Wang Fei, Cai Yangjian, Lin Qiang
Institute of Optical Information Engineering, Zhejiang Normal University, Jinhua, China.
J Opt Soc Am A Opt Image Sci Vis. 2008 Aug;25(8):2001-10. doi: 10.1364/josaa.25.002001.
The truncated fractional Fourier transform (FRT) is applied to a partially coherent Gaussian Schell-model (GSM) beam. The analytical propagation formula for a partially coherent GSM beam propagating through a truncated FRT optical system is derived by using a tensor method. Furthermore, we report the experimental observation of the truncated FRT for a partially coherent GSM beam. The experimental results are consistent with the theoretical results. Our results show that initial source coherence, fractional order, and aperture width (i.e., truncation parameter) have strong influences on the intensity and coherence properties of the partially coherent beam in the FRT plane. When the aperture width is large, both the intensity and the spectral degree of coherence in the FRT plane are of Gaussian distribution. As the aperture width decreases, the diffraction pattern gradually appears in the FRT plane, and the spectral degree of coherence becomes of non-Gaussian distribution. As the coherence of the initial GSM beam decreases, the diffraction pattern for the case of small aperture widths gradually disappears.
截断分数傅里叶变换（FRT）应用于部分相干高斯谢尔模型（GSM）光束。利用张量方法推导了部分相干GSM光束通过截断FRT光学系统传播的解析传播公式。此外，我们报道了部分相干GSM光束截断FRT的实验观测结果。实验结果与理论结果一致。我们的结果表明，初始光源相干性、分数阶和孔径宽度（即截断参数）对FRT平面中部分相干光束的强度和相干特性有强烈影响。当孔径宽度较大时，FRT平面中的强度和光谱相干度均呈高斯分布。随着孔径宽度减小，FRT平面中逐渐出现衍射图样，光谱相干度变为非高斯分布。随着初始GSM光束的相干性降低，小孔径宽度情况下的衍射图样逐渐消失。
