Abstract

The intensity and noise properties of decay transients obtained in a generic pulsed cavity ringdown experiment are analyzed experimentally and theoretically. A weighted nonlinear least-squares analysis of digitized decay transients is shown that avoids baseline offset effects that induce systematic deviations in the estimation of decay rates. As follows from simulations not only is it a method that provides correct estimates for the values of the fit parameters, but moreover it also yields a correct estimate of the precision of the fit parameters. It is shown experimentally that a properly aligned stable optical resonator can effectively yield monoexponential decays under multimode excitation. An on-line method has been developed, based on a statistical analysis of the noise properties of the decay transients, to align a stable resonator toward this monoexponential decay.

© 2001 Optical Society of America

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    [CrossRef]

2000

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

I. Labazan, S. Rustić, S. Milos̆ević, “Nonlinear effects in pulsed cavity-ringdown spectroscopy of lithium vapor,” Chem. Phys. Lett. 320, 613–622 (2000).
[CrossRef]

C. R. Bucher, K. K. Lehmann, D. F. Plusquellic, G. T. Fraser, “Doppler-free nonlinear absorption in ethylene by use of continuous-wave ringdown spectroscopy,” Appl. Opt. 39, 3154–3164 (2000).
[CrossRef]

1999

A. O’Keefe, J. J. Scherer, J. B. Paul, “Integrated cavity output analysis of ultraweak absorption,” Chem. Phys. Lett. 307, 343–349 (1999).
[CrossRef]

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Complex traversal time for optical pulse transmission in a Fabry–Perot cavity,” Jpn. J. Appl. Phys. 38, 6287–6297 (1999).
[CrossRef]

R. van Zee, J. T. Hodges, J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951–3960 (1999).
[CrossRef]

1998

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

J. Ye, L.-S. Ma, 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. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

A. O’Keefe, “CW integrated cavity output spectroscopy,” Chem. Phys. Lett. 293, 331–336 (1998).
[CrossRef]

1997

H. Naus, A. de Lange, W. Ubachs, “b1∑g+ - X3∑g- (0,0) band of oxygen isotopomers in relation to tests of the symmetrization postulate in 16O2,” Phys. Rev. A 56, 4755–4763 (1997).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

1996

J. T. Hodges, J. P. Looney, R. D. van Zee, “Laser bandwidth effects in quantitative cavity ringdown spectroscopy,” Appl. Opt. 35, 4112–4116 (1996).
[CrossRef] [PubMed]

K. K. Lehmann, D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ringdown cavity to arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

1995

M. G. H. Boogaarts, G. Meijer, “Measurement of the beam intensity in a laser-desorption jet-cooling mass-spectrometer,” J. Chem. Phys. 103, 5269–5274 (1995).
[CrossRef]

I. H. M. van Stokkum, W. A. van der Graaf, D. Lenstra, “Weighted fit of optical spectra,” Opt. Commun. 121, 103–108 (1995).
[CrossRef]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

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

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

1994

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

1993

D. Romanini, K. K. Lehmann, “Ringdown-cavity absorption spectroscopy of the very weak HCN overtone bands with 6, 7, and 8 stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

1988

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

1981

1980

1972

T. W. Hänsch, A. L. Schawlow, P. E. Toshek, “Ultrasensitive response of a cw dye laser to selective extinction,” IEEE J. Quantum. Electron. 8, 802–804 (1972).
[CrossRef]

1962

Ashfold, M. N. R.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Bates, D. M.

D. M. Bates, D. G. Watts, Nonlinear Regression and its Applications (Wiley, New York, 1988).
[CrossRef]

Beers, Y.

Y. Beers, Introduction to the Theory of Error (Addision-Wesley, Cambridge, Mass., 1957).

Berden, G.

R. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

Bernard, D. J.

Boogaarts, M. G. H.

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

M. G. H. Boogaarts, G. Meijer, “Measurement of the beam intensity in a laser-desorption jet-cooling mass-spectrometer,” J. Chem. Phys. 103, 5269–5274 (1995).
[CrossRef]

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

Bucher, C. R.

Byer, R. L.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

Carroll, R. J.

R. J. Carroll, D. Ruppert, Transformation and Weighting in Regression (Chapman & Hall, New York, 1988).
[CrossRef]

Collier, C. P.

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

de Lange, A.

H. Naus, A. de Lange, W. Ubachs, “b1∑g+ - X3∑g- (0,0) band of oxygen isotopomers in relation to tests of the symmetrization postulate in 16O2,” Phys. Rev. A 56, 4755–4763 (1997).
[CrossRef]

Deacon, D. A. G.

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

Engeln, R.

R. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1993).

Fraser, G. T.

Hahn, J. W.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Complex traversal time for optical pulse transmission in a Fabry–Perot cavity,” Jpn. J. Appl. Phys. 38, 6287–6297 (1999).
[CrossRef]

Hall, J. L.

Hänsch, T. W.

T. W. Hänsch, A. L. Schawlow, P. E. Toshek, “Ultrasensitive response of a cw dye laser to selective extinction,” IEEE J. Quantum. Electron. 8, 802–804 (1972).
[CrossRef]

Harb, C. C.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Harris, J. S.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Herbelin, J. M.

Hodges, J. T.

Holleman, I.

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

Jongma, R. T.

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

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

Kastler, A.

Kruger, C. H.

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Kwok, M. A.

Labazan, I.

I. Labazan, S. Rustić, S. Milos̆ević, “Nonlinear effects in pulsed cavity-ringdown spectroscopy of lithium vapor,” Chem. Phys. Lett. 320, 613–622 (2000).
[CrossRef]

Lee, H.-W.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Complex traversal time for optical pulse transmission in a Fabry–Perot cavity,” Jpn. J. Appl. Phys. 38, 6287–6297 (1999).
[CrossRef]

Lee, J. Y.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Complex traversal time for optical pulse transmission in a Fabry–Perot cavity,” Jpn. J. Appl. Phys. 38, 6287–6297 (1999).
[CrossRef]

Lehmann, K. K.

C. R. Bucher, K. K. Lehmann, D. F. Plusquellic, G. T. Fraser, “Doppler-free nonlinear absorption in ethylene by use of continuous-wave ringdown spectroscopy,” Appl. Opt. 39, 3154–3164 (2000).
[CrossRef]

K. K. Lehmann, D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini, K. K. Lehmann, “Ringdown-cavity absorption spectroscopy of the very weak HCN overtone bands with 6, 7, and 8 stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Lenstra, D.

I. H. M. van Stokkum, W. A. van der Graaf, D. Lenstra, “Weighted fit of optical spectra,” Opt. Commun. 121, 103–108 (1995).
[CrossRef]

Looney, J. P.

Ma, L.-S.

Martin, J.

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

McKay, J. A.

Meijer, G.

R. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

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

M. G. H. Boogaarts, G. Meijer, “Measurement of the beam intensity in a laser-desorption jet-cooling mass-spectrometer,” J. Chem. Phys. 103, 5269–5274 (1995).
[CrossRef]

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

Milos?evic, S.

I. Labazan, S. Rustić, S. Milos̆ević, “Nonlinear effects in pulsed cavity-ringdown spectroscopy of lithium vapor,” Chem. Phys. Lett. 320, 613–622 (2000).
[CrossRef]

Naus, H.

H. Naus, A. de Lange, W. Ubachs, “b1∑g+ - X3∑g- (0,0) band of oxygen isotopomers in relation to tests of the symmetrization postulate in 16O2,” Phys. Rev. A 56, 4755–4763 (1997).
[CrossRef]

Newman, S. M.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

O’Keefe, A.

A. O’Keefe, J. J. Scherer, J. B. Paul, “Integrated cavity output analysis of ultraweak absorption,” Chem. Phys. Lett. 307, 343–349 (1999).
[CrossRef]

A. O’Keefe, “CW integrated cavity output spectroscopy,” Chem. Phys. Lett. 293, 331–336 (1998).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

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

Orr-Ewing, A. J.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Owano, T. G.

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Paldus, B. A.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Parker, D. H.

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

Paul, J. B.

A. O’Keefe, J. J. Scherer, J. B. Paul, “Integrated cavity output analysis of ultraweak absorption,” Chem. Phys. Lett. 307, 343–349 (1999).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

Peeters, R.

R. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

Plusquellic, D. F.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1993).

Rakestraw, D. J.

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

Remo, J. L.

Romanini, D.

K. K. Lehmann, D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini, K. K. Lehmann, “Ringdown-cavity absorption spectroscopy of the very weak HCN overtone bands with 6, 7, and 8 stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

Ruppert, D.

R. J. Carroll, D. Ruppert, Transformation and Weighting in Regression (Chapman & Hall, New York, 1988).
[CrossRef]

Rustic, S.

I. Labazan, S. Rustić, S. Milos̆ević, “Nonlinear effects in pulsed cavity-ringdown spectroscopy of lithium vapor,” Chem. Phys. Lett. 320, 613–622 (2000).
[CrossRef]

Saykally, R. J.

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

Schawlow, A. L.

T. W. Hänsch, A. L. Schawlow, P. E. Toshek, “Ultrasensitive response of a cw dye laser to selective extinction,” IEEE J. Quantum. Electron. 8, 802–804 (1972).
[CrossRef]

Scherer, J. J.

A. O’Keefe, J. J. Scherer, J. B. Paul, “Integrated cavity output analysis of ultraweak absorption,” Chem. Phys. Lett. 307, 343–349 (1999).
[CrossRef]

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

Spence, T. G.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Spencer, D. J.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1993).

Toshek, P. E.

T. W. Hänsch, A. L. Schawlow, P. E. Toshek, “Ultrasensitive response of a cw dye laser to selective extinction,” IEEE J. Quantum. Electron. 8, 802–804 (1972).
[CrossRef]

Ubachs, W.

H. Naus, A. de Lange, W. Ubachs, “b1∑g+ - X3∑g- (0,0) band of oxygen isotopomers in relation to tests of the symmetrization postulate in 16O2,” Phys. Rev. A 56, 4755–4763 (1997).
[CrossRef]

Uenten, R. H.

Urevig, D. S.

van der Graaf, W. A.

I. H. M. van Stokkum, W. A. van der Graaf, D. Lenstra, “Weighted fit of optical spectra,” Opt. Commun. 121, 103–108 (1995).
[CrossRef]

van Stokkum, I. H. M.

I. H. M. van Stokkum, W. A. van der Graaf, D. Lenstra, “Weighted fit of optical spectra,” Opt. Commun. 121, 103–108 (1995).
[CrossRef]

van Zee, R.

van Zee, R. D.

J. T. Hodges, J. P. Looney, R. D. van Zee, “Laser bandwidth effects in quantitative cavity ringdown spectroscopy,” Appl. Opt. 35, 4112–4116 (1996).
[CrossRef] [PubMed]

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ringdown cavity to arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1993).

Voelkel, D.

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

Wahl, E. H.

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Watts, D. G.

D. M. Bates, D. G. Watts, Nonlinear Regression and its Applications (Wiley, New York, 1988).
[CrossRef]

Wheeler, M. D.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

Willke, B.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Wodtke, A. M.

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

Xie, J.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

Ye, J.

Zalicki, P.

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

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

Zare, R. N.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

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

Appl. Opt.

Chem. Phys. Lett.

I. Labazan, S. Rustić, S. Milos̆ević, “Nonlinear effects in pulsed cavity-ringdown spectroscopy of lithium vapor,” Chem. Phys. Lett. 320, 613–622 (2000).
[CrossRef]

J. J. Scherer, D. Voelkel, D. J. Rakestraw, J. B. Paul, C. P. Collier, R. J. Saykally, A. O’Keefe, “Infrared cavity-ringdown spectroscopy laser-absorption spectroscopy (IR-CLAS),” Chem. Phys. Lett. 245, 273–280 (1995).
[CrossRef]

G. Meijer, M. G. H. Boogaarts, R. T. Jongma, D. H. Parker, A. M. Wodtke, “Coherent cavity ringdown spectroscopy,” Chem. Phys. Lett. 217, 112–116 (1994).
[CrossRef]

A. O’Keefe, “CW integrated cavity output spectroscopy,” Chem. Phys. Lett. 293, 331–336 (1998).
[CrossRef]

A. O’Keefe, J. J. Scherer, J. B. Paul, “Integrated cavity output analysis of ultraweak absorption,” Chem. Phys. Lett. 307, 343–349 (1999).
[CrossRef]

J. Martin, B. A. Paldus, P. Zalicki, E. H. Wahl, T. G. Owano, J. S. Harris, C. H. Kruger, R. N. Zare, “Cavity ringdown spectroscopy with Fourier-transform-limited pulses,” Chem. Phys. Lett. 258, 63–70 (1996).
[CrossRef]

Chem. Rev.

J. J. Scherer, J. B. Paul, A. O’Keefe, R. J. Saykally, “Cavity ringdown laser absorption spectroscopy: history, development, and application to pulsed molecular beams,” Chem. Rev. 97, 25–52 (1997).
[CrossRef] [PubMed]

IEEE J. Quantum. Electron.

T. W. Hänsch, A. L. Schawlow, P. E. Toshek, “Ultrasensitive response of a cw dye laser to selective extinction,” IEEE J. Quantum. Electron. 8, 802–804 (1972).
[CrossRef]

J. Appl. Phys.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Willke, J. Xie, J. S. Harris, R. N. Zare, “Cavity-locked ringdown spectroscopy,” J. Appl. Phys. 83, 3991–3997 (1998).
[CrossRef]

J. Chem. Phys.

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

K. K. Lehmann, D. Romanini, “The superposition principle and cavity ringdown spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

D. Romanini, K. K. Lehmann, “Ringdown-cavity absorption spectroscopy of the very weak HCN overtone bands with 6, 7, and 8 stretching quanta,” J. Chem. Phys. 99, 6287–6301 (1993).
[CrossRef]

M. G. H. Boogaarts, G. Meijer, “Measurement of the beam intensity in a laser-desorption jet-cooling mass-spectrometer,” J. Chem. Phys. 103, 5269–5274 (1995).
[CrossRef]

J. T. Hodges, J. P. Looney, R. D. van Zee, “Response of a ringdown cavity to arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

J. Chem. Soc. Faraday Trans.

M. D. Wheeler, S. M. Newman, A. J. Orr-Ewing, M. N. R. Ashfold, “Cavity ringdown spectroscopy,” J. Chem. Soc. Faraday Trans. 94, 337–351 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

J. Y. Lee, H.-W. Lee, J. W. Hahn, “Complex traversal time for optical pulse transmission in a Fabry–Perot cavity,” Jpn. J. Appl. Phys. 38, 6287–6297 (1999).
[CrossRef]

Opt. Commun.

I. H. M. van Stokkum, W. A. van der Graaf, D. Lenstra, “Weighted fit of optical spectra,” Opt. Commun. 121, 103–108 (1995).
[CrossRef]

Phys. Rev. A

H. Naus, A. de Lange, W. Ubachs, “b1∑g+ - X3∑g- (0,0) band of oxygen isotopomers in relation to tests of the symmetrization postulate in 16O2,” Phys. Rev. A 56, 4755–4763 (1997).
[CrossRef]

Rev. Sci. Instrum.

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

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, R. L. Byer, “A laser-locked cavity-ringdown spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

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

R. Engeln, G. Berden, R. Peeters, G. Meijer, “Cavity-enhanced absorption and cavity enhanced magnetic rotation spectroscopy,” Rev. Sci. Instrum. 69, 3763–3769 (1998).
[CrossRef]

Other

Splus Reference Manual (Statistical Sciences, Seattle, Wash., 1991).

Photomultiplier Tubes, (Catalog) (Hamamatsu Photonics, Shizuoka Prefecture, Japan, 1996).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, Cambridge, England, 1993).

Y. Beers, Introduction to the Theory of Error (Addision-Wesley, Cambridge, Mass., 1957).

D. M. Bates, D. G. Watts, Nonlinear Regression and its Applications (Wiley, New York, 1988).
[CrossRef]

R. J. Carroll, D. Ruppert, Transformation and Weighting in Regression (Chapman & Hall, New York, 1988).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Exponential decay rate estimated by integrating the decay inside two successive time windows. The situation represents settings used by Romanini and Lehmann20 (see text). A possible third time window to estimate the baseline (see text) is not shown.

Fig. 2
Fig. 2

Effect of small offset on the logarithm of I (t): solid curve, effect on the logarithm of a 0.5% biased exponential decay (see text); dashed curve, logarithm of an exponential decay with no offset; dashed curve, difference between the two logarithms.

Fig. 3
Fig. 3

Experimental single-shot decay transient as recorded with the digital oscilloscope. The signal before the ringdown event (baseline) is used to determine the offset.

Fig. 4
Fig. 4

Residuals of a monoexponential fit to the decay shown in Fig. 3. Discretization effects due to the 8-bit resolution of the digitizer are visible on the right-hand side. In the first part of the decay the noise due to Poisson statistics is dominant.

Fig. 5
Fig. 5

Scatterplot of the absolute values of the residuals from the unweighted fit versus the fitted intensity. The slope (0.453) of a line fitted to the data (solid line) in the scatterplot indicates that the intensity-dependent noise on the recorded transient originates from a Poisson-distributed counting process.

Fig. 6
Fig. 6

Residuals of a weighted monoexponential fit to the decay as shown in Fig. 3.

Fig. 7
Fig. 7

Effect of the 8-bit resolution of the digitizer. The digitized signal will remain constant during a certain time interval (neglecting noise) until the slowly decreasing signal reaches the next bit level. This effect results in striation in the residuals (Fig. 6) of the fit. Solid white curve, fitted decay.

Fig. 8
Fig. 8

Distributions estimated from the weighted fit: (a) deviation Δβ of the estimated decay rate parameter β; (b) approximate standard error σβ; (c) solid curve, ratio of Δβ and σβ; dashed curve, t df distribution.

Fig. 9
Fig. 9

Distributions estimated from an unweighted fit. Layout as in Fig. 8.

Tables (2)

Tables Icon

Table 1 Results of the Unweighted and Weighted Fit of the Decay Shown in Fig. 3

Tables Icon

Table 2 Results (rms average) from Fitting 1024 Simulations of a CRDS Decaya

Equations (17)

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

αν=βc-|ln R|l,
It=Ioff+I0 exp-βt,
A=tg1 Itdt,  B=tg2 Itdt,
β=1ΔglnAB.
β=1ΔglnA-CB-C.
0 I0 exp-βtdt=I0β.
It=0.005+exp-tI0.
EIc=varIc.
varImgEImg=g.
varĪm=1N2NvarEIcn=1NvarIc.
varĪmEĪm=1N.
varĪmgEĪmg=gN=αpN,
varIt=vare+varIp,
αˆp=1Kk=1KvarImkEIk=1Kk=1KImk-EIk2EIk,
αˆp=1Kk=1KvarImk-vareEIk=1Kk=1KImk-EIk2-σbase2EIk.
αpN=αp1N.
I0ph=I0fitηαpNN,

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