Electromagnetic prospection via homogeneous and inhomogeneous plane waves: The case of an embedded slab

This paper deals with the linear approximation of the inverse scattering problem for a dielectric slab embedded into a homogeneous half-space. After a proper normalization of the scattered field, the problem at hand is recognized to be related to a Fourier transform inversion with limited data. This permits to resort to the well-known results available in signal processing in order to discuss about the class of the retrievable unknowns and the resolution limits achievable by inversion. In particular, the role of both homogeneous and inhomogeneous incident plane waves in carrying out information about the profile under test is investigated and the role played by the dielectric permittivity of the host medium in determining the information content of the scattered field is pointed out.