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Introduction to Imaging from Scattered Fields [Hardback]

4.50/5 (4 ratings by Goodreads)
(University of North Carolina at Charlotte), (Perigon Engineering, Charlotte, North Carolina, USA)
  • Format: Hardback, 246 pages, height x width: 254x178 mm, weight: 620 g, 1 Tables, color; 39 Tables, black and white; 33 Illustrations, color; 1062 Illustrations, black and white
  • Pub. Date: 10-Nov-2014
  • Publisher: CRC Press Inc
  • ISBN-10: 1466569581
  • ISBN-13: 9781466569584
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Introduction to Imaging from Scattered FieldsLarger Image
  • Format: Hardback, 246 pages, height x width: 254x178 mm, weight: 620 g, 1 Tables, color; 39 Tables, black and white; 33 Illustrations, color; 1062 Illustrations, black and white
  • Pub. Date: 10-Nov-2014
  • Publisher: CRC Press Inc
  • ISBN-10: 1466569581
  • ISBN-13: 9781466569584
Other books in subject:
Permanent link: https://www.kriso.ee/db/9781466569584.html
Keywords:
The authors discuss the problem of determining information about an object from measurements of the field scattered from that object and approaches to recovering information about it. They address the fundamentals, including inverse scattering, electromagnetic waves, and scattering; inversion methods, including data processing, born approximation observations, alternate inverse methods, and homomorphic (cepstral) filtering; and applications to real measured data, advanced cepstral filtering, and advanced topics. Understanding of basic electromagnetic principles, background in calculus and Fourier analysis, and familiarity with MATLAB is needed. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Obtain the Best Estimate of a Strongly Scattering Object from Limited Scattered Field Data

Introduction to Imaging from Scattered Fields presents an overview of the challenging problem of determining information about an object from measurements of the field scattered from that object. It covers widely used approaches to recover information about the objects and examines the assumptions made a priori about the object and the consequences of recovering object information from limited numbers of noisy measurements of the scattered fields.

The book explores the strengths and weaknesses of using inverse methods for weak scattering. These methods, including Fourier-based signal and image processing techniques, allow more straightforward inverse algorithms to be exploited based on a simple mapping of scattered field data.

The authors also discuss their recent approach based on a nonlinear filtering step in the inverse algorithm. They illustrate how to use this algorithm through numerous two-dimensional electromagnetic scattering examples. MATLAB® code is provided to help readers quickly apply the approach to a wide variety of inverse scattering problems.

In later chapters of the book, the authors focus on important and often forgotten overarching constraints associated with exploiting inverse scattering algorithms. They explain how the number of degrees of freedom associated with any given scattering experiment can be found and how this allows one to specify a minimum number of data that should be measured. They also describe how the prior discrete Fourier transform (PDFT) algorithm helps in estimating the properties of an object from scattered field measurements. The PDFT restores stability and improves estimates of the object even with severely limited data (provided it is sufficient to meet a criterion based on the number of degrees of freedom).

Suitable for graduate students and researchers working on medical, geophysical, defense, and industrial inspection inverse problems, this self-contained book provides the necessary details for readers to design improved experiments and process measured data more effectively. It shows how to obtain the best estimate of a strongly scattering object from limited scattered field data.

Reviews

"It has gone straight to the top of my recommended reading list for students interested in the fundamental theory of waves and inverse scattering." Optics & Photonics News, April 2015

"Introduction to Imaging from Scattered Fields is an essential guide to diffraction tomography and inverse methods. The text combines theoretical analysis of scattering models with practical numerical analysis in a highly accessible narrative." David J. Brady, Professor of Electrical and Computer Engineering and Michael J. Fitzpatrick Professor of Photonics, Duke University

"This excellent text provides a clear and systematic treatment of the fundamental theory of waves and inverse scattering whilst remaining accessible to practitioners in remote sensing and imaging. It includes a range of examples and MATLAB code, and it should prove a valuable reference and textbook " Dr. Mark Spivack, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

" bring[ s] the practitioner or student of imaging up to the necessary level for understanding the physical and mathematical underpinnings of scattered fields and inverse scattering problems, with an ultimate eye on practical implementation to real problems in a variety of real-world imaging applications." Dr. Michael Kotlarchyk, Professor and Head of School of Physics and Astronomy, Rochester Institute of Technology

Preface xi
Authors xiii
List of Symbols
xv
SECTION I Fundamentals
Chapter 1 Introduction to Inverse Scattering
3(12)
1.1 Introduction
3(1)
1.2 Inverse Scattering Problem Overview
4(3)
1.3 Diffraction Tomography
7(3)
1.4 Theoretical Issues and Concerns
10(5)
References
12(3)
Chapter 2 Electromagnetic Waves
15(16)
2.1 Maxwell's Equations
15(3)
2.2 Green's Function
18(8)
2.2.1 Solving Differential Equations
19(2)
2.2.2 The Integral Equation of Scattering
21(5)
2.3 Plane Waves
26(3)
2.4 Evanescent and Propagating Waves
29(2)
Chapter 3 Scattering Fundamentals
31(12)
3.1 Material Properties and Modeling
31(4)
3.1.1 The Model for Conductivity
31(1)
3.1.2 Time-Dependent Maxwell's Equations
31(1)
3.1.3 Effective Permittivity and Conducting Medium
32(1)
3.1.4 Increasing N and Local Fields
33(2)
3.2 Weak Scatterers
35(1)
3.3 Scattering from Compact Structures
35(8)
3.3.1 Scattering from Obstacles
36(1)
3.3.2 Rayleigh Scattering
37(1)
3.3.3 Mie Scattering
38(3)
References
41(2)
Chapter 4 Inverse Scattering Fundamentals
43(14)
4.1 Categorization of Inverse Scattering Problems
43(1)
4.2 Inverse Scattering in Two Dimensions
43(5)
4.3 First Born Approximation
48(3)
4.4 Rytov Approximation
51(6)
References
52(5)
SECTION II Inversion Methods
Chapter 5 Data Processing
57(8)
5.1 Data Inversion in k-Space: A Fourier Perspective
57(2)
5.2 Target Modeling and Data Generation
59(2)
5.3 Target Modeling Environment
61(1)
5.4 Imaging Algorithm Implementations: Example Reconstructions
61(4)
References
63(2)
Chapter 6 Born Approximation Observations
65(32)
6.1 Degrees of Freedom
65(2)
6.2 Requirements for Degrees of Freedom for Sources
67(1)
6.3 Requirements for Degrees of Freedom for Receivers
68(12)
6.4 Imaging Relationship between Born Approximation and Mie Q Factor
80(17)
References
96(1)
Chapter 7 Alternate Inverse Methods
97(6)
7.1 Iterative Methods
97(1)
7.2 Born Iterative Method (BIM)
97(1)
7.3 Distorted Born Iterative Method (DBIM)
98(1)
7.4 Conjugate Gradient Method (CGM)
98(1)
7.5 Prior Discrete Fourier Transform (PDFT)
99(4)
References
101(2)
Chapter 8 Homomorphic (Cepstral) Filtering
103(14)
8.1 Cepstral Filtering
103(1)
8.2 Cepstral Filtering with Minimum Phase
104(2)
8.3 Generating the Minimum Phase Function
106(2)
8.4 Preprocessing Data
108(2)
8.5 Two-Dimensional Filtering Methods
110(1)
8.6 Removing the Reference
111(6)
References
113(4)
SECTION III Applications
Chapter 9 Applications to Real Measured Data
117(28)
9.1 Ipswich Data Results
117(5)
9.1.1 IPS008
117(2)
9.1.2 IPS010
119(3)
9.2 Institut Fresnel Data Results
122(12)
9.2.1 FoamDielInt
124(7)
9.2.2 FoamDielExt
131(1)
9.2.3 FoamTwinExt
131(3)
9.2.4 FoamMetExt
134(1)
9.3 Comparison of Reconstruction Methods
134(5)
9.4 Final Remarks and Summary
139(6)
References
142(3)
Chapter 10 Advanced Cepstral Filtering
145(30)
10.1 Independent Processing of Source Data
145(6)
10.2 Effects of Modified Filters in Cepstral Domain
151(9)
10.3 Effects of Random Undersampling
160(15)
References
174(1)
Chapter 11 Advanced Topics in Inverse Imaging
175(14)
11.1 Practical Steps for Imaging Strong Scatterers
175(4)
11.2 An Overall Approach to the Degrees of Freedom in Imaging
179(4)
11.3 Conclusion
183(6)
References
186(3)
SECTION IV Appendices
Appendix A Review of Fourier Analysis 189(6)
Appendix B The Phase Retrieval Problem 195(6)
Appendix C Prior Discrete Fourier Transform 201(10)
Appendix D The Poynting Vector 211(2)
Appendix E Resolution and Degrees of Freedom 213(4)
Appendix F MATLAB® Exercises with COMSOL® Data 217(6)
Index 223
Michael A. Fiddy received his PhD from the University of London in 1977, and was a research fellow in the Department of Electronic and Electrical Engineering at University College London before becoming a faculty member at London University (Kings College) in 1979. He moved to the University of Massachusetts Lowell in 1987 where he was ECE Department Head from 1994 until 2001. In January 2002 he was appointed the founding director of the newly created Center for Optoelectronics and Optical Communications at UNC Charlotte. He has been a visiting professor at the Institute of Optics Rochester NY, Mathematics Department Catholic University, Washington DC, Nanophotonics Laboratory Nanyang Technical University Singapore and ECE Department University of Christchurch NZ. He has also been the editor-in-chief of the journal Waves in Random and Complex Media since 1996, and holds editorial positions with several other academic journals. He was the topical editor for signal and image processing for the journal of the Optical Society of America from 1994 until 2001. He has chaired 20 conferences in his field, and is a fellow of the OSA, IOP and SPIE. His current research interests are inverse problems related to super resolution and metamaterial design.

R. Shane Ritter is currently the Chair of the Engineering Department in the School of Professional Studies at Olivet Nazarene University in Bourbonnais, IL where he also serves as a Professor of Electrical and Computer Engineering. He has also served as the Director of Electrical Engineering for a number of engineering firms as well as an independent consulting electrical engineer in many different aspect of electrical engineering. He is currently licensed as a professional engineering in over 35 states, and he is also Registered Communication Distribution Designer (RCDD). Shane served as an adjunct faculty member in mathematics, statistics, and research for the University of Phoenix from 2001-2009. Shane also served as an adjunct faculty member in electrical and electronics engineering for the ITT Technical Institute in Charlotte, NC in 2010. Shane holds a BS and MS in Electrical Engineering from Mississippi State University, and a PhD in Electrical Engineering from the University of North Carolina at Charlotte.