LGS WFS on ELTs II: Impact of the sodium layer fluctuations
S. Thomas, N. Muller, V. Michau, T. Fusco, D. gavel
UCO/Lick Osbervatory Onera
The application of laser guide stars to large aperture telescopes has spurred many new studies in wavefront sensing. For the particular case of the Shack-Hartmann wavefront sensor (WFS), wavefront sensing is prone to new sources of errors not previously considered. The primary source of error is spot elongation resulting from the resolution of the finite thickness of the sodium layer. The elongation spreads the signal over several pixels, resulting in a decrease of the signal to noise ratio and an increase of non-linearity. Also, the SHWFS performance becomes sensitive to temporal and spatial variations of the density of the sodium atoms. Among the different centroid algorithms to be used with this WFS, the most powerful methods (correlation, matched filter, WCoG) require a reference. Although straightforward for a point source, the use of a resolved laser guide star is more cumbersome because the sodium layer variations affect their performance. In this paper we look at the impact of the sodium layer fluctuations and the reference choice on the performance of the WFS. We consider real as well as analytical non-symmetric profiles and investigate errors both at the subaperture level and at the wavefront reconstruction level. We conclude on the compromise between the use of the best possible reference versus the difficulty of implementation.