Characteristic Analysis of Adaptive FFT Demodulation Algorithm Applied to Extrinsic Fiber-Optic Fabry-Perot Sensors
Objective Extrinsic fiber-optic Fabry-Perot(F-P)sensors measure external physical quantities by detecting changes in the interference spectra caused by cavity length variations or refractive index variations within the medium.Compared with traditional sensing technologies,F-P sensors are characterized by high sensitivity,small size,and immunity to electromagnetic interference,and widely employed in the measurement of a variety of external parameters such as pressure,temperature,vibration,displacement,acceleration,and gas.Fiber-optic sensing demodulation technology is an indispensable part of fiber optic sensing systems,which can influence the detection capability of a sensing system to a certain extent,and often needs to meet the requirements of high accuracy and fast calculation speed.Based on this,some demodulation algorithms introduce fast Fourier transform(FFT)as a fast spectrum analysis tool,but how to balance the demodulation accuracy and computational speed has become a major challenge.In our study,an adaptive FFT demodulation algorithm based on white light interference is proposed.Compared with the traditional FFT algorithm,this algorithm combines the efficient computational characteristics of the FFT algorithm and the idea of adaptive sampling length and realizes accurate eigenfrequency calculation by adjusting the spectral sampling length adaptively.Meanwhile,it performs the whole-cycle orthogonal phase-locked detection of spectra to realize accurate phase information extraction,which can improve the demodulation precision during the dynamic signal demodulation.During dynamic signal demodulation,on the one hand,the demodulation accuracy and stability can be improved,and on the other hand,the real-time spectrum refinement process required by the traditional FFT cavity length demodulation method under the dynamically changing cavity length can be avoided.Additionally,the phase demodulation accuracy can be significantly improved,with fast signal demodulation ensured.Methods White light interference technology is employed to obtain the interference spectrum of the F-P sensor,and by adopting adaptive adjustment to the spectral sampling length,the maximum number Nmax of whole cycles within the sampling range and the exact value of the eigenfrequency are obtained to meet the conditions of the whole cycle simultaneously.Meanwhile,this can ensure that the signal demodulation of the noise spectral level is not affected,thus achieving the sensing signals of the low-noise,high-precision,fast signal demodulation.We also utilize theoretical analysis and numerical simulation to analyze the effects of signal amplitude,signal frequency,sensor cavity length,and initial phase on the signal demodulation performance of the adaptive FFT demodulation algorithm by adopting the control variable method and comparing it with the traditional FFT.Compared with the traditional FFT scheme,the adaptive FFT demodulation algorithm can improve eigenfrequency calculation accuracy,and reduce the noise,relative amplitude error Km of the fundamental frequency signal,and total harmonic distortion(THD).The ability of the adaptive FFT algorithm to demodulate the superposition spectra of the multiplexed array is also simulated,showing strong suppression capability of fundamental frequency crosstalk(FFC).Results and Discussions As the signal amplitude increases,the relative amplitude error of the base frequency signal of the adaptive FFT demodulation algorithm is basically maintained near 0,and the fluctuation at the lower amplitude is much smaller than the FFT demodulation result,which realizes more stable and more accurate signal demodulation.As the signal amplitude rises,the two demodulation algorithms show distortion at the same time,but the THD of the adaptive FFT demodulation result is always lower than that of the traditional FFT demodulation result(Fig.2).Additionally,the stability of the adaptive FFT demodulation algorithm is much higher than that of the traditional FFT,and when the first phase changes,the relative amplitude error fluctuation of the fundamental frequency signal is only 1/40 of that of the traditional algorithm.Meanwhile,the THD is 25 dB lower than that of the traditional FFT(Fig.4),which greatly improves the signal demodulation stability and accuracy.At the same time,the adaptive FFT also shows excellent cavity length adaptability,and with the changing cavity length,the eigenfrequency estimation error is only 10-4.Compared with the traditional FFT,the computational accuracy has been improved by nearly ten times,the noise level has been reduced by about 2 dB,and the variation of noise level with the cavity length fluctuation is only 1 dB,which is 1/3 of the fluctuation of the traditional FFT algorithm(Fig.5).What's more,the relative amplitude error fluctuation of the demodulated fundamental frequency signal of the FFT algorithm is about 0.6 dB,12 times the amplitude error fluctuation of the demodulated fundamental frequency signal of the adaptive FFT algorithm.The THD of the adaptive FFT demodulation result is 10-20 dB lower than that of the traditional algorithm with smaller fluctuation amplitude,which demonstrates higher accuracy and cavity length adaptability(Fig.6).In multiplexed system simulation,the adaptive FFT then shows stronger crosstalk suppression capability,reducing the FFC by about 20 dB(Fig.7).Conclusions We propose an adaptive FFT demodulation algorithm for white light interference and conduct simulations and analysis to verify the demodulation performance of the algorithm.The demodulation algorithm adaptively adjusts the sampling length according to the eigenfrequency of the F-P sensor,improves the eigenfrequency estimation accuracy,and realizes the whole period calculation of the periodic white light spectrum.Additionally,this can reduce the phase-locking calculation error in the phase demodulation algorithm,and improve the demodulation adaptability and demodulation stability of the demodulation algorithm for the F-P cavities of different cavity lengths.Simulation comparison shows that the adaptive FFT demodulation algorithm is better than the FFT demodulation algorithm in terms of demodulation accuracy,demodulation stability,and cavity length adaptation range.This algorithm can also be stably applied to sensors with different cavity lengths in different external environments,thus providing a more reliable and effective signal demodulation method for the fiber optic F-P sensors in various application scenarios.Meanwhile,it can be very well applied to small-sized sensor arrays and high-precision and low-noise sensor arrays.At the same time,the adaptive FFT can accurately identify the frequencies corresponding to all the peaks in the spectra,demodulate the superposition spectra of multiplexed arrays,and reduce the inter-channel crosstalk,which is expected to be applied to the signal demodulation of large-scale extrinsic fiber-optic F-P sensing arrays.
white light interferencephase demodulationfast Fourier transformextrinsic fiber-optic Fabry-Perot sensoradaptivity
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