Adaptive optics (AO) systems can suppress the signal fade induced by atmospheric turbulence in satellite-to-ground coherent optical communication. The lower bound of the signal fade under AO compensation was investigated by analyzing the pattern of aberration modes for a one-stage imaging AO system. The distribution of the root mean square of the residual aberration is discussed on the basis of the spatial and temporal characteristics of the residual aberration of the AO system. The effectiveness of the AO system for improving the performance of coherent optical communication is presented in terms of the bit error rate and system availability.

For performance evaluation of an adaptive optics (AO) system, the probability of the system residual wavefront variance can provide more information than the wavefront variance average. By studying the Zernike coefficients of an AO system residual wavefront, we derived the exact expressions for the probability density functions of the wavefront variance and the Strehl ratio, for instantaneous and long-term exposures owing to the insufficient control loop bandwidth of the AO system. Our calculations agree with the residual wavefront data of a closed loop AO system. Using these functions, we investigated the relationship between the AO system bandwidth and the distribution of the residual wavefront variance. Additionally, we analyzed the availability of an AO system for evaluating the AO performance. These results will assist in designing and probabilistic analysis of AO systems.

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We present the probability density function (PDF) for the residual wavefront variance of an adaptive optics system that includes control error, the fitting error of a deformable mirror, and Hartmann sensor detecting noise. The PDF is directly connected to adaptive optics system parameters and the spatiotemporal strength parameters of atmospheric turbulence, and it can be described as a generalized Chi square distribution. Our results provide a more precise theory for adaptive optics systems compared to the current theory based on the ensemble average. Thus, this study can contribute to the development of high-resolution and high-stability adaptive optics systems for astronomy and optical communications in the atmosphere.

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