Performance of a Shack-Hartmann Wavefront sensor using real sodium laser data.

The future of adaptive optics includes laser guide stars. While they are a great solution to sky coverage, they do introduce additional errors in the adaptive optics system. In particular, because of the finite thickness of the sodium layer, there is reduced centroiding accuracy due to elongated spots in the wavefront sensor. These become even more pronounced on large telescope apertures. In this paper we focus on the performance of a Shack-Hartmann wavefront sensor for 30m-plus large aperture telescopes studying the consequences of both the decrease in signal to noise ratio due to the spot elongation and the variations of the sodium density variations in the mesosphere. We incorporate real on-sky measurements of the return from the sodium layer using images of the laser guide star taken at Lick Observatory and simulate the expected wavefront reconstruction performance in the case of a Thirty Meter Telescope. Using this ensemble of data, we compare performance for various Hartmann centroiding methods, including correlation and weighted least square algorithms.