The effects of turbulence-induced anisoplanatism cause the performance of an adaptive-optics system to be dependent on the separation angle between the imaged object and the source used as a reference. One method of quantifying this performance is through the optical transfer function (OTF). A new method is presented for calculating the upper bound on the OTF that is due to the residual or uncorrected phase and amplitude variations in an adaptive-optics system. The method includes diffraction effects, which in turn result in phase and amplitude effects. These results are compared with the geometric optics and are shown to yield a larger isoplanatic angle. A general expression for the OTF is obtained that permits evaluation of the effect of the inner- and outer-scale size of turbulence. A method is presented for layering the atmosphere and scaling the transfer function to different values of r0 and Cn2 profiles without the need to recompute the entire OTF. We show that with four layers placed at 200 m, 2 km, 10 km, and 18 km the calculated OTF’s are within 1% of the OTF’s obtained with a continuous atmosphere.
© 1994 Optical Society of America
Original Manuscript: October 13, 1993
Revised Manuscript: January 10, 1994
Manuscript Accepted: January 11, 1994
Published: July 1, 1994
Steven E. Troxel, Michael C. Roggemann, and Byron M. Welsh, "Off-axis optical transfer function calculations in an adaptive-optics system by means of a diffraction calculation for weak index fluctuations," J. Opt. Soc. Am. A 11, 2100-2111 (1994)