Influence of speckle and Poisson noise on exoplanet detection with a coronagraph

We study in this communication the statistical spatial properties of the residual speckles in the Point Spread Function (PSF) of a large telescope with Adaptive Optics. These speckles form a noisy background outside the PSF central core, which makes it very difficult to detect an exoplanet. It can be shown that these speckles are due to small defaults of the wavefront, amplified by the coherent part of the wave. Using reasonable physical assumptions, their statistics is described by a modified Rice distribution. A simple analytic form can be derived for the Moment Generating Function (MGF). Analytical expressions can also be obtained for the statistics at photon counting levels. Using properties of the MGF, simple expressions are obtained for the variances of the noise. We discuss the relative importance of speckle and photon noise and present conclusions on the limits of coronagraphy for the detection of an exoplanet.