Super-Gaussian apodization in ground based telescopes for high contrast coronagraph imaging

We introduce the use of Super-Gaussian apodizing functions in the telescope pupil plane and/or the coronagraph Lyot plane to improve the imaging contrast in ground-based coronagraphs. We describe the properties of the Super-Gaussian function, we estimate its second-order moment in the pupil and Fourier planes and we check it as an apodizing function. We then use Super-Gaussian function to apodize the telescope pupil, the coronagraph Lyot plane or both of them. The result is that a proper apodizing masks combination can reduce the exoplanet detection distance up to a 45% with respect to the classic Lyot coronagraph, for moderately aberrated wavefronts. Compared to the prolate spheroidal function the Super-Gaussian apodizing function allows the planet light up to 3 times brighter. An extra help to increase the extinction rate is to perform a frame selection (Lucky Imaging technique). We show that a selection of the 10% best frames will reduce up to a 20% the detection angular distance when using the classic Lyot coronagraph but that the reduction is only around the 5% when using an apodized coronagraph.