The Interior Inverse Electromagnetic Scattering for an Inhomogeneous Cavity

TL;DR

This paper addresses the inverse electromagnetic scattering problem for an inhomogeneous cavity, proving uniqueness of shape determination from interior measurements and developing a linear sampling method for reconstruction, supported by numerical examples.

Contribution

It introduces a novel approach to uniquely determine cavity shape using interior measurements and designs a linear sampling method for reconstruction.

Findings

Uniqueness of cavity shape determined from interior measurements

Development of a linear sampling reconstruction algorithm

Numerical validation of the proposed method

Abstract

In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such scattered wave fields are due to sources emitted on the same surface. We first prove that the measurements uniquely determine the shape of the cavity, where we make use of a boundary value problem called the exterior transmission problem. We then complete the inverse scattering problem by designing the linear sampling method to reconstruct the cavity. Numerical examples are further provided to illustrate the viability of our algorithm.