Determination of index profiles by time domain reflectometry
Résumé
A numerical approach of the reconstruction of an inhomogeneous slab is described, the relative permittivity or the index of which are unknown. This one-dimensional dielectric medium is assumed to be linear, isotropic and non-magnetic, its conductivity being known, generally equal to zero. Its frequency independent permittivity arbitrarily varies, normally to its interfaces. A TEM plane wave of arbitrary causal time dependence illuminates this slab. A solution of this inverse problem is based upon a space-time discretization of a field integral formulation, in time-domain. A checked iterative process makes it possible to determine the index profile step by step. Some examples are given to illustrate the main features of this reconstruction method; simulation of experimental errors is considered with a special attention.