穆勒椭偏标定方法中LM算法研究  

Study on LM algorithm in Mueller’s ellipsometry calibration method

作　　者：管钰晴 唐冬梅[2] 傅云霞[2] 孙佳媛[2] 韩志国 张波[2] 孔明 曹程明[2] 雷李华 Guan Yuqing;Tang Dongmei;Fu Yunxia;Sun Jiayuan;Han Zhiguo;Zhang Bo;Kong Ming;Cao Chengming;Lei Lihua(College of Metrology and Measurement Engineering,China Jiliang University,Hangzhou 310018,China;Shanghai Institute of Measurement and Testing Technology,Shanghai 201203,China;The 13th Research Institute of CETC,Shijiazhuang 050051,China)

机构地区：[1]中国计量大学计量测试工程学院,浙江杭州310018 [2]上海市计量测试技术研究院,上海201203 [3]中国电子电科集团第十三研究所,河北石家庄050051

出　　处：《红外与激光工程》2020年第8期160-168,共9页Infrared and Laser Engineering

基　　金：国家重点研发计划项目(SQ2019YFB20002503);航空科学基金项目(201856Y5001);国家市场监管总局科技项目(2019MK016)。

摘　　要：依据穆勒椭偏测量方法中偏振光的传输方式,提出了一种椭偏系统中光学元件参数的定标方法。通过建立出射光强关于起偏器和检偏器透光轴方位角、旋转补偿器方位角和相位延迟的非线性最小二乘模型,用列文伯格-马夸尔特(Levenberg-Marquardt,LM)算法对初始参数进行迭代。求解出光学元件参数的精确值,从而实现对元件的定标。通过仿真实验,利用已知穆勒(Mueller)矩阵且标定值为(24.90±0.30)nm的SiO2/Si标准样片,基于LM算法迭代计算光强值的残差平方和。实验可得当迭代次数为50次时,残差平方和收敛到最小值0.24;与传统多点标定法进行对比试验,验证了基于LM算法求解光学参数的可行性;用标定值为(91.21±0.36)nm的SiO2/Si标准样片进行验证,得到膜厚的计算值为91.53 nm,相对误差为0.35%。结果表明:在穆勒椭偏系统参数标定中,LM算法具有收敛速度快,计算精度高等优点。According to the transmission method of polarized light in Mueller ellipsometry method,this paper presented a method for calibrating the optical element parameters in ellipsometry system.By establishing a nonlinear least squares model of outgoing light intensity with respect to orientations of transmission axis of the polarizer and analyzer and orientations and retardation of the rotation compensator,the initial parameters were iterated with Levenberg-Marquardt(LM)algorithm.Accurate values of optical element parameters could be obtained,so as to achieve the calibration of components.Through the simulation experiment,using the SiO2/Si standard sample with the known Mueller matrix and the calibration value of(24.90±0.30)nm,the residual square sum of the light intensity value was calculated based on LM algorithm.When numbers of iterations accumulate to 50,the sum of squares converges of the residuals of the measurement and calculation was limited to0.24.Then compared with the traditional multi-point calibration method,the feasibility of solving optical parameters based on LM algorithm was verified.Fitting results were validated by SiO2/Si standard sample with calibration value of(91.21±0.36)nm.Calculated film thickness was 91.53 nm and the relative error is 0.35%.Results proved that LM algorithm has advantages of rapidly converging and high precision in the parameter calibration of the Mueller ellipsometry system.

关 键 词：参数定标 穆勒矩阵 椭偏测量 LM算法 标准样片 

分 类 号：TB96[机械工程—光学工程]