INCLUDING OUTER SCALE EFFECTS IN ZONAL ADAPTIVE OPTICS CALCULATIONS

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ra y paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is f or the case of a finite outer scale and a von Karman turbulence spectr um. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects a re neglected. The resulting formula for the covariance is a power seri es in one variable for the case of a fixed atmospheric wind velocity p rofile and a power series in two variables for a fixed wind-speed prof ile with a random and uniformly distributed wind direction. These form ulas are computationally efficient and can be easily integrated into c omputer codes for the numerical evaluation of adaptive optics system p erformance. Sample numerical results are presented to illustrate the e ffect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used f or full-aperture tip/tilt sensing is offset from the science field. Th e reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide sta r adaptive optics system is not significantly improved. (C) 1997 Optic al Society of America.