基于标准样品回归算法和腔增强光谱的NO<sub>2</sub>检测方法

卞晓鸽; 周胜; 张磊; 何天博; 李劲松

doi:10.7498/aps.70.20201322

摘要

腔增强吸收光谱技术作为一种高灵敏的痕量气体测量技术, 其吸收光谱的浓度反演是极其关键的环节. 为消除因吸收截面和仪器响应函数的不确定性引入的测量误差, 本文提出了一种基于标准样品吸收光谱的浓度回归算法, 该方法在浓度反演过程上进行优化, 采用标准气体样品吸收光谱直接拟合未知浓度气体吸收光谱. 采用中心波长在440 nm处的蓝色发光二极管(LED)作为光源, 建立了一套非相干光腔增强吸收光谱技术(IBBCEAS)系统, 实测腔镜反射率为99.915%, 利用NO₂气体的实测吸收光谱对该算法的有效性进行了验证. 与常规吸收截面回归算法比较, 结果表明本文提出的标准样品回归算法具有显著的优越性, 测量精度提升约4倍. 利用改进的算法结合标准样品配制的多个NO₂气体对实验系统性能进行了深入评估, 测量结果与理论值具有很好的一致性. Allan方差分析显示在积分时间为360 s的情况下, NO₂检测限可达到5.3 ppb (1 ppb = 10^–9).

关键词:

Abstract

Cavity-enhanced absorption spectroscopy is a highly sensitive trace gas measurement technology, and the algorithm for retrieving gas concentrations is critical. The absorption cross-section is traditionally used to retrieve the concentration. However, the absorption cross-section used in the fitting process is affected not only by the response function of the instrument and the light source, but also by temperature and pressure. The uncertainty of the absorption cross-section will influence the accuracy of the result. Therefore, in order to eliminate the measurement error introduced by the uncertainty of the absorption cross-section and the instrument response function, a concentration regression algorithm based on the absorption spectrum of the standard sample is proposed. The process of concentration inversion is optimized. The absorption spectrum of standard gas is used to fit the unknown spectrum. In order to verify the effectiveness of the algorithm, the incoherent cavity enhanced absorption spectroscopy (IBBCEAS) system based on a blue light-emitting diode (LED) operating at 440 nm is established to analyze the absorption spectrum of NO₂; and the fitting effect, measurement accuracy and stability are compared with the counter parts from the traditional absorption cross-section method. In the experiment, the measured reflectance of the cavity mirror is 99.915%. Compared with the conventional absorption cross-section regression algorithm, the standard sample regression algorithm proposed in this paper shows good results, in which the measurement accuracy is increased by about quadruple. The Allan deviation shows that a detection limit of 5.3 ppb can be achieved at an integration time of 360 s. Finally, the performance of the experimental system is evaluated by measuring the NO₂ with different concentrations prepared by standard samples. The result shows good agreement with the theoretical value, which indicates that the improved spectral analysis algorithm is feasible and reliable for gas detection. This method can be used not only to measure NO₂, but also to detect other gases, which shows great potential applications in monitoring the industrial emissions, atmospheric chemistry and exhaled breath analysis.

Keywords:

incoherent broadband cavity enhanced absorption spectroscopy /
NO₂ /
visible spectrum /
multiple linear regression

作者及机构信息

安徽大学物理与材料科学学院, 合肥　230601

通信作者: 周胜, optzsh@ahu.edu.cn ; 李劲松, ljs0625@126.com

基金项目: 国家自然科学基金(批准号: 61905001, 41875158, 61705001, 61705002, 61675005)、国家重点研发计划(批准号: 2016YFC0302202)、安徽省自然科学基金(批准号: 1908085QF276, 1808085QF198, 1508085MF118)和安徽省高校自然科学项目(批准号: KJ2018A0034)资助的课题.

Authors and contacts

Department of Physics and Materials Science, Anhui University, Hefei 230601, China

Corresponding author: Zhou Sheng, optzsh@ahu.edu.cn ; Li Jin-Song, ljs0625@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61905001, 41875158, 61705001, 61705002, 61675005), the National Key R&D Project of China (Grant No. 2016YFC0302202), the Natural Science Foundation of Anhui Province, China (Grant Nos. 1908085QF276, 1808085QF198, 1508085MF118), and the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2018A0034)

文章全文 : translate this paragraph

参考文献

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[15]	吴涛, 陈卫东, 何兴道 2015 光谱学与光谱分析 35 2989 Google Scholar Wu T, Chen W D, He X D 2015 Spectrosc. Spect. Anal. 35 2989 Google Scholar
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[33]	Bessant C, Saini S 2000 J. Electroanal. Chem. 489 76 Google Scholar
[34]	Sun J, Ding J Y, Liu N W, Yang G X, Li J S 2018 Spectrochim. Acta, Part A 191 532 Google Scholar
[35]	Brown S S, Stark H, Ciciora S J, Mclaughlin R J, Ravishankara A R 2002 Rev. Sci. Instrum. 73 3291 Google Scholar
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施引文献

图 1 实验装置图

Fig. 1. Schematic of experimental setup.

下载: 全尺寸图片幻灯片

图 2 (a) NO₂吸收截面(蓝线)与LED发射光谱(红线); (b) LED输出功率与电流关系

Fig. 2. (a) NO₂ absorption cross-section (blue line) and LED emission spectrum (red line); (b) relationship between LED output power and current.

下载: 全尺寸图片幻灯片

图 3 拟合流程图

Fig. 3. Flow chart of fitting.

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图 4 (a)随波长变化的反射率曲线; (b)腔损耗(黑线)和有效路径长度(绿线)

Fig. 4. (a) Mirror reflectivity as a function of wavelength; (b) cavity loss (black line) and corresponding effective path length (green line).

下载: 全尺寸图片幻灯片

图 5 NO₂吸收截面的卷积

Fig. 5. Convolution of the NO₂ absorption cross-section.

下载: 全尺寸图片幻灯片

图 6 NO₂拟合结果　(a)实测吸收系数与标准吸收截面拟合; (b)拟合残差

Fig. 6. The results of NO₂ fitting: (a) Fitting between the measured absorption coefficient and the standard absorption cross section; (b) fitting residuals.

下载: 全尺寸图片幻灯片

图 7 多元线性拟合示意图

Fig. 7. Multiple linear fitting diagram.

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图 8 NO₂拟合结果　(a)实测吸收系数与标准气体吸收系数拟合; (b)−(g)拟合残差

Fig. 8. The results of NO₂ fitting: (a) Fitting of absorption coefficient between measured and standard gas; (b)−(g) fitting residuals.

下载: 全尺寸图片幻灯片

图 9 浓度值对比　(a)浓度计算结果; (b)绝对误差; (c)相对误差

Fig. 9. Concentration comparison: (a) The calculated value of concentration; (b) absolute error; (c) relative error.

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图 10 系统稳定性评估　(a) 2 h的浓度数据; (b) Allan偏差图; (c)直方图分析

Fig. 10. System stability assessment: (a) Concentration data recorded for 2 hours; (b) Allan deviation plots; (c) histogram analysis.

下载: 全尺寸图片幻灯片

图 11 (a) NO₂气体的不同浓度; (b)浓度梯度平均值及标准偏差

Fig. 11. (a) Different concentrations of NO₂; (b) average and standard deviation of concentration gradient.

下载: 全尺寸图片幻灯片

表 1 不同NO₂浓度对应的拟合残差的标准偏差和信噪比

Table 1. Standard deviation and signal-to-noise ratio of fitting residuals corresponding to different NO₂ concentrations.

浓度/ppm 7.86 5.08 3.28 2.07 1.42 0.75

标准偏差/(10^–6 cm^–1) 12.35 8.13 5.27 3.44 2.62 1.57
信噪比 11.23 11.08 10.95 10.38 9.72 8.94

下载: 导出CSV

表 2 不同NO₂浓度对应的拟合残差的标准偏差和信噪比

Table 2. Standard deviation and signal-to-noise ratio of fitting residuals corresponding to different NO₂ concentrations.

浓度/ppm 7.86 5.08 3.28 2.07 1.42 0.75

标准偏差/(10^–6 cm^–1) 2.7 1.67 1.36 0.78 0.62 0.59
信噪比 52.6 49.9 44.6 42.7 37.4 25.1

下载: 导出CSV

[1]	段秋宴 2019 环境与发展 31 155 Google Scholar Duan Q Y 2019 Environ. Dev. 31 155 Google Scholar
[2]	韩荦, 夏滑, 董凤忠, 张志荣, 庞涛, 孙鹏帅, 吴边, 崔小娟, 李哲, 余润磬 2018 中国激光 45 43 Google Scholar Han L, Xia H, Dong F Z, Zhang Z R, Pang T, Sun P S, Wu B, Cui X J, Li Z, Yu R Q 2018 Chin. J. Lasers 45 43 Google Scholar
[3]	Min K E, Washenfelder R A, Dubé W P, Langford A O, Edwards P, Zarzana K J, Stutz J, Lu K, Rohrer F, Zhang Y H, Brown S S 2015 Atmos. Meas. Tech. 9 11209 Google Scholar
[4]	Engeln R, Berden G, Peeters R, Meijei G 1998 Rev. Sci. Instrum. 69 3763 Google Scholar
[5]	O’keefe A 1998 Chem. Phys. Lett. 293 331 Google Scholar
[6]	Fiedler S E, Hoheisel G, Ruth A A, Hese A 2003 Chem. Phys. Lett. 382 447 Google Scholar
[7]	Wu T, Zha Q Z, Chen W D, Xu Z, Wang T, He X D 2014 Atmos. Environ. 95 544 Google Scholar
[8]	Nakashima Y, Sadanaga Y 2017 Anal. Sci. 33 519 Google Scholar
[9]	段俊, 秦敏, 方武, 胡仁志, 卢雪, 沈兰兰, 王丹, 谢品华, 刘建国, 刘文清 2016 光谱学与光谱分析 36 466 Google Scholar Duan J, Qin M, Fang W, Hu R Z, Lu X, Shen L L, Wang D, Xie P H, Liu J G, Liu W Q 2016 Spectrosc. Spect. Anal. 36 466 Google Scholar
[10]	Liu J W, Li X, Yang Y M, Wang H C, Wu Y S, Lu X W, Chen M D, Hu J L, Fan X B, Zeng L M, Zhang Y H 2019 Atmos. Meas. Tech. 12 4439 Google Scholar
[11]	Jordan N, Ye C Z, Ghosh S, Washenfelder R A, Brown S S, Osthoff H D 2019 Atmos. Meas. Tech. 12 1277 Google Scholar
[12]	Jodan N, Osthoff H D 2020 Atmos. Meas. Tech. 13 285 Google Scholar
[13]	Duan J, Qin M, Ouyang B, Fang W, Li X, Lu K D, Tang K, Liang S X, Meng F H, Hu Z K, Xie P H, Liu W Q, Häsler R 2018 Atmos. Meas. Tech. 11 4531 Google Scholar
[14]	Liang S X, Qin M, Xie P H, Duan J, Fang W, He Y B, Xu J, Liu J W, Li X, Tang K, Meng F H, Ye K D, Liu J G, Liu W Q 2019 Atmos. Meas. Tech. 12 2499 Google Scholar
[15]	吴涛, 陈卫东, 何兴道 2015 光谱学与光谱分析 35 2989 Google Scholar Wu T, Chen W D, He X D 2015 Spectrosc. Spect. Anal. 35 2989 Google Scholar
[16]	凌六一, 秦敏, 谢品华, 胡仁志, 方武, 江宇, 刘建国, 刘文清 2012 物理学报 61 140703 Google Scholar Ling L Y, Qin M, Xie P H, Hu R Z, Fang W, Jiang Y, Liu J G, Liu W Q 2012 Acta Phys. Sin. 61 140703 Google Scholar
[17]	Thalman R, Zarzana K J, Tolbert M A, Volkamer R 2014 J. Quant. Spectrosc. Radiat. Transfer 147 171 Google Scholar
[18]	Meng L S, Wang G X, Augustin P, Fourmentin M, Gou Q, Fertein E, Ba T N, Coeur C, Tomas A, Chen W D 2020 Opt. Lett. 45 1611 Google Scholar
[19]	庞学霞, 邓泽超, 贾鹏英, 梁伟华 2011 物理学报 60 125201 Google Scholar Pang X X, Deng Z C, Jia P Y, Liang W H 2011 Acta Phys. Sin. 60 125201 Google Scholar
[20]	赵士彬 2018 环境与发展 30 140 Google Scholar Zhao S B 2018 Environ. Dev. 30 140 Google Scholar
[21]	崔厚欣, 杜振辉, 陈文亮, 齐汝宾, 徐可欣 2008 天津大学学报 41 1162 Cui H X, Du Z H, Chen W L, Qi R B, Xu K X 2008 J. Tianjin Univ. 41 1162
[22]	郑海明, 蔡小舒 2007 动力工程 27 130 Zheng H M, Cai X S 2007 J. Power Eng. 27 130
[23]	Bogumil K, Orphal J, Burrows J P, Flaud J M 2001 Chem. Phys. Lett. 349 241 Google Scholar
[24]	Mellqvist J, Rosen A 1996 J. Quant. Spectrosc. Radiat. Transfer 56 187 Google Scholar
[25]	Roehl C M, Orlando J J, Tyndall G S, Shetter R E, Vazquez G J, Cantrell C A, Calvert J G 1994 J. Phys. Chem. 98 7837 Google Scholar
[26]	凌六一, 韦颖, 黄友锐, 胡仁志, 谢品华 2018 光谱学与光谱分析 38 670 Google Scholar Ling L, Wei Y, Huang Y R, Hu R Z, Xie P H 2018 Spectrosc. Spect. Anal. 38 670 Google Scholar
[27]	Washenfelder R A, Langford A O, Fuchs H, Brown S S 2008 Atmos. Chem. Phys. 8 7779 Google Scholar
[28]	Ling L Y, Xie P H, Qin M, Fang W, Jiang Y, Hu R Z, Zheng N N 2013 Chin. Opt. Lett. 11 063001 Google Scholar
[29]	Sneep M, Ubachs W 2005 J. Quant. Spectrosc. Radiat. Transfer 92 293 Google Scholar
[30]	Shardanand S, Rao A D P 1977 NASA Technical Note (Washington D.C.: National Aeronautics and Space Administration)
[31]	Washenfelder R A, Attwood A R, Flores J M, Zarzana K J, Rudich Y, Brown S S 2015 Atmos. Meas. Tech. 9 41 Google Scholar
[32]	Wu T, Chen W D, Fertein E, Cazier F, Dewaele D, Gao X M 2012 Appl. Phys. B 106 501 Google Scholar
[33]	Bessant C, Saini S 2000 J. Electroanal. Chem. 489 76 Google Scholar
[34]	Sun J, Ding J Y, Liu N W, Yang G X, Li J S 2018 Spectrochim. Acta, Part A 191 532 Google Scholar
[35]	Brown S S, Stark H, Ciciora S J, Mclaughlin R J, Ravishankara A R 2002 Rev. Sci. Instrum. 73 3291 Google Scholar
[36]	Huang H F, Lehmann K K 2010 Appl. Opt. 49 1387 Google Scholar
[37]	Li J S, Deng H, Sun J, Yu B L, Fischer H 2016 Sens. Actuators, B 231 723 Google Scholar

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