Method of Moments Based Coronagraph Pupil Design for Exoplanet Exploration

Telescope coronagraph is an instrument to observe faint exoplanets located at very close proximities to their star by shielding the direct starlight. In this paper, the coronagraph pupil-mask system is described through a series of Fourier transforms, which leads to an eigenvalue system described by an integral equation. The method of moments (MoM) is applied to solve such an eigenvalue problem to obtain the eigen modes that represent an optimal set of refractive index distributions on the pupil. Due to the application of the MoM, the shape of coronagraph pupil can be arbitrary. A numerical example considering a circular pupil is given to demonstrate capability of the proposed method. The accuracy of the MoM solution is validate by comparing the numerical solutions with the analytical solutions given by the generalized prolate spheroidal wave functions.