Analytical solution for the covariance and for the decorrelation time of the angle of arrival of a wave front corrugated by atmospheric turbulence.

The two-dimensional (2D) spatial covariance of the angle-of-arrival (AA) fluctuations is often used to investigate the properties of wave fronts corrugated by the atmosphere for high-angular-resolution techniques. Theoretical series expansions of this covariance are presented. The fast convergence of these series reduces the calculation time of the covariance done by numerical integration. The 2D covariance is a nonradial function. A physical interpretation of this anisotropy is proposed. The spatiotemporal correlation of the AA is deduced from the covariance assuming the "frozen-flow" hypothesis. The impact of the anisotropy on the evaluation of the number of predominant turbulent layers and on the corresponding winds is investigated, and an analysis of temporal correlations is performed. A simple theoretical approximation of the decorrelation time of the AA is given, which is found to be in agreement with experimental results.

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