A disk-covering problem with application in optical interferometry

Abstract

Given a disk O in the plane called the objective, we want to find n small disks P_1,...,P_n called the pupils such that $\bigcup_{i,j=1}^n P_i \ominus P_j \supseteq O$, where $\ominus$ denotes the Minkowski difference operator, while minimizing the number of pupils, the sum of the radii or the total area of the pupils. This problem is motivated by the construction of very large telescopes from several smaller ones by so-called Optical Aperture Synthesis. In this paper, we provide exact, approximate and heuristic solutions to several variations of the problem.