Total coronagraphic extinction of rectangular apertures using linear prolate apodizations

This paper presents a theoretical study of stellar coronagraphy with apodized entrance apertures. The study is restricted to a perfect telescope operating in space, and a monochromatic on-axis unresolved star. It is shown that linear prolate functions are the optimal apodizers for rectangular apertures in stellar coronagraphy. With the phase mask technique (Roddier & Roddier 1997), prolate functions can produce a total extinction of the star light. For Lyot's coronagraphy, the extinction is not complete, but prolate apodizations lead to an optimal star residual intensity with surprising interesting properties: the residual star light and the planet enjoy the same apodized intensity pattern (but different dynamic) with the optimal light concentration. With this technique, very high rejection rates can be obtained for Lyot's coronagraphy, with smaller mask sizes.