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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
[1] Lumbers B, Agar D W, Gebel J, Platte F 2022 Int. J. Hydrogen Energy 47 4265
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[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
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Zhang S F, Lan L J, Ding Y J, Jia J W, Peng Z M 2015 Acta Phys. Sin. 64 053301
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[7] 阚瑞峰, 刘文清, 张玉钧, 刘建国, 董凤忠, 高山虎, 王敏, 陈军 2005 物理学报 54 1927
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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 物理学报 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 物理学报 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 物理学报 60 070701
Google Scholar
Li N, Weng C S 2011 Acta Phys. Sin. 60 070701
Google Scholar
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Google Scholar
Wang Z, Du Y J, Ding Y J, Peng Z M 2020 Acta Phys. Sin. 69 064205
Google Scholar
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Google Scholar
[24] 王飞, 黄群星, 李宁, 严建华, 池涌, 岑可法 2007 物理学报 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
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Google Scholar
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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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图 1 1653 nm附近处的甲烷吸收线型(P = 1 × 105 Pa, T = 296 K)
Figure 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
Figure 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
Figure 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
Figure 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
Figure 5. Illustration of the modified-WMS-based methane measuring system.
图 6 参考通道波形示意图
Figure 6. Illustration of the waveform of the reference channel.
图 7 测量通道波形示意图
Figure 7. Illustration of the waveform of the measurment channel.
图 8 改进的WMS实验中甲烷的二次谐波信号示例
Figure 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
Figure 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Figure 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
Figure 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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