Uniqueness in potential scattering with reduced near field data

TL;DR

This paper proves that in inverse potential scattering problems, using measurements of scattered waves on a surface at a fixed energy uniquely determines the bounded potential, even with limited near-field data.

Contribution

It establishes the uniqueness of potential recovery from near-field data measured on a surface at a fixed energy level.

Findings

Potential uniquely determined by near-field data

Results apply to smooth closed surfaces outside the inhomogeneity

Addresses inverse scattering with limited data

Abstract

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value of the energy. We show that this data determines the bounded potential uniquely.