Analytical Computation of the Lyot Coronagraph Response to an Extended Source

This paper 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 the decomposition of the impinging waves on Zernike functions which allows the computation of the expansion of the intensities on infinite series. The expression in the final plane assumes that the sizes of the Lyot stop and the pupil are the same. An analysis of the truncation error is provided. These expressions are validated by computer simulations which makes it possible to recover known results such as the so-called diffraction ring observed by solar astronomers inside the Lyot stop. These analytical results and simulations bring deeper insight into the understanding of a Lyot coronagraph, for example, 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.