A Fixed Energy Fixed Angle Inverse Uniqueness in Interior Transmission Problem

TL;DR

This paper establishes a uniqueness result for identifying radially symmetric perturbations in an inverse scattering problem by analyzing fixed interior transmission eigenvalues and spherical harmonics.

Contribution

It introduces a novel approach linking interior transmission eigenvalues to the unique determination of radially symmetric scatterers.

Findings

Uniqueness of scatterer identification with fixed interior transmission eigenvalues.

Method for analyzing spherical harmonics at far fields.

Applicable to radially symmetric perturbations.

Abstract

We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics at far fields, we can decide the perturbation uniquely for the radially symmetric perturbations.