Abstract The Talbot effect of the finite phase grating is theoretically, computationally and experimentally investigated. The diffraction of finite periodic phase arrays in the Fresnel region is analyzed according to the scalar diffraction theory. The simulations can be performed with any PC using a MATLAB program developed by authors. Talbot images are generated for any light wavelength, grating period and any distance from the grating to screen. The algorithm details and MATLAB code are given, as well as the interesting insights than can be gained from the program. The additional intensity maximums over the borders of grating aperture on Talbot images are predicted to appear. The evolution of diffraction patterns on the fractional Talbot distances for the phase grating is simulated and compared with images for the grating with amplitude transmission. Phase gratings are produced and Talbot images of them are successfully measured. A comparative analysis of the theoretical results with the experimental ones is illustrated.

中文翻译：

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使用菲涅耳积分法模拟二元相位光栅的 Talbot 效应

摘要 从理论上、计算上和实验上研究了有限相位光栅的塔尔博特效应。根据标量衍射理论分析了菲涅耳区有限周期相阵列的衍射现象。可以使用作者开发的 MATLAB 程序在任何 PC 上执行仿真。Talbot 图像可针对任何光波长、光栅周期和光栅到屏幕的任何距离生成。给出了算法细节和 MATLAB 代码，以及可以从程序中获得的有趣见解。预计会出现在 Talbot 图像上光栅孔径边界上的附加强度最大值。模拟了相位光栅分数 Talbot 距离上衍射图案的演变，并与具有振幅传输的光栅图像进行了比较。产生相位光栅并成功测量它们的 Talbot 图像。说明了理论结果与实验结果的比较分析。