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

Abstract

The most direct and efficient method to improve the sensitivity of gas sensor is to increase the effective optical path length (Leff) 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 Leff, 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 (Lave) 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 Leff values of the cubic cavities using TDLAS, with that and the theoretical formula between Leff and Lave, which in relation to the side length a, the diffuse reflectivity of coating and port fraction f, the experimental values of the Lave 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 Lave and the number of reflections established by the finite element method, the relative errors between the simulation values and the theoretical values of Lave are less than 3.6%, when each inner surface of the diffuse cubic cavity is divided into 10001000 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 Leff values of three different cubic cavities with side lengths of 5 cm, 8 cm, and 12 cm, and the corresponding experimental values of the Lave are calculated indirectly. A comparison among the theoretical values, simulation values and experimentical values of the Lave, 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.