Efficiency of optimum Kolmogorov estimators for different atmospheric statistics: Hartmann test

The performance of wavefront sensing with Hartmann sensors is generally sub optimal when the statistics associated to the random processes is not accur ately known. Turbulence-induced atmospheric phase distortions are commonly described in terms of the Kolmogorov power spectral density or -11/3 power law, although different atmospheric behaviors have also been reported. In t his work we investigated how the wavefront sensing accuracy is degraded whe n optimum estimators computed under the usual assumption of Kolmogorov turb ulence are used to reconstruct sets of wavefronts whose statistics differs from the Kolmogorov one. The results assuming noiseless measurements show t hat optimum Kolmogorov estimators demonstrate a noticeable robustness, with a small loss of accuracy if the real turbulence statistics deviate from th is model. The cases of the generalized power law spectrum and the outer-sca le dependent exponential model are investigated. The influence of noise is briefly discussed. (C) 1999 Elsevier Science B.V. All rights reserved.