Numerical results of implementing a two-dimensional layer stripping algorithm to solve the two-dimensional Schrodinger equation inverse potential problem are presented and discussed. This is the first exact (all multiple scattering and diffraction effects are included) numerical solution of a multi-dimensional Schrtidinger equation inverse potential problem, excluding optimization-based approaches. The results are as follows: (1) the layer stripping algorithm successfully reconstructed the potential from scattering data measured on a plane (as it would be in many applications); (2) the algorithm avoids multiple scattering errors present in Born approximation reconstructions; and (3) the algorithm is insensitive to small amounts of noise in the scattering data. Simplifications of layer stripping and invariant imbedding algorithms under the Born approximation are also discussed.

This paper presents an alternative numerical scheme for a class of forward and inverse scattering problems based on invariant imbedding method [Corones et al., J. Acoust. Soc. Am. 74, 1535–1541 (1983)]. The algorithm presented in this paper is decoupled more than the previous implementations and hence, readily amenable to parallel processing. It is also shown that the effect of this decoupling on error can be expressed in terms of the estimated reflection coefficients, facilitating the decision to accept or reject any computed parameter.