摘要
根据Sellmeir方程的系数在Lorentz模型中的意义所表明的数量关系,将该方程简化。对实验数据作适当的组合和变量替换,将修正的Sellmeir方程展开成多项式对实验数据进行拟合。根据对误差曲线的分析以及有关系数在Lorentz模型中作用,对该系数作进一步优化,最后确定修正的Sellmeir方程系数。得到在近紫外和近红外光谱区,方解石的修正的Sellmeir方程的系数分别为Ao=2.6926,Bo=0.0192,Co=0.0195,Do=0.0143;和Ae=2.1846,Be=0.0085,Ce=0.0143,De=0.0023,拟合结果的误差平方和分别为1.13×10-7和1.72×10-8。本结果可在计算方解石色散特性时使用,本方法可在拟合其它材料的色散方程时使用。
According to the magnitude relation indicated by the coefficients of Sellmeir equation in the Lorentz＇s modal, the equation was simplified. Then experiment data was suitably combined and variable substitutions were made, and polynomial of the improved Sellmeir equation was given to fit the experiment data. Based on the analysis of the residual curves and effect of a concerned coefficient in Sellmeir equation, the coefficient was optimized further. In the region near ultraviolet and infrared, the coefficients of the Sellmeir equation for calcite are Ao=2.6926, Bo=0.0192, Co=0.0195, Do=0.0143; and Ae=2.1846, Be=0.0085, Ce=0.0143, De=0.0023, respectively. The summed square of residuals is 1.13×10^-7 and 1.72×10^-8, respectively. The results can be used to calculate dispersive properties of calcite and the method can be used to obtain fitting formulas for other material.
出处
《光电工程》
EI
CAS
CSCD
北大核心
2007年第5期38-42,共5页
Opto-Electronic Engineering
关键词
色散方程
拟合
优化
方解石
Dispersion equations
Fitting
Optimization
Calcite
