REFERENCES

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Tsang, L., J. A. Kong, ami R. T. Shin (1985), Th.eory of Microwave Remote Sensing, WileyInterscience, New York. Tsang, L., C, Mandt, and K. H. Ding (1992), Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations, Optics Lett., 17(5), 314-316, Twersky, V. (1962), On scattering of waves by random distributions I. Free space scatterer formalism, J. Math, Phys., 3, 700-715, Twersky, V. (1964), On propagation in random media of scatterers, Proc. Symp. Appl. Math., 16,84-116, Am, Math, Soc., Providence, RI. Twersky, V. (1977), Coherent scalar field in pair-correlated random distributions of aligned scatterers, J. Math. Ph.ys., 18, 2468-2486. Twersky, V. (1978), Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers, J. Math. Phys" 19, 215-230. van Albada, M. P., B. A. van Tiggelen, A. Langendijk, and A. Tip (1991), Speed of propagation of classical waves in strongly scattering media, Phys. Rev. Lett., 66(24), 3132-3135, Varadan, V. K., V. N. Bringi, V. A. Vamdan, and A. Ishimaru (1983), Multiple scattering theory for waves in discrete random media and comparison with experiments, Radio Sci., 18, 321-327. Waterman. P. C. (1965), IVlatrix formulation of electromagnetic scattering, Pmc. IEEE, 53, 805-811. Waterman, P. C., and R. Truell (1961), I\lllltiple scattering of waves, J. Math. Phys., 2(4), 512-537, West, R., D, Gibbs, L. Tsang, and A. K. Fung (1994), Comparison of optical scattering experiments and the quasi-crystalline approximation for dense media, J. Opt. Soc. Am., 11(6),1854-1858, West, R., L. Tsang, and D. P. Winebrenner (1993), Dense medium radiative transfer theory for two scattering layers with a Kayleigh distribution of particle sizes, IEEE Trans. Geosci. Remote Sen~., 31,426-437. Winebrenner, D. P., L. Tsang, B. Wen, and R. West (1989), Sea-ice characterization meaHurements needed for testing of microwave remote Hensing modelH, IEEEJ. Ocean. Eng., 14(2),149-158, Winebrenner, D. P., L. Tsang, B. Wen, and R. West (1992), Sensitivities for two polarimetric backscattering models for sea ice to geophysical parameters, in DiT'eet and Inverse Methods in Radar Polarimetry, Part 2, edited by W. Boerner, 1191-1212, Kluwer Academic Publishers, The Netherlands. Zurk, L. M. (1995), Electromagnetic wave propagation and scattering in dense, discrete random media with application to remote Hensing of snow, Ph.D. thesiH, University of Washington, Seattle. Zurk, L. IV1., L. THang, K. H. Ding, and D. P. Winebrenner (1995), Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and non-clustered geometries, J. Opt. Soc. Am., 12(8), 1772-1781. Zurk, L. M., L. Tsang, and D. P. Winebrenner (1996), Scattering properties of dense media from Monte Carlo simulationH with applicatioll to active remote Hensing of HIIOW, Radio Sci., 31(4), 803-819, Zurk, L. M., L. Tsang, D. P. Winebrenner, .1. Shi, and R. E. Davis (1997), Electromagnetic scattering calculated from pair distributiou functions retrieved from planar snow sections, IEEE Trans. Geosci. Renwte Sens., 35(6),1419-1428.

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Scattering of Electromagnetic Waves: Advanced Topics. Leung Tsang, Jin Au Kong. Copyright 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38801-7 (Hardback); 0-471-22427-8 (Electronic)

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DENSE MEDIA SCATTERING

Introduction Effective Propagation Constants, Mean Green's Function, and Mean Field for Half-Space Discrete Random Medium of Multiple Species

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Derivation of Dense Media Radiative Transfer Equation 329 (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

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7 DENSE MEDIA SCATTERING

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In 5, Section 4, we showed that the QCA-CP on the Dyson's equation and the correlated ladder approximation on the Bethe-Salpeter equation obeys energy conservation. In this chapter, we derive the dense media radiative transfer equation (DMRT) rigorously from these two approximations for the case of small dielectric scatterers. We consider dense discrete random media with multiple species of particles. The multiple species refers to the fact that the medium is a mixture of particles with different sizes and permittivities. The governing equations of Dyson's equation under QCA-CP approximation and the Bethe-Salpeter equation under the correlated ladder approximation for multiple species of particles that are correlated in positions. Expressions for the mass operator and the intensity operator are given. In Section 2, we calculate the effective propagation constants, the mean Green's function, and the mean field for a half-space discrete random medium of multiple species based on QCA-CP. In Section 3, we derive rigorously the dense media radiative transfer equations as well as the boundary conditions from the integral form of the correlated ladder approximation of multiple species. The pair distribution functions of multiple species are calculated by using the Percus-Yevick equation for noninterpenetrable spheres. The final results of dense media radiative transfer equations for active and passive remote sensing are respectively in Sections 4 and 6. All four Stokes parameters are included so that the results are applicable to polarimetric remote sensing of dense media. The numerical results of dense media radiative transfer equations for active and passive remote sensing are illustrated in Section 7 for media with non-sticky particles of multiple sizes and permittivities. The input physical parameters of the dense medium radiative transfer theory are the background medium permittivity, the particles permittivities, and their size distributions. Dense media scattering is a subject of continual interests because of the importance of the effects from the correlation of scatterers [Tsang and Kong, 1980, 1982; Tsang, 1987, 1991; Ding and Tsang, 1988]. It is also important in the subject of backscattering enhancement and wave localization [Tsang and Ishimaru, 1984; Barabanenkov et al. 1991a,b; Barabanenkov and Kryukov, 1992; Sheng, 1990, 199~.

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