Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave

TL;DR

This paper proves that the potential function in an inverse scattering problem can be uniquely determined from scattering data at a fixed incident wave direction across all observation directions and frequencies.

Contribution

It establishes the uniqueness of the inverse scattering solution when scattering data is known for all observation directions and frequencies at a fixed incident wave direction.

Findings

Unique determination of the potential from fixed incident direction data

Scattering data at all observation directions and frequencies suffices for uniqueness

Advances understanding of inverse scattering with limited incident data

Abstract

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed direction of the incident plane wave.