Tip-tilt retrieval using trilateration of a sodium laser guide star

Tip, tilt (TT) and focus modes cannot be directly measured from a laser guide star (LGS). For optical communications, residual TT errors in the pre-compensation of a ground-to-satellite optical communications link will lead to beam wander, resulting in signal fades at the receiver. We describe a method for retrieving the full TT solely with LGSs. This method uses trilateration, in which the differential arrival times of a pulsed LGS at ≥3 detectors at different locations around the laser transmitter are used to find the position of the LGS, and therefore the TT from only the uplink path of the LGS. We study the feasibility of this method and the technological developments needed to enable it. The simulation results show that, given a detector with a timing resolution t_res =10^-12 s, and ≥ 10⁸ photons s^-1 are collected at each detector, the tip and tilt modes can be measured to an accuracy of θ ≈ 0.45 arcsec. For pre-compensation to a low earth orbit (LEO) satellite, this can increase the power received at the satellite by over 2 dB when compared to pre-compensation using the TT from the downlink beam.