Reconstruction of an embedded slab from multifrequency scattered field data under the distorted Born approximation

This paper deals with the inverse scattering problem regarding a loss-less dielectric slab embedded in a loss-less homogeneous half-space starting out from the knowledge of multifrequency scattered field data. The distorted Born approximation of the electromagnetic scattering is assumed and the features of two linear operators, accounting for the electromagnetic scattering and differing on account of the excitation law of the impinging plane wave, are discussed in terms of model error and class of retrievable unknowns by means of singular value decomposition (SVD) analysis. In particular, it is outlined how a suitable choice of the excitation of the impinging wave makes it possible to improve the reconstruction capabilities of the solution algorithm. In addition, the SVD-based solution approach makes it possible to handle the ill-posedness and to regularize the problem. Numerical results confirm the effectiveness of the approach and the theoretical expectations.