Abstract

In the tunable diode laser absorption spectroscopy-based diagnostics, the absorption of the measured target species may be influenced by the interference absorption from other vapor-phase species and the extinction from particles and liquid droplets, especially at high temperatures and pressures. Here, we report the first application (to our knowledge) of a differential absorption diagnostic for interference-free, simultaneous measurement of temperature and ethylene concentration using a single distributed-feedback diode laser near 1.62 μm. According to the detailed study of the C2H4 spectra in this region, two wavelength pairs are chosen to measure the temperature based on six selection criteria. C2H4 concentration is measured by one of the selected wavelength pairs with higher differential absorption. To validate the developed system, experiments are performed in a well-controlled heated static cell at a range of temperatures (300-900 K) and pressures (1-6 atm). The measurement accuracies for temperature and ethylene concentration are 1.83% and 1.65%, respectively, over the considered ranges. The precision, stability, and detection limit are also analyzed to validate the system’s performance. This system can potentially be applied in a variety of combustion applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]

2019 (1)

2018 (3)

T. C. Parise, D. F. Davidson, and R. K. Hanson, “Development of a two-wavelength IR laser absorption diagnostic for propene and ethylene,” Meas. Sci. Technol. 29(5), 055202 (2018).
[Crossref]

Y. Du, Z. Peng, and Y. Ding, “High-accuracy sinewave-scanned direct absorption spectroscopy,” Opt. Express 26(22), 29550–29560 (2018).
[Crossref] [PubMed]

F. Toldra-Reig and J. M. Serra, “Development of potentiometric sensors for C2H4 detection,” Sensors (Basel) 18(9), 2992 (2018).
[Crossref] [PubMed]

2017 (4)

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energ. Combust. 60, 132–176 (2017).
[Crossref]

K. Tanaka, K. Akishima, M. Sekita, K. Tonokura, and M. Konno, “Measurement of ethylene in combustion exhaust using a 3.3-μm distributed feedback interband cascade laser with wavelength modulation spectroscopy,” Appl. Phys. B 123(8), 219 (2017).
[Crossref]

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

M. S. Niu, P. G. Han, L. K. Song, D. Z. Hao, J. H. Zhang, and L. Ma, “Comparison and application of wavelet transform and Kalman filtering for denoising in δ13CO2 measurement by tunable diode laser absorption spectroscopy at 2.008 µm,” Opt. Express 25(20), A896–A905 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (4)

D. A. Morgott, “Anthropogenic and biogenic sources of ethylene and the potential for human exposure: A literature review,” Chem. Biol. Interact. 241, 10–22 (2015).
[Crossref] [PubMed]

T. Nguyen Ba, M. Triki, G. Desbrosses, and A. Vicet, “Quartz-enhanced photoacoustic spectroscopy sensor for ethylene detection with a 3.32 μm distributed feedback laser diode,” Rev. Sci. Instrum. 86(2), 023111 (2015).
[Crossref] [PubMed]

M. B. Sajid, T. Javed, and A. Farooq, “High-temperature measurements of methane and acetylene using quantum cascade laser absorption near 8 μm,” J. Quant. Spectrosc. Ra. 155, 66–74 (2015).
[Crossref]

T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “Simultaneous measurements of temperature and CO2 concentration employing diode laser absorption near 2.0 μm,” Appl. Phys. B 118(3), 471–480 (2015).
[Crossref]

2014 (1)

I. Stranic and R. K. Hanson, “Laser absorption diagnostic for measuring acetylene concentrations in shock tubes,” J. Quant. Spectrosc. Ra. 142, 58–65 (2014).
[Crossref]

2013 (1)

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

2012 (3)

I. Mappe-Fogaing, L. Joly, G. Durry, N. Dumelié, T. Decarpenterie, J. Cousin, B. Parvitte, and V. Zéninari, “Wavelet denoising for infrared laser spectroscopy and gas detection,” Appl. Spectrosc. 66(6), 700–710 (2012).
[Crossref] [PubMed]

M. S. Aziz and A. J. Orr-Ewing, “Development and application of an optical sensor for ethene in ambient air using near infra-red cavity ring down spectroscopy and sample preconcentration,” J. Environ. Monit. 14(12), 3094–3100 (2012).
[Crossref] [PubMed]

J. Shemshad, S. M. Aminossadati, and M. S. Kizil, “A review of developments in near infrared methane detection based on tunable diode laser,” Sens. Actuators B Chem. 171–172, 77–92 (2012).
[Crossref]

2011 (1)

S. H. Pyun, J. Cho, D. F. Davidson, and R. K. Hanson, “Interference-free mid-IR laser absorption detection of methane,” Meas. Sci. Technol. 22(2), 025303 (2011).
[Crossref]

2009 (2)

S. Schilt, A. A. Kosterev, and F. K. Tittel, “Performance evaluation of a near infrared QEPAS based ethylene sensor,” Appl. Phys. B 95(4), 813–824 (2009).
[Crossref]

J. Manne, W. Jager, and J. Tulip, “Sensitive detection of ammonia and ethylene with a pulsed quantum cascade laser using intra and interpulse spectroscopic techniques,” Appl. Phys. B 94(2), 337–344 (2009).
[Crossref]

2007 (1)

M. Lackner, “Tunable diode laser absorption spectroscopy (TDLAS) in the process industries–a review,” Rev. Chem. Eng. 23(2), 65–147 (2007).
[Crossref]

2006 (1)

2005 (2)

M. T. McCulloch, N. Langford, and G. Duxbury, “Real-time trace-level detection of carbon dioxide and ethylene in car exhaust gases,” Appl. Opt. 44(14), 2887–2894 (2005).
[Crossref] [PubMed]

P. M. Ramos and I. Ruisánchez, “Noise and background removal in Raman spectra of ancient pigments using wavelet transform,” J. Raman Spectrosc. 36(9), 848–856 (2005).
[Crossref]

2003 (1)

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

2002 (4)

L. Ma, S. T. Sanders, J. B. Jeffries, and R. K. Hanson, “Monitoring and control of a pulse detonation engine using a diode-laser fuel concentration and temperature sensor,” Proc. Combust. Inst. 29(1), 161–166 (2002).
[Crossref]

K. L. Wang, H. Li, and J. R. Ecker, “Ethylene biosynthesis and signaling networks,” Plant Cell 14, S131–S151 (2002).

R. F. Curl and F. K. Tittel, “Tunable infrared laser spectroscopy,” Annu. Rep. Prog. Chem, Sect. C: Phys. Chem. 98, 219–272 (2002).

P. Werle, F. Slemr, K. Maurer, R. Kormann, R. Mücke, and B. Jänker, “Near- and mid-infrared laser-optical sensors for gas analysis,” Opt. Lasers Eng. 37(2–3), 101–114 (2002).
[Crossref]

1997 (1)

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. Rowland, and D. B. Kell, “Wavelet denoising of infrared spectra,” Analyst (Lond.) 122(7), 645–652 (1997).
[Crossref]

1994 (1)

A. Brock, N. Mina-Camilde, and I. C. Manzanares, “Vibrational spectroscopy of CH bonds of C2H4 liquid and C2H4 in liquid argon solutions,” J. Phys. Chem. 98(18), 4800–4808 (1994).
[Crossref]

Akishima, K.

K. Tanaka, K. Akishima, M. Sekita, K. Tonokura, and M. Konno, “Measurement of ethylene in combustion exhaust using a 3.3-μm distributed feedback interband cascade laser with wavelength modulation spectroscopy,” Appl. Phys. B 123(8), 219 (2017).
[Crossref]

Alsberg, B. K.

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. Rowland, and D. B. Kell, “Wavelet denoising of infrared spectra,” Analyst (Lond.) 122(7), 645–652 (1997).
[Crossref]

Aminossadati, S. M.

J. Shemshad, S. M. Aminossadati, and M. S. Kizil, “A review of developments in near infrared methane detection based on tunable diode laser,” Sens. Actuators B Chem. 171–172, 77–92 (2012).
[Crossref]

Aziz, M. S.

M. S. Aziz and A. J. Orr-Ewing, “Development and application of an optical sensor for ethene in ambient air using near infra-red cavity ring down spectroscopy and sample preconcentration,” J. Environ. Monit. 14(12), 3094–3100 (2012).
[Crossref] [PubMed]

Barbe, A.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Bernath, P.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Birk, M.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Biswell, D.

Boudon, V.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Brock, A.

A. Brock, N. Mina-Camilde, and I. C. Manzanares, “Vibrational spectroscopy of CH bonds of C2H4 liquid and C2H4 in liquid argon solutions,” J. Phys. Chem. 98(18), 4800–4808 (1994).
[Crossref]

Cai, T.

T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “High-pressure measurements of temperature and CO2 concentration using tunable diode lasers at 2 μm,” Appl. Spectrosc. 70(3), 474–484 (2016).
[Crossref] [PubMed]

T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “Simultaneous measurements of temperature and CO2 concentration employing diode laser absorption near 2.0 μm,” Appl. Phys. B 118(3), 471–480 (2015).
[Crossref]

Campargue, A.

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T. C. Parise, D. F. Davidson, and R. K. Hanson, “Development of a two-wavelength IR laser absorption diagnostic for propene and ethylene,” Meas. Sci. Technol. 29(5), 055202 (2018).
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Desbrosses, G.

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Drouin, B. J.

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M. B. Sajid, T. Javed, and A. Farooq, “Shock tube/laser absorption measurements of methane, acetylene and ethylene during the pyrolysis of n-pentane and iso-pentane,” Combust. Flame 164, 1–9 (2016).
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I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Gamache, R. R.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Gao, X.

Goldenstein, C. S.

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Gordon, I. E.

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Han, P. G.

Hanson, R. K.

T. C. Parise, D. F. Davidson, and R. K. Hanson, “Development of a two-wavelength IR laser absorption diagnostic for propene and ethylene,” Meas. Sci. Technol. 29(5), 055202 (2018).
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C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energ. Combust. 60, 132–176 (2017).
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I. Stranic and R. K. Hanson, “Laser absorption diagnostic for measuring acetylene concentrations in shock tubes,” J. Quant. Spectrosc. Ra. 142, 58–65 (2014).
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[Crossref]

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
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L. Ma, S. T. Sanders, J. B. Jeffries, and R. K. Hanson, “Monitoring and control of a pulse detonation engine using a diode-laser fuel concentration and temperature sensor,” Proc. Combust. Inst. 29(1), 161–166 (2002).
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Hao, D. Z.

Harrison, J. J.

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Hartmann, J.-M.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Hill, C.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Hodges, J. T.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Jacquemart, D.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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J. Manne, W. Jager, and J. Tulip, “Sensitive detection of ammonia and ethylene with a pulsed quantum cascade laser using intra and interpulse spectroscopic techniques,” Appl. Phys. B 94(2), 337–344 (2009).
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Jänker, B.

P. Werle, F. Slemr, K. Maurer, R. Kormann, R. Mücke, and B. Jänker, “Near- and mid-infrared laser-optical sensors for gas analysis,” Opt. Lasers Eng. 37(2–3), 101–114 (2002).
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Javed, T.

M. B. Sajid, T. Javed, and A. Farooq, “Shock tube/laser absorption measurements of methane, acetylene and ethylene during the pyrolysis of n-pentane and iso-pentane,” Combust. Flame 164, 1–9 (2016).
[Crossref]

M. B. Sajid, T. Javed, and A. Farooq, “High-temperature measurements of methane and acetylene using quantum cascade laser absorption near 8 μm,” J. Quant. Spectrosc. Ra. 155, 66–74 (2015).
[Crossref]

Jeffries, J. B.

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energ. Combust. 60, 132–176 (2017).
[Crossref]

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

L. Ma, S. T. Sanders, J. B. Jeffries, and R. K. Hanson, “Monitoring and control of a pulse detonation engine using a diode-laser fuel concentration and temperature sensor,” Proc. Combust. Inst. 29(1), 161–166 (2002).
[Crossref]

Johnson, T. J.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Vicet, A.

T. Nguyen Ba, M. Triki, G. Desbrosses, and A. Vicet, “Quartz-enhanced photoacoustic spectroscopy sensor for ethylene detection with a 3.32 μm distributed feedback laser diode,” Rev. Sci. Instrum. 86(2), 023111 (2015).
[Crossref] [PubMed]

Wagner, G.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Wahl, E.

Wang, G.

Wang, K. L.

K. L. Wang, H. Li, and J. R. Ecker, “Ethylene biosynthesis and signaling networks,” Plant Cell 14, S131–S151 (2002).

Wang, M.

T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “High-pressure measurements of temperature and CO2 concentration using tunable diode lasers at 2 μm,” Appl. Spectrosc. 70(3), 474–484 (2016).
[Crossref] [PubMed]

T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “Simultaneous measurements of temperature and CO2 concentration employing diode laser absorption near 2.0 μm,” Appl. Phys. B 118(3), 471–480 (2015).
[Crossref]

Wang, Z.

Wcislo, P.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Werle, P.

P. Werle, F. Slemr, K. Maurer, R. Kormann, R. Mücke, and B. Jänker, “Near- and mid-infrared laser-optical sensors for gas analysis,” Opt. Lasers Eng. 37(2–3), 101–114 (2002).
[Crossref]

Wilzewski, J.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Winson, M. K.

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. Rowland, and D. B. Kell, “Wavelet denoising of infrared spectra,” Analyst (Lond.) 122(7), 645–652 (1997).
[Crossref]

Woodward, A. M.

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. Rowland, and D. B. Kell, “Wavelet denoising of infrared spectra,” Analyst (Lond.) 122(7), 645–652 (1997).
[Crossref]

Xin, Y.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

Yu, H. B.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
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Yu, S.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
[Crossref]

Zak, E. J.

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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Zéninari, V.

Zhang, B.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

Zhang, J. H.

Zhou, X.

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

Analyst (Lond.) (1)

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. Rowland, and D. B. Kell, “Wavelet denoising of infrared spectra,” Analyst (Lond.) 122(7), 645–652 (1997).
[Crossref]

Annu. Rep. Prog. Chem, Sect. C: Phys. Chem. (1)

R. F. Curl and F. K. Tittel, “Tunable infrared laser spectroscopy,” Annu. Rep. Prog. Chem, Sect. C: Phys. Chem. 98, 219–272 (2002).

Appl. Opt. (1)

Appl. Phys. B (4)

K. Tanaka, K. Akishima, M. Sekita, K. Tonokura, and M. Konno, “Measurement of ethylene in combustion exhaust using a 3.3-μm distributed feedback interband cascade laser with wavelength modulation spectroscopy,” Appl. Phys. B 123(8), 219 (2017).
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T. Cai, G. Gao, M. Wang, G. Wang, Y. Liu, and X. Gao, “Simultaneous measurements of temperature and CO2 concentration employing diode laser absorption near 2.0 μm,” Appl. Phys. B 118(3), 471–480 (2015).
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J. Manne, W. Jager, and J. Tulip, “Sensitive detection of ammonia and ethylene with a pulsed quantum cascade laser using intra and interpulse spectroscopic techniques,” Appl. Phys. B 94(2), 337–344 (2009).
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S. Schilt, A. A. Kosterev, and F. K. Tittel, “Performance evaluation of a near infrared QEPAS based ethylene sensor,” Appl. Phys. B 95(4), 813–824 (2009).
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Appl. Spectrosc. (2)

Chem. Biol. Interact. (1)

D. A. Morgott, “Anthropogenic and biogenic sources of ethylene and the potential for human exposure: A literature review,” Chem. Biol. Interact. 241, 10–22 (2015).
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Combust. Flame (1)

M. B. Sajid, T. Javed, and A. Farooq, “Shock tube/laser absorption measurements of methane, acetylene and ethylene during the pyrolysis of n-pentane and iso-pentane,” Combust. Flame 164, 1–9 (2016).
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J. Anal. At. Spectrom. (1)

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
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J. Environ. Monit. (1)

M. S. Aziz and A. J. Orr-Ewing, “Development and application of an optical sensor for ethene in ambient air using near infra-red cavity ring down spectroscopy and sample preconcentration,” J. Environ. Monit. 14(12), 3094–3100 (2012).
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J. Phys. Chem. (1)

A. Brock, N. Mina-Camilde, and I. C. Manzanares, “Vibrational spectroscopy of CH bonds of C2H4 liquid and C2H4 in liquid argon solutions,” J. Phys. Chem. 98(18), 4800–4808 (1994).
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J. Quant. Spectrosc. Ra. (3)

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Ra. 203, 3–69 (2017).
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I. Stranic and R. K. Hanson, “Laser absorption diagnostic for measuring acetylene concentrations in shock tubes,” J. Quant. Spectrosc. Ra. 142, 58–65 (2014).
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M. B. Sajid, T. Javed, and A. Farooq, “High-temperature measurements of methane and acetylene using quantum cascade laser absorption near 8 μm,” J. Quant. Spectrosc. Ra. 155, 66–74 (2015).
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J. Raman Spectrosc. (1)

P. M. Ramos and I. Ruisánchez, “Noise and background removal in Raman spectra of ancient pigments using wavelet transform,” J. Raman Spectrosc. 36(9), 848–856 (2005).
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Meas. Sci. Technol. (3)

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
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S. H. Pyun, J. Cho, D. F. Davidson, and R. K. Hanson, “Interference-free mid-IR laser absorption detection of methane,” Meas. Sci. Technol. 22(2), 025303 (2011).
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T. C. Parise, D. F. Davidson, and R. K. Hanson, “Development of a two-wavelength IR laser absorption diagnostic for propene and ethylene,” Meas. Sci. Technol. 29(5), 055202 (2018).
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Opt. Express (5)

Opt. Lasers Eng. (1)

P. Werle, F. Slemr, K. Maurer, R. Kormann, R. Mücke, and B. Jänker, “Near- and mid-infrared laser-optical sensors for gas analysis,” Opt. Lasers Eng. 37(2–3), 101–114 (2002).
[Crossref]

Plant Cell (1)

K. L. Wang, H. Li, and J. R. Ecker, “Ethylene biosynthesis and signaling networks,” Plant Cell 14, S131–S151 (2002).

Proc. Combust. Inst. (1)

L. Ma, S. T. Sanders, J. B. Jeffries, and R. K. Hanson, “Monitoring and control of a pulse detonation engine using a diode-laser fuel concentration and temperature sensor,” Proc. Combust. Inst. 29(1), 161–166 (2002).
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C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energ. Combust. 60, 132–176 (2017).
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M. Lackner, “Tunable diode laser absorption spectroscopy (TDLAS) in the process industries–a review,” Rev. Chem. Eng. 23(2), 65–147 (2007).
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Rev. Sci. Instrum. (1)

T. Nguyen Ba, M. Triki, G. Desbrosses, and A. Vicet, “Quartz-enhanced photoacoustic spectroscopy sensor for ethylene detection with a 3.32 μm distributed feedback laser diode,” Rev. Sci. Instrum. 86(2), 023111 (2015).
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F. Toldra-Reig and J. M. Serra, “Development of potentiometric sensors for C2H4 detection,” Sensors (Basel) 18(9), 2992 (2018).
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Research and Markets, “Ethylene (ET): 2019 world market outlook and forecast up to 2023” (Research and Markets, January 2019), www.researchandmarkets.com .

C. F. Edwards, K. Y. Teh, and S. L. Miller, “Development of lowenergy-loss, high-efficiency chemical engines,” Stanford University Global Climate and Energy Project Technical Report (2006).

Y. Aoyagi, H. Osada, M. Misawa, Y. Goto, and H. Ishii, “Advanced diesel combustion using of wide range, high boosted and cooled EGR system by single cylinder engine,” SAE Technical Paper no. 2006–01–0077 (2006).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 (a) Measured C2H4 spectrum near 1.62 μm and a simulated one near 3.3 μm for the same conditions (PC2H4 = 49 torr, T = 296 K). (b) Absorption lines of other primary combustion products at 1000 K near 1.62 μm and 3.3 μm.
Fig. 2
Fig. 2 Schematic of the experimental setup.
Fig. 3
Fig. 3 Q branch of pure C2H4 near 1.62 μm in the temperature range of 300-900 K, measured in a heated static cell with 21 cm absorption path length at 0.2 atm.
Fig. 4
Fig. 4 Measured absorbance profile of C2H4 (5% in N2) along with simulated absorbance of H2O and CO2 (10% in N2). Simulations are performed using the HITRAN 2016 database. The peaks and valleys for the selected wavelength pairs are indicated in the graph.
Fig. 5
Fig. 5 Absorption cross-section measurements for the peak wavelength of wavelength pair A at various temperatures and 1 atm.
Fig. 6
Fig. 6 Measured absorption cross-sections at peaks and valleys of the two selected wavelength pairs and their differential cross-sections (σν, p-v) as a function of temperature for a pressure of 1 atm: (a) wavelength pair A and (b) wavelength pair B.
Fig. 7
Fig. 7 Measured differential absorption cross-section as a function of temperature and pressure for the two selected wavelength pairs: (a) wavelength pair A and (b) wavelength pair B.
Fig. 8
Fig. 8 Ratios of differential absorption cross-sections of the two selected wavelength pairs as a function of temperature at each pressure.
Fig. 9
Fig. 9 Measured transmitted intensity I for ∼1 kPa C2H4 and N2. The inset shows the calculated spectra from the measured I0 and the fitted one.
Fig. 10
Fig. 10 Comparison between the raw signal (gray line) and the denoised signal (red line).
Fig. 11
Fig. 11 (a) Comparison between the measured temperatures (Tmeasured) and the thermocouple readings (Treading) at different pressures. (b) Ratio of the C2H4 concentrations measured by the system (xmeasured) and the concentrations recorded (xreference) when the mixtures are prepared.
Fig. 12
Fig. 12 Successive measurements for ~0.275% and ~0.543% C2H4-N2 mixtures for 1000 s at (a) 900 K and 1 atm and (b) 900 K and 6 atm. (c) and (d) The histogram plots obtained from time series measurements.
Fig. 13
Fig. 13 Allan variance from time series measurements of C2H4-N2 mixtures at 900 K and 1 atm and 900 K and 6 atm.
Fig. 14
Fig. 14 Estimated C2H4 concentration detection limit (SNR = 1) at different temperature and pressure conditions with a path length of 21 cm, laser power of 10 mW, and 1 kHz bandwidth.

Tables (2)

Tables Icon

Table 1 Selection rules for the optimum wavelength pairs used in the experiment.

Tables Icon

Table 2 Properties of the Two Selected Wavelength Pairs for the Differential Absorption Scheme for Measurements of Temperature and C2H4 Concentration

Equations (8)

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ln ( I I 0 ) ν =α(ν,T,P)=σ(ν,T,P)x P RT L,
ln ( I I 0 ) ν = α tar + α int + τ ext ,
( α tar + α int + τ ext ) ν ,p ( α tar + α int + τ ext ) ν ,v α tar(ν,p) α tar(ν,v) = σ ν,pv x P RT L.
x= ln ( I I 0 ) ν,p (ln ( I I 0 ) ν,v ) σ ν,pv P RT L = ln( ( I I 0 ) ν,p ( I 0 I ) ν,v ) σ ν,pv P RT L .
f(T,P)= ln ( I I 0 ) ν 1 ,p (ln ( I I 0 ) ν 1 ,v ) ln ( I I 0 ) ν 2 ,p (ln ( I I 0 ) ν 2 ,v ) = ( σ ν 1 ,p σ ν 1 ,v )xnL ( σ ν 2 ,p σ ν 2 ,v )xnL = σ ν 1 ,pv σ ν 2 ,pv .
σ ν 1 ,pv (T,P)= σ ν 1 ,pv ( T 0 , P 0 ) ( T 0 T ) a ( P 0 P ) b ,
σ ν 2 ,pv (T,P)= σ ν 2 ,pv ( T 0 , P 0 ) ( T 0 T ) c ( P 0 P ) d ,
f(T,P)= σ ν 1 ,pv σ ν 2 ,pv = σ ν 1 ,pv ( T 0 , P 0 ) σ ν 2 ,pv ( T 0 , P 0 ) ( T 0 T ) ac ( P 0 P ) bd .