Convex Solutions to the Virtual Source Reflector Problem

TL;DR

This paper advances the mathematical understanding of the virtual source reflector problem by establishing new results on uniqueness and existence under various conditions, extending prior work significantly.

Contribution

It provides new proofs of uniqueness in the general case and existence results for symmetric and small target sets, broadening the theoretical framework.

Findings

Uniqueness results for the general virtual source reflector problem

Existence results for rotationally symmetric cases

Existence for small target sets

Abstract

We greatly expand upon the results of Kochengin, Oliker and Tempeski [S. Kochengin, V. Oliker, O. von Tempeski, On the design of reflectors with prescribed distribution of virtual sources and intensities, Inverse Problems 14 (1998) 661-678.] to include results for uniqueness in the general case. We also include results for existence in the rotationally symmetric case and the case where the target set is sufficiently small.