Method of Moments for 2D Scattering Problems

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.

Auteur

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.

Résumé

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.

Contenu

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

1.3. Method of moments with point-matching method 12

1.4. Application to a surface 14

1.5. Forward-Backward (FB) method 19

1.6. Random rough surface generation 21

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

2.4. PO approximation 55

2.5. FB method 69

2.6. Conclusion 71

CHAPTER 3. SCATT…