Astrometry was not a science case of the Gemini Multiconjugate adaptive optics System (GeMS) at its design stage. However, since GeMS has been in regular science operation with the Gemini South Adaptive Optics Imager (GSAOI), their astrometric performances have been deeply analysed. The non-linear component of the distortion map model shows a characteristic pattern which is similarly repeated in each detector of GSAOI. The nature of this pattern was unknown and subjected to different hypotheses. This paper describes the origin of the GeMS distortion pattern as well as its multi-epoch variation. At the end, it is showed a comparison with the current design of the Multiconjugate Adaptive Optics RelaY (MAORY) of the Extremely Large Telescope (ELT).
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