The Electromagnetic Inverse Scattering Problem for Partially Coated Lipschitz Domains

We consider the inverse scattering problem of determining the shape of a partially coated obstacle in R 3 from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method. 1. Introduction. The inverse scattering problem we consider in this paper is to determine the shape of a (possibly disconnected) scattering obstacle from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave. Although this problem is a basic one in inverse scattering theory, until now only partial solutions have been obtained [16], [18], [9]. The difficulty lies in what a priori assumptions need to be made on the material properties of the scattering object D, e.g. is D penetrable, perfectly conducting or coated? In particular, for iterative methods such as those of [16] and [18] some a priori knowledge of this type is needed in order to implement the inversion scheme. On the other hand, the linear sampling method used in [9] for solving this problem requires that each component of the scattering object has the same boundary condition although this boundary condition can vary from component to component and does not have to be known a priori. Excluded in this analysis is the case of partially coated obstacles, i.e. the case of possibly mixed boundary conditions on each component and it is this problem that we are concerned with in this paper. The inverse scattering problem for partially coated obstacles was first considered in [4] for the special case of an infinite cylinder where the Maxwell systems decouples into a two dimensional scalar Helmholtz equation. This problem, and in particular the three dimensional analogue considered in this paper, is particularly important in the use of electromagnetic waves to detect " hostile " objects where the boundary, or more generally a portion of the boundary, is coated with an unknown material in order to avoid detection. Since in general such objects have corners and edges, which are in fact responsible for strong scattering effects, it is important to consider the general case of disconnected obstacles where each component is allowed to have a Lipschitz boundary. These considerations are the motivation for the problem considered in this paper. …