Interferometric apodization of rectangular apertures - Application to stellar coronagraphy

We describe the principle of an apodization technique for rectangular apertures that can be implemented using a Michelson or a Mach-Zender interferometer. Using several interferometers, any integer power of cosine functions can be obtained. The technique is considered for application to the Apodized Square Aperture (ASA) concept recently proposed by Nisenson & Papaliolios (2001). Simple analytic expressions for the Point Spread Functions of such apodized apertures are given. For a cosine to the power N apodization, the resulting focal plane amplitude is simply the sum of N+1 weighted and shifted sine cardinal functions. The interest of such apodized apertures for coronagraphy is investigated. It appears that these apodization functions are very efficient provided that only a central part of the cosine-arch is used. Analytic expressions are derived for the residual amplitude left in an image of the aperture after the coronagraphic experiment. Best results are obtained with a cosine squared apodization.