Estimation of the laser guide star uplink tip-tilt using aperture size diversity

Laser guide star (LGS) adaptive optics cannot directly measure tip-tilt (TT), forcing reliance on natural guide stars and limiting sky coverage. We propose estimating the uplink TT from telemetry acquired at the laser launch telescope (LLT) alone, operated in a monostatic configuration as both emitter and receiver. Extracting TT over concentric disks of different diameters within the receiving pupil yields signals mixing uplink and downlink contributions in different proportions; this aperture size diversity, combined with a linear minimum mean square error (LMMSE) estimator, disentangles the uplink component. Simulations show a residual error of 20-35 mas under median seeing (0.65^'') conditions.