Co-design approach to aperture masking for imaging through atmospheric turbulence

Aperture masking interferometry is a technique originally designed to alleviate the influence of atmospheric turbulence on images recorded on ground-based telescopes. In this communication, we explore the optimization of the aperture mask by an optical/digital co-design approach in order to obtain diffraction-limited images of relatively bright objects imaged through turbulence. We show that, with a few simplifying assumptions, it is possible to express the Mean Square Error of the restored image as a function of the chosen mask, of the spatial Power Spectral Density of the observed object and of the noise level, without actually computing any image. This allows us to optimize the aperture mask with a reduced computing cost. We also implement a multi-frame myopic algorithm to estimate jointly the observed object, the piston and the tip-tilt in front of each sub-aperture, and check by simulations that the aperture masks obtained indeed allow a satisfactory image reconstruction.