On stability for a translated obstacle with impedance boundary condition Original Research Article

This paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves. We firstly derive a concrete formula of the far-field pattern due to a translation of the obstacle and perturbation of its boundary impedance. Based on this formula, we establish Lipschitz stability for the recovery of translation of an obstacle with one incident wave. In the special case of obstacle being a ball, Lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves.