Numerical performance of layer stripping algorithms for two-dimensional inverse scattering problems

Abstract

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 Schrodinger 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.