A performance prediction model for ground-based adaptive optics systems has been developed which permits the optimization of the spatial and temporal system response at a fixed throughput. The temporal response of the system is approximated to be that of a single-pole filter with a time constant (tau) . Approximate fits to actuator influence functions are used to model the adaptive mirror response, which is included as a high-pass spatial filter of the incident wavefront. The incident wavefront is also assumed to be spatially filtered by the sampling apertures of the wavefront sensor. The computed rms deviation of the corrected wavefront is used as the system performance measure. This system performance is parameterized in terms of the throughput a2v(tau) , where a is the actuator spacing and subaperture size and v is the pseudo-wind speed characteristic of the turbulence producing the wavefront aberrations, and the ratio of the temporal and spatial sampling intervals v(tau) /a. For large aperture telescopes with D >> r0, the performance curves are found to be independent of D and the optimal spatial and temporal bandwidths may be readily selected for the desired throughput, this parameterization provides a simple means of evaluating total system performance from typical wavefront sensor noise models.
The effects of focal and angular anisoplanatism are computed in order to evaluate the utility of using a single laser-produced guide star for the correction of ground-based astronomical imaging. The equations for the calculation of these effects are derived and the performance of a sodium-layer laser guide star system is computed for a Hufnagel atmospheric turbulence model. These results are presented in scaled units and for selected telescope apertures from 2-8 m in diameter operating at wavelengths from 0.5 to 2.0 microns. The limiting telescope aperture size which can be adequately corrected using a single sodium-layer guide star is shown to be much larger than previously estimated.