This paper studies the direct scattering and inverse source problems for an one-dimensional inhomogeneous slab. The method used is the time domain wave splitting and invariant imbedding technique. For the case when the internal source j is a product, i.e., j(x,s) equals D(x) i(s)Y, a new current scattering operator J that maps the function i(s) into the scattered waves at the boundaries of the slab is defined. A system of coupled nonlinear integrodifferential equations for the current scattering operator kernel J(x,s) and the reflection operator kernel R(x,s) is derived. The inverse source problem solved in this paper is recovering the source space distribution function D(x) from the given permittivity profile and current scattering operator kernel J(0,s) for 0 <EQ s <EQ 1. Numerical results of the computation of the J kernel and the reconstruction of D(x) are presented.

Date Published: 29 December 1992
PDF: 8 pages
Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992); doi: 10.1117/12.139025

Published in SPIE Proceedings Vol. 1767:
Inverse Problems in Scattering and Imaging
Michael A. Fiddy, Editor(s)