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SAXO+ is the name of the proposed second-stage adaptive optics module to increase the performance of the
SPHERE instrument at the Very Large Telescope (Chile). This upgrade aims at improving the raw contrast
(up to 10−5, goal 10−6) close to the optical axis (at a separation of 0.2 arcseconds, with a goal of 0.1), enabling
the observation of fainter and redder targets. SAXO+ will be implemented on a mezzanine above the main
bench and it will be fed by an exchange mechanism deploying a pick-off mirror in order to preserve all the
functionalities of the original instrument. The wavefront sensing will be based on pyramid wavefront sensor in
the near-infrared. In order to define the main requirements for the second-stage module design, a few trade-offs
need to be carried out. We present in this paper an analytical approach, based on spatial PSD analysis, to study
some error terms affecting the SAXO+ system and to directly compute the AO residual phase screens. For this
purpose, a second-stage correction filter in the spatial frequency domain has been implemented in PAOLA, a
software tool for the analytical modeling of Adaptive Optics systems.
