Authors

André Ferrari, Claude Aime and R. Soummer

Affiliations

FIZEAU

Abstract

This communication gives analytical expressions of the intensity in a Lyot coronagraph when the object is a resolved uniform disk. Intensities are given inside the Lyot stop and in the final plane. The derivation relies on a rather unusual Zernike expansion of the pupil complex amplitude, as opposed to the traditional Zernike expansion of the wavefront, which allows the computation of the expansion of the intensities on infinite series. An analysis of the truncation error is provided.

These expressions are validated by computer simulations. We provide illustrations for stellar diameters ranging from a Sun-like star at 30pc to Betelgeuse, in the case of a 10m telescope observing in the visible. These results provide analytical insight into a few effects such as the diffraction ring observed observed by solar astronomers inside the Lyot stop, and the fact that although the geometrical image of the source is behind the mask, a ghost image of the source can still be observed in the final plane.

These results are limited at the moment to the case of a classical Lyot coronagraph and the expression in the final plane assumes that the sizes of the Lyot stop and the pupil are the same. However, they provide a basis for future developments targeted at better understanding of more advanced coronagraphs.