基于多项式求根的双厚度透射法确定液体光学常数  

Determination of Liquid Optical Constants by Double Thickness Transmission Method Based on Polynomial Root Finding

作　　者：杨百愚[1] 李磊[1] 王伟宇 武晓亮[1] 王翠香 范琦 刘静[1] 徐翠莲 YANG Bai-yu;LI Lei;WANG Wei-yu;WU Xiao-liang;WANG Cui-xiang;FAN Qi;LIU Jing;XU Cui-lian(Fundamentals Department,Air Force Engineering University,Xi'an 710051,China)

机构地区：[1]空军工程大学基础部,陕西西安710051

出　　处：《光谱学与光谱分析》2024年第10期2733-2738,共6页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(12004437)资助。

摘　　要：光谱反演法可实现液体光学常数(消光系数和折射率)的确定,其中双厚度透射法是有代表性的光谱反演法之一。由于液体自身无法形成确定的形状,需要盛放在透明容器(液体池)中,因而通过实验测量得到的光谱透射率包含了液体池光学常数的影响,这使得基于双厚度透射法所建立的光谱透射率方程极为复杂,难以求得解析解,通常采用反演法来计算液体的光学常数。现有的反演法存在如下问题:一是反演迭代耗费时间,二是反演迭代会引入误差,三是反演法得到的液体折射率存在二值问题。为解决上述问题,基于三层介质结构(液体池),考虑光在两种介质分界面上的多次反射,建立液体厚度满足整数比的光谱透射率方程组。通过代数运算获得与消光系数有关的多项式方程,求解并选择大于0小于1的实数根来计算消光系数;另求解关于液体池光学窗口反射率的一元二次方程,选择大于0小于1的根来计算液体和容器分界面的反射率,进而计算得到液体折射率的两个值。再用另一材料制作的液体池测量液体的光谱透射率,然后结合已经得到的消光系数作相关计算,会另外得到液体折射率的两个值,从四个值中选择相同者即为液体的折射率。作为应用示例,选用文献中水在0.5~1.0μm光谱范围的光学常数作为“理论值”、光学常数已知的石英玻璃和有机玻璃作为液体池材料。在不考虑仪器测量误差的情况下,将上述文献数据代入光谱透射率方程,计算得到的透射率作为“实验数据”。然后用多项式求根的方法确定水的光学常数,所得结果与“理论值”完全符合。模拟过程和计算结果表明:新方法是可用的,该方法解决了反演法的计算耗时、迭代误差以及折射率的二值问题,为液体光学常数的确定提供了一个新选择。The liquid's optical constants(extinction coefficient and refractive index)can be determined by the spectral inversion method,among which the double-thickness transmission is most representative.Since the liquid itself cannot form a definite shape,it needs to be stored in a transparent container(liquid cell),so the spectral transmittance obtained through experimental measurement includes the influence of the optical constant of the liquid cell,which makes the spectral transmittance equation established based on the double-thickness transmission method extremely complex and difficult to obtain an analytical solution.Usually,the inversion method is used to calculate the optical constant of the liquid.The existing inversion methods have the following problems:first,the inversion iteration consumes time;second,the inversion iteration will introduce errors;and third,the liquid refractive index obtained by the inversion method has a binary problem.To solve the above problems,based on the three-layer medium structure(liquid cell),considering the multiple reflections of light on the interface of the two media,a set of spectral transmittance equations satisfying the integral ratio of liquid thickness is established.The polynomial equation related to the extinction coefficient is obtained through algebraic operation,and the extinction coefficient is calculated by solving and selecting the real number root greater than 0 and less than 1.In addition,the quadratic equation about the reflectance of the optical window of the liquid cell is solved.The reflectance of the interface between the liquid and the container is calculated with the root greater than 0 and less than 1,and two values of the liquid refractive index are obtained.Then,the liquid cell made of another material is used to measure the spectral transmittance of the liquid,and then combined with the extinction coefficient that has been obtained for related calculation,two other values of the liquid refractive index are obtained,and the refractive index of the liquid

关 键 词：光学常数 折射率 消光系数 衰减系数 双厚度透射率模型 

分 类 号：O433.1[机械工程—光学工程]