Minimum Variance Split Tomography for Laser Guide Star Adaptive Optics

Tomographic wavefront estimation using laser and natural guide stars is under development for ground-based extremely large telescopes. Typical wavefront sensing requirements include several bright mesospheric sodium laser guide stars (LGSs) supplemented by a few dim natural guide stars (NGSs) required to sense at low frame rate a small number of low-order atmospheric modes poorly measured by the LGS wavefront sensors (WFSs). A conditional mean formulation of minimum variance wavefront estimation is given in this context to split the LGS and NGS components of the estimation in such a way that the LGS component does not depend upon the NGS asterism (location and brightness). This split formulation is analytically equivalent to the standard (integrated) formulation of minimum variance wavefront estimation and is therefore optimal and fully applicable to all laser tomography systems (multi conjugate and multi object). Temporal blending for closed loop feedback systems is discussed, and detailed multi-rate Monte Carlo simulations of the Thirty Meter Telescope (TMT) multi conjugate adaptive optics (MCAO) system are presented, demonstrating the potential of minimum variance split tomography compared to a simpler ad hoc split developed a decade ago for the MCAO system of the Gemini South telescope.