Aperture configuration optimization for extended scene observation by an interferometric telescope

In this Letter, we aim at optimizing the aperture configuration of an optical interferometric imager for observing extended objects. We exploit combinatorial theory results from different authors to prove the existence of solutions to some problems of aperture configuration optimization in dimension 1. We determine in which cases these solutions exist for a compact frequency coverage, and provide an explicit solution whatever the number of apertures. We apply these results and provide an illustration in two cases: the first is an interferometer composed of radially disposed arms and the second consists in an innovative hybrid architecture involving a small monolithic telescope, which covers short spatial frequencies, added at the center of the first case design. Lastly, we carry out an analysis to determine under which condition a monolithic telescope placed at the center of this hybrid instrument can complete its frequency coverage without gaps.