Optimal apodizations for on-axis vector vortex coronagraphs

Imaging planets requires instruments capable of dealing with extreme contrast ratios and that have a high resolution. Coronagraphs that can reach a contrast ratio in a neighborhood of 10^9 will be capable of observing Jupiter-like planets, while those with a contrast greater than a benchmark number of 10^(10) to within a few λ/D of an on-axis star will render possible imaging of Earth-like planets. Plans for achieving this feat have been developed for use on telescopes with unobscured, circularly symmetric apertures. However; given that the next generation of large telescopes are on-axis designs with support structures in the telescope aperture and a central obstruction due to the secondary mirror, it has proven necessary to develop coronagraphic techniques that compensate for obstructions. Pueyo and Norman (2012) present a possible solution to the problem of the support structures using ACAD. In this paper, we present a coronagraphic design that uses a vector vortex and pupil apodization to compensate for the secondary mirror that could possibly be used in conjunction with a wavefront control system and/or ACAD. This coronagraph is capable of achieving a contrast ratio of at least 10^(10) in a working angle of (1:5 - 30) λ/D in conjunction with an on-axis telescope. We can construct our pupil using a classical transmissive apodizer or pupil remapping. We find that the mirror shapes required are relatively simple (requiring ≤ 40 degrees of freedom to describe) and we expect they will be feasible to manufacture, and potentially even to implement with deformable mirrors. By combining existing high-contrast imaging techniques, we demonstrate that a relatively simple design may be used to image exo-Earths.