The turbulence moment of order m (μ_m) is defined as the refractive index structure constant C_n² integrated over the whole path z with path-weighting function z^m. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ₀) and five-thirds-order moments of turbulence (μ_5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ₂) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ₂ can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ₂ as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ₀ and μ_5/3.

中文翻译：

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大气湍流二阶矩的测量方法

的顺序的湍流力矩米（μ_米）被定义为折射率结构常数c ^ _Ñ ²集成在整个路径Ž与路径的加权函数ž^米。大气湍流的光学效应与湍流矩直接相关。为了评估大气湍流的光学效应，有必要测量湍流矩。它公知的是湍流的零阶矩（μ ₀）和五个三分之二次矩湍流（μ _5/3分别对应于观察角和等平面角的）已在天文现场测试中作为常规参数进行了监视。然而，湍流（二阶矩直接测量μ ₂尚未见报道整个层气氛）。使用星作为光源，已经发现，μ ₂可以通过辐照度的协方差与合适的孔尺寸和孔分离两个接收孔口来测量。数值结果表明，在所有典型的湍流模型中，这种新方法的理论误差都可以忽略不计。这种方法使我们能够监测μ ₂如在天文现场测试的例程的参数，它是有助于理解大气湍流的更好联合特性μ ₀和μ _5/3。