  One of two approaches to implementing NASA's 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 telescope's 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 telescope's aperture and given a search region for a detector, we
solve an integral equation to determine an amplitude modulation (an apodizer)
which suppresses the star's 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.
