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 (θ<sub>0</sub>) 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 (V<sub>rf</sub>) as the effective anisoplanatic error in which the piston is removed, divided by the anisoplantic error described by θ<sub>0</sub>. Through theoretical derivation and numerical evaluation, it is found that the V<sub>rf </sub>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 V<sub>rf</sub> 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 V<sub>rf</sub> is proposed, which can be used easily in practical applications to evaluate the performance of AO systems.
In order to thoroughly understand the characteristics of the aperture-averaging effect of atmospheric scintillation in terrestrial optical wireless communication and provide references for engineering design and performance evaluation of the optics system employed in the atmosphere, we have theoretically deduced the generally analytic expression of the aperture-averaging factor of atmospheric scintillation, and numerically investigated characteristics of the apertureaveraging factor under different propagation conditions. The limitations of the current commonly used approximate calculation formula of aperture-averaging factor have been discussed, and the results showed that the current calculation formula is not applicable for the small receiving aperture under non-uniform turbulence link. Numerical calculation has showed that aperture-averaging factor of atmospheric scintillation presented an exponential decline model for the small receiving aperture under non-uniform turbulent link, and the general expression of the model was given. This model has certain guiding significance for evaluating the aperture-averaging effect in the terrestrial optical wireless communication.