Electromagnetic Wave Scattering from Random Rough Surfaces E-Book

Nicolas Pinel

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 217

Veröffentlichungsjahr: 2013

Beschreibung

Electromagnetic wave scattering from random rough surfaces is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing. Focusing on the case of random rough surfaces, this book presents classical asymptotic models used to describe electromagnetic wave scattering. The authors begin by outlining the basic concepts relevant to the topic before moving on to look at the derivation of the scattered field under asymptotic models, based on the Kirchhoff-tangent plane, in order to calculate both the scattered field and the statistical average intensity. More elaborated asymptotic models are also described for dealing with specific cases, and numerical results are presented to illustrate these models. Comparisons with a reference numerical method are made to confirm and refine the theoretical validity domains. The final chapter derives the expressions of the scattering intensities of random rough surfaces under the asymptotic models. Its expressions are given for their incoherent contributions, from statistical calculations. These results are then compared with numerical computations using a Monte-Carlo process, as well as with experimental models, for sea surface backscattering. Contents 1. Electromagnetic Wave Scattering from Random Rough Surfaces: Basics. 2. Derivation of the Scattered Field under Asymptotic Models. 3. Derivation of the Normalized Radar Cross-Section under Asymptotic Models. APPENDIX 1. Far-Field Scattered Fields under the Method of Stationary Phase. APPENDIX 2. Calculation of the Scattering Coefficients under the GO for 3D Problems. About the Authors Nicolas Pinel worked as a Research Engineer at the IETR (Institut d'Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) before joining Alyotech Technologies in Rennes, France, in July 2013. 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. Christophe Bourlier works at the IETR (Institut d'Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) and is also 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.

Leseprobe

Contents

Preface

Introduction

Chapter 1. Electromagnetic Wave Scattering from Random Rough Surfaces: basics

1.1. Introduction

1.2. Generalities

1.3. Random rough surfaces: statistical description and electromagnetic roughness

1.4. Scattering of electromagnetic waves from rough surfaces: basics

Chapter 2. Derivation of the Scattered Field Under Asymptotic Models

2.1. Bibliography on existing models

2.2. Scattering in reflection and transmission under the KA with shadowing effect

2.3. Scattering in reflection for 3D problems under various asymptotic models

Chapter 3. Derivation of the Normalized Radar Cross-Section Under Asymptotic Models

3.1. Derivation of incoherent normalized radar cross-section under the GO for 2D problems

3.2. General properties and energy conservation of the GO for 2D problems

3.3. Scattering coefficients under the GO with shadowing effect for 3D problems

3.4. Energy conservation of the GO model for 3D problems

3.5. Scattering in reflection for 3D problems under various asymptotic models

Appendix 1. Far-Field Scattered Fields under the Method of Stationary Phase

Appendix 2. Calculation of the Scattering Coefficients under the GO for 3D Problems

Bibliography

Index

First published 2013 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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© ISTE Ltd 2013

The rights of Nicolas Pinel and Christophe Bourlier to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013945049

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISSN: 2051-2481 (Print)ISSN: 2051-249X (Online)ISBN: 978-1-84821-471-2

Preface

This book is dedicated to young scientists who are entering the field of electromagnetic wave scattering from random rough surfaces. It presents classical asymptotic models used to describe the electromagnetic wave scattering from rough surfaces, and deals with the case of random rough surfaces, which can be described statistically. Focus is given to the Kirchhoff-tangent plane approximation, as well as its high-frequency further approximation. The derivations of classical asymptotic models (Kirchhoff-tangent plane approximation, small perturbation method, etc.) are given for calculating both the scattered field and the statistical average intensity. Their validity domains are given theoretically and are illustrated by comparison with a reference numerical method (Method of Moments) for 2D problems, and with experimental data for 3D problems. The description of numerical methods for 2D problems is the subject of a companion book (same editor) by Bourlier et al. [BOU 13] called Method of Moments for 2D Scattering Problems: Basic concepts and applications.

Our thanks go to several people who made this book possible. We are first grateful to Professor Joseph Saillard (retired) for suggesting the writing of this book, and to both Professors Joseph Saillard and Serge Toutain (retired) for giving us the means to develop this research. We would like to thank the University of Nantes and the National Centre for Scientific Research, our respective employers (at the time of writing) and the Army Research Office (DGA – Direction Générale des Armées) for their financial support.

Nicolas PinelChristophe BourlierSeptember 2013

Introduction

In this book, the problem of electromagnetic wave scattering from random rough surfaces is addressed by means of approximate models qualified as asymptotic. Both simple two-dimensional (2D) problems and more general three-dimensional (3D) problems are dealt with by focusing on a widely used model called the Kirchhoff-tangent plane approximation (KA). Other famous asymptotic models are presented and compared to one other, as well as a numerical reference method for 2D problems [BOU 13] or experimental data for 3D problems.

The first chapter recalls the basic, necessary concepts for dealing with electromagnetic wave scattering from random rough surfaces, using integral equations. First, it recalls the notions of Maxwell equations, plane wave propagation, polarization and Snell–Descartes laws. Second, it gives a statistical description of the heights of random rough surfaces. Finally, it gives the integral equations describing the electromagnetic scattering, and the necessary Green functions, for both 2D and 3D problems and introduces the concept of a normalized radar cross section (NRCS).

The second chapter describes classical asymptotic models used to estimate the field scattered by random rough surfaces, based on KA and the small perturbation method. Their theoretical validity domains are given. More elaborated asymptotic models are also described for dealing with specific cases, such as scattering from sea surfaces. Numerical results are presented to illustrate these models, and comparisons with a reference numerical method are made to confirm and refine the theoretical validity domains.

Finally, the third chapter derives the expressions of the random rough surfaces’ scattering intensities, called the normalized radar cross-section (NRCS), under the asymptotic methods described in the previous chapter. Its expressions are given for their incoherent contributions, from statistical calculations. Then, by assuming ergodic random processes, the numerical results of these asymptotic models are compared with results from a reference numerical method combined with a Monte Carlo process for 2D problems, by focusing on the case of sea surfaces. A comparison is also made with measurements for 3D problems.

1

Electromagnetic Wave Scattering from Random Rough Surfaces: Basics

This chapter recalls the basic necessary concepts for dealing with electromagnetic wave scattering from random rough surfaces, by using integral equations. First, it recalls the notions of Maxwell equations, plane wave propagation, polarization, Snell–Descartes laws. Second, it gives a statistical description of the heights of random rough surfaces and defines the concept of electromagnetic roughness through the Rayleigh roughness parameter. Last, it introduces the integral equations describing the electromagnetic scattering, and the necessary Green functions, for both 2D and 3D problems, and defines the notion of a normalized radar cross section.

1.1. Introduction

In this book, the incident wave illuminating the surfaces will be considered as a plane wave. A wave can be called locally plane if it is located in the so-called Fraunhofer zone1 of the transmitter source, or far-field zone of the source. This assumes that the source is far enough from the surface such that the incident wave may appear as a plane on a distance greater than any dimension of the surface [LYN 70a]. The media are assumed to be linear, homogeneous and isotropic (LHI), stationary and non-magnetic. The incident medium is perfectly dielectric2, and can be assimilated to vacuum in general, although we will endeavor to write the equations in the general case of any lossless perfect dielectric medium.

The problem of electromagnetic (EM) wave scattering from non-flat surfaces, called rough surfaces, has been studied for decades. In particular, let us quote the works of Lord Rayleigh [RAY 45, RAY 07], who was the first to give a rigorous definition of the EM roughness of a surface (characterized by the so-called Rayleigh roughness criterion, which will be detailed further). Among rough surfaces, two main categories may be distinguished: periodic surfaces (such as square surfaces, triangular surfaces, sawtooth surfaces and sinusoidal surfaces), which are deterministic, and random surfaces for which only some statistical features are known. This latter category is discussed in this book.