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Normally one of the two approaches is used to evaluate the performance of an adaptive optics system. In the first approach the normalized antenna gain (or Strehl ratio) associated with a variety of degrading effects acting alone is evaluated. The normalized antenna gain of the system when degraded by a combination of these effects is then found by forming the product of the individual antenna gains involved. The second approach is to evaluate system performance by simulation on a large mainframe computer. In the work presented here, physical optics formulas and elementary statistical concepts are used to develop an approach that shares some of the advantages of both of these previous approaches. By working in the time domain, relatively simple formulas are developed that shed insight into the factors that degrade adaptive optics system performance. In addition, the impact of several degrading factors acting simultaneously can be evaluated. In this study the normalized antenna gain is evaluated for a system degraded by turbulence, anisoplanatism, a finite servo bandwidth and a combination of anisoplanatism and a finite servo bandwidth. In the finite servo bandwidth study, system performance is evaluated as a function of diameter illustrating that the resulting antenna gain decays from the diffraction limited antenna gain to the large diameter asymptotic limit antenna gain first predicted by Greenwood. The diameter dependence of this effect is similar to that due to anisoplanatism but not as severe at intermediate diameters. The last study evaluating the combined degradation associated with anisoplanatism and a finite servo bandwidth illustrates the important role played by high temporal frequency phase information. Introducing a finite bandwidth to a system already degraded by anisoplanatism can actually improve performance slightly, in certain cases, because highly distorted high frequency information is lost.
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