Medium-fineness fiber optic Fabry?Perot (F-P) sensors possess greater reflected light intensity compared with low-fineness ones, which effectively improves the utilization of optical energy. In contrast to high-fineness fiber optic F-P sensors, their fabrication process reduces the requirement for optical path alignment, facilitating large-scale production. White light interferometry technology is highly prone to noise during the signal recovery process, making it difficult to maintain stable demodulation accuracy in complex environments, thus restricting its application in the field of medium-fineness fiber optic F-P sensors. In recent years, to enhance the accuracy and reliability of white light interferometric signal demodulation, many scholars have been dedicated to exploring effective signal extraction and noise suppression techniques. However, research on additive noise caused by quantization processing and other factors in fast Fourier transform (FFT) signal demodulation methods based on white light interferometry is still insufficient, posing a greater challenge to the signal detection performance and noise stability of medium-fineness fiber optic F-P sensors.

To address the issue of significant demodulation noise resulting from non-integer period sampling in the FFT signal demodulation method based on white light interferometry technology, we analyze the principles of the FFT demodulation method for medium-fineness fiber optic F-P sensors. We build a phase change model induced by additive noise, focusing on the variations of two key parameters, the light intensity coefficient ratio (fineness) and the initial phase. We study the mechanisms affecting the stability of demodulation noise in medium-fineness fiber optic F-P sensors. We propose an improved FFT signal demodulation method based on white light interferometry technology. By integrating the phase changes of multiple eigen-peaks and optimizing the weighted average, different weights are selected to achieve the best suppression effect on additive noise. The weighted average operation does not influence the demodulation phase caused by additive noise, while simultaneously suppressing noise signals. To verify the noise suppression effect of this method, we analyze the demodulation phases of the two eigen-peaks and assess the suppression effect on additive noise through power spectral density.

We conduct simulations and experiments to verify the performance of the weighted average demodulation method. The simulation results show that as the fineness of the sensor increases, the influence of additive noise on the demodulation phase error decreases. With the variation of the initial phase, the radio values of the eigen-peaks exhibit a periodic cosine change pattern. The higher the order of the eigen-peak, the more remarkable the phase change caused by additive noise, and the poorer the recovery effect of the demodulated signal (Figs. 2 and 3). Lower-order eigen-peaks contain more phase information and are more sensitive to fluctuations due to variations of initial phase. In contrast, additive noise has a greater effect on higher order eigen-peaks, although their fluctuation amplitude changes less with the initial phase. In this research, we propose an improved FFT signal demodulation method based on white light interferometry technology. By integrating the phase changes of multiple eigen-peaks and optimizing the weighted average, different weights are selected to achieve the best suppression effect on additive noise. The weighted average operation does not influence the demodulation phase caused by additive noise, while simultaneously suppressing noise signals. To validate the noise suppression effect of this method, we analyze the demodulation phases of two eigen-peaks and assess the suppression effect on additive noise through power spectral density (Fig. 8). The optimal phase noise level of the weighted average optimization method can reach -102.1 dB, enhancing its noise suppression capability by 3.8 dB (Fig. 8). The experimental results confirm the effectiveness of the weighted average optimization method.

We build a noise model for medium-fineness fiber optic F-P sensors, analyze and deduce the influence of additive noise on the demodulation results, and propose a method of weighted averaging based on multiple eigen-peaks. Compared with the demodulation method that only uses the first-order eigen-peak, our method can effectively reduce the influence of additive noise on the demodulation phase and enhance the anti-interference performance of the demodulated signal. The simulation and experimental results are in line with the theoretical analysis of the model. As the requirements for noise performance of medium-fineness fiber optic F-P sensors in signal detection and multiplexing applications continue to grow, the noise model and the weighted average based noise suppression method proposed in our study possess research and practical significance.