A single far-field uniquely determines the shape of a scattering screen.

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and it scatters acoustic waves to three-dimensional space. The model is particularly relevant in the study and design of reflecting sonars and antennas. Our main result is that given the plane where the screen is located, a single far-field pattern determines the exact shape of the screen. It is true even for screens whose shape is an arbitrary simply connected smooth domain. This is in stark contrast with earlier single measurement inverse scattering results where only polygonal scatterers are determined, or other very restrictive a priori conditions are imposed.