  In this paper, we consider inverse time-harmonic acoustic and electromagnetic
scattering from locally perturbed rough surfaces in three dimensions. The
scattering 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 incident 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.
