Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging sys tem is determined by a combination of the residual time-varying phase disto rtions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the e ffects of these two errors on the time-averaged Strehl ratio and the time-a veraged optical transfer function (OTF) of the AO system are not formally s eparable, such an approximation is found to be accurate to within a few per cent for a range of representative residual wave-front errors. In these cal culations, we combined static optical system aberrations and time-varying r esidual phase distortion characteristics of a deformable mirror fitting err or, wave-front sensor noise, and anisoplanatism. The static aberrations con sist of focus errors of varying magnitudes as well as a combination of unse nsed and uncorrectable mirror figure errors derived from modeling by the Ge mini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that a re due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations , as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lowe r bounds on the actual Values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging te chniques are usually not required. (C) 1999 Optical Society of America.