Inverse scattering of dielectric cylinders by a second-order Born approximation

The inverse problem of the reconstruction of the permittivity profile of a dielectric cylinder from the knowledge of the scattered electric field is examined. The proposed method is based on a quadratic approximation of the nonlinear operator defining the scattered field. This choice overcomes the typical limitations of linear approaches and, due to the quadraticity of the operator involved, makes it possible to discuss and avoid the presence of local minima in the inversion procedure. The main features of the approach are shown for the simple case of dielectric cylinders with only angular dependence of permittivity, pointing out the higher sensitivity of the proposed approach with respect to fast varying profiles and the possibility to increase the spatial resolution when the number of available independent data are sufficiently larger than the number of unknowns