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Dyson's Equation for the Mean Field
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Bilocal Approximation Nonlinear Approximation
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Second Moment of the Field
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Bethe-Salpeter Equation Energy Conservation
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Strong Permittivity Fluctuations
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Random Medium with Spherically Symmetric Correlation Function Very Low Frequency Effective Permittivity Effective Permittivity Under the Bilocal Approximation Backscattering Coefficients
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Results of Effective Permittivity and Bistatic Coefficients
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3.1 3.2 3.3 3.4 3.5 3.6 3.7
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Transition Operator Multiple Scattering Equations Approximations of Multiple Scattering Equations
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Configurational Average of Multiple Scattering Equations Quasi-crystalline Approximation (QCA) Coherent Potential (CP) Quasi-crystalline Approximation with Coherent Potential (QCA-CP) Low-Frequency Solutions QCA-CP for Multiple Species of Particles
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Effective Field Approximation (EFA, Foldy's Approximation) 207
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Ward's Identity and Energy Conservation Derivation of Radiative Transfer Equation from Ladder Approximation References and Additional Readings
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CHAPTER 6 QUASI-CRYSTALLINE APPROXIMATION IN DENSE MEDIA SCATTERING 1 Scattering of Electromagnetic Waves from a Half-Space of Dielectric ScatterersNormal Incidence
Coherent Wave Propagation Effective Phase Velocity and Attenuation Rate in the Low-Frequency Limit Dispersion Relations at Higher Frequencies
247 257 259
1.1 1.2 1.3
Scattering of Electromagnetic Waves from a Half-Space of Dielectric ScatterersOblique Incidence Dispersion Relation and Coherent Reflected Wave Vertically and Horizontally Polarized Incidence Cases with Size Distributions Coherent Field Incoherent Field Using Distorted Born Approximation Dense Media Radiative Transfer Theory Based on Quasi-crystalline Approximation Phase Matrix, Extinction, Scattering, and Absorption Coefficients Brightness Temperature Computed with QCA-based DMRT Numerical Results for Sticky and Non-Sticky Particles References and Additional Readings
2.1 2.2
266 266
3.1 3.2
281 287
301 307 309
CHAPTER 7 DENSE MEDIA SCATTERING 1 2 Introduction Effective Propagation Constants, Mean Green's Function, and Mean Field for Half-Space Discrete Random Medium of Multiple Species Derivation of Dense Media Radiative Transfer Equation (DMRT) Dense Media Radiative Transfer Equations for Active Remote Sensing General Relation between Active and Passive Remote Sensing with Temperature Distribution Dense Media Radiative Transfer Equations for Passive Remote Sensing Numerical Illustrations of Active and Passive Remote Sensing References and Additional Readings
323 324
325 329
340 344
349 351 357
359 360
Volume Scattering Volume Scattering in the Presence of Reflective Boundary
1.1 1.2
361 362
Second-Order Volume Scattering Theory of Isotropic Point Scatterers 366 Summation of Ladder Terms and Cyclical Terms for Isotropic Point Scatterers
Formulation Numerical Illustrations
3.1 3.2
375 380
Anisotropic Scatterers and Diffusion Approximation
Summation of Ladder Terms and Cyclical Terms Unidirectional Point Source Green's Function Second-Order Multiple-Scattering Theory Diffusion Approximation Numerical Results
4.1 4.2 4.3 4.4 4.5
386 391 393 395 399
403 407
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 www.emwave.com. 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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