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Ultraviolet broadband absorption spectroscopy (UV-BAS) has been widely used to measure the concentration of gas pollutant, such as NO. However, the nonlinear dependence of the absorbance on the optical thickness (XL) caused by the broadening effect of instrument function is observed. In this paper, the nonlinear behavior of NO absorbance is investigated both theoretically and experimentally, and a database using a polynomial to describe the nonlinearity is established to present a simple method of measuring NO concentration. First, the nonlinear relationship between absorbance and XL is deduced. Second, the nonlinearity of an isolated spectral line is simulated, and the dependence of nonlinear behavior on instrument width is investigated. Third, the nonlinerities of peak absorbance in γ (0, 0) band with different instrumental widths are calculated, the nonlinear expression is given in a polynomial form, and the corresponding coefficient database is established. In addition, the nonlinearities in different vibration bands with the same instrumental width are compared with each other. Finally, two spectrometers are used to measure NO absorption spectra in different instrumental widths in order to validate the above-mentioned results of theoretical analysis. The relative error between the measured peak absorbance and theoretical calculation is less than 4%, and that between experimental results and the interpolation polynomial results is less than 8%. The experimental results demonstrate the accuracy of theoretical calculation and the reliability of database.
[1] Yan J, Wang G, Yang P, Li D, Bian J 2022 Sci. Total Environ. 817 152776
Google Scholar
[2] Liu Y, Tang G, Liu B, et al. 2022 Atmos. Environ. 275 119018
Google Scholar
[3] Breeze P 2017 Electricity Generation and the Environment (Academic Press) pp33–47
[4] Abdul-Wahab S A, Azzi M, Johnson G M, et al. 2003 Process Saf. Environ. 81 363
Google Scholar
[5] Salome C M, Brown N J, Marks G B, et al. 1996 Eur. Respir. J. 9 910
Google Scholar
[6] Li H, Liu W, Kan R 2019 Rev. Sci. Instrum. 90 46103
Google Scholar
[7] Fereja T H, Hymete A, Gunasekaran T 2013 ISRN Spectroscopy 230858
Google Scholar
[8] Steffenson D M, Stedman D H 1974 Anal. Chem. 46 1704
Google Scholar
[9] Ridley B A, Grahek F E 1990 J. Atmos. Ocean. Tech. 7 307
Google Scholar
[10] 蓝丽娟, 丁艳军, 贾军伟, 杜艳君, 彭志敏 2014 物理学报 63 083301
Google Scholar
Lan L J, Ding Y J, Jia J W, Du Y J, Peng Z M, 2014 Acta Phys. Sin. 63 083301
Google Scholar
[11] Kormann R, Fischer H, Gurk C, et al. 2002 Spectrochim Acta A Mol. Biomol. Spectrosc. 58 2489
Google Scholar
[12] Cui X, Dong F, Zhang Z, Sun P, Xia H, Fertein E, Chen W 2018 Atmos. Environ. 189 125
Google Scholar
[13] Chao X, Jeffries J B, Hanson R K 2012 Appl. Phys. B 106 987
Google Scholar
[14] Magne L, Pasquiers S 2005 C. R. Phys. 6 908
Google Scholar
[15] Liao W, Hecobian A, Mastromarino J, Tan D 2006 Atmos. Environ. 40 17
Google Scholar
[16] Miyazaki K, Matsumoto J, Kato S, Kajii Y 2008 Atmos. Environ. 42 7812
Google Scholar
[17] 崔执凤 陈 东 凤尔银 季学韩 陆同兴 李学初 2000 物理学报 49 2151
Google Scholar
Cui Z F, Chen D, Feng E Y, Ji X H, Lu T X, Li X C 2000 Acta Phys. Sin. 49 2151
Google Scholar
[18] Peng B, Zhou Y, Liu G, He Y, Gao C, Guo Y 2020 Spectrochi. Acta. A 233 118169
Google Scholar
[19] Wang L, Zhang Y, Zhou X, Qin F, Zhang Z 2017 Sens. Actuators B Chem. 241 146
Google Scholar
[20] Peng B, Gao C, Zhou Y, Guo Y 2020 Sens. Actuators B Chem. 312 127988
Google Scholar
[21] Yang X, Peng Z, Ding Y, Du Y 2021 Fuel 288 119666
Google Scholar
[22] Zhang Y G, Wang H S, Somesfalean G, Wang Z Y, Lou X T, Wu S H, Zhang Z G, Qin Y K 2010 Atmos. Environ. 44 4266
Google Scholar
[23] Li Y, Zhang X, Li X, et al. 2018 Appl. Spectrosc. 72 1244
Google Scholar
[24] Sepman A, Gullberg M, Wiinikka H 2020 Appl. Phys. B 126 100
Google Scholar
[25] 段俊, 唐科, 秦敏, 王丹, 王牧笛, 方武, 孟凡昊, 谢品华, 刘建国, 刘文清 2021 物理学报 70 010702
Google Scholar
Duan J, Tang K, Qin M, Wang D, Wang M D, Fang W, Meng F H, Xie P H, Liu J G, Liu W Q 2021 Acta Phys. Sin. 70 010702
Google Scholar
[26] Buijs K, Maurice M J 1969 Anal. Chim. Acta 47 469
Google Scholar
[27] Donovan R J, Hussain D, Kirsch L J 1970 Trans. Faraday. Soc. 66 2551
Google Scholar
[28] Mellqvist J, Rosén A 1996 J. Quant. Spectrosc. Radiat. Transf 56 209
Google Scholar
[29] Trad H, Higelin P, Djebaı̈li-Chaumeix N, Mounaim-Rousselle C 2005 J. Quant. Spectrosc. Radiat. Transf. 90 275
Google Scholar
[30] Wong A, Yurchenko S N, Bernath P, et al. 2017 Mon. Not. R. Astron. Soc. 470 882
Google Scholar
[31] Luque J, Crosley D R LIFBASE: Database and Spectral Simulation Program (Version 1.5) 1999 SRI International Report MP 99 009
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图 1 UV-BAS测量系统示意图
Figure 1. Schematic of the experimental setup for UV-BAS measurements.
图 2 单谱线峰值随光学厚度变化的非线性行为
Figure 2. Nonlinearity of single line peak with optical thickness
图 3 单根谱线非线性度及其导数
Figure 3. Nonlinearity of single line and its derivative.
图 4 γ (0, 0)带系吸收光谱 (a) 真实光谱; (b) 不同仪器展宽下的测量光谱
Figure 4. Absorption spectra of γ (0, 0): (a) True spectrum; (b) detect spectra in different instrument widths.
图 5 不同仪器展宽下γ (0, 0)带系吸收率峰值非线性行为
Figure 5. Nonlinearity of the peak absorbance in γ (0, 0) in different instrument widths.
图 6 A1, |A2|与非线性度随仪器展宽的变化规律
Figure 6. Dependence of A1, |A2|, and the relative nonlinearity on the instrumental width.
图 7 NO不同振动谱带紫外吸收光谱
Figure 7. NO absorbption spectra in different vibration bands.
图 8 (a) 不同谱带吸收率峰值非线性行为; (b) 等最大线强度各谱带峰值非线性行为
Figure 8. (a) Nonlinearity of peak absorbance in different bands; (b) nonlinearity of peak absorbance with the same maximum line strength in different bands.
图 9 (a) 不同谱带吸收比例积分面积非线性行为; (b) 等最大线强度各谱带面积非线性行为
Figure 9. (a) Nonlinearity of absorption fraction the integral area in different bands; (b) nonlinearity of the integral area with the same maximum line strength in different bands.
图 10 UV-BAS测量光谱强度与吸收率 (a), (b) BAS光谱强度; (c), (d) BAS测量吸收率
Figure 10. Spectrum intensities and absorbances measured by BAS: (a), (b) BAS spectrum intensity; (c), (d) BAS measures absorption
图 11 吸收率峰值随光学厚度变化规律
Figure 11. Dependence of the peak absorbance on optical thickness.
图 12 数据库系数插值多项式与实验结果对比
Figure 12. Comparison between interpolation polynomial and experimental result.
图 13 吸收分数积分面积随光学厚度变化规律
Figure 13. Dependence of integral area of absorption fraction on optical thickness.
表 1 NO非线性行为的多项式系数
Table 1. Polynomial coefficient for NO nonlinearity
Δνin/nm A1/10–3 A2/10–5 A3/10–8 0.01 16.572 –2.120 1.499 0.05 8.779 –1.041 0.846 0.10 7.379 –0.890 0.689 0.50 4.037 –0.620 0.493 1.00 2.810 –0.429 0.341 5.00 0.720 –0.130 0.107 
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表 A1 不同仪器展宽Δνin下多项式系数
Table A1. Polynomial coefficients in different Δνin.
Δνin/nm A1/10–3 A2/10–5 A3/10–8 0.010 16.572 –2.120 1.499 0.015 13.854 –2.170 1.728 0.020 11.977 –1.912 1.646 0.025 10.828 –1.624 1.460 0.030 10.087 –1.374 1.208 0.035 9.619 –1.229 1.046 0.040 9.281 –1.143 0.952 0.045 9.010 –1.084 0.891 0.050 8.779 –1.041 0.846 0.055 8.576 –1.008 0.812 0.060 8.395 –0.982 0.785 0.065 8.231 –0.962 0.763 0.070 8.081 –0.945 0.745 0.075 7.943 –0.932 0.731 0.080 7.815 –0.921 0.719 0.085 7.696 –0.911 0.709 0.090 7.584 –0.903 0.702 0.095 7.479 –0.896 0.695 0.10 7.379 –0.890 0.689 0.15 6.596 –0.849 0.653 0.20 6.038 –0.818 0.631 0.25 5.577 –0.786 0.609 0.30 5.178 –0.753 0.587 0.35 4.829 –0.718 0.564 0.40 4.526 –0.683 0.540 0.45 4.264 –0.650 0.516 0.50 4.037 –0.620 0.493 0.55 3.842 –0.591 0.472 0.60 3.673 –0.566 0.452 0.65 3.525 –0.542 0.433 0.70 3.395 –0.521 0.416 0.75 3.278 –0.501 0.400 0.80 3.171 –0.484 0.386 0.85 3.073 –0.468 0.373 0.90 2.981 –0.454 0.362 0.95 2.893 –0.441 0.351 1.0 2.810 –0.429 0.341 1.2 2.510 –0.389 0.309 1.4 2.256 –0.355 0.283 1.6 2.039 –0.327 0.261 1.8 1.855 –0.302 0.242 2.0 1.698 –0.280 0.225 2.5 1.394 –0.237 0.192 3.0 1.178 –0.204 0.166 3.5 1.018 –0.179 0.146 4.0 0.895 –0.159 0.131 4.5 0.798 –0.143 0.118 5.0 0.720 –0.130 0.107
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[1] Yan J, Wang G, Yang P, Li D, Bian J 2022 Sci. Total Environ. 817 152776
Google Scholar
[2] Liu Y, Tang G, Liu B, et al. 2022 Atmos. Environ. 275 119018
Google Scholar
[3] Breeze P 2017 Electricity Generation and the Environment (Academic Press) pp33–47
[4] Abdul-Wahab S A, Azzi M, Johnson G M, et al. 2003 Process Saf. Environ. 81 363
Google Scholar
[5] Salome C M, Brown N J, Marks G B, et al. 1996 Eur. Respir. J. 9 910
Google Scholar
[6] Li H, Liu W, Kan R 2019 Rev. Sci. Instrum. 90 46103
Google Scholar
[7] Fereja T H, Hymete A, Gunasekaran T 2013 ISRN Spectroscopy 230858
Google Scholar
[8] Steffenson D M, Stedman D H 1974 Anal. Chem. 46 1704
Google Scholar
[9] Ridley B A, Grahek F E 1990 J. Atmos. Ocean. Tech. 7 307
Google Scholar
[10] 蓝丽娟, 丁艳军, 贾军伟, 杜艳君, 彭志敏 2014 物理学报 63 083301
Google Scholar
Lan L J, Ding Y J, Jia J W, Du Y J, Peng Z M, 2014 Acta Phys. Sin. 63 083301
Google Scholar
[11] Kormann R, Fischer H, Gurk C, et al. 2002 Spectrochim Acta A Mol. Biomol. Spectrosc. 58 2489
Google Scholar
[12] Cui X, Dong F, Zhang Z, Sun P, Xia H, Fertein E, Chen W 2018 Atmos. Environ. 189 125
Google Scholar
[13] Chao X, Jeffries J B, Hanson R K 2012 Appl. Phys. B 106 987
Google Scholar
[14] Magne L, Pasquiers S 2005 C. R. Phys. 6 908
Google Scholar
[15] Liao W, Hecobian A, Mastromarino J, Tan D 2006 Atmos. Environ. 40 17
Google Scholar
[16] Miyazaki K, Matsumoto J, Kato S, Kajii Y 2008 Atmos. Environ. 42 7812
Google Scholar
[17] 崔执凤 陈 东 凤尔银 季学韩 陆同兴 李学初 2000 物理学报 49 2151
Google Scholar
Cui Z F, Chen D, Feng E Y, Ji X H, Lu T X, Li X C 2000 Acta Phys. Sin. 49 2151
Google Scholar
[18] Peng B, Zhou Y, Liu G, He Y, Gao C, Guo Y 2020 Spectrochi. Acta. A 233 118169
Google Scholar
[19] Wang L, Zhang Y, Zhou X, Qin F, Zhang Z 2017 Sens. Actuators B Chem. 241 146
Google Scholar
[20] Peng B, Gao C, Zhou Y, Guo Y 2020 Sens. Actuators B Chem. 312 127988
Google Scholar
[21] Yang X, Peng Z, Ding Y, Du Y 2021 Fuel 288 119666
Google Scholar
[22] Zhang Y G, Wang H S, Somesfalean G, Wang Z Y, Lou X T, Wu S H, Zhang Z G, Qin Y K 2010 Atmos. Environ. 44 4266
Google Scholar
[23] Li Y, Zhang X, Li X, et al. 2018 Appl. Spectrosc. 72 1244
Google Scholar
[24] Sepman A, Gullberg M, Wiinikka H 2020 Appl. Phys. B 126 100
Google Scholar
[25] 段俊, 唐科, 秦敏, 王丹, 王牧笛, 方武, 孟凡昊, 谢品华, 刘建国, 刘文清 2021 物理学报 70 010702
Google Scholar
Duan J, Tang K, Qin M, Wang D, Wang M D, Fang W, Meng F H, Xie P H, Liu J G, Liu W Q 2021 Acta Phys. Sin. 70 010702
Google Scholar
[26] Buijs K, Maurice M J 1969 Anal. Chim. Acta 47 469
Google Scholar
[27] Donovan R J, Hussain D, Kirsch L J 1970 Trans. Faraday. Soc. 66 2551
Google Scholar
[28] Mellqvist J, Rosén A 1996 J. Quant. Spectrosc. Radiat. Transf 56 209
Google Scholar
[29] Trad H, Higelin P, Djebaı̈li-Chaumeix N, Mounaim-Rousselle C 2005 J. Quant. Spectrosc. Radiat. Transf. 90 275
Google Scholar
[30] Wong A, Yurchenko S N, Bernath P, et al. 2017 Mon. Not. R. Astron. Soc. 470 882
Google Scholar
[31] Luque J, Crosley D R LIFBASE: Database and Spectral Simulation Program (Version 1.5) 1999 SRI International Report MP 99 009
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