Scattering, Natural Surfaces, and Fractals (eBook)

Giorgio Franceschetti, Daniele Riccio (Autoren)

eBook Download: PDF

2006 | 1. Auflage
304 Seiten
Elsevier Science (Verlag)
978-0-08-046901-0 (ISBN)

Infos

This book provides a comprehensive overview of electromagnetic scattering from natural surfaces, ranging from the classical to the more recent (fractal) approach. As remote sensing applications become increasingly important, this text provides readers with a solid background in interpretation, classification and thematization of microwave images. The scattering problem is discussed in detail with emphasis on its application to electromagnetic wave propagation, remote sensing, radar detection, and electromagnetic diagnostics. Natural surface and fractals complete this treatise focusing on how the fractal model represents our natural environment and other planets in our solar system, most recently as used to research the planet Venus and Titan, one of the moons of Saturn. An example of how scattering, fractals, and natural surfaces are of great importance is the following: Natural oil slicks in the ocean have been found to be fractal while man-made ones (generated by illegal washing of oil carrying ships) are not. Processing of an ocean image from space may detect the latter by means of a fractal analysis.

*An elegant and clear treatment of a rigorous topic with informative prose and realistic illustrations of scattering
*Provides readers with a solid background in interpretation, classification, and thematization of microwave images
*The only book available on fractal models and their application to scattering

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Scattering, Natural Surfaces, and Fractals provides a comprehensive overview of electromagnetic scattering from natural surfaces, ranging from the classical to the more recent (fractal) approach. As remote sensing applications become increasingly important, this text provides readers with a solid background in interpretation, classification and thematization of microwave images. The "e;scattering problem is discussed in detail with emphasis on its application to electromagnetic wave propagation, remote sensing, radar detection, and electromagnetic diagnostics. Natural surface and fractals complete this treatise focusing on how the fractal model represents our natural environment and other planets in our solar system, most recently as used to research the planet Venus and Titan, one of the moons of Saturn. An example of how scattering, fractals, and natural surfaces are of great importance is the following: Natural oil slicks in the ocean have been found to be fractal while man-made ones (generated by illegal washing of oil carrying ships) are not. Processing of an ocean image from space may detect the latter by means of a fractal analysis. - An elegant and clear treatment of a rigorous topic with informative prose and realistic illustrations of scattering- Provides readers with a solid background in interpretation, classification, and thematization of microwave images- The only book available on fractal models and their application to scattering

Inhalt

Front cover 1
Scattering, Natural Surfaces and Fractals 4
Copyright page 5
Table of contents 8
Preface 14
Chapter 1. The Scattering Problem 18
1.1. Introduction and Chapter Outline 18
1.2. The Scattering-Problem Definition 19
1.3. Motivations 20
1.4. Surface Models and Electromagnetic Methods 21
1.5. Deterministic versus Stochastic Models for the Natural Surfaces 22
1.6. Deterministic versus Stochastic Evaluation for the Scattered Field 26
1.7. Analytic versus Numerical Evaluation of the Scattered Field 29
1.8. Closed-Form Evaluation of the Electromagnetic Field Scattered from a Natural Surface 31
1.9. Book Outline 35
1.10. References and Further Readings 36
Chapter 2. Surface Classical Models 38
2.1. Introduction and Chapter Outline 38
2.2. Fundamentals of Stochastic Processes 39
2.3. Spectral Characterization of Stochastic Processes 43
2.4. Isotropic Surfaces 47
2.5. Classical Models for Natural Surfaces: First-Order Stochastic Characterization 50
2.6. Classical Models for Natural Surfaces: Second-Order Stochastic Characterization 51
2.7. Physical Counterpart of Natural-Surfaces Classical Parameters 57
2.8. Surface Classical Models Selection for Electromagnetic Scattering 61
2.9. References and Further Readings 61
Appendix 2.A Surface Classical Models 62
Chapter 3. Surface Fractal Models 78
3.1. Introduction and Chapter Outline 78
3.2. Fundamentals of Fractal Sets 80
3.3. Mathematical versus Physical Fractal Sets 85
3.4. Deterministic versus Stochastic Fractal Description of Natural Surfaces 88
3.5. Fractional Brownian Motion Process 89
3.6. Weierstrass-Mandelbrot Function 111
3.7. Connection between fBm and WM Models 115
3.8. A Chosen Reference Fractal Surface for the Scattering Problem 117
3.9. Fractal-Surface Models and their Comparison with Classical Ones 118
3.10. References and Further Readings 123
Appendix 3.A Generalized Functions 123
Appendix 3.B Space-Frequency and Space-Scale Analysis of Nonstationary Signals 124
Chapter 4. Analytic Formulations of Electromagnetic Scattering 132
4.1. Introduction and Chapter Outline 132
4.2. Maxwell Equations 133
4.3. The Integral-Equation Method 135
4.4. Incident and Scattered-Field Coordinate-Reference Systems 142
4.5. The Kirchhoff Approximation 145
4.6. Physical-Optics Solution 149
4.7. Extended-Boundary-Condition Method 151
4.8. Small-Perturbation Method 155
4.9. References and Further Readings 157
Chapter 5. Scattering from Weierstrass-Mandelbrot Surfaces: Physical-Optics Solution 160
5.1. Introduction and Chapter Outline 160
5.2. Analytic Derivation of the Scattered Field 161
5.3. Scattered-Field Structure 165
5.4. Limits of Validity 173
5.5. Influence of Fractal and Electromagnetic Parameters over the Scattered Field 174
5.6. Statistics of the Scattered Field 186
5.7. References and Further Readings 187
Chapter 6. Scattering from Fractional Brownian Surfaces: Physical-Optics Solution 188
6.1. Introduction and Chapter Outline 188
6.2. Scattered Power-Density Evaluation 189
6.3. Scattered Power Density 196
6.4. Scattered Power Density: Special Cases 197
6.5. Backscattering Coefficient 199
6.6. Validity Limits 201
6.7. Influence of Fractal and Electromagnetic Parameters over the Scattered Field 203
6.8. References and Further Readings 208
Chapter 7. Scattering from Weierstrass-Mandelbrot Profiles: Extended-Boundary-Condition Method 210
7.1. Introduction and Chapter Outline 210
7.2. Profile Model 212
7.3. Setup of the Extended-Boundary-Condition Method 213
7.4. Surface-Fields Evaluation 221
7.5. Fields Expansions 222
7.6. EBCM Equations in Matrix Form 224
7.7. Matrix-Equations Solution 226
7.8. Matrices Organizations 227
7.9. Scattering-Modes Superposition, Matrices Truncation, and Ill-Conditioning 230
7.10. Influence of Fractal and Electromagnetic Parameters over the Scattered Field 232
7.11. References and Further Readings 246
Appendix 7.A Evaluation of the Dirichlet- and Neumann-Type Integrals 247
Chapter 8. Scattering from Fractional Brownian Surfaces: Small-Perturbation Method 256
8.1. Introduction and Chapter Outline 256
8.2. Rationale of the SPM Solution 257
8.3. Extended Boundary Condition Method in the Transformed Domain 260
8.4. Set up the Small Perturbation Method 265
8.5. An Appropriate Coordinate System 268
8.6. Zero-order Solution 269
8.7. First-order Solution 273
8.8. Small Perturbation Method Limits of Validity 277
8.9. Influence of Fractal and Electromagnetic Parameters Over the Scattered Field 279
8.10. References and Further Readings 284
Appendix A. Mathematical Formulae 286
Appendix B. Glossary 290
Appendix C. References 294
Index 300

Produkt-Details

• Erscheint lt. Verlag: 8.12.2006
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• ISBN-10: 0-08-046901-9 / 0080469019
• ISBN-13: 978-0-08-046901-0 / 9780080469010