Improving the sensitivity of astronomical curvature wavefront sensor using dual-stroke curvature

Curvature wavefront sensors measure wavefront phase aberration by acquiring two intensity images on either side of the pupil plane. Low-order adaptive optics (AO) systems using curvature wavefront sensing (CWFS) have proved to be highly efficient for astronomical applications: they are more sensitive, use fewer detector elements, and achieve, for the same number of actuators, higher Strehl ratios than AO systems using more traditional Shack-Hartmann wavefront sensors. In higher-order systems, however, curvature wavefront sensors lose sensitivity to low spatial frequencies wavefront aberrations. This effect, often described as "noise propagation," limits the usefulness of curvature wavefront sensing for high-order AO systems and/or large telescopes. In this paper, we first explain how this noise propagation effect occurs and then show that this limitation can be overcome by acquiring four defocused images of the pupil instead of two. This solution can be implemented without significant technology development and can run with a simple linear wavefront reconstruction algorithm at > kHz speed. We have successfully demonstrated in the laboratory that the four conjugation planes can be sequentially obtained at > kHz speed using a speaker-vibrating membrane assembly commonly used in current curvature AO systems. Closed loop simulations show that implementing this scheme is equivalent to making the guide star 1 to 1.5 magnitude brighter for the configuration tested (188 actuator elements on 8-m telescope). Higher sensitivity gains are expected on curvature systems with higher number of actuators.