Spatio-angular minimum-variance tomographic controller for multi-object adaptive-optics systems

Multi-object astronomical adaptive optics (MOAO) is now a mature wide-field observation mode to enlarge the adaptive-optics-corrected field in a few specific locations over tens of arcminutes. The work-scope provided by open-loop tomography and pupil conjugation is amenable to a spatio-angular linear-quadratic-Gaussian (SA-LQG) formulation aiming to provide enhanced correction across the field with improved performance over static reconstruction methods and less stringent computational complexity scaling laws. Starting from our previous work [J. Opt. Soc. Am. A31, 101 (2014)10.1364/JOSAA.31.000101JOAOD61084-7529], we use stochastic time-progression models coupled to approximate sparse measurement operators to outline a suitable SA-LQG formulation capable of delivering near optimal correction. Under the spatio-angular framework the wavefronts are never explicitly estimated in the volume, providing considerable computational savings on 10-m-class telescopes and beyond. We find that for Raven, a 10-m-class MOAO system with two science channels, the SA-LQG improves the limiting magnitude by two stellar magnitudes when both the Strehl ratio and the ensquared energy are used as figures of merit. The sky coverage is therefore improved by a factor of ~5.