Information content of Born scattered fields: results in the circular cylindrical case

Abstract

In this analysis some limitations of the linear Born approximation in the diffraction tomography problem from far-zone data are pointed out. The analysis is performed by means of singular-value decomposition of the scattering operator in the scalar two-dimensional case of a circular dielectric cylinder illuminated by a TM-polarized plane wave. It is shown that the validity of the Born approximation entails the important condition that the scattering object not present too-fast spatial variations of the permittivity profile. For the rotationally symmetric cylinder, evidence is presented that the imaginary part of the normalized scattered far field has no information content for real permittivity objects. Moreover, for angularly varying cylinders the information content of the scattered far field for a single view is approximately the same as in the multiview case. Examples of singular-value and singular-function behavior and of profile reconstruction are depicted for the considered geometries.