High Contrast Imaging with an Arbitrary Aperture: Active Correction of Aperture Discontinuities

We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential Deformable Mirrors to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of Deformable Mirror Surfaces that yield high contrast Point Spread Functions is not linear, and non-linear methods are needed to find the true minimum in the optimization topology. We solve the highly non-linear Monge-Ampere equation that is the fundamental equation describing the physics of phase induced amplitude modulation. We determine the optimum configuration for our two sequential Deformable Mirror system and show that high-throughput and high contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to JWST, ACAD can attain at least 10^-7 in contrast and an order of magnitude higher for both the future Extremely Large Telescopes and on-axis architectures reminiscent of HST. We show that the converging non-linear mappings resulting from our Deformable Mirror shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Consequently, ACAD is a true broadband solution to the problem of high-contrast imaging with segmented and/or on-axis apertures. We finally show that once the non-linear solution is found, fine tuning with linear methods used in wavefront control can be applied to further contrast by another order of magnitude. Generally speaking, the ACAD technique can be used to significantly improve a broad class of telescope designs for a variety of problems.