Lens Rigidity in Scattering by Unions of Strictly Convex Bodies in $\R^2$

TL;DR

This paper provides a new proof for the unique determination of unions of strictly convex obstacles in the plane using billiard trajectory data, extending previous results to the case where dimension d=2.

Contribution

It offers a different proof for the 2D case of obstacle determination from scattering data, previously established only for higher dimensions.

Findings

Unique determination of obstacle unions in ^2 from scattering data

Extension of previous results to the 2D case

New proof technique for obstacle scattering problem

Abstract

It was proved in \cite{NS1} that obstacles $K$ in $\R^d$ that are finite disjoint unions of strictly convex domains with $C^3$ boundaries are uniquely determined by the travelling times of billiard trajectories in their exteriors and also by their so called scattering length spectra. However the case $d = 2$ is not properly covered in \cite{NS1}. In the present paper we give a separate different proof of the same result in the case $d = 2$.