Abstract

This Letter presents offline estimation results for the decay-time constant for an experimental Fabry–Perot optical cavity for cavity ring-down spectroscopy (CRDS). The cavity dynamics are modeled in terms of a low pass filter (LPF) with unity DC gain. This model is used by an extended Kalman filter (EKF) along with the recorded light intensity at the output of the cavity in order to estimate the decay-time constant. The estimation results using the LPF cavity model are compared to those obtained using the quadrature model for the cavity presented in previous work by Kallapur et al. The estimation process derived using the LPF model comprises two states as opposed to three states in the quadrature model. When considering the EKF, this means propagating two states and a (2×2) covariance matrix using the LPF model, as opposed to propagating three states and a (3×3) covariance matrix using the quadrature model. This gives the former model a computational advantage over the latter and leads to faster execution times for the corresponding EKF. It is shown in this Letter that the LPF model for the cavity with two filter states is computationally more efficient, converges faster, and is hence a more suitable method than the three-state quadrature model presented in previous work for real-time estimation of the decay-time constant for the cavity.

© 2012 Optical Society of America

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2011 (1)

2008 (1)

M. A. Everest and D. B. Atkinson, Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef]

2005 (1)

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

2000 (1)

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

1999 (1)

A. A. Istratov and O. F. Vyvenko, Rev. Sci. Instrum. 70, 1233 (1999).
[CrossRef]

1998 (1)

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

1996 (1)

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

1988 (1)

A. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

1980 (1)

Atkinson, D. B.

M. A. Everest and D. B. Atkinson, Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef]

Bachor, H. A.

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

Bar-Shalom, Y.

Y. Bar-Shalom and X. Li, Estimation and Tracking: Principles, Techniques, and Software (Artech House, 1993).

Beames, J. M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Benard, D. J.

Berden, G.

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Boyson, T. K.

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, Opt. Express 19, 6377 (2011).
[CrossRef]

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, in IEEE International Conference on Control Applications (CCA) (IEEE, 2011), p. 556.

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, 1999).

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, 1999).

Butler, T. J. A.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Byer, R. L.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Engeln, R.

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Everest, M. A.

M. A. Everest and D. B. Atkinson, Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef]

Gardiner, C. W.

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

Harb, C. C.

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, Opt. Express 19, 6377 (2011).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, in IEEE International Conference on Control Applications (CCA) (IEEE, 2011), p. 556.

Harris, J. S.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Helden, G. V.

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

Herbelin, J. M.

Istratov, A. A.

A. A. Istratov and O. F. Vyvenko, Rev. Sci. Instrum. 70, 1233 (1999).
[CrossRef]

Kallapur, A. G.

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, Opt. Express 19, 6377 (2011).
[CrossRef]

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, in IEEE International Conference on Control Applications (CCA) (IEEE, 2011), p. 556.

Kwok, M. A.

Li, X.

Y. Bar-Shalom and X. Li, Estimation and Tracking: Principles, Techniques, and Software (Artech House, 1993).

Mazurenka, M.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

McKay, J. A.

Meijer, G.

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

O’Keefe, A.

A. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 (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, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Paldus, B. A.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Petersen, I. R.

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, Opt. Express 19, 6377 (2011).
[CrossRef]

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, in IEEE International Conference on Control Applications (CCA) (IEEE, 2011), p. 556.

Ralph, T. C.

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

Shillings, A. J. L.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Spence, T. G.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Spencer, D. J.

Ueunten, R. H.

Urevig, D. S.

Vyvenko, O. F.

A. A. Istratov and O. F. Vyvenko, Rev. Sci. Instrum. 70, 1233 (1999).
[CrossRef]

Wada, R.

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Wilke, B.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Willke, B.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

Xie, J.

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Zare, R. N.

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Zoller, P.

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

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (1)

M. Mazurenka, R. Wada, A. J. L. Shillings, T. J. A. Butler, J. M. Beames, and A. J. Orr-Ewing, Appl. Phys. B: Lasers Opt. 81, 135 (2005).
[CrossRef]

Chem. Phys. Lett. (1)

R. Engeln, G. V. Helden, G. Berden, and G. Meijer, Chem. Phys. Lett. 262, 105 (1996).
[CrossRef]

J. Appl. Phys. (1)

B. A. Paldus, C. C. Harb, T. G. Spence, B. Wilke, J. Xie, J. S. Harris, and R. N. Zare, J. Appl. Phys. 83, 3991 (1998).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (4)

M. A. Everest and D. B. Atkinson, Rev. Sci. Instrum. 79, 023108 (2008).
[CrossRef]

T. G. Spence, C. C. Harb, B. A. Paldus, R. N. Zare, B. Willke, and R. L. Byer, Rev. Sci. Instrum. 71, 347 (2000).
[CrossRef]

A. A. Istratov and O. F. Vyvenko, Rev. Sci. Instrum. 70, 1233 (1999).
[CrossRef]

A. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Other (5)

Y. Bar-Shalom and X. Li, Estimation and Tracking: Principles, Techniques, and Software (Artech House, 1993).

A. G. Kallapur, T. K. Boyson, I. R. Petersen, and C. C. Harb, in IEEE International Conference on Control Applications (CCA) (IEEE, 2011), p. 556.

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

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

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

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Figures (1)

Fig. 1.
Fig. 1.

Comparison of EKF estimation result for τ: quadrature model in [7,8] versus LPF model for the cavity.

Tables (1)

Tables Icon

Table 1. Comparison of Average EKF Execution Times From 1000 MC Runs

Equations (21)

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

I(t)=I0exp(t/τ),
a˙=(γ2+iΔ)aγm(a¯in+w);y=γmaa+v.
G(s)=γ/(s+γ),
x˙(t)=γx(t)+u(t)+w(t),
y(t)=γx(t)+v(t),
[x˙1(t)x˙2(t)]=[x2(t)000][x1(t)x2(t)]+[10]u(t)+[w1(t)w2(t)],
y(t)=x1(t)x2(t)+v(t).
x˙(t)=fc(x(t),u(t))+Dcw(t),
y(t)=h(x(t))+v(t).
xk=f(xk,uk)+Ddwk,
yk+1=h(xk+1)+vk+1.
yk+1=h(xk+1)+vk+1=x1k+1x2k+1+vk+1.
xk+1=f(xk+,uk),
Pk+1=FkPk+FkT+Qδ.
Kk+1=Pk+1Hk+1T(Hk+1Pk+1Hk+1T+R)1,
xk+1+=xk+1+Kk+1(yk+1h(xk+1)),
Pk+1+=IKk+1Hk+1Pk+1.
Fk=f(x,u)x|x=xk+;Hk+1=h(x)x|x=xk+1.
Q=[9.98×1017000];R=108;P0=[9.98×101700105];x0=[01.9×104].
f(x,u)x=[x2(t)x1(t)00],
h(x)x=[x2(t)x1(t)].

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