistatic target detection system . In the course o f the experiments, the system scans over the composite target-soil medium contained in the sand box. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 40 (a) Attenuation constant (b) Relative permittivity constant 10i------■ ------■ ------■ ------■ ------ -m >■» 8 > CD Q_ I 4' cd —--- 1 — CD “ 2 0I / 8 9 10 11 7 12 ,-------------,------,------,-----8 9 10 11 12 13 frequency in GHz frequency in GHz x 1 0 -3 (c) Soil ACF 0.02 (d) Soil ACF 4 0.015 CD 3 h 0.01 E u_ u. O <c o 0.005 0 20 40 incident angle in degrees 1 0 0 20 40 60 incident angle in degrees Figure 3.7: Frequency dependence o f the dielectric parameters o f the soil medium used in the experiment: (a) attenuation constant, (b) relative permittivity constant, (c) A C F magnitude along (solid line) and perpen dicular to (dotted line) the angular memory line for { 0 i , 9 a) = (2 0 ° , - 2 0 ° ) and (d) ACF magnitude along (solid line) and perpendicular to (dotted line) the angular memory line for (0 i , 9 s ) = (2 0 °, —40°) R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 41 3.2.2 Experimental results To investigate the feasibility of detecting buried targets using ACF at X-band frequencies. An approach similar to the one discussed in Section 3.1.1 for millimeter-wave frequencies is employed - a long conducting cylinder of diameter a = 3 cm is buried under the soilair interface at a depth of d = 6 cm. By adopting scanning schemes (angular scan and spatial scan) identical with the previous millimeter-wave experiments, both ACF and RCS variation profiles as a function of footprint location x and frequency are obtained. The corresponding results are presented in Fig. 3.8. The location of the buried cylinder lies within the region of [50,60] cm. It is clear from the figure that while the traditional RCS (intensity) approach in Fig. 3.8(a) produces inconclusive information about the location of the buried object, ACF measurement in Fig. 3.8(b) distinguishes itself by exhibiting one single sharp peak at the same physical location occupied by the object. From this comparison, it is clear that ACF technique is more effective than RCS technique in target detection through better clutter suppression. Finally, as a controlled demonstration on the superiority of the ACF technique over the RCS approach, the same cylinder is removed from the medium and placed on top of the soil surface. Intuitively, this setup should result in high target visibility using either ACF or RCS technqiue. With the same reference and variable antenna configurations m , 0 s) — (20°, —20°) and (0i: 0S) = (20°, —40°)) as before, the corresponding variations of ACF and RCS signatures are recorded as a function of footprint and frequency. The corresponding experimental results are depicted in Fig. 3.8(c) and 3.8(d), respectively. Consistent with intuition, both ACF and RCS data produce visually conclusive information in this case, allowing one to make unambiguous decision about the existence of the exposed object easily. Nevertheless, it is clear from Fig. 3.8(d) that ACF technique detection technique, among other advantages over RCS detection technique, provides far better spatial resolution (finer peak width) about the object location. In practice, this R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 42 ■10$ ) 6cm-cylinder below: (30°,-30°) [ 10 $ ) 6cm-cylinder below: (50°,-50°) 3 c: o CD 6 o03 “2 ca CO o o Ll_ o CO ■°1 CO 1 0 0 20 40 60 distance in cm 80 0 100 20 40 60 distance in cm 80 100 (d) 6cm-cylinder above: (50o,-50°) (c) 6cm-cylinder above: (30°,-30°) 0.04 0.015 0.03 0.01 0 0 .0 0 5 <8 0 20 40 60 distance in cm 80 100 0 20 40 60 distance in cm 80 100 Figure 3.8: Object buried at 6 cm below the surface with (9i,9s ) = ( 3 0 ° ,- 3 0 ° ): (a) radar cross section as a function o f footprint. ( 9^8,) = (3 0 ° ,—30°), (b) AC F magnitude as a function o f footprint. (d\,9'a) = (5 0 ° ,—50°). Object placed above the surface with i.6i,9s ) = (3 0 ° ,—30°): (c) radar cross section as a function o f footprint. (8{,9S) = (3 0 °,—30°), (d) ACF magnitude as a function o f footprint. {9'i,9s ) = (5 0 ° ,—5 0 °). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 43 improvement in spatial resolution achieved by ACF technique is an especially attractive feature for accurate localized search for dangerous objects such as abandoned landmines by military or civilian agencies. 3.3 Summary o f target detection using correlation technique In this chapter, experimental results are presented for wave scattering by random media. The results clearly illustrate the existence of angular memory effect over a wide range of (1) scattering media (such as fine sand, rough sand, gravel, rock and garden soil) and (2) frequencies (such as millimeter-wave (75-110 GHz) and X-band (7-13 GHz) frequencies). The key to applying this unique correlation phenomenon in practical detection is sues comes from a simple observation: field correlation due to scattering by incoherent mechanisms is completely different from that by coherent mechanisms - while low-level correlation manifests itself in the former, high-level correlation appears in the latter at points (represented by antenna locations) far away from angular memory line on the sin(0-) — s in (^ ) plane. It is this high-to-low ratio that allows ACF technique to yield higher target visibility contrast than the traditional RCS technique. It is important to note that this clutter-rejection property is nothing more than an inherent property of ACF measurement, and the corresponding improvement in target-to-clutter ratio does not come at the cost of sophisticated signal processing or expensive hardware component additions. Therefore, in view of practical implementability, ACF technique should fit into existing detection radar systems without too much modification. In next chapter, the details of applying correlation technique in target imaging to pro duce clutter-suppressed imaging will be presented. In particular, key emphases are made on a novel 3-D radar imaging system called circular SAR. The development, construction, operation and application will form the core of the discussion that follows. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Chapter 4 CORRELATION TECHNIQUE IN TARGET IMAGING In Chapter 3, the concept of correlation is introduced in target detection applications for clutter-suppressed measurement. It is demonstrated that by incorporating correlation operation in data processing, enhanced target-to-clutter ratio can be obtained, leading to a higher detection rate. In comparison with detection applications where a mere binary decision (i.e. ab sence/presence) is all that is required, imaging applications, on the other hand, require more detailed information such as target size and/or shape. For this reason, high-resolution detection tools were developed in the past and among different alternatives, SAR has evolved to be the standard choice of imaging tools in existence nowadays. Since its emergence in the late 1950’s, SAR has remained one of the most robust and popular imaging techniques available for civilian and military applications [25], Among these applications are terrain mapping, imaging of vegetation features (e.g. trees, rivers and grasslands), as well as subsurface imaging of concealed military facilities in battlefields. As shown in Fig. 4.1(a) and discussed in Chapter I, most traditional SAR-based systems operate along a straight flight path [31], producing an equivalent linear antenna array with an azimuthal resolution (also known as “along-track resolution” or “cross-range resolution”) of D / 2 , where D is the aperture size of the antenna [5]. The range resolution (also known as “across-track resolution” or “down-range resolution” ) is then determined by the bandwidth of the transmitting pulse [5], For brevity in the following discussion, the term linear SAR is used to refer to these SAR systems. Note that the images produced by these linear SAR systems are projection images only and are therefore 2 -D in nature [27]. As a result, for a given illuminated R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. 45 spotlight linear SAR illumination spots (a) LSAR d2 = d d- d / b\ ' \ \ \ / / / natural terrain Linear SAR cannot resolve altitude ambiguity since d1 is equal to d 2. (b) Figure 4.1: (a) The geometry o f spotlight-mode linear SAR. (b) Altitude ambiguity caused by propagation paths o f equal lengths (di = do). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission . 46 structure such as a hill in Fig. 4.1(b), radar echoes due to those scattering centers lying along a common wavefront but at different altitudes will all be mapped undesirably as one single projection image pixel, with no resolution in vertical dimension. To remedy this altitude ambiguity of linear SAR, the interferometric SAR (InSAR) technique, which requires either multiple antennas or repeated flight paths, was developed and is widely used within remote sensing community [10]. 4.1 3 -D imaging using circular SAR In this section, an alternative way for radar topographical (3-D) imaging is introduced. This particular variant of SAR, known as circular SAR [26], requires the SAR sensor to move in a circular orbit as shown in Fig. 4.2(a). The advantages of circular SAR over linear SAR are discussed as follows. First, by virtue of its obvious geometry circular SAR provides a full-rotation (360°) view of the illuminated area. Second, the spotlight nature of its operation [3] makes circular SAR capable of achieving image pixel resolution on the order of A (analogous to the diffraction limit of a lens in optics), where A is the center wavelength of the wideband radiation produced by the pulse-sending SAR system. Third, the altitude ambiguity encountered by linear SAR described above can now be resolved using circular SAR measurements made from several different azimuthal angles, as shown in Fig. 4.2(b). Because of this altitude-resolving capability, it is possible to use circular SAR to perform 3 -D image reconstruction of objects at microwave frequencies. Lastly, from a budget point of view circular SAR can be implemented relatively easily by mounting SAR sensors on lowflying aircraft or helicopters without major costly modifications in existing hardware. To summarize, the features of linear and circular SARs are briefly outlined in Table 4.1. Note that the 3-D image reconstruction feature of circular SAR at microwave fre quencies finds its close counterpart at optical frequencies, namely, confocal imaging us ing optical confocal microscopes. Currently, such microscopes are widely available to R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 47 spotlight circular SAR illumination spot (a) CSAR / ¥ A natural terrain Circular SAR can resolve altitude ambiguity since d 1 is not equal to d 2. (b) Figure 4.2: (a) The geometry o f spotlight-mode circular SAR. (b) Altitude ambiguity resolved by propagation paths o f different lengths (d\ ^ do). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 48 Table 4.1: Specification comparison between linear SAR and circular SAR Features Linear SAR Circular SAR Coverage large ( ~ 1-10 km) medium (~ 10-100 m) Maximum spatial resolution ~ antenna size (D ) ~ wavelength (A) Image processing time intensive intensive Image view partial (one-sided) full (360°) 3-D imaging capability No Yes SAR platform aircraft, satellite helicopter, aircraft achieve confocal imaging where it finds extensive applications in medical microscopy for examination of various kinds o f translucent tissues [17, 20]. In essence, optical confocal imaging refers to an imaging scheme in which optical sectioning is applied to a given illuminated target. The resulting layer images so individually obtained are then stacked up together to reconstruct the original volume image. In addition to the inherent close similarity discussed above, it is important to observe the difference between these imaging techniques from an image processing point of view. In optical confocal imaging, focusing is achieved by properly positioned pinholes whereas image formation is performed by the Fourier-transform computations inherently introduced by light transmission through optical lenses. Since such Fourier-transform operations proceed almost instantaneously, real-time 3-D imaging can be achieved with ease at optical frequencies. At microwave frequencies, on the other hand, both focusing and image formation processes are achieved by applying signal processing technqiues (the processing algorithms are to be detailed in the next section) to raw measurement on digital computing facilities. As a result, compared with its optical counterpart at, 3 D image reconstruction using circular SAR at microwave frequencies involves intensive computation efforts and is usually a time-consuming process. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 49 In an attempt to combine the usefulness of correlation technqiues in clutter suppression covered in Chapter 3 and the desirable feature of circular SAR in achieving 3-D confocal image to be elaborated in this chapter, it is the goal of subsequent sections to develop the bridge these two concepts together and explore from the resulting combined technique the feasibility of achieving 3-D clutter-suppressed image reconstruction for remote sensing applications. 4.2 Circular SAR processing algorithm In general, SAR imaging involves temporal field measurement over a Finite bandwidth B along a flight path P. Assuming the following discretization scheme • M points over the bandwidth B and • N points over the flight path P , one can construct a matrix E ( u, r ) to hold the raw frequency-domain field measurement as follows E(uJi,ri) E{u)i,r2) E(a;1:r,V- i) E ( j j x, r N) E{u>2 , r x) E (ijo 1^ 2) E ( ll)o,T n - i ) E(jJo,rx) (4.1) E{ u m - i , t x) E ( u M , r i) E { u M. u r 2) ... E(uiM l r 2) . . . E(u;jV/ - i , r jV- i) E{ ujM- u r N) E(u>M , r N_ i) E {u M, r N) where each matrix element is a complex number, containing both magnitude and phase information. For typical circular SAR imaging measurement in which field measurement is acquired at 1° increment over a bandwidth of 7-13 GHz sampled at 201 points, the corresponding E (u, r), for instance, is therefore a 201-by-360 matrix, holding a total of 72,360 complex numbers, or 2 x 72,360 = 144,720 real numbers. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 50 Prior to focusing at a particular point r Qwithin the illumination footprint, it is necessary to apply gating to the raw data to eliminate the direct coupling between the antennas. More importantly, application of gating can help minimizing other undesirable contributions to the received signal due to reflections by various parts of the experimental setup. In simple terms, gating around r Q involves column-wise convolution of the SAR matrix E (^ . r) with a gating matrix G {w, r;r0) whose columns contain the appropriate gating filter responses. A typical gating matrix has the following form: G (u > i,ri;r0) G (uJ i,r2:ra) & ( M , f v - i ; r 0) G ( u J i , r ^ : r a) G{uj2, r i : r 0) G(ui2,r2',r0) G{uj 2j T v- i ;To) G(uj2, r,v ; f 0) G ^ v r - i : n ; r o) G(uJM , r i ; r 0) r 2; r Q) . • G(ujm-i-. r ;V-i: r a) G(u!\[.r2',ra) G{ ujm-J n - f f o ) G { ^ \ { • r.V, f a ) (4.2) Note that the convolution procedure mentioned above is generally a time-consuming pro cess, especially when long data sequences are involved. Fortunately, the advent of Fast Fourier Transform (FFT) algorithms since late 60’s has made it possible to alleviate this computation burden significantly by performing the convolution operation in its equivalent time-domain operation, namely, multiplication between the inverse Fourier transforms of E ( u , r ) and G (uj.r:r0). This equivalence can be summarized as follows E (t , r ) x G ( t , r ; r a) <==>E (^,r)<g> G (c u ,r;r0) (4.3) where both ® and x are understood to operate in column fashion on their respective operands. Because of this equivalence, performing time-domain gating on E {t- f ) is thus equivalent to multiplying time-domain raw data with window functions appropriately centered at different times. Fig. 4.3 depicts the use of time-domain window functions. After time-domain gating and Fourier transform, the raw gated data, denoted by Eg ( uj , f :r0), should then be phase-adjusted by a focusing matrix </> (uj. r; r Q) which com- R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 51 focal point N d2 N> ! di \ \ \ \ r2 > 7 ~ window function at q distance.tim e window function at £ distance,tim e Figure 4.3: Different window functions are used at different data-acquisition positions in order to capture the “clean” responses from target located at the focal point. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 52 pensates, with respect to a reference range1, the path differences between the focal point r Q and each of the N points (i.e., r ^ r o , . . . , rN _i,r/v) along the flight path. Precisely speaking, 0 ( w ,r ;r 0) should perform not only phase compensation but also magnitude compensation with the following form: r 2e 2j e I7*1 r°l r 2e 2 j~cLl7'2 r°l r 2 e 2i — | r i - rd r 2e 2 j - f \ r , - r 0 r 2 e 2j ^ |r ,-r .| r 2e2 j ^ Irx-rol ■aJOi— _ 2 r^e -• r7v _ i e 2^ l r ^ - > - r °l r 2v e 2 i ^ - | r w - r 0 | r ^ !e2j^ r 2v e2J ^ ^ - ?0' - 1“Fo' 0 r o —r 0 | OJ-, Mr . v - r o l rs e 0 r ^2ve2 e ^ | r A- F ol >■2—ro| (4.4) where c is the speed of light in free space and has a value of 3 x 108 m s 1. By multiplying E g (uj,r;ra) with 0 (a/, r ; r 0), the phase-adjusted, gated matrix ( u ;,r ;r 0) results /?g,c5 (a2, r ; r 0) = £ ’g ( u ;,r ;r 0)x 0 ( u ;,r ;r 0) (4.5) that is ready for coherent summation to produce focusing (a process also known as beamform ing in basic antenna theory [13]), forming the final image < 7 Sa r { t 0) at the focal point r Q: M 0SA R (ro) ;V = (4 -6 ) r Numerically, the summation over frequency in Eq. 4.6 above is has the same effect as uj applying inverse Fourier transform to the coherent sum with the transform evaluate at time t = 0 / F(uj)eJUJtdui t=o = ^ 2 F( m A u ) A u ) . (4.7) and is equivalent to retrieving radar echo from the focal point in time domain if the calibration plane of the SAR system has been extended to that point prior to measurement. Finally, to obtain a complete image mapping, procedures expressed from Eq. 4.2 to Eq. 4.6 above are repeated for each discrete point within the illumination scene. For 'S ee Appendix C R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 53 the case of 3-D imaging, r Q can be any point within the illumination volume. In Sec tion 4.5.1, the algorithm presented here will be cast into a slightly different form for parallel algorithmic comparison with other SAR processing algorithms. 4.3 Generalized ambiguity function o f circular SAR From previous discussion, it is clear that SAR and confocal imaging are principally similar. W hile SAR mainly operates at microwave frequencies for terrain mapping applications, confocal imaging commonly performs at optical frequencies for medical sub-tissue imaging applications. In this section, an effort is made to combine these two techniques to achieve space-time confocal imaging using SAR on a circular, or more generally, a curved path. The general SAR imaging formulation based on the conventional SAR technique is first developed. Then, numerical and experimental demonstrations are presented to illustrate that 3-D imaging capability and improved spatial resolutions (on the order o f a fraction of wavelength) are possible with circular SARs. 4.3.1 Analytic formulation In radar engineering, given an imaging radar system it is a common mathematical practice to analyze its azimuth and range resolutions using the concept of ambiguity function [25]. In this section, the ambiguity function of circular SAR system, assuming Gaussian chirp pulse input [31], is derived. As shown in Fig. 4.4, circular SAR is an ordinary SAR sensor moving along a circular track to obtain data over 360°. To perform confocal imaging of a point r G located on a plane at a depth h 0 below the track, it is important to first note following the conventional SAR formulation that the signal received by the radar at r sn( f sn = ( xsn, 0), where n = 1 ,2 ,..., N ) is given by [6, 25] volum e R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (4.8) 54 where g n ( t , r) is the convolution of the input pulse ut (£) and the two-way Green’s function from r s n to r and back to r s n , and S ( r ) is the volume reflectivity of the incident wave from r s n to r . In general, S ( r ) depends also on the direction of the incident wave. In this simplified model, however, it is assumed that S ( r ) is almost independent of the incident direction. This signal h n ( t ) is then filtered with the focusing filter function / „ ( i . r 0) matched to a point target at r Q. The filter function / „ ( i , r 0) is the convolution of the gate function u j ( t ) and the two-way delay phase factor for focusing at r c from a radar located at r s n . Therefore, the filter output v n ( r Q ) is given by j V n (r0) = f t ( t , r 0)h n (t)d t. (4.9) The SAR output v ( r a ) is the coherent sum of all v n ( r a ) along the entire flight track and is therefore given by x v (To) = 2 2 v*(r °)- (4.10) n With Eq. (4.8) and Eq. (4.9), Eq. (4.10) can be rewritten in the following form v ( r a) = [ S ( r ) x ( r , r 0)d r (4.11) J v o lu m e where N r x ( r . r 0 ) = Y 1 j 9n ( t , r ) f * ( t , r 0 ) d t (4.12) n is called the “generalized ambiguity function” [25]. The functions g n { t , r ) and f n ( t , r 0 ) can be expressed by their Fourier transforms, ~gn ( u i , r ) and f n ( u j , r 0 ) , respectively, as follows 9 n(l, r) = -^ /n((,T 0) = f J (4.13) J n( u , r 0 )e~tuJtdw (4.14) where g n ( u j , r ) is given by the product of the spectra o f the input pulse and the two-way Green’s function j n( w , r ) = i i i (w )G o(a;,rB), and R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (4.15) 55 circular flight path / 1 //■ / / SAR platform rsn = (Xsn-°) 'On focal point # I'd = (x o--ho) / r = (x,-h) Figure 4.4: Geometry o f a circular SAR system. Focal point r a being located at ( x 0, —h 0 ). R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 56 g*~2rn G 0( u ,r n ) - (4.16) — ------------ (47rrn r and f n ( u j . f 0 ) is given by the product of the spectra of the gate function and the focusing function with r n = 7 n( u , r 0) = u f (u>)Gf(w,ron), and (4.17) G f ( u , r o„) = el c2ro" (4.18) |r3n —r| and r on = |rsn —r 0|. Substituting Eq. (4.13) and Eq. (4.14) into Eq. (4.12), the following equation results [25] -v 1 r -* X ( r , r a) = ]T — / 9 n { u , r ) f n(u},r0)cLj. „ 27t J (4.19) This is the general expression for the generalized ambiguity function, where 9 n ( ^ : r ) and f n ( i u . r 0 ) are given in Eq. (4.15) and Eq. (4.17). Denote in thefollowing the input pulse Ui(t) and the gate function u/ ( t ) . For SAR, it is normal to use a chirp for both Uj(£) and uj (t ) [31]. The chirp is given by -iuj0t-iyt 2 { U| < T ° \t\ > T 0 o For mathematical convenience, the equations above can be combined as Ui(t) = Uf (t ) = e-^o t-(a '+ la")l2 _ O Q < t < l30 (4.20) The frequency is thus given by uiQ+ 2a"t and the bandwidth of the chirp for the pulse in rT 0 -To Thus, / oo i 2 e~a d t= [To Eq. (4.20) is uii = 4a "T a. Also, one can choose a dt (4.21) J -T o -oo i n a = a + ta = 7T JJh + i— (4.22) Making use of Eq. (4.20) and Eq. (4.22), the spectra Ui(ui) and u/(cu) can be written as /» tr (u ~ (Jn ^ Ui(u) = Uf{uj) - -r—rs/cF e- 41“I- “ _,Q O' R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (4.23) 57 Substituting Eq. (4.23) into Eq. (4.15) and Eq. (4.17), the generalized ambiguity function in Eq. (4.19) becomes l— — \ f 1 * - i ^ ^ - Q' + ^ 2 ( r n - r o n ) , X (r,r0) = 2 V^ 7 2Ttt 7-00 T(47rrn)-|o;| s v n ~ \e _ ^ _V 27^ V ^ i s^ - 2 ( r „ - r 0n ) - 4 r ( ^ T + ^ - ) ( r n - r o n ) 2 (4 ttr„)2 ° (4 ‘24) where r n = |r sn — r| and r on = |r sn — T0|, u Q is the carrier frequency, Ub is the chirp bandwidth, and T 0 is the sweep time. This is the general expression for x (r, r 0) applicable to SAR on any curved path. The radar is located at r sn and radiates a Gaussian chirp signal in Eq. (4.20), and the received signal is multiplied by the complex conjugate of focusing filter function to obtain confocal imaging at r 0. The output at r sn is then coherently summed to give the final SAR output v(rQ). Pixel resolution For ideal focusing at r — r Q, Eq. (4.24) should resemble a delta function S(r — r Q) and therefore, by examining Eq. (4.24), it is possible to determine the resolution of the imaging system. Although Eq. (4.24) gives a general expression which can be numerically calculated, it is instructive to examine its approximate analytical expression for resolutions in a few special cases. For a down-looking circular SAR focusing at a point T0 lying on the plane 2 = —h0, note that rsn =Zsn <pn r T0 — a(cos 6 nx + sin (pny) (4.25) = n A 0 = ^(2 7 t) (4.26) —x — h z (4.27) = Xo - hoi. (4.28) The resolution can be obtained by examining the normalized ambiguity function W (r,f^) = | ^ i l | . X{T0 , r 0) R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (4.29) 58 Altitude resolution To consider the on-axis resolution. Let x = x Q = 0, resulting rn Assuming A h = \ h — h 0 \ r on = y / h , 2 + a 2 - - \Jh 2 + a 2. (4.30) h 0, r n - r an ~ h 0A h . ------- (4.31) Substituting Eq. (4.31) into Eq. (4.29), _ 1 / jr ■ \ (hgAh)“ iV(r,r0) cxe (4 32) Thus, the resolution A h which reduces N ( r , r a ) to e ~ l is given by Ah = — where 6 dp = sin 2 c ------------- -3----- (4.33) (—? % = ) is the depression angle. The factor of 2 in Eq. (4.33) signifies X /13 +a2 the symmetry of N ( r , r a) about the focal point r 0 = (0. —hQ). Note also that if the sweep time T 0 is much longer than the inverse of the bandwidth (u;^1), then, A h is approximately given by , , A/i « 2 \Z2 tt , c ) sin 6'dp idfj (4.34) Azimuthal resolutions Next, consider the resolution in the transverse plane (z = —h. where h — h 0) where rn — i"o n = \Jh 2 + |x sn — x \2 — \Jh 2 + |xsn — X o \ 2 . If one considers the resolution near the axis (|x| ha and |xQ| <§: hQ), then rn ~ r on = X STl • ( X o — / x) ’ (4.35) Substitute Eq. (4.35) into Eq. (4.24) and note N r2 ir (4 3 6 ) R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 59 Also note that the ^ 2 (rn — r on) term in the exponent in Eq. (4.24) makes a dominant contribution to the summation since u/Q N ( r , r Q) oc = ujb / 2 t t Jo T ~ l . Therefore, d(pel~^2('rn r°n^ Jo(— 2cos0dP\xo —x\). c (4.37) Noting that the first zero of Bessel function J 0(") is approximately 2.4 and including the symmetry of N( r , r c) about the focal point r Q = ( x0, —h a), the resolution in the transverse plane is obtained as follows 4.8 Aa; = |a:0 - x\ w M -2 cos (7dp c In the above, special cases of resolution on and near an axis are discussed. (4.38) It is significant to note that the axial resolution (Eq. (4.34)) comes primarily from the band width while the transverse resolution (Eq. (4.38)) depends mostly on the wavelength. In general, however, the pixel resolution at an arbitrary point r in space depends on both the bandwidth and the wavelength. 4.3.2 Numerical calculations In this section, the confocal imaging capability of circular SAR is demonstrated analyti cally using the generalized ambiguity function x ( r , r Q) derived in Section 4.3.1. Define in the following a set of numerical parameters pertaining to a particular circular SAR system operating at X-band frequencies • bandwidth B = 7-13 GHz, • sweep time Ta = 4 s. Chirp rate a" = ^ • radius a of the circular SAR flight track = 1.0 m, • depth hQ of the plane to be confocally imaged = 1.0 m below the track. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 60 • sampling rate of SAR measurement along the flight track = every 1°. Let x ( x ), x(y)> and x(2) denote the magnitude variations of x (^ ? r0) projected re spectively along the x - , y~, and z-axes with the focal point located at (0, - h 0). Plots of x (^ ), x(y)> and x(z ) are depicted in Fig. 4.5 With reference to the figure, it is apparent that both x(x) and x(y) bear functional variation closely similar to that of a delta function, as discussed briefly for the case of ideal focusing at the end of Section 4.3.1. In addition, at a center frequency f Q= 10 GHz (A0 = 3.0 cm), the 3-dB peak widths 0.25Ao) of x( x ) and x(y) are indeed on the order of a fraction of wavelength. This fact should make circular SAR a competitive candidate for high-resolution imaging applications. Compared with x( x ) and x(y) in Fig. 4.5, x ( 2)’ however, shows a broader peak around the focal point. In fact, given a fixed bandwidth the peak width of x{z) is approximately given by Eq. (4.34). By setting the focal point r Q to be located at (0, —h), the peak widths of x(^)> x(l/)> and x ( z ) as a function of depression angle (= ta n -1 (£)) are shown in Fig. 4.6, which show dependence on the depression angle in a manner consistent with Eq. (4.34) and Eq. (4.38). It is obvious from the figure that at a depression angle of about 77.5°, circular SAR produces uniform pixel resolutions in the x - , y-, and z-axes. Finally, it is instructive to compare the focusing capability of a circular SAR system with that of a conventional linear SAR system. By applying Eq. (4.24) with r sn located along a a straight line (of length 2a) on the y-axis , xC^h x(y)> and x(z) are calculated and shown in Fig. 4.7. Unlike circular SAR for which x(^), x(y)> and xiz) converge to a common resolution at about 77.5° (corresponding to an incidence angle of 12.5°), conventional SAR achieves uniform resolution only for x(y) and x{z ) at a depression angle of 45°. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 61 IX(x/0 = ((U io)) IX<y,ro = (0,-tio)) 0.8 <*> •5 x-range in wavelength 0 5 y-range in wavelength IX(z;o =(0,-ho))l ■5 0 5 z-range in wavelength (shifted by +h Figure 4.5: Magnitude variations o f the generalized ambiguity function x ( r , r Q) projected along the x - , y - , and r-a x e s. Bandwidth: 7 -1 3 GHz. Sweep tim e = 4 s. Depth h 0 o f the focal plane = 1 m below the flight track. Depression angle 6dp = 45°. rc = (0, - h 0). R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 62 circular SAR image resolutions: X(x), Y(+), and Z(o). 10 20 30 40 50 depression angle in degrees 60 70 80 Figure 4.6: Pixel resolution (in terms o f wavelength) along the x - , y - , and r -a x e s as a function o f depression angles Qdp for circular SA R system . Bandwidth: 7 -1 3 GHz. Sweep time = 4 s. r 0 = ( 0 . - / i ) , where h — a x tan(0jp ). R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 63 linear SAR image resolutions: X(x), Y(+), and Z(o). 10 20 30 40 50 depression angle in degrees 60 70 SO Figure 4.7: Pixel resolution (in terms o f wavelength) along the x - , y - , and c -a x e s as a function of depression angles 0<fp for linear SAR system. Bandwidth: 7 -1 3 G H z. Sweep time = 4 s. r 0 = (0, - h ) , where h = a x ta n (Odp)- R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 64 4.3.3 Experimental results In order to verify the correctness of the analytic formulation and numerical calculations presented previously, a simple imaging experiment using circular SAR at microwave fre quencies (the details of the experimental setup will be discussed fully in Section 4.4 below) is conducted. In this experiment, a 63 mm conducting sphere is placed on top of a thick absorbing sheet at a distance of 15 cm from the center of the illumination footprint. By focusing the circular SAR system right at the location of the sphere, a sharp image is obtained. The processed image is shown in Fig. 4.8. To examine the “sharpness” of the sphere image, the data points along the x-axis that contains the peak in Fig. 4.8 were extracted and plotted in Fig. 4.9. As evident in the figure, the 3dB peak width, which is roughly equal to 0.25A, is indeed on the order of a fraction of the wavelength. Up to this point, it has been demonstrated analytically, numerically and experimentally that by using circular SAR, imagery with super-resolution can be achieved. While super resolution is a desirable feature in imaging, it usually entails forbiddenly long processing time. In subsequent sections, however, attention will be directed more to the 3-D imag ing issues of circular SAR and its combined use with correlation technique to produce enhanced target-to-clutter ratio for imaging in heavy-clutter environment. 4.4 Experimental studies on 3-D imaging using circular SAR To illustrate the principle of circular SAR in performing 3-D confocal imaging, controlled laboratory experiments are performed at X-band frequencies (7-13 GHz). In particular, 3 sets of experiments are conducted. They are, in sequential presentation order, 3-D confocal reconstruction of (A) layers of spheres, (B) a single sphere, and (C) a palm-sized conducting model helicopter. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 65 SARimage of a sphere infree space x-range pixel resolution inI Figure 4.8: 2-D circular SAR image of a conducting sphere in free space. The sphere was located at a distance of 15 cm (or 5A at a center frequency of 10 GHz). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 66 Generalized am biguityfunctionof circularSAR 0.35 0.25 £ 0.2 0.05 -8 -6 4 -2 0 2 4 6 8 pixel resolution inI Figure 4.9: 1-D extraction o f data points along the x -a x is that contains the bright im age in Fig. 4.8. The 3dB peak width o f the generalized ambiguity function o f circular SAR system is approximately 0.25A. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 67 4.4.1 Experiment A: Confocal reconstruction o f layers o f spheres X-band microwave imaging experiments are conducted to investigate the feasibility of imaging of multiple layers of conducting spheres, as shown in Fig. 4.10. The trans mitting and receiving antennas are mounted on a stationary stage and positioned in the backscattering direction, radiating at W -polarization at a 45° depression angle. At a slant reference range of 140.0 cm the dimension of the illuminated volume is 37.4 cm. Within the illuminated volume, spheres are supported on a rotation table by two thick sheets of Styrofoam (a household insulation material that is nearly transparent at microwave frequencies). The lower sheet supports three uniformly-spaced metal spheres of different diameters (one of 5.0 cm and two of 2.5 cm, with a 10.2 cm separation) and the upper sheet supports one metal sphere with a diameter of 6.4 cm located at the center of rotation. The two sheets are separated by a distance of 19.0 cm. A frequency-domain SAR measurement is made every 5° along the circular path over a frequency band of 7-13 GHz. To process the SAR data, procedures expressed from Eq. 4.2 to Eq. 4.6 above are used for each discrete point within the illumination volume. In particular, the illuminated volume is first discretized into 77 x 77 x 9 cells (that is, 77 x 77 cells on each of the 9 layers at a pixel resolution of 6 points/wavelength). To each of these cells, a unique set of time-domain, Kaiser-based gating functions is computed and applied to each of the measurements made along the circular antenna path. The resulting gated measurements are then magnitude-phase adjusted and coherently added for beam-forming. Since this spotlight-mode focusing process can be done on any plane within the illumination volume, three-dimensional images can be obtained by focusing one slice at a time and using surface or volume rendering software on the stacked-up image slices. The images of a few selected layers (out of the 9 layers in total) are processed and they are presented as contour plots in Fig. 4.11. As evident from the contour plots, each subplot addresses correctly the arrangement of the metal sphere(s) shown in Fig. 4.10. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 68 V antenna layer (a) 6.4cm H h layer (b) T 1 19.0cm i ^ " - 1 y / / / y y y / / '/{■/ 2.5cm +1\ k r A W '/'/////" /.■ , /V /y /X 'Z / Styrofoam sh eet 2.5cm 6.4cm z k r >z1 rk a V layer (c) Styrofoam sh eet layer (d) Figure 4.10: Schem atic for 3 -D confocal imaging o f layers o f metallic spheres using circular SAR. Band width: 7 -1 3 GHz. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 69 As the focal plane descends from top to bottom, the contour plots undergo the transitions from no sphere to one sphere, then from one sphere to three spheres and finally from three spheres to no sphere again. From this experiment, it is clear that circular SA R can focus at a given plane while defocusing all other planes within the illumination volume, thus demonstrating its 3-D confocal imaging capability once available only at optical frequencies. 4.4.2 Experiment B: Confocal reconstruction o f a single sphere As an additional illustration, this section describes another experimental imaging setup used to reconstruct the 3-D image of a metal sphere suspended in free space. For full bistatic surveillance capability to be utilized in near future, the simple setup discussed in Section 4.4.1 is modified from ground up, resulting in the circular SAR system schemat ically shown in Fig. 4.12. With reference to the figure, this circular SAR system is constructed for use at X-band frequencies (7-13 GHz). The dimensions of this system are approximately 2 m x 2 m x 2 m and is built almost entirely of 4 ’ x 4 ’ wooden poles. To provide full bistatic surveillance capability, the transmitting and receiving an tennas are mounted on two separate circular rings, each of which is individually driven by computer-controlled stepping motors with an angular precision of approximately 0.02°. To perform SAR imaging, a 63 mm conducting sphere is placed on top of a Styrofoam support located at the center of the illumination footprint. At a slant range of 0.97 m and a depression angle of 46°, an illuminated scene of size 42 cm x 42 cm is imaged by the circular SAR system which performs frequency-domain SAR measurement at an angular increment of 1° along the circular track. By applying similar SAR processing procedures outlined previously, the corresponding 3-D image is obtained and shown in Fig. 4.13. Note that the apparent dark line that connects the top and bottom contour layers is produced by the PLOT3 routine in MATLAB and has nothing to do with the actual image. Once again, this experiment confirms the 3-D imaging capability of circular SAR. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 0.5 - 0.2 - x-range in m eters 0.1 0 0.1 0.2 x-range in meters (c) (d) 1.1 1.1 CO CO Jj ® 1 1 CD 05 E in .S t -0.9 t * CD CO E CD CD 05 cn c c= 20.8 20.8 >* 0.7 - 0.2 0.7 - 0.1 0 0.1 x-range in m eters 0.2 - 0.2 - 0.1 0 0.1 0.2 x-range in meters Figure 4.11: Experimental result for the imaging experiment shown in Fig. 4.10: (a) no sphere, corresponding to “layer (a)” in Fig. 4.10, (b) one sphere, corresponding to “layer (b)” in Fig. 4 .1 0 , (c) three spheres, corresponding to “layer (c)” in Fig. 4.10 and (d) no sphere, corresponding to “layer (d)” in Fig. 4.10. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 71 bearing supports w ooden ring antenna antenna w ooden ring metal sp h ere _ -styrofoam support ........... at absorber sh e e t -. turntable ■ ' ' / / / / / / ' ■ ' / / / / / / / / / / / / / / / / / / / / / / / r V / / ' " ‘' / / / / ' s ' /,■' ' / ■ ' / / s’ / / ' / ' / ' / ' ' / / y ///'■'■' y/ ' / ■ '/ / . Figure 4.12: Schematic for 3 -D confocal imaging o f a metal sphere suspended in free space using circular SAR. Bandwidth: 7 -1 3 GHz. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 72 3D reconstruction of a sphere using circular SAR 0.07 0.06 0.05 0.04 0.03 0.02 - 0.01 - 0.01 0.02 • -0.094 -0.096 -0.098 • 0.102 x10'3 -0.104 -0.106 -6 Figure 4.13: Experimental result for the imaging experiment shown in Fig. 4.12. The image is displayed as a stack o f uniformly spaced (vertically) contours. The apparent dark line that connects the top and bottom contour layers is produced by the PLOT3 routine in MATLAB and has nothing to do with the actual image. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 73 4 .4 .3 E x p e r im e n t C : C o n fo c a l r e c o n s tr u c tio n o f a m o d e l h e lic o p te r So far both Experiment A and B deal with isotropic scatterers only (those objects that radiate uniformly over the entire 4 it steradians). In order to demonstrate the imaging versatility of circular SAR, an imaging experiment for a non-isotropic object is conducted and specifically, a palm-sized toy plastic helicopter is used for this purpose, the schematic of this experimental setup is shown in Fig. 4.14. In this experiment, the plastic helicopter is first painted with a kind of fluid metallic paint (known as “Nickel print”) so that it becomes conducting at microwave frequencies. Next, it is placed on top o f the same Styrofoam support used in the previous experiment and is then imaged by the circular SAR system which performs frequency-domain SAR measurement at an angular increment o f 1° along the circular track. By applying similar SAR processing procedures outlined previously in Experiments A and B, the resulting 3-D image of helicopter is reconstructed is obtained and displayed as distributed clusters of dots in Fig. 4.15. From the figure, it is clear to see the main features of the helicopter such as propellers, head, body shaft and tail. In particular, it is interesting to correlate the com er structures located at the helicopter tail with the strong reflection shown in Fig. 4.15. In addition, note that the length of the aircraft shown in Fig. 4.14 agrees with that of the processed image in Fig. 4.15. 4 .5 C lu tte r s u p p r e s s io n u s in g c o r r e la tio n im a g in g Radar imaging in heavy-clutter environment has never been a trivial issue to radar design ers [25, 31]. The undesirable effects of clutter manifest themselves in the form of speckles (bright spots) in the processed radar images, making image interpretation inaccurate. In reality, this failure to characterize radar images accurately could lead to costly and/or dangerous consequences in applications such as detection of unexposed active landmines in abandoned battlefields. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 74 bearing supports w o o d en nng antenna antenna w ood en nng 30 cm toy helicopter styrofoam support ' 'sSfis absorber s h e e t tum tabe Figure 4.14: Schematic for 3 - D confocal imaging o f a palm-sized model helicopter suspended in free space using circular SAR. Bandwidth: 7 -1 3 GHz. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. ^ ft} ,gure , tf/V. Ae// 0.15 AS; c- ^ botM Pcn'ty, * * ,l r **§0 P'CVn ftcprl *"7p „ a^ees > * & * * ^ /6/f ^Periff. w tb ,L g strn„ ‘h v 7/ * -//f c , '-TSs&sfeij ’** ^ e 0^r c° ^ 'eo^/s, S/bo °^ 6 C°P^ er ’e r re/0r, °afo ecy 0(7/ 7^6 Pen^/s, Von. 76 From the theory of scattering by random media, it is a well-known fact that the scattered waves produced by random scattering carry almost no coherent information (e.g. polarization, amplitude, phase, frequency, angle o f incidence and so forth) of the original incident wave [13]. In contrast, for scattering by most man-made targets (e.g. buried landmines or underground utility pipes which are characterized by well-defined scattering structures) where deterministic scattering is the dominant scattering mechanism, however, the scattered waves tend to retain a decent amount of coherence. One way of taking advantage of this intuitive absence/presence of coherence in scat tered waves to achieve clutter suppression is to consider the correlation of waves, where the weak correlation response from clutter (random scattering) is brought into sharp con trast with the strong correlation response from man-made targets (deterministic scattering) - it is these distinct correlation behaviors between clutter and targets that permit enhanced target-to-clutter ratio using correlation techniques. Obviously, the success of this corre lation approach depends on the dissimilarity between clutter and target responses: the more dissimilar between clutter and target responses, the more enhanced the resulting target-to-clutter ratio is. In Chapter 3, ACF technique has been successfully incorporated to achieve superior detection capability over traditional cross-section (intensity) technique in detection applications. In parallel with this development, the remaining sections in this C hapter describes different SAR processing schemes and compare their relative figure of merits. In particular, heavy emphasis is put on the combined use of ACF and circular SAR. The resulting technique, known as angular-correlation SAR, is to be an effective means of suppressing clutter for imaging in heavy-clutter environment. Before comparing conventional circular SAR processing with other types of correlation SAR processing, it may be helpful to examine the details of each type of these SAR processing schemes. Specifically, two types of correlation SAR processing schemes will be examined in addition to the conventional circular SAR processing scheme. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 77 4.5.1 Conventional SAR processing Although the conventional SAR processing algorithm has been adequately elaborated in Section 4.2, the expressions derived in that section are not in the most convenient forms for comparison purposes in this section. For this reason, the same conventional SAR processing algorithm developed in Section 4.2 will be cast into slightly different forms in the formulation below. In a conventional focused SAR system, raw vector frequency measurement E (u, r) is first acquired as a function of space. Given a point r a to be focused, this raw vector data matrix E (a;, r) is then frequency-convolved with a gating filter G (u , r : r 0) to minimize directcoupling between antennas and multipath interference produced by experimental artifacts. Next,the resulting gated data matrix is phase-compensated by d (uj,r:ra) and then coherently summed together over frequency and space for focusing and beamforming. The operations described above can be summarized as f r e q space _ <rsAR(r0) = I _ _ H [E ( ^ , r ) 0 G ( a /,r ;r 0)]x 0 («;, r: r 0)|2 uj (4.39) r where crsAR{ra) is the processed cross section with the beam focusing at r 0 and ® denotes convolution operation implemented using FFT algorithms. Note that the gating filter G is a function of the focal point T0. In effect, this functional dependence on space of gating allows spatial tracking in addition to focusing operation, resulting in more effective gating. 4.5.2 Frequency-correlation SAR processing One common technique for speckle suppression in SAR processing is to perform frequency correlation between SAR images processed at different pairs of sub-bands [cjf] and [ujj] over the entire measurement bandwidth. In many ways this technique is very similar to conventional SAR processing discussed above and involves the following operations: freq Vu-SARifo) = \< space _ _ _ ^ 2 {[E ( K ] , r ) 0 G ([w<],T;r0)]x <b ([w i],r;r0)} KI.KI r V i^ j R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 78 { [ E ( K ] ,r ) ® G ([o ;j],r;r0)]x 0 ([u!j\,r‘, r Q) }* > | (4.40) where * and () represent complex conjugation and ensemble averaging operation, respec tively. In effect, this correlation approach involves partitioning SAR measurement into a number of sub-bands of SAR data over the entire measurement bandwidth. For sufficient statistical independence among these sub-bands of SAR data, the partitioned sub-bands should be separated by at least the decorrelation bandwidth of the measurement. Con ventional SAR processing is then applied to each pair of the sub-band SAR data before correlation between images takes place. The resulting correlated image is then averaged with other correlated images obtained at different sub-band pairs to produce the final frequency-correlation SAR image cf^ - s a r ■ Fig- 4.16 describes this correlation scheme for the cases of (a) 4 partitions and (b) 8 partitions. It is important to observe that the clutter suppression achieved by this correlation approach does not come without cost. By partitioning bandwidth into smaller sub-bands, however, the spatial resolution is degraded. 4.5.3 Angular-correlation SAR processing In addition to frequency correlation, an alternative way of performing correlation is to cor relate waves scattered at different observation angles over the entire measurement band width. Because of its consideration on angular dependence of scattered waves, this cor relation approach is appropriately called angular-correlation SAR processing. It involves the following operations: fr e q v*-SAR(ro) = | < Y, space J2 _ _ _ {[E ( u . T i ) ® d (u>,ri;r0) ] x d) ( u j , r i : r 0)} V (i—j)=Att>'s {[E G (a;.rj;T 0)]x 0 ( u j . r j - . r ^ Y > |. (4.41) In contrast with frequency-correlation SAR in which a full view (360°) of SAR mea surement is available for bandwidth partitioning, angular-correlation SAR involves correla tion between spatially partitioned SAR data over the entire measurement bandwidth. With R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 79 4 partitions final image = < im a g e l, image2 > im agel image2 ' Y //,V / / / / . ' / / / . (a) 8 partitions final image = < im ag el, image2, image3, image4 > im agel im age2 im age3 im age4 (b) Figure 4.16: Schem atic o f bandwidth partitioning in the frequency-correlation SAR for (a) 4 partitions and (b) 8 partitions. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 80 the particular geometry of circular SAR, this correlation scheme is depicted in Fig. 4.17. As shown in the figure, this scheme begins with correlational imaging at a small included angle A 0. For instance, at an included angle A <p of 3° (as in Fig. 4.17(a)), this approach correlates the SAR pairs at {0°; 3°}, {1°,4°}, {2°, 5°}, . . . , {357°; 0°}, {358°, 1°} and {359°, 2°}. The correlation products are then averaged to produce an image I\. Next, at an included angle of, say, 30° (as in Fig. 4.17(b)), the same correlation operation is applied to the SAR pairs at {0°,30°}, {1°,310}, {2°, 32°}, .. .,{357°, 27°}, {358°, 28°} and {359°. 29°}. The resulting correlation products are then averaged to produce another image U. As this correlation procedure continues for larger A o ’s, an image stack con sisting of l\. In. h , • • - ; I m - l: 7 v / will be generated, where M is the number of correlation angles or simple a measure of the “length” of the image stack. Note that in general larger M implies more clutter suppression (and hence more processing time). By taking average over the length of the image stack, an angular-correlation SAR image is formed. Note that the use of multiple decorrelation angles in this summation process is analogous to performing ensemble averaging. Therefore, this compact imaging scheme effectively combines imaging formation (indicated by coherent summation) and ensemble averaging in one procedure. To illustrate experimentally this useful relationship between image formation and en semble averaging, a 63 mm conducting sphere is placed off-center on top of an absorber sheet below the circular SAR system. Frequency-domain SAR measurement is then ac quired at an 1° angular increment over 360° along the circular flight track. Both con ventional SAR and angular-correlation SAR processing schemes are performed for image formation. Fig. 4.18 shows the corresponding conventional SAR image. The presence of the bright dot in the figure suggests strongly that the conventional SAR processing algorithm, when combined with circular SAR configuration, is indeed very effective for high-resolution imaging. In contrast, the angular-correlation SAR image with single decor relation angle (2°) in Fig. 4.19 produces a relatively vague (and broad) dot compared with that in Fig. 4.18. Besides the contribution by the faint reflections from the absorber sheet, R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 81 (c) O * f 0 Figure 4.17: Schematic o f angle partitioning in the angular-correlation SAR for (a) 3 °, (b) 3 0°, (c) 4 5 °, (d) 90°, (e) 120° and (f) 150°. A ngles are not drawn to scale. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 82 summation over many highly-correlated terms (due to the small decorrelation angle used in the processing) in Eq. 4.41 is the primary mechanism leading to the bright annular image surrounding the sphere. To obtain an improved version of this correlation image, one could therefore make use of multiple decorrelation angles in the processing algorithm. Based on the argument presented in previous paragraph, a sensible choice on multiple decorrelation angles in Eq. 4.41 will thus include large number of large decorrelation angles. Fig. 4.20 shows the improved image with a decorrelation angle of 20°. As the number o f large decorrelation angles increases, the image becomes more enhanced, leading to the one in Fig. 4.21. This image demonstrates the importance of using large number of large decorrelation angles in angular-correlation SAR processing in low-clutter environment. As most man-made targets reflect strongly only for a relatively narrow range of obser vation angles, it is important to include both small and large A 0 ’s in the stacking process discussed above. Such inclusion is especially important for imaging in heavy-clutter en vironment where small Aci’s help distinguishing target response from clutter response and large A o ’s warrant low clutter response to the final angular-correlation SAR image a < S > -S A R - Like frequency-correlation SAR processing, the clutter suppression brought by angularcorrelation SAR processing does not come without cost. By partitioning the full 360° field of view (FOV) into smaller sub-FOV’s of various angular widths, image of the targets which have fine angular-dependent radiation pattern may be smeared, thus degrading angular resolution of the final angular-correlation SAR image. Note that the success of angular-correlation SAR processing depends heavily on the difference between the decorrelation rates of clutter and target responses. In low-clutter imaging environment such as previous experiment where clutter response decorrelates at about the same rate as target response, inclusion of large number of rapidly decorrelating terms in the coherent summation process is necessary for quality images. In heavy-clutter imaging environment, on the other hand, clutter response tends to decorrelate far more R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 83 Conventional SAR x-range inmeters Figure 4.18: Conventional SA R image o f a 63 mm conducting sphere on top o f absorber material. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 84 Angular-correlation SAR: 2° -0.3 -0.2 -0.1 0 0.1 x-range inm eters Figure 4.19: Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with a decorrelation angle of 2°. The bright annular ring results from the highly-correlated terms in the summation mechanism in Eq. 4.41. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 85 Angular-correlation SAR: 20° x-range inmeters Figure 4.20: Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with a decorrelation angle of 20°. Note that the previous bright annular image in Fig. 4.19 has dimmed significantly as a result of using large decorrelation angle (i.e. 20°) in this case. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 86 Angular-correlation SAR: 20°, 40° and 60' x-range inmeters Figure 4.21: Angular-correlation SAR image of a 63 mm conducting sphere on top of absorber material. The image was processed with multiple decorrelation angles of 20°, 40° and 60°. Note that the previous annular image in Fig. 4.20 has disappeared almost completely. This image demonstrates the importance of using large number of large decorrelation angles in angular-correlation SAR processing in low-clutter environment. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 87 rapidly than target response, and inclusion o f large number o f rapidly decorrelating terms will thus desirably de-emphasize the masking effect of clutter on the target response. In the next section, experimental results will be presented to illustrate the effectiveness of angular-correlation SAR processing over conventional SAR processing in heavy-clutter environment. 4.5.4 Experimental comparison To compare the relative merits among different SAR processing procedures (conventional SAR, frequency-correlation SAR and angular-correlation SAR) described previously, two sets of SAR imaging experiments are conducted at X-band frequencies (7-13 GHz). Ex periment A examines the relative performance of these processing schemes in mediumclutter environment whereas Experiment B focuses on the distinct effectiveness of angularcorrelation SAR processing in heavy-clutter environment. Experiment A With the circular SAR setup described in Section 4.4.2, two identical metal spheres (diameter = 25 mm) are placed on top of a large Styrofoam imaging platform supported by thick absorbing sheets. The spheres are separated from each other by 20 cm and symmetrically located about the center of the circular flight path. To simulate a mediumclutter environment, tiny gravel particles are poured onto another layer of Styrofoam sheet placed directly on top of the spheres. The resulting experimental setup is schematically shown in Fig. 4.22. Conventional SAR processing is applied to the raw data, yielding the image in Fig. 4.23. As shown in the figure, it is clear that conventional SAR processing continues to produce faithful image of the scene. The two spheres are indicated unambiguously by the bright dots in the figure. On the other hand, the corresponding image using frequency-correlation SAR process- R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 88 tiny gravel particles Styrofoam sheet metal sphere metal sphere Styrofoam sheet c ^ 'T s y ///////////////,- /, v/ / / / / / / / / / / / / Absorber material Figure 4.22: Experiment A: a schematic for microwave imaging in medium-clutter environment using different kinds o f SAR processing methods. The size o f spheres (diameter = 25 mm) is much larger than the size (mean diameter ~ 3 mm) o f the gravel particles. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 89 Conventional SAR x-range in m eters Figure 4.23: Experiment A: conventional SAR processing continues to produce faithful image of the scene in medium-clutter environment The two spheres are indicated unambiguously by the bright dots in the figure. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 90 ing is displayed in Fig. 4.24. Again, the presence of the spheres is clearly represented by the same two bright dots in the figure. Essentially, both Fig. 4.23 and Fig. 4.24 convey the same information. Finally, angular-correlation SAR technique is used to process the image from the raw data and the resulting image is portrayed in Fig. 4.25. Coincidentally, the processed image looks alike those depicted in Fig. 4.23 and Fig. 4.24. It appears that even in mediumclutter environment, the three processing schemes appear to produce consistent images - an observation which finds close counterpart in low-clutter environment elaborated in Section 4.5. Experiment B To study the effectiveness of angular-correlation SAR processing over other two SAR processing schemes examined in this chapter, an imaging experiment in heavy-clutter environment is conducted. Specifically, the setup is shown in Fig. 4.26 in which the two spheres (diameter = 25 mm) used in the previous experiment were placed on top of a layer of large gravel particles (mean particle diameter « 30 mm). As before, the spheres are separated from each other by 20 cm and symmetrically located about the center of the circular flight path. The top view of this assembly is shown in fig. 4.27. In view of the heavy clutter introduced by the volume scattering medium made up o f large gravel particles, it is expected that the processed images, unlike those presented in previous section, contain a modest amount of speckles. At a frequency bandwidth from 7-13 GHz (wavelength A = 3 mm at a center frequency of 10 GHz), SAR measurement is performed over the circular flight path at every 1° increment. The resulting SAR data is then processed individually using Eq. 4.39, 4.40 and 4.41, with the results being summarized in Fig. 4.28-Fig. 4.30. In Fig. 4.28 and Fig. 4.29, it is evident that although both conventional SAR processing (in Fig. 4.28) and frequency-correlation SAR processing (in Fig. 4.29) are capable of R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 91 Frequency-correlation SAR x-range in m eters Figure 4.24: Experiment A: frequency-correlation SAR processing results in an image strikingly similar to that produced by conventional SAR processing. This mage demonstrates that the benefit of applying frequency correlation technique is not obvious in not only low-clutter environment, but also medium-clutter environment R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 92 Angular-correlation SAR x-range in m eters Figure 4.25: Experiment A: angular-correlation SAR processing results in an image strikingly similar to that produced by conventional SAR processing. This image demonstrates that the benefit of applying angular correlation technique is not obvious in not only low-clutter environment, but also medium-clutter environment R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 93 metal sphere metal sphere large gravel particles Absorber material Styrofoam sheet Figure 4.26: Experiment B: a schematic for m icrowave imaging in heavy-clutter environment using different kinds o f SAR processing methods. The size o f spheres (diameter = 25 mm) is about the same as that (mean diameter « 30 mm) o f the gravel particles. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 94 metal sp h eres SAR s e n so r i i i i Figure 4.27: Experiment B: a top view o f Fig. 4.26. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 95 capturing the image of one sphere (appearing as bright dots in the figures), both o f them fail to depict the image of the other sphere (located at +10 cm along the y-axis), which may have been half buried in the gravel medium. In fact, the clutter in this experiment is so strong that even the frequency-correlation SAR processing does not bring about much improvement over conventional SAR processing - the two images are almost identical. The angular-correlation SAR processing algorithm expressed in Eq. 4.41, on the other hand, produces the image shown in Fig. 4.30. With reference to the figure, the processed image correctly depicts the existence of the two spheres with reasonably low level of clutter. From this experiment, one can conclude that in heavy-clutter environment, the use of ACF technique is an effective tool of achieving a higher degree of clutter suppression compared with the conventional technique, resulting in a higher target-to-clutter ratio. 4.6 Summary o f target imaging using correlation technique In this chapter, a novel approach for 3-D imaging in heavy-clutter environment at RF frequencies is described. In essence, this approach involves the use of circular SAR. As a slight modification on flight-path geometry of the conventional linear SAR, the circular SAR has the advantages of offering a full-view (360° image and higher spatial resolution. In addition to these advantages, it is illustrated, both analytically and experimentally, that circular SAR is also capable of performing decent 3-D imaging. Experimental studies are conducted for imaging of (1) layered structure, (2) single sphere and (3) toy helicopter, showing promising results. On the issue of clutter suppression, on the other hand, due attention is paid to the investigation into relative performance among three SAR processing algorithms which are (1) conventional SAR, (2) frequency-correlation SAR and (3) angular-correlation SAR. Algorithmic formulations are given to each of these SAR processing schemes and ex perimental results are included to examine the relative merits o f these schemes. It is found that in low-clutter imaging environment all three types of processing methods es- R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 96 Conventional SAR x-range inm eters Figure 4.28: Experiment B: conventional SAR processing fails to display the correct image of spheres in heavy-clutter environment Sphere size = 25 mm, mean gravel particle size « 30 mm, bandwidth = 7-13 GHz. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 97 Frequency-correlation SAR x-range inmeters Figure 4.29: Experiment B: frequency-correlation SAR processing results in an image strikingly similar to that produced by conventional SAR processing. Again, frequency-correlation SAR processing fails to display the correct image of spheres in heavy-clutter environment. Sphere size = 25 mm, mean gravel particle size ~ 30 mm, bandwidth = 7-13 GHz. This image demonstrates that in heavy-clutter environment, frequency-correlation SAR processing may not be an effective means for clutter suppression. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 98 Angular-correlation SAR -0.1 0 0.1 x-range in meters Figure 4.30: Experiment B: angular-correlation SAR processing results in an image that correctly accounts for the presence of the spheres. In fact, it is the only means among other SAR processing schemes examined in this investigation that brings clutter level down to a reasonably low level, leading to clear visibility of spheres in the presence of strong clutter. Sphere size = 25 mm, mean gravel particle size ~ 30 mm, bandwidth = 7-13 GHz. This images demonstrates that in the presence of strong clutter, angular correlation SAR processing is an effective tool of achieving a higher degree of clutter suppression compared with the conventional SAR technique, resulting in a higher target-to-clutter ratio. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 99 sentially converge at the same image quality, whereas in heavy-clutter imaging environ ment, angular-correlation SAR processing greatly outperforms both conventional SAR and frequency-correlation SAR, resulting in a higher degree of clutter suppression and thus an enhanced target-to-clutter ratio. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. Chapter 5 CONCLUSION 5.1 Summary In this dissertation, experimental studies on radar detection and imaging of targets em bedded in clutter environment using correlation techniques are presented. First, a brief analytical treatment of angular memory effect is given in Chapter 2, where it is emphasized that the effect becomes observable when the scattering mechanism is random in nature. One of the implications of this sole dependence on random scattering is that the effect, together with its applications, is observable over a wide range of circumstances in natural remote-sensing problems. In simple terms, angular memory effect states that a non-zero correlation exists among scattered waves observed in different directions as a result of a change in the direction of incident waves. Included in the chapter is an analytical in troduction on the concept of ACF and its properties. It is shown that angular memory effect exhibits little dependence on observation orientation and manifests itself in 9 - or ©-scattering planes, or both. Angular memory effect is thus a rather universal scattering phenomenon. In fact, it is this apparent “universality” (lack of dependence on scattering media and observation orientations) that makes angular memory effect applicable in a wide variety of detection and imaging issues to be examined in this research. In Chapter 3, applications of angular memory effect (observed in the ^-scattering plane) in target detection are considered. Specifically, wideband radar experiments on tar get detection in natural geophysical clutter environment are considered at millimeter-wave (75-110 GHz) and X-band frequencies (7-13 GHz). The purposes of these controlled experiments are twofold. First, they illustrate the existence of angular memory effect due R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 101 to the combined scattering (surface and volume) o f natural random scattering media (such as fine sand, rough sand, gravel, rock and garden soil). Second, they serve as realis tic studies for obtaining higher target-to-clutter ratio using practical ACF measurement in practice. To compare the relative performance between ACF technique and traditional RCS technique in real-life, strong-clutter environment, metallic objects of appropriate size are embedded in various natural “noisy” geophysical media and tested with both ACF and RCS detection schemes. With reference to the results detailed in Chapter 3, it is found that ACF technique generally works better than traditional RCS technique, resulting in higher target visibility in strong-clutter environment. In ACF technique, clutter suppres sion is achieved by means of correlation between two apparently independent random variables. In the RCS approach, on the other hand, clutter suppression is achieved by means of ensemble averaging over many scalar intensity measurement samples. Although this ensemble average operation helps smooth out the fluctuation of clutter, it does not reduce the “dc le v e r of clutter as effectively as ACF technique does. From previous discussion, application of this unique correlation phenomenon in practi cal detection problems rests on an understanding of a simple observation: field correlation due to scattering by an incoherent mechanism is very much different from scattering by a coherent mechanism. While low-level correlation appears in the case of incoherent scattering, high-level correlation appears in the case of coherent scattering. It is this high-to-low correlation ratio that provides the high target-to-clutter ratio achieved using ACF technique. From a wave scattering point of view, it is important to realize that this clutter-suppression property is an inherent property of wave correlation implicit in ACF measurement. The corresponding improvement in target visibility does not come at the cost of sophisticated signal-processing algorithms or expensive hardware component addi tions. In view of practical implementability, ACF technique, therefore, should fit without too much modification into existing detection radar systems. In target imaging applications, angular memory effect in the o-plane is considered. In particular, considerable attention is paid to 3-D imaging using a novel SAR configuration R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission . 102 known as circular S AR. It is illustrated, both analytically and experimentally, in Chapter 4 that such SAR configuration, apart from providing down-range and cross-range resolutions in horizontal directions, is capable of resolving altitude information in a vertical direction. Furthermore, the unique circular geometry of circular SAR’s permits a finer theoretical resolution than that achievable by traditional SA R ’s. These two features, namely, 3-D imaging ability and improved imaging resolution, should make circular SAR a suitable candidate for localized 3-D imaging purposes. The 3-D imaging capability is rigorously pursued in Section 4.3, in which a general expression for the generalized ambiguity function is derived. W hile the general expression is given in Eq. (4.19), the expression for chirp input signal, as a special case of Eq. (4.19), is given in Eq. (4.24). The axial resolution x{z) as given in Eq. (4.33) and Eq. (4.34) shows that it depends primarily on the bandwidth of the system. On the other hand, the transverse resolutions (x{x) and x(y)) as given by Eq. (4.38) show that they depend primarily on the wavelength. Numerical calculations and microwave experiments are presented in Section 4.3.2 and Section 4.3.3, respectively, to verify the theoretical predictions. It should be noted, however, that detailed as the mathematical formulation appears, it is only a simplified theoretical model. Further studies are needed to include the polarization characteristics of targets. It is also noted that the volume reflectivity in Eq. (4.8) is applicable for single scattering or Bom approximations, and therefore it requires further study to include diffraction and multiple scattering effects. On the issue of clutter suppression discussed at the end of Chapter 4, on the other hand, due attention is paid to the investigation into relative performance among three SAR processing algorithms. They are, namely, (1) conventional SAR, (2) frequency correlation SAR and (3) angular correlation SAR. Algorithmic formulations are given for each of these SAR processing schemes, and experimental results are presented to examine the relative merits of these image-processing schemes. It is found that in a weak-clutter imaging environment all three types of these processing methods essentially converge at the same image quality, whereas in a strong-clutter imaging environment, angular correlation SAR R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 103 processing greatly outperforms both convention SAR and frequency correlational SAR processing methods, resulting in a higher degree of clutter suppression and hence target visibility. 5.2 Further studies Although this dissertation has provided an adequate glimpse of how the concept of field correlation can be applied in practical detection and imaging applications, there is little doubt that many technical areas in this research effort still remain underexplored and unexplored. In view of Section 2.5, for instance, there is much room for further research on other forms of correlation techniques that make use of polarization or time measurement. Although a “universal” correlation tool for detection and imaging, is unlikely to work well in all practical circumstances, a systematic study in the future on a proper combination of these correlation concepts would definitely be a great aid to researchers. In a practical remote-sensing environment, scattering loss (due to scattering by, for instance, raindrops, snow particles, turbulence, etc.) alone can not adequately account for the signal attenuation mechanism. To obtain a picture that is closer to reality, one must consider the dissipative effect (due to absorption by vegetation, moist soil, etc.) of the media. Although this important aspect is largely ignored in this research for simplicity reasons, a careful relational study on wave scattering and moisture content should enhance current understanding on the range of validity for the correlation techniques examined in this dissertation. On the issue of 3-D image reconstruction, further studies are required to fully char acterize the imaging capability of circular SAR. To proceed in this direction, one could start with imaging of 3-D dielectric targets of arbitrary shape, rather than exclusively conducting bodies as examined in this dissertation. As a result of microwave energy penetration in the same manner as light passing through translucent materials, imaging of these dielectric targets at microwave frequencies should serve as a useful benchmark to R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 104 evaluate the sectioning characteristic of circular SAR. To extend the usefulness of correlation technique in clutter-suppressed imaging men tioned in Section 4.5, additional refinement on the partitioning scheme in angular correla tion SAR processing is desired. Although it is found that the inclusion of both small and large decorrelation angles A (p’s is necessary to determine weak target from strong clutter response (see Section 4.5.3), it remains unresolved at this point what precise steps lead to a workable selection of different A 0 ’s for a particular imaging problem. An adaptive approach seems to be a viable avenue to proceed in this regard. Seldom can a study be considered as “final”. This short but truthful statement also applies to the work outlined in this dissertation. It is the author’s honest hope that this work will serve as a useful reference to those who pursue this exciting research topic at a greater depth in the future and stretch the range of applications of correlation techniques in related scientific disciplines to its farthest extent. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. BIBLIOGRAPHY [1] Frequency and angular correlations o f waves scattered by rough surface, Jul 1994. paper presented at the Progress in Electromagnetics Research Symposium (PIERS), Noordwijk, the Netherlands. [2] L. J. Battan. Radar Observation o f the Atmosphere. University of Chicago Press, 1973. [3] W. G. Carrara, R. S. Goodman, and R. M. Majewski. Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Artech House, 1995. [4] T. K. Chan, Y. Kuga, and A. Ishimaru. Angular memory effect of millimeter-wave scattering from two-dimensional conducting random rough surfaces. Radio Science, 31(5): 1067-1076, 1996. [5] C. Elachi. Introduction to the Physics and Techniques o f Remote Sensing. John Wiley & Sons, Inc., 1987. [6] R. L. Fante. Turbulence-induced distortion o f synthetic aperture radar images. IEEE Trans, on Geoscience and Remote Sensing, 32(4):958-961, Jul 1994. [7] S. Feng, C. Kane, P. Lee, and A. D. Stone. Correlations and fluctuations of coherent wave transmission through disordered media. Phys. Rev. Lett., 61 (7):834—837, 1988. [8] I. Freund and M. Rosenbluh. Memory effects in propagation of optical waves through disordered media. Phys. Rev. Lett., 61(20):2328-2331, 1988. [9] G. Gonzalez. Microwave Transistor Amplifiers: Analysis and Design. 2nd edition. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. 106 [10] L. C. Graham. Synthetic interferometric radar for topographic mapping. Proc. IEEE, 62:763-768, 1974. [11] S. A. Hovanessian. Introduction to Synthetic Array and Imaging Radars. Artech House, 1980. [12] A. Ishimaru. Wave Propagation and Scattering in Random Media. Academic Press, 1978. [13] A. Ishimaru. Electromagnetic Wave Propagation, Radiation, and Scattering. Prentice Hall, 1991. [14] L. Jackson. Signals, Systems, and Transforms. Addison-Wesley, 1990. [15] J. A. Kong. Electromagnetic Wave Theory. Wiley-Interscience, 1985. [16] C. Le, Y. Kuga, and A. Ishimaru. Angular correlation function based on the secondorder kirchhoff approximation and comparison with experiments. J. Opt. Soc. Am., 13(5): 1057-1067, 1996. [17] J. W. Lichtman. Confocal microscopy. Scientific American, pages 40—45, Aug 1994. [18] D. L. Mensa. High Resolution Radar Imaging. Artech House, 1981. [19] T. R. Michel and K. A. O ’Donnell. Angular correlation functions of amplitudes scattered from a one-dimensionally, perfectly conducting rough surface. J. Opt. Soc. Am., 9(8): 1374-1384, 1992. [20] M. Minsky. Memoir on inventing the confocal scanning microscope. Scanning, 10(4): 128-138, Jul/Aug 1998. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 107 [21] College of Engineering. Engineering summer conferences: Radar scattering and image interpretation. Technical report, University of Michigan, 1988. [22] L. Jr. Peters, J. J. Daniels, and J. D. Young. Ground penetrating radar as a subsurface environmental sensing tool. Proc. IEEE, 82(12): 1802-1822, Dec 1994. [23] P. Phu, A. Ishimaru, and Y. Kuga. Controlled millimeter wave experiments and numerical simulations on the enhanced backscattering from one-dimensional very rough surfaces. Radio Science, 28:533-548, 1993. [24] P. Phu, A. Ishimaru, and Y. Kuga. Co-polarized and cross-polarized enhanced backscattering from two-dimensional very rough surfaces at millimeter wave fre quencies. Radio Science, 29:1275-1291, 1994. [25] M. Skolnik. Radar Handbook. McGraw-Hill Publishing Company, 2nd edition, 1990. [26] M. Soumekh. Reconnaissance with slant plane circular sar imaging. IEEE Trans, on Image Processing, 5(8): 1252-1265, Aug 1996. [27] B. D. Steinberg and H. Subbaram. Microwave Imaging Techniques. John Wiley & Sons, 1991. [28] L. Tsang, J. A. Kong, and R. Shin. Theory o f Microwave Remote Sensing. WileyInterscience, 1985. [29] L. Tsang, G. Zhang, and K. Pak. Detection of a buried object under a single random rough surface with angular correlation function in em wave scattering. Microwave and Optical Technology Letters, 11(6):300-304, Apr 1996. [30] E T. Ulaby and C. Elachi. Radar Polarimetry fo r Geoscience Applications. Artech House, 1990. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 108 [31] F. T. Ulaby, R. K. Moore, and A. K. Fung. Microwave Remote Sensing: Active and Passive. Addison-Wesley Publishing Company, 1982. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Appendix A SYSTEM CALIBRATION As in any measurement process of S parameters [9], the measuring system must first be calibrated using some known transmission/reflection standards. In this study, the millimeter-wave system was calibrated using the reflection response of a large flat conducting plate. The observed specularly reflected signal was then used to establish the correct reference plane position and frequency response of the system accordingly. To ensure the working condition of the system, the ACF of the plate was measured along the specular memory line defined by &\ —0* = d's —0 3 on the sin 0^-sin d's plane for 0 L = 20° and 9S — —40°. As apparent from the corresponding ACF response shown in Fig. A. 1, the measured correlation attains a level close to unity along the entire memory line. Because of the finite physical size of the conducting plate, however, the measurement also shows a slightly stronger correlation when both the transmitter and receiver arms are perpendicular to the plate, as manifest in the small peak at 0\ = 30°. It is important to realize that in the actual measurement process, it is S parameters that were being measured. Therefore the process of retrieving measurements of scattering am plitudes fij, and hence ACF, from S parameter measurements deserves detailed treatment and is considered below. On the basis of the image method, the following radar equation can be established for the conducting plate calibration process mentioned above: n _ p A2 G°lGo2 ° ‘ (4tt)2 ( r „ |+ r„2)* (A' ° where Pa is the received power due to the flat plate, Pt is the transmitted power, and (rol, r o2) and (G0i, G 02 ) represent the distances of the transmitter and receiver, respectively, R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 110 ACF signature due to a large flat plate tilted at 30° 2 1.6 1.4 ,12 CD o) 1 co 1 E li es * ' 0.8 0.6 0.4 02 0 0 10 20 30 angle of incidence 9. 40 50 60 Figure A. 1: ACF signature measurement o f a large tilted metal flat plate. The way the antennas are moved describes an angular memory line for ( 9 i , 9 s ) = ( 3 0 ° ,- 3 0 ° ) on the s in 9l -sinOs plane. As expected, the correlation level approaches to 1 over a wide range o f variable incident angles 9i R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . Ill from the plate and their boresight gains. With r ol = r o2 = r Q, Eq. A.l reduces to P =Pt G olG °2 ° £ (4 tr)2 4r2 (A 2) (A ’2) Since P 0 oc |V^|2 and Pt oc |Ut |2, it follows from Eq. A.2 that w = |Vil I < A J) In phasor notation, VQ can be expressed as Vo = IK .I e ~ i+ (A.4) where o — 2 k 0 r 0 represents the phase introduced by wave propagating in free space over a distance of r Q. Substituting |K>| in Eq. A.3 into Eq. A.4, v; = ^ s \ / ^ (A -5) In parallel with the derivation developed above, the radar equation for extended targets assumes the following form: Pr = Pt l(4F tt) la J[a r;r; (A-6) where Pr and Pt are the received and transmitted power, respectively, a is the bistatic cross section to be measured, and (rr , r t) and (G'r , G t) represent the distances of the transmitter and receiver, respectively, from the target and their gains. Making use of the arguments in transition from Eq. A.2 to Eq. A.5 and noticing that with r r = r t — r and a = 4 7 t|/|2, where / represents the scattering amplitude, one can write v' =W*;L\l-7r-e~m’rfds Using Eq. A.5 and Eq. A.7, it follows that R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. ( A ' 7 ) 112 4r 02 _,2. r„ r ej2fcar° J a Vr V V0 J G a\Go2 lG rGt _ - Z p - e - j2k°rf d S (A.8 ) The ensemble-averaged correlation of voltages is therefore < > 4 r° GoiG0o GrG t < f j o > dS r4 Il A, Va V* Vri Ko _ _ (A.9) 4 r 02 / ^ dS (A.10) Since the half-power beamwidth of the receiver is smaller than that o f the transmitter and is fairly narrow, r remains nearly constant over the illuminated area A , and therefore the integral in Eq. A. 10 can be approximated as [24] GrGt — .-i rj ~ d S /, ~ G rG t JO ^ — 4 dS « I>A, r4 1 Go\G0o Zi r‘ , G 01G 02 * r lA 0 r 2 ----- 7----- z------- 57r 4 4 co s0 s (A -n ) (A. 12) where A 0 r is the half-power beamwidth of the receiver and is roughly equal to 6° over 95-100 GHz for the experimental setup in this study and 9's refers to the scattering angle at which the receiver is looking. With Eq. A. 12, Eq. A. 10 can be simplified as = N < h i;- > R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . (AI4) 113 where N is the normalization factor which relates measurements of S parameters, which are the quantities actually measured by the system, to scattering amplitude measurements. Therefore, by performing angular correlation on measured data and multiplying the result with the inverse of N , absolute measurement of angular correlation between scattering amplitudes can be obtained. As a result of the asymmetry between the sizes of the spots projected by the antennas on the surfaces, however, N in fact depends on the amount of overlapped footprints of the two antennas. This amount of overlapped area is in turn a function of antenna positions (Q\, d's). A simplified treatment from projection geometry was included in N in Eq. A. 14 to incorporate its dependence on antenna positions for final presentation of experimental data in this experimental work [16]. R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . Appendix B CHIRP RADAR Chirp radars are used when the length of the time-domain pulse required for a pulse radar is so short that the pulse must have a very high peak power. From a hardware, implementation point of view, it is difficult to generate a high peak-power pulse within very short duration. Therefore, a method has been devised to address this difficulty. Basically, this method involves the use of some kind of longer pulse with a modulation interior to the pulse, thus allowing fine resolution associated with the wider bandwidths of the modulation. Although the resulting modulated pulse will possess the same amount of power as the unmodulated one does, the power is spread in time (and hence space) with the peak power level being reduced. In this appendix, only FM-modulated pulse will be considered since it is the modulation type employed by the Hewlett-Packard’s network analyzer (HP8720) used in this radar imaging study. The operation of a FM chirp radar can be understood from the spectrogram shown in Fig. B .l. The figure shows the instantaneous frequency of the transmitted pulse (linear upward sweep of frequency as a function of time), the instantaneous frequency of the received pulse ( ideally from a point target) and the effect of “de-chirping” such a pulse by passing it through a filter whose time delay is a function of frequency. As shown in the figure, the pulse duration is denoted by r and the modulation bandwidth by B. Intuitively, the filter should have a time delay characteristic such that the frequency transmitted first (the low end of B) is delayed long enough so that it arrives at the filter output at the same time as the frequency transmitted last (the high end of B), as in Fig. B.2. For ideal de-chirping, all the frequencies in-between should also arrive at this time, so they are superimposed at a single time instant at the filter output. Ideally, this results in a R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 115 d'-function de-chirped pulse, which is not possible with the finite bandwidth in practical frequency-sweeping radar systems. Instead of being a vertical straight line shown in the rightmost part o f the figure, the received signal will smear into a finite-duration pulse. With a bandwidth B the approximate pulse width at the filter output is 1 /B , and if the transmitted amplitude is kept constant during the pulse, the resulting pulse takes the shape of sin(:r) / x dependence. The net effect of this chirping/de-chirping process is to compression of a r-long pulse into a 1/ZMong pulse, allowing fine spatial resolution without injection of excessive power into a short 1 /B -lo n g pulse before modulation. A brief analysis is presented below for two cases. Case A assumes infinite pulse duration whereas case B assumes finite pulse duration. The former aims at projecting physical insights from idealized settings whereas the latter deals with practical consider ations encounter in real-life chirp radars. B .l C a s e A : I n fin ite p u ls e d u r a tio n If the pulse were allowed to have infinite duration, the subsequent analysis for the de chirped pulse would be easy. As mentioned before, the resulting waveform at the filter output will have a J-function shape. Assume the following waveform for the transmitted pulse vr {t) = eJ'(tt,ot+*ata) (B .l) where a is the “chirp rate” cbj/dt. Its Fourier spectrum will be Vr{ u ) = [ +°° eiluot+?at2 - ut)dt. J — CO (B.2) By completing the square in the exponent, the above equation reduces to V rH = )2/ 2a_ (B J) V Ja From matched-filter theory [14], the response F{u>) o f a filter that matches this transmitted pulse with maximum signal-to-noise (SNR) ratio should be the complex conjugate of the R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 116 freq u en cy il transmitted pulse received pulse T I de-chirped pulse 1 B T time Figure B.L: Frequency-time plot o f transmitted pulse, received pulse, and the de-chirped pulse. The net effect o f this chirping/de-chirping process is to com pression o f a T-Iong pulse into a 1 /B -lon g pulse, allow ing fine spatial resolution. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 117 delay time f, f2 freq uency Figure B.2: Delay-time characteristic o f a de-chirping filter matched to the transmitted chirp pulse, assuming linear FM modulation. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 118 above spectrum with its amplitude inversed: (B.4) Therefore, the spectrum of the filter output will be the product of Vr {uj) and F { uj), which is I/crut{u !) — 1- (B.5) The inverse Fourier transform of V0 ut{uj), which is equal to the time-domain variation of the filter output, is Vout(t) = S {t). (B.6 ) Note that the an infinite-duration sweep implies an infinite bandwidth, so that the infinite time resolution (and hence spatial resolution) offered by the 5-function filter output cannot be obtained in practice. B.2 Case B: Finite pulse duration In practice, the transmitted pulse must have finite duration and bandwidth, so the above simple analysis does not quite apply. Real waveforms rather than complex waveforms will be used in the following analysis to demonstrate the effect of a finite-duration-finitebandwidth on pulse broadening at the filter output. It is assumed that the received pulse comes from a point target and has the same waveform as the transmitted pulse. Note that in the following analysis the time axis is backward-shifted by r / 2 to achieve symmetric properties of Fourier transforms for simpler mathematics. Define the following window function n T/2: (B.7) 0 otherwise Assume the following waveform for the received pulse v r (t): vr(t) = n 7 / 2(<) cos(u;0t + ^ a t2). 6 R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. (B.8 ) 119 Note that the phase 4> of v r{t) is given by 1 9 (f) — uj0t + —at , (B.9) so that the instantaneous angular frequency v is dcj) u} = — = uj0 + at. at (B.10) In order to cancel the quadrature term introduced in FM modulation on the transmitted pulse (and hence the received pulse vr(t)), the de-chirping matched filter should have an impulse response f ( t ) given by f ( t ) = q n T / 2 (t)c o s (u 0t - ^ 2), (B.l 1) where q is so selected so that the filter produces unity gain at its center frequency. The time delay td of thisfilter response is given by the derivative of the filter phase response tp with respect to angular frequency v dib d . 1 td = — = — [uiQt - -a t-] . cLj dui 2 (B .l2) From Eq. B.10, t can be obtained as t = ~— — . a (B.13) Substitute this t into Eq. B.12, td can be expressed as td — d fid0(aJ — JJa) (id — ^o)", ------------------------------= dui a 2a — 2 iU0 — UJ . a (D.14) Note that td is a decreasing function of uj. This means that longer time delay is associated with the higher end of B and shorter time is associated with the lowerend of B, as expected from previous discussion. The output of the filter is given by the tme-convolution of the received signal with the filter response: / +0O Vr( t ) f ( t - x )d x (B.15) -O O / +oo n r / 2 ( 2 ) n r /2 (I ~ x) cos ( l j -O O 0 x + - a x 2) 2 x cos[u0(t — x) — ^ a ( t — x ) 2 ]dx. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (B.16) 120 Make use of cos A cos B = ^[cos(A 4- B ) + cos(A. — 5 )], (B. 17) the cosine product in the integrand in Eq. B.16 can be expressed as ^ cos[u;0x 4- ^arr2 4- uja(t —x) — ^a(£ - a:)2] 4- ^ cos[u;0:r 4- ^ ax2 —uja(t — x) + ^ a (t — = cos[aa0f —- a t 2 + atx\ 4- cos[2a;0a; 4- a x 2 — ujat — a tx 4- ^ a t2]. x )2] (B .l8) The second term will disappear after filtering, leaving Eq. B.16 as ' ^cmi( 0 — I t _ rt+ 772 1 .2 o I - t / 2 ~ 9 c° s [ua0£ — ^a t 4- a tx \d x for —T < t < 0 k ft'-T /2 <lC0S[uot — \ a t 2 4- atx]dx for 0 < t < T (B.19) Make use of the following identity sin A — sin B = 2 sin ^(4 . - B) cos ^(.4 4- B ). (B.20) in Eq. B.19, the filter output can be written as = ^ s in [ ^ ( T ’ 4- t)\cosu>0t for —T < t < 0 ^ s in [ 7r(T — i)] cosujat for 0 < t < T i si n [ f ( r - | f | ) ] for —T < t < T . After EFfiltering, the cosine term in Eq. B.21 disappears. Therefore, (B.21) the filter output Vout(t) becomes Vaat{t) = for - T < t < T . Note that a = 2-k B / T (from Eq. B.10). The terms of the sine argument inEq. B.22 become aTt — (B.22) = at2 2T = *Bl at t t ~2 T = W t T R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 121 For large values of B T , which is often the case for practical wideband chirp radars, the quadratic term is negligible compared with the linear term near the origin. Thus, the location of the first null is roughly the same as it would be in the absence of the quadratic term. Hence, JfB t-u rid ih — (■width = 7T 1IB , (B.23) so that the null-to-null time width of the filter output is 2/ B , which also defines the finest spatial resolution achievable by this chirping/ de-chirping scheme. To summarize, the effect of applying FM chirp and compression filter is to take a long pulse of duration T and convert it at the filter output to a short pulse having null-to-null width 2/ B and approximate effective width l / B . A plot o f Eq. B.22 is shown in Fig. B.3 with T = 4 s and B — 6 GHz. The 3dB width of the de-chirped pulse is shown to be 1.057/5. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 122 De-chirped signal at compression filter output with T = 4s and B = 6 GHz. = 02 -02 •0.4 - 0.8 0.6 • -0.4 -02 0 02 0.4 0.6 0.8 time in ns Figure B.3: Plot o f Eq. B.22 with sweeping time T = 4 s and chirp bandwidth B = 6 G H z. The 3dB width o f the de-chirped signal is about 1.057/B . R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Appendix C DETERMINATION OF REFERENCE SLANT RANGE As noted earlier in Section 4.2, the quality of focusing depends critically on the accuracy in the determination of the reference slant range shown in Fig. C .l. Ideally, this reference slant range (represented by the dotted line in the figure) should intersect the base of circular SAR system at a point cv = ce (ignoring the altitude difference), where Zv and q refer to the center of rotation and the center of illumination, respectively. In practice, however, it is difficult to construct a circular SAR system with the con dition c,. = ce satisfied. In order to study the spatial discrepancy between the two centers (and hence evaluating the quality of focusing capability of the system), a controlled exper iment is derived to measure their relative locations indirectly. Specifically, the experiment involves placing a conducting sphere (63 mm in diameter) on top of a thick absorber sheet. The level of the absorber sheet is maintained at the same altitude of the base of the SAR system. The location of the sphere relative to the center of rotation is precisely noted. The top view of this experiment is shown in Fig. C.2. Note that in the figure the location of the sphere has been exaggeratedly misplaced so as to illustrate the variables-to-be-solved like p and 0. Also, it is understood that the 2-D plane shown in the figure is at an altitude of h below the SAR flight track. Consequently, the variable h is suppressed in the figure. C .l Analytic formulation With reference to Fig. C.2 and making use of the cosine rule, the following independent equations can be developed: r\ = a 2 + p 2 + hr + 2ap cos 0 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. (C .l) 124 r2 = dr + p 2 + dr + la p sin 0 (C.2) rf a 2 + p 2 + hr —2 a p co s0 (C.3) 1 (r r 2t +, r 2\ p 2 +, /il2 = — 3) - a 2 = k 2. (C.4) = (Eq. C. 1 + Eq. C.3) gives rise to Making use of the notation in Eq. C.4 and the identity cos2 0 + sin2 0 = 1 in Eq. C. 1 and Eq. C.2, I have cos 9 / 9 9 9\ 9 (rr — a“ — « r r . 9 + sin 0 = —■■— — Aal pr 0 / 9 (r^ — >- + v 2 9 9\ 9 — k t r -----,---- ,- = l. Aazp2 _ (C.5) Solving Eq. C.5, Eq. C. 1 and Eq. C.4 in sequential order, I have With p, 0 ^ r *7 p = 0 = sin- l C 2 h = O 9 \9 a~ la p K~) \ O / To O\ ^ V (rr - a- - « -)- 4- (r-5 - a- - /c-)- ^ k 2 - p2. and /i, the reference slant range /?Q and the depression angle (C.6) (C.7) (C.8) can be expressed as R 0 = %/a2 + /i2 0<Wi = ta n _1( - ) a C.2 (C.9) (C.10) Experimental results From the analytic development in previous section, it is clear that in order to measure the reference slant range R Q, it suffices to obtain the triplet { rl7r 2. r 3} and radius a of the circular SAR flight track (a = 0.7 m from direct measurement). Note that the value of triplet depends only on the SAR geometry and has nothing to do with the scene to be im aged. Therefore, in designing experiments for measuring { r i ,r 2, r 3} one is free to choose R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 125 appropriate scenes for convenience. In this regard, I carried out two independent “sphereon-axis” experiments and selected measurement points to be located on the quadrant edges shown in Fig. C.2, leading to the simple relationships expressed by Eq. C. 1-C.3. In prin ciple, these two experiments would yield the same result if the measurement system were to have infinite bandwidth. Experiment A: Single sphere along x-axis C.2.1 As the first attempt to obtain { r i .r 2, r 3}, a 63 mm conducting sphere was placed on top of a thick absorber sheet at a distance of 15 cm from the center of rotation cr along the x-axis. The level of the absorber sheet was maintained at the same altitude h of the base of the SAR system. Reflection measurements were performed at locations shown in Fig. C.2. By going through the analytical derivation developed early in this Appendix, I have • reference slant range R 0 = 0.94372 m, • depression angle 9l{own = 42.1158° below the horizon, • p = 0.1493 m, • 0 = —3.1798°, and • h = 0.63291 m below the circular SAR flight track. The center of illumination q is thus off from the center of rotation cv by 0.1539 m 0.1493 m, or 0.7 mm. at an angle of 180° —3.1798°, or 176.8202° from the x-axis. C.2.2 Experiment B: Single sphere along y-axis As the second attempt to obtain { r i , r 2 . r 3}, a 63 mm conducting sphere was placed on top of a thick absorber sheet at a distance of 15 cm from the center of rotation £v along R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 126 the y-axis. The level of the absorber sheet was maintained at the same altitude h of the base of the SAR system. Reflection measurements were performed at locations shown in Fig. C.2. By going through the analytical derivation developed early in this Appendix, I have • reference slant range R a = 0.93989 m, • depression angle Odoum = 41.8576° below the horizon, • p = 0.15391 m, 9 0 = 84.0305°, and • h = 0.62718 m below the circular SAR flight track. The center of illumination q is thus off from the center of rotation ev by 0.1539 m 0.1500 m, or 3.9 mm. at an angle o f 84.0305° from the x-axis. Based on the results from these experiments, the average spatial discrepancy between eg a n d c r is therefore ^(0.7/176.8202°+ 3.9/84.0305°) = 1.9643/94.2819° mm, which is negligible (equivalent to about j~X at a center frequency of 10 GHz) at X-band frequencies. The calculated center of illumination ce and the ideal center of illumination eg (= cT, the center of rotation) are shown in Fig. C.3. These experiment demonstrate that the circular SAR system used in this experimental study possesses superb construction accuracy. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 127 SAR platform center of rotation center of illumination illumination footprint Figure C .I: Experimental determination o f reference slant range. Ideally, the center o f rotation should be the sam e as the center o f illumination (except for the obvious altitude difference). R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 128 metal sphere radius = a center of rotation Figure C.2: Experimental setup for determination o f reference slant range in which a 63 mm conducting sphere, located at an altitude o f h below the circular SAR flight track, was placed at a distance o f 15 cm along the x -a x is relative to the center o f rotation. Three independent reflection measurements were made to solve for variables p , <b and h. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 129 ideal cen ter of illumination = center of rotation center of illumination (calculated) Figure C.3: The relative locations o f the calculated center o f illumination and the ideal center o f illumination. The negligible spatial discrepancy verifies the superb construction accuracy o f the circular SAR system used in this experimental research. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. Appendix D MATLAB CODES FOR CIRCULAR SAR PROCESSING With the advent of highly efficient computation packages like MATLAB for matrix manipulations, coding for SAR processing, which inherently takes advantage o f using matrices as the primary data structure, can be very simple. Although in general MATLAB codes are not as optimized as other contemporary scientific programming languages such as FORTRAN or C/C++ in terms of run-time speed, its easy o f use and high productivity (due to the availability of a large built-in collection o f efficient algorithms and graphics routines) are unparalleled compared with its rivals. Furthermore, MATLAB’s high degree of programming flexibility and interactive computation workspace introduce significant shortcut to users whose primary concern is shorter code-development cycle in a limited time frame. As a result of the considerations presented above, MATLAB was chosen to be the primary processing language for this research. In this Appendix, I will outline briefly the structure of the main computation codes collectively grouped in the program CORRSAR.M. Then, I will append the MATLAB source codes for it and all other relevant subroutines. D .l Main program The structure of CORRS AR.M is shown in Fig. D. 1. The source codes of CORRS AR.M and its subroutines are included are appended in Fig. D .2-Fig. D .l7 D.2 Other subroutines R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 131 C O RRSAR G E T D A T A retrieve raw data, put it in freqsp a ce matrix representation 1 V O LSIZE FO CUSG RID compute dimension of the HPBW volume generate grid points on a focal plane 1 LEN SG R ID generate grid points along the circular SAR flight track I R A D IX up-sample raw data over frequency 1 SCREENINFO display useful processing parameters on screen 1 G A T IN G construct gating matrix with respect to a focal point V C H O PBA N D perform freq correlation SAR by bandwidth partition T IM E _A C F perform angular correlation SAR by spatial partition N O R M A L normalize p ro cessed images, make them have magnitude = 1 Figure D .l: The structural com ponents o f CORRS AR.M. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 132 36C O R R SA Rperforms spotlight-mode SAR-processing for circular SA Rsystem 36using 1.) C O R R E L A T IO N(new) technique and 2.) C O N V E N T IO N A L(old) technique. 36 36C O R R SA Rrequires the following m-files: 36 35 36C H O PB A N D : Perform freq-SARimage processing. 36FO C U SG R ID : Construct in spatial domain the grid points for the focus (object) plane. 36freq_A C F: Perform FR EQ -A C Fimage processing. 36G A TIN G : construct in time domain the gating matrix for agivenfocusplane. 36getdata: Load radar data and measurement parameters fromthe input datafile. 36K A ISER : Construct Kaiser windowused by G A TIN G . FromM A T L A B toolbox. 36lensgrid: construct in spatial domain the grid points for the lens (source) plane. 36normal: Normalize processed images to have magnitude of 1. 36R A D IX : Adjust the num ber of rowof the original rawFDdata for faster fft. 36SCREENINFO:Display useful processing parameters on the screen. 36TIM E_A C F: Perform time-aC Fimage processing. 36VO LSIZE: Com pute volume dimension fromparameters notincluded in input .INF file. 36 36C O R R SA Ris optimized for M A T L A B5‘s newfeatures. It requires slight modifications 36for it to run under matlab 4. 36 36M odify the value of M A X _C U B E _H E IG H Tto accommodate for 3-D imaging. Avalue of 36m a x _C U BE _H E IG H T= 0 m eans 2-d imaging only. 36 36Last update: 03/30/98 36Declare constants clc; clear; c = 3e8; rad = pi/180; cm ax = 0; tol = 1.0e-3; 0 = 0.15; max_cube_height = 0; xstep = 0.010; ystep = 0.010; zstep = 0.010; 36 speed of light in free space 36 conversion factor fromdegrees to radians 36initial m axim umof colorscale 36 tolerance for user's input 36 aperture size of the antennasinmeters 36height of the illumination cube around zcentroid 36resolution inx- direction in meters 36resolution in y- direction in meters 36resolution in z- direction in meters 36 [getdata] Read raw radar data disp(['Spotlight-mode circular sar data processor']); dispC '); basename = input(['enter the basename (<= 7 characters) of the input .asc *monostatic* data file here: '] , 's'); extension = '.asc'; calibration = 'n'; disp(['Loading radar data...']); [TRUE_FD_raw,startf,stopf,TRUE_npoint,TRUE_npair,TRUE_antang,nsam ple, ref_R,dnangle] = getdata(basename,extension); disp(['Done.']); resultname = basename; 36workspace nam e to be the sam e as filename dnangle = 90 - dnangle; 36original "dnangle" measured fromvertical! B= stopf - startf; 36measurement bandwidth in hz wavelength = c/(mean([startf stopf])); 36wavelength in meters hpbw= wavelength/D; 36half-power beam width in radian deltaT = 1.057/B; 36approximate pulsewidth in seconds [Ulaby v2] refji = ref_R * sin(dnangle *rad); 36altitude of the plane being focused in meters ref_a = sqrt(ref_RA2 - ref_hA 2); 36radius of the circular orbit in meters clear getdata; Figure D.2: MATLAB code o f CORRSAR.M. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission . 133 * [volsize] Com pute the dimension of illuminated volume % xspotlength = 1.50*Dx; yspotlength = 1.50*Dy; zspotlength = 1.50*Dz; [dx,dy,dz,Dx,Dy,Dz] = vol si ze(B, hpbw,ref_R,dnangle); clear volsize; xspotlength = 2.15*Dx; yspotlength = 2.15*Dy; zspotlength = 2.15*dz; % [FO C U SG R ID ] Construct the focal-plane matrix [FO CUS,xgridaxis,ygridaxis,zgridaxis] = focusgrid(ref_R,dnangle,xspotlength,yspotlength,zspotlength,xstep,ystep,zstep); clear fcusgrid; xgridlength = length(xgridaxis); ygridlength = 1ength(ygridaxis); zgridl ength = length(zgridaxis); zcentroid = -ref_R * sin(dnangle * rad); % plane z = 0 coincides with antenna level % [lensgrid] Construct the lens-plane matrix disp([' ’]); wantANG= inputC'Apply angle interpolation [linear method]? [n]: '.'s'); if wantANG= 'y' iNTfactor = inputCEnter the up-sampling factor [2]: '); else INTfactor = 1; end; [lens,txlens,rxlens] = lensgrid(ref_a, TRUE_antang,INTfactor); clear lensgrid T X L EN SR X L E N S; % txlens and rxlens are redundant in monostatic processing % [RADIX2] Perform frequency interpolation for faster FFT disp([' ']); % FFTis most efficient when word length = 2*n (n: integer) wantFFT = inputC'Apply frequency interpolation [linear method] for faster FFT? [y]: V s '); [FD_raw,npoint] = radix(TRUE_FD_raw,TRUE_npoint,wantFFTtlNTfactor); clear radix; % [SCREENINFO] Display the processing parameters for C O R R SA R screeni nfo(ref_R,dnangle,xgridlength,ygridlength,zgridlength,xspotl ength,yspotl ength,zsp otlength,Dx,Dy,Dz,dx,dy,dz,xstep,ystep,zstep); clear screeninfo; % Pre-allocate memory for faster processing pack; npair = INTfactor * TRUE_npair; k = repmat(2*pi/c*linspace(startf,stopf.npoint).', [1 npair]); viewocm= 0.50*100*mean( [ ( max(xgridaxis) - min(xgridaxis) ) ( max(ygridaxis) min(ygridaxis) ) ] ); viewo = viewOcm/100; halfw_index = round(viewD/c/deltaT); filtershape = kaiser(2*halfW_index+l,10); % Initialize all arrays r = zeros(npoint.npair); G A T E M X= zeros(npoint,npair); TD_raw= zeros(npoint,npair); FD_gated_focused = zeros(npoint,npair); TD_gated_focused = zeros(npoint,npair); SA R= zeros(xgridlength,ygridlength); freqSAR = zeros(xgridlength,ygridlength); tim eACF = zeros(xgridlength,ygridlength); freqACF = zeros(xgridlength,ygridlength); Figure D.3: MATLAB code o f CORRS A R .M , continued from Fig. D .2 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 134 % This Xconsiders both +ve z and -ve z I = sort(find(abs(zgridaxis - zcentroid) <= max_cube_height * wavelength)); % This I considers only +ve. SO R Tm akes sure that layer images are calculated in ascending-z sequence % I = sort(find( ( (zgridaxis - zcentroid) <= max_cube_height * wavelength ) & ( (zgridaxis - zcentroid) >= 0 ) ) ); * Correlation SA Rprocessing below totaltime = clock; TD_raw= ifft(FD_raw); for z = min(l):max(l); % layer images arecalculated in bottom-to-top order SARimagez = [resultname 's' num2str(z)]; freqSARimagez = [resultname 'cFs' num2str(z)]; timeACFimagez = [resultname 'cT' num2str(z)]; freqACFimagez = [resultname 'cf' num2str(z)]; planedepth = zgridaxis(z); R O= ref_R; % reference slantrange forfocusing dispC '); disp([’Processing the ' num2str(z-min(l)+l) 'th focal slice out of a total of ' num2str(length(X)) ' slice(s)']); for m= 1:xgri dlength; t_row = clock; m ; for n = l:ygridlength; r = repmat(sqrt(abs(LENS - FOCUS(m,n)).A2 + pianedepthA2),[npoint 1]); % T IM E -D O M A ING A T IN GU SIN G FFTT OR E PL A C E D IR EC TFR E Q U E N C Y -D O M A INC O N V O L U T IO N G A T E M X= gating(r(l,:), r(l,:) ,viewOcm,deltaT,npoint,npair.filtershape); clear gating; % % % % % FR E Q U E N C Y -D O M A INFO C U SIN G FD_gated_focused = (r .a 2) .* exp(2 * i * k .* ( r - ref_R ) ) .* fft(G ATEM X .* TD_raw); TD_gated_focused = i fft(FD_gated_focused); TR A D IT IO N A LSAR's SAR(m .n) = abs( m ax( ifft( sum ( FD_gated_focused.' ) ) ) )A2; freqSAR(m.n) = chopband(FD_gated_focused); C O R R E L A T IO NM E T H O DB A SE DO N A N G U L A R C O R R E L A T IO N FU N C T IO N target_phi =03; npizza4target = 30; cluter_phi =10; npizza4cluter = 0; freqACF(m.n) = freq_acf(FD_gated_focused,target_phi ,cluter_phi, npizza4target,npizza4cluter); timeACF(m.n) = time_acf(TD_gated_focused,target_phi ,cluter_phi, npizza4target,npizza4cluter); timeACF(m,n) = SAR(m ,n) - 2*real( time_acf(TD_gated_focused,target_phi,cluter_phi, npizza4target,npizza4cluter) ) time_acf(TD_gated_focused,0, cl uter_phi , 1,npizza4cluter); freqACF(m.n) = SAR(m ,n) - 2*real( freq_acf(FD_gated_focused,target_phi ,cluter_phi, npizza4target,npizza4cluter) ) freq_acf(FD_gated_focused,0, cl uter_phi , 1,npizza4cluter); clear time_acf freq_acf chopband end; 3S n t_row = etime(clock,t_row); disp([num2str(m) '). This image rowtakes ' num2str(t_row/60) ' minutes.']); end; %m Figure D.4: MATLAB code o f CORRSAR.M , continued from Fig. D.3 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 135 eval([SARimagez ■= SAR;']); eval([freqSARimagez ' = freqSAR;']); eval([timeACFimagez ' = timeACF;']); eval([freqACFimagez ' = freqACF;']); layertime = xgridlength*t_row; disp([’This layer takes ' num2str(layertime/3600) 1 hours.']); end; %z % [normal] Normalize the processed images nSA R= normal(SAR); nfreqSAR = norm al (freqSAR); ntimeACF = norm al (timeACF); nfreqACF = normal(freqACF); disp(' ’); disp(['lmage plot variables are stored in "portable.mat''.']); save portable xgridaxis ygridaxis zgridaxis nSA RnfreqSAR ntim eACF nfreqACF disp(['All workspace variables are stored in ' resultname '.mat']); eval(['save ' resultname]); figure(l); colormap(jet);pcolor(xgridaxis,ygridaxis,abs(nSAR.') ); colorbar('vert');caxis([0 1]);axis('equal');shading interp; titleCConvention SAR'); xlabel('x-range in meters'); ylabel('y-range in meters'); figure(2); colormap(jet) ;pcolor(xgridaxistygridaxis,abs(ntimeACF.')); colorbar('vert');caxis([0 1]);axis('equal');shading interp; title('Angular Correlation SAR'); xlabel('x-range in meters'); ylabel('y-range in meters'); figure(3); col orm ap(jet);pcolor(xgridaxis,ygridaxis,abs(nfreqSAR.') ); colorbar('vert');caxis([0 1]);axis('equal');shading interp; titleC Frequency Correlation SAR'); xlabel('x-range in meters'); ylabel('y-range in meters'); Figure D.5: MATLAB code o f CORRS AR.M , continued from Fig. D.4 R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 136 function — ” [TRUE_FD_raw,startf,stopf,TR U E_npoint,TRUE_npair,TRUE_antang,nsam ple , ref_R, dnangle] = getdata(basename,extension); 1 5G E T D A T Agets radar data and reshape the input column data into > 5a matrix of dimension TRUE_npoint x TRUE_npair x nsample matrix. “ lATfile = [basename 'z.mat']; if exist(MATfile) = 2 eval(['load ' MATfile]); else iNFfile = [basename '.inf']; iNFid = evalC['fopen(’" INFfile frewind(INFid); DUM text = fscanf(INFid,'55s',1); DUM text = fscanf(lNFid,'55s\n',1); DUM text = fscanf(INFid, '55s' ,1); DUM text = fscanf(lNFid,'55s\n',1); DUM text = fscanf(INFid,'55s',1); startf = fscanf(lNFid,'55f\n',l)*le9; DUM text = fscanf(INFid,'55s',1); stopf = fscanf(lNFid, '55f\n' ,l)*le9; DUM text = fscanf(lNFid,'55s',1); TRUE_npoint = fscanf(lNFid, '55f\n' ,1); DUM text = fscanf(INFid,'55s',1); dumnyTX_startang = fscanf(iNFid, '55f\n' ,1); DUM text = fscanf(INFid, '55s' ,1); dum nyTX_stopang = fscanf(INFid, '55f\n' ,1); DUM text = fscanf(lNFid,'55s',1); dum nyTX_incang = fscanf(lNFid,'55f\n',1); DUM text = fscanf(lNFid, '55s' ,1); dumnyRX_startang = fscanf(lNFid,'55f\n',1); DUM text = fscanf(INFid,'55s',1); dum nyRX_stopang = fscanf(INFid, '55f\n' ,1); DUM text = fscanf(INFid,'55s',1); dum nyRX_incang = fscanf(INFid, '55f\n' ,1); DUM text = fscanf(lNFid,'55s',1); ref_R = fscanf(INFid, *55An' ,1); DlM text = fscanf(INFid, '55s' ,1); dnangle = fscanf(INFid, '55f\n' ,1); DUM text = fscanf(iNFid, '55s' ,1); nsample = fscanf(lNFid,'55f\n',1); DUM text = fscanf(INFid,'55s',1); sam plingRANG E = fscanf(INFid,'55An',1); DUM text = fscanf(INFid,'55s',1); TRUE_npair = fscanf(INFid, '5!An' ,1); TRUE_antang = zeros(TRUE_npair,l); for n = l:TRUE_npair; tmp_r = fscanf(INFid, '55f' ,1); tmp_i = fscanf(INFid, '55An', 1); TRUE_antang(n) = tmp_r + i * tmp_i; end; DATAfi1e = [basename extension]; D A TA id = eval(['fopen("' D A TA fi1e '")']); total = TRUE_npair * TRUE_npoint * nsample; duirniy = zeros(total ,1); for n = 1:total; tmp_r = fscanf(DATAid, '5Sf' ,1); tmp_i = fscanf(D A TA id, '55An', 1); dummy(n,l) = tmp_r + i * tmp_i; end; TRUE_FD_raw= reshape(dummy,TRUE_npoint*nsample,TRUE_npair); eval (['save ' M ATA'le]); end Figure D.6: MATLAB code o f GETDATA.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 137 Function [dx,dy,dz,Dx,Dy,Dz] = volsize(B,hpbw,ref_R,dnangle) KThis function calculates the dimension of the illumination volume based on Kthe user-specified values of * S (1) depression angle, and K (2) reference slant range. % I&dnangle: depression angle in degrees. K 8 ref_R: reference slant range in meters. K Kdx, dy, dz: spatial resolution in x-, y-, and z-directions, respectively. £ KDx, Dy, Dz: dimension of the illumination volume in x-, y-, and zKdirections, respectively, rad = pi/180; c = 3e8; % speed of light in m dnangle = dnangle*rad; M = c/2/B; % pulse width in min aropagation direction dx = pw/cos(dnangle); % x-range resolution inm dy = dx; % y-range resolution inm dz = pw/sin(dnangle); % z-range resolution inm ax = ref_R*sin(0.5*hpbw)*(l/sin(dnangle+0.5*hpbw) + l/sin(dnangle-O.S*hpbw)); 3y = Dx; az = ref_R*sin(0.5*hpbw)*(l/cos(dnangle+0.5*hpbw) + l/cos(dnangle-0.5*hpbw)); Figure D.7: MATLAB code o f VOLSIZE.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 138 function [FOCUS.xgridaxis.ygridaxis.zgridaxis] = fcusgri d(ref_R,dnangle,xspotlength,yspotlength,zspotlength,xstep,ystep,zstep) 1 5This function computes the xy coordinates of the grid points on 1 5focal planes: 1 5 1 5 x 1 5 a « | e % I +-I -+ « I I I £ y< j-z-j 1 5 | | Note that FOCUS(i,j) = xgridaxis(i) + sqrt(-l)*ygridaxis(j) 1 5 +—+ rad = pi/180; xcentroid = 0; /centroid = 0; zcentroid = -ref_R * sinCdnangle * rad); lumxhalf = ceil(xspotlength/2/xstep); lumyhalf = ceil(yspotlength/2/ystep); fiumzhalf = ceil (zspotlength/2/zstep); xgridaxis = [ numxhalf*xstep : -xstep : -numxhalf*xstep] .'; ygridaxis = [ numyhalf*ystep : -ystep : -numyhalf*ystep].'; zgridaxis = [-numzhalf*zstep : zstep : numzhalf*zstep].' + zcentroid; xdum= xgridaxis; ydum= ygridaxis.'; FX= xdum(:,ones(l,length(xgridaxis))); f y = ydum (ones(length(ygri daxis),1),:); FO C U S = fx + i*FY; Figure D.8: MATLAB code o f FCUSGRID.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 139 function [LENS,TX LEN S,rxlens] = 1ensgrid(ref_a,TRUE_antang,iNTfactor) KThis function m aps T Xand R Xangles to xy coordinates ISusing forward scattering convention of sign, rad = pi/ISO; ntUE_npair = 1ength(TRUH_antang); rxang = realC interpl( [l:TRUE_npair],TRUE_antangIlinspace(l,TRUE_npair,lNTfactor*TRUE_npair) ) ) + 180; R X ang = im agC interplC [l:TRUE_npair]ITRUE_antang,linspace(lITRUE_npair,lNTfactor*TRUE_npair) ) ); rX L E N S = ref_a * C cos(TXang*rad) + i*sin(Txang*rad) ); rxlens = ref_a * ( cos(Rxang*rad) + i*sin(Rxang*rad) ); L E N S = TX LEN S; Figure D.9: MATLAB code o f LENSGRID.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 140 Function [FD_raw,npoint] = radix(TRUE_FD_raw,TRUE_npoint,wantFFT,iNTfactor) £R A D IXinterpolates the rawdata over frequency domain so that the Klength of the interpolated data vector is optim umfor FFT fispCr ']); disp([’Existing num ber of frequency-sampling points: ’ num2str(TRUE_npoint)]); if wantFFT== 'y' TRUE_npoint_FFT= 2Aceil(loglO(TRUE_npoint)/loglO(2)); disp([' ']); disp([’Closest num ber of radix-2 points: 1 num2str(TRUE_npoint_FFT)]); disp([' ']): newnpoint = input(['=> C H A N G E(if no aliasing) the existing num ber of points to (e.g. 512, 256, or 128) [128]: ']); npoint = newnpoint: dispC Frequency interpolation...'); FD _raw _FR EQ= interpl(l:TRUE_npoint,TRUE_FD_raw,linspace(l,TRUE_npoint,newnpoint), 'linear') ; else disp([' ']); newnpoint = input(['=> c h a n g e (if no aliasing) the existing num ber of points to (e.g. 401, 201, or 101) [101]: ']); dfreq = round((TRUE_npoint-l)/(newnpoint-l)); npoint = newnpoint; FD _raw _FR EQ= TRUE_FD_raw(l:dfreq:TRUE_npoint,:); end; if INTfactor ~= 1 dispC Angle interpolation...'); end; dispC Done.'); TRUE_npair = size(TRUE_FD_raw,2); FD_raw= ( interpl( [l:TRUE_npair], (FD_raw_FREQ ) •' ,linspace(l,TRUE_npai r,iNTfactor*TRUE_npair) ) ).'; Figure D.10: MATLAB code o f RADIX.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 141 Function screeni nfo(ref_R,dnangle,xgridlength,ygridlength,zgri dlength, xspotl ength,yspotlength,zspotl ength,Dx,Dy,d z ,dx,dy,dz, xstep,ystep,zstep); £ SC R EEN IN FOsimply display the processing parameters for the £ main programC O R R SA R iispC ’); diSp(’ 1 -■ - dispC' '); disp(['Radar looking disp(['Matrix size = disp(['Actual size =' disp(['xbecunwidth = disp(['ybeamwidth = disp(['zbeanwridth = disp([’xresolution = disp(['yresolution = disp(['zresolution = disp(' '); dispC '); ------ ‘) ; at ' num2str(ref_R) 'm '' num2str(dnangle) ’ deg. down.' ]); 'num2str(ygridlength) ' x ' num2str(xgridlength)]) num2str(yspotlength*100) 'em x ' num2str(xspotlength*100) 'an']) 'num2str(Dx) 'm=> xspotlength = ' num2str(xspotlength) 'm.']); 'num2str(Dy) 'm=> yspotlength = ' num2str(yspotlength) 'm.']); 'num2str(Dz) 'm=> zspotlength = ' num2str(zspotlength) 'm.']); 'num2str(dx) 'm=> xresolution = xstep = ’ num2str(xstep) 'm.’]); 'num2str(dy) 'm=> yresolution = ystep = ' num2str(ystep) 'm.’]); 'num2str(dz) 'm=> zresolution = zstep = ' num2str(zstep) 'm.']); disp(['Hit [R ETU R N ] to start processing ...']); pause; Figure D. l l : MATLAB code o f SCREENINFO.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission. 142 function w= kaiser(nn,beta) & AISERKAiSER(N.beta) returns the BETA-valued N-point Kaiser window. 1 5 Author(s): L. Shure, 3-4-87 1 5 Copyright (c) 1988-97 by The M athworks, inc. 1 5 jRevision: 1.8 $ $Date: 1997/02/06 21:55:10 5 = round(nn); :es = abs(besseli(0, beta)); 3dd = rem(nw,2); <ind = (nw-l)A2; i = fix((rwH-l)/2); <i = (0:n-l) + .5*(1-odd); <i = 4*xi .*2; n = besseli(0,beta*sqrt(l-xi/xind))/bes; n = abs([w(n:-l:odd+l) w])'; tw Figure D.12: MATLAB code o f KAISER.M R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission. 143 function GATEMX = gating(tmp_rl,tmp_r2,viev\®cm,deltaT1npoint,npair, filtershape) 1 5This function constructs a gating matrix for time-domain gating on 1 5the original frequency-domain sar measurement. 1 5 &tmp_rl: distances between T Xpositions and the focal point K 1 5tmp_r2: distances between R Xpositions and the focal point 1 5 1 5vieitfjcm: diameter(cm) of the sphere of view around the focal point 1 5 S 5deltaT: time resolution, determined by the measurement bandwidth 5 5 £ npoint: num ber of frequency points 1 5 1 5npair: num ber of bistatic/monostatic angle combinations 1 5 1 5filtershape: Kaiser window shape 1 5 1 5G A T E M X : gating matrix used for time-domain multiplication (filtering) 1 5 with the original inverse-FOurier-transformed SA Rmeasurement. 1 5 GATEMX contains colum ns of appropriately shifted finite-width 1 5 shaped sequences. The gate centers are determined by both 1 5 tmp_rl and tmp_r2. The gate width is determined by viewocm. : = 3e8; riewD= viewDcm/100; centerindex = round((tmp__rl + tmp_r2)/c/deltaT); ialfw_index = round(viewD/c/deltaT); Filterindex = zeros(2*halfw_index + 1,1); 3A T E M X= zeros(npoint,npai r); For i = l:npair; filterindex = (centerindex(i) - halfw_index : centerindex(i) + halfw_index) + (i-l)*npoint; GATEMX(filterindex) = filte r s h a p e : end; Figure D.13: MATLAB code o f GATING.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 144 kinction acf = chopband(FD_gated_focused) KC O R K : 8 Frequency decorrelation by bandwidth partitioning condirioning_factor = 100; ipartition = 16; %must be power of 2 irow= size(FD_gated_focused,l); %must be power of 2 icol = size(FO_gated_fdcused,2); %must be an even number fVridth = round(nrow/npartiti on); subSARjlD= zeros(npartition, 1); subSAR_2D= zeros(npartition,npartition); ^CFarray = zeros(npartition*(npartition+l)/2,l); for ipartition = l:npartition row_i = 1 + (ipartition - 1) * fvridth; row_f = ipartition * fvridth; subSAR_lD(ipartition) = m ax( ifft( sum ( FD_gated_focused(row_i:row_f, ' ) ) ); and; subSAR_2D= subSAR_lD * conj( subSAR_lD).'; ivCFarray = subSAR_2D( find(triu( subSAR_2o ) -= 0) ); ^C F= (l/conditioning_factor) * ( prod( conditioning_factor * ACFarray ) )*( l/( length(ACFarray) ) ); Figure D.14: MATLAB code o f CHO PBA N D .M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 145 function ACF = chopband(FD_gated_focused) * CORR: ISFrequency decorrelation by bandwidth partitioning conditi oni ng_factor = 100; npartition =16; * must be power of 2 nrow= size(FD_gated_fbcused,l); %must be power of 2 ncol = size(FD_gated_focused,2); %must be an even number fvridth = roundCnrow/npartition); subSAR_lD = zeros(npartition.l); subSAR_2D = zeros(npartition, npartition); iXCFarray = zeros(npartition*(npartition+l)/2,l); For ip a rtitio n = 1: npartiti on row_i = 1 + (ipartition - 1) * fvridth; row_f = ipartition * fvridth; subSAR_lD(ipartition) = m ax( ifft( sum( FD_gated_focused(row_i :row_f,:).' ) ) ); end; subSAR_2D = subSAR_lD * conj( subSAR_lD ) . ’; Farray = subSAR_2D( find(triu( subSAR_2D ) ~= 0) ); < V C F= (1/conditioning_factor) * ( prod( conditi oning_factor * ACFarray ) ) a ( i/( 1ength(ACFarray) ) ); Figure D.15: MATLAB code o f FREQ-ACF.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 1 46 Function acf = rime_jacfCTD_gated_focused,target_phi ,cluter_phi,npizza4target,npizza4cluter); IStime_acf: ISThis subroutine takes in the gated and focused data as ISinput. A n arbitrary angular separation is chosen for ISangular correlation in -time domain-. IS ISsmall target_phi is good for target detection, but badfor clutter s uppression ISlarge C LurER_PH i is good for clutter suppression, but bad fortarget detection IS irow = size(TD_gated_fbcused,l); icol = size(7t>_gated_fbcused,2); tm p = zeros(nrow.ncol); For i i = l:npizza4target; delta_ang1e = ii*target_phi; tm p = tm p + TD_gated_focused .* conj( TD_gated_focused(:,[ (delta_angle+l):360 L:delta_angle ]) ); end; for ii = l:npizza4cluter; delta_angle = ii*cluter_phi; tm p = tm p + TD_gated_focused .* conjf TD_gated_focused(:, [ (deltcL_angle+l):360 L:delta_angle ]) ); end; rawacf = tmp/(npizza4target + npizza4cluter); \CF = m ax( sum ( ( rawacf ).' ) ); Figure D.16: MATLAB code of TIME-ACF.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 147 function nomuimage = norm al (org_image) ISn o rm a l: ISt o normalize a given matrix ORGLXMAGE,shifting the m inlevel of ISorgjcm age back to zero level. Thennormalize theshifted matrix ISto 1.00 nin_level = min( min( org_image ) ); nax_level = max( max( org_image ) ); nag_level = abs( max_level - min_level ); iorm_image = ( org_image - min_level )/mag_level; Figure D.17: MATLAB code of NORMAL.M R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. VITA Tsz-King Chan was bom in Hong Kong in 1971. He received his Bachelor degree in Electrical Engineering (with higher honors) in 1993 from Portland State University in Portland, Oregon, USA. After graduation he continued for further education and in 1995, he completed his Master degree in Electrical Engineering from the University of Washington in Seattle, Washington, USA. The title of his Master thesis is “MillimeterWave Experiments on Bistatic Scattering and Angular Memory Effect of Two-Dimensional Conducting Random Rough Surfaces” . From September 1995 to June 1998, he was a research assistant at the Electromagnetics and Remote Sensing Laboratory at the University of Washington, where he was devoted to his doctoral research under the guidance of Professor Kuga on radar detection/imaging using correlation techniques. His research interests include R&D in all areas of RF electromagnetics with emphasis on medical imaging, broadband system design, wireless communications, implementation o f targetlocating system in multipath environment and development of clutter-suppression software algorithms. Book Chapter 1. A. Ishimaru, C. Le, Y. Kuga, L. Ailes-Sengers, and T. K. Chan, “Polarimetric scattering theory fo r large slope rough surfaces,” Progress in Electromagnetics Research, 14, EMW Publishing, Cambridge, Massachusetts, 1996. Journal Articles 1. T. K. Chan, Y. Kuga, A. Ishimaru and K. Pinyan, “Confocal Imaging in Clutter En vironment Using Circular-Correlation Synthetic Aperture Radar,” IEEE Geoscience and Remote Sensing, submitted 1998. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 149 2. A. Ishimaru, T. K. Chan and Y. Kuga, “An Imaging Technique Using Confocal Cir cular Synthetic Aperture Radar,” IEEE Geoscience and Remote Sensing, submitted 1997. 3. T. K. Chan, Y. Kuga and A. Ishimaru, “Subsurface Detection of a Buried Object Using Angular Correlation Function Measurement,” Waves in Random M edia, 7(3), pp. 457-465, 1997. 4. T. K. Chan, Y. Kuga and A. Ishimaru, “Angular Memory Effect of Millimeter-Wave Scattering from Two-Dimensional Conducting Random Rough Surfaces,” Radio Science, 31(5), pp. 1067-1076, 1996. 5. T. K. Chan, Y. Kuga, A. Ishimaru and C. Le, “Experimental Studies of Bistatic Scat tering from Two-Dimensional Conducting Random Rough Surfaces,” IEEE Geo science and Remote Sensing, 34(3), pp. 674—680, 1996. 6. A. Ishimaru, C. Le, Y. Kuga, L. Ailes-Sengers and T. K. Chan, “Polarimetric Scatter ing Theory for High Slope Rough Surface: Summary,” Journal o f Electromagnetics Waves and Applications, 10(4), pp. 489^491, 1996. Conference Papers 1. A. Ishimaru, T. K. Chan and Y. Kuga, “Confocal Imaging Using Circular Synthetic Aperture Radar,” National Radio Science Meeting, Boulder, Colorado, USA, 1998. 2. T. K. Chan, Y. Kuga and A. Ishimaru, “Feasibility Study on Localized Subsurface Imaging Using Circular Synthetic Aperture Radar and Angular Correlation Function Measurement,” International Geoscience And Remote Sensing Symposium, Singa pore, 1997. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. 150 3. T. K. Chan, Y. Kuga, and A. Ishimaru, “Detection o f a Buried Target Based on An gular Correlation Function Measurement,” Progress in Electromagnetics Research Symposium, Hong Kong, 1997. 4. T. K. Chan, Y. Kuga and A. Ishimaru, “Detection of a Target in a Homogeneous Medium Using Angular Correlation Function,” International Geoscience A nd Re mote Sensing Symposium, Lincoln, Nebraska, USA, 1996. 5. A. Ishimaru, C. Le, Y. Kuga, J. H. Yea, K. Pak, and T. K. Chan, “Interferometric Technique of Determining the Average Height Profiles of Rough Surfaces” , Inter national Geoscience And Remote Sensing Symposium, Lincoln, Nebraska, 1996. 6 . Y. Kuga, T. K. Chan and A. Ishimaru, “Applications of Angular Correlation Func tion Measurement in Target Detection,” International Symposium on Antennas and Propagation, Japan, 1996. 7. C. Penwell, T. K. Chan, and Y. Kuga, “Detection of Buried Objects Using Xband Radar and Angular Memory Effect,” Progress in Electromagnetics Research Symposium, Baltimore, Washington D. C., USA, 1996. 8. T. K. Chan, Y. Kuga and A. Ishimaru, “Detailed Experimental Studies on Scattering from Two-Dimensional Conducting Rough Surfaces,” Progress in Electromagnetics Research Symposium, Seattle, Washington, USA, 1995. R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission. IMAGE EVALUATION TEST TARGET (Q A -3 ) 15 0 m m IIW IG E .In c 1653 East Main Street Rochester, NY 14609 USA Phone: 716/482-0300 Pax: 716/288-5989 0 1993. Applied Image. Inc.. All Rights Reserved R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout p erm ission.

1/--страниц