Extrinsic Fabry-Perot interferometers (EFPIs) are widely used in fiber optic sensors. In many applications, the measurand is a mixture of static and dynamic signals. However, laser interference demodulation algorithms used for dynamic signal measurement are significantly different from white light interference demodulation algorithms used for static signal measurement. Laser interference demodulation algorithms require laser wavelengths to remain stable, while white light interference demodulation algorithms require wavelength scanning to obtain the spectrum of the sensor to achieve measurement. Therefore, these measurement techniques can only measure different dynamic signals or different static signals and cannot achieve measurement of static/dynamic composite signals. For EFPI sensors, it is expected to achieve the measurement of static/dynamic composite signals through high-speed white light interferometry demodulation technologies. However, these demodulation technologies are still unable to meet the measurement requirements of high-frequency signals due to limitations in scanning speed. Some high-speed white light interferometry demodulation technologies rely on high-tuning-speed laser sources, but the bandwidth of such light sources is narrow, which limits the measurement range. At the same time, this type of technology requires a large amount of calculations and sometimes requires offline signal processing. Various laser interference demodulation algorithms have been proposed to extract dynamic signals from EFPI sensors. However, these demodulation techniques will collapse if the EFPI cavity length changes significantly since the cavity length and laser wavelengths must be strictly matched to obtain orthogonal signals. In this article, a correction symmetrical demodulation method for the measurement of static/dynamic composite signals is proposed. Static/dynamic composite signal demodulation is experimentally demonstrated.

The change in sensor cavity length is judged by the direct current component of the output signal of the symmetrical demodulation method. Then, the output signal is divided into stable segments and abrupt segments. The measurand is then re-demodulated segment by segment to improve the demodulation accuracy of the dynamic component. Phase differences calculated before and after the abrupt segment are used to compensate for the change in cavity length, and the demodulation accuracy of static components is improved. The process of static/dynamic composite signal demodulation is as follows: 1) the preliminary demodulation signal d_f is recovered through Eq. (11). 2) the signal d_f is divided into stable segments and abrupt segments. 3) the phase difference δ for each stable segment is calculated. 4) the average value of δ before and after the abrupt segment is used as the phase difference of the abrupt segment to re-demodulate the signal. Eq. (4) is then used to calculate cavity lengths before and after the abrupt segment, and the cavity length change of the abrupt segment is calibrated. 5) the measurand of each stable segment is re-demodulated and combined with the calibrated abrupt segment demodulation signals to obtain the complete output signal d_s.

Static/dynamic composite signals can be demodulated by the proposed demodulation method, which is experimentally demonstrated, as shown in Fig. 4. The cavity length change of the c-sym in Fig. 4(a) is 50.86 μm, which is consistent with the cavity length change measured by the white light interference demodulation algorithm. The measurement error of the static component is 2.07%. Figures 4 (b)-(e) show that the dynamic component of the c-sym remains consistent despite the cavity length changes significantly. The peak-to-peak amplitudes are 408.33 nm, 407.58 nm, and 402.17 nm. The amplitude variation is 1.53%. The power spectrum of the dynamic component of the c-sym is plotted in Fig. 5. The frequency is 100 Hz, which is consistent with the frequency of the input signal. The proposed demodulation method can be performed normally even if the cavity length changes up to 100 μm, as shown in Fig. 6. The frequency range of the proposed demodulation method is consistent with that of the symmetrical demodulation method and is not limited by the demodulation principle. The frequency range of the demodulator is only limited by the sampling frequency of the analog-to-digital converter and the bandwidth of electronic devices such as photodiodes. The analog-to-digital converter of the demodulator has a sampling frequency of 200 kHz. According to the Nyquist sampling theorem, the maximum frequency of the signal which the demodulator can demodulate is 100 kHz.

In conclusion, a correction symmetrical demodulation method for the measurement of static/dynamic composite signals is proposed. The demodulation capability of the demodulator to static/dynamic composite signals is experimentally investigated. The measurement of a cavity length change with an amplitude of 100 μm is achieved. The measurement error is about 2% for large changes in cavity length. The technique is applicable to static/dynamic composite signals applied on sensors with different cavity lengths.