A forthcoming step in the study of extrasolar planetary systems is the direct detection and characterization of Earth-like planets. An asset of the ELTs in that context is their very high angular resolution and their collecting area. The luminosity ratio between a terrestrial planet and its star ($10^{-10}$) is such an ambitious goal that a thorough study needs to be carried out. We started with a simple analysis of the fundamental limitations for the detection of extraterrestrial planets with ELTs. Here, we considered an extreme adaptive optics device upstream of a perfect coronagraph. Even with high Strehl ratios, the coronagraphic halo level is only $10^{-6}$ to $10^{-7}$ at typical exo-Earth angular distances. A calibration device is therefore mandatory to reach the contrast between a terrestrial planet and its star in the near infra-red. We considered a simple but realistic model taking into account dynamic aberrations left uncorrected by the adaptive optics system, static aberrations of optical system and differential static aberrations due to the calibration channel itself. Numerical simulations prove that, after the calibration, the limitations are set by the static aberrations which cannot be neglected anymore.