基于光的反射与折射定律的表述方法推导及应用  

Derivation and application of expression methods based on law of reflection and refraction of light

作　　者：周旭环 龚云辉 吴绍华 王元康[1] 黄娅芳 叶洪伟 王光伟 王一成 ZHOU Xuhuan;GONG Yunhui;WU Shaohua;WANG Yuankang;HUANG Yafang;YE Hongwei;WANG Guangwei;WANG Yicheng(Yunnan KIRO Photonics Co.,Ltd.,Kunming 650217,China;Kunming Institute of Physics,Kunming 650223,China;The Second Military Representative Department Garrisoned in Kunming of Chongqing Military Representative Bureau,Army Armaments Department of PLA,Kunming 650032,China)

机构地区：[1]云南北方光学科技有限公司,云南昆明650217 [2]昆明物理研究所,云南昆明650223 [3]陆装重庆军代局驻昆地区第二军事代表室,云南昆明650032

出　　处：《应用光学》2022年第3期510-517,共8页Journal of Applied Optics

基　　金：中国兵器工业集团有限公司科技开发费项目。

摘　　要：光的反射和光的折射是几何光学应用中最基本的方法。在现代精密光学元件加工过程中,其不同的表述方法可以为光线追迹、棱镜误差分析以及棱镜装调提供不同的解决思路。介绍了光的反射定律和折射定律的传统形式表述方法,并推导了光的反射定律和折射定律的矢量、矩阵及四元数3种表述方法。通过Matlab辅助下的模拟计算,得到施密特棱镜检验光路中2个不同区域入射光线的反射在水平方向上对称分布于前表面反射像两侧,与实际应用相符,实现了矢量、矩阵和四元数表述方法在施密特棱镜检验光路中的应用。3种表述方法可以为光线追迹、棱镜误差分析以及棱镜装调提供科学、实用的解决方法。The reflection and refraction of light are the most basic methods for the application of geometric optics.In the processing of modern precision optical elements,the different expression methods can provide different solutions for light tracing,prism error analysis as well as prism assembly and adjustment.The traditional form expression methods of the law of reflection and the law of refraction of light were introduced,and the expression methods of vector,matrix and quaternion were derived.Through the simulation calculation assisted by Matlab,the reflected rays of incident light in two different areas of the Schmidt prism inspection optical path was symmetrically distributed on both sides of the reflected rays on the front surface in the horizontal direction,which was consistent with the practical application.The application of expression methods of vector,matrix and quaternion in Schmidt prism inspection optical path was realized.The three expression methods can provide scientific and practical solutions for light tracing,prism error analysis as well as prism assembly and adjustment.

关 键 词：四元数法 矢量和矩阵 表述方法 施密特棱镜 反射定律 折射定律 

分 类 号：TN209[电子电信—物理电子学] TN206