穆勒椭偏标定方法中LM算法研究

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。

Study on LM algorithm in Mueller's ellipsometry calibration method

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 to 0.24. 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.