  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 lambda/20 (resp. lambda/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 6.5m space telescope such as the
JWST with the optical quality of the HST.
