The 3-D distribution of sources of optical scattering computed from complex-amplitude far-field data

Abstract

We present a fast computer algorithm to solve the scalar inverse scattering problem numerically by inverting a linear transformation which maps a 3-D distribution of scattering sources into the angular distribution of the resultant scattered far field. We show how an approximate solution to the problem can be found in discrete form which leads to non-singular systems of linear equations of a type whose matrix can be inverted readily by fast algorithms.The method uses Born's first approximation and is valid for a slowly varying refractive index: the resultant numerical problem can be solved by a fast algorithm which reduces computing time by ~10−7, storage requirement by ~10−5, as compared with Gaussian elimination applied to 125 000 sample points. With this algorithm, computerized 3-D reconstruction becomes feasible.