一种改进的三波长EFPI小信号解调方法

A Modified Three-wavelength Demodulation Method for Small Signals of EFPI

针对非本征法布里-珀罗干涉型(EFPI)传感器采用对称三波长解调法检测小信号时可能存在的波形变差问题,提出一种针对小信号的改进的对称三波长解调方法。利用三角函数的小信号近似,得到简化的公式计算求出三路信号的相位差,解决EFPI干涉信号的衰落问题。仿真与实验结果表明,该方法在针对小信号解调方面比现有三波长法具有更高的算法稳定性与更小的误差,同时在低信噪比的场景下对波形具有更好的恢复效果。实验上分别用本文方法和现有方法对相同声波信号进行解调,本文方法解调的信噪比较现有方法高12 dB以上。

Fiber optic Extrinsic Fabry-Perot Interferometers (EFPI) are frequently utilized in many acoustic sensing scenarios due to their simple structure,ease of fabrication,high sensitivity,high phase consistency,and strong resistance to electromagnetic interference.However,the cavity length of the EFPI sensor is susceptible to environmental variables such as temperature and air pressure,and the drifting of the orthogonal working point caused by the change of cavity length will lead to signal fading and distortion.Nevertheless,several demodulation methods are less practical or even ineffective when dealing with small signals:Dual-wavelength method for Mach-Zehnder interferometer is inconvenient to apply to the EFPI demodulation;the Ellipse-Fitting Algorithm's (EFA) Lissajous figure will degenerate into a straight line for small signals,and there are also the disadvantages of poor real-time performance and slow demodulation speed;the second-order Differentiate-and-Cross-Multiply (DCM) operation has wide applicability,but the Direct Current (DC) term must be accurately removed,for small signals,the removal of DC term is difficult;the Bessel method has the same difficulties as DCM,and it can only demodulate single-frequency signals;The method of using tunable laser feedback to control the orthogonal working point has the drawback of high cost,and lasers with wavelength scanning function have high requirements for hardware reliability;Phase Generated Carrier (PGC) technology requires a complex carrier modulation system with a limited frequency response range,and the system is complex and large when PGC uses piezoelectric transducer to generate phase carriers.In contrast,intensity demodulation has the advantages of a linear transfer function,simple signal processing,high sensitivity and is suitable for the detection of high-speed and small signal.JIANG Yi et al.proposed a Symmetrical Demodulation Method(SDM) suitable for unstable cavity length and unknown cavity length,which constructs two equal interference phase differences between the three output signals by selecting specific three wavelengths,and then recovers the phase of the signal through mathematical operations.This method has the advantages of large dynamic range and simple operation,and it is more suitable for the detection of large signals.However,in the case of small signals,the SDM algorithm may lead to increased noise and error in the demodulation result.If the wavelength of the light source is 1 550 nm,the interference phase of EFPI changes 0~2π,corresponding to the cavity length variation range of 775 nm.When the cavity length change caused by vibration is less than 30.11 nm,that is,the radian value in the interference phase is less than 0.22 rad,the approximate error of sinx and x is less than 1%.Under this condition,we can directly remove the DC term of interference signal reflected by EFPI to avoid the difficulty of distinguishing DC terms in small signals,Bsinφ■_ can be regarded as the approximation of an interference signal.Three specific wavelengths are selected to construct two equal interference phase differences between the three output signals,and on the basis of these three signals,the two intermediate formulas can be compensated for each other to avoid the cancellation phenomenon,it ensure that at least one of the intermediate formulas has a better waveform,so as to obtain an intensity demodulation result with better Signal-To-Noise Ratio (SNR) and this approach is summarized as a Modified Symmetrical Demodulation Method (MSDM).Both theoretical analysis and numerical simulation demonstrate that MSDM performs better than SDM for small signals.Theoretical analysis indicates MSDM has a smaller and smoother error bound and relative condition number than SDM.In the numerical simulation,MSDM has less error than SDM in cavity length,frequency,and signal amplitude.After adding Gaussian white noise to the simulated signal,more high-frequency noise appears in SDM,while MSDM achieves superior demodulation results for the signal waveform.In the experiment,the SNR of the three signals ranges from 60~65 dB,and the experiment results align well with the simulation.Due to the complicated noise in practical applications and the high sensitivity of SDM,high-frequency noise appears in the demodulation results of SDM,resulting in a decrease in SNR.MSDM effectively improves the SNR of the demodulation results,the power spectra of MSDM's results are smoother than those of SDM,and the SNR near the main frequency increases from74 dB to 86 dB.Values of cosδ measured in experiments consistently maintain between 0.55~0.7,in agreement with the theoretical predictions,thus confirming the reliability of MSDM.Additionally,the outputs of MSDM perform good linearity with the sound pressure of the speaker,and the linearity coefficient reaches 0.995 11.When the signal frequencies are 100 Hz,500 Hz,1 kHz,and 10 kHz,respectively,the MSDM demodulation results still have good SNR.An improved three-wavelength demodulation method for small signals of EFPI sensors is proposed by enhancing the existing three-wavelength phase demodulation algorithm.Our research group uses the approximate relationship of the sinusoidal function under small signal conditions to calculate the phase difference by calculating the intensity of the three signals,thereby solving the fading problem of EFPI interference signals.Through numerical analysis,simulations and experiments,it is proved that the proposed method has higher algorithm stability and smaller error in demodulation for small signals and better recovery on waveforms.Besides,the algorithm also theoretically has certain demodulation capabilities for non-periodic signals,which can potentially expand its application in the future.