Optimal wavefront reconstruction from a Shack-Hartmann sensor by use of a Bayesian algorithm

An optimal algorithm has been derived for the reconstruction of random wavefronts using information on local slopes obtained with Hartmann-type sensors. The approach is based on calculation of the Bayesian posterior mean of the distribution. The accuracy of the method has been investigated via derivation of the error covariance matrix and subsequent calculation of the residual mean square error for waves which have propagated through the turbulent atmosphere. The dependence of the accuracy on the spatial correlation scale of the wavefront, the number of sensor channels and their signal-to-noise ratio is also discussed.