Aims. We present a solution to improve the performance of coronagraphs for the detection of exo-planets.Methods. We simulate numerically several kinds of coronagraphic systems, with the aim of evaluating the gain obtained with an adaptive hologram.Results. The detection limit in flux ratio between a star and a planet (Fs /Fp ) observed with an apodized Lyot coronagraph characterized by wavefront bumpiness imperfections of λ/20 (resp. λ/100) turns out to be increased by a factor of 10^3.4 (resp. 10^5.1 ) when equipped with a hologram.Conclusions. This technique could provide direct imaging of an exo-Earth at a distance of 11 parsec with a 6.5 m space telescope such as the JWST with the optical quality of the HST.
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