A set of pupil apodization functions for use with a vortex coronagraph on telescopes with obscured apertures is presented. We show analytically that pupil amplitudes given by real-valued Zernike polynomials offer ideal on-axis starlight cancellation when applied to unobscured circular apertures. The charge of the vortex phase element must be a nonzero even integer, greater than the sum of the degree and the absolute value of its azimuthal order of the Zernike polynomial. Zero-valued lines and points of Zernike polynomials, or linear combinations thereof, can be matched to obstructions in the pupils of ground-based telescopes to improve the contrast achieved by a vortex coronagraph. This approach works well in the presence of a central obscuration and radial support structures. We analyze the contrast, off-axis throughput, and post-coronagraph point spread functions of an apodized vortex coronagraph designed for the European Extremely Large Telescope (E-ELT). This technique offers very good performance on apertures with large obscuring support structures similar to those on future 30-40m class ground-based telescopes.
@article{arxiv.1412.8731,
title = {Zernike amplitude pupil apodization for vortex coronagraphy with obscured apertures},
author = {Garreth J. Ruane and Mark R. Dennis and Grover A. Swartzlander},
journal= {arXiv preprint arXiv:1412.8731},
year = {2015}
}