An asymptotic theory of saturated fluctuations of laser irradiance diffracted by a thin layer of turbulent medium is built. The treatment is carried out in the phase screen approximation for the case of a power law spectrum of inhomogeneities in the layer. Asymptotic forms of the covariance of irradiance fluctuations are obtained and the character of the scintillation index approach to the asymptotic value is investigated. Calculations are made for collimated and focused laser beams.
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