The quasiclassical distribution function for photon density in the phase space is obtained from solution of the kinetic equation. This equation describes propagation of paraxial laser beams in the Earth atmosphere where "collision integral" embodies the influence of turbulence. The anisotropy of photon distribution is shown and explained. For long propagation path, the explicit expression for fourth-order moment of light is obtained as a sum of linear and quadratic forms of the average distribution function. This moment describes a spatial correlation of four light waves, giving the information about the photon distribution in the cross-section of the beam. The fourth moment can be measured using two small detectors outside the central part of the beam. The linear form describes the shot noise (quantum fluctuations) of photons. The range where the shot noise exceeds the classical noise is found analytically. Derived photon fluctuations are the valuable source of information about statistical properties and local structure of the laser radiation that can be used for applications.

中文翻译：

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大气中光场的四阶矩

相空间中光子密度的准经典分布函数是从动力学方程的解中获得的。该方程描述了近轴激光束在地球大气中的传播，其中“碰撞积分”体现了湍流的影响。显示并解释了光子分布的各向异性。对于长传播路径，光的四阶矩的显式表达为平均分布函数的线性和二次形式的和。这个矩描述了四个光波的空间相关性，给出了光束横截面中光子分布的信息。可以使用光束中心部分外的两个小型探测器测量四阶矩。线性形式描述了光子的散粒噪声（量子涨落）。通过分析找到散粒噪声超过经典噪声的范围。衍生的光子波动是有关激光辐射的统计特性和局部结构的宝贵信息来源，可用于应用。