LGS WFS on ELTs I: Wave Front Sensor Design & Analysis
N. Muller, S. Thomas, V. Michau, T. Fusco
N. Muller: Onera DOTA / HRA, France S. Thomas: UCO / Lick Observatory, USA V. Michau, T. Fusco: Onera DOTA / HRA, France
Adaptive Optics (AO) relies on a Wave Front Sensor (WFS) to measure properly the perturbations induced by the turbulence. In case of a Shack-Hartmann (SH) WFS, the elongation of the spot due to the longitudinal extension of Laser Guide Stars (LGS) affects the quality of the WFS measurements. As the diameter of the telescope increases, non-linearities appear through spot truncation and sampling effects. Various centroid algorithms have been proposed to reduce the effects of these non-linearities. In addition, the spatial structure of the LGS, set by the Sodium layer density profile, has an impact on the measurements. Both effects are coupled.
In this paper we aim at optimizing the design of a SH WFS in the case of a LGS on an ELT. Considering a Gaussian Sodium profile, we show that the impact of the WFS non-linearities can be neglected with regards to the noise. Therefore, taking into account the reconstruction filtering, the impact of the longitudinal extent of the LGS on the WFS measurement accuracy is moderate. Moreover this result is established with an extensive range of analytical Sodium profiles, provided that the Sodium density profile is known. The impact of the Sodium layer fluctuations is specifically studied in the second part of this paper, namely LGS WFS on ELTs II.