Abstract

In this paper we report on the development of a Fourier-transform based signal processing method for laser-locked Continuous Wave Cavity Ringdown Spectroscopy (CWCRDS). Rather than analysing single ringdowns, as is the norm in traditional methods, we amplitude modulate the incident light, and analyse the entire waveform output of the optical cavity; our method has more in common with Cavity Attenuated Phase Shift Spectroscopy than with traditional data analysis methods. We have compared our method to Levenburg-Marquardt non linear least squares fitting, and have found that, for signals with a noise level typical of that from a locked CWCRDS instrument, our method has a comparable accuracy and comparable or higher precision. Moreover, the analysis time is approximately 500 times faster (normalised to the same number of time domain points). Our method allows us to analyse any number of periods of the ringdown waveform at once: this allows the method to be optimised for speed and precision for a given spectrometer.

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  1. S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
    [CrossRef]
  2. J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
    [CrossRef]
  3. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 254-4-2551 (1988).
  4. A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 70(2), 1233–1257 (1999).
    [CrossRef]
  5. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
    [CrossRef]
  6. P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
    [CrossRef]
  7. M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
    [CrossRef]
  8. M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. 79, 023108 (2008).
    [CrossRef] [PubMed]
  9. D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
    [CrossRef]
  10. R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
    [CrossRef]
  11. R. W. P. Drever, J. L. Hall, F. 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]
  12. S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
    [CrossRef]
  13. B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
    [CrossRef]
  14. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
    [CrossRef]

2009 (1)

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

2008 (1)

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef] [PubMed]

2005 (1)

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

2004 (1)

D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
[CrossRef]

2001 (1)

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

2000 (1)

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

1999 (1)

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 70(2), 1233–1257 (1999).
[CrossRef]

1998 (2)

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

1996 (1)

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

1995 (1)

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

1988 (1)

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 254-4-2551 (1988).

1983 (1)

R. W. P. Drever, J. L. Hall, F. 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]

1981 (1)

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Atkinson, D. B.

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef] [PubMed]

Ball, S. M

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

Beames, J. M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Berden, G.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

Butler, T. J. A.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Byer, R. L.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

Chappell, T. I.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 254-4-2551 (1988).

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. 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]

Eastman, L. F.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Engeln, R.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

Everest, M. A.

M. A. Everest and D. B. Atkinson, “Discrete sums for the rapid determination of exponential decay constants,” Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. 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]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. 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]

Halmer, D.

D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
[CrossRef]

Harb, C. C.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

Harris, J. S.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Hering, P.

D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
[CrossRef]

Heurs, M.

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. 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]

Huntington, E. H.

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

Istratov, A. A.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 70(2), 1233–1257 (1999).
[CrossRef]

James, M. R.

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

Jones, R. L.

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

Kirchner, P. D.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Kowalski, F.

R. W. P. Drever, J. L. Hall, F. 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]

Kruger, C. H.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Maracas, G. N.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Martin, J.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Mazurenka, M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Meijer, G.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. 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]

Murtz, M.

D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
[CrossRef]

Norton, E. G.

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

O’Keefe, A.

A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 254-4-2551 (1988).

Orr-Ewing, A. J.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Owano, T. G.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Paldus, B. A.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

Petersen, I. R.

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

Povey, I. M.

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

Ransom, C. M.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Sayed Hassen, S. Z.

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. R. James, “Frequency locking of an optical cavity using linear quadratic Gaussian integral control,” J. Phys. B 42(17), 175501 (2009).
[CrossRef]

Schaff, W. J.

P. D. Kirchner, W. J. Schaff, G. N. Maracas, L. F. Eastman, T. I. Chappell, and C. M. Ransom, “The analysis of exponential and nonexponential transients in deep level transient spectroscopy,” J. Appl. Phys. 52, 6462–6470 (1981).
[CrossRef]

Shillings, A. J. L.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Spence, T. G.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

von Basum, G.

D. Halmer, G. von Basum, P. Hering, and M. Murtz, “Fast exponential fitting algorithm for real-time instrumental use,” Rev. Sci. Instrum. 75, 2187 (2004).
[CrossRef]

von Helden, G.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

Vyvenko, O. F.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 70(2), 1233–1257 (1999).
[CrossRef]

Wada, R.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Wahl, E. H.

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. 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]

Wilke, B.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

Xie, J.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

Zalicki, P.

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

Zare, R. N.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Wilke, and R. L. Byer, “A laser-locked cavity ring-down spectrometer employing an analog detection scheme,” Rev. Sci. Instrum. 71(2), 347–353 (2000).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, “Cavity-locked ring-down spectroscopy,” J. Appl. Phys. 83(8), 3991–3997 (1998)
[CrossRef]

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

Appl. Phys. B (1)

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, “Fast Fourier transform analysis in cavity ring-down spectroscopy: application to an optical detector for atmospheric NO2,” Appl. Phys. B 81, 135–141 (2005).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

R. W. P. Drever, J. L. Hall, F. 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]

Chem. Phys. Lett. (3)

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105–109 (1996).
[CrossRef]

S. M Ball, I. M. Povey, E. G. Norton, and R. L. Jones, “Broadband cavity ringdown spectroscopy of the NO3 radical,” Chem. Phys. Lett. 342, 113–120 (2001).
[CrossRef]

J. Xie, B. A. Paldus, E. H. Wahl, J. Martin, T. G. Owano, C. H. Kruger, J. S. Harris, and R. N. Zare, “Near-infrared cavity ringdown spectroscopy of water vapor in an atmospheric flame,” Chem. Phys. Lett. 284(5), 387–395 (1998).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Simulated 25 kHz squarewave and ringdown waveforms used to analyse and extract τ. The squarewave is the light before the cavity; the ringdown waveform is the light after passing through a cavity with a decay time of 5μs .

Fig. 2
Fig. 2

Normalized histograms of Tau for various lengths of the ringdown waveform using our frequency domain method, and for Levenburg-Marquardt fitting. A sample waveform, consisting of 10,000 ringups and ringdowns, with a SNR of 40 dB was synthesised. For our method, the data were trimmed into various lengths, analysed, and the set of answers used to construct the probability histogram. For LM, the ringups were discarded, the ringdowns fit in Matlab, and the probability histogram generated from the set of answers. In reality, for our method, we would analyse the 10,000 period-long waveform as a whole, giving a single answer. This figure shows how the precision of our method increases with the length of the input data. All data lengths have a similar accuracy to LM, but for any length longer than 2 periods, our method has higher precision.

Fig. 3
Fig. 3

Ringdown time vs. standard deviation for various numbers of periods analysed. This figure shows that our fourier method has a comparable precision and accuracy to LM fitting for all data lengths. The error bars represent one standard deviation.

Fig. 4
Fig. 4

Standard deviation vs. signal-to-noise for our fourier method, and for LM fitting.

Fig. 5
Fig. 5

Schematic diagram of laser-locked CRDS system. Abbreviations are as follows: ISO is the Faraday isolator; MMO are mode matching optics; HWP are half wave plates; EOM is the electro-optic modulator; AOM is the acousto-optic modulator; MOD1 is the RF generator and amplifier for phase modulation; MOD2 is the signal generator and amplifier used to generate the chopping waveform; M1 and M2 are beam steering mirrors; PCB is a polarizing cube beamsplitter; PD are photodetectors; QWP is a quarter wave plate; SERVO is the controller; HV AMP is a ±200V amplifier to drive PZT, the piezoelectric actuator that controls the cavity length.

Fig. 6
Fig. 6

25 kHz CW Ringdown waveform, taken from our spectrometer. These are the data that we have analysed using our method and LM fitting.

Fig. 7
Fig. 7

Normalized histograms of Tau from experimental data. 40 ms of data at a 25 kHz chopping frequency were captured from our spectrometer. For our method, the data were chopped into lengths of 2 and 5 periods of the ringdown waveform, and the solutions used to construct the probability histogram. For LM, the ringups were discarded, the ringdowns fit using the aforementioned procedure, and the histgram constructed. It can be seen that our method has a comparable (but slightly higher) precision to LM for a waveform of 2 periods, and a higher precision for 5 periods. This supports our findings in the simulations we have performed. We have only analysed up to 5 periods here, as any longer data length does not give enough solutions for τ to generate reliable statistics.

Equations (17)

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I ( t ) = α e ( t τ ) + b
τ = T r t ( ɛ ( λ ) c + n ( 1 R ) + A )
I ( t ) = α exp ( t τ )
F ( ω ) = 0 I ( t ) e j ω t d t
F ( ω ) = α τ τ ω j + 1
( F ( ω ) ) = α τ ω 2 τ 2 + 1
( F ( ω ) ) = ω α τ 2 ω 2 τ 2 + 1
( F ( ω ) ) = α τ ω 2 τ 2 + 1
( F ( a ω ) ) = α τ ( a ω ) 2 τ 2 + 1
( F ( ω ) ) ( F ( a ω ) ) = a 2 ω 2 τ 2 + 1 ω 2 τ 2 + 1
τ = 1 ω 1 P P a 2
s ( t ) = 4 π n = 1 , 3 , 5... 1 n sin ( n π t L )
τ = 1 ω 1 P P 9
F ( ω ) = n = 0 N 1 f [ n ] e ( 2 π j n k N ) , k = 0 , 1 , 2 , , N 1
F ( ω ) = n = 0 N 1 f [ n ] e ( 2 π j n N )
( ω ) = n = 0 N 1 f [ n ] cos ( 2 π n N )
( ω ) = n = 0 N 1 f [ n ] cos ( ω n )

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