Research Of Vibration Measurement Technology Based On Multiple Self-Mixing Interference

When self-mixing interference(SMI)occurs in an asymmetrical cavity,the output light and the external object are not strictly vertical.The light will experience multiple reflections between the external object and the laser,and then returned light and the output light form the optical feedback effect.This phenomenon is called multiple self-mixing interference(MSMI).Because MSMI has the advantage of higher resolution than SMI,it is of great significance to improve the accuracy of the measuring instrument without increasing the hardware and the complex algorithm.Numerous studies have been conducted on the MSMI phenomenon and the mechanism of occurrence.However,there are few studies on vibration measurement technique based on MSMI and the determination of multiple feedback times.In this paper,we use the characteristics of MSMI,such as high resolution,simple optical path,capable of discriminating direction,self-collimation,compact structure,low cost and so on,the research aims to study the reconstruction algorithm of the MSMI for vibration measurement to solve its problems on low accuracy,poor real-time performance,weak anti-interference ability,and slight versatility and to improve the measurement accuracy and versatility.In this paper,the main object of study is the frequency of less than 50 Hz micro-nano-level vibration measurement.In the low frequency range,the vibration intensity is proportional to the displacement,so the vibration of this paper is characterized by vibration displacement.The main contents are as follows:First,MSMI for vibration measurement has no corresponding theoretical support.We deduced the general phase,power,and vibration displacement equations of MSMI for vibration measurement and analyzed the measurement resolution based on the three-cavity model(F-P)of SMI theory,which provides a theoretical basis for MSMI vibration measurement.The effect of external cavity length and tilt angle on MSMI is studied by experimental method.Second,an improved jump point detection algorithm which does not need to judge the threshold is proposed for the problem of jump point detection threshold judgment in the phase-unwrapping algorithm.The algorithm takes advantage of the interference signal after differential processing which has the characteristics of large trend of effective fringe and small fluctuation of invalid fringe.The effective interference fringes are distinguished by the identification pulse.According to the effective interference fringes to determine the location of the peak and valley points,the key parameters of the reconstructed vibration displacement in the phase-unwrapping algorithm are determined,and the accuracy of the interference fringe detection is improved.And the algorithm is applied to the vibration reconstruction of MSMI.The experimental results show that the reconstruction error of the MSMI is 38% lower than that of the SMI.Third,a fast demodulation algorithm for MSMI vibration based on power spectrum analysis is proposed to solve the problem of joint estimation of optical feedback factor and the linewidth enhancement factor in the phase-unwrapping algorithm.The maximum value in the power spectrum of the MSMI signals corresponds to the maximum value of the first class Bessel function.The corresponding relationship between the maximum value of the power spectrum and the amplitude of the external object and identification rules of the main frequency of the power spectrum are established,therefore,the vibration frequency and amplitude of the external object can be calculated quickly.The algorithm does not require joint estimation of the optical feedback factor and the linewidth enhancement factor.In the process of obtaining the frequency and amplitude of the external object vibration,it only requires the extraction of the frequency of the first harmonic and the dominant frequency of the power spectrum,and the other interference information is blocked,which improves the anti-interference ability and demodulation speed of the algorithm.The experimental results show that when the amplitude of the external object is less than 5?m,the maximum error of amplitude demodulation is 75 nm,which is 53% lower than that of SMI.At the same time,this chapter proposes the method of judging the number of feedback of MSMI,which solves the problem that MSMI feedback times can not be distinguished and verified by experiment.Fourth,in the light of the large reconstruction error of MSMI vibration reconstruction technology,it can not be measured with high precision,and the vibration displacement reconstruction technique based on sinusoidal phase modulation is proposed.The electro-optic crystal modulator(EOM)introduces sinusoidal phase modulation to MSMI signals.Because of the correspondence relationship between the first harmonic and second harmonic of the modulation signal spectrum and the first and second order of the first class Bessel function,the real-time phase calculation is carried out by extracting the first harmonic and the second harmonic of the spectrum.Then,the vibration displacement of the external object is reconstructed by the real-time phase.The experimental results show that the reconstruction error is less than 5nm for low frequency vibra tion with amplitude less than 5?m.Since only the first harmonic and the second harmonic are extracted at the time of vibration reconstruction and the other components are shielded,the proposed algorithm has good anti-noise performance.Finally,to verify the performance of the MSMI based on sinusoidal phase modulation,it is compared with the laser Doppler vibrometer(LDV)from different amplitudes and frequencies.The experimental results show that the reconsruction velocity algorithm is well consistent with LDV in two aspects of different amplitudes and frequencies.The MSMI is applied to the pipeline leak detection.A single point positioning method for pipeline leak detection is proposed.Two MSMI vibration sensors are installed at the same end of the pipe,one for measuring the horizontal vibration of the pipe and the other for measuring the longitudinal vibration of the pipe.The distance between the leakage point and the detection point is measured by the time difference between the horizontal wave an d the longitudinal wave propagation velocity in the pipe wall,and the direction of the sound source is determined by the interference fringe inclination direction.The experimental results show that the designed single point positioning sensor can measure the leakage position correctly at the end of the pipeline and the positioning error is less than 5%.