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使用辅助光栅的平面变间距全息光栅加工理论研究
引用本文:凌青,吴刚,王秋平.使用辅助光栅的平面变间距全息光栅加工理论研究[J].光学学报,2006,26(7):85-990.
作者姓名:凌青  吴刚  王秋平
作者单位:中国科学技术大学自动化系,合肥,230027;中国科学技术大学国家同步辐射实验室,合肥,230029
基金项目:中国科学院知识创新工程项目
摘    要:变间距全息光栅具有自聚焦和消像差功能,是高分辨率光谱仪与同步辐射单色器中的重要元件。研究了使用平面等间距光栅产生非球面波,记录平面变间距全息光栅的方法。根据几何光学的光线追迹理论,推导了光栅参量的四阶解析表达式。并基于费马原理,提出了记录光路的光线追迹数值算法。应用所推导的光栅参量四阶表达式,仿真设计了变间距全息光栅。通过合理选择记录参量,可以避免光栅基底受到零级及高阶衍射光场的影响。设计结果表明,理论光栅线密度与要求值相当符合;经光线追迹数值算法验证,解析表达式的展开误差在整个记录区域内小于1.5线;考虑到实际加工工艺允许误差,使用辅助光栅的记录光路对记录参量的误差并不敏感;设计实例证明了解析表达式的有效性,以及使用辅助光栅的记录光路的优越性。

关 键 词:几何光学  平面变间距全息光栅  光线追迹  费马原理
文章编号:0253-2239(2006)07-0985-6
收稿时间:2005-08-12
修稿时间:2005-10-03

Theoretical Study of Recording Varied Line Spacing Plane Holographic Gratings by Using Auxiliary Gratings
Ling Qing,Wu Gang,Wang Qiuping.Theoretical Study of Recording Varied Line Spacing Plane Holographic Gratings by Using Auxiliary Gratings[J].Acta Optica Sinica,2006,26(7):85-990.
Authors:Ling Qing  Wu Gang  Wang Qiuping
Institution:1Automation Department, University of Science and Technology of China, Hefei 230027;2 National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029
Abstract:Due to the ability of self-focusing and aberration-eliminating,varied line spacing holographic gratings have been the significant elements in high-resolution spectrometers and synchrotron radiation monochromators.Uniform line spacing plane gratings are introduced into recording systems to generate aspheric wavefronts to record varied line spacing plane holographic gratings.Analytical expressions of groove parameters are derived up to the forth order with(ray-tracing) theory of geometry optics.A numerical raytracing algorithm is provided based on(Fermat's) principle.A varied line spacing holographic grating is designed by applying the derived forth order expressions of grating parameters.Other diffractive light will not disturb the recording process when the recording parameters are properly selected.According to the design example,theoretical groove density parameters are very close to the required value.The truncation error of series expansion is less than 1.5 lines in the recording area through the validation of numerical ray-tracing algorithm.Considering the tolerances in practical fabrication,this mounting is not sensitive to the errors of recording parameters.Design results demonstrate the exactness of analytical expressions,and the superiority of recording optics with auxiliary gratings.
Keywords:geometrical optics  varied line spacing plane holographic grating  ray tracing  Fermat's principle
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