A fast real-time demodulation method based on the coarsely sampled spectrum is proposed for transient signals of fiber optic extrinsic Fabry-Perot interferometers (EFPI) sensors. The feasibility of phase demodulation using a coarse spectrum is theoretically analyzed. Based on the coarse spectrum, fast Fourier transform (FFT) algorithm is used to roughly estimate the cavity length. According to the rough estimation, the maximum likelihood estimation (MLE) algorithm is applied to calculate the cavity length accurately. The dense wavelength division multiplexer (DWDM) is used to split the broadband spectrum into the coarse spectrum, and the high-speed synchronous ADC collects the spectrum. The experimental results show that the system can achieve a real-time dynamic demodulation speed of 50 kHz, a static measurement root mean square error (RMSE) of 0.184 nm, and a maximum absolute and relative error distribution of 15 nm and 0.005% of the measurement cavity length compared with optical spectrum analyzers (OSA).

When the signal-to-noise ratio (SNR) of an optical fiber sensor is lower than a specific value, jump errors will appear in the maximum-likelihood-estimation (MLE) algorithm. This research proposes a quantitative calculation method based on the MLE algorithm. This method can calculate the probability of jump errors by different SNRs. The SNR threshold can also be obtained in the MLE algorithm for the low-finesse interference spectrum. From the simulation, we find that when the SNR varies from 0 dB to 25 dB, the possibility of jump errors decreases exponentially. Subsequent experiments also verify the correctness of the simulation results.

To improve the precision of dynamic distance measurement based on the frequency-swept interferometry (FSI) system, a Doppler-induced error compensation model based on a scheme increasing the frequency sweeping rate is proposed. A distance demodulation method based on a Fourier transformation is investigated when the defined quasi-stationary coefficient approaches a constant. Simulations and experiments based on dynamic distance with a sinusoidal change demonstrate that the proposed method has a standard deviation of 0.09 μm within a distance range of 4 μm at a sweeping rate of 60 KHz.

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