Fundamental limitations on Earth-like planet detection with extremely large telescopes

We analyse the fundamental limitations for the detection of extraterrestrial planets with Extremely Large Telescopes. For this task, a coronagraphic device combined with a very high order wavefront correction system is required but is not sufficient to achieve the 10-10 contrast level needed to detect an Earth-like planet. The stellar residuals left uncorrected by the wavefront correction system need to be calibrated and subtracted. We consider a general model including the dynamic phase aberrations downstream of 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 assumed. As a result of the analytical study, the limitation is found to mostly come from the static aberrations. We confirm this result using numerical simulations and evaluate the requirements in terms of phase aberrations to detect Earth-like planets with Extremely Large Telescopes.