The interior inverse scattering problem for cavities with an artificial obstacle

The interior inverse scattering by an impenetrable cavity is considered. Both the sources and the measurements are placed on a curve or surface inside the cavity. As a rule of thumb, both the direct and the inverse problems suffer from interior eigenvalues. The interior eigenvalues are removed by adding an artificial obstacle with impedance boundary condition to the underlying scattering system. For this new system, we prove a reciprocity relation for the scattered field and a uniqueness theorem for the inverse problem. Some new techniques are used in the arguments of the uniqueness proof because of the Lipschitz regularity of the boundary of the cavity. The linear sampling method is used for this new scattering system for reconstructing the shape of the cavity. Finally, some numerical experiments are presented to demonstrate the feasibility and effectiveness of the linear sampling method. In particular, the introduction of the artificial obstacle makes the linear sampling method robust to frequency.