The advent of a new generation of Wide Field AO (WFAO) systems marks the beginning of a new era in high spatial resolution imaging. By using multiple Laser Guide Stars, WFAO significantly increases the field of view of the AOcorrected images, and the fraction of the sky that can benefit from such correction. The newly commissioned Gemini South Multi-Conjugate Adaptive Optics System (GeMS) combined with the infrared camera GSAOI is delivering almost di raction-limited images over a field of   2 arc-minutes across. In this paper, we first present recent observations of the young star-forming region N159W located in the Large Magellanic Cloud. We obtained deep JHKs images from the GeMS/ GSAOI instrument and developed reduction tools, in order to photometrically study the properties of the stellar members of the cluster and to bring new elements to our understanding of the process of massive star formation. However, despite the excellent performance of the GeMS/ GSAOI system, some variable residues are still limiting the correction quality over the field. In particular, GSAOI is severely a ected by distortion that can strongly degrade the resolution when combining multiple frames and can consequently reduce the sensitivity. The accuracy of the distortion correction of an instrument is critical for its use for high- precision astrometry and photometry. In a second part of this paper, we investigate an optimal way to correct for the distortion following an inverse problem approach. The formalism as well as first simulation results are presented.