Inversion Procedure for Inverse Scattering within the Distorted-Wave Born Approximation

Abstract

The problem of determining the deviation $\ensuremath{\delta}V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ of a local scattering potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})={V}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})+\ensuremath{\delta}V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ from a known background potential ${V}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ by use of scattered-field data is addressed within the distorted-wave Born approximation. A procedure is presented that allows $\ensuremath{\delta}V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ to be approximately reconstructed from the potential's scattering amplitude $f(k\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}},k{\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{0})$ assumed specified for fixed $k$ and all incident (${\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}}_{0}$) and observation ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$) directions. The reconstruction method is shown to be a generalization of an inversion procedure developed earlier, to which it reduces when ${V}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})\ensuremath{\equiv}0$.