Bos Jeremy P, Rao Gudimetla V S, Schmidt Jason D
J Opt Soc Am A Opt Image Sci Vis. 2017 Aug 1;34(8):1433-1440. doi: 10.1364/JOSAA.34.001433.
We derive a generalized expression for the differential piston phase variance in non-Kolmogorov turbulence. Specifically, our result applies in the case where index of refraction is described by a power-law medium with an exponent between 0 and 1. Kolmogorov assumptions of homogeneity and isotropy are maintained. After some development, our expression is derived using the Mellin-transform techniques and may be generalized to other forms for the three-dimensional index of refraction turbulence power spectrum. This analytical result has two regions of convergence. The separation between these regions is defined by a characteristic time given as the ratio of the mean wind speed and aperture size. By evaluating this expression, we find the differential piston phase variance exhibits a power-law behavior roughly proportional to that of the medium. In addition, we find that piston phase variance decreases with increase in aperture size. We also find that the differential piston phase variance is independent of aperture size as the power law approaches unity.
我们推导了非柯尔莫哥洛夫湍流中微分活塞相位方差的广义表达式。具体而言，我们的结果适用于折射率由指数在0到1之间的幂律介质描述的情况。保持了柯尔莫哥洛夫的均匀性和各向同性假设。经过一些推导，我们的表达式是使用梅林变换技术得出的，并且可以推广到三维折射率湍流功率谱的其他形式。这个解析结果有两个收敛区域。这些区域之间的分隔由一个特征时间定义，该特征时间为平均风速与孔径大小的比值。通过评估这个表达式，我们发现微分活塞相位方差呈现出大致与介质成比例的幂律行为。此外，我们发现活塞相位方差随着孔径大小的增加而减小。我们还发现，当幂律趋近于1时，微分活塞相位方差与孔径大小无关。
