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A comprehensive performance analysis for adaptive optics systems that use natural stars as a wavefront reference is presented,. This analysis demonstrates how the system performance can be optimized at any given level of sky coverage by choosing the appropriate reference star, subaperture size, and system bandwidth. Performance calculations are performed using the observed Galactic stellar populations and for a range of seeing conditions.
It is found that for fairly typical seeing conditions, a wavefront phase error of less than 1 rad (corresponding to a Strehl ratio of greater than 0.37) can be obtained for M band (5 $\mu$m) over only a few percent of the sky. However, in excellent seeing conditions (such as may often be found at Mauna Kea and other superior astronomical sites), a wavefront phase error of less than 1 rad can be obtained for M band (5 $\mu$m) over nearly the entire sky, and can be obtained for K band (2.2 $\mu$m) over about 10\% of the sky.
