Abstract

This paper discusses the application of a discrete-time extended Kalman filter (EKF) to the problem of estimating the decay time constant for a Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The data for the estimation process is obtained from a CRDS experimental setup in terms of the light intensity at the output of the cavity. The cavity is held in lock with the input laser frequency by controlling the distance between the mirrors within the cavity by means of a proportional-integral (PI) controller. The cavity is purged with nitrogen and placed under vacuum before chopping the incident light at 25KHz and recording the light intensity at its output. In spite of beginning the EKF estimation process with uncertainties in the initial value for the decay time constant, its estimates converge well within a small neighborhood of the expected value for the decay time constant of the cavity within a few ring-down cycles. Also, the EKF estimation results for the decay time constant are compared to those obtained using the Levenberg-Marquardt estimation scheme.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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, 2544–2551 (1988).
    [CrossRef]
  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, 3991–3997 (1998).
    [CrossRef]
  3. K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy. An Ultratrace-Absorption Measurement Technique, vol. 720 of ACS Symposium Series (American Chemical Society, Washington, DC, 1999).
    [CrossRef] [PubMed]
  4. T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
    [CrossRef]
  5. 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, 387–395 (1998).
    [CrossRef]
  6. A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 701233 (1999).
    [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: Lasers Opt. 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, 023108–023108–9 (2008).
    [CrossRef] [PubMed]
  9. C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications , Theoretical, Mathematical & Computational Physics (Springer-Verlag, Berlin, Heidelberg, Germany, 2009), 4th ed.
  10. A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in “IEEE International Conference on Control Applications (CCA) ,” (Yokohama, Japan, 2010), pp. 298–303.
  11. S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.
  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: At. Mol. Opt. Phys. 42, 175501 (2009).
    [CrossRef]
  13. S. Z. Sayed Hassen and I. R. Petersen, “A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity,” in “American Control Conference ,” (Baltimore, MD, USA, 2010), pp. 2736–2741.
  14. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, Germany, 2000).
  15. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, Germany, 2004), 2nd ed.
    [CrossRef]
  16. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
    [CrossRef]

2009

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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

2008

M. A. Everest and D. B. Atkinson, “Discrete Sums for the Rapid Determination of Exponential Decay Constants,” Rev. Sci. Instrum. 79, 023108–023108–9 (2008).
[CrossRef] [PubMed]

2005

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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

2000

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

1999

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 701233 (1999).
[CrossRef]

1998

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, 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, 3991–3997 (1998).
[CrossRef]

1988

A. O’Keefe and D. A. G. Deacon, “Cavity Ring-Down Optical Spectrometer for Absorption Measurements using Pulsed Laser Sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[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, 023108–023108–9 (2008).
[CrossRef] [PubMed]

Bachor, H. A.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, Germany, 2004), 2nd ed.
[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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

Busch, K. W.

K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy. An Ultratrace-Absorption Measurement Technique, vol. 720 of ACS Symposium Series (American Chemical Society, Washington, DC, 1999).
[CrossRef] [PubMed]

Busch, M. A.

K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy. An Ultratrace-Absorption Measurement Technique, vol. 720 of ACS Symposium Series (American Chemical Society, Washington, DC, 1999).
[CrossRef] [PubMed]

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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

Byer, R. L.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

Chen, G.

C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications , Theoretical, Mathematical & Computational Physics (Springer-Verlag, Berlin, Heidelberg, Germany, 2009), 4th ed.

Chui, C. K.

C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications , Theoretical, Mathematical & Computational Physics (Springer-Verlag, Berlin, Heidelberg, Germany, 2009), 4th ed.

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, 2544–2551 (1988).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[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, 023108–023108–9 (2008).
[CrossRef] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, Germany, 2000).

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Harb, C. C.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 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, 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, 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, 387–395 (1998).
[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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Huntington, E.

S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.

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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

Istratov, A. A.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 701233 (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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 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, 387–395 (1998).
[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, 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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[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, 2544–2551 (1988).
[CrossRef]

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: Lasers Opt. 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, 387–395 (1998).
[CrossRef]

Paldus, B. A.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 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, 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, 387–395 (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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.

S. Z. Sayed Hassen and I. R. Petersen, “A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity,” in “American Control Conference ,” (Baltimore, MD, USA, 2010), pp. 2736–2741.

Ralph, T. C.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, Germany, 2004), 2nd ed.
[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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.

S. Z. Sayed Hassen and I. R. Petersen, “A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity,” in “American Control Conference ,” (Baltimore, MD, USA, 2010), pp. 2736–2741.

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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

Spence, T. G.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 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, 3991–3997 (1998).
[CrossRef]

Vyvenko, O. F.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 701233 (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: Lasers Opt. 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, 387–395 (1998).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Wilke, B.

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, 3991–3997 (1998).
[CrossRef]

Willke, B.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[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, 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, 387–395 (1998).
[CrossRef]

Zare, R. N.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 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, 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, 387–395 (1998).
[CrossRef]

Zoller, P.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, Germany, 2000).

Appl. Phys. B: Lasers Opt.

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: Lasers Opt. 81, 135–141 (2005).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization using an Optical Resonator,” Appl. Phys. B: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Chem. Phys. Lett.

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, 387–395 (1998).
[CrossRef]

J. Appl. Phys.

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, 3991–3997 (1998).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys.

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: At. Mol. Opt. Phys. 42, 175501 (2009).
[CrossRef]

Rev. Sci. Instrum.

A. A. Istratov and O. F. Vyvenko, “Exponential analysis in physical phenomena,” Rev. Sci. Instrum. 701233 (1999).
[CrossRef]

A. O’Keefe and D. A. G. Deacon, “Cavity Ring-Down Optical Spectrometer for Absorption Measurements using Pulsed Laser Sources,” Rev. Sci. Instrum. 59, 2544–2551 (1988).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, “A Laser-Locked Cavity Ring-DOWN Spectrometer Employing an Analog Detection Scheme,” Rev. Sci. Instrum. 71, 347–353 (2000).
[CrossRef]

M. A. Everest and D. B. Atkinson, “Discrete Sums for the Rapid Determination of Exponential Decay Constants,” Rev. Sci. Instrum. 79, 023108–023108–9 (2008).
[CrossRef] [PubMed]

Other

C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications , Theoretical, Mathematical & Computational Physics (Springer-Verlag, Berlin, Heidelberg, Germany, 2009), 4th ed.

A. G. Kallapur, I. R. Petersen, T. K. Boyson, and C. C. Harb, “Nonlinear Estimation of a Fabry-Perot Optical Cavity for Cavity Ring-Down Spectroscopy,” in “IEEE International Conference on Control Applications (CCA) ,” (Yokohama, Japan, 2010), pp. 298–303.

S. Z. Sayed Hassen, E. Huntington, I. R. Petersen, and M. R. James, “Frequency Locking of an Optical Cavity Using LQG Integral Control,” in “17th IFAC World Congress ,” (Seoul, South-Korea, 2008), pp. 1821–1826.

K. W. Busch and M. A. Busch, Cavity-Ringdown Spectroscopy. An Ultratrace-Absorption Measurement Technique, vol. 720 of ACS Symposium Series (American Chemical Society, Washington, DC, 1999).
[CrossRef] [PubMed]

S. Z. Sayed Hassen and I. R. Petersen, “A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity,” in “American Control Conference ,” (Baltimore, MD, USA, 2010), pp. 2736–2741.

C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, Germany, 2000).

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, Germany, 2004), 2nd ed.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Proposed CRDS setup with an EKF estimator and a controller.

Fig. 2
Fig. 2

Block diagram of CRDS experimental setup: The red and green lines represent optical signal paths whereas the blue line represents the path for electronic signals. Also, 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. 3
Fig. 3

Sample light intensity data obtained at the output of the cavity.

Fig. 4
Fig. 4

A comparison of EKF and LM estimation results for τ at the end of each ring-down cycle, plotted against the expected true value for τ.

Equations (26)

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

I ( t ) = I 0 exp ( t τ ) ,
τ = t rt c ε ( λ ) + n ( 1 R ) + α ,
a ˙ = ( γ 2 + i Δ ) a γ m ( a ¯ in + w ) ,
y = γ m a a + v .
q = a + a ; p = a a i
q ˙ = a ˙ + a ˙ ; p ˙ = a ˙ a ˙ i .
q ˙ = γ 2 ( a + a ) i Δ ( a a ) 2 γ m a ¯ in γ m ( w + w ) , = γ 2 q + Δ p 2 γ m a ¯ in γ m w q ,
p ˙ = γ 2 ( a a i ) Δ ( a + a ) γ m ( w w i ) , = γ 2 p Δ q γ m w p ,
[ q ˙ ( t ) p ˙ ( t ) ] = [ γ / 2 Δ Δ γ / 2 ] [ q ( t ) p ( t ) ] γ m [ 1 1 0 0 0 1 ] [ 2 a ¯ in w q ( t ) w p ( t ) ]
x ¯ ( t ) = A c x ¯ ( t ) + B c u ¯ ( t ) + D c w ¯ ( t ) ,
y ( t ) = h ( x ( t ) ) + v ( t ) ,
x k = f ( x k , u k ) + w k ,
y k + 1 = h ( x k + 1 ) + v k + 1 ,
x k + 1 = f ( x k + , u k )
P k + 1 = F k P k + F k T + Q δ .
K k + 1 = P k + 1 H k + 1 T ( H k + 1 P k + 1 H k + 1 T + R ) 1 ,
x k + 1 + = x k + 1 + K k + 1 ( y k + 1 h ( x k + 1 ) ) ,
P k + 1 + = I K k + 1 H k + 1 P k + 1 .
F k = f ( x , u ) x | x = x k + ; H k + 1 = h ( x ) x | x = x k + 1 .
x ˙ ( t ) = A ˜ c x ( t ) + B ˜ c u ( t ) + D ˜ c ( t ) w ( t ) , = [ γ ( t ) / 2 Δ ( t ) 0 Δ ( t ) γ ( t ) / 2 0 0 0 0 ] [ q ( t ) p ( t ) γ ( t ) ] + [ γ m 0 0 ] 2 a ¯ in + γ m [ 1 0 0 1 0 0 ] [ w q ( t ) w p ( t ) 0 ]
f ( x k , u k ) = A d x k + B d u k ,
A d = e [ A ˜ c · δ ] ; B d = 0 δ { e [ A ˜ c · δ ] d s · B ˜ c }
D d = 0 δ { e [ A ˜ c · δ ] d s · D ˜ c }
y k + 1 = h ( x k + 1 ) + v k + 1 = γ m 4 ( q k + 1 2 + q k + 1 2 ) + v k + 1 .
Q = [ 0.171 × 10 12 0 0 0 0.171 × 10 12 0 0 0 0 ] ; R = 2 × 10 10 .
P 0 = [ 0.171 × 10 12 0 0 0 0.171 × 10 12 0 0 0 10 9 ] .

Metrics