Polychromatic phase retrieval with Kolmogorov self-adapting prior constraints

Phase retrieval is a very promising approach for wavefront sensing in the focal plane of ground-based large telescopes. It is a non-linear problem that must be solved by means of global optimization. Currently only multi-focal phase diversity algorithms are used in adaptive optics. They enable the correction of static aberrations. For speckle imaging the problem is increasingly multi-modal with the ratio D/r0. Yet thanks to an iterative Newton algorithm with self-adapting Kolmogorov prior information, we show from consistent modeling and simulations, that we could efficiently sense short exposure wavefronts at high D/r0 from a single focal plane. We show that using data at different wavelengths with a proper polychromatic model would even enforce the convergence, thus making it an envisageable method to sense the returned flux of a polychromatic laser guide star (PLGS). For instance, we show that if we suppose the PLGS is not resolved, phase retrieval would enable an improvement in the centroid estimation in agreement with the Cramer-Rao lower bound. As a post-processing technique, our algorithm already has numerous potential applications for astronomy and for other domains. Thanks to the improvement of computing workstations and the optimization of the algorithm, applications involving realtime wavefront corrections should be soon possible.