An inverse electromagnetic scattering problem for a cavity

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting cavity from measurement of the scattered electric field due to electric-dipole sources on a surface inside the cavity. We prove a reciprocity relation for the scattered electric field and a uniqueness theorem for the inverse problem. Then, the near-field linear sampling method is employed to reconstruct the shape of the cavity. Preliminary numerical examples are provided to show the viability of the method. (paper)