Inverse scattering under the distorted Born approximation for cylindrical geometries

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 al gorithms, we analyze the class of retrievable profiles with reference to so me canonical geometries for which either analytical or numerical details ca n be worked through easily. The tool for such an analysis consists of the s ingular-value decomposition of the relevant scattering operators. For a con stant reference permittivity function, the different behavior of linear inv ersion algorithms with respect to either radial or angular variations of th e permittivity profiles is pointed out. In the last-named case the general situation of a multiview radiation is accounted for, and, unlike for the Bo rn approximation, profiles that cannot be reconstructed by linear inversion comprise slowly varying functions. Moreover, the effect of an angularly va rying reference profile is examined for a thin circular shell, permitting t he possibility of reconstruction of rapidly varying angular profiles by lin ear inversion. Numerical results of linear inversions that confirm the pred ictions are shown. (C) 1999 Optical Society of America [S0740-3232(99)00607 -9].