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本文对波长调制光谱(WMS)技术进行了改进, 并以其为基础测量了高吸收度的甲烷气体. WMS常被用于气体浓度测量, 其依赖于二次谐波幅值与气体浓度之间的线性关系, 但是传统的WMS技术只适用于气体吸收度远小于1的情况, 这是因为在传统WMS理论的推导中, 需要对朗伯比尔定律进行一阶近似, 而一阶近似仅在低吸收度下成立, 所以在高吸收度下二次谐波与气体浓度的线性关系不成立. 在本文的改进方案中, 不需要对朗伯比尔定律做任何近似处理. 将激光分为测量光与参考光两路, 测量光被待测气体充分吸收后由光电探测器收集光强信号, 参考光的光强信号不被吸收直接由另一个光电探测器直接探测, 两个光电探测器的输出信号经模数转换后传输至上位机, 上位机对两路信号均先取自然对数, 然后根据参考信号确定二次谐波的解调相位, 这样解调出来的二次谐波信号即使在高吸收度下也与气体的浓度保持线性关系. 本文介绍了传统WMS理论与改进后的WMS理论, 并分别测量了一系列浓度梯度的甲烷气体, 对比了传统WMS和改进WMS的实验结果, 证实了在高吸收度下, 传统WMS理论中的线性不再成立, 但改进的WMS仍能保证二次谐波与甲烷浓度之间的线性关系, 验证了改进方案的优势; 最后通过艾伦标准差分析, 得到该甲烷测量系统在平均时间103.6 s时稳定性达到最优, 对应的艾伦标准差为26.62×10–9分之一体积.In this paper, the wavelength modulation spectroscopy (WMS) technique is modified and used for measuring methane with large absorbance. The WMS has been frequently used for gas measurement and relies on the linear relationship between the second harmonic amplitude and the gas volume concentration. However, the conventional WMS technique is only applicable for the gas whose absorbance is much smaller than 1, which is because the first-order approximation of Lambert-Beer's law is required in the derivation of the traditional WMS theory, and the first-order approximation holds only at low absorbance, hence the linear relationship between the second harmonic and the gas concentration does not hold at large absorbance. In the modified WMS in this work, it is not necessary to make any approximation to Lambert-Beer's law. The measured light is absorbed by the gas to be measured and then collected by the photodetector. The reference light is directly detected by another photodetector without being absorbed. The output signals of the two photodetectors are transmitted to the computer after implementing analog-to-digital conversion. In this way, the demodulated second harmonic signal remains linear with the gas concentration even at large absorbance. In this work, the traditional WMS theory and the modified WMS theory are both introduced, and a series of methane gas with concentration gradients are measured separately. The experimental results of the traditional WMS and the modified WMS are compared with each other. It is confirmed that the linearity in the traditional WMS theory no longer holds under large absorbance, but the improved WMS can still guarantee the linear relationship between the second harmonic and the methane concentration, which verifies the advantages of the modified scheme. Finally, through Allan's standard deviation analysis, the stability of this methane measurement system reaches the optimal value at the average time of 103.6 s, and the corresponding Allan's standard deviation is 1/26.62×10–9 volume.
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Keywords:
- wavelength modulated spectroscopy /
- methane measurement /
- infrared spectroscopy /
- large absorbance
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Yan G M, Li S H 2012 Inertial Instrumentation Testing and Data Analysis (Beijing: National Defense Industry Press) pp159–160 (in Chinese)
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图 1 1653 nm附近处的甲烷吸收线型(P = 1 × 105 Pa, T = 296 K)
Fig. 1. Absorption profile of methane around 1653 nm (P = 1 × 105 Pa, T = 296 K).
图 2 基于WMS技术测量甲烷气体的实验装置示意图
Fig. 2. Illustration of the WMS-based methane measuring system.
图 3 WMS实验中甲烷的二次谐波信号示例
Fig. 3. Illustration of the 2nd harmonic of methane in the WMS experiment.
图 4 WMS实验中甲烷的二次谐波幅值与甲烷浓度之间的关系
Fig. 4. Relationship between the amplitude of the 2nd harmonic of methane and the concentration of methane in the WMS experiment
图 5 基于改进的WMS技术测量甲烷气体的实验装置示意图
Fig. 5. Illustration of the modified-WMS-based methane measuring system.
图 8 改进的WMS实验中甲烷的二次谐波信号示例
Fig. 8. Illustration of the 2nd harmonic of methane in the modified-WMS experiment.
图 9 改进的WMS实验中甲烷的二次谐波幅值与浓度的关系
Fig. 9. Relationship between the amplitude of the 2nd harmonic of methane and the concentration of methane in the modified-WMS experiment.
图 10 1000次连续测量中解算出的
$ \xi $ 值的频率分布直方图Fig. 10. Frequency histogram of the value of
$ \xi $ calculated in 1000 continuous measurements.
图 11 基于改进的WMS的甲烷测量系统的艾伦标准差分析
Fig. 11. Allan deviation analysis of the modified-WMS-based methane measurement system.
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[1] Lumbers B, Agar D W, Gebel J, Platte F 2022 Int. J. Hydrogen Energy 47 4265
Google Scholar
[2] Lumbers B, Barley J, Platte F 2022 Int. J. Hydrogen Energy 47 16347
Google Scholar
[3] Wikipedia contributors https://en.wikipedia.org/w/index.php?title=Methane&oldid=1103638016 [2022-9-1]
[4] IPCC 2013 Climate Change 2013: The Physical Science Basis. (Cambridge: Cambridge University Press) pp164–167
[5] Shindell D T, Faluvegi G, Koch D M, Schmidt G A, Unger N, Bauer S E 2009 Science 326 716
Google Scholar
[6] 张书锋, 蓝丽娟, 丁艳军, 贾军伟, 彭志敏 2015 64 053301
Google Scholar
Zhang S F, Lan L J, Ding Y J, Jia J W, Peng Z M 2015 Acta Phys. Sin. 64 053301
Google Scholar
[7] 阚瑞峰, 刘文清, 张玉钧, 刘建国, 董凤忠, 高山虎, 王敏, 陈军 2005 54 1927
Google Scholar
Kan R F, Liu W Q, Zhang Y J, Liu J G, Dong F Z, Gao S H, Wang M, Chen J 2005 Acta Phys. Sin. 54 1927
Google Scholar
[8] 丁武文, 孙利群, 衣路英 2017 66 100702
Google Scholar
Ding W W, Sun L Q, Yi L Y 2017 Acta Phys. Sin. 66 100702
Google Scholar
[9] 丁武文, 孙利群 2017 66 120601
Google Scholar
Ding W W, Sun L Q 2017 Acta Phys. Sin. 66 120601
Google Scholar
[10] Ding W W, Sun L Q, Yi L Y 2016 Meas. Sci. Technol. 27 085202
Google Scholar
[11] He Q X, Dang P P, Liu Z W, Zheng C T, Wang Y D 2017 Opt. Quantum Electron. 49 115
Google Scholar
[12] Shemshad J 2015 Sens. Actuators, A 222 96
Google Scholar
[13] Zhang Z W, Chang J, Sun J C, Feng Y W, Sun H R, Zhang Q D, Fan Y M, Zhang Z F 2020 Appl. Opt. 59 8217
Google Scholar
[14] 孙利群, 邹明丽, 王旋 2021 中国激光 48 1511001
Google Scholar
Sun L Q, Zou M L, W X 2021 Chin. J. Lasers 48 1511001
Google Scholar
[15] Kyle Owen, Farooq A 2014 Appl. Phys. B. 116 371
[16] Lan L J, Ghasemifard H, Yuan Y, Hachinger S, Zhao X X, Bhattacharjee S, Bi X, Bai Y, Menzel A, Chen J 2020 Atmosphere 11 58
Google Scholar
[17] Geng J X, Lan L J, Luo Q W, Yang C H 2021 Proc. SPIE 11780, Global Intelligent Industry Conference Guangzhou, China, March 18, 2021 p117801V
[18] Chao X, Jeffries J B, Hanson R K 2009 Meas. Sci. Technol. 20 115201
Google Scholar
[19] Chao X, Jeffries J B, Hanson R K 2012 Appl. Phys. B 106 987
Google Scholar
[20] Ku R T, Hinkley E D, Sample J O 1975 Appl. Opt. 14 854
Google Scholar
[21] 李宁, 翁春生 2011 60 070701
Google Scholar
Li N, Weng C S 2011 Acta Phys. Sin. 60 070701
Google Scholar
[22] 王振, 杜艳君, 丁艳军, 彭志敏 2020 69 064205
Google Scholar
Wang Z, Du Y J, Ding Y J, Peng Z M 2020 Acta Phys. Sin. 69 064205
Google Scholar
[23] Upadhyay A, Chakraborty L A 2015 Opt. Lett. 40 4086
Google Scholar
[24] 王飞, 黄群星, 李宁, 严建华, 池涌, 岑可法 2007 56 3867
Google Scholar
Wang F, Huang Q X, Li N, Yan J H, Chi Y, Cen K F 2007 Acta Phys. Sin. 56 3867
Google Scholar
[25] Rieker G B, Jeffries J B, Hanson R K 2009 Appl. Opt. 48 5546
Google Scholar
[26] Huang A, Cao Z, Zhao W S, Zhang H Y, Xu L J 2020 IEEE Trans. Instrum. Meas. 69 9087
Google Scholar
[27] Gordon I E, Rothman L S, Hargreaves R J, Hashemi R, Karlovets E V, Skinner F M, Conway E K, Hill C, Kochanov R V, Tan Y, Wcisło P, Finenko A A, Nelson K, Bernath P F, Birk M, Boudon V, Campargue A, Chance K V, Coustenis A, Drouin B J, Flaud J M, Gamache R R, Hodges J T, Jacquemart D, Mlawer E J, Nikitin A V, Perevalov V I, Rotger M, Tennyson J, Toon G C, Tran H, Tyuterev V G, Adkins E M, Baker A, Barbe A, Canè E, Császár A G, Dudaryonok A, Egorov O, Fleisher A J, Fleurbaey H, Foltynowicz A, Furtenbacher T, Harrison J J, Hartmann J M, Horneman V M, Huang X, Karman T, Karns J, Kassi S, Kleiner I, Kofman V, Kwabia–Tchana F, Lavrentieva N N, Lee T J, Long D A, Lukashevskaya A A, Lyulin O M, Makhnev Y V, Matt W, Massie S T, Melosso M, Mikhailenko S N, Mondelain D, Müller H S P, Naumenko O V, Perrin A, Polyansky O L, Raddaoui E, Raston P L, Reed Z D, Rey M, Richard C, Tóbiás R, Sadiek I, Schwenke D W, Starikova E, Sung K, Tamassia F, Tashkun S A, Vander Auwera J, Vasilenko I A, Vigasin A A, Villanueva G L, Vispoel B, Wagner G, Yachmenev A, Yurchenko S N 2021 J. Quant. Spectrosc. Radiat. Transfer 277 107949
[28] Li H J, Rieker G B, Liu X, Jeffries J B, Hanson R K 2006 Appl. Opt. 45 1052
Google Scholar
[29] 严恭敏, 李四海 2012 惯性仪器测试与数据分析 (北京: 国防工业出版社) 第159—160页
Yan G M, Li S H 2012 Inertial Instrumentation Testing and Data Analysis (Beijing: National Defense Industry Press) pp159–160 (in Chinese)
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