Blind deconvolution and reconstruction of complex point spread functions

International audience ; The emergence of extreme adaptive optics (AO) systems in the last two decades pushed to unprecedented limits the resolution achievable by ground-based telescopes. Nonetheless, despite the always increasing performances of AO systems, the correction is never perfect, still degrading the images compared to the theoretical limits of the telescope pupil. Using a reference point spread function (PSF) obtained by simulation or by pointing a bright star is not always sufficient due to the random nature of the turbulence. The only solution is thus to extract and reconstruct the AO-PSF directly from the data of interest, a problem known as blind deconvolution. In recent years, marginal approaches emerged, based on a parametric modelling of the AO-PSF with a limited number of physical parameters. These methods correctly grasp the global structure of AO-PSFs (such as full width at half maximum or the AO-cutoff frequency), but they produce perfect PSF that fail at fitting the complex structures of real AO-PSFs such as coherent speckles or multi-lobbed cores in presence of low wind effect or motion blur. With pupil segmented in multiple mirrors and fragmented by the large structures holding the secondary mirror, AO-PSFs of giant telescopes will even more suffer from these effects. To achieve the theoretical performances, it will be necessary to retrieve the 2D image of the AO-PSF in its full complexity. In this work, we present our blind deconvolution method that reconstructs the AO-PSF directly in the data of interest in the presence of sharp-edge objects, such as resolved asteroids, without any prior on the instrument. The PSF faint extensions are reconstructed with a robust penalization optimization, discarding outliers on-the-fly such as cosmic rays or defective pixels. Our methods is successfully applied to a variety of real AO-systems and simulated ELT PSFs.