Time-domain techniques for reconstructing lossy layered media from one-sided scattering

Abstract

The electromagnetic (EM) inverse scattering problem under consideration is to compute the parameter profile (i.e., permittivity, attenuation constant, thickness) of a layered dielectric from scattering data (i.e., reflection response to an impulsive plane wave). It is well known that EM plane wave propagation through a dielectric varying in only one dimension can be modeled as voltage or current propagation through a 1-D transmission line. Furthermore, a media consisting of a stack of homogeneous but parametrically different dielectric layers can be modeled as a discrete transmission line. Here, we model the lossy layered dielectric as an asymmetric discrete lattice filter and employ digital signal processing (DSP) techniques to the reconstruction of the media. Often, it is not practical or even possible to measure the two-sided scattering of a media (e.g., soils, forest canopies, walls). This is the problem under consideration in this paper. We present a discussion and comparison of two algorithms for reconstructing lossy layered media from one-sided time-domain plane wave impulse reflection responses. Unique features of these algorithms are that they: (1) have their origins in DSP theory; (2) are fast algorithms that have been modified to solve both the forward and inverse scattering problem; (3) solve the scattering problems exactly, including accounting for multiple reflections; and (4) solve the lossy media problem using only one-sided impulse reflection response data. In addition, the algorithm stability and time sampling constraints are introduced.