Uniqueness in Inverse Electromagnetic Conductive Scattering by Penetrable and Inhomogeneous Obstacles with a Lipschitz Boundary

Abstract

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves by a penetrable, inhomogeneous, Lipschitz obstacle covered with a thin layer of high conductivity. The well posedness of the direct problem is established by the variational method. The inverse problem is also considered in this paper. Under certain assumptions, a uniqueness result is obtained for determining the shape and location of the obstacle and the corresponding surface parameter $\lambda (x)$ from the knowledge of the near field data, assuming that the incident fields are electric dipoles located on a large sphere with polarization $p\in {ℝ}^{\mathrm{3}}$. Our results extend those in the paper by F. Hettlich (1996) to the case of inhomogeneous Lipschitz obstacles.