Direct detection and characterization of Earth-like planets from the ground is a very challenging issue. Among the projects, the Extremely Large Telescopes are very promising to improve the angular resolution and to increase the total number of collected photons. We studied this type of instruments in a very optimistic case to evaluate what level of aberrations limits fundamentally the detection. For that purpose, we considered a perfect coronagraph coupled with an extreme adaptive optics device. Even with a Strehl ratio of more than 96%, it only provides a contrast of $10^{-6}-10^{-7}$ at $30\lambda/D$. A calibration system downstream the coronagraph is therefore mandatory to reach the contrast of $10^{-10}$ between a terrestrial planet and its star in the near infra-red. We modelized a very general system taking into account dynamic aberrations left uncorrected by the adaptive optics system, static aberrations of the system and differential static aberrations due to the calibration channel. Numerical simulations demonstrate that the static aberrations are becoming very limitative and must not be neglected. Indeed, to achieve a contrast of $10^{-10}$, with common aberrations of 5 nm on a 100 meter telescope, the differential aberrations must be controlled at the level of 200 picometers. We also compare this speckle noise to the limitation due to the photon noise.