Inequalities in Inverse Scattering Theory ∗

Until recently, reconstruction algorithms for solving inverse electromagnetic scattering problems have been based on either nonlinear optimization techniques or on linearized models based on weak scattering approximations [6]. In the past ten years a third approach to reconstruction has been developed which comes under the rubric of qualitative methods in inverse scattering theory, the most popular of which is the linear sampling method [1]. In particular, qualitative methods determine the shape of the scattering obstacle without needing any a priori information on the material properties of the scatterer but provide little or no information on the physical properties of the scatterer. However, in the past few years it has been noted that qualitative methods in inverse scattering theory can in certain circumstances provide lower bounds on relevant physical properties of the scatterer [2] [3] and it is to this theme that this paper is directed. We will illustrate our ideas by considering a simple scattering problem for an infinite dielectric cylinder that is partially coated by a thin metallic coating. For Maxwell’s equations in R, scattering problems for such coated objects arise when an effort is made to make benign dielectric objects look