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 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 t...

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Bibliographic Details
Published in:arXiv.org 2006-12
Main Authors: Nguyen, Trung, Jean-Daniel Boissonnat, Falzon, Frederic, Knauer, Christian
Format: Article
Language:English
Subjects:
Apertures
Disks
Finite differences
Operators (mathematics)
Pupils
Telescopes
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Summary: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.
ISSN:2331-8422