The resolution of ground-based telescopes is dramatically limited by the atmospheric turbulence.. Adaptative optics (AO) is a real-time opto-mechanical approach which allows to correct for the turbulence effect and to reach the ultimate diffraction limit astronomical telescopes and their associated instrumentation. Nevertheless, the AO correction is never perfect especially when it has to deal with large Field of View (FoV). Hence, a posteriori image processing really improves the final estimation of astrophysical data. Such techniques require an accurate knowledge of the system response at any position in the FoV The purpose of this work is then the estimation of the AO response in the particular case of the MUSE [1] /GALACSI [2] instrument (a 3D mult-object spectrograph combined with a Laser-assisted wide field AO system which will be installed at the VLT in 2013). Using telemetry data coming from both AO Laser and natural guide stars, a Point Spread Function (PSF) is derived at any location of the FoV and for every wavelength of the MUSE spectrograph. This document presents the preliminary design of the MUSE WFM PSF reconstruction process. The various hypothesis and approximations are detailed and justified. A first description of the overall process is proposed. Some alternative strategies to improve the performance (in terms of computation time and storage) are described and have been implemented. Finally, after a validation of the proposed algorithm using end-to-end models, a performance analysis is conducted (with the help of a full end-to-end model). This performance analysis will help us to populate an exhaustive error budget table.
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