Inverse scattering under the distorted Born approximation for cylindrical geometries

Abstract

The problem of reconstructing dielectric permittivity from scattered field data is dealt with for scalar two-dimensional geometry at a fixed frequency by use of a linearized approximation about a chosen reference permittivity profile. To investigate the capabilities and limits of linear inversion algorithms, we analyze the class of retrievable profiles with reference to some canonical geometries for which either analytical or numerical details can be worked through easily. The tool for such an analysis consists of the singular-value decomposition of the relevant scattering operators. For a constant reference permittivity function, the different behavior of linear inversion algorithms with respect to either radial or angular variations of the permittivity profiles is pointed out. In the last-named case the general situation of a multiview radiation is accounted for, and, unlike for the Born approximation, profiles that cannot be reconstructed by linear inversion comprise slowly varying functions. Moreover, the effect of an angularly varying reference profile is examined for a thin circular shell, permitting the possibility of reconstruction of rapidly varying angular profiles by linear inversion. Numerical results of linear inversions that confirm the predictions are shown.