  Current state-of-the-art high contrast imaging instruments take advantage of
a number of elegant coronagraph designs to suppress starlight and image nearby
faint objects, such as exoplanets and circumstellar disks. The ideal
performance and complexity of the optical systems depends strongly on the shape
of the telescope aperture. Unfortunately, large primary mirrors tend to be
segmented and have various obstructions, which limit the performance of most
conventional coronagraph designs. We present a new family of vortex
coronagraphs with numerically-optimized gray-scale apodizers that provide the
sensitivity needed to directly image faint exoplanets with large, segmented
aperture telescopes, including the Thirty Meter Telescope (TMT) as well as
potential next-generation space telescopes.
