Direct detection of Earth-like planets is one of the major objectives for the next generation of ground based telescopes (Extremely Large Telescopes, ELT). ELT instruments will be conditionned by such scientific programs. Here, we consider here a system made with an adaptive optics device, a coronagraph and a simultaneous calibration system. We refined this simple model by including static aberrations upstream the coronagraph and differential aberrations downstream. Using numerical simulations, we evaluate how these static aberrations limit the detectability of telluric planets.