Error budget for tip/tilt retrieval from laser guide stars using the propagation-delay method

Abstract

The low density of sufficiently bright natural guide stars (NGS) remains a key limitation for sky coverage in adaptive optics (AO) systems. Partial recovery of tip/tilt from Laser Guide Stars (LGS) could increase NGS integration times, potentially enabling full sky coverage. While the absolute tip/tilt is not detectable from an LGS, a small differential tip/tilt arises from the evolving turbulence during the roughly 0.6 ms round-trip time between the laser uplink and LGS downlink. The Propagation-Delay method suggests that, if observed by a monostatic AO system (launch and reception in the same aperture), this signal can be integrated to estimate the atmospheric tip/tilt seen on an NGS. However, this differential LGS tip/tilt signal is expected to be 2 to 3 orders of magnitude smaller than the NGS tip/tilt and thus could be swamped by noise. We therefore analyse the main noise and error contributions in the detection process using CaNaPy as a representative system, a monostatic LGS-AO demonstrator jointly developed by ESO, ESA, and partner institutions, operating at the ESA Optical Ground Station in Tenerife. We consider contributions from read-out noise as well as shot noise from the LGS and Rayleigh scattering. We then evaluate the sensitivity limits for detecting the differential LGS tip/tilt with a Shack-Hartmann wavefront sensor compared to a scoring camera. We obtain an error budget from the corresponding signal-to-noise ratios as a function of the relevant system parameters.