Astronomy with High Contrast Imaging II C. Aime and R. Soummer (eds) EAS Publications Series, 12 (2004) 89-101 THE EFFECT OF A CORONAGRAPH ON THE STATISTICS OF ADAPTIVE OPTICS PINNED SPECKLES C. Aime 1 and R. Soummer 2 Abstract. In this communication we study the statistics of Adaptive Optics remnant speckles, and we discuss how a coronagraph can defeat the noise associated with these speckles. At high Strehl Ratio regimes, residual speckles are pinned on the diffraction rings of the airy pat- tern. It can be shown that these speckles are due to small defaults of the wavefront, amplified by the coherent part of the wave and that the statistics of their intensity can be described by a modified Rice distribution. At low flux levels, a Poisson-Mandel transformation pro- vides an analytical expression of the Probablility Density Function. We show the results of a numerical simulation and compare the results to the theoretical model. Simple analytical expressions can be derived for the variance of the noise. We discuss the efficiency of a coronagraph in terms of Signal to Noise Ratio, based on the analysis of the noise contributions which can be reduced by a coronagraph. 1 INTRODUCTION Direct imaging of faint sources near a bright star (exoplanets, circumstellar disks) is an ambitious goal with strong astrophysical drivers. The problem is to detect a very faint object (a planet) above a bright background produced by the stellar diffraction wings. The dynamic range is limited by many sources of noise including the speckle and photon noise. In the case of ground based observations with adaptive optics (AO) the uncorrected aberrations of the wavefront produce random intensity fluctuations of this background (residual speckles). Even at very high AO correction, those speckles still exist, but are “pinned” on the first diffraction rings for short exposure images (Bloemhof et al. 2001; Sivaramakrishnan et al. 2002; Bloemhof 2003; Perrin et al. 2003) (Fig. 1). 1 UMR 6525 LUAN, University of Nice Sophia-Antipolis, 06108 Nice Cedex 2, France 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD21218, USA c  EAS, EDP Sciences 2004 DOI: 10.1051/eas:2004025