A Disk-Covering Problem with Application in Optical Interferometry

Given a disk O in the plane called the objective, we want to find n small disks P1, . . . , Pn called the pupils such that n i,j=1 Pi Pj ⊇ O, where 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.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Trung Nguyen, Jean-Daniel Boissonnat, Frédéric Falzon, Christian Knauer
• Keywords: CCCG 2007, Computational Geometry, Minkowski Difference Operator, Small Disks P1, So-called Optical Aperture