本文選題：塔爾博特效應 + 高密光柵��； 參考：《山西師范大學》2017年碩士論文

【摘要】：塔爾博特效應為相干照明下光柵衍射區(qū)等距離地重現(xiàn)光柵分布的現(xiàn)象。對傳統(tǒng)單位寬度刻線較少的光柵,幾乎可以完全重現(xiàn)光柵后表面的光場復振幅。在標量衍射理論下可以得到成像平面的位置,及分數(shù)塔爾博特效應。隨著技術的提高,1mm內刻線接近2000條,光柵的周期可以和波長相比擬的時候,標量衍射理論失效。對光柵衍射規(guī)律的研究應該采用嚴格的衍射理論�；诳沼�,頻域,空頻域的標量衍射理論,對比分析得出了光柵衍射在其衍射區(qū)等距離平面上重現(xiàn)光柵后表面復振幅的原因。其一為光柵的周期性結構使得經光柵出射的光場具有分立的頻譜,即出射的光場可以表示為具有特定頻率的一些平面波的組合。其二為菲涅耳近似條件下,傳遞函數(shù)為二次復指數(shù)函數(shù)�；跁r域有限差分法,采用CPML邊界條件,研究了二維情況下光柵衍射的規(guī)律,得到當光柵周期大于2倍波長時,周期性成像依然存在,光柵周期小于二倍波長時,周期性成像逐漸消失。利用矢勢方法對光柵衍射規(guī)律的分析得到了相同的結論,當周期性的結構的周期小于二倍波長時,周期性成像現(xiàn)象消失,周期大于二倍波長時,依舊存在塔爾博特效應。在應用塔爾博特效應進行結構測量,陣列照明等應用上可能存在指導意義。在更短波長的探測波可以探測更精細的結構。
[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.
【學位授予單位】：山西師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN25;O436.1

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