One-dimensional inverse scattering with a Born model in a three-layered medium

This paper deals with the inverse scattering problem for a dielectric slab embedded in a three layered medium starting from multi-frequency scattered field data under the framework of the Born approximation. This allows to state the problem as a linear inverse one and the Singular Value Decomposition (SVD) of the relevant operator makes it possible to investigate and to solve it.In particular, the SVD tool allows an analysis of the reconstruction capabilities of the algorithm in terms of spatial variability of the unknowns that is possible to retrieve. The new contribution of this paper consists in an analysis of the role of the discontinuity of the dielectric properties between the second and the third medium. This analysis is performed with regard both to the class of retrievable dielectric profiles and to the model-error deriving from Born Approximation, and it shows at last that that discontinuity can be troublesome.