Two Dimensional Phase Unwrapping Theory Alogrithms and Software

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少.463 y22 TWO-DIMENSIONAL PHASE UNWRAPPING THEORY ALGORITHMS AND SOFTWARE Dennis C. Higl Sandia National Laboratories Albuquerque, New Mexico Mark D. Pritt Lockheed Martin Corporation hersburg, Maryland A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY SONS, INC New York Chichester Weinheim Brisbane Singapore Toronto 2005060 COVER c radar interferogram en the complexvalued fferences. but the phase differences must fi ped. wrapping problem In reg:ons of steep terrain. the phase wraps very quickly and corrupted where there are radar shadow and"layover"effects. Surface sturbances that occurred between the two passes, which were 24 days apart. also This ima quired as part of a program for the Terrain Modeling Project Office Engineering Center. T he SaR data was provided by Radarsat Intemational, Th inter ferogram was generated and provided by Vexcel Corporation. Boulder, Colorad p00 Copyright o 1998 by John Wiley Sons, Inc. All rights reserved Published simultaneously in Canada No part of this publication ystem or transmitted in any form or by any means, electron xcept as permitted under Sections 107 or I0% of the 1976 United otten pemission of the Publisher, or authorization through payment of the Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax(978) 750-4744. Requests to the publisher for permission shouid b addressed to the Permissions Department, John Wiley Sons c, 605 Third A venue. New York, NY 10158-0012,(212)850. 6011fax(212)850-6008E-Mail:PERMREQ@WILEY.COM Two-dimensional phase unwrapping: theory, algorithms, and ofware/Dennis C. Ghiglia and Mark D Pritt. index ISBN 0-471-24935-I (cloth: alk. paper) Synthetic aperture radar. 2. Signal processing-Mi 3. Interfer 1. Pritt. Mark D. II. Title. 621.367-d2 97-38034 Printed in the United States of America 10987654321 TWO-DIMENSIONAL PHASE UNWRAPPING FOREWORD Two-dimensional phase unwrapping is the type of problem that is typically the domain of the mathematician. It is both complex and abstract. However, phase unwrapping is also the core technology that enables radar interferometry data. Radar data are now used for precise measurement of surface topography in clouded regions. Additionally, spaceborne radar systems have proved effective for measuring surface changes from earthquakes and volcanic eruptions. These applications have created a new class of radar data users primarily involved in napping and remote sensing applications. In TwO-Dimensional Phase Unwrapping: Theory, Algorithms, and Software he authors unlock the mystery of phase unwrapping in interferometric data processing. This text provides a clear, concise treatment of phase unwrapping that cannot be found in any other source. It presents for the first time the relationship between theory and application, Its uniform treatment of the various phase unwrapping techniques makes it a valuable resource for any engineer or scientist involved in processing or exploitation of interferometric expect that radar interferometry will increase in importance over the coming decade with the development of airborne and spaceborne sensor systems designed to optimally exploit this tcchnology. Two-Dimensional Phase Unwrap- ping: Theory, Algorithms, and Software is an important contribution to our understanding of radar interferometry that will bencfit both research into advanced techniques and the design of these future sensor systems JOHN C. CURLANDER Vexcel Corporation PREFACE Two-dimensional phase unwrapping arises most naturally in, but is not restricted to, interferometric applicatio asured or calculated phase values from two or more mutually coherent multidimensional signals are related in a nonlinear manner to a desired physical quantity of interest. The nonlinearity is in the form of"wraps"or cycle discontinuities where an underlying two- dimensional phase is wrapped into the interval (T, The wrapped phase must somehow be unwrapped in order to provide an estimate of the underlying physical quantity. Estimation of surface topography from interferometric synthetic aperture radar(SAR) or extremely accurate profiling of mechanical parts by optical interferometers are two such examples riginally developed for military reconnaissance, SAR is now experiencing new life in civil applications. In fact civilian and commercial in becoming the drivers of technology. Clever utilization of the coherent SAr imagery in interferometric configurations makes possible the measurement of surface topography to accuracies much better than the spatial resolution( 0.3 meters to several meters)of the SAR images themselves. Indeed, as is common place with interferometers, measurement sensitivities are on the order of the operating wavelength, which is typically a few centimeters for SAR Imaging geometrics, noisc, and other operational factors degrade performance some- what from centimeter-scale accuracies, but nevertheless SAR interferometry makes possible global topographic mapping in a timely fashion, in daylight or at night, in all weather conditions, and with unprecedented accuracy. SAR interferometry also can detect deformations of the earths crust on the order of millimeters, a capability that shows promise for the timely detection of earthquakes or volcanic eruptions These exciting possibilities have led to an explosive growth in the field of phase unwrapping as indicated by the increasing number of journal publication Newcomers to SAR interferometry and related disciplines will eventually confront the phase unwrapping problem and, undoubtedly, will encounter a rather bewildering variety of ideas and algorithms, including those based on neural networks, simulated annealing, cellular automata, genetic algorithms, and other unusual constructs. Which of these are good? which are not? We do Throughout this book we use the notation(-π,可 to represent the interval-丌<x≤丌 PREFACE not have complete answers to these questions, and in all likelihood there never will be a complete answer. However, we can help researchers approach the problem in the context of their own applications with some guidance from those who have been through the" school of hard knocks e have greatly simplified the investigative process by categorizing phase inwrapping approaches into two general classes: path-following and minimum- norm methods. We have provided detailed descriptions and analyses of four path-following approaches and four minimum-norm approaches. As is the case with politics, there are plenty of partisan participants firmly entrenched in their own camp with nary a nod of recognition to an opposing view. We ourselves guilty of this to some degree. However, we provide enough theory philosophy, algorithms, and references to allow researchers to make up their own minds in a much more timely fashion than if some sifting had not been done. Fortunately, unlike politics, sound scientific investigation makes it easier to switch"part affiliations"if necessary While this book is slanted toward SAR interferometry applications, it has much in common with other disciplines in which phase unwrapping plays an important role. In fact it is safe to say that the phase unwrapping problems encountered in SAR are about"as hard as they come. Practical solutions for SAR interferometry should easily find a place in related applications outside the field of SAR. We believe readers of this book will have no trouble bridging the gap. This book provides another useful function. Most researchers are"quick studies"and soon learn which algorithms they would like to try. Newcomers usually lack the basic building blocks of operational codes from which timely esults spring forth. As we all know, it takes time to develop and successfully implement a working algorithm. To this end, we have supplied a suite of language programs and routines comprising over 6000 lines of source code that implement the ideas and algorithms discussed in this book. We have already done the laborious part of coding the algorithms, fixing the bugs, and contacting the authors of the algorithms to discover the"tricks"necessary to get them to work correctly. We encourage the reader to understand how the algorithms work, use them properly, modify them as appropriate, and improve them. These programs, which are listed in Appendix A, are available for downloading on the wiley ftp server, along with a number of phase unwrapping datasets. See Appendix C for details The supplied software comprises only a subset of the vast suite ite of published nd unpublished algorithms. We have selected and implemented those that we believe are representative of the current"state-of-the-art "in phase unwrapping, such as Flynn s minimum discontinuity algorithm, while not neglecting the older and more"classic "algorithms, such as the residue and branch cut algorithm of Goldstein, Zebker, and Werner. Omissions of certain algorithms are not a suggestion of inadequacy. We just could not include them all. By contrast. inclusion is not a claim of superiority. Instead, they should be viewed for the insight and perspective they provide. Indeed new and potentially powerful and useful algorithms are being developed all the time. This is the sign of a vital and dynamic field, and we should be encouraged rather than befuddled Many of the ideas, concepts, philosophies, and algorithms discussed are not f course, our own. We have been fortunate to work with many tal colleagues who have helped us immensely for many years in many diverse s. Assistance has he in the form of developing challenging problems. providing experimental data, offering first-rate mathematical and algorithmic ssistance, supplying hardware and software support, and providing a stimulat ing and supportive work environment. For all of these reasons and more we wish to extend sincere thanks to Charles V. Jakowatz, Jr, Louis A. Romero, Gary A Mastin, Daniel E. WahL, Paul A. Thompson, Bruce C. Walker, William H Hensley, David K. Johnson, Terry M. Calloway, Terry A. Bacon, Michael J Roth and Edward J. Nowicki We especially wish to thank Thomas J. Flynn, Paul H. Eichel, and Doug L. Bickel of Sandia National Laboratories for their thorough and insightful reviews of this book. Tom Flynn was especially helpful with his collaboration during the preparation of this work and the actual research investigations. He developed one of the phase unwrapping codes, and he graciously allowed us to esent and distribute it to the research community. Michael J. Roth of the Johns Hopkins University Applied Physics Laboratory supplied us with two phase unwrapping examples that were generated by his IFSAR simulator. In addition Richard M. Goldstein of the Jet Propulsion Laboratory provided invaluable assistance with our understanding of the subtleties of the widely used algorithm credited to him and his colleagues, Howard A. Zebker and Charles L. Werner Finally we wish to thank John C. Curlander of Vexcel Corporation for writing the Foreword This work was performed in part at Sandia National Laboratories, Albu querque, NM. Sandia is a multiprogram laboratory operated by Sandia Cor- poration, a Lockheed Martin company, for the United States Department of Energy under Contract DE-AC04-94AL85000. Dennis C. Ghiglia would like to express his thanks and appreciation to the management of Sandia National Laboratories and the U. S. Department of Energy for their support throughout his career. He also wishes to thank his son, Daniel C Ghiglia, for his expertise and invaluable assistance with the artwork development and LATEX typesetting, and his wife Ruth Ann and daughter Carla for their understanding and support during the time-consuming process of book writing Mark D. Pritt would like to express his thanks and appreciation to Hal Garner, a vice president of Lockheed Martin Corporation, for funding the research and writing of this book. He also wishes to thank his former manager, Sharon L. Smith, for her invaluable support of this effort, and his current manager, Rick w. Duke, for helping bring it to completion. Last, but certainly not least he wishes to thank his wife christine and his children anna, Jacob. Emily, Samuel, and Noah for their enthusiastic support and encouragement MARK D. PRITT Lockheed Marlin Corporarion Apri! /9y

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