Abstract

In this paper, a new method for recovering gas absorbance shape using wavelength modulation spectroscopy is proposed. We have mathematically proven that the gas absorbance shape can be directly recovered using the data of X and Y components of odd harmonics, regardless of the value of the modulation depth. The transitions of NH3 near 1531 nm are selected to recover the absorbance shape using numerical simulation and experimental technique. The simulation and experiment results show that our proposed method can simply and accurately recover the gas absorbance shape.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
    [CrossRef]
  2. R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
    [CrossRef]
  3. H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio measurements in gas turbine combustors with a near-infrared diode laser sensor,” Proc. Combust. Inst. 33(1), 717–724 (2011).
    [CrossRef]
  4. N. Goldstein, S. Adler-Golden, J. Lee, and F. Bien, “Measurement of molecular concentrations and line parameters using line-locked second harmonic spectroscopy with an AlGaAs diode laser,” Appl. Opt. 31(18), 3409–3415 (1992).
    [CrossRef] [PubMed]
  5. A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
    [CrossRef]
  6. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
    [CrossRef]
  7. E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
    [CrossRef]
  8. G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009).
    [CrossRef] [PubMed]
  9. A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
    [CrossRef]
  10. K. Duffin, A. J. McGettrick, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: A calibration-free approach to the recovery of absolute gas absorption line-shapes,” J. Lightwave Technol. 25(10), 3114–3125 (2007).
    [CrossRef]
  11. W. Johnstone, A. J. McGettrick, K. Duffin, A. Cheung, and G. Stewart, “Tunable diode laser spectroscopy for industrial process applications: System characterization in conventional and new approaches,” IEEE Sens. J. 8(7), 1079–1088 (2008).
    [CrossRef]
  12. A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: A phasor decomposition method for calibrationfree measurements of gas concentration and pressure,” J. Lightwave Technol. 26(4), 432–440 (2008).
    [CrossRef]
  13. G. Stewart, W. Johnstone, J. R. P. Bain, K. Ruxton, and K. Duffin, “Recovery of absolute gas absorption line shapes using tunable diode laser spectroscopy with wavelength modulation—part 1: Theoretical analysis,” J. Lightwave Technol. 29(6), 811–821 (2011).
  14. J. R. P. Bain, W. Johnstone, K. Ruxton, G. Stewart, M. Lengden, and K. Duffin, “Recovery of absolute gas absorption line shapes using tuneable diode laser spectroscopy with wavelength modulation—Part 2: Experimental investigation,” J. Lightwave Technol. 29(7), 987–996 (2011).
    [CrossRef]
  15. P. Kluczynski and O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38(27), 5803–5815 (1999).
    [CrossRef] [PubMed]
  16. P. Zhimin, D. Yanjun, C. Lu, L. Xiaohang, and Z. Kangjie, “Calibration-free wavelength modulated TDLAS under high absorbance conditions,” Opt. Express 19(23), 23104–23110 (2011).
    [CrossRef] [PubMed]
  17. A. N. Dharamsi, “A theory of modulation spectroscopy with applications of higher harmonic detection,” J. Phys. D Appl. Phys. 29(3), 540–549 (1996).
    [CrossRef]
  18. J. Henningsen and H. Simonsen, “Quantitative wavelength-modulation spectroscopy without certified gas mixtures,” Appl. Phys. B 70(4), 627–633 (2000).
    [CrossRef]
  19. H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
    [CrossRef] [PubMed]
  20. H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
    [CrossRef]

2011 (4)

2010 (1)

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

2009 (3)

A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
[CrossRef]

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009).
[CrossRef] [PubMed]

2008 (3)

A. J. McGettrick, K. Duffin, W. Johnstone, G. Stewart, and D. G. Moodie, “Tunable diode laser spectroscopy with wavelength modulation: A phasor decomposition method for calibrationfree measurements of gas concentration and pressure,” J. Lightwave Technol. 26(4), 432–440 (2008).
[CrossRef]

W. Johnstone, A. J. McGettrick, K. Duffin, A. Cheung, and G. Stewart, “Tunable diode laser spectroscopy for industrial process applications: System characterization in conventional and new approaches,” IEEE Sens. J. 8(7), 1079–1088 (2008).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
[CrossRef]

2007 (1)

2006 (3)

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
[CrossRef]

2004 (1)

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
[CrossRef]

2000 (1)

J. Henningsen and H. Simonsen, “Quantitative wavelength-modulation spectroscopy without certified gas mixtures,” Appl. Phys. B 70(4), 627–633 (2000).
[CrossRef]

1999 (1)

1996 (1)

A. N. Dharamsi, “A theory of modulation spectroscopy with applications of higher harmonic detection,” J. Phys. D Appl. Phys. 29(3), 540–549 (1996).
[CrossRef]

1992 (1)

Adler-Golden, S.

Axner, O.

Bain, J. R. P.

Bien, F.

Boucher, T. J.

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

Cai, T. D.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Casa, G.

E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
[CrossRef]

Cetegen, B. M.

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

Chen, W. D.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Cheung, A.

W. Johnstone, A. J. McGettrick, K. Duffin, A. Cheung, and G. Stewart, “Tunable diode laser spectroscopy for industrial process applications: System characterization in conventional and new approaches,” IEEE Sens. J. 8(7), 1079–1088 (2008).
[CrossRef]

Dharamsi, A. N.

A. N. Dharamsi, “A theory of modulation spectroscopy with applications of higher harmonic detection,” J. Phys. D Appl. Phys. 29(3), 540–549 (1996).
[CrossRef]

Duffin, K.

Farooq, A.

A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
[CrossRef]

Gao, X. M.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Gianfrani, L.

E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
[CrossRef]

Goldstein, N.

Hanson, R. K.

G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009).
[CrossRef] [PubMed]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
[CrossRef]

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
[CrossRef]

Henningsen, J.

J. Henningsen and H. Simonsen, “Quantitative wavelength-modulation spectroscopy without certified gas mixtures,” Appl. Phys. B 70(4), 627–633 (2000).
[CrossRef]

Hinckley, K. M.

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

Jeffries, J. B.

G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009).
[CrossRef] [PubMed]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
[CrossRef]

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
[CrossRef]

Jia, H.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Johnstone, W.

Kangjie, Z.

Kluczynski, P.

Lee, J.

Lengden, M.

Li, H.

H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio measurements in gas turbine combustors with a near-infrared diode laser sensor,” Proc. Combust. Inst. 33(1), 717–724 (2011).
[CrossRef]

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

Liu, J. T. C.

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
[CrossRef]

Liu, X.

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006).
[CrossRef] [PubMed]

Lu, C.

McGettrick, A. J.

McManus, K. R.

H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio measurements in gas turbine combustors with a near-infrared diode laser sensor,” Proc. Combust. Inst. 33(1), 717–724 (2011).
[CrossRef]

Moodie, D. G.

Renfro, M. W.

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

Rieker, G. B.

Ruxton, K.

Simonsen, H.

J. Henningsen and H. Simonsen, “Quantitative wavelength-modulation spectroscopy without certified gas mixtures,” Appl. Phys. B 70(4), 627–633 (2000).
[CrossRef]

Stewart, G.

Sur, R.

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

Tommasi, E. D.

E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
[CrossRef]

Wehe, S. D.

H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio measurements in gas turbine combustors with a near-infrared diode laser sensor,” Proc. Combust. Inst. 33(1), 717–724 (2011).
[CrossRef]

Woodmansee, M. A.

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

Xiaohang, L.

Yanjun, D.

Zhang, W. J.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Zhao, W. X.

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Zhimin, P.

Appl. Opt. (4)

Appl. Phys. B (6)

J. Henningsen and H. Simonsen, “Quantitative wavelength-modulation spectroscopy without certified gas mixtures,” Appl. Phys. B 70(4), 627–633 (2000).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7μm,” Appl. Phys. B 96(1), 161–173 (2009).
[CrossRef]

X. Liu, J. B. Jeffries, R. K. Hanson, K. M. Hinckley, and M. A. Woodmansee, “Development of a tunable diode laser sensor for measurements of gas turbine exhaust temperature,” Appl. Phys. B 82(3), 469–478 (2006).
[CrossRef]

A. Farooq, J. B. Jeffries, and R. K. Hanson, “CO2 concentration and temperature sensor for combustion gases using diode-laser absorption near 2.7μm,” Appl. Phys. B 90(3–4), 619–628 (2008).
[CrossRef]

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3–4), 503–511 (2004).
[CrossRef]

E. D. Tommasi, G. Casa, and L. Gianfrani, “High precision determinations of NH3 concentration by means of diode laser spectrometry at 2.005 μm,” Appl. Phys. B 85(2–3), 257–263 (2006).
[CrossRef]

IEEE Sens. J. (1)

W. Johnstone, A. J. McGettrick, K. Duffin, A. Cheung, and G. Stewart, “Tunable diode laser spectroscopy for industrial process applications: System characterization in conventional and new approaches,” IEEE Sens. J. 8(7), 1079–1088 (2008).
[CrossRef]

J. Electrochem. Soc. (1)

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010).
[CrossRef]

J. Lightwave Technol. (4)

J. Phys. D Appl. Phys. (1)

A. N. Dharamsi, “A theory of modulation spectroscopy with applications of higher harmonic detection,” J. Phys. D Appl. Phys. 29(3), 540–549 (1996).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

H. Jia, W. X. Zhao, T. D. Cai, W. D. Chen, W. J. Zhang, and X. M. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6–7), 347–357 (2009).
[CrossRef]

Opt. Express (1)

Proc. Combust. Inst. (1)

H. Li, S. D. Wehe, and K. R. McManus, “Real-time equivalence ratio measurements in gas turbine combustors with a near-infrared diode laser sensor,” Proc. Combust. Inst. 33(1), 717–724 (2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Gas absorbance shape of NH3 near 1531 nm recovered by Λk (k = 1, 2, 3, 4) at different modulation depths (P = 0.1atm, T = 296K, L = 25.5cm, X = 3.0%).

Fig. 2
Fig. 2

Gas absorbance shape of NH3 near 1531 nm recovered by Λk (k = 1,2,3,4) at different modulation depths (P = 1.0 atm, T = 296K, L = 25.5cm, X = 3.0%).

Fig. 3
Fig. 3

Experimental set-up of the recovery of absorbance shape of NH3 near 1531 nm.

Fig. 4
Fig. 4

(a) Experimental data of the X and Y components of the first, third and fifth harmonics; (b) absorbance shape recovered by Λk (k = 1, 2, 3) (P = 0.1atm, T = 296K, L = 25.5cm, X = 3.0%, m ≈1.95).

Fig. 5
Fig. 5

Absorbance shape recovered by Λ4 under different pressure conditions (T = 296 K, L = 25.5 cm, X = 3.0%, ψ1 = 45.5°).

Tables (1)

Tables Icon

Table 1 Spectroscopic Parameters for the Selected Transitions near 1531 nm (296K)

Equations (16)

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

{ ν= ν 1 +acos( ωt ), I 0 = I 1 +ΔIcos( ωt+ ψ 1 ),
τ( ν )= I t I 0 =exp[ α( ν ) ]= H 0 2 + k=1 H k cos( kωt ) ,
H k = 1 π π π τ( ν 1 +acosθ ) coskθdθ.
I t = C 00 + k=1 [ C k1 cos( kωt )+ C k2 sin( kωt ) ] ,
{ C 00 = 1 2 ( I 1 H 0 +ΔI H 1 cos ψ 1 ) , C k1 = I 1 H k + ΔI 2 ( H k1 + H k+1 )cos ψ 1 , C k2 = ΔI 2 ( H k1 + H k+1 )sin ψ 1 .
{ R Xk =Vcos( kωt+β ), R Yk =Vsin( kωt+β ),
{ X k = GV 2 [ C k1 cos( β ) C k2 sin( β ) ], Y k = GV 2 [ C k1 sin( β )+ C k2 cos( β ) ].
{ X 1back = GVΔI 2 cos( β ψ 1 ) Y 1back = GVΔI 2 sin( β ψ 1 ) S 1back = ( X 1back ) 2 + ( Y 1back ) 2 = GVΔI 2
fu n 2k1 = X 2k1 sinβ Y 2k1 cosβ S 1back = sin ψ 1 2 [ H 2k2 H 2k ], k=1,2....
τ( ν 1 +acosθ )=τ( ν 1 )+ k=1 τ ( k ) ( ν 1 ) ( acosθ ) k k! .
{ H 0 2 =τ( ν 1 )+ τ ( 2 ) ( ν 1 ) a 2 4 + τ ( 4 ) ( ν 1 ) a 4 64 + τ ( 6 ) ( ν 1 ) a 6 2304 +... H 2 = τ ( 2 ) ( ν 1 ) a 2 4 + τ ( 4 ) ( ν 1 ) a 4 48 + τ ( 6 ) ( ν 1 ) a 6 1536 +... H 4 = τ ( 4 ) ( ν 1 ) a 4 192 + τ ( 6 ) ( ν 1 ) a 6 3840 +... H 2k = n=k 1 ( n+k )! 1 ( nk )! 1 2 2n1 τ ( 2n ) ( ν 1 ) a 2n .
Fu n k =fu n 1 fu n 3 +fu n 5 +... ( 1 ) k1 fu n 2k1 = n=1 k ( 1 ) n1 fu n 2n1 =sin ψ 1 [ H 0 2 H 2 + H 4 +... ( 1 ) k H 2k + ( 1 ) k1 H 2k 2 ] =sin ψ 1 [ τ( ν 1 )+ ( 1 ) k1 n=k a n+k ( n+k )! a nk ( nk )! k n 2 2n τ ( 2n ) ( ν 1 ) ] =sin ψ 1 Λ k , k=1,2....
{ Λ 1 =τ( ν 1 )+ τ ( 2 ) ( ν 1 ) a 2 8 + τ ( 4 ) ( ν 1 ) a 4 192 + τ ( 6 ) ( ν 1 ) a 6 9216 +... Λ 2 =τ( ν 1 ) τ ( 4 ) ( ν 1 ) a 4 384 τ ( 6 ) ( ν 1 ) a 6 11520 +... Λ 3 =τ( ν 1 )+ τ ( 6 ) ( ν 1 ) a 6 46080 +... Λ k =τ( ν 1 )+ ( 1 ) k1 n=k a n+k ( n+k )! a nk ( nk )! k n 2 2n τ ( 2n ) ( ν 1 ).
Λ k | k =τ( ν 1 )=exp[ α( ν 1 ) ].
exp[ α( ν 1 ) ]=τ( ν 1 )= Λ k | k = Fu n k sin ψ 1 | k .
α( ν 1 )= ln( Fu n k sin ψ 1 ) | k ,

Metrics