Coronagraph Design Optimization for Segmented Aperture Telescopes

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of
coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o
between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a
stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization
masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including
phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal
of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents
a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom.
We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary
Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization
problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem
containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets
to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the
algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective
function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane).
Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis
segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem
has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end
telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm
reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to
be encountered in a real segmented aperture space telescope.