## Amplitude and Phase Drift Correction of EFPI Sensor Systems Using Both Adaptive Kalman Filter and Temperature Compensation for Nanometric Displacement Estimation

Journal of Lightwave Technology, Vol. 30, Issue 13, pp. 2195-2202 (2012)

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### 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

**Citation**

P. Chawah, A. Sourice, G. Plantier, H. C. Seat, F. Boudin, J. Chéry, M. Cattoen, P. Bernard, C. Brunet, S. Gaffet, and D. Boyer, "Amplitude and Phase Drift Correction of EFPI Sensor Systems Using Both Adaptive Kalman Filter and Temperature Compensation for Nanometric Displacement Estimation," J. Lightwave Technol. **30**, 2195-2202 (2012)

http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-30-13-2195

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