  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.
