A specificity of direct imaging systems for extra solar planet detection is that neither the residuals of the turbulence, nor the ideal coronagraphed point spread function can be neglected with respect to the planet. This has a direct consequence on the nature of the statistical distribution of the images, which plays a central part in the derivation of a powerful detection algorithm. The purpose of this paper is to study these specific effects: the response of the coronagraph is first analyzed then the statistical distribution of the images is characterized.