Lens rigidity in scattering by non-trapping obstacles

TL;DR

This paper proves that under certain conditions, non-trapping obstacles with similar scattering data are actually identical, advancing the understanding of inverse scattering problems.

Contribution

It establishes the uniqueness of obstacle shapes in scattering problems based on travel time or scattering length spectrum data.

Findings

Obstacles with matching scattering data are identical under weak conditions.

The result applies to non-trapping obstacles in Euclidean space.

Provides a theoretical foundation for inverse scattering uniqueness.

Abstract

We prove that if two non-trapping obstacles in $\mathbb{R}^n$ satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling times or (almost) the same scattering length spectrum, then they coincide.