关键词: 光栅衍射, 衍射调节, 菲涅尔衍射:MATLAB, 仿真模拟

Abstract: This artide is to study the influence of the ratio of the slit width to the wavelength in the university physics wave optics section on the diffraction factor and the error of the Fresnel half-wave band method. The article first uses matlab simulation to calculate grating diffraction distribution under the slit number N=2,100λ~0.01λ slit width, the influence of the ratio of slit width to wavelength on the diffraction factor is then initially obtained. The research conclusion shows that when xa/λ=10 mm, it can be considered that the diffraction factor can be ignored at this time, and xa/λ=10 mm is the diffraction limit constant. In the observation scale of 10 mm, when a/λ≤0.01, the diffraction factor is almost disappeared, so it can be quantitatively shown that the adjustment of the grating single-slit diffraction is negligible at this time, only the superposition of multi-slit interference is present. In order to quantitatively study the half-wave band complex amplitude change in the Fresnel circular aperture diffraction, the ratio method is used. The approximate error formula of the Fresnel half-wave band method is obtained, and finally the error of the Fresnel half-wave band method and the wavelength of the half-wave band number are obtained through MATLAB- DOI:10.3969/j.issn.1000-1565.2022.01.003基于衍射理论定量研究衍射调节与振幅误差路彦珍,张腾远,王泽宇,王凤平(北京科技大学 数理学院, 北京 100083)摘 要:为研究大学物理波动光学部分中缝宽与波长的比值对衍射因子的影响以及菲涅尔半波带法的误差问题,利用MATLAB仿真模拟,计算了在缝数N=2条件下,100λ~0.01λ缝宽的光栅衍射分布,初步得到了缝宽与波长的比值对衍射因子的影响规律.研究结果表明,当xa/λ=10 mm时,可认为此时恰好可以将衍射因子忽略.在10 mm观察尺度内,当a/λ≤0.01时,衍射因子的调节作用几乎消失,故可以定量表明此时光栅单缝衍射调节可忽略不计,只有多缝干涉的叠加.为定量研究菲涅尔圆孔衍射中半波带复振幅变化,通过比值的方法得到了菲涅尔半波带法的近似误差公式,最终再通过MATLAB模拟得到了菲涅尔半波带法的误差与半波带数所用光波长,以及圆孔的中心到场点的距离关系.由于公式的简洁性,在实际对衍射积分公式求解的过程中可以很方便地将参数代入公式计算误差,在实际应用时提供了理论支持.关键词:光栅衍射;衍射调节;菲涅尔衍射:MATLAB;仿真模拟中图分类号:O436.1 文献标志码:A 文章编号:1000-1565(2022)01-0016-06Quantitative study of diffraction adjustment and amplitude error based on diffraction theoryLU Yanzhen,ZHANG Tengyuan, WANG Zeyu, WANG Fengping(School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)Abstract: This artide is to study the influence of the ratio of the slit width to the wavelength in the university physics wave optics section on the diffraction factor and the error of the Fresnel half-wave band method. The article first uses matlab simulation to calculate grating diffraction distribution under the slit number N=2,100λ~0.01λ slit width, the influence of the ratio of slit width to wavelength on the diffraction factor is then initially obtained. The research conclusion shows that when xa/λ=10 mm, it can be considered that the diffraction factor can be ignored at this time, and xa/λ=10 mm is the diffraction limit constant. In the observation scale of 10 mm, when a/λ≤0.01, the diffraction factor is almost disappeared, so it can be quantitatively shown that the adjustment of the grating single-slit diffraction is negligible at this time, only the superposition of multi-slit interference is present. In order to quantitatively study the half-wave band complex amplitude change in the Fresnel circular aperture diffraction, the ratio method is used. The approximate error formula of the Fresnel half-wave band method is obtained, and finally the error of the Fresnel half-wave band method and the wavelength of the half-wave band number are obtained through MATLAB- 收稿日期:2021-06-03 基金项目:中央高校基本科研业务费资助项目(06108282) 第一作者:路彦珍(1971—),女, 河北临城人,北京科技大学讲师, 主要从事光电功能材料及其器件方向研究.Email: yzlu@ustb.edu.cn 通信作者:王凤平(1962—),女,黑龙江巴彦人,北京科技大学教授,主要从事光电功能材料及其器件研究.E-mail:fpwang@ustb.edu.cn第1期路彦珍等:基于衍射理论定量研究衍射调节与振幅误差simulation, and the distance between the center of the circular hole and the field point is obtained. Due to the simplicity of the formula, it is convenient to substitute parameters into the formula to calculate the error in the actual process of solving the diffraction integral formula, which provides theoretical support in practical applications.

Key words: grating diffraction, diffraction adjustment, Fresnel diffraction, MATLAB, simulation