Abstract

We present a detailed study of the properties of off-axis-aligned high-finesse optical cavities under output time integration for spectroscopic applications. The dependence of the characteristics of the sample absorption spectra on a number of experimental parameters is investigated by developing a general model, where a Voigt absorption line shape is included into the cavity-transfer function. In this way, we address the issue of the measurement of trace amounts of gases in ambient air and single out the optimum conditions to give accurate estimates of the gas mixing ratio by the extraction of the integrated absorbance of the spectra. Quantitative results by the model are displayed for the detection of natural-abundance methane at 3μm as a function of the air-sample total pressure. Finally, we compare the model predictions with the results of a previous experiment, evidencing their consistency.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (2)

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, "Combining a difference-frequency source to an off-axis high-finesse cavity for trace-gas monitoring around 3 μm," Opt. Express 14, 1304-1313 (2006).
[CrossRef] [PubMed]

2005 (2)

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

2004 (4)

2002 (5)

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

2001 (3)

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

J. B. Paul, L. Lapson, and J. Anderson, "Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment," Appl. Opt. 40, 4904-4910 (2001).
[CrossRef]

2000 (2)

A. Asfaw, "A fast method of modeling spectral lines," J. Quant. Spectrosc. Radiat. Transf. 70, 129-137 (2000).
[CrossRef]

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

1998 (2)

J. Ye, L.-S. Ma, and J. L. Hall, "Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy," J. Opt. Soc. Am. B 15, 6-15 (1998).
[CrossRef]

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

1997 (1)

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

1994 (2)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

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

1964 (1)

Allen, M. G.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

Anderson, J.

Apituley, A.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

Asfaw, A.

A. Asfaw, "A fast method of modeling spectral lines," J. Quant. Spectrosc. Radiat. Transf. 70, 129-137 (2000).
[CrossRef]

Baer, D. S.

S. Williams, M. Gupta, T. Owano, D. S. Baer, A. O'Keefe, D. R. Yarkony, and S. Matsika, "Quantitative detection of O2 by cavity-enhanced spectroscopy," Opt. Lett. 29, 1066-1068 (2004).
[CrossRef] [PubMed]

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Baillargeon, J. N.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

Bakhirkin, Y. A.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, "Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection," Appl. Opt. 43, 2257-2266 (2004).
[CrossRef] [PubMed]

Bakowski, B.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Berden, G.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

Canosa-Mas, C. E.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

Capasso, F.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Casa, G.

Castrillo, A.

Chapman, W. B.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Cho, A. Y.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Corner, L.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Curl, R. F.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, "Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection," Appl. Opt. 43, 2257-2266 (2004).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

Dahnke, H.

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

de Labachelerie, M.

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

De Natale, P.

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, "Combining a difference-frequency source to an off-axis high-finesse cavity for trace-gas monitoring around 3 μm," Opt. Express 14, 1304-1313 (2006).
[CrossRef] [PubMed]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

Ebrahimzadeh, M.

M. Ebrahimzadeh, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), p. 179.
[CrossRef]

Faddeyeva, V. N.

V. N. Faddeyeva and N. M. Terent'ev, Table of Values of the Function w(z) (Pergamon, 1961), p. 15.

Faist, J.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Feller, G. S.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Fried, A.

F. K. Tittel, D. Richter, and A. Fried, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), pp. 445-451.
[CrossRef]

Gagliardi, G.

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, "Combining a difference-frequency source to an off-axis high-finesse cavity for trace-gas monitoring around 3 μm," Opt. Express 14, 1304-1313 (2006).
[CrossRef] [PubMed]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

Gianfrani, L.

Giovannini, M.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Gmachl, C.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

Gupta, M.

S. Williams, M. Gupta, T. Owano, D. S. Baer, A. O'Keefe, D. R. Yarkony, and S. Matsika, "Quantitative detection of O2 by cavity-enhanced spectroscopy," Opt. Lett. 29, 1066-1068 (2004).
[CrossRef] [PubMed]

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

Hall, J. L.

Halmer, D.

Hancock, G.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Hanson, R. K.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Hering, P.

G. von Basum, D. Halmer, P. Hering, M. Mürtz, S. Schiller, F. Müller, A. Popp, and F. Kühnemann, "Parts per trillion sensitivity for ethane in air with an optical parametric oscillator cavity leak-out spectrometer," Opt. Lett. 29, 797-799 (2004).
[CrossRef] [PubMed]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

Herriott, D.

Hutchinson, A. L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Hvozdara, L.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Kachanov, A. A.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Kasyutich, V. L.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

Katsuda, T.

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

Kelly, K. K.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Kleine, D.

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

Kogelnik, H.

Kompfner, R.

Kosterev, A. A.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, "Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection," Appl. Opt. 43, 2257-2266 (2004).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

Kotchie, R.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Kühnemann, F.

Lapson, L.

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford Science, 1973), pp. 74-78.

Ma, L.-S.

Maddaloni, P.

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, "Combining a difference-frequency source to an off-axis high-finesse cavity for trace-gas monitoring around 3 μm," Opt. Express 14, 1304-1313 (2006).
[CrossRef] [PubMed]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

Malara, P.

P. Malara, P. Maddaloni, G. Gagliardi, and P. De Natale, "Combining a difference-frequency source to an off-axis high-finesse cavity for trace-gas monitoring around 3 μm," Opt. Express 14, 1304-1313 (2006).
[CrossRef] [PubMed]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

Matsika, S.

Mclaughlin, R. J.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Meijer, G.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

Menzel, L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

Mihalcea, R. M.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Müller, F.

Mürtz, M.

G. von Basum, D. Halmer, P. Hering, M. Mürtz, S. Schiller, F. Müller, A. Popp, and F. Kühnemann, "Parts per trillion sensitivity for ethane in air with an optical parametric oscillator cavity leak-out spectrometer," Opt. Lett. 29, 797-799 (2004).
[CrossRef] [PubMed]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

Nakagawa, K.

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

Ohtsu, M.

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

O'Keefe, A.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

S. Williams, M. Gupta, T. Owano, D. S. Baer, A. O'Keefe, D. R. Yarkony, and S. Matsika, "Quantitative detection of O2 by cavity-enhanced spectroscopy," Opt. Lett. 29, 1066-1068 (2004).
[CrossRef] [PubMed]

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

Owano, T.

Paul, J. B.

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

J. B. Paul, L. Lapson, and J. Anderson, "Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment," Appl. Opt. 40, 4904-4910 (2001).
[CrossRef]

Peeters, R.

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

Peverall, R.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Pfrang, C.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

Popp, A.

Richard, E. C.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Richter, D.

F. K. Tittel, D. Richter, and A. Fried, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), pp. 445-451.
[CrossRef]

Ritchie, G. A. D.

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

Roller, C.

Romanini, D.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Rosen, D. I.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

Sadeghi, N.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Schiller, S.

Schmeltekopf, A. L.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Shelkovnikov, A. S.

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

Silva, M. L.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Sivco, D. L.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Sonnenfroh, D. M.

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

Stockel, F.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Tedesco, D.

Terent'ev, N. M.

V. N. Faddeyeva and N. M. Terent'ev, Table of Values of the Function w(z) (Pergamon, 1961), p. 15.

Thompson, T. L.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Tittel, F. K.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Y. A. Bakhirkin, A. A. Kosterev, C. Roller, R. F. Curl, and F. K. Tittel, "Mid-infrared quantum cascade laser based off-axis integrated output spectroscopy of biogenic nitric oxide detection," Appl. Opt. 43, 2257-2266 (2004).
[CrossRef] [PubMed]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

F. K. Tittel, D. Richter, and A. Fried, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), pp. 445-451.
[CrossRef]

Tuck, A. F.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Urban, W.

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

van Burgel, M.

Vaughan, S.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

von Basum, G.

Wayne, R. P.

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

Webber, M. E.

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

Williams, S.

Wilson, R.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Winkler, R. H.

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

Yarekha, D. A.

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

Yarkony, D. R.

Ye, J.

Appl. Opt. (3)

Appl. Phys. B (12)

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, "A 3.5-mW continuous-wave difference-frequency source around 3 μm for sub-Doppler molecular spectroscopy," Appl. Phys. B B80, 141-145 (2005).
[CrossRef]

R. Peeters, G. Berden, A. Apituley, and G. Meijer, "Open-path trace gas detection of ammonia based on cavity-enhanced absorption spectroscopy," Appl. Phys. B 71, 231-236 (2000).
[CrossRef]

D. S. Baer, J. B. Paul, M. Gupta, and A. O'Keefe, "Sensitive absorption measurements in the near-infrared region using off-axis integrated-cavity-output spectroscopy," Appl. Phys. B 75, 261-265 (2002).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

V. L. Kasyutich, C. E. Canosa-Mas, C. Pfrang, S. Vaughan, and R. P. Wayne, "Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers," Appl. Phys. B B75, 755-761 (2002).
[CrossRef]

M. L. Silva, D. M. Sonnenfroh, D. I. Rosen, M. G. Allen, and A. O'Keefe, "Integrated cavity output spectroscopy measurements of nitric oxide in breath with a pulsed room-temperature quantum cascade laser," Appl. Phys. B 81, 705-710 (2005).
[CrossRef]

Y. A. Bakhirkin, A. A. Kosterev, R. F. Curl, F. K. Tittel, D. A. Yarekha, L. Hvozdara, M. Giovannini, and J. Faist, "Sub-ppbv nitric oxide concentration measurements using cw thermoelectrically cooled quantum cascade laser-based integrated cavity output spectroscopy," Appl. Phys. B 82, 149-154 (2006).
[CrossRef]

B. Bakowski, L. Corner, G. Hancock, R. Kotchie, R. Peverall, and G. A. D. Ritchie, "Cavity-enhanced absorption spectroscopy with a rapidly swept diode laser," Appl. Phys. B 75, 745-750 (2002).
[CrossRef]

R. M. Mihalcea, M. E. Webber, D. S. Baer, R. K. Hanson, G. S. Feller, and W. B. Chapman, "Diode-laser absorption measurements of CO2, H2O, N2O, and NH3 near 2.0 μm," Appl. Phys. B 67, 283-288 (1998).
[CrossRef]

E. C. Richard, K. K. Kelly, R. H. Winkler, R. Wilson, T. L. Thompson, R. J. Mclaughlin, A. L. Schmeltekopf, and A. F. Tuck, "A fast-response near-infrared tunable diode laser absorption spectrometer for in situ measurements of CH4 in the upper troposphere and lower stratosphere," Appl. Phys. B 75, 183-194 (2002).
[CrossRef]

L. Menzel, A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, A. Y. Cho, and W. Urban, "Spectroscopic detection of biological NO with a quantum cascade laser," Appl. Phys. B 72, 1-5 (2001).
[CrossRef]

H. Dahnke, D. Kleine, W. Urban, P. Hering, and M. Mürtz, "Isotopic ratio measurement of methane in ambient air using mid-infrared cavity leak-out spectroscopy," Appl. Phys. B 72, 121-125 (2001).
[CrossRef]

Chem. Phys. Lett. (1)

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stockel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

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

A. Asfaw, "A fast method of modeling spectral lines," J. Quant. Spectrosc. Radiat. Transf. 70, 129-137 (2000).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (2)

Science (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, "Quantum cascade laser," Science 264, 553-556 (1994).
[CrossRef] [PubMed]

Other (5)

M. Ebrahimzadeh, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), p. 179.
[CrossRef]

F. K. Tittel, D. Richter, and A. Fried, in Solid-State Mid-Infrared Laser Sources, Vol. 89 of Topics in Applied Physics, I.T.Sorokina and K.L.Vodopyanov, eds. (Springer-Verlag, 2003), pp. 445-451.
[CrossRef]

Harvard Smithsonian Center for Astrophysics, The HITRAN Database 2004http://www.hitran.com.

R. Loudon, The Quantum Theory of Light (Oxford Science, 1973), pp. 74-78.

V. N. Faddeyeva and N. M. Terent'ev, Table of Values of the Function w(z) (Pergamon, 1961), p. 15.

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the off-axis cavity alignment evidencing the multiple-reflection beam path. If m equals the number of optical round-trip passes, the pattern becomes re-entrant for a cavity-effective free spectral range FSR = c 2 m L . In graph (b), a typical empty-cavity transmission spectrum is shown in the case of an on-axis FSR of 166 MHz and an alignment with m = 11 , so that FSR = 15 MHz . To wash out the cavity mode structure, both laser-frequency and cavity-length modulations are introduced and combined to time integration of the output signal. As an example, graph (c) also shows a typical sample absorption profile recorded in a 50   Torr ambient-air C H 4 sample at 2948.108 cm 1 .

Fig. 2
Fig. 2

IA as a function of the total air-sample pressure for a gas concentration n = 1 ppmv , calculated by means of Eqs. (3, 7). In the inset, the peak value of the normalized cavity transmission is also shown, indicating how rapidly the saturation regime is approached. Calculation was carried out for a specific C H 4 rovibrational transition, whose parameters are listed in Table 1.

Fig. 3
Fig. 3

IA (continuous curve) and normalized peak cavity transmission (inset) as a function of C H 4 concentration at fixed air pressure ( P a = 760   Torr ) , for the line at 2948.108 cm 1 and an effective absorption path-length L eq = 2 km .

Fig. 4
Fig. 4

IA calculated for different values of P a as a function of C H 4 concentration from 20 ppbv to 1 ppmv . In the inset, the behavior at lower values of n ( 1 10 ppbv ) is represented for P a = atmospheric pressure.

Fig. 5
Fig. 5

FWHM of the line profile on the cavity output plotted versus total pressure (continuous curve) for the considered C H 4 rovibrational transition. The dashed curve shows the pressure broadening of the direct Voigt absorption line shape, obtained from Eq. (7). The FWHM calculated by the Lambert–Beer law, assuming the same equivalent length as the optical cavity, is also plotted (dotted line).

Fig. 6
Fig. 6

Line contrast Q = t ( ω 0 ) FWHM as a function of the total pressure (main frame) for fixed C H 4 concentration ( n = 1 ppbv ) . The inset shows the behavior of Q versus the effective path length for the same gas concentration and P a = 350   Torr .

Fig. 7
Fig. 7

Experimental setup. ECDL, external-cavity diode laser; OI, optical isolator; FP, fiber port; C, collimating lens; HWP (QWP), half-wave plate (quarter-wave plate); L1/L2, lenses for spatial mode matching; DM, dichroic mirror; AL, achromatic lens; PPLN, periodically poled Li Nb O 3 nonlinear crystal; Ge-F, Ge filter. The function generator on the external-cavity diode laser provides current modulation, while the one connected to the cavity piezoelement is used for cavity-length modulation.

Fig. 8
Fig. 8

Calculated FWHM values compared to the measured linewidths. Good agreement is found for the low-pressure values, while at pressures above 500   Torr the measured linewidths appear slightly underestimated (see also the text). However, even the last three measurements are consistent with the theoretical values within 3 σ .

Fig. 9
Fig. 9

Calculated values of integrated absorbance versus pressure compared to the experimental points, which are all consistent with the model within 2 σ .

Tables (2)

Tables Icon

Table 1 List of Experimental Parameters and Constants Used in the Numerical Calculation a

Tables Icon

Table 2 C H 4 Concentration Values (with Corresponding Standard Errors) Retrieved by the Calibration Curves of Fig. 4 for Different Values of Air-Sample Pressure

Equations (13)

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

d I d t = c 2 L [ I 0 C p T m 2 I ( 1 R m ) ] ,
I t ( ω ) = I 0 C p T m 2 2 [ ( 1 R m ) + R m α ( ω ) P s L ] ,
IA I t , α = 0 I t ( ω ) I t , α = 0 d ω = α ( ω ) α ( ω ) + ( 1 n P a L eq ) d ω ,
V ( ω ) = Γ L ln 2 Γ D π 3 2 + e ln 2 ( ω ν ) 2 Γ D 2 ( ω 0 ν ) 2 + Γ L 2 d ν .
V ( x , y ) = 1 Γ D ln 2 π K ( x , y ) ,
K ( x , y ) = Re { e z 2 [ 1 + i Erf i ( z ) ] } .
V ( x , y ) = 1 Γ D ln 2 π Re { e z 2 [ 1 + i Erf i ( z ) ] } ,
α L ( ω ) = S N L π Γ L ( ω ω 0 ) 2 + Γ L 2 .
IA L = P a π ( B γ c + B 2 ) 1 ,
t L ( ω 0 ) α L ( ω 0 ) α L ( ω 0 ) + 1 n P a L eq = ( 1 + B γ c ) 1 .
α L ( ω ) α L ( ω ) + 1 n P a L eq = t L ( ω 0 ) 2 ,
FWHM L = 2 γ c P a 1 + 1 B γ c = 2 Γ L 1 + 1 B γ c ,
t ( P a , ω 0 ) α V ( ω 0 ) α V ( ω 0 ) + 1 n P a L eq .

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