Optimal correction of distortion for high-angular-resolution images: Application to GeMS data

Whether 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 instruments corrected with adaptive optics on ground-based telescope has increased the relative importance of the error terms induced by optical distortions. In particular, the variable distortion in multi-conjugate adaptive optics (MCAO) data limits the astrometric and photometric accuracy of such high-resolution instruments. These phenomena have 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 prior knowledge of the static distortion, the method aims to correct the dynamic distortion for each observation set and each frame. The method follows an inverse problem approach based on the work by Gratadour, Mugnier & Rouan on image re-centring, and we aim to generalize this to any kind of distortion mode. The complete formalism of a weighted least-squares 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, the density of the field (sparse or crowed images), the noise level and 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 of as well as the gain brought by this method are presented.