Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems

The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m- and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O(n) operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).