  The scintillation index is obtained for the practically important range of
weak and moderate atmospheric turbulence. To study this challenging range, the
Boltzman-Langevin kinetic equation, describing light propagation, is derived
from first principles of quantum optics based on the technique of the photon
distribution function (PDF) [G. P. Berman et al., Phys. Rev. A 74, 013805
(2006)]. The paraxial approximation for laser beams reduces the collision
integral for the PDF to a two-dimensional operator in the momentum space.
Analytical solutions for the average value of PDF as well as for its
fluctuating constituent are obtained using an iterative procedure. The
calculated scintillation index is considerably greater than that obtained
within the Rytov approximation even at moderate turbulence strength. The
relevant explanation is proposed.
