Optimizing the accuracy and efficiency of optical turbulence profiling using adaptive optics telemetry for extremely large telescopes

Advanced adaptive optics (AO) instruments on ground-based telescopes require accurate knowledge of the atmospheric turbulence strength as a function of altitude. This information assists point spread function reconstruction, AO temporal control techniques and is required by wide-field AO systems to optimize the reconstruction of an observed wavefront. The variability of the atmosphere makes it important to have a measure of the optical turbulence profile in real time. This measurement can be performed by fitting an analytically generated covariance matrix to the cross-covariance of Shack-Hartmann wavefront sensor (SHWFS) centroids. In this study we explore the benefits of reducing cross-covariance data points to a covariance map region of interest (ROI). A technique for using the covariance map ROI to measure and compensate for SHWFS misalignments is also introduced. We compare the accuracy of covariance matrix and map ROI optical turbulence profiling using both simulated and on-sky data from CANARY, an AO demonstrator on the 4.2 m William Herschel telescope, La Palma. On-sky CANARY results are compared to contemporaneous profiles from Stereo-SCIDAR - a dedicated high-resolution optical turbulence profiler. It is shown that the covariance map ROI optimizes the accuracy of AO telemetry optical turbulence profiling. In addition, we show that the covariance map ROI reduces the fitting time for an extremely large telescope-scale system by a factor of 72. The software package we developed to collect all of the presented results is now open source.