# Modification of a telescope to detect Earth-like planets

## Abstract

A central problem in the search for Earth-like planets is to suppress the light from a star so as to reveal a planet which might be 8 to 12 orders of magnitude fainter than the star and might be in quite close to the star. We show how to design a real, non-negative, continuous tone mask (an apodizer) to place in the telescope such that image of a star has a compact peak with minimal spread beyond the core of the star. Given the shape of a telescope's aperture and given a search region for the detector, we solve an integral equation to determine the apodizer. The math uncovers the prolate spheroidal wave functions, a set of orthogonal functions with remarkable properties. The method is quite general and yields as special cases some apodizers reported by current researchers. We show computer simulations for various aperture-detector configurations.