Centroiding and extraction of tip/tilt information from nonlinear curvature wavefront sensor measurements

The nonlinear curvature wavefront sensor (nlCWFS) uses multiple (typically four) out-of-focus images to reconstruct the phase and amplitude of a propagating light beam. Because these images are located between the pupil and focal planes, they contain tip/tilt information. Rather than using a separate sensor to measure image locations, it would be beneficial to extract tip/tilt information directly and routinely as part of the reconstruction process. In the presence of atmospheric turbulence, recovering precise centroid offsets for each out-of-focus image becomes a dynamic process as image structure is altered by changing aberrations. We examine several tip/tilt extraction methods and compare their precision and accuracy using numerical simulations. With knowledge of the z-distance to each plane, we find that applying a best-fit linear model to multiple image centroid locations can offer fast and accurate tip/tilt (jitter) mode retrieval. We also develop a nonlinear tip/tilt extraction method that self-consistently uses the speckle field to compensate for jitter but find that algorithm latency precludes practical implementation. Simulations of closed-loop adaptive optics correction demonstrate that centroiding precisions may reach the diffraction limit despite using images with a finite region of interest that is purposefully defocused.