Laser guide star Shack-Hartmann wavefront sensor modeling: matched filtering, wavefront sensor nonlinearity, and impact of sodium layer variability for the Thirty Meter Telescope

This paper describes modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. Using a contiguous set of LIDAR measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photo-detected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel read out noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range and their bias when detuned from the current sodium profile