Abstract

Nanometric displacement measurements by Extrinsic Fiber Fabry-Perot interferometers (EFPI) is extremely susceptible to external environmental changes. Temperature, in particular, has a remarkable influence on the optical power and wavelength of the laser diode in use, in addition to the thermal expansion of the mechanical structure. In this paper we propose an optimization of the EFPI sensor in order to use it for very long-term (more than one year) and for high-precision displacement measurements. For this purpose, a real time and adaptive estimation procedure based on a homodyne technique and a Kalman filter is established. During a sinusoidal laser diode current modulation, the Kalman filter provides a correction of the amplitude drift caused by the resultant optical power modulation and external perturbations. Besides, stationary temperature transfer operators are estimated via experimental measurements to reduce the additive thermal noise induced in the optical phase and mechanical components. The tracking algorithm is presented while the complete sensor system integrating the novel Kalman filter and the demodulation scheme have been programmed on an FPGA board for real time processing. Short time experimental results demonstrate an estimation error of 2 nm over a 7000 nm sinusoidal displacement while temperature correction of long-term records reduces errors by considerable factors (above 10).

© 2012 IEEE

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  1. C. K. Kirkendall, A. Dandridge, "Overview of high performance fiber-optic sensing," J. Phys. D: Appl. Phys. 37, R197-R216 (2004).
  2. T. R. Christian, Ph. A. Frank, B. H. Houston, "Real-time analog and digital demodulator for interferometric fiber optic sensors," Proc.Smart Structures and Materials 1994: Smart Sensing, Processing, and Instrumentation (1994) pp. 94-102.
  3. H. C. Seat, S. Pullteap, "An extrinsic fiber Fabry-Perot interferometer for dynamic displacement measurement," Proc. IEEE-ICMA (2007) pp. 3027-3032.
  4. X. Zhou, Q. Yu, "Wide-Range displacement sensor based on fiber-optic Fabry-Perot interferometer for subnanometer measurement," IEEE Sens. J. 11, 1602-1606 (2011).
  5. A. M. Abdi, S. E. Watkins, "Demodulation of fiber-optic sensors for frequency response measurement," IEEE Sens. J. 7, 667-675 (2007).
  6. M. A. Zumberge, J. Berger, M. A. Dzieciuch, R. L. Parker, "Resolving quadrature fringes in real time," Appl. Opt. 43, 771-775 (2004).
  7. A. Dandridge, A. Tveten, T. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. 18, 1647-1653 (1982).
  8. P. Chawah, A. Sourice, G. Plantier, J. Chéry, "Real time and adaptive Kalman filter for joint nanometric displacement estimation, parameters tracking and drift correction of EFFPI sensor systems," Proc. IEEE Sens. Conf. (2011) pp. 882-885.
  9. Z. Li, X. Wang, P. Bu, B. Huang, D. Zheng, "Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source," Optik—Int. J. Light Electron Optics 120, 799-803 (2009).
  10. O. Loffeld, "Demodulation of noisy phase or frequency modulated signals with Kalman filters," Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process. (1994) pp. IV/177-IV/180.
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  12. F. Dufrenois, "Ellipse fitting with uncertainty and fuzzy decision stage for detection. Application in videomicroscopy," Symbolic Quantitative Approaches to Reasoning Uncertainty 432-443 (2001).
  13. J. Cabrera, P. Meer, "Unbiased estimation of ellipses by bootstrapping," IEEE Trans. Pattern Anal. Mach. Intell. 18, 752-756 (1996).
  14. R. Halir, J. Flusser, "Numerically stable direct least squares fitting of ellipses," Int. Conf. Central Eur. Computer Graphics Visualisation (1998) pp. 125-132.
  15. T. Ellis, A. Abbood, B. Brillault, "Ellipse detection and matching with uncertainty," J. Image Vis. Comp. 10, 271-276 (1992).
  16. Z. Zhang, "Parameter estimation techniques: A tutorial with application to conic fitting," Image Vis. Comput. 15, 59-76 (1997).
  17. P. L. Rosin, "A note on the least squares fitting of ellipses," Pattern Recognit. Lett. 14, 799-808 (1993).
  18. D. L. Boley, K. T. Sutherland, “Recursive Total Least Squares: An Alternative to the Discrete Kalman Filter,” Tech. Rep. Dept. Comp. Sci. Univ. Minnesota (1993).
  19. P. L. Rosin, G. A. W. West, "Segmenting curves into elliptic arcs and straight lines," Proc. 3rd Int. Conf. Comput. Vis. (1990) pp. 75-78.
  20. J. Porill, "Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter," Image Vis. Comput. 8, 37-41 (1990).
  21. B. Matei, P. Meer, "Reduction of bias in maximum likelihood ellipse fitting," Proc. Int. Conf. Pattern Recognition (2000) pp. 3802-3806.
  22. Y. Kanazawa, K. Kanatani, "Optimal conic fitting and reliability evaluation," IEICE Trans. Inf. Syst. E79-D, 1323-1328 (1996).
  23. N. Werghi, C. Doignon, G. Abba, "Ellipse fitting and three-dimensional localization of objects based on elliptic features," Proc. ICIP 1, 57-60 (1996).
  24. N. Werghi, C. Doignon, G. Abba, "Contour feature extraction with Wavelet transform and parametrization of elliptic curves with an unbiased extended Kalman filter," Proc. ACCV95 (1995) pp. 186-190.
  25. S. Haykin, Adaptive Filter Theory (Prentice-Hall, 1991) pp. 244-266.

2011 (1)

X. Zhou, Q. Yu, "Wide-Range displacement sensor based on fiber-optic Fabry-Perot interferometer for subnanometer measurement," IEEE Sens. J. 11, 1602-1606 (2011).

2009 (1)

Z. Li, X. Wang, P. Bu, B. Huang, D. Zheng, "Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source," Optik—Int. J. Light Electron Optics 120, 799-803 (2009).

2007 (1)

A. M. Abdi, S. E. Watkins, "Demodulation of fiber-optic sensors for frequency response measurement," IEEE Sens. J. 7, 667-675 (2007).

2004 (2)

M. A. Zumberge, J. Berger, M. A. Dzieciuch, R. L. Parker, "Resolving quadrature fringes in real time," Appl. Opt. 43, 771-775 (2004).

C. K. Kirkendall, A. Dandridge, "Overview of high performance fiber-optic sensing," J. Phys. D: Appl. Phys. 37, R197-R216 (2004).

2001 (1)

F. Dufrenois, "Ellipse fitting with uncertainty and fuzzy decision stage for detection. Application in videomicroscopy," Symbolic Quantitative Approaches to Reasoning Uncertainty 432-443 (2001).

1998 (1)

D. L. Boley, K. T. Sutherland, "A rapidly converging recursive method for mobile robot localization," Int. J. Robotic Res. 17, 1027-1039 (1998).

1997 (1)

Z. Zhang, "Parameter estimation techniques: A tutorial with application to conic fitting," Image Vis. Comput. 15, 59-76 (1997).

1996 (3)

Y. Kanazawa, K. Kanatani, "Optimal conic fitting and reliability evaluation," IEICE Trans. Inf. Syst. E79-D, 1323-1328 (1996).

N. Werghi, C. Doignon, G. Abba, "Ellipse fitting and three-dimensional localization of objects based on elliptic features," Proc. ICIP 1, 57-60 (1996).

J. Cabrera, P. Meer, "Unbiased estimation of ellipses by bootstrapping," IEEE Trans. Pattern Anal. Mach. Intell. 18, 752-756 (1996).

1993 (1)

P. L. Rosin, "A note on the least squares fitting of ellipses," Pattern Recognit. Lett. 14, 799-808 (1993).

1992 (1)

T. Ellis, A. Abbood, B. Brillault, "Ellipse detection and matching with uncertainty," J. Image Vis. Comp. 10, 271-276 (1992).

1990 (1)

J. Porill, "Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter," Image Vis. Comput. 8, 37-41 (1990).

1982 (1)

A. Dandridge, A. Tveten, T. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. 18, 1647-1653 (1982).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Dandridge, A. Tveten, T. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. 18, 1647-1653 (1982).

IEEE Sens. J. (1)

A. M. Abdi, S. E. Watkins, "Demodulation of fiber-optic sensors for frequency response measurement," IEEE Sens. J. 7, 667-675 (2007).

IEEE Sens. J. (1)

X. Zhou, Q. Yu, "Wide-Range displacement sensor based on fiber-optic Fabry-Perot interferometer for subnanometer measurement," IEEE Sens. J. 11, 1602-1606 (2011).

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Cabrera, P. Meer, "Unbiased estimation of ellipses by bootstrapping," IEEE Trans. Pattern Anal. Mach. Intell. 18, 752-756 (1996).

IEICE Trans. Inf. Syst. (1)

Y. Kanazawa, K. Kanatani, "Optimal conic fitting and reliability evaluation," IEICE Trans. Inf. Syst. E79-D, 1323-1328 (1996).

Image Vis. Comput. (1)

Z. Zhang, "Parameter estimation techniques: A tutorial with application to conic fitting," Image Vis. Comput. 15, 59-76 (1997).

Image Vis. Comput. (1)

J. Porill, "Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter," Image Vis. Comput. 8, 37-41 (1990).

Int. J. Robotic Res. (1)

D. L. Boley, K. T. Sutherland, "A rapidly converging recursive method for mobile robot localization," Int. J. Robotic Res. 17, 1027-1039 (1998).

J. Image Vis. Comp. (1)

T. Ellis, A. Abbood, B. Brillault, "Ellipse detection and matching with uncertainty," J. Image Vis. Comp. 10, 271-276 (1992).

J. Phys. D: Appl. Phys. (1)

C. K. Kirkendall, A. Dandridge, "Overview of high performance fiber-optic sensing," J. Phys. D: Appl. Phys. 37, R197-R216 (2004).

Optik—Int. J. Light Electron Optics (1)

Z. Li, X. Wang, P. Bu, B. Huang, D. Zheng, "Sinusoidal phase-modulating laser diode interferometer insensitive to the intensity modulation of the light source," Optik—Int. J. Light Electron Optics 120, 799-803 (2009).

Pattern Recognit. Lett. (1)

P. L. Rosin, "A note on the least squares fitting of ellipses," Pattern Recognit. Lett. 14, 799-808 (1993).

Proc. ICIP (1)

N. Werghi, C. Doignon, G. Abba, "Ellipse fitting and three-dimensional localization of objects based on elliptic features," Proc. ICIP 1, 57-60 (1996).

Symbolic Quantitative Approaches to Reasoning Uncertainty (1)

F. Dufrenois, "Ellipse fitting with uncertainty and fuzzy decision stage for detection. Application in videomicroscopy," Symbolic Quantitative Approaches to Reasoning Uncertainty 432-443 (2001).

Other (10)

R. Halir, J. Flusser, "Numerically stable direct least squares fitting of ellipses," Int. Conf. Central Eur. Computer Graphics Visualisation (1998) pp. 125-132.

O. Loffeld, "Demodulation of noisy phase or frequency modulated signals with Kalman filters," Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process. (1994) pp. IV/177-IV/180.

P. Chawah, A. Sourice, G. Plantier, J. Chéry, "Real time and adaptive Kalman filter for joint nanometric displacement estimation, parameters tracking and drift correction of EFFPI sensor systems," Proc. IEEE Sens. Conf. (2011) pp. 882-885.

N. Werghi, C. Doignon, G. Abba, "Contour feature extraction with Wavelet transform and parametrization of elliptic curves with an unbiased extended Kalman filter," Proc. ACCV95 (1995) pp. 186-190.

S. Haykin, Adaptive Filter Theory (Prentice-Hall, 1991) pp. 244-266.

D. L. Boley, K. T. Sutherland, “Recursive Total Least Squares: An Alternative to the Discrete Kalman Filter,” Tech. Rep. Dept. Comp. Sci. Univ. Minnesota (1993).

P. L. Rosin, G. A. W. West, "Segmenting curves into elliptic arcs and straight lines," Proc. 3rd Int. Conf. Comput. Vis. (1990) pp. 75-78.

T. R. Christian, Ph. A. Frank, B. H. Houston, "Real-time analog and digital demodulator for interferometric fiber optic sensors," Proc.Smart Structures and Materials 1994: Smart Sensing, Processing, and Instrumentation (1994) pp. 94-102.

H. C. Seat, S. Pullteap, "An extrinsic fiber Fabry-Perot interferometer for dynamic displacement measurement," Proc. IEEE-ICMA (2007) pp. 3027-3032.

B. Matei, P. Meer, "Reduction of bias in maximum likelihood ellipse fitting," Proc. Int. Conf. Pattern Recognition (2000) pp. 3802-3806.

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