One of two approaches to implementing NASAs Terrestrial Planet Finder is to build a space telescope that utilizes the techniques of coronagraphy and apodization to suppress diffraction and image exo-planets. We present a method for calculation of a telescopes apodizer which suppresses the side lobes of the image of a star so as to optimally detect an Earth-like planet. Given the shape of a telescopes aperture and given a search region for a detector, we solve an integral equation to determine an amplitude modulation (an apodizer) which suppresses the stars energy in the focal plane search region. The method is quite general and yields as special cases the product apodizer reported by Nisenson and Papaliolios (2001) and the Prolate spheroidal apodizer of Kasdin et al (2002), and Aime et al (2002). We show computer simulations of the apodizers and the corresponding point spread functions for various aperture-detector configurations.
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