An Accurate Demodulation Method for Fiber-Optic Interferometric Sensors Based on the Expanded Free Spectral Range

We propose and demonstrate an accurate demodulation method for fiber-optic interferometric sensors (FOISs) by utilizing an expanded free spectral range (EFSR). Unlike conventional demodulation schemes, this method selects a pair of resonant wavelengths (peaks or dips) with an interval of multiple free spectral ranges (FSRs) to determine the optical path difference (OPD) of the FOIS. This demodulation method significantly improves the measurement accuracy of the FOIS while maintaining a fast processing speed. The feasibility of the proposed method is experimentally demonstrated by our recently developed fiber-optic piezometer using a 178- $\mu \text{m}$ -gap air extrinsic Fabry-Perot interferometer (EFPI). Liquid level measurement in the range of 0-90 cm with a step of 15 cm is conducted with this method, and the experimental results demonstrate improved performance in terms of linearity, standard error (SE), and resolution. The measurement resolution increases significantly from 8.57 to 1.48 cm when the EFSR orders vary from 1, 4, 8, 12, 16, to 20. To further validate the proposed method, the measurement in the range of 0-24 cm with a step of 4 cm is performed for comparison, and the resolution is exponentially improved from a failed state to as high as 0.41 cm. Furthermore, five sets of historical data are chosen to establish regression models, and the results are consistent with the rest 14 sets of measured data. The proposed demodulation method is precise, rapid, and versatile, which would be useful in the further development and application of FOISs.