One-dimensional inverse scattering with a Born model in a three-layered medium.
We deal with the inverse-scattering problem for a dielectric slab embedded in a three-layered medium starting from multifrequency scattered field data under the framework of the Born approximation. This allows us 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 can be retrieved. The new contribution 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 the Born approximation and shows, finally, that this discontinuity can be troublesome.