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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6377–6386

Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity

Abhijit G. Kallapur, Toby K. Boyson, Ian R. Petersen, and Charles C. Harb  »View Author Affiliations

Optics Express, Vol. 19, Issue 7, pp. 6377-6386 (2011)

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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

OCIS Codes
(050.2230) Diffraction and gratings : Fabry-Perot
(200.3050) Optics in computing : Information processing
(300.6360) Spectroscopy : Spectroscopy, laser

ToC Category:

Original Manuscript: February 2, 2011
Revised Manuscript: March 3, 2011
Manuscript Accepted: March 7, 2011
Published: March 21, 2011

Abhijit G. Kallapur, Toby K. Boyson, Ian R. Petersen, and Charles C. Harb, "Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity," Opt. Express 19, 6377-6386 (2011)

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  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]

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