Abstract

Tunable diode laser absorption spectroscopy has been widely employed for gas sensing, where the gas concentration is often obtained from the absorption signal with a known or a fixed absorption path length. Nevertheless, there are also numerous applications in which the absorption path length is very challenging to retrieve, e.g., open path remote sensing and gas absorption in scattering media. In this work, a new approach, based on the wavelength modulation spectroscopy (WMS), has been developed to measure the gas absorption signal and the corresponding absorption path length simultaneously. The phase angle of the first harmonic signal (1f phase angle) in the WMS technique is utilized for retrieving the absorption path length as well as the gas absorption signal. This approach has been experimentally validated by measuring carbon dioxide (CO2) concentration in open path environment. The CO2 concentration is evaluated by measuring the reflectance signal from a distant object with hundreds of meters away from the system. The measurement accuracy of the absorption path length, evaluated from a 7-day continuous measurement, can reach up to 1%. The promising result has shown a great potential of utilizing the 1f phase angle for gas concentration measurements, e.g., open path remote sensing applications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Wavelength modulation spectroscopy by employing the first harmonic phase angle method

Chenguang Yang, Liang Mei, Hao Deng, Zhenyu Xu, Bing Chen, and Ruifeng Kan
Opt. Express 27(9) 12137-12146 (2019)

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2019 (2)

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

C. G. Yang, L. Mei, H. Deng, Z. Y. Xu, B. Chen, and R. F. Kan, “Wavelength modulation spectroscopy by employing the first harmonic phase angle method,” Opt. Express 27(9), 12137–12146 (2019).
[Crossref]

2018 (1)

2017 (3)

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

M. Queisser, M. Burton, G. R. Allan, and A. Chiarugi, “Portable laser spectrometer for airborne and ground-based remote sensing of geological CO2 emissions,” Opt. Lett. 42(14), 2782–2785 (2017).
[Crossref]

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

2016 (2)

M. Queisser, D. Granieri, and M. Burton, “A new frontier in CO2 flux measurements using a highly portable DIAL laser system,” Sci. Rep. 6(1), 33834 (2016).
[Crossref]

Z. H. Du, H. Gao, and X. H. Cao, “Direct high-precision measurement of the effective optical path length of multi-pass cell with optical frequency domain reflectometer,” Opt. Express 24(1), 417–426 (2016).
[Crossref]

2015 (3)

P. Geiser, “New opportunities in mid-infrared emission control,” Sensors 15(9), 22724–22736 (2015).
[Crossref]

S. Reuter, J. S. Sousa, G. D. Stancu, and J.-P. Hubertus van Helden, “Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets,” Plasma Sources Sci. Technol. 24(5), 054001 (2015).
[Crossref]

L. Mei and S. Svanberg, “Wavelength modulation spectroscopy-digital detection of gas absorption harmonics based on Fourier analysis,” Appl. Opt. 54(9), 2234–2243 (2015).
[Crossref]

2014 (1)

L. Mei, G. Somesfalean, and S. Svanberg, “Pathlength determination for gas in scattering media absorption spectroscopy,” Sensors 14(3), 3871–3890 (2014).
[Crossref]

2013 (2)

S. Svanberg, “Gas in scattering media absorption spectroscopy – From basic studies to biomedical applications,” Laser Photonics Rev. 7(5), 779–796 (2013).
[Crossref]

H. Nasim and Y. Jamil, “Recent advancements in spectroscopy using tunable diode lasers,” Laser Phys. Lett. 10(4), 043001 (2013).
[Crossref]

2012 (1)

2011 (2)

2009 (1)

C. Wang and P. Sahay, “Breath analysis using laser spectroscopic techniques: breath biomarkers, spectral fingerprints, and detection limits,” Sensors 9(10), 8230–8262 (2009).
[Crossref]

2006 (1)

G. Galbács, “A review of applications and experimental improvements related to diode laser atomic spectroscopy,” Appl. Spectrosc. Rev. 41(3), 259–303 (2006).
[Crossref]

2003 (2)

K. Song and E. C. Jung, “Recent developments in modulation spectroscopy for trace gas detection using tunable diode lasers,” Appl. Spectrosc. Rev. 38(4), 395–432 (2003).
[Crossref]

A. Castrillo, G. Gagliardi, G. Casa, and L. Gianfrani, “Combined interferometric and absorption-spectroscopic technique for determining molecular line strengths: Applications to CO2,” Phys. Rev. A 67(6), 062503 (2003).
[Crossref]

Allan, G. R.

Blume, N.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Botos, C.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Braun, M.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Broquet, G.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Burton, M.

M. Queisser, M. Burton, G. R. Allan, and A. Chiarugi, “Portable laser spectrometer for airborne and ground-based remote sensing of geological CO2 emissions,” Opt. Lett. 42(14), 2782–2785 (2017).
[Crossref]

M. Queisser, D. Granieri, and M. Burton, “A new frontier in CO2 flux measurements using a highly portable DIAL laser system,” Sci. Rep. 6(1), 33834 (2016).
[Crossref]

Cao, X. H.

Casa, G.

A. Castrillo, G. Gagliardi, G. Casa, and L. Gianfrani, “Combined interferometric and absorption-spectroscopic technique for determining molecular line strengths: Applications to CO2,” Phys. Rev. A 67(6), 062503 (2003).
[Crossref]

Castrillo, A.

A. Castrillo, G. Gagliardi, G. Casa, and L. Gianfrani, “Combined interferometric and absorption-spectroscopic technique for determining molecular line strengths: Applications to CO2,” Phys. Rev. A 67(6), 062503 (2003).
[Crossref]

Chen, B.

C. G. Yang, L. Mei, H. Deng, Z. Y. Xu, B. Chen, and R. F. Kan, “Wavelength modulation spectroscopy by employing the first harmonic phase angle method,” Opt. Express 27(9), 12137–12146 (2019).
[Crossref]

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Chen, C.

Chen, X.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Chiarugi, A.

Ciais, P.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Das, D.

D. Das and A. C. Wilson, “Very long optical path-length from a compact multi-pass cell,” Appl. Phys. B 103(3), 749–754 (2011).
[Crossref]

Deng, H.

Dobler, J. T.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Dong, J.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Dong, Y. K.

Du, Z. H.

Fan, X. L.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Feng, Y.

Gagliardi, G.

A. Castrillo, G. Gagliardi, G. Casa, and L. Gianfrani, “Combined interferometric and absorption-spectroscopic technique for determining molecular line strengths: Applications to CO2,” Phys. Rev. A 67(6), 062503 (2003).
[Crossref]

Galbács, G.

G. Galbács, “A review of applications and experimental improvements related to diode laser atomic spectroscopy,” Appl. Spectrosc. Rev. 41(3), 259–303 (2006).
[Crossref]

Gao, H.

Geiser, P.

P. Geiser, “New opportunities in mid-infrared emission control,” Sensors 15(9), 22724–22736 (2015).
[Crossref]

Gianfrani, L.

A. Castrillo, G. Gagliardi, G. Casa, and L. Gianfrani, “Combined interferometric and absorption-spectroscopic technique for determining molecular line strengths: Applications to CO2,” Phys. Rev. A 67(6), 062503 (2003).
[Crossref]

Granieri, D.

M. Queisser, D. Granieri, and M. Burton, “A new frontier in CO2 flux measurements using a highly portable DIAL laser system,” Sci. Rep. 6(1), 33834 (2016).
[Crossref]

He, Y.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Hu, M.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Hubertus van Helden, J.-P.

S. Reuter, J. S. Sousa, G. D. Stancu, and J.-P. Hubertus van Helden, “Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets,” Plasma Sources Sci. Technol. 24(5), 054001 (2015).
[Crossref]

Jamil, Y.

H. Nasim and Y. Jamil, “Recent advancements in spectroscopy using tunable diode lasers,” Laser Phys. Lett. 10(4), 043001 (2013).
[Crossref]

Jayaweera, H.

Jung, E. C.

K. Song and E. C. Jung, “Recent developments in modulation spectroscopy for trace gas detection using tunable diode lasers,” Appl. Spectrosc. Rev. 38(4), 395–432 (2003).
[Crossref]

Kan, R. F.

C. G. Yang, L. Mei, H. Deng, Z. Y. Xu, B. Chen, and R. F. Kan, “Wavelength modulation spectroscopy by employing the first harmonic phase angle method,” Opt. Express 27(9), 12137–12146 (2019).
[Crossref]

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Kolomenskii, A.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Liu, J. G.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Lou, X. T.

Lundin, P.

Mei, L.

Nasim, H.

H. Nasim and Y. Jamil, “Recent advancements in spectroscopy using tunable diode lasers,” Laser Phys. Lett. 10(4), 043001 (2013).
[Crossref]

Okada, K.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Pernini, T. G.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Queisser, M.

M. Queisser, M. Burton, G. R. Allan, and A. Chiarugi, “Portable laser spectrometer for airborne and ground-based remote sensing of geological CO2 emissions,” Opt. Lett. 42(14), 2782–2785 (2017).
[Crossref]

M. Queisser, D. Granieri, and M. Burton, “A new frontier in CO2 flux measurements using a highly portable DIAL laser system,” Sci. Rep. 6(1), 33834 (2016).
[Crossref]

Ramonet, M.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Reuter, S.

S. Reuter, J. S. Sousa, G. D. Stancu, and J.-P. Hubertus van Helden, “Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets,” Plasma Sources Sci. Technol. 24(5), 054001 (2015).
[Crossref]

Sahay, P.

C. Wang and P. Sahay, “Breath analysis using laser spectroscopic techniques: breath biomarkers, spectral fingerprints, and detection limits,” Sensors 9(10), 8230–8262 (2009).
[Crossref]

Schuessler, H. A.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Somesfalean, G.

Song, K.

K. Song and E. C. Jung, “Recent developments in modulation spectroscopy for trace gas detection using tunable diode lasers,” Appl. Spectrosc. Rev. 38(4), 395–432 (2003).
[Crossref]

Sousa, J. S.

S. Reuter, J. S. Sousa, G. D. Stancu, and J.-P. Hubertus van Helden, “Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets,” Plasma Sources Sci. Technol. 24(5), 054001 (2015).
[Crossref]

Stancu, G. D.

S. Reuter, J. S. Sousa, G. D. Stancu, and J.-P. Hubertus van Helden, “Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets,” Plasma Sources Sci. Technol. 24(5), 054001 (2015).
[Crossref]

Staufer, J.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Strohaber, J.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Svanberg, S.

Vogel, F.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Wang, C.

C. Wang and P. Sahay, “Breath analysis using laser spectroscopic techniques: breath biomarkers, spectral fingerprints, and detection limits,” Sensors 9(10), 8230–8262 (2009).
[Crossref]

Wang, W.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Wei, M.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Wilson, A. C.

D. Das and A. C. Wilson, “Very long optical path-length from a compact multi-pass cell,” Appl. Phys. B 103(3), 749–754 (2011).
[Crossref]

Xia, H. H.

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Xia, J.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Xu, Z. Y.

C. G. Yang, L. Mei, H. Deng, Z. Y. Xu, B. Chen, and R. F. Kan, “Wavelength modulation spectroscopy by employing the first harmonic phase angle method,” Opt. Express 27(9), 12137–12146 (2019).
[Crossref]

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Yang, C. G.

C. G. Yang, L. Mei, H. Deng, Z. Y. Xu, B. Chen, and R. F. Kan, “Wavelength modulation spectroscopy by employing the first harmonic phase angle method,” Opt. Express 27(9), 12137–12146 (2019).
[Crossref]

M. Wei, R. F. Kan, B. Chen, Z. Y. Xu, C. G. Yang, X. Chen, H. H. Xia, M. Hu, Y. He, J. G. Liu, X. L. Fan, and W. Wang, “Calibration-free wavelength modulation spectroscopy for gas concentration measurements using a quantum cascade laser,” Appl. Phys. B 123(5), 149–158 (2017).
[Crossref]

Zaccheo, T. S.

J. T. Dobler, T. S. Zaccheo, T. G. Pernini, N. Blume, G. Broquet, F. Vogel, M. Ramonet, M. Braun, J. Staufer, P. Ciais, and C. Botos, “Demonstration of spatial greenhouse gas mapping using laser absorption spectrometers on local scales,” J. Appl. Remote Sens. 11(1), 014002 (2017).
[Crossref]

Zhang, S.

J. Xia, F. Zhu, S. Zhang, A. Kolomenskii, J. Dong, K. Okada, J. Strohaber, and H. A. Schuessler, “Probing greenhouse gases in turbulent atmosphere by long-range open-path wavelength modulation spectroscopy,” Opt. Lasers Eng. 117(1), 21–28 (2019).
[Crossref]

Zhu, F.

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Figures (7)

Fig. 1.
Fig. 1. (a) Diagram of the experiment setup for carbon dioxide measurement in open path environment; (b) Photograph of the experimental field; (c) Map of the experimental field. DFB-distributed feedback diode laser, AO-Analog Output, AI-Analog Input, PD-photo diode, PC-Personal Computer.
Fig. 2.
Fig. 2. (a) The original open-path and zero-path signals; (b) the open-path 1f-PA (${\theta _{1f - \textrm{open}}}$), zero-path 1f-PA (${\theta _{1f - \textrm{zero}}}$), and the difference between them ($\theta _{1f - \textrm{open}}^\ast $). The red box illustrates the non-absorption region for calculating absorption length path.
Fig. 3.
Fig. 3. Allen deviation of absorption path length.
Fig. 4.
Fig. 4. Continuous measurements of absorption path length at (a) site NO.2 and (b) site NO.1.
Fig. 5.
Fig. 5. The open-path, zero-path and zero-path subtracted signals of (a) the 1f-PA differential signal and (b) root-sum-square 2f/1f.
Fig. 6.
Fig. 6. Calibration-free spectral fitting result (upper panel) and the residual (lower panel) of the 1f-PA differential signals (${\theta _{1f - \textrm{open}}}$) measured for (a) the near-range reflective sheet (NO.1) and (b) the far-range reflective sheet (NO.2).
Fig. 7.
Fig. 7. Temporal evolution of the CO2 average concentration between the host and the far-range reflective sheet (NO.2) during a seven-day continuous measurement.

Equations (10)

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I 0 ( t ) = I 0 e + ( I 1 e ) 2 + ( I 1 o ) 2 cos ( 2 π f m t + φ ) = I 0 e + I 1 e cos ( 2 π f m t ) + I 1 o sin ( 2 π f m t )
φ = 2 π f m ( τ ν m τ I )
R 1 f = [ ( 1 H 0 ) ( I 1 e i I 1 o ) 1 H 1 I 0 e 2 H 2 2 ( I 1 e + i I 1 o ) 3 ] exp ( i 2 π f m τ ν m ) .
H 0 ( ν 0 , ν 1 ) = 1 2 π π π L N σ ( ν ) d ε H k ( ν 0 , ν 1 ) = 1 π π π L N σ ( ν ) cos ( k ε ) d ε } .
R 1 f [ ( I 1 e i I 1 o ) H 1 I 0 e ] exp ( i 2 π f m τ ν m ) .
θ 1 f H 1 I 0 e sin φ ( I 1 e ) 2 + ( I 1 o ) 2 + φ 2 π f m τ ν m = H 1 I 0 e sin φ ( I 1 e ) 2 + ( I 1 o ) 2 2 π f m τ I .
θ 1 f baseline = 2 π f m τ I .
θ 1 f baseline = θ 1 f baseline θ 1 f zero .
L = c τ p a t h = c θ 1 f baseline 2 π f m
θ 1 f = H 1 I 0 e sin φ ( I 1 e ) 2 + ( I 1 o ) 2 .

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