A new integral-functional equation is derived for the four-dimensional Fourier transform of the four-point coherence function of laser beams in turbulent media and two families of exact analytical solutions of this equation are found. These solutions hold for any level of fluctuations of the refractive index of air. They are used to obtain exact analytic representations of the integral characteristics of the four-point coherence function. In particular, the truncated spectral characteristics of the spatial correlation function of the intensities are found. These representations can be used to test asymptotic, numerical, and other methods for finding this function and to describe its integral properties.

中文翻译：

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湍流介质中激光束四点相干函数积分特性的精确解析表示

导出了湍流介质中激光束四点相干函数的四维傅里叶变换的新积分函数方程，并找到了该方程的两个精确解析解。这些解决方案适用于任何水平的空气折射率波动。它们用于获得四点相干函数积分特征的精确解析表示。特别地，发现强度的空间相关函数的截短的光谱特性。这些表示可用于测试渐近线，数值和其他方法来查找此函数并描述其积分特性。