Electromagnetic Wave Scattering by Discrete Random Media with Remote Sensing Applications

The scattering of electromagnetic waves in medium with randomly distributed discrete scatterers is studied. Analytical and numerical solutions to several problems with implications for the active and passive remote sensing of the Earth environment are obtained. The quasi-magnetostatic (QMS) solution for a conducting and permeable spheroid under arbitrary excitation is presented. The spheroid is surrounded by a weakly conducting background medium. The magnetic field inside the spheroid satisfies the vector wave equation, while the magnetic field outside can be expressed as the gradient of the Laplace solution. We solve this problem exactly using the separation of variables method in spheroidal coordinates by expanding the internal field in terms of vector spheroidal wavefunctions. The exact formulation works well for low to moderate frequencies; however, the solution breaks down at high frequency due to numerical difficulty in computing the spheroidal wavefunctions. To circumvent this difficulty, an approximate theory known as the small penetration-depth approximation (SPA) is developed. The SPA relates the internal field in terms of the external field by making use of the fact that at high frequency, the external field can only penetrate slightly into a thin skin layer below the surface of the spheroid. For spheroids with general permeability, the SPA works well at high frequency and complements the exact formulation. However, for high permeability, the SPA is found to give accurate broadband results. By neglecting mutual interactions, the QMS frequency response from a collection of conducting and permeable spheroids is also studied. In a dense medium, the failure to properly take into account of multiple scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by dense packed dielectric spheroids is studied both numerically through Monte Carlo simulations and analytically through the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. 3 In the numerical simulations, the Metropolis shuffling method is used to generate realizations of configurations for non-interpenetrable spheroids. The multiple scattering problem is formulated with the volume integral equation and solved using the method of moments with electrostatic basis functions. General expressions for the self-interaction elements are obtained using the low-frequency expansion of the dyadic Green’s function, and radiative correction terms are included. Results of scattering coefficient, absorption coefficient, and scattering matrix for spheroids in random and aligned orientation configurations are presented. It is shown that independent scattering approximation can give grossly incorrect results when the fractional volume of the spheroids is appreciable. In the analytical approach, only spheroids in the aligned configuration are solved. Low-frequency QCA and QCA-CP solutions are obtained for the average Green’s function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green’s function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the MaxwellGarnett mixing formula. QCA gives identical result to the mixing formula, while QCA-CP gives slightly higher values. The extinction coefficients from QCA and QCA-CP are compared with results from Monte Carlo simulations. Both QCA and QCA-CP agree well with simulations, although qualitative disagreement is evident at higher fractional volumes. QCA can also be used with Mie scattering to yield solution that is valid for particle sizes comparable to or larger than the wavelength. This formulation is used to investigate thermal emission from sea foam, which is modeled here as a layer of randomly distributed air bubbles coated with sea water. The extinction behavior of sea foam is illustrated, and the extinction is shown to be dominated by absorption. Using QCA-derived parameters, the radiative transfer equation is solved. The brightness temperatures of the sea foam are presented as a function of observation angle and frequency. Large-scale rough ocean effects are also considered using a simple geometric tilting model. The final result is found by averaging the brightness temperatures over the Cox-Munk slope distribution. Thus a physical model of foam emission is obtained that relates observed brightness temperatures to the microstructure of foam as well as ocean surface wind vector. Thesis Supervisor: Jin Au Kong Title: Professor, Department of Electrical Engineering and Computer Science