Wang Wei
J Opt Soc Am A Opt Image Sci Vis. 2024 Feb 1;41(2):261-271. doi: 10.1364/JOSAA.513833.
As a continuation of a previous investigation on the temporal integration of partially polarized thermal light and/or the spatial integration of polarization speckle, we calculate more accurate probability density functions for integrated Stokes parameters. With the aid of the unitary linear transformation and the Karhunen-Loève expansion of the stochastic electric field, the light of interest has been decomposed into an infinite number of statistically independent modes and the integrated Stokes parameters have been expressed as the sums of infinite numbers of random variables known as the polarization-related mode shape. A mathematical formalism of the exact solutions for the distributions of the integrated Stokes parameters has been derived. Through some approximations to the exact solutions, we also make a comparison of the "exact" and approximate solutions to understand the entire statistics of the integrated stochastic phenomena in optics.
作为之前关于部分偏振热光的时间积分和/或偏振散斑的空间积分研究的延续，我们计算了积分斯托克斯参数更精确的概率密度函数。借助随机电场的酉线性变换和卡尔胡宁 - 勒夫展开，感兴趣的光已被分解为无限多个统计独立的模式，并且积分斯托克斯参数已表示为无限多个称为偏振相关模式形状的随机变量之和。已经推导了积分斯托克斯参数分布的精确解的数学形式。通过对精确解的一些近似，我们还对“精确”解和近似解进行了比较，以了解光学中积分随机现象的整体统计特性。
