漫反射立方腔单次反射平均光程的理论和实验研究

根据Beer-Lambert定律可知,增加气体池的有效光程是提高气体监测灵敏度最直接而有效的途径.通过实验研究和分析,漫反射立方腔作为气体池能显著地增加有效光程,因此研究其内部的光线传播规律具有重要意义.基于对漫反射立方腔内光线传播规律的理论分析,得到了单次反射平均光程的理论值,建立了漫反射立方腔内光线传播的理论近似模型,并通过有限元法仿真获得了单次反射平均光程的模拟值.利用可调谐二极管激光吸收光谱技术得到了立方腔的有效光程,间接求得了单次反射平均光程的实验值.对理论值、模拟值和实验值进行比较分析,验证了理论近似模型和有限元法仿真的准确性和稳定性.

Theoretical and experimental study of average reflection optical path length of diffuse cubic cavity

The most direct and efficient method to improve the sensitivity of gas sensor is to increase the effective optical path length (L_eff) of gas cell according to the Beer-Lambert law. Moreover through experimental research and analysis, the diffuse cubic cavity, as a kind of gas cell, can effectively increase the value of L_eff, which is crucial to the study of the reflection law of light in the diffuse cubic cavity. Based on the analysis of the reflection law of light in the diffuse cubic cavity, the theoretical value of the single reflection average optical path length (L_ave) is obtained, the theoretical approximation model of the light reflection in the diffuse cubic cavity is established, and the simulation values are obtained by the finite element method. The tunable diode laser absorption spectroscopy (TDLAS) is a perferred gas dection technique with high selectivity, fast response and non-contact measuring. We develop diffuse cubic cavities of different sizes and study the reflection law and characteristics of the light in the cavities. We obtain the L_eff values of the cubic cavities using TDLAS, with that and the theoretical formula between L_eff and L_ave, which in relation to the side length a, the diffuse reflectivity of coating ρ and port fraction f, the experimental values of the L_ave are obtained. The accuracies and stabilities of the theoretical approximation model and the simulation results by the finite element method are verified. According to the relationship between the L_ave and the number of reflections established by the finite element method, the relative errors between the simulation values and the theoretical values of L_ave are less than 3.6%, when each inner surface of the diffuse cubic cavity is divided into 1000×1000 or more small patches. It shows that the finite element method has a satisfactory effect on the cubic cavities with different sizes, and the error range is less than 0.1%. The TDLAS is used to measure the L_eff values of three different cubic cavities with side lengths of 5 cm, 8 cm, and 12 cm, and the corresponding experimental values of the L_ave are calculated indirectly. A comparison among the theoretical values, simulation values and experimentical values of the L_ave, shows that these three values are well consistent with each other, which indicates that the simulation of the reflection law of light in the diffuse reflection cubic cavity has a significant reference value for the experimental study. Also, the present study of the diffuse cubic cavity will provide a technical support for studying the diffuse cavity of arbitrary shape in the future.