Scattering, Natural Surfaces, and Fractals

Scattering, Natural Surfaces, and Fractals

1st Edition - December 8, 2006

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  • Authors: Giorgio Franceschetti, Daniele Riccio
  • eBook ISBN: 9780080469010

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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 “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.

Key Features

  • 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


Geoscience and remote sensing technical and scientific community ie. engineers, physicists, geologists, applied mathematicians, earth scientists, graduate courses on electromagnetic scattering and remote sensing.

Table of Contents

    • Dedication
    • Preface
    • Chapter 1: The Scattering Problem
      • 1.1 Introduction and Chapter Outline
      • 1.2 The Scattering-Problem Definition
      • 1.3 Motivations
      • 1.4 Surface Models and Electromagnetic Methods
      • 1.5 Deterministic versus Stochastic Models for the Natural Surfaces
      • 1.6 Deterministic versus Stochastic Evaluation for the Scattered Field
      • 1.7 Analytic versus Numerical Evaluation of the Scattered Field
      • 1.8 Closed-Form Evaluation of the Electromagnetic Field Scattered from a Natural Surface
      • 1.9 Book Outline
      • 1.10 References and Further Readings
    • Chapter 2: Surface Classical Models
      • 2.1 Introduction and Chapter Outline
      • 2.2 Fundamentals of Stochastic Processes
      • 2.3 Spectral Characterization of Stochastic Processes
      • 2.4 Isotropic Surfaces
      • 2.5 Classical Models for Natural Surfaces: First-Order Stochastic Characterization
      • 2.6 Classical Models for Natural Surfaces: Second-Order Stochastic Characterization
      • 2.7 Physical Counterpart of Natural-Surfaces Classical Parameters
      • 2.8 Surface Classical Models Selection for Electromagnetic Scattering
      • 2.9 References and Further Readings
      • Appendix 2.A Surface Classical Models
    • Chapter 3: Surface Fractal Models
      • 3.1 Introduction and Chapter Outline
      • 3.2 Fundamentals of Fractal Sets
      • 3.3 Mathematical versus Physical Fractal Sets
      • 3.4 Deterministic versus Stochastic Fractal Description of Natural Surfaces
      • 3.5 Fractional Brownian Motion Process
      • 3.6 Weierstrass-Mandelbrot Function
      • 3.7 Connection between fBm and WM Models
      • 3.8 A Chosen Reference Fractal Surface for the Scattering Problem
      • 3.9 Fractal-Surface Models and their Comparison with Classical Ones
      • 3.10 References and Further Readings
      • Appendix 3.A Generalized Functions
      • Appendix 3.B Space-Frequency and Space-Scale Analysis of Nonstationary Signals
    • Chapter 4: Analytic Formulations of Electromagnetic Scattering
      • 4.1 Introduction and Chapter Outline
      • 4.2 Maxwell Equations
      • 4.3 The Integral-Equation Method
      • 4.4 Incident and Scattered-Field Coordinate-Reference Systems
      • 4.5 The Kirchhoff Approximation
      • 4.6 Physical-Optics Solution
      • 4.7 Extended-Boundary-Condition Method
      • 4.8 Small-Perturbation Method
      • 4.9 References and Further Readings
    • Chapter 5: Scattering from Weierstrass-Mandelbrot Surfaces: Physical-Optics Solution
      • 5.1 Introduction and Chapter Outline
      • 5.2 Analytic Derivation of the Scattered Field
      • 5.3 Scattered-Field Structure
      • 5.4 Limits of Validity
      • 5.5 Influence of Fractal and Electromagnetic Parameters over the Scattered Field
      • 5.6 Statistics of the Scattered Field
      • 5.7 References and Further Readings
    • Chapter 6: Scattering from Fractional Brownian Surfaces: Physical-Optics Solution
      • 6.1 Introduction and Chapter Outline
      • 6.2 Scattered Power-Density Evaluation
      • 6.3 Scattered Power Density
      • 6.4 Scattered Power Density: Special Cases
      • 6.5 Backscattering Coefficient
      • 6.6 Validity Limits
      • 6.7 Influence of Fractal and Electromagnetic Parameters over the Scattered Field
      • 6.8 References and Further Readings
    • Chapter 7: Scattering from Weierstrass-Mandelbrot Profiles: Extended-Boundary-Condition Method
      • 7.1 Introduction and Chapter Outline
      • 7.2 Profile Model
      • 7.3 Setup of the Extended-Boundary-Condition Method
      • 7.4 Surface-Fields Evaluation
      • 7.5 Fields Expansions
      • 7.6 EBCM Equations in Matrix Form
      • 7.7 Matrix-Equations Solution
      • 7.8 Matrices Organizations
      • 7.9 Scattering-Modes Superposition, Matrices Truncation, and Ill-Conditioning
      • 7.10 Influence of Fractal and Electromagnetic Parameters over the Scattered Field
      • 7.11 References and Further Readings
      • Appendix 7.A Evaluation of the Dirichlet- and Neumann-Type Integrals
    • Chapter 8: Scattering from Fractional Brownian Surfaces: Small-Perturbation Method
      • 8.1 Introduction and Chapter Outline
      • 8.2 Rationale of the SPM Solution
      • 8.3 Extended Boundary Condition Method in the Transformed Domain
      • 8.4 Set up the Small Perturbation Method
      • 8.5 An Appropriate Coordinate System
      • 8.6 Zero-order Solution
      • 8.7 First-order Solution
      • 8.8 Small Perturbation Method Limits of Validity
      • 8.9 Influence of Fractal and Electromagnetic Parameters Over the Scattered Field
      • 8.10 References and Further Readings
    • Appendix A: Mathematical Formulae
    • Glossary
    • References
    • Index

Product details

  • No. of pages: 304
  • Language: English
  • Copyright: © Academic Press 2006
  • Published: December 8, 2006
  • Imprint: Academic Press
  • eBook ISBN: 9780080469010

About the Authors

Giorgio Franceschetti

Giorgio Franceschetti was appointed professor of Electromagnetic Theory at the University Federico II of Napoli, Italy in 1969, a position that he holds to this day. He has been Fulbright Scholar and Research Associate at Caltech, Visiting Professor at the University of Illinois, at UCLA, at the Somali University (Somalia) and at the University of Santiago de Compostela (Spain). He is currently Adjunct Professor at UCLA, Distinguished Visiting Scientist at JPL and Lecturer at the Top-Tech Master of University of Delft, The Netherlands, in Satellite Navigation.

Affiliations and Expertise

JPL - Jet Propulsion Laboratory , Pasadena, CA, U.S.A.

Daniele Riccio

Daniele Riccio is professor of Electromagnetic Theory at the University of Napoli Federico II, Italy where he teaches courses on Applied Electromagnetic and Remote Sensing. He has also been Guest Scientist at DLR, Munich, Germany and Visiting Professor at UPC, Barcelona, Spain. The material of this book is included in the courses that he delivers at University.

Affiliations and Expertise

Università "Federico II" di Napoli, Italy

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