使用辅助光栅的平面变间距全息光栅加工理论研究  

Theoretical Study of Recording Varied Line Spacing Plane Holographic Gratings by Using Auxiliary Gratings

作　　者：凌青[1] 吴刚[1] 王秋平[2] 

机构地区：[1]中国科学技术大学自动化系,合肥230027 [2]中国科学技术大学国家同步辐射实验室,合肥230029

出　　处：《光学学报》2006年第7期985-990,共6页Acta Optica Sinica

基　　金：中国科学院知识创新项目(KY4206)资助课题

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。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 ray-tracing 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.

关 键 词：几何光学 平面变间距全息光栅 光线追迹 费马原理 

分 类 号：O436.1[机械工程—光学工程]