Scaling multi-conjugate adaptive optics performance estimates to extremely large telescopes

Multi-conjugate adaptive optics (MCAO) is a key technology for extremely large, ground-based telescopes (ELT's) because it enables near-uniform atmospheric turbulence compensation over fields-of-view considerably larger than can be corrected with more conventional AO systems. Quantitative performance evaluation using detailed analytical or simulation models is difficult, however, due to the very large number of deformable mirror (DM) actuators, wave front sensor (WFS) subapertures, and guide stars which might comprise an MCAO system for an ELT. This paper employs more restricted minimal variance estimation methods to evaluate the fundamental performance limits imposed by anisoplanatism alone upon MCAO performance for a range of sample cases. Each case is defined by a atmospheric turbulence profile, telescope aperture diameter, field-of-view, guide star constellation, and set of DM conjugate ranges. For a Kolmogorov turbulence spectrum with an infinite outer scale, MCAO performance for a whole range of aperture diameters and proportional fields-of-view can be computed at once using a scaling law analogous to the (D/d(0))(5/3) formula for the cone effect. For 30 meter telescopes, useful levels of performance are possible across a 1.0-2.0 are minute square field-of-view using 5 laser guide stars (LGS's) and 3 DM's, and somewhat larger fields can be corrected using 9 guide stars and 4 mirrors. 3 or more tip/tilt natural guide stars (NGS's) are necessary to detect modes of tilt anisoplanatism which cannot be detected using LGS's, however. LGS MCAO performance is a quite weak function of aperture diameter for a fixed field-of-view, and it is tempting to scale these results to larger apertures. NGS MCAO performance is moderately superior to LGS MCAO if the NGS constellation is within the compensated field-of-view, but degrades rapidly as the guide stars move away from the field. The penalty relaxes slowly with increasing aperture diameter, but how to extrapolate this trend to telescopes with diameters much larger than 30 meters is unclear.