Probability of the residual wavefront variance of an adaptive optics system and its application

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.