Two Dimensional Phase Unwrapping Theory Algorithms and Software

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G TWO-DIMENSIONAL PHASE UNWRAPPING THEORY ALGORITHMS AND SOFTWARE Dennis C. ghiglia Sandia National Laboratories Albuquerque, New Mex Mark D. Pritt Lockheed Martin Corporation Gaithersburg, Maryland 藏 A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY SONS, INC New York Chichester Weinheim Brisbane Singapore / Toronto 2005060 radar interferogram generated by Death on each pass, The terrain elevations can be computed from the but the phase differences must fi g problem In regions of steep rrupted where there are radar shadow and "layover"effects. Surface occurred between the two passes, which were 24 days apar also p This image was acquired as part of a program for the Terrain Modeling Project Office nded by Engineering Center. The SAR data was provided by Radarsat Intenational TH interferogram was generated and provided by Vexcel Corporation, Boulder, Colorado p00 This text is printed on acid-free paper. Copyright o 1998 by John Wiley Sons, Inc. All rights reserved No part of this publication reproduced, stored in a retrieval system or transmitted in any form or by any means, el echanical photocopying, recording, scanning or otherwise, xcept as permitted under Sections 107 or 1O% of the 1976 of the Publisher or authorization through payment of theon tates Copyright Act, without cither the ppropriate per-copy fee to the Copyright Clearance Center, 222 750-4744. Requests to the Publisher for permission show(978) ood Drive, Danvers, MA 01923, (978)750-8400, fax nc.. 605 Third A venue. New York, NY 10158-0012(212)850- 6011fax(212)850-6008,E-Mail:PERMREQ@WILEY.COM Two-dimensional phase unwrapping: theory, algorithms, and software/Dennis C Ghiglia and Mark D Pritt. SBN0-471-24935-1(cloth: alk. paper) 1. Synthetic aperture radar. 2. Signal processing--Mathematics 3. Interferometry. I Pritt. Mark D. [L. Title 621.367-dc2l 97-38034 10987654321 ;4 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 Over the past decade interferometry has changed the way that we use radar 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 mapping and remote sensing application In Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software the authors unlock the mystery of phase unwrapping in interferometric data rocessing. 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- Dimensions ping: Theory, Algorithms, and Software is an important contribution to our inderstanding of radar interferometry that will bencfit both research into advanced techniques and the design of these future sensor systems JOHN C. CURLANDE President and CEO Vexcel Corporation PREFACE Two-dimensional phase unwrapping arises most naturally in, but is not restricted to, interferometric applications. Measured or calculated phase values from two or more mutually coherent multidimensional signals are related n 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, r. 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 mechanica parts by optical interferometers are two such examples Originally developed for military reconnaissance, SAR is now experiencing new life in civil applications. In fact civilian and commercial interests are rapidl 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 geometries, noise, 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 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 publications Newcomers to SAR interferometry and related disciplines will eventually onfront 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(-丌,丌 to represent the interval-丌<x≤丌 PREFACE lot 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 somc guidance from those who have been through the"school of hard knock We have greatly simplified the investigative process by categorizing phase unwrapping 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 guilty of this to some degree. However, we prom posing view. We ourselves are own camp with nary a nod of recognition to an o ide enough theory, philosophy algorithms, and references to allow researchers to make up their own minds in a nuch more timely fashion than if some sifting had not been done Fortunate unlike politics, sound scientific investigation makes it easier to switch"party affiliations"if necessary. While this book is slanted toward SAR interferometry applications, it has luch 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 rela ted applications outside the field of SAR. We believe readers of this book will have no trouble bridging the 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 results 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 c 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 improv These programs, which are listed in Appendix A, are available for downed Wiley ftp server, along with a number of phase unwrapping ts. see Appendix C for details The supplied software comprises only a subset of the vast suite of published d 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 Flynns 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 PREFACE usion 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 of course, our own. We have been fortunate to work with many talented colleagues who have helped us immensely for many years in many diverse s.Assistance has come in the form of developing challenging problems providing experimental data, offering first-rate mathematical and algorithmic assistance, 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 olied us with two pha 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 his work was performed in part at Sandia National Laborat querque, NM. Sandia is a multiprogram laboratory operated by Sandia Cor poration, a Lockheed martin any, 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 C. gr MARK D, PRITT Lockheed Marlin Corporation

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