Modified gradient profile inversion using multi-frequency data

A method for reconstructing the complex permittivity of a bounded inhomogeneous object from measured scattered field data is presented. Consider the scattering object to be an inhomogeneous lossy dielectric cylinder of arbitrary cross-section embedded in a bounded domain D of free space. The incident excitation consists of electromagnetic waves with the electric field vector polarized along the cylinder axis. To reconstruct the permittivity and conductivity of an unknown scatterer from a knowledge of the scattered field we assume that the object is illuminated successively by a number of line sources at different locations and different frequencies. For each excitation we then have a scalar problem. We assume that, for the description of the material dispersion, the Maxwell model holds. We then introduce the frequency dependent contrast.