Abstract：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 is the same one by selecting from the four values. As an application example, this paper selects the optical constant of water in the literature at 0.5～1.0 μm as the “theoretical value”, and the quartz and polymethyl methacrylate glasses with known optical constants are taken as the liquid cell materials. Without considering the instrument measurement error, the above literature data are substituted into the spectral transmittance equation, and the calculated transmittance is taken as “experimental data”. Then, the optical constants of water are determined by finding the roots of polynomials, and the results are in full agreement with the “theoretical values”. The simulation process and calculation results show that the new method is available and solves the problems of the inversion method such as time-consume, iteration error, and the binary of refractive index, and provides a new option for determining the optical constants of liquids.
杨百愚，李 磊，王伟宇，武晓亮，王翠香，范 琦，刘 静，徐翠莲. 基于多项式求根的双厚度透射法确定液体光学常数[J]. 光谱学与光谱分析, 2024, 44(10): 2733-2738.
YANG Bai-yu, LI Lei, WANG Wei-yu, WU Xiao-liang, WANG Cui-xiang, FAN Qi, LIU Jing, XU Cui-lian. Determination of Liquid Optical Constants by Double Thickness
Transmission Method Based on Polynomial Root Finding. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(10): 2733-2738.
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