Optimal correction of distortion for High Angular Resolution images. Application to GeMS data

Whether is ground-based or space-based, any optical instrument suffers from some amount of optical geometric distortion. Recently, the diffraction-limited image quality afforded by space-based telescopes and by Adaptive Optics (AO) corrected instruments on ground based-telescope, have increased the relative importance of the error terms induced by optical distortions. In particular, variable distortions present in Multi-Conjugated Adaptive Optics (MCAO) data are limiting the astrometry and photometry accuracy of such high resolution instruments. From there, the ability to deal with those phenomenon had become a critical issue for high-precision studies. We present in this paper an optimal method of distortion correction for high angular resolution images. Based on a prior-knowledge of the static distortion the method aims to correct the dynamical distortions specifically for each observation set and each frame. The method follows an inverse problem approach based on the work done by Gratadour et al. 2005 on image re-centering, and we aim to generalized it to any kind of distortion mode. The complete formalism of a Weighted Least Square minimization, as well as a detailed characterization of the error budget are presented. In particular we study the influence of different parameters such as the number of frames and the density of the field (sparse or crowed images), of the noise level, and of the aliasing effect. Finally, we show the first application of the method on real observations collected with the Gemini MCAO instrument, GeMS/GSAOI. The performance as well as the gain brought by this method are presented.