Lin Qiang, Cai Yangjian
Opt Lett. 2002 Oct 1;27(19):1672-4. doi: 10.1364/ol.27.001672.
The fractional Fourier transform (FRT) is applied to partially coherent twisted anisotropic Gaussian-Schell model (GSM) beams based directly on the cross-spectral density. An analytical and concise formula is derived for the cross-spectral density of partially coherent twisted anisotropic GSM beams passing through a FRT system in terms of the tensor method. The corresponding tensor ABCD law for performing a FRT is obtained. The connection between the FRT formula and the generalized Collins formula for partially coherent beams is discussed. The formulas derived provide a powerful tool for analyzing and calculating the FRTs of partially coherent beams.
分数傅里叶变换（FRT）直接基于交叉谱密度应用于部分相干扭曲各向异性高斯 - 谢尔模型（GSM）光束。利用张量方法，推导了部分相干扭曲各向异性GSM光束通过FRT系统时交叉谱密度的解析且简洁的公式。得到了用于执行FRT的相应张量ABCD定律。讨论了FRT公式与部分相干光束广义柯林斯公式之间的联系。所推导的公式为分析和计算部分相干光束的FRT提供了有力工具。
