Temporal statistics of residual wavefront variance of an adaptive optics system

Abstract

Abstract 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.