Synopses & Reviews
Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing.
In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks.
Contents
1. Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces.
2. Validation of the Method of Moments for a Single Scatterer.
3. Scattering from Two Illuminated Scatterers.
4. Scattering from Two Scatterers Where Only One is Illuminated.
Appendix. Matlab Codes.
About the Authors
Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers.
Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers.
Gildas Kubické is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction Générale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.
Review
This textbook is intended for graduate students who wish to learn howto analyze the scattering of electromagnetic waves from randomly rough surfaces in the presence of scatterers, and for engineers andresearchers who need to solve such problems. It presents both asymptotic approaches such as the Kirchoff approximation, andnumerical methods such as the method of moments. The topics are integral equations for a single scatterer: method of moments andrough surfaces, the validation of the method of moments for a single scatterer, scattering from two illuminated scatterers, and scattering from two scatterers where only one is illuminated.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Review
This textbook is intended for graduate students who wish to learn howto analyze the scattering of electromagnetic waves from randomly rough surfaces in the presence of scatterers, and for engineers andresearchers who need to solve such problems. It presents both asymptotic approaches such as the Kirchoff approximation, andnumerical methods such as the method of moments. The topics are integral equations for a single scatterer: method of moments andrough surfaces, the validation of the method of moments for a single scatterer, scattering from two illuminated scatterers, and scattering from two scatterers where only one is illuminated.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Review
This textbook is intended for graduate students who wish to learn howto analyze the scattering of electromagnetic waves from randomly rough surfaces in the presence of scatterers, and for engineers andresearchers who need to solve such problems. It presents both asymptotic approaches such as the Kirchoff approximation, andnumerical methods such as the method of moments. The topics are integral equations for a single scatterer: method of moments andrough surfaces, the validation of the method of moments for a single scatterer, scattering from two illuminated scatterers, and scattering from two scatterers where only one is illuminated.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Review
This textbook is intended for graduate students who wish to learn howto analyze the scattering of electromagnetic waves from randomly rough surfaces in the presence of scatterers, and for engineers andresearchers who need to solve such problems. It presents both asymptotic approaches such as the Kirchoff approximation, andnumerical methods such as the method of moments. The topics are integral equations for a single scatterer: method of moments andrough surfaces, the validation of the method of moments for a single scatterer, scattering from two illuminated scatterers, and scattering from two scatterers where only one is illuminated.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Synopsis
Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing.
In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks.
Synopsis
This book applies the method of moments (MoM) to compute the field scattered by scatterers as well as by an object above or below a random rough surface. Since the problem is considered as 2D, the integral equations are scalar and only the TE and TM polarizations are addressed. The book compares the MoM with the exact solution of the field scattered by a cylinder in free space and with the physical optics approximation for the scattering from a plate in free space. It then presents numerical results of the coherent and incoherent intensities scattered by different means. Coupling between the two scatterers is also examined.
About the Author
Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conferences papers.
Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers.
Gildas Kubické is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction Générale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.
Table of Contents
PREFACE ix
INTRODUCTION xi
CHAPTER 1. INTEGRAL EQUATIONS FOR A SINGLE SCATTERER: METHOD OF MOMENTS AND ROUGH SURFACES 1
1.1. Introduction 1
1.2. Integral equations 2
1.2.1. TE and TM polarizations and boundary conditions 2
1.2.2. Electric and magnetic currents for a 2D problem 3
1.2.3. Huygens’ principle and extinction theorem 4
1.2.4. Radar cross-section (RCS) 8
1.2.5. Normalized radar cross-section (NRCS) 10
1.3. Method of moments with point-matching method 12
1.4. Application to a surface 14
1.4.1. The Dirichlet boundary conditions 14
1.4.2. The Neumann boundary conditions 16
1.4.3. General case 17
1.4.4. Impedance boundary condition 18
1.5. Forward–Backward (FB) method 19
1.6. Random rough surface generation 21
1.6.1. Statistical parameters 21
1.6.2. Generation of a random profile 23
1.6.3. Simulations 26
1.6.4. Conclusion 30
CHAPTER 2. VALIDATION OF THE METHOD OF MOMENTS FOR A SINGLE SCATTERER 31
2.1. Introduction 31
2.2. Solutions of a scattering problem 31
2.3. Comparison with the exact solution of a circular cylinder in free space 34
2.3.1. Solution of the Helmholtz equation 35
2.3.2. Dirichlet boundary conditions 37
2.3.3. Neumann boundary conditions 39
2.3.4. Dielectric cylinder 42
2.3.5. MoM for an elliptical cylinder 45
2.3.6. Numerical comparisons for a circular cylinder 47
2.3.7. Conclusion 54
2.4. PO approximation 55
2.4.1. Formulation 55
2.4.2. Applications 56
2.4.3. Sea-like surface 66
2.5. FB method 69
2.6. Conclusion 71
CHAPTER 3. SCATTERING FROM TWO ILLUMINATED SCATTERERS 73
3.1. Introduction 73
3.2. Integral equations and method of moments 75
3.2.1. Integral equations for two scatterers 75
3.2.2. Method of moments for two scatterers 77
3.2.3. Method of moments for P scatterers 84
3.3. Efficient inversion of the impedance matrix: E-PILE method for two scatterers 86
3.3.1. Mathematical formulation 86
3.3.2. Numerical results 89
3.4. E-PILE method combined with PO and FB 94
3.4.1. E-PILE hybridized with FB 94
3.4.2. E-PILE hybridized with PO 96
3.5. Conclusion 107
CHAPTER 4. SCATTERING FROM TWO SCATTERERS WHERE ONLY ONE IS ILLUMINATED 109
4.1. Introduction 109
4.2. Integral equations and method of moments 110
4.2.1. Integral equations 110
4.2.2. Method of moments 113
4.2.3. Case for which scatterer 2 is perfectly conducting 116
4.2.4. Numerical results 117
4.3. Efficient inversion of the impedance matrix: PILE method 122
4.3.1. Mathematical formulation 122
4.3.2. Numerical results 123
4.4. PILE method combined with FB or PO 128
4.4.1. PILE hybridized with FB 128
4.4.2. PILE hybridized with PO 130
4.5. Conclusion 138
APPENDIX MATLAB CODES 139
BIBLIOGRAPHY 141
INDEX 147