Abstract

We present a theoretical description of the ultrasensitive cavity-enhanced spectroscopic technique called noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE OHMS) for the case of transitions described by a Voigt line shape. The two levels of modulation used in NICE OHMS are treated with the standard theory for frequency modulation spectroscopy and a Fourier description of wavelength modulation spectroscopy. We compare predicted line shapes with experimental results for pressure-broadened transitions in molecular oxygen and show that our description can be used to determine the spectroscopic parameters. A key aspect of this research is the application of NICE OHMS to broad absorption features across a range of wavelengths, and etalon effects are shown to limit the detection sensitivity.

© 2004 Optical Society of America

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  28. An exhaustive effort to eliminate etalon effects for a single transition was not attempted because, in this study, we want to emphasize the practical limitations faced by spectroscopists who want to apply the technique to multiple transitions.
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2003

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

N. J. van Leeuwen, J. C. Diettrich, and A. C. Wilson, “Periodically locked continuous-wave cavity ringdown spectroscopy,” Appl. Opt. 42, 3670–3677 (2003).
[CrossRef] [PubMed]

2002

R. W. Fox and L. Hollberg, “Role of spurious reflections in ring-down spectroscopy,” Opt. Lett. 27, 1833–1835 (2002).
[CrossRef]

G. Gagliardi and L. Gianfrani, “Trace-gas analysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers Eng. 37, 509–520 (2002).
[CrossRef]

A. S. C. Cheung, T. M. Ma, and H. B. Chen, “High-resolution cavity enhanced absorption spectroscopy using an optical cavity with ultra-high reflectivity mirrors,” Chem. Phys. Lett. 353, 275–280 (2002).
[CrossRef]

2001

C. Petridis, I. D. Lindsay, D. J. M. Stothard, and M. Ebrahimzadeh, “Mode-hop-free tuning over 80 GHz of an extended cavity diode laser without antireflection coating,” Rev. Sci. Instrum. 72, 3811–3815 (2001).
[CrossRef]

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, “Wavelength modulation absorption spectrometry—an extensive scrutiny of the generation of signals,” Spectrochim. Acta, Part B 56, 1277–1354 (2001).
[CrossRef]

2000

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65-μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef] [PubMed]

1999

1998

1996

1994

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

1987

1986

1985

1984

R. G. DeVoe and R. G. Brewer, “Laser-frequency division and stabilization,” Appl. Phys. A: Solids Surf. 30, 2827–2829 (1984).

1983

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

1980

1971

Auwera, J. V.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Axner, O.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, “Wavelength modulation absorption spectrometry—an extensive scrutiny of the generation of signals,” Spectrochim. Acta, Part B 56, 1277–1354 (2001).
[CrossRef]

Barbe, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Benner, D. C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15–17 (1980).
[CrossRef] [PubMed]

Brewer, R. G.

R. G. DeVoe and R. G. Brewer, “Laser-frequency division and stabilization,” Appl. Phys. A: Solids Surf. 30, 2827–2829 (1984).

Brown, L. R.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Camy-Peyret, C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Canagaratna, M. R.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Carleer, M. R.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Carlisle, C. B.

Chance, K.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Chen, H. B.

A. S. C. Cheung, T. M. Ma, and H. B. Chen, “High-resolution cavity enhanced absorption spectroscopy using an optical cavity with ultra-high reflectivity mirrors,” Chem. Phys. Lett. 353, 275–280 (2002).
[CrossRef]

Cheung, A. S. C.

A. S. C. Cheung, T. M. Ma, and H. B. Chen, “High-resolution cavity enhanced absorption spectroscopy using an optical cavity with ultra-high reflectivity mirrors,” Chem. Phys. Lett. 353, 275–280 (2002).
[CrossRef]

Clerbaux, C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Cooper, D. E.

Coy, S. L.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Dana, V.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

de La- bachelerie, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Devi, V. M.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

DeVoe, R. G.

R. G. DeVoe and R. G. Brewer, “Laser-frequency division and stabilization,” Appl. Phys. A: Solids Surf. 30, 2827–2829 (1984).

Diettrich, J. C.

Drever, R.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Dube, P.

Ebrahimzadeh, M.

C. Petridis, I. D. Lindsay, D. J. M. Stothard, and M. Ebrahimzadeh, “Mode-hop-free tuning over 80 GHz of an extended cavity diode laser without antireflection coating,” Rev. Sci. Instrum. 72, 3811–3815 (2001).
[CrossRef]

Fayt, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Fei, R.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Field, R. W.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Flaud, J. M.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Ford, G. M.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Fox, R. W.

Gagliardi, G.

G. Gagliardi and L. Gianfrani, “Trace-gas analysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers Eng. 37, 509–520 (2002).
[CrossRef]

Gallagher, T. F.

Gamache, R. R.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Gianfrani, L.

G. Gagliardi and L. Gianfrani, “Trace-gas analysis using diode lasers in the near-IR and long-path techniques,” Opt. Lasers Eng. 37, 509–520 (2002).
[CrossRef]

L. Gianfrani, R. W. Fox, and L. Hollberg, “Cavity-enhanced absorption spectroscopy of molecular oxygen,” J. Opt. Soc. Am. B 16, 2247–2254 (1999).
[CrossRef]

Goldman, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Gustafsson, J.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, “Wavelength modulation absorption spectrometry—an extensive scrutiny of the generation of signals,” Spectrochim. Acta, Part B 56, 1277–1354 (2001).
[CrossRef]

Hall, G. E.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Hall, J. L.

Hollberg, L.

Hough, J.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Ishibashi, C.

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65-μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef] [PubMed]

C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66 μm tunable diode laser,” Jpn. J. Appl. Phys., Part 1 38, 920–922 (1999).
[CrossRef]

Jacquemart, D.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Janik, G.

Jucks, K. W.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Kachanov, A. A.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Katsuda, T.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Kluczynski, P.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, “Wavelength modulation absorption spectrometry—an extensive scrutiny of the generation of signals,” Spectrochim. Acta, Part B 56, 1277–1354 (2001).
[CrossRef]

Kowalski, F. V.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Lafferty, W. J.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

Lindberg, A. M.

P. Kluczynski, J. Gustafsson, A. M. Lindberg, and O. Axner, “Wavelength modulation absorption spectrometry—an extensive scrutiny of the generation of signals,” Spectrochim. Acta, Part B 56, 1277–1354 (2001).
[CrossRef]

Lindsay, I. D.

C. Petridis, I. D. Lindsay, D. J. M. Stothard, and M. Ebrahimzadeh, “Mode-hop-free tuning over 80 GHz of an extended cavity diode laser without antireflection coating,” Rev. Sci. Instrum. 72, 3811–3815 (2001).
[CrossRef]

Ma, L. S.

Ma, T. M.

A. S. C. Cheung, T. M. Ma, and H. B. Chen, “High-resolution cavity enhanced absorption spectroscopy using an optical cavity with ultra-high reflectivity mirrors,” Chem. Phys. Lett. 353, 275–280 (2002).
[CrossRef]

Mandin, J. Y.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Massie, S. T.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Munley, A. J.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Nakagawa, K.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Nemtchinov, V.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Newnham, D. A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

North, S. W.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Ohtsu, M.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

Perrin, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Petridis, C.

C. Petridis, I. D. Lindsay, D. J. M. Stothard, and M. Ebrahimzadeh, “Mode-hop-free tuning over 80 GHz of an extended cavity diode laser without antireflection coating,” Rev. Sci. Instrum. 72, 3811–3815 (2001).
[CrossRef]

Rinsland, C. P.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Rothman, L. S.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Sasada, H.

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65-μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
[CrossRef] [PubMed]

C. Ishibashi and H. Sasada, “Highly sensitive cavity-enhanced sub-Doppler spectroscopy of a molecular overtone band with a 1.66 μm tunable diode laser,” Jpn. J. Appl. Phys., Part 1 38, 920–922 (1999).
[CrossRef]

Schroeder, J.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Shelkovnikov, A. S.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de La- bachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Smith, K. M.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Smith, M. A. H.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Smith, R. L.

Steinfeld, J. I.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Stothard, D. J. M.

C. Petridis, I. D. Lindsay, D. J. M. Stothard, and M. Ebrahimzadeh, “Mode-hop-free tuning over 80 GHz of an extended cavity diode laser without antireflection coating,” Rev. Sci. Instrum. 72, 3811–3815 (2001).
[CrossRef]

Tang, K.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Toth, R. A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

van Leeuwen, N. J.

Varanasi, P.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Ward, H.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Warren, R. E.

Wilson, A. C.

Witonsky, S. K.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Wong, N. C.

Yang, S.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

Ye, J.

Yoshino, K.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J. Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. V. Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. Radiat. Transf. 82, 5–44 (2003).
[CrossRef]

Zheng, X. S.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

Appl. Opt.

Appl. Phys. A: Solids Surf.

R. G. DeVoe and R. G. Brewer, “Laser-frequency division and stabilization,” Appl. Phys. A: Solids Surf. 30, 2827–2829 (1984).

Appl. Phys. B: Photophys. Laser Chem.

R. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B: Photophys. Laser Chem. 32, 145–152 (1983).
[CrossRef]

Chem. Phys. Lett.

A. S. C. Cheung, T. M. Ma, and H. B. Chen, “High-resolution cavity enhanced absorption spectroscopy using an optical cavity with ultra-high reflectivity mirrors,” Chem. Phys. Lett. 353, 275–280 (2002).
[CrossRef]

J. Chem. Phys.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104, 2129–2135 (1996).
[CrossRef]

J. Mol. Spectrosc.

S. Yang, M. R. Canagaratna, S. K. Witonsky, S. L. Coy, J. I. Steinfeld, R. W. Field, and A. A. Kachanov, “Intensity measurements and collision-broadening coefficients for the oxygen A band measured by intracavity laser absorption spectroscopy,” J. Mol. Spectrosc. 201, 188–197 (2000).
[CrossRef] [PubMed]

C. Ishibashi and H. Sasada, “Near-infrared laser spectrometer with sub-Doppler resolution, high sensitivity, and wide tunability: a case study in the 1.65-μm region of CH3I spectrum,” J. Mol. Spectrosc. 200, 147–149 (2000).
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Other

The peak-normalized line shape can be converted to the standard-area normalized line shape by multiplication of the factor Re [w(iΔLG )](4 ln 2/pi)1/2 /ΔνLG.

w(z)=exp (−z2)[1−erf (−iz)], where erf is the ordinary error function.

R. W. Fox, National Institute for Standards and Technology, Boulder, Colorado (personal communication, 2002).

R. W. Fox, C. Oates, and L. Hollberg, “Stabilizing diode lasers to high finesse cavities,” in Cavity-Enhanced Spectroscopies (Academic, Amsterdam, 2002).

An exhaustive effort to eliminate etalon effects for a single transition was not attempted because, in this study, we want to emphasize the practical limitations faced by spectroscopists who want to apply the technique to multiple transitions.

N. J. van Leeuwen, H. G. Kjaergaard, D. L. Howard, and A. C. Wilson, “Measurement of ultraweak transitions in the visible region of molecular oxygen,” J. Mol. Spectrosc. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Setup for our NICE OHMS apparatus. OI, optical isolator; PBS, polarizing beam splitter; PD1, photodiode for laser and fFSR locking; PD2, photodiode for NICE OHMS detection; DBM, double-balanced mixer.

Fig. 2
Fig. 2

NICE OHMS signal for the P7P7 transition of the hot band at 12,947.31 cm-1 (dots) with the fit to the expected line shape (solid curve) and the corresponding residual to the fit (bottom graph).

Fig. 3
Fig. 3

NICE OHMS signal for the weak P35Q34 transition from the A band of  16O 18O (dots) with a curve fit to the expected line shape (solid curve) and the corresponding residual to the fit (bottom graph).

Fig. 4
Fig. 4

NICE OHMS signal (dots) for three overlapping lines, of which one is a factor of 8 smaller than the other two. Two theoretical fits to the data are shown, one containing two transitions (dotted curve) and the second containing three transitions (solid curve).

Tables (2)

Tables Icon

Table 1 Line Parameters at 397.4 mbar and 22 °C for the P7P7 Transitiona

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Table 2 Parameters from the Theoretical Fit of NICE OHMS Data Containing Three Overlapping Transitions

Equations (12)

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E(t)=E0 exp(i2πνt){J0(β)+J1(β)[exp(i2πνmt)-exp(-i2πνmt)]},
I(νm)=2I0J0(β)J1(β)[(δ-1-δ1)cos (2πνmt)+(ϕ1+ϕ-1-2ϕ0)sin (2πνmt)],
SFM=I0ηFMJ0(β)J1(β)(α-1L-α1L),
SCEFM=2FπI0ηFMJ0(β)J1(β)(α-1L-α1L).
ν(t)=νc+νa cos(2πft),
S(x, νc, t)=n=0Sneven(x, νc)cos(2πnft)+n=1Snodd(x, νc)sin(2πnft),
SWM=ηLISneven(x, νc),
SCEFM(x, ν, t)=2FπI0ηFMJ0(β)J1(β)αpL[χ¯(x, ν-νm, t)-χ¯(x, ν+νm, t)],
SNICEOHMS(x, ν)=2FπI0ηFMηLIJ0(β)J1(β)αp×L[χ¯1even(x, ν-νm)×-χ¯1even(x, ν+νm)],
χ¯V(x, ν)=Re[w(ν¯d+iΔLG)]Re[w(iΔLG)],
χ¯V,1even(x, νc)=2τ Re[w(iΔLG)] 0τ Re[w(ν¯d+ν¯a cos(2πft)+iΔLG)]cos(2πft)dt,
(αL)min=π2F 2eBηP01/2 2J0(β)J1(β),

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