Uniqueness Theorem in Scattering Theory

A reflecting convex obstacle is uniquely defined by the scattering amplitude $f(k_0,{\nu }_0,n)$ known at a fixed frequency $k_0$, for a fixed direction ${\nu }_0$ of the incident wave, and for all directions $n$ of the scattered waves in a solid angle. Earlier the uniqueness theorem was proved under the assumption that $f(k,{\nu }_0,n)$ is known for $a<~k<~b$, $b>a$, and all $n$.