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Contact Functions of Two Ellipsoids Illustrations of Contact Functions
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5.1 5.2
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References and Additional Readings
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Extinction as a Function of Concentration Extinction as a Function of Frequency
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Random Positions of Cylinders
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458 Simulations of Pair Distribution Functions 460 Percus-Yevick Approximation of Pair Distribution Functions 461 Results of Simulations 463 Monte Carlo Simulations of Sticky Disks 463
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Monte Carlo Simulations of Scattering by Cylinders
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Scattering by a Single Cylinder Foldy-Lax Multiple Scattering Equations for Cylinders Coherent Field, Incoherent Field, and Scattering Coefficient Scattered Field and Internal Field Formulations Low Frequency Formulas Independent Scattering Simulation Results for Sticky and Non-Sticky Cylinders
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3.1 3.2 3.3 3.4 3.5 3.6 3.7
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Sparse-Matrix Canonical-Grid Method for Scattering by Many Cylinders 486
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4.1 4.2 4.3
The Two-Dimensional Scattering Problem of Many Dielectric 489 Cylinders Numerical Results of Scattering and CPU Comparisons
References and Additional Readings
2.1 2.2 2.3 2.4
495 496 496
496 500 505 510
Introduction Simple Analytical Models For Scattering From a Dense Medium
Effective Permittivity Scattering Attenuation and Coherent Propagation Constant Coherent Reflection and Incoherent Scattering From a Half-Space of Scatterers A Simple Dense Media Radiative Transfer Theory
3.1 3.2 3.3
Simulations Using Volume Integral Equations
Volume Integral Equation Simulation of Densely Packed Dielectric Spheres Densely Packed Spheroids
512 514 518
4.1 4.2 4.3 4.4
Numerical Simulations Using T-Matrix Formalism
Multiple Scattering Equations Computational Considerations Results and Comparisons with Analytic Theory Simulation of Absorption Coefficient
533 541 545 547
551 552 553
553 553 555
Introduction Two-Dimensional Simulations of Angular Memory Effect and Detection of Buried Object
Introduction Simple and General Derivation of Memory Effect ACF of Random Rough Surfaces with Different Averaging Methods
2.1 2.2 2.3
Scattering by a Buried Object Under a Rough Surface
Angular Correlation Function of Scattering by a Buried Object Under a 2-D Random Rough Surface (3-D Scattering)
Introduction Formulation of Integral Equations Statistics of Scattered Fields Numerical Illustrations of ACF and PACF
564 565 570 571
3.1 3.2 3.3 3.4
4.1 4.2 4.3
Angular Correlation Function Applied to Correlation Imaging in Target Detection 575
Introduction Formulation of Imaging Simulations of SAR Data and ACF Processing 575 578 580
2.1 2.2 2.3
593 594
Scattering by Dielectric Cylinders Above a Dielectric Half-Space 594
Scattering from a Layer of Vertical Cylinders: First-Order Solution First- and Second-Order Solutions Results of Monte Carlo Simulations 594 603 613
3.1 3.2 3.3 3.4
Scattering by Cylinders in the Presence of Two Reflective Boundaries
Vector Cylindrical Wave Expansion of Dyadic Green's Function Between Two Perfect Conductors Dyadic Green's Function of a Cylindrical Scatterer Between Two PEC Dyadic Green's Function with Multiple Cylinders Excitation of Magnetic Ring Currents
622 629 631 635
3.4.1 First Order Solution 3.4.2 Numerical Results References and Additional Readings CHAPTER 13 ELECTROMAGNETIC WAVES SCATTERING BY VEGETATION 1 2 Introduction Plant Modeling by Using L-Systems
Lindenmayer Systems Turtle Interpretation of L-Systems Computer Simulations of Stochastic L-Systems and Input Files
637 638
641 642 644
2.1 2.2 2.3
644 646 649
Scattering from Trees Generated by L-Systems Based on Coherent Addition Approximation
Single Scattering by a Particle in the Presence of Reflective Boundary
3.1.1 Electric Field and Dyadic Green's Function 3.1.2 Scattering by a Single Particle
Scattering by Trees
655 655 656 659
667 669
Coherent Addition Approximation with Attenuation Scattering from Plants Generated by L-Systems Based on Discrete Dipole Approximation
Formulation of Discrete Dipole Approximation (DDA) Method Scattering by Simple Trees Scattering by Honda Trees
5.1 5.2 5.3
670 672 677
Rice Canopy Scattering Model
Model Description Model Simulation
6.1 6.2
685 689
691 693
References and Additional Readings INDEX
Scattering of Electromagnetic Waves
Volume I: Theories and Applications (Tsang, Kong, and Ding) Volume II: Numerical Simulations (Tsang, Kong, Ding, and Ao) Volume III: Advanced Topics (Tsang and Kong)
Electromagnetic wave scattering is an active, interdisciplinary area of research with myriad practical applications in fields ranging from atomic physics to medical imaging to geoscience and remote sensing. In particular, the subject of wave scattering by random discrete scatterers and rough surfaces presents great theoretical challenges due to the large degrees of freedom in these systems and the need to include multiple scattering effects accurately. In the past three decades, considerable theoretical progress has been made in elucidating and understanding the scattering processes involved in such problems. Diagrammatic techniques and effective medium theories remain essential for analytical studies; however, rapid advances in computer technology have opened new doors for researchers with the full power of Monte Carlo simulations in the numerical analysis of random media scattering. Numerical simulations allow us to solve the Maxwell equations exactly without the limitations of analytical approximations, whose regimes of validity are often difficult to assess. Thus it is our aim to present in these three volumes a balanced picture of both theoretical and numerical methods that are commonly used for tackling electromagnetic wave scattering problems. While our book places an emphasis on remote sensing applications, the materials covered here should be useful for students and researchers from a variety of backgrounds as in, for example, composite materials, photonic devices, optical thin films, lasers, optical tomography, and X-ray lithography. Introductory chapters and sections are also added so that the materials can be readily understood by graduate students. We hope that our book would help stimulate new ideas and innovative approaches to electromagnetic wave scattering in the years to come. The increasingly important role of numerical simulations in solving electromagnetic wave scattering problems has motivated us to host a companion web site that contains computer codes on topics relevant to the book. These computer codes are written in the MATLAB programming language and are available for download from our web site at They are provided to serve two main purposes. The first is to supply our readers a hands-on laboratory for performing numerical experiments, through which the concepts in the book can be more dynamically relayed. The second is to give new researchers a set of basic tools with which they could quickly build on projects of their own. The fluid nature of the web site would also allow us to regularly update the contents and keep pace with new research developments.
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