Modified linear sampling method for inverse scattering by a partially coated dielectric

Consider time-harmonic electromagnetic wave scattering by an infinitely long, cylindrical, orthotropic dielectric partially coated with a very thin layer of a highly conductive material, which can be modeled by a transmission problem with mixed boundary conditions. Having established the well-posedness of the direct and interior transmission problem by the variational method under certain conditions, we make use of the classical linear sampling method to reconstruct the shape of the obstacle. Then, based on a modification of the general data-to-pattern operator G, we propose a novel and simple method to justify the modified linear sampling method.