Calculation of minimum-variance estimators for Hartmann sensing using random wave vector simulations

The random wave vector approach (RWV) allows us to simulate phase samples w ith arbitrary statistics. In this paper we show how to apply this method to compute minimum variance estimators for Shack-Hartmann sensors dealing wit h the analysis of turbulence-distorted wavefronts. The RWV approach provide s straightforward and closed-form expressions for the Zernike coefficients of the simulated phases as well as for the associated sensor measurements. A wide range of subpupil shapes, e.g. square, hexagonal, circular or polar, can be easily handled. Linear minimum mean square error estimators can be calculated from ensemble averages of those samples by a direct application of the Gauss-Markov theorem. These results are applied to the assessment of the efficiency of several Hartmann masks with different subpupil geometrie s.