Permittivity Profile Reconstructions Using Transient Electromagnetic Reflection Data

Abstract

This paper is concerned with the permittivity reconstruction of inhomogeneous dielectric media. The method applies to profiles that vary with depth only, i.e., it provides a one-dimensional profile reconstruction. The data are collected and analyzed in the time domain. In the first part of the paper the theory of the method is reviewed. It is shown that a finite time trace of reflection data suffices to uniquely reconstruct the permittivity profile of the medium. The latter part of the paper presents the experimental set-up and contains also a thorough discussion of the errors that affect the measurements. The inverse scattering algorithm that is used is either based upon an imbedding procedure or on a Green functions approach. The input to either of these algorithms is the reflection kernel or the impulse response of the medium, i.e., the delta function response of the medium. Therefore, a deconvolution of the the measured reflected field and the incident field must be performed. This deconvolution problem is also addressed briefly in this paper.