球面波入射二维光栅的泰伯效应  

Talbot Effect from Spherical Wave Illuminating on Two-Dimensional Grating

作　　者：尹东旭 周素梅[1] 谢意木男 Yin Dongxu;Zhou Sumei;Xie Yimunan(School of Physical Science and Technology,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学物理科学与技术学院,重庆400715

出　　处：《激光与光电子学进展》2021年第11期73-78,共6页Laser & Optoelectronics Progress

基　　金：中央高校基本科研业务费专项基金项目(XDJK2016C123);重庆市研究生科研创新项目(CYS14052)。

摘　　要：从理论和实验两方面研究了球面波入射二维光栅的泰伯效应。首先,分析球面波入射光栅后,菲涅耳衍射区光场的复振幅分布;其次,讨论了泰伯像及分数泰伯像的成像条件,得出成像位置及成像周期由光源至光栅的距离、光栅至观察面的距离共同决定,并且球面波入射光栅的泰伯距离等于其周期放大率与平面波入射光栅泰伯距离的乘积。实验结果与理论结果相符合,在特定位置处可观察到清晰的泰伯像及分数泰伯像。改变光源平面与光栅的距离,泰伯像按特定规律发生变化。由于光栅周期小于两倍孔径边长、球面波自身发散特性,分数泰伯像中出现像元交叠现象,按交叠程度可将交叠图像分为两种分数泰伯像,即点状离散分布及棋盘分布。本文研究可促进泰伯效应在光学测量及阵列照明等方面的应用。The Talbot effect from the spherical wave illuminating on two-dimensional(2 D) grating is investigated theoretically and experimentally. First, the complex amplitude distribution of the light field in the Fresnel diffraction region after the spherical wave is illuminating on the grating is analyzed. Second, the imaging conditions of the Talbot image and fractional Talbot image are discussed. The imaging position and imaging period are determined by the distance from the light source to the grating and the distance from the grating to the observation surface, and the Talbot distance of the spherical wave incident grating is equal to the product of its periodic magnification and the Talbot distance of the plane wave incident grating. Experimental results are consistent with the theoretical results,and the clear Talbot image and fractional Talbot image can be observed at specific location. By changing the distance from the light source plane to the grating, the Talbot image changes according to a specific law. Because the grating period is less than twice the aperture side length and based on the divergent characteristics of the spherical wave itself, the pixel overlap phenomenon appears in the fractional Talbot image. According to the degree of overlap, the overlapped image can be divided into two types(discrete point distribution and checkerboard distribution) of fractional Talbot images. The research in this paper can promote the application of the Talbot effect in optical measurement and array lighting.

关 键 词：衍射 二维光栅 泰伯效应 菲涅耳衍射 球面波 像元交叠 

分 类 号：O436[机械工程—光学工程]