A fast linear reconstructor for the nonlinear curvature wavefront sensor (NLCWFS)

The Nonlinear Curvature Wavefront Sensor (nlCWFS), first proposed by Guyon,^[1] determines wavefront shape from images of a reference beacon in a number of “Fresnel planes” between the pupil and focal plane of a telescope. We previously described a fast linear algorithm^[2] that used refractive strong scintillation theory as an inspiration to use appropriately smoothed or binned Fresnel plane images to recover low spatial frequency aberrations. Since a given aberration causes both linear and nonlinear irradiance variations, we had suggested that the linear method be used to estimate the larger aberrations and that an unspecified nonlinear algorithm be used to estimate the nonlinear residual. In this paper we show that while there is always a nonlinear residual, if we only use the linear algorithm in a closed loop AO system, the nonlinear residual will never be an important term in the error budget. This greatly simplifies the nlCWFS system concept, allowing a closed-loop AO system to be driven from a linear algorithm operating on images from a selection of Fresnel plane cameras. The relationship between a localized variation in the irradiance and the pupil phase has a spatial frequency structure that can be used to select the Fresnel planes. The required number of Fresnel planes increases with D/r0. The required image processing can be parallelized per-camera, including binning, spatial moments, normalization, and contributions to the estimated wavefront.