高密光栅的塔尔博特效应研究

发布时间：2018-06-15 13:31

本文选题：塔尔博特效应 + 高密光栅　；参考：《山西师范大学》2017年硕士论文

【摘要】：塔尔博特效应为相干照明下光栅衍射区等距离地重现光栅分布的现象。对传统单位宽度刻线较少的光栅,几乎可以完全重现光栅后表面的光场复振幅。在标量衍射理论下可以得到成像平面的位置,及分数塔尔博特效应。随着技术的提高,1mm内刻线接近2000条,光栅的周期可以和波长相比拟的时候,标量衍射理论失效。对光栅衍射规律的研究应该采用严格的衍射理论。基于空域,频域,空频域的标量衍射理论,对比分析得出了光栅衍射在其衍射区等距离平面上重现光栅后表面复振幅的原因。其一为光栅的周期性结构使得经光栅出射的光场具有分立的频谱,即出射的光场可以表示为具有特定频率的一些平面波的组合。其二为菲涅耳近似条件下,传递函数为二次复指数函数。基于时域有限差分法,采用CPML边界条件,研究了二维情况下光栅衍射的规律,得到当光栅周期大于2倍波长时,周期性成像依然存在,光栅周期小于二倍波长时,周期性成像逐渐消失。利用矢势方法对光栅衍射规律的分析得到了相同的结论,当周期性的结构的周期小于二倍波长时,周期性成像现象消失,周期大于二倍波长时,依旧存在塔尔博特效应。在应用塔尔博特效应进行结构测量,阵列照明等应用上可能存在指导意义。在更短波长的探测波可以探测更精细的结构。
[Abstract]:The Talbot effect is a phenomenon that the grating diffraction region reproduces the grating distribution at the same distance under coherent illumination. The complex amplitude of the light field on the surface of the grating can be almost completely reconstructed for the grating with less unit width. The position of the imaging plane and the fractional Talbot effect can be obtained under the scalar diffraction theory. The scalar diffraction theory fails when the grating period is comparable to that of the wavelength with the improvement of the technique when the internal lines of 1 mm are close to 2000, and the grating period can be compared with the wavelength of the grating. The strict diffraction theory should be used to study the diffraction law of grating. Based on the scalar diffraction theory in spatial domain, frequency domain and space-frequency domain, the reason why grating diffraction reproduces the complex amplitude of grating surface on the plane of equal distance in its diffraction region is obtained by comparison and analysis. The first is that the periodic structure of the grating makes the light field emitted by the grating have a discrete spectrum, that is, the emitted light field can be expressed as a combination of some plane waves with a specific frequency. The other is that the transfer function is a quadratic complex exponential function under Fresnel approximation. Based on the finite difference time-domain (FDTD) method and using CPML boundary condition, the law of grating diffraction is studied. When the grating period is more than 2 times wavelength, the periodic imaging still exists, and the grating period is less than two times wavelength. The periodic imaging gradually disappeared. The diffraction law of grating is analyzed by vector potential method. When the period of periodic structure is less than two times wavelength, the phenomenon of periodic imaging disappears, and the Talbot effect still exists when the period is larger than two times wavelength. The application of Talbot effect in structural measurement and array lighting may be of guiding significance. Detection waves at shorter wavelengths can detect finer structures.
【学位授予单位】：山西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN25;O436.1

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