Gao Yan-Qi, Zhu Bao-Qiang, Liu Dai-Zhong, Lin Zun-Qi
Shanghai Institute of Optics and Fine Mechanics, Shanghai 201800, China.
J Opt Soc Am A Opt Image Sci Vis. 2010 Feb 1;27(2):358-65. doi: 10.1364/JOSAA.27.000358.
The fractional Fourier transform (FRFT) of the flat-topped multi-Gaussian beam (FMGB) is investigated based on the three kinds of FRFT optical systems: Lohmann I, Lohmann II, and quadratic graded-index systems. The analytical expressions for the FRFT of the FMGB are derived based on the propagation of the FMGB through the three systems. By introducing a hard-edge aperture function, the analytical expressions for the FRFT of the FMGB carried out by the apertured FRFT optical systems are presented. The FRFT characteristics of the FMGB for the three kinds of FRFT optical systems with and without apertures are discussed in detail. Results show that the three types of FRFT optical systems have the same function when the apertures are ignored but that significantly different characteristics are exhibited when the apertures appear.
基于三种分数傅里叶变换（FRFT）光学系统：罗曼I型、罗曼II型和二次渐变折射率系统，研究了平顶多高斯光束（FMGB）的分数傅里叶变换。基于FMGB在这三种系统中的传播，推导了FMGB的FRFT解析表达式。通过引入硬边光阑函数，给出了有光阑的FRFT光学系统对FMGB进行FRFT的解析表达式。详细讨论了有光阑和无光阑情况下，三种FRFT光学系统中FMGB的FRFT特性。结果表明，当忽略光阑时，这三种类型的FRFT光学系统具有相同的功能，但当存在光阑时，会表现出显著不同的特性。
