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漫反射立方腔单次反射平均光程的理论和实验研究

张云刚 刘如慧 汪梅婷 王允轩 李占勋 童凯

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漫反射立方腔单次反射平均光程的理论和实验研究

张云刚, 刘如慧, 汪梅婷, 王允轩, 李占勋, 童凯

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

Zhang Yun-Gang, Liu Ru-Hui, Wang Mei-Ting, Wang Yun-Xuan, Li Zhan-Xun, Tong Kai
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  • 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.
    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.
      通信作者: 刘如慧, liuruhuizjk@126.com
    • 基金项目: 国家自然科学基金(批准号:61308065)和河北省自然科学基金(批准号:E2015203014)资助的课题.
      Corresponding author: Liu Ru-Hui, liuruhuizjk@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61308065) and the Natural Science Foundation of Hebei Province, China (Grant No. E2015203014).
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    Hwang J, Shin D J, Jeong K R 2016 Metrologia 53 1231

    [13]

    Fukutomi D, Ishii K, Awazu K 2015 Lasers Med. Sci. 30 1335

    [14]

    Lackner M 2007 Rev. Chem. Eng. 23 65

    [15]

    Wang F, Cen K F, Li N, Jeffries J B, Huang Q X, Yan J H, Chi Y 2010 Meas. Sci. Technol. 21 45301

    [16]

    Gao Y W, Zhang Y J, Chen D, He Y, You K, Chen C, Liu W Q 2016 Chin. Opt. Lett. 36 275(in Chinese) [高彦伟, 张玉钧, 陈东, 何莹, 尤坤, 陈晨, 刘文清 2016 光学学报 36 275]

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    Gao G Z, Cai T D, Hu B, Jia T J 2015 Spectrosc. Spect. Anal. 35 34(in Chinese) [高光珍, 蔡廷栋, 胡波, 贾天俊 2015 光谱学与光谱分析 35 34]

    [19]

    Yu J, Zheng F, Gao Q, Li Y J, Zhang Y G, Zhang Z G, Wu S H 2014 Appl. Phys.. 116 135

    [20]

    Fry E S, Musser J, Kattawar G W, Zhai P W 2006 Appl. Opt. 45 9053

    [21]

    Manojlovic L M, Marincic A S 2011 Meas. Sci. Technol. 22 075303

    [22]

    Yu J 2014 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [虞佳 2014 博士学位论文 (哈尔滨: 哈尔滨工业大学)]

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  • [1]

    Tang G H, Xu C L, Shao L T, Wang S M 2008 Chin. J. Sci. Instru. 29 244(in Chinese) [汤光华, 许传龙, 邵礼堂, 王式民 2008 仪器仪表学报 29 244]

    [2]

    Yu M J, Liu M H, Dong Z R, Sun Y G, Cai H W, Wei F 2015 Chin. J. Laser 42 351(in Chinese) [郁敏捷, 刘铭晖, 董作人, 孙延光, 蔡海文, 魏芳 2015 中国激光 42 351]

    [3]

    Liu J, Si F Q, Zhou H J, Zhao M J, Dou K, Wang Y, Liu W Q 2015 Chin. Opt. Lett. 35 337(in Chinese) [刘进, 司福祺, 周海金, 赵敏杰, 窦科, 王煜, 刘文清 2015 光学学报 35 337]

    [4]

    Liang H Z, Zhang X, Rao J, Chen H W 2008 Chin. J. Biotechnol. 28 124(in Chinese) [梁华正, 张燮, 饶军, 陈焕文 2008 中国生物工程杂志 28 124]

    [5]

    D'Amico A, Pennazza G, Santonico M, Martinelli E, Roscioni C, Galluccio G, Paolesse R, Natale C D 2010 Lung Cancer 68 170

    [6]

    Teh S K, Zheng W, Ho K Y, Teh M, Yeoh K G, Huang Z W 2010 Int. J. Cancer 126 1920

    [7]

    Yang X B, Zhao W X, Tao L, Gao X M, Zhang W J 2010 Acta Phys. Sin. 59 5154(in Chinese) [杨西斌, 赵卫雄, 陶玲, 高晓明, 张为俊 2010 物理学报 59 5154]

    [8]

    Hu R Z, Wang D, Xie P H, Ling L Y, Qin M, Li C X, Liu J G 2014 Acta Phys. Sin. 63 110707(in Chinese) [胡仁志, 王丹, 谢品华, 凌六一, 秦敏, 李传新, 刘建国 2014 物理学报 63 110707]

    [9]

    Sjoholm M, Somesfalean G, Alnis J, Andersson-Engels S, Svanberg S 2011 Opt. Lett. 26 16

    [10]

    Tranchart S, Bachir I H, Destombes J L 1996 Appl. Opt. 35 7070

    [11]

    Lucke R L 2007 Appl. Opt. 46 6966

    [12]

    Hwang J, Shin D J, Jeong K R 2016 Metrologia 53 1231

    [13]

    Fukutomi D, Ishii K, Awazu K 2015 Lasers Med. Sci. 30 1335

    [14]

    Lackner M 2007 Rev. Chem. Eng. 23 65

    [15]

    Wang F, Cen K F, Li N, Jeffries J B, Huang Q X, Yan J H, Chi Y 2010 Meas. Sci. Technol. 21 45301

    [16]

    Gao Y W, Zhang Y J, Chen D, He Y, You K, Chen C, Liu W Q 2016 Chin. Opt. Lett. 36 275(in Chinese) [高彦伟, 张玉钧, 陈东, 何莹, 尤坤, 陈晨, 刘文清 2016 光学学报 36 275]

    [17]

    Zhou X, Yu J, Wang L, Gao Q, Zhang Z G 2017 Sens. Actuators B: Chem. 241 1076

    [18]

    Gao G Z, Cai T D, Hu B, Jia T J 2015 Spectrosc. Spect. Anal. 35 34(in Chinese) [高光珍, 蔡廷栋, 胡波, 贾天俊 2015 光谱学与光谱分析 35 34]

    [19]

    Yu J, Zheng F, Gao Q, Li Y J, Zhang Y G, Zhang Z G, Wu S H 2014 Appl. Phys.. 116 135

    [20]

    Fry E S, Musser J, Kattawar G W, Zhai P W 2006 Appl. Opt. 45 9053

    [21]

    Manojlovic L M, Marincic A S 2011 Meas. Sci. Technol. 22 075303

    [22]

    Yu J 2014 Ph. D. Dissertation (Harbin: Harbin Institute of Technology) (in Chinese) [虞佳 2014 博士学位论文 (哈尔滨: 哈尔滨工业大学)]

    [23]

    Yu J, Zhang Y G, Gao Q, Hu G, Zhang Z G, Wu S H 2014 Opt. Lett. 39 1941

    [24]

    Yu J, Gao Q, Zhang Y G, Zhang Z G, Wu S H 2014 J. Opt. 16 125708

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出版历程
  • 收稿日期:  2017-08-09
  • 修回日期:  2017-10-09
  • 刊出日期:  2018-01-05

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