Retrieval of Parameters for Layered non-Smooth Interface Media: Theory and Experiment.

Abstract

Many naturally occurring or manmade objects can be modeled as three layer media with non-smooth interfaces. Most of the existing forward and inverse scattering models that can be applied to such media are either too inefficient or have limited regions of validity. In this dissertation an efficient forward scattering model based on the Extended Boundary Condition Method is developed for a three layer medium. The boundary between the first and the second layers is periodic while the boundary between the second and third layers is rough. The model is then extended by including an arbitrarily shaped cylinder placed into the third layer. Both TM and TE polarizations and PEC and Dielectric cylinder cases are considered. The Method of Moments (MOM) is used to obtain an impedance matrix, which is then transformed into a T-matrix. The T-matrix is transformed into a scattering matrix and cascaded with scattering matrices for the periodic and rough interfaces to obtain a generalized scattering matrix for the total system. A solution to the inverse problem for a three-layer medium is developed using simulated radar data. The retrieval of the layered- medium parameters is accomplished by sequential nonlinear optimizaxiii tion starting from the top layer and progressively characterizing the layers below. The optimization process is achieved by an efficient iterative technique built around the solution of the forward scattering problem. To be efficiently utilized in the inverse problem, the forward scattering model is simulated over a wide range of unknowns to obtain a complete set of subspace-based equivalent closed-form models that relate radar backscattering coefficients to the sought-for parameters, including the dielectric constants of each layer and the thickness of the middle layer. The inversion algorithm is implemented as a modified conjugate-gradient-based nonlinear optimization. It is shown that this technique results in accurate retrieval of surface and subsurface parameters, even in the presence of noise. To validate forward and inverse scattering models, a compact tower-based radar system is built. The data collected with the instrument is used to demonstrate sensitivity of radar measurements to changes in soil moisture and the potential for estimating surface and subsurface parameters.