Abstract
In this paper, we consider the inverse scattering problem of recovering the shape of a perfectly conducting cavity from one source and several measurements placed on a curve inside the cavity. Under restrictive assumptions on the size of the cavity, a uniqueness theorem for finitely many excitations is given. Based on a system of nonlinear and ill-posed integral equations for the unknown boundary, we apply a regularized Newton iterative approach to find the boundary. We present the mathematical foundation of the method and give several numerical examples to show the viability of the method.