Fixed angle inverse scattering in the presence of a Riemannian metric

TL;DR

This paper investigates fixed angle inverse scattering with a known Riemannian metric, establishing uniqueness and stability results under symmetry assumptions and extending Euclidean case findings to Riemannian settings.

Contribution

It extends inverse scattering results from Euclidean space to Riemannian metrics, providing new uniqueness and stability theorems under symmetry conditions.

Findings

Uniqueness and stability for two incident waves

Single measurement results under symmetry assumptions

Extension of Euclidean inverse scattering results to Riemannian metrics

Abstract

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential with data generated by two incident waves from opposite directions. Further, similar results are given using one measurement provided the potential also satisfies a symmetry assumption. This work extends the results of [23,24] from the Euclidean case to certain Riemannian metrics.