  We analyse the fundamental limitations for the detection of extraterrestrial
planets with Extremely Large Telescopes. For this task, a coronagraphic device
combined to a very high order wavefront correction system is required but not
sufficient to achieve the $10^{-10}$ contrast level needed for detecting an
Earth-like planet. The stellar residuals left uncorrected by the wavefront
correction system need to be calibrated and subtracted. In this paper, we
consider a general model including the dynamic phase aberrations downstream the
wavefront correction system, the static phase aberrations of the instrument and
some differential aberrations provided by the calibration unit. A rather
optimistic case of a filled circular pupil and of a perfect coronagraph is
elsewhere assumed. As a result of the analytical study, the limitation mostly
comes from the static aberrations. Using numerical simulations we confirm this
result and evaluate the requirements in terms of phase aberrations to detect
Earth-like planets on Extremely Large Telescopes.
