Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects

TL;DR

This paper introduces a novel method to uniquely determine penetrable obstacles with embedded objects in inverse acoustic and electromagnetic scattering, using far-field data at a fixed frequency and leveraging interior transmission problems.

Contribution

The paper presents a unified approach for acoustic and electromagnetic inverse scattering, employing interior transmission problems and a priori estimates to establish uniqueness.

Findings

Unique determination of obstacles from far-field data.

Development of a unified method for acoustic and electromagnetic cases.

Establishment of a priori estimates for transmission problems.

Abstract

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed interior transmission problem in a small domain associated with the Helmholtz or modified Helmholtz equation and the Maxwell or modified Maxwell equations. A key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem. Another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in Lp (1<p<2), which are established in this paper by using the integral equation method. A main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces.