Abstract

A method for measuring the temporal temperature and number density in a rapid compression machine (RCM) using quantum cascade laser absorption spectroscopy near 7.6 μm is developed and presented in this paper. The ratios of H2O absorption peaks at 1316.55cm1 and 1316.97cm1 are used for these measurements. In order to isolate the effects of chemical reactions, an inert mixture of argon with 2.87% water vapor is used for the present investigation. The end of compression pressures and temperatures in the RCM measurements are PC=10, 15, and 20 bar in the range of TC=1000 to 1200 K. The measured temperature history is compared with that calculated based on the adiabatic core assumption and is found to be within ±5K. The measured temporal number density of H2O to an accuracy of 1%, using the absolute absorption of the two rovibrational lines, show that the mixture is highly uniform in temperature. A six-pass, 5.08 cm Herriott cell is used to calibrate the line strengths in air and broadening in an Ar bath gas.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
    [CrossRef]
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    [CrossRef]
  10. M. Brandstetter and B. Lendl, “Tunable mid-infrared lasers in physical chemosensors towards the detection of physiologically relevant parameters in biofluids,” Sens. Actuators B, doi: 10.1016/j.snb.2011.06.081 (2011), available online 7 July 2011.
  11. C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
    [CrossRef]
  12. V. L. Kasyutich and P. A. Martin, “A CO2 sensor based upon a continuous-wave thermoelectrically-cooled quantum cascade laser,” Sens. Actuators B 157, 635–640 (2011).
    [CrossRef]
  13. L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
    [CrossRef]
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    [CrossRef]
  15. A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
    [CrossRef]
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    [CrossRef]
  17. L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
    [CrossRef]
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    [CrossRef]
  19. X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
    [CrossRef]
  20. D. Herriott, H. Kogelnik, and R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3, 523–526 (1964).
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  21. C. G. Tarsitano and C. R. Webster, “Multilaser Herriott cell for planetary tunable laser spectrometers,” Appl. Opt. 46, 6923–6935(2007).
    [CrossRef]
  22. A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
    [CrossRef]
  23. X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
    [CrossRef]
  24. C. N. Banwell, Fundamentals of Molecular Spectroscopy (McGraw-Hill, 1983).
  25. H. W. Coleman and W. G. Steele, Experimentation and Uncertainty Analysis for Engineers (Wiley, 1989).

2012 (1)

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

2011 (2)

X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
[CrossRef]

V. L. Kasyutich and P. A. Martin, “A CO2 sensor based upon a continuous-wave thermoelectrically-cooled quantum cascade laser,” Sens. Actuators B 157, 635–640 (2011).
[CrossRef]

2010 (2)

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

J. Vanderover and M. A. Oehlschlaeger, “A mid-infrared scanned-wavelength laser absorption sensor for carbon monoxide and temperature measurements from 900 to 4000 K,” Appl. Phys. B 99, 353–362 (2010).
[CrossRef]

2009 (4)

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

2008 (2)

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

2007 (2)

G. Mittal and C. J. Sung, “A rapid compression machine for chemical kinetic studies at elevated pressure and temperatures,” Combust. Sci. Technol. 179, 497–530 (2007).
[CrossRef]

C. G. Tarsitano and C. R. Webster, “Multilaser Herriott cell for planetary tunable laser spectrometers,” Appl. Opt. 46, 6923–6935(2007).
[CrossRef]

2006 (3)

G. Mittal and C. J. Sung, “Aerodynamics inside a rapid compression machine,” Combust. Flame 145, 160–180 (2006).
[CrossRef]

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

B. W. M. Moeskops, S. M. Cristescu, and F. J. M. Harren, “Sub-part-per-billion monitoring of nitric oxide by use of wavelength modulation spectroscopy in combination with a thermoelectrically cooled, continuous-wave quantum cascade laser,” Opt. Lett. 31, 823–825 (2006).
[CrossRef]

2005 (1)

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

2001 (1)

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

1995 (1)

P. Desgroux, L. Gasnot, and L. R. Sochet, “Instantaneous temperature measurement in a rapid-compression machine using laser Rayleigh scattering,” Appl. Phys. B 61, 69–72 (1995).
[CrossRef]

1964 (1)

An, Y.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Arnone, D.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Banwell, C. N.

C. N. Banwell, Fundamentals of Molecular Spectroscopy (McGraw-Hill, 1983).

Barber, R. J.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Bellenoue, M.

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

Bour, D.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Brandstetter, M.

M. Brandstetter and B. Lendl, “Tunable mid-infrared lasers in physical chemosensors towards the detection of physiologically relevant parameters in biofluids,” Sens. Actuators B, doi: 10.1016/j.snb.2011.06.081 (2011), available online 7 July 2011.

Cao, F.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Capasso, F.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Chao, X.

X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
[CrossRef]

Clarkson, J.

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

Coleman, H. W.

H. W. Coleman and W. G. Steele, Experimentation and Uncertainty Analysis for Engineers (Wiley, 1989).

Cong, M.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Corzine, S.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Cristescu, S. M.

B. W. M. Moeskops, S. M. Cristescu, and F. J. M. Harren, “Sub-part-per-billion monitoring of nitric oxide by use of wavelength modulation spectroscopy in combination with a thermoelectrically cooled, continuous-wave quantum cascade laser,” Opt. Lett. 31, 823–825 (2006).
[CrossRef]

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

Curl, R. F.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Das, A. K.

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

Day, T.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Desgroux, P.

P. Desgroux, L. Gasnot, and L. R. Sochet, “Instantaneous temperature measurement in a rapid-compression machine using laser Rayleigh scattering,” Appl. Phys. B 61, 69–72 (1995).
[CrossRef]

Diehl, L.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Dothe, H.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Elia, A.

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Faist, J.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Franco, C. D.

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Gamache, R. R.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Gasnot, L.

P. Desgroux, L. Gasnot, and L. R. Sochet, “Instantaneous temperature measurement in a rapid-compression machine using laser Rayleigh scattering,” Appl. Phys. B 61, 69–72 (1995).
[CrossRef]

Giovannini, M.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Glenn, D. E.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Goldman, A.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Gordon, I. E.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Griffiths, J. F.

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

Guo, S.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Hanson, R. K.

X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
[CrossRef]

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

Harren, F. J. M.

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

B. W. M. Moeskops, S. M. Cristescu, and F. J. M. Harren, “Sub-part-per-billion monitoring of nitric oxide by use of wavelength modulation spectroscopy in combination with a thermoelectrically cooled, continuous-wave quantum cascade laser,” Opt. Lett. 31, 823–825 (2006).
[CrossRef]

Herriott, D.

Hofler, G.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Jeffries, J. B.

X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
[CrossRef]

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

Kasyutich, V. L.

V. L. Kasyutich and P. A. Martin, “A CO2 sensor based upon a continuous-wave thermoelectrically-cooled quantum cascade laser,” Sens. Actuators B 157, 635–640 (2011).
[CrossRef]

Kee, R. J.

R. J. Kee, F. M. Rupley, and J. A. Miller, CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics. Report No. SAND 89-8009 (Sandia National Laboratories, 1989).

A. E. Lutz, R. J. Kee, and J. A. Miller, SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. Report No. SAND 87-8248 (Sandia National Laboratories, 1998).

Kim, S.-S.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Kogelnik, H.

Kompfner, R.

Lendl, B.

M. Brandstetter and B. Lendl, “Tunable mid-infrared lasers in physical chemosensors towards the detection of physiologically relevant parameters in biofluids,” Sens. Actuators B, doi: 10.1016/j.snb.2011.06.081 (2011), available online 7 July 2011.

Lewicki, R.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Li, L.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Liu, F.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Liu, X.

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

Lugarà, P. M.

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Lutz, A. E.

A. E. Lutz, R. J. Kee, and J. A. Miller, SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. Report No. SAND 87-8248 (Sandia National Laboratories, 1998).

Luzinova, Y.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Macnamara, J. P.

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

Martin, P. A.

V. L. Kasyutich and P. A. Martin, “A CO2 sensor based upon a continuous-wave thermoelectrically-cooled quantum cascade laser,” Sens. Actuators B 157, 635–640 (2011).
[CrossRef]

Maulini, R.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

McGovern, R. M.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

McManus, J. B.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Miller, J. A.

R. J. Kee, F. M. Rupley, and J. A. Miller, CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics. Report No. SAND 89-8009 (Sandia National Laboratories, 1989).

A. E. Lutz, R. J. Kee, and J. A. Miller, SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. Report No. SAND 87-8248 (Sandia National Laboratories, 1998).

Mittal, G.

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

G. Mittal and C. J. Sung, “A rapid compression machine for chemical kinetic studies at elevated pressure and temperatures,” Combust. Sci. Technol. 179, 497–530 (2007).
[CrossRef]

G. Mittal and C. J. Sung, “Aerodynamics inside a rapid compression machine,” Combust. Flame 145, 160–180 (2006).
[CrossRef]

Mizaikoff, B.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Moeskops, B. W. M.

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

B. W. M. Moeskops, S. M. Cristescu, and F. J. M. Harren, “Sub-part-per-billion monitoring of nitric oxide by use of wavelength modulation spectroscopy in combination with a thermoelectrically cooled, continuous-wave quantum cascade laser,” Opt. Lett. 31, 823–825 (2006).
[CrossRef]

Mura, A.

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

Naus, H.

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

Nelson, D. D.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Oehlschlaeger, M. A.

J. Vanderover and M. A. Oehlschlaeger, “A mid-infrared scanned-wavelength laser absorption sensor for carbon monoxide and temperature measurements from 900 to 4000 K,” Appl. Phys. B 99, 353–362 (2010).
[CrossRef]

Perevalov, V. I.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Rothman, L. S.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Rupley, F. M.

R. J. Kee, F. M. Rupley, and J. A. Miller, CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics. Report No. SAND 89-8009 (Sandia National Laboratories, 1989).

Scamarcio, G.

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Shorter, J. H.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Sochet, L. R.

P. Desgroux, L. Gasnot, and L. R. Sochet, “Instantaneous temperature measurement in a rapid-compression machine using laser Rayleigh scattering,” Appl. Phys. B 61, 69–72 (1995).
[CrossRef]

Song, Z.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Sotton, J.

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

Spagnolo, V.

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Steele, W. G.

H. W. Coleman and W. G. Steele, Experimentation and Uncertainty Analysis for Engineers (Wiley, 1989).

Strozzi, C.

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

Sung, C. J.

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

G. Mittal and C. J. Sung, “A rapid compression machine for chemical kinetic studies at elevated pressure and temperatures,” Combust. Sci. Technol. 179, 497–530 (2007).
[CrossRef]

G. Mittal and C. J. Sung, “Aerodynamics inside a rapid compression machine,” Combust. Flame 145, 160–180 (2006).
[CrossRef]

Takeuchi, E.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Tarsitano, C. G.

Tashkun, S. A.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Tennyson, J.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Tittel, F. K.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Troccoli, M.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Vanderover, J.

J. Vanderover and M. A. Oehlschlaeger, “A mid-infrared scanned-wavelength laser absorption sensor for carbon monoxide and temperature measurements from 900 to 4000 K,” Appl. Phys. B 99, 353–362 (2010).
[CrossRef]

Wang, L.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Wang, Y.

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Webster, C. R.

Weida, M.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Whitaker, B. J.

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

Wysocki, G.

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Young, C.

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

Zahniser, M. S.

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Zhang, Y.

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

Zhou, X.

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (5)

J. Vanderover and M. A. Oehlschlaeger, “A mid-infrared scanned-wavelength laser absorption sensor for carbon monoxide and temperature measurements from 900 to 4000 K,” Appl. Phys. B 99, 353–362 (2010).
[CrossRef]

P. Desgroux, L. Gasnot, and L. R. Sochet, “Instantaneous temperature measurement in a rapid-compression machine using laser Rayleigh scattering,” Appl. Phys. B 61, 69–72 (1995).
[CrossRef]

G. Wysocki, R. Lewicki, R. F. Curl, F. K. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

B. W. M. Moeskops, H. Naus, S. M. Cristescu, and F. J. M. Harren, “Quantum cascade laser-based carbon monoxide detection on a second time scale from human breath,” Appl. Phys. B 82, 649–654 (2006).
[CrossRef]

J. B. McManus, J. H. Shorter, D. D. Nelson, M. S. Zahniser, D. E. Glenn, and R. M. McGovern, “Pulsed quantum cascade laser instrument with compact design for rapid, high sensitivity measurements of trace gases in air,” Appl. Phys. B 92, 387–392 (2008).
[CrossRef]

Combust. Flame (2)

J. Clarkson, J. F. Griffiths, J. P. Macnamara, and B. J. Whitaker, “Temperature fields during the development of combustion in a rapid compression machine,” Combust. Flame 125, 1162–1175 (2001).
[CrossRef]

G. Mittal and C. J. Sung, “Aerodynamics inside a rapid compression machine,” Combust. Flame 145, 160–180 (2006).
[CrossRef]

Combust. Sci. Technol. (1)

G. Mittal and C. J. Sung, “A rapid compression machine for chemical kinetic studies at elevated pressure and temperatures,” Combust. Sci. Technol. 179, 497–530 (2007).
[CrossRef]

Int. J. Hydrogen Energy (1)

A. K. Das, C. J. Sung, Y. Zhang, and G. Mittal, “Ignition delay study of moist hydrogen/oxidizer mixtures using a rapid compression machine,” Int. J. Hydrogen Energy 37, 6901–6911 (2012).
[CrossRef]

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

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111, 2139–2150 (2010).
[CrossRef]

Meas. Sci. Technol. (2)

X. Zhou, X. Liu, J. B. Jeffries, and R. K. Hanson, “Selection of NIR H2O absorption transitions for in-cylinder measurement of temperature in IC engines,” Meas. Sci. Technol. 16, 2437–2445 (2005).
[CrossRef]

C. Strozzi, J. Sotton, A. Mura, and M. Bellenoue, “Characterization of a two dimensional temperature field within a rapid compression machine using a toluene planar laser induced fluorescence imaging technique,” Meas. Sci. Technol. 20, 125403 (2009).
[CrossRef]

Opt. Lett. (1)

Proc. Combust. Inst. (1)

X. Chao, J. B. Jeffries, and R. K. Hanson, “In situ absorption sensor for NO in combustion gases with a 5.2 μm quantum-cascade laser,” Proc. Combust. Inst. 33, 725–733 (2011).
[CrossRef]

Sens. Actuators B (3)

C. Young, S.-S. Kim, Y. Luzinova, M. Weida, D. Arnone, E. Takeuchi, T. Day, and B. Mizaikoff, “External cavity widely tunable quantum cascade laser based hollow waveguide gas sensors for multianalyte detection,” Sens. Actuators B 140, 24–28 (2009).
[CrossRef]

V. L. Kasyutich and P. A. Martin, “A CO2 sensor based upon a continuous-wave thermoelectrically-cooled quantum cascade laser,” Sens. Actuators B 157, 635–640 (2011).
[CrossRef]

L. Li, F. Cao, Y. Wang, M. Cong, L. Li, Y. An, Z. Song, S. Guo, F. Liu, and L. Wang, “Design and characteristics of quantum cascade laser-based CO detection system,” Sens. Actuators B 142, 33–38 (2009).
[CrossRef]

Sensors (1)

A. Elia, C. D. Franco, V. Spagnolo, P. M. Lugarà, and G. Scamarcio, “Quantum cascade laser-based photoacoustic sensor for trace detection of formaldehyde gas,” Sensors 9, 2697–2705 (2009).
[CrossRef]

Other (5)

A. E. Lutz, R. J. Kee, and J. A. Miller, SENKIN: A FORTRAN program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis. Report No. SAND 87-8248 (Sandia National Laboratories, 1998).

R. J. Kee, F. M. Rupley, and J. A. Miller, CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics. Report No. SAND 89-8009 (Sandia National Laboratories, 1989).

C. N. Banwell, Fundamentals of Molecular Spectroscopy (McGraw-Hill, 1983).

H. W. Coleman and W. G. Steele, Experimentation and Uncertainty Analysis for Engineers (Wiley, 1989).

M. Brandstetter and B. Lendl, “Tunable mid-infrared lasers in physical chemosensors towards the detection of physiologically relevant parameters in biofluids,” Sens. Actuators B, doi: 10.1016/j.snb.2011.06.081 (2011), available online 7 July 2011.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of the experimental setup (not to scale).

Fig. 2.
Fig. 2.

Transmitted signal through the etalon with sinusoidal voltage ramp (0–100 V) applied to piezo of the laser. The etalon peaks are marked by filled symbols.

Fig. 3.
Fig. 3.

Scan rate of laser with a sinusoidal voltage ramp (0–100 V) applied to piezo of the laser, showing the phase difference.

Fig. 4.
Fig. 4.

Simulated water absorption cross section in Ar at different temperature and pressure conditions used for line selection. The axis on the left corresponds to the profiles at 10 atm, while the axis on the right corresponds to the profile at 0.026 atm.

Fig. 5.
Fig. 5.

Variation of simulated line pair ratios of the three peaks indicated in Fig. 4 with temperature for different pressures.

Fig. 6.
Fig. 6.

Comparison of normalized measured water linewidth at 1336.66cm1 in air with calculations using HITRAN. The linewidths have been normalized with respect to linewidth at atmospheric pressure.

Fig. 7.
Fig. 7.

Least-squares Voigt fit (curve) to the normalized experimental absorbance (symbols) in air for lines A and B in Fig. 4 at two different pressures. Every 20th data point is shown in the figure for clarity.

Fig. 8.
Fig. 8.

Raw experimental data from a typical RCM experiment. Voltage ramp is divided by a factor of 500 for plotting purpose.

Fig. 9.
Fig. 9.

Comparison of experimentally determined temperatures with estimated temperatures using adiabatic core hypothesis for 10 bar EOC pressure.

Fig. 10.
Fig. 10.

Comparison of absorbance profiles obtained from experiments and HITRAN simulations for three representative conditions of a typical RCM experiment denoted in Fig. 9.

Fig. 11.
Fig. 11.

Comparison of experimentally determined temperatures with estimated temperatures using adiabatic core hypothesis for 15 bar EOC pressure.

Fig. 12.
Fig. 12.

Comparison of experimentally determined temperatures with estimated temperatures using adiabatic core hypothesis for 20 bar EOC pressure.

Fig. 13.
Fig. 13.

Comparison of absorbance profiles obtained from experiments and HITRAN simulations for two representative conditions of RCM experiments at 15 and 20 bar, denoted in Figs. 11 and 12, respectively.

Tables (2)

Tables Icon

Table 1. Measured H2O Collisional Line Broadening Parameters for Argon Bath Gas

Tables Icon

Table 2. Quantum Numbers for Five Transitions in Table 1

Equations (24)

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

TITCΓΓ1dTT=ln(PCPI),
IνI0ν=exp(α(ν,P,T)NL)=exp(iSi(T)gV(νiν)NL).
Sνi(T)=Sνi(T0)Q(T0)Q(T)exp[hcEikB(1T1T0)][1exp(hcνikBT)][1exp(hcνikBT0)].
ln(Iν1/I0ν1)ln(Iν2/I0ν2)=Sν1(T)gV(ν1)Sν2(T)gV(ν2).
gV(νiν)=1αDln2πK(x,y),
K(x,y)=yπet2y2+(xt)2dt,
y=αLαDln2,
x=ννi100cαDln2.
αD=νi100c22kBTln2m,
αL=Pjγ0jχj(T0T)nj,
HL1=ln(I1I10)=Sν(T)gV(0)NL1,
HL2=ln(I2I20)=Sν(T)gV(0)NL2,
L2=HL2HL1L1.
Sν(T)=IANL=IAkBTχPL.
Aν=ln(IνI0ν)=NLiSνi(T)gV(νiν).
Δvi=0,±1,±2,,ΔJ=0,±1,ΔKa=0,±1,±2,,ΔKc=0,±1,±2,.
Hmax=STcoreNact,coreL(1δ)+STBLNact,BLLδ=STcalcNcalcL.
Hmax=STcoreχactPkBTcoreL(1δ)+STBLχactPkBTBLLδ=STcalcχcalcPkBTcalcL.
χcalc=(TcalcSTcalc)[STcoreTcore(1δ)+STBLTBLδ]χact.
ΔTΔRdR/dT,
R=H1H2,
ΔR=RUR=RUSν12+USν22+UH12+UH22,
ΔS=(SIAΔIA)2+(SPΔP)2+(SχΔχ)2+(SLΔL)2+(STΔT)2,
US=ΔSS=UIA2+UP2+Uχ2+UL2+(S/STΔT)2.

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