基于多项式求根的双厚度透射率模型确定光学常数

为解决光谱反演法确定物质光学常数的一些问题，基于传统的双厚度透射率模型，建立厚度分别为L和2L的光谱透射率方程，通过代数运算获得与衰减系数有关的八次多项式方程，求解并选择其大于0小于1的实数根来计算衰减系数和消光系数；再求解关于界面反射率的一元二次方程，选择其大于0小于1的根来计算折射率。在确定光学常数的过程中，新方法没有反演误差和迭代计算耗时问题。利用已知文献中庚烷的光学常数验证新方法的可靠性，并分析了双厚度不满足2倍关系时对计算结果的影响，结论是第二厚度2L的相对误差不超过1%时，消光系数的计算误差不超过2.03%，不考虑3个强吸收点时，折射率的计算误差不超过1%。

Determination of Optical Constants by Double Thickness Transmittance Model Based on Polynomial Root

To solve some problems in the determination of substance optical constants by spectral inversion, based on the traditional double thickness transmittance model, spectral transmittance equations with thicknesses of L and 2L are established. The eighth-order polynomial equation related to the attenuation coefficient is obtained through an algebraic operation. Real roots greater than 0 and less than 1 are solved to calculate the attenuation coefficient and extinction coefficient. Then, the quadratic equation with one unknown quantity about the interface reflectivity is solved, and the roots greater than 0 and less than 1 are selected to calculate the refractive index. In the process of determining the optical constants, the new method has no inversion error or iterative calculation time-consuming problems. The reliability of the new method is verified using the known optical constants of heptane from the literature, and the influence on the calculation results was analyzed when the double thickness does not satisfy the double relationship. In conclusion, when the relative error of the second thickness 2L was no more than 1%, the calculation error of the extinction coefficient was no more than 2.03%, and when three strong absorption points were not considered, the calculation error of the refractive index was no more than 1%.