Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.