Two-dimensional inverse scattering problems connected with bodies buried in a slab

A general theory of two-dimensional scalar inverse scattering problem, whose aim is to recover the geometrical as well as the physical (electromagnetic) properties of a cylindrical body buried in a slab, is established through a continuous spectral representation of the scattered field. The slab as well as the half-spaces below and above it are supposed to be filled with non-magnetic lossless simple materials. Then the theory permits one to determine with Born approximation the permittivity and conductivity of the body which is also supposed to be non-magnetic. The reflections from two sides of the slab give rise to the interaction of the body in the spectral domain with four waves, which makes the problem interesting from both mathematical and physical points of view. An illustrative example shows the practical applicability of the theory.