Se. Troxel et al., OFF-AXIS OPTICAL TRANSFER-FUNCTION CALCULATIONS IN AN ADAPTIVE-OPTICSSYSTEM BY MEANS OF A DIFFRACTION CALCULATION FOR WEAK INDEX FLUCTUATIONS, Journal of the Optical Society of America. A, Optics, image science,and vision., 11(7), 1994, pp. 2100-2111
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 meth
od of quantifying this performance is through the optical transfer fun
ction (OTF). A new method is presented for calculating the upper bound
on the OTF that is due to the residual or uncorrected phase and ampli
tude variations in an adaptive-optics system. The method includes diff
raction 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 atmo
sphere and scaling the transfer function to different values of r0 and
C(n)2 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 calc
ulated OTF's are within 1% of the OTF's obtained with a continuous atm
osphere.