Electromagnetic Wave Scattering from Random Rough Surfaces (eBook)

Dr. Nicolas Pinel is PhD in the Radar team of IREENA Laboratory at University of? Nantes Angers Le Mans, France. Christophe Bourlier is works at IREENA (Institut de Recherche en Electrotechnique et Electronique de Nantes Atlantique, France) Laboratory, University of Nantes, France.

PREFACE ix

INTRODUCTION x

CHAPTER 1. ELECTROMAGNETIC WAVE SCATTERING FROM RANDOM ROUGH
SURFACES: BASICS 1

1.1. Introduction 1

1.2. Generalities 2

1.2.1. Maxwell equations and boundary conditions 2

1.2.2. Propagation of a plane wave (Helmholtz equation and plane
wave) 5

1.2.3. Incident wave at an interface: polarization 7

1.3. Random rough surfaces: statistical description and
electromagnetic roughness 12

1.3.1. Statistical description of random rough surfaces 12

1.3.2. Specific case of sea surfaces 19

1.3.3. Electromagnetic roughness and Rayleigh roughness
criterion 21

1.4. Scattering of electromagnetic waves from rough surfaces:
basics 28

1.4.1. Presentation of the problem (2D/3D) 28

1.4.2. Huygens' principle and extinction theorem 30

1.4.3. Green functions (2D/3D) 33

1.4.4. Scattered powers and scattering coefficients 36

CHAPTER 2. DERIVATION OF THE SCATTERED FIELD UNDER ASYMPTOTIC
MODELS 41

2.1. Bibliography on existing models 42

2.1.1. Introduction 42

2.1.2. Rigorous models 43

2.1.3. Asymptotic models 44

2.1.4. General properties of scattering 52

2.1.5. A few details on the KA and the GO 55

2.2. Scattering in reflection and transmission under the KA with
shadowing effect 58

2.2.1. KA in reflection and transmission with shadowing effect
for 2D problems 58

2.2.2. Extension of the KA model to 3D problems 62

2.3. Scattering in reflection for 3D problems under various
asymptotic models 69

2.3.1. Context and specific notations 69

2.3.2. The small perturbation model 71

2.3.3. The Kirchhoff approximation-high-frequency regime
73

2.3.4. The weighted curvature approximation 75

2.3.5. The small slope approximation 75

2.3.6. The local curvature approximation 76

2.3.7. The resonant curvature approximation 76

2.3.8. Validation of the different asymptotic numerical models
for 2D problems 77

CHAPTER 3. DERIVATION OF THE NORMALIZED RADAR CROSS-SECTION
UNDER ASYMPTOTIC MODELS 81

3.1. Derivation of incoherent normalized radar cross-section
under the GO for 2D problems 82

3.1.1. Incoherent NRCS under the GO with shadowing effect for 2D
problems 82

3.1.2. Calculation of the bistatic shadowing functions in
reflection and transmission 86

3.2. General properties and energy conservation of the GO for 2D
problems 97

3.2.1. General properties of the GO for 2D problems 97

3.2.2. Study of energy conservation under the GO for 2D problems
99

3.3. Scattering coefficients under the GO with shadowing effect
for 3D problems 108

3.4. Energy conservation of the GO model for 3D problems 111

3.4.1. Case of a perfectly conducting lower medium 112

3.4.2. Case of a lossless dielectric lower medium 115

3.5. Scattering in reflection for 3D problems under various
asymptotic models 117

3.5.1. Expression of the NRCS under the SPM1 118

3.5.2. Expression of the NRCS under the GO 118

3.5.3. Expression of the NRCS under the SSA 119

3.5.4. Validation and comparison of the different asymptotic
analytical models for 2D problems 119

3.5.5. Comparison between numerical and analytical asymptotic
models for 3D problems 121

APPENDIX 1. FAR-FIELD SCATTERED FIELDS UNDER THE METHOD OF
STATIONARY PHASE 125

APPENDIX 2. CALCULATION OF THE SCATTERING COEFFICIENTS UNDER
THE GO FOR 3D PROBLEMS 131

BIBLIOGRAPHY 137

INDEX 149