Direct imaging with highly diluted apertures – II. Properties of the point spread function of a hypertelescope

In the future, optical stellar interferometers will provide true images thanks to larger number of telescopes and to advanced cophasing subsystems. These conditions are required to have sufficient resolution elements (resel) in the image and to provide direct images in the hypertelescope mode. It has already been shown that hypertelescopes provide snapshot images with a significant gain in sensitivity without inducing any loss of the useful field of view for direct imaging applications. This paper aims at studying the properties of the point spread functions of future large arrays using the hypertelescope mode. Numerical simulations have been performed and criteria have been defined to study the image properties. It is shown that the choice of the configuration of the array is a trade-off between the resolution, the halo level and the field of view. A regular pattern of the array of telescopes optimizes the image quality (low halo level and maximum encircled energy in the central peak), but decreases the useful field of view. Moreover, a non-redundant array is less sensitive to the space aliasing effect than a redundant array.