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In this paper, we consider inverse time-harmonic acoustic and electromagneticscattering from locally perturbed rough surfaces in three dimensions. Thescattering interface is supposed to be the graph of a Lipschitz continuousfunction with compact support. It is proved that an acoustically sound-soft orsound-hard surface can be uniquely determined by the far-field pattern ofinfinite number of incident plane waves with distinct directions. Moreover, asingle point source or plane wave can be used to uniquely determine ascattering surface of polyhedral type. These uniqueness results apply toMaxwell equations with the perfectly conducting boundary condition. Ourarguments rely on the mixed reciprocity relation in a half space and thereflection principle for Helmholtz and Maxwell equations.

Uniqueness to Inverse Acoustic and Electromagnetic Scattering From Locally Perturbed Rough Surfaces