The performance of wavefront sensing with Hartmann sensors is generally suboptimal when the statistics associated to the random processes is not accurately 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 this work we investigated how the wavefront sensing accuracy is degraded when optimum estimators computed under the usual assumption of Kolmogorov turbulence are used to reconstruct sets of wavefronts whose statistics differs from the Kolmogorov one. The results assuming noiseless measurements show that optimum Kolmogorov estimators demonstrate a noticeable robustness, with a small loss of accuracy if the real turbulence statistics deviate from this model. The cases of the generalized power law spectrum and the outer-scale dependent exponential model are investigated. The influence of noise is briefly discussed.
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