Abstract

We present a fiber-optic photoacoustic (PA) sensor for remote monitoring of gas micro-leakage. The gas sensing head is a miniature ferrule-top PA cavity with a cantilever beam. Gas diffuses into the cavity from the gap around the cantilever beam, and a small hole opens on the side wall. The volume of the optimized PA cavity is only 70 μL. An erbium-doped fiber amplified laser is used as a light source of acoustic excitation. The PA pressure signal is obtained by measuring the deflection of the cantilever beam with a fiber-optic white-light interferometric readout. The experimental result of leaking acetylene (C2H2) gas measurement shows a real-time response of 11.2 s. A detection limit is achieved to be 20 ppb with a 1 s lock-in integration time and a 1 km conductive fiber. Since both the excitation light and probe light are transmitted by the optical fiber, the designed sensing system has the advantages of remote detection and intrinsic safety.

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

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References

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  1. T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
    [Crossref]
  2. J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
    [Crossref] [PubMed]
  3. H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
    [Crossref]
  4. P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
    [Crossref]
  5. M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
    [Crossref]
  6. Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
    [Crossref] [PubMed]
  7. A. Sampaolo, P. Patimisco, M. Giglio, L. Chieco, G. Scamarcio, F. K. Tittel, and V. Spagnolo, “Highly sensitive gas leak detector based on a quartz-enhanced photoacoustic SF6 sensor,” Opt. Express 24(14), 15872–15881 (2016).
    [Crossref] [PubMed]
  8. M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
    [Crossref]
  9. Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
    [Crossref]
  10. L. Tombez, E. J. Zhang, J. S. Orcutt, S. Kamlapurkar, and W. M. J. Green, “Methane absorption spectroscopy on a silicon photonic chip,” Optica 4(11), 1322–1325 (2017).
    [Crossref]
  11. J. H. Northern, S. O’Hagan, B. Fletcher, B. Gras, P. Ewart, C. S. Kim, M. Kim, C. D. Merritt, W. W. Bewley, C. L. Canedy, J. Abell, I. Vurgaftman, and J. R. Meyer, “Mid-infrared multi-mode absorption spectroscopy using interband cascade lasers for multi-species sensing,” Opt. Lett. 40(17), 4186–4189 (2015).
    [Crossref] [PubMed]
  12. L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
    [Crossref] [PubMed]
  13. 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, 77–92 (2012).
    [Crossref]
  14. R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
    [Crossref]
  15. C. S. Goldenstein, R. Mitchell Spearrin, and R. K. Hanson, “Fiber-coupled diode-laser sensors for calibration-free stand-off measurements of gas temperature, pressure, and composition,” Appl. Opt. 55(3), 479–484 (2016).
    [Crossref] [PubMed]
  16. G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
    [Crossref] [PubMed]
  17. B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
    [Crossref]
  18. S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
    [Crossref]
  19. C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
    [Crossref]
  20. A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 27(21), 1902–1904 (2002).
    [Crossref] [PubMed]
  21. H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
    [Crossref] [PubMed]
  22. K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
    [Crossref] [PubMed]
  23. Y. He, Y. Ma, Y. Tong, X. Yu, and F. K. Tittel, “HCN ppt-level detection based on a QEPAS sensor with amplified laser and a miniaturized 3D-printed photoacoustic detection channel,” Opt. Express 26(8), 9666–9675 (2018).
    [Crossref] [PubMed]
  24. K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
    [Crossref]
  25. Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
    [Crossref]
  26. X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
    [Crossref]
  27. Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
    [Crossref]
  28. K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
    [Crossref]
  29. K. Chen, Z. Yu, Z. Gong, and Q. Yu, “Lock-in white-light-interferometry-based all-optical photoacoustic spectrometer,” Opt. Lett. 43(20), 5038–5041 (2018).
    [Crossref] [PubMed]
  30. Y. Cao, W. Jin, H. L. Ho, and J. Ma, “Miniature fiber-tip photoacoustic spectrometer for trace gas detection,” Opt. Lett. 38(4), 434–436 (2013).
    [Crossref] [PubMed]
  31. G. Gruca, K. Heeck, J. Rector, and D. Iannuzzi, “Demonstration of a miniature all-optical photoacoustic spectrometer based on ferrule-top technology,” Opt. Lett. 38(10), 1672–1674 (2013).
    [Crossref] [PubMed]
  32. S. Zhou, M. Slaman, and D. Iannuzzi, “Demonstration of a highly sensitive photoacoustic spectrometer based on a miniaturized all-optical detecting sensor,” Opt. Express 25(15), 17541–17548 (2017).
    [Crossref] [PubMed]
  33. T. Kuusela and J. Kauppinen, “Photoacoustic gas analysis using interferometric cantilever microphone,” Appl. Spectrosc. Rev. 42(5), 443–474 (2007).
    [Crossref]
  34. K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
    [Crossref]
  35. Z. Yu and A. Wang, “Fast white light interferometry demodulation algorithm for low-finesse Fabry–Pérot sensors,” IEEE Photonic. Tech. L. 27(8), 817–820 (2015).
    [Crossref]
  36. K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
    [Crossref] [PubMed]
  37. P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
    [Crossref]
  38. P. O. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993).
    [Crossref]

2018 (6)

Y. He, Y. Ma, Y. Tong, X. Yu, and F. K. Tittel, “HCN ppt-level detection based on a QEPAS sensor with amplified laser and a miniaturized 3D-printed photoacoustic detection channel,” Opt. Express 26(8), 9666–9675 (2018).
[Crossref] [PubMed]

K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
[Crossref]

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

K. Chen, Z. Yu, Z. Gong, and Q. Yu, “Lock-in white-light-interferometry-based all-optical photoacoustic spectrometer,” Opt. Lett. 43(20), 5038–5041 (2018).
[Crossref] [PubMed]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

2017 (6)

S. Zhou, M. Slaman, and D. Iannuzzi, “Demonstration of a highly sensitive photoacoustic spectrometer based on a miniaturized all-optical detecting sensor,” Opt. Express 25(15), 17541–17548 (2017).
[Crossref] [PubMed]

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

L. Tombez, E. J. Zhang, J. S. Orcutt, S. Kamlapurkar, and W. M. J. Green, “Methane absorption spectroscopy on a silicon photonic chip,” Optica 4(11), 1322–1325 (2017).
[Crossref]

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017).
[Crossref] [PubMed]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

2016 (8)

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
[Crossref] [PubMed]

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
[Crossref]

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

A. Sampaolo, P. Patimisco, M. Giglio, L. Chieco, G. Scamarcio, F. K. Tittel, and V. Spagnolo, “Highly sensitive gas leak detector based on a quartz-enhanced photoacoustic SF6 sensor,” Opt. Express 24(14), 15872–15881 (2016).
[Crossref] [PubMed]

C. S. Goldenstein, R. Mitchell Spearrin, and R. K. Hanson, “Fiber-coupled diode-laser sensors for calibration-free stand-off measurements of gas temperature, pressure, and composition,” Appl. Opt. 55(3), 479–484 (2016).
[Crossref] [PubMed]

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

2015 (3)

Z. Yu and A. Wang, “Fast white light interferometry demodulation algorithm for low-finesse Fabry–Pérot sensors,” IEEE Photonic. Tech. L. 27(8), 817–820 (2015).
[Crossref]

J. H. Northern, S. O’Hagan, B. Fletcher, B. Gras, P. Ewart, C. S. Kim, M. Kim, C. D. Merritt, W. W. Bewley, C. L. Canedy, J. Abell, I. Vurgaftman, and J. R. Meyer, “Mid-infrared multi-mode absorption spectroscopy using interband cascade lasers for multi-species sensing,” Opt. Lett. 40(17), 4186–4189 (2015).
[Crossref] [PubMed]

S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
[Crossref]

2013 (4)

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Y. Cao, W. Jin, H. L. Ho, and J. Ma, “Miniature fiber-tip photoacoustic spectrometer for trace gas detection,” Opt. Lett. 38(4), 434–436 (2013).
[Crossref] [PubMed]

G. Gruca, K. Heeck, J. Rector, and D. Iannuzzi, “Demonstration of a miniature all-optical photoacoustic spectrometer based on ferrule-top technology,” Opt. Lett. 38(10), 1672–1674 (2013).
[Crossref] [PubMed]

2012 (3)

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
[Crossref]

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, 77–92 (2012).
[Crossref]

2011 (1)

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

2010 (1)

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

2007 (2)

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

T. Kuusela and J. Kauppinen, “Photoacoustic gas analysis using interferometric cantilever microphone,” Appl. Spectrosc. Rev. 42(5), 443–474 (2007).
[Crossref]

2002 (2)

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. 27(21), 1902–1904 (2002).
[Crossref] [PubMed]

2001 (1)

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
[Crossref]

1993 (1)

P. O. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993).
[Crossref]

Abell, J.

Allen, M. G.

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[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, 77–92 (2012).
[Crossref]

Bakhirkin, Y. A.

Berger, C.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Bewley, W. W.

Blake, D. R.

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
[Crossref]

Brosha, E. L.

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
[Crossref]

Canedy, C. L.

Cao, Y.

Chekurov, N.

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

Chen, K.

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
[Crossref]

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

K. Chen, Z. Yu, Z. Gong, and Q. Yu, “Lock-in white-light-interferometry-based all-optical photoacoustic spectrometer,” Opt. Lett. 43(20), 5038–5041 (2018).
[Crossref] [PubMed]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

Chen, T. Y.

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
[Crossref]

Chen, Y.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Chieco, L.

Curl, R. F.

Ding, J.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Divan, R.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Dong, L.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
[Crossref] [PubMed]

Drewes, J.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Edgar, M. P.

Ewart, P.

Feng, R.

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Fletcher, B.

Frish, M. B.

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

Gao, Q.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Gibson, G. M.

Giglio, M.

Goldenstein, C. S.

Gong, Z.

K. Chen, Z. Yu, Z. Gong, and Q. Yu, “Lock-in white-light-interferometry-based all-optical photoacoustic spectrometer,” Opt. Lett. 43(20), 5038–5041 (2018).
[Crossref] [PubMed]

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

Gosztola, D.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Gras, B.

Green, B. D.

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

Green, W. M. J.

Griffin, R. J.

Gruca, G.

Gundel, L.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Guo, M.

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

Guo, W.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Hahtela, O.

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

Haisch, C.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Hanson, R. K.

He, Q.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

He, Y.

Heeck, K.

Hempler, N.

Ho, H. L.

Humayun, M. T.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Iannuzzi, D.

Ji, H.

H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
[Crossref]

Jia, S.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Jin, W.

Johnson, M. R.

S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
[Crossref]

Kamlapurkar, S.

Kauppinen, J.

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

T. Kuusela and J. Kauppinen, “Photoacoustic gas analysis using interferometric cantilever microphone,” Appl. Spectrosc. Rev. 42(5), 443–474 (2007).
[Crossref]

Kim, C. S.

Kim, M.

Kizil, M. S.

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, 77–92 (2012).
[Crossref]

Kosterev, A. A.

Kreller, C. R.

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
[Crossref]

Kuusela, T.

T. Kuusela and J. Kauppinen, “Photoacoustic gas analysis using interferometric cantilever microphone,” Appl. Spectrosc. Rev. 42(5), 443–474 (2007).
[Crossref]

Kysar, J.

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
[Crossref]

Laderer, M. C.

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

Leix, C.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Li, B.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Li, C.

Li, L.

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

Liang, T.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Liu, G.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Liu, H.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Liu, J.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Lou, X.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Ma, J.

Ma, W.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Ma, Y.

Maker, G. T.

Malcolm, G. P. A.

Mao, X.

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

Merritt, C. D.

Meyer, J. R.

Mitchell Spearrin, R.

Mücke, R.

P. O. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993).
[Crossref]

Naper, R.

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

Niessner, R.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Northern, J. H.

O’Hagan, S.

Orcutt, J. S.

Padgett, M. J.

Pan, J.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Paprotny, I.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Patimisco, P.

Pei, X.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Peng, W.

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

Phillips, D. B.

Qu, C.

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

Rector, J.

Rosenmann, D.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Rowland, F. S.

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
[Crossref]

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P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

Sampaolo, A.

Sanchez, N. P.

Scamarcio, G.

Schoonbaert, S. B.

S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
[Crossref]

Sekhar, P. K.

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
[Crossref]

Shemshad, J.

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, 77–92 (2012).
[Crossref]

Si, H.

H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
[Crossref]

Sievilä, P.

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

Simpson, I. J.

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
[Crossref]

Slaman, M.

Slemr, F.

P. O. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993).
[Crossref]

Solomon, P. A.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Spagnolo, V.

Stafford-Evans, J.

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

Stan, L.

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
[Crossref]

Sun, B.

Sun, C.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Sun, D.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Tan, Q.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Thaler, K. M.

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Tittel, F. K.

Tittonen, I.

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
[Crossref]

Tombez, L.

Tong, Y.

Tyner, D. R.

S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
[Crossref]

Vurgaftman, I.

Wainner, R. T.

M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
[Crossref]

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

Wan, J.

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Wang, A.

Z. Yu and A. Wang, “Fast white light interferometry demodulation algorithm for low-finesse Fabry–Pérot sensors,” IEEE Photonic. Tech. L. 27(8), 817–820 (2015).
[Crossref]

Wang, F.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Wang, J.

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

Wang, Q.

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

Wang, Y.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Werle, P. O.

P. O. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993).
[Crossref]

White, M. A.

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
[Crossref]

Wu, H.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
[Crossref] [PubMed]

Wu, S.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Wu, Y.

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Xiao, L.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Xiong, J.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Xue, C.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Yang, Y.

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

Ye, W.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Yin, W.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Yu, J.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Yu, N.

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Yu, Q.

K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

K. Chen, Z. Yu, Q. Yu, M. Guo, Z. Zhao, C. Qu, Z. Gong, and Y. Yang, “Fast demodulated white-light interferometry-based fiber-optic Fabry-Perot cantilever microphone,” Opt. Lett. 43(14), 3417–3420 (2018).
[Crossref] [PubMed]

K. Chen, Z. Yu, Z. Gong, and Q. Yu, “Lock-in white-light-interferometry-based all-optical photoacoustic spectrometer,” Opt. Lett. 43(20), 5038–5041 (2018).
[Crossref] [PubMed]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

Yu, S.

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

Yu, X.

Yu, Y.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
[Crossref] [PubMed]

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Yu, Z.

Zeng, X.

H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
[Crossref]

Zhang, E. J.

Zhang, G.

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

Zhang, L.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Zhang, W.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Zhang, Y.

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Zhang, Z.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Zhao, Z.

Zheng, C.

L. Dong, F. K. Tittel, C. Li, N. P. Sanchez, H. Wu, C. Zheng, Y. Yu, A. Sampaolo, and R. J. Griffin, “Compact TDLAS based sensor design using interband cascade lasers for mid-IR trace gas sensing,” Opt. Express 24(6), A528–A535 (2016).
[Crossref] [PubMed]

B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Zheng, F.

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

Zheng, H.

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Zhou, S.

Zhou, X.

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

Zhu, S.

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

Anal. Chem. (1)

K. M. Thaler, C. Berger, C. Leix, J. Drewes, R. Niessner, and C. Haisch, “Photoacoustic spectroscopy for the quantification of N2O in the off-gas of wastewater treatment plants,” Anal. Chem. 89(6), 3795–3801 (2017).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (3)

R. T. Wainner, B. D. Green, M. G. Allen, M. A. White, J. Stafford-Evans, and R. Naper, “Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes,” Appl. Phys. B 75(2–3), 249–254 (2002).
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S. B. Schoonbaert, D. R. Tyner, and M. R. Johnson, “Remote ambient methane monitoring using fiber-optically coupled optical sensors,” Appl. Phys. B 119(1), 133–142 (2015).
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Appl. Spectrosc. Rev. (1)

T. Kuusela and J. Kauppinen, “Photoacoustic gas analysis using interferometric cantilever microphone,” Appl. Spectrosc. Rev. 42(5), 443–474 (2007).
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Geophys. Res. Lett. (1)

T. Y. Chen, I. J. Simpson, D. R. Blake, and F. S. Rowland, “Impact of the leakage of liquefied petroleum gas (LPG) on Santiago air quality,” Geophys. Res. Lett. 28(11), 2193–2196 (2001).
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IEEE Photonic. Tech. L. (2)

Z. Yu and A. Wang, “Fast white light interferometry demodulation algorithm for low-finesse Fabry–Pérot sensors,” IEEE Photonic. Tech. L. 27(8), 817–820 (2015).
[Crossref]

C. Sun, Y. Chen, G. Zhang, F. Wang, G. Liu, and J. Ding, “Multipoint remote methane measurement system based on spectrum absorption and reflective TDM,” IEEE Photonic. Tech. L. 28(22), 2487–2490 (2016).
[Crossref]

IEEE Sens. J. (2)

M. T. Humayun, R. Divan, L. Stan, D. Rosenmann, D. Gosztola, L. Gundel, P. A. Solomon, and I. Paprotny, “Ubiquitous low-cost functionalized multi-walled carbon nanotube sensors for distributed methane leak detection,” IEEE Sens. J. 16(24), 8692–8699 (2016).
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M. B. Frish, R. T. Wainner, M. C. Laderer, B. D. Green, and M. G. Allen, “Standoff and miniature chemical vapor detectors based on tunable diode laser absorption spectroscopy,” IEEE Sens. J. 10(3), 639–646 (2010).
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J. Micromech. Microeng. (1)

P. Sievilä, V. P. Rytkönen, O. Hahtela, N. Chekurov, J. Kauppinen, and I. Tittonen, “Fabrication and characterization of an ultrasensitive acousto-optical cantilever,” J. Micromech. Microeng. 17(5), 852–859 (2007).
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Nat. Commun. (1)

H. Wu, L. Dong, H. Zheng, Y. Yu, W. Ma, L. Zhang, W. Yin, L. Xiao, S. Jia, and F. K. Tittel, “Beat frequency quartz-enhanced photoacoustic spectroscopy for fast and calibration-free continuous trace-gas monitoring,” Nat. Commun. 8, 15331 (2017).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (6)

Optica (1)

Saf. Sci. (1)

H. Si, H. Ji, and X. Zeng, “Quantitative risk assessment model of hazardous chemicals leakage and application,” Saf. Sci. 50(7), 1452–1461 (2012).
[Crossref]

Sens. Actuators A Phys. (3)

Q. Gao, Y. Zhang, J. Yu, S. Wu, Z. Zhang, F. Zheng, X. Lou, and W. Guo, “Tunable multi-mode diode laser absorption spectroscopy for methane detection,” Sens. Actuators A Phys. 199, 106–110 (2013).
[Crossref]

K. Chen, Z. Gong, M. Guo, S. Yu, C. Qu, X. Zhou, and Q. Yu, “Fiber-optic Fabry-Perot interferometer based high sensitive cantilever microphone,” Sens. Actuators A Phys. 279, 107–112 (2018).
[Crossref]

K. Chen, Z. Gong, and Q. Yu, “Fiber-amplifier-enhanced resonant photoacoustic sensor for sub-ppb level acetylene detection,” Sens. Actuators A Phys. 274, 184–188 (2018).
[Crossref]

Sens. Actuators B Chem. (7)

Q. Wang, J. Wang, L. Li, and Q. Yu, “An all-optical photoacoustic spectrometer for trace gas detection,” Sens. Actuators B Chem. 153(1), 214–218 (2011).
[Crossref]

X. Mao, X. Zhou, Z. Gong, and Q. Yu, “An all-optical photoacoustic spectrometer for multi-gas analysis,” Sens. Actuators B Chem. 232, 251–256 (2016).
[Crossref]

Z. Gong, K. Chen, Y. Yang, X. Zhou, W. Peng, and Q. Yu, “High-sensitivity fiber-optic acoustic sensor for photoacoustic spectroscopy based traces gas detection,” Sens. Actuators B Chem. 247, 290–295 (2017).
[Crossref]

K. Chen, Q. Yu, Z. Gong, M. Guo, and C. Qu, “Ultra-high sensitive fiber-optic Fabry-Perot cantilever enhanced resonant photoacoustic spectroscopy,” Sens. Actuators B Chem. 268, 205–209 (2018).
[Crossref]

P. K. Sekhar, J. Kysar, E. L. Brosha, and C. R. Kreller, “Development and testing of an electrochemical methane sensor,” Sens. Actuators B Chem. 228, 162–167 (2016).
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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, 77–92 (2012).
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B. Li, C. Zheng, H. Liu, Q. He, W. Ye, Y. Zhang, J. Pan, and Y. Wang, “Development and measurement of a near-infrared CH4 detection system using 1.654 μm wavelength-modulated diode laser and open reflective gas sensing probe,” Sens. Actuators B Chem. 225, 188–198 (2016).
[Crossref]

Sensors (Basel) (2)

J. Wan, Y. Yu, Y. Wu, R. Feng, and N. Yu, “Hierarchical leak detection and localization method in natural gas pipeline monitoring sensor networks,” Sensors (Basel) 12(1), 189–214 (2012).
[Crossref] [PubMed]

Q. Tan, X. Pei, S. Zhu, D. Sun, J. Liu, C. Xue, T. Liang, W. Zhang, and J. Xiong, “Development of an optical gas leak sensor for detecting ethylene, dimethyl ether and methane,” Sensors (Basel) 13(4), 4157–4169 (2013).
[Crossref] [PubMed]

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Figures (11)

Fig. 1
Fig. 1 (a) Schematic structure of the fiber-optic PA sensing head. (b) Schematic diagram of the cantilever diaphragm.
Fig. 2
Fig. 2 (a) Calculated amplitude of the PA pressure as a function of frequency. (b) Calculated amplitude of the PA pressure as a function of the inner radius of a non-resonant PA cavity.
Fig. 3
Fig. 3 (a) Calculated amplitude-frequency response of the PA system with different PA cavity lengths. (b) The peak amplitude of the PA response as a function of the PA cavity length.
Fig. 4
Fig. 4 (a) Simulated gas diffusion concentration cloud map. (b) Simulated average gas concentration curve in the PA cavity with different PA cavity length.
Fig. 5
Fig. 5 Interference spectrum of the fiber-optic cantilever acoustic transducer.
Fig. 6
Fig. 6 Schematic structure of the test setup for remote monitoring of gas micro-leakage.
Fig. 7
Fig. 7 (a) Frequency response of the fiber-optic cantilever acoustic transducer. (b) Sound pressure response of the fiber-optic cantilever acoustic transducer at the frequency of 1132 Hz.
Fig. 8
Fig. 8 (a) Frequency response of the fiber-optic PA sensor. (b) Response to different laser excitation light power at the modulation frequency of 566 Hz.
Fig. 9
Fig. 9 (a) 2f-WMS spectrum with different concentrations of C2H2/N2 gas mixture. (b) Peak value as a function of concentration. Error bars represent one standard deviation with 1 s lock-in integration time.
Fig. 10
Fig. 10 Continuous measurement result of continuous flow of C2H2/N2 gas mixture.
Fig. 11
Fig. 11 (a) Output of the PA demodulator with a lock-in integration time of 1 s when the chamber was filled with a 300 ppb C2H2/N2 mixture and pure N2 gas. (b) Allan-Werle deviation for detection of the 300 ppb C2H2/N2 mixture as a function of the data averaging time.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P PA ( f )= α(γ1) P 0 l V τ 1 1+ ( 2πf τ 1 ) 2 2πf τ 2 1+ ( 2πf τ 2 ) 2 ,
τ 1 = r 2 5.78 D T ,
τ 2 = 4 γ V 3 A g υ ,
r m ( z )= r 0 1+ ( z π r 0 2 /λ ) 2 ,
R c ( f )= 1 m ( (2π f 0 ) 2 (2πf) 2 ) 2 + ( 2πfD/m ) 2 2πf τ 2 1+ ( 2πf τ 2 ) 2 ,
f 0 = 1 2π k m = 1 2π 2 3 E w c ( t c l c ) 3 + γ A c 2 p 2.5V 0.647 m c +Vρ ,
A( f )= P PA ( f ) A c R c ( f ).