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The advent of photonic integrated circuits (PICs) will allow the replacement of the large aperture of an optical telescope by a dense array of small apertures combined interferometically. The light coming from aperture pairs can be combined by a PIC in order to extract interferogram characteristics known as complex visibilities, from which the observed object can then be reconstructed. In such a compact interferometric imager, the optical components dedicated to image formation in a regular telescope are no longer necessary. In particular, such a concept is relevant for space missions where weight and size are critical. To date, the proposed concepts are made of one-dimensional arrays radially disposed in a circular instrument. The way of combining the apertures defines the optical transfer function of the instrument, which is key to the imaging performance. In this communication, our goal is to optimize the aperture configuration. Signal-to-noise considerations suggest using each aperture once and only once in order to avoid splitting the flux received on each aperture. Moreover, non-redundant configurations allow a broader spatial frequency coverage. We study aperture configurations based on these two conditions. We describe this problematic formally and we apply results from combinatorial theory to prove the existence of solutions to some problems of aperture configuration optimization, and to exhibit some explicit solutions. Firstly, we suggest new aperture configurations leading to a dense spatial frequency coverage. Secondly, we use these results to propose an optimal frequency coverage for a SPIDER-like design. Then, by complementing the latter instrument with a monolithic telescope, we propose a new aperture configuration that extends the spatial frequency coverage. Lastly, additional strategies to further extend the cut-off spatial frequency are explored and presented.
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