Fourth-order moment of the light field in atmosphere for moderate and strong turbulence

Collisionless Boltzmann equation is used to describe the intensity correlations in partially saturated and fully saturated regimes in terms of photon distribution function in the phase space. Explicit expression for fourth moment of the light fields is obtained for the case of moderate and strong turbulence. Such expression consists of two terms accounting for two regions in the phase space that independently contribute to the correlation function. It is shown that present solution agrees with previous results for fully saturated regime. Additionally it embodies the effect of partially saturated radiation where the correlations of photon trajectories are important and the magnitude of the scintillation index is well above the unity. Fourth moment is used to study the fluctuations of transmittance which consider the effect of finite detector aperture.