阻尼最小二乘算法CARS光谱温度拟合

为了解决相干反斯托克斯喇曼散射（CARS）光谱CARSFT计算程序在温度拟合过程中，对初值依赖大、测量光谱信噪比差、不易收敛的问题，通过分析非线性迭代算法，采用了阻尼最小二乘算法对氮气CARS光谱进行温度拟合。针对CARS理论光谱计算公式较为复杂的特点，采用数值差分的方式来获得迭代计算时所需要的设计矩阵。分析了横向偏移、纵向偏移和温度三个主要参量对拟合残差的影响，发现纵向偏移的初值设置对温度拟合影响较大。拟合温度2000 K时的标准理论CARS光谱，设置偏离较大的初始值，采用阻尼最小二乘法获得了较好的结果。迭代计算167步后，温度拟合为2 005.6 K，残差为0.027 463。拟合光谱信噪比较差的CARS光谱，阻尼最小二乘法也能稳定收敛。结果验证了阻尼最小二乘法对初值的依赖不大，并且当拟合谱信噪比较差时也能收敛，可用于在恶劣环境下CARS测量光谱的拟合。

Temperature estimation of coherent anti-stokes Raman scattering spectra using Levenberg-Marquarat algorithm

In order to solve the defects of CARSFT program found in parameter estimation of coherent anti-Stokes Raman scattering (CARS) spectra, Levenberg-Marquarat (L-M) algorithm was used. Due to the complexity of CARS spectrum theoretical formulas. The Jacobian matrix was obtained by numerical differentiation. On the basis of analyzing the effects of lateral deviation, longitudinal deviation, and temperature on the fitting residual error, the initial value of the longitudinal deviation is considered to be more important on the rate of convergence. L-M algorithm was applied to fit a standard CARS spectrum in 2000 K. The more deviant the initial values of parameters are, the better result is obtained. After running 167 iterations, the temperature is stabilized to 2 005.6 K, and its residual error is 0.027 463. Another example with low signal-to-noise ratio data was followed, and the result converges. The results show that Levenberg-Marquarat algorithm has little dependence on initial values, and could be applied to temperature estimation of CARS spectra in harsh environments.