Uniqueness To Inverse Acoustic And Electromagnetic Scattering From Locally Perturbed Rough Surfaces

In this paper,we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions.The scatter-ing interface is supposed to be the graph of a Lipschitz continuous function with compact support.It is proved that an acoustically sound-soft or sound-hard surface can be uniquely determined by the far-field pattern of infinite number of inciden-t plane waves with distinct directions.Moreover,a single point source or plane wave can be used to uniquely determine a scattering surface of polyhedral type.These uniqueness results apply to Maxwell equations with the perfectly conducting boundary condition.Our arguments rely on the mixed reciprocity relation in a half space and the reflection principle for Helmholtz and Maxwell equations.