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) fl uctuations is often used to investigate the properties of wave fronts corru gated by the atmosphere for high-angular-resolution techniques. Theoretical series expansions of this covariance are presented. The fast convergence o f these series reduces the calculation time of the covariance done by numer ical integration. The 2D covariance is a nonradial function. A physical int erpretation of this anisotropy is proposed. The spatiotemporal correlation of the AA is deduced from the covariance assuming the "frozen-flow" hypothe sis. The impact of the anisotropy on the evaluation of the number of predom inant turbulent layers and on the corresponding winds is investigated, and an analysis of temporal correlations is pet-formed. A simple theoretical ap proximation of the decorrelation time of the AA is given, which is found to be in agreement with experimental results. (C) 2000 Optical Society of Ame rica [S0740-3232(00)01909-8]. OCIS codes: 010.1080, 010.1330, 010.7350.