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In adaptive optics (AO) systems, when the paths of the beacon source and the object source separate at an angle θ, a socalled angular anisoplanatism is produced. The angular anisoplanatic error described by isoplanatic angle (θ0) overestimates the degradation in AO correction, for it includes the piston component which has no effect on optical quality. So, it is necessary to study the effective error of angular anisoplanatism which has actual influence on AO performance. Define the variance reduction factor (Vrf) as the effective anisoplanatic error in which the piston is removed, divided by the anisoplantic error described by θ0. Through theoretical derivation and numerical evaluation, it is found that the Vrf is primarily influenced by a normalized coefficient b (b =θL /D, where L is the path length in turbulence and D is the receiver aperture diameter), and mildly influenced by the turbulence distribution. The major influence factor for Vrf with fixed b is turbulence strength in the high altitude while the influence from turbulence near the ground is negligible. Finally, a fitting formula of the Vrf is proposed, which can be used easily in practical applications to evaluate the performance of AO systems.
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