Abstract

We have investigated the effects of laser bandwidth on quantitative cavity ring-down spectroscopy using the r R transitions of the b(υ = 0) ← X(υ = 0) band of molecular oxygen. It is found that failure to account properly for the laser bandwidth leads to systematic errors in the number densities determined from measured ring-down signals. When the frequency-integrated expression for the ring-down signal is fitted and measured laser line shapes are used, excellent agreement between measured and predicted number densities is found.

© 1996 Optical Society of America

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References

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  1. A. O’Keefe, D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
    [CrossRef]
  2. A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
    [CrossRef]
  3. D. Romanini, K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
    [CrossRef]
  4. P. Zalicki, R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
    [CrossRef]
  5. R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
    [CrossRef]
  6. This number assumes a 1-m-long cavity, total mirror losses of 1 ppm, a monochromatic laser, and the ability to measure a 1% change in ring-down time. See also G. Rempe, R. J. Thompson, H. J. Kimble, R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363–365 (1992).
    [CrossRef] [PubMed]
  7. H. D. Babcock, L. Herzberg, “Fine structure of the red system of atmospheric oxygen bands,” Astrophys. J. 108, 167–190 (1929).
    [CrossRef]
  8. K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1979), p. 498.
  9. K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A band,” J. Mol. Spectrosc. 121, 1–19 (1987).
    [CrossRef]
  10. Manufacturers and product names are listed solely for completeness. These specific citations neither constitute an endorsement of the products nor imply that similar products from other companies would be less suitable.
  11. For the cavity length (118 cm) and mirror radius of curvature (100 cm) used, light injected into the cavity is not reentrant as the cavity is nonconfocal. However, the observed two-spot pattern can be understood in the context of transverse mode locking; see the discussion of off-axis beam propagation in P. W. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342– 1357 (1970).
    [CrossRef]
  12. This formula is Eq. 10 of Zalicki and Zare (Ref. 4), where the summation over cavity modes has been replaced by the corresponding integration. Because the data presented here are time averaged and neither the lasers nor the cavity were stabilized, the use of an integration is believed to be operationally correct.
  13. D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
    [CrossRef]
  14. R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
    [CrossRef]

1995 (2)

P. Zalicki, R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

1994 (2)

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
[CrossRef]

1993 (1)

D. Romanini, K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

1992 (1)

1990 (1)

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

1988 (1)

A. O’Keefe, D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

1987 (1)

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

1970 (1)

For the cavity length (118 cm) and mirror radius of curvature (100 cm) used, light injected into the cavity is not reentrant as the cavity is nonconfocal. However, the observed two-spot pattern can be understood in the context of transverse mode locking; see the discussion of off-axis beam propagation in P. W. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342– 1357 (1970).
[CrossRef]

1929 (1)

H. D. Babcock, L. Herzberg, “Fine structure of the red system of atmospheric oxygen bands,” Astrophys. J. 108, 167–190 (1929).
[CrossRef]

Babcock, H. D.

H. D. Babcock, L. Herzberg, “Fine structure of the red system of atmospheric oxygen bands,” Astrophys. J. 108, 167–190 (1929).
[CrossRef]

Boogaarts, M. G. H.

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
[CrossRef]

Cooksy, A. L.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

Copeland, R. A.

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe, D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

Heath, J.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

Herzberg, G.

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1979), p. 498.

Herzberg, L.

H. D. Babcock, L. Herzberg, “Fine structure of the red system of atmospheric oxygen bands,” Astrophys. J. 108, 167–190 (1929).
[CrossRef]

Holleman, I.

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

Huber, K. P.

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1979), p. 498.

Huestis, D. L.

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

Jongma, R. T.

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
[CrossRef]

Kimble, H. J.

Knutsen, K.

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

Lalezari, R.

Lehmann, K. K.

D. Romanini, K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Meijer, G.

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
[CrossRef]

O’Keefe, A.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

A. O’Keefe, D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

Rempe, G.

Ritter, K. J.

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Romanini, D.

D. Romanini, K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Saykally, R. J.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

Scherer, J. J.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

Sheeks, R.

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

Slanger, T. G.

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

Smith, P. W.

For the cavity length (118 cm) and mirror radius of curvature (100 cm) used, light injected into the cavity is not reentrant as the cavity is nonconfocal. However, the observed two-spot pattern can be understood in the context of transverse mode locking; see the discussion of off-axis beam propagation in P. W. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342– 1357 (1970).
[CrossRef]

Thompson, R. J.

Wilkerson, T. D.

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Zalicki, P.

P. Zalicki, R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Zare, R. N.

P. Zalicki, R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Astrophys. J. (1)

H. D. Babcock, L. Herzberg, “Fine structure of the red system of atmospheric oxygen bands,” Astrophys. J. 108, 167–190 (1929).
[CrossRef]

Can. J. Phys. (1)

D. L. Huestis, R. A. Copeland, K. Knutsen, T. G. Slanger, R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Branch intensities and oscillator strengths for the Herzberg absorption systems in oxygen,” Can. J. Phys. 72, 1109 (1994).
[CrossRef]

Chem. Phys. Lett. (1)

A. O’Keefe, J. J. Scherer, A. L. Cooksy, R. Sheeks, J. Heath, R. J. Saykally, “Cavity ring-down dye laser spectroscopy of jet-cooled metal clusters: Cu2 and Cu3,” Chem. Phys. Lett. 172, 214–218 (1990).
[CrossRef]

J. Chem. Phys. (2)

D. Romanini, K. K. Lehmann, “Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

P. Zalicki, R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

J. Mol. Spectrosc. (2)

R. T. Jongma, M. G. H. Boogaarts, G. Meijer, “Double-resonance spectroscopy on triple states of CO,” J. Mol. Spectrosc. 165, 303–314 (1994).
[CrossRef]

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

For the cavity length (118 cm) and mirror radius of curvature (100 cm) used, light injected into the cavity is not reentrant as the cavity is nonconfocal. However, the observed two-spot pattern can be understood in the context of transverse mode locking; see the discussion of off-axis beam propagation in P. W. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342– 1357 (1970).
[CrossRef]

Rev. Sci. Instrum. (2)

A. O’Keefe, D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

R. T. Jongma, M. G. H. Boogaarts, I. Holleman, G. Meijer, “Trace gas detection with cavity ring-down spectroscopy,” Rev. Sci. Instrum. 66, 2821–2828 (1995).
[CrossRef]

Other (3)

This formula is Eq. 10 of Zalicki and Zare (Ref. 4), where the summation over cavity modes has been replaced by the corresponding integration. Because the data presented here are time averaged and neither the lasers nor the cavity were stabilized, the use of an integration is believed to be operationally correct.

Manufacturers and product names are listed solely for completeness. These specific citations neither constitute an endorsement of the products nor imply that similar products from other companies would be less suitable.

K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1979), p. 498.

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Figures (5)

Fig. 1
Fig. 1

Ring-down spectrum of the O2 r R(9) line measured with the dye laser. The three traces correspond to three different time windows over which the a single exponential was fit to the measured ring-down singal. Note that as the time window was decreased and placed near t = 0, the apparent absorptive losses increased. Expected peak losses for cell condition (1294 Pa, 296.6 K) are 8980 ppm per pass.

Fig. 2
Fig. 2

Ring-down spectrum of the O2 r R(9) line recorded with the Ti:Al2O3 laser. The losses were determined by a single exponential fit to the ring-down signal over the window shown. Note that the apparent absorptive losses are five to eight times larger than those in Fig. 1. The cell conditions were essentially the same as in Fig. 1.

Fig. 3
Fig. 3

Ring-down signal as a function of time measured with the dye laser at the peak of the O2 r R(9) transition (▲). The measured dye laser spectrum is shown in the inset (solid curve). Also shown in the inset is a single Gaussian (1.5-GHz HWHM) approximation to the laser spectrum (dashed curve). Superimposed on the measured ring-down signal are the calculated ring-down signals with the measured (solid curve) and single-mode Gaussian approximation (dashed curve).

Fig. 4
Fig. 4

Ring-down signal as a function of time measured with the Ti:Al2O3 laser at the peak of the O2 r R(9) transition (▲). The measured laser spectrum is shown in the inset. Superimposed on the measured ring-down signal is the ring-down signal calculated with the measured laser spectrum.

Fig. 5
Fig. 5

Number density per rotational quantum state divided by the state degeneracy as a function of state energy, as inferred from the measured ring-down signals and corrected for finite laser bandwidth (●). Also shown (solid line) is the calculated number density per state for the sample cell conditions (1331 Pa, 296.6 K). A linear regression to the data yields a temperature of 296.2 K.

Equations (2)

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S ( t ) = exp [ t c l ( 1 R ) ] d ν I ( ν ν l ) × exp [ t c l L ( ν ν 0 ) ] .
L ( ν ν 0 ) = n l S f ( ν ν 0 ) ,

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