Method for calibrating dynamic nonlinear error in a laser Doppler vibrometer

Abstract

A method for correcting dynamic nonlinear errors in a laser Doppler vibrometer, belonging to the field of laser vibration testing. The present invention aims at the problem that the existing segmented Heydemann correction method is used to eliminate nonlinear errors for time-varying multipath interference, and the accuracy of measurement results is poor. It includes: performing quadrature demodulation on the original measurement signal and the reference signal under multipath interference to obtain the quadrature signal expression; performing Taylor expansion on the multipath interference term, and removing the Taylor expansion remainder term to obtain a simplified expression of the multipath interference term; then transforming the quadrature signal expression, and obtaining the Lissajous curve expression according to the transformed quadrature signal expression; using the least squares method for spiral correction fitting to obtain the calculation results of 6 set variables in the Lissajous curve expression; then calculating the calculation result of the demodulation phase after eliminating multipath interference, and calculating the distance change caused by the vibration of the measurement target to achieve nonlinear correction. The present invention realizes the correction of nonlinear errors in measurement results.

Description

Technical Field

[0001] The present invention relates to a method for correcting dynamic non - linear errors in a laser Doppler vibrometer, and belongs to the field of laser vibration testing. Background Art

[0002] A laser Doppler vibrometer (LDV) can be used to perform high - precision non - contact optical measurements of the vibration velocity and amplitude of a surface without mass effects, and thus is widely used in fields such as aerospace, precision manufacturing, structural health monitoring, and life sciences.

[0003] The overall accuracy of LDV measurements depends on various factors. Different from interferometers used for dimensional measurements, the instability of the laser wavelength and the change of the air refractive index are not the main error sources for measuring vibrations with relatively low displacement amplitudes. Poor reflections in the optical path, namely so - called multipath interference, become the main error source in LDV measurements, which distorts the measurement signal and introduces non - linear errors. Therefore, it is necessary to correct the non - linear errors to improve the accuracy of the measurement results.

[0004] The non - linear errors can be corrected by a carefully selected post - processing algorithm. A commonly used correction method based on ellipse fitting was proposed by Heydemann. The Heydemann correction method has been applied to many studies to compensate for non - linear errors caused by polarization mixing, unequal gains of detectors, and lack of orthogonality. However, in some studies, by adjusting the gains of the quadrature detectors of a homodyne interferometer and readjusting the axis of the wave plate to a specific angle of the homodyne interferometer, the non - linear errors have been reduced. Although good results have been obtained in these studies, the non - linear errors introduced by ghost reflections of wave plates, lenses, and other optical devices in the optical system have been ignored, and the compensated signal retains such non - linear errors. Since ghost reflections are multi - order, complex non - linear errors are introduced. Many models for these ghost reflections have been developed, but no specific correction methods have been proposed. Some people have tried to reduce ghost reflections by improving the optical system, such as coating optical devices, adjusting the ghost reflection angle, and using spatial filtering, etc. Li et al. developed a compensation algorithm for strong second - order ghost reflections caused by lenses in the optical system. This algorithm can eliminate the non - linear errors caused by ghost reflections to a certain extent, but the results will deteriorate due to very strong or very weak second - order ghost reflections.

[0005] The above method is proposed on the premise of stable multipath interference and the formation of an ellipse in the Lissajous curve, and its parameters can be regarded as constants. The constant ellipse parameters can be used to correct the nonlinear error. However, in actual measurements, multipath interference is usually time-varying, especially in measurements carried out in a noisy environment. For example, when the target to be measured is located in a vacuum chamber, the multipath interference introduced by the vacuum window will change sharply with the vibration of the vacuum chamber. In this case, the nonlinear error will change dynamically and cannot be completely eliminated by the Heydemann correction. Usually, the piecewise Heydemann correction method is used to overcome this problem, but this is still based on ellipse fitting. And for severe environmental vibrations, the results produced by this method are very poor and the computational amount is very large. Summary of the Invention

[0006] Aiming at the problem that the existing piecewise Heydemann correction method for time-varying multipath interference to eliminate the nonlinear error has poor measurement result accuracy, the present invention provides a method for correcting the dynamic nonlinear error in a laser Doppler vibrometer.

[0007] A method for correcting the dynamic nonlinear error in a laser Doppler vibrometer according to the present invention includes:

[0008] Using a laser Doppler vibrometer to measure a measurement target to determine the original measurement signal and the reference signal under multipath interference;

[0009] Performing quadrature demodulation on the original measurement signal and the reference signal to obtain an expression of the quadrature signal containing the multipath interference term;

[0010] Performing Taylor expansion on the multipath interference term in the expression of the quadrature signal to obtain a Taylor expansion formula of the multipath interference term; removing the Taylor expansion remainder from the Taylor expansion formula to obtain a simplified expression of the multipath interference term;

[0011] According to the simplified expression of the multipath interference term, deform the expression of the quadrature signal containing the multipath interference term to obtain a deformed expression of the quadrature signal; the deformed expression of the quadrature signal includes six set variables;

[0012] Obtaining an expression of the Lissajous curve according to the deformed expression of the quadrature signal;

[0013] Performing spiral correction fitting on the expression of the Lissajous curve by using the least squares method to obtain calculation results of six set variables in the expression of the Lissajous curve;

[0014] Calculating a calculation result of the demodulation phase after eliminating the multipath interference from the calculation results of the six set variables, and obtaining the distance change caused by the vibration of the measurement target from the calculation result of the demodulation phase to realize the nonlinear correction of the original measurement signal.

[0015] Method for correcting dynamic nonlinear error in laser Doppler vibrometer according to the present invention, the original measurement signal I of the laser Doppler vibrometer under multipath interference m (t) is:

[0016] I m (t) = A m cos[2πf AOM t + θ(t)] + A e [2πf AOM t + θ e (t)],

[0017] where t is time, A m is the amplitude of the measurement signal, f AOM is the frequency difference between two acousto-optic modulators in the laser Doppler vibrometer, θ(t) is the Doppler phase change caused by the vibration of the measurement target, A e is the amplitude of the multipath interference, θ e (t) is the Doppler phase change brought by the multipath interference;

[0018] The original reference signal I a (t) is:

[0019] I a (t) = A a cos(2πf AOM t),

[0020] where A a is the amplitude of the reference signal.

[0021] Method for correcting dynamic nonlinear error in laser Doppler vibrometer according to the present invention, orthogonal demodulation is performed on the original measurement signal and the reference signal, and the expressions of the orthogonal signal I(t) and the orthogonal signal Q(t) obtained are:

[0022]

[0023]

[0024] where

[0025] Method for correcting dynamic nonlinear error in laser Doppler vibrometer according to the present invention, the multipath interference terms in the expressions of the orthogonal signal I(t) and the orthogonal signal Q(t) are defined as follows:

[0026] I e (t) = Bcos[θ e (t)],

[0027] Q e (t) = Bsin[θ e (t)],

[0028] where I e (t) is the multipath interference term in the orthogonal signal I(t), and Q e (t) is the multipath interference term in the orthogonal signal Q(t);

[0029] For I e (t) and Q e (t), a Taylor expansion is performed in the range of (t0 = 0, |t - t0| < 1) to obtain the Taylor expansion formula of the multipath interference term:

[0030] I e (t) = B * cos[θ e (0)] - B * θ e '(0) * sin[θ e (0)] * t

[0031] -0.5 * B * {[θ e '(0)] 2 * cos[θ e (0)] + θ e ”(0) * sin[θ e (0)]} * t 2 + R In (t),

[0032] Q e (t) = B * sin[θ e (0)] + B * θ e '(0) * cos[θ e (0)] * t

[0033] -0.5 * B * {[θ e '(0)] 2 * sin[θ e (0)] - θ e ”(0) * cos[θ e (0)]} * t 2 + R Qn (t),

[0034] In the formula, R In (t) is the Taylor expansion remainder of I e (t), and R Qn (t) is the Taylor expansion remainder of Q e (t).

[0035] According to the method for correcting the dynamic nonlinear error in the calibration laser Doppler vibrometer of the present invention, the specific expression of the Taylor expansion remainder R In (t) is:

[0036]

[0037] Taylor expansion remainder R Qn (t) has the following specific expression:

[0038]

[0039] According to the environmental vibration frequency being in the order of hundreds of Hertz, when the time t is in the order of milliseconds, the first three terms of the Taylor expansion in the Taylor expansion of the multipath interference term are much larger than the corresponding Taylor expansion remainder. Then, the Taylor expansion of the multipath interference term is simplified to:

[0040]

[0041]

[0042] Among them, the six set variables include: a 1 is the quadratic term coefficient of the orthogonal signal I(t), b 1 is the linear term coefficient of the orthogonal signal I(t), c 1 is the constant term of the orthogonal signal I(t); a 2 is the quadratic term coefficient of the orthogonal signal Q(t), b 2 is the linear term coefficient of the orthogonal signal Q(t), c 2 is the constant term of the orthogonal signal Q(t).

[0043] According to the method for correcting the dynamic nonlinear error in the calibration laser Doppler vibrometer of the present invention, based on the simplified expression of the multipath interference term, the orthogonal signal expression containing the multipath interference term is deformed to obtain the deformed orthogonal signal expression:

[0044] I(t) = A cos[θ(t)] + a 1 t 2 + b 1 t + c 1 ,

[0045] Q(t) = A sin[θ(t)] + a 2 t 2 + b 2 t + c 2 .

[0046] According to the method for correcting the dynamic nonlinear error in the calibration laser Doppler vibrometer of the present invention, according to the deformed orthogonal signal expression, the Lissajous curve expression is obtained as follows:

[0047] [I(t) - a 1 t 2 - b 1 t - c 1 2 + [Q(t) - a 2 ​t 2 -b 2 t - c 2 2 -A 2 = 0,

[0048] Using the least squares method, the values of six set variables are calculated and obtained.

[0049] According to the method for calibrating the dynamic nonlinear error in a laser Doppler vibrometer according to the present invention, based on the orthogonal signal expression containing the multipath interference term, the demodulation phase θ c ′ al (t):

[0050]

[0051] According to the calculation results of the six set variables, the multipath interference term is removed, and the demodulation phase θ after removing the multipath interference term is obtained cal (t):

[0052]

[0053] According to the method for calibrating the dynamic nonlinear error in a laser Doppler vibrometer according to the present invention, the laser Doppler vibrometer includes:

[0054] The output of the single-frequency laser is split by beam splitter 1 into two beams with an intensity ratio of 99:1, which respectively enter acousto-optic modulator 1 and acousto-optic modulator 2 to generate frequency shifts;

[0055] The light passing through acousto-optic modulator 1 is split by beam splitter 2 into two beams with an intensity ratio of 99:1. Among them, 99% of the light is used as the measurement light and passes through collimating mirror 1, polarization beam splitter, focusing lens and 1 / 4 wave plate to hit the measurement target; the light reflected by the measurement target carries the Doppler frequency shift generated by the vibration of the measurement target, passes through the 1 / 4 wave plate and focusing lens again, and enters collimating mirror 2 through the reflection of the polarization beam splitter and the mirror;

[0056] The light passing through acousto-optic modulator 2 is split by beam splitter 3 into two beams with an intensity ratio of 50:50; one of the beams and the beam output from collimating mirror 2 enter photodetector 1 through coupler 1 for interference to generate the original measurement signal;

[0057] 1% of the light generated by beam splitter 2 and the other beam output from beam splitter 3 enter photodetector 2 through coupler 2 for interference to generate the reference signal.

[0058] The beneficial effects of the present invention: Through the analysis of dynamic multipath interference, the present invention finds the spiral trajectory of the Lissajous curve corresponding to the noise environment, establishes a model to describe the dynamic nonlinear error generated in the noisy environment, and reduces signal distortion through compensation. ​

[0059] The method of the present invention describes the Lissajous curve of the orthogonal signal through a model, and this model is in turn used to develop a method based on the spiral fitting method to correct the non-linear error. The simulation experimental results show that the residual error obtained by the method of the present invention is one order of magnitude lower than the error obtained by using the existing method. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a schematic structural diagram of the laser Doppler vibrometer of the present invention; in the figure, AOM represents an acousto-optic modulator, and PBS represents a polarization beam splitter;

[0061] Figure 2 is a schematic diagram of quadrature demodulation of the original measurement signal and the reference signal;

[0062] Figure 3 is a schematic diagram of multipath interference;

[0063] Figure 4 is a Lissajous curve diagram in a dynamic multipath interference environment;

[0064] Figure 5 is for Figure 4 the target vibration diagram obtained by demodulation;

[0065] Figure 6 is a flowchart of quadrature demodulation based on the spiral fitting correction method;

[0066] Figure 7 is a comparison diagram of Lissajous curves corrected by different methods;

[0067] Figure 8 is the demodulation result of the uncorrected Lissajous curve;

[0068] Figure 9 is the demodulation result of the Lissajous curve using piecewise Heydemann correction;

[0069] Figure 10 is the demodulation result of the Lissajous curve using the spiral fitting correction of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0070] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0071] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0072] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but it is not intended to limit the present invention.

[0073] Specific Embodiment 1. In combination with Figures 1 to 6 As shown, the present invention provides a method for correcting dynamic nonlinear errors in a laser Doppler vibrometer, including

[0074] Using a laser Doppler vibrometer to measure a measurement target to determine the original measurement signal and reference signal under multipath interference;

[0075] Performing quadrature demodulation on the original measurement signal and the reference signal to obtain a quadrature signal expression containing multipath interference terms;

[0076] Performing Taylor expansion on the multipath interference terms in the quadrature signal expression to obtain a Taylor expansion formula of the multipath interference terms; removing the Taylor expansion remainder from the Taylor expansion formula to obtain a simplified expression of the multipath interference terms;

[0077] According to the simplified expression of the multipath interference terms, deform the quadrature signal expression containing the multipath interference terms to obtain a deformed quadrature signal expression; the deformed quadrature signal expression includes six set variables;

[0078] Obtain a Lissajous curve expression according to the deformed quadrature signal expression;

[0079] Performing spiral correction fitting on the Lissajous curve expression by using the least squares method to obtain the calculation results of the six set variables in the Lissajous curve expression;

[0080] Calculate the calculation result of the demodulation phase after eliminating multipath interference from the calculation results of the six set variables, and obtain the distance change caused by the vibration of the measurement target from the calculation result of the demodulation phase to realize the nonlinear correction of the original measurement signal.

[0081] Using Figure 1 When measuring with the laser Doppler vibrometer shown, when multipath interference is not considered, the measurement signal detected by the photodetector 1 is:

[0082]

[0083] where Δd is the distance change caused by the vibration of the target, and λ is the wavelength of the single-frequency laser.

[0084] Furthermore, the original measurement signal I m (t) of the laser Doppler vibrometer under multipath interference is:

[0085] I m (t) = A m cos[2πf AOM t + θ(t)] + Ae [2πf AOM t + θ e (t)],

[0086] where t is time, A m is the amplitude of the measurement signal, f AOM is the frequency difference between two acousto-optic modulators in the laser Doppler vibrometer, θ(t) is the Doppler phase change caused by the vibration of the measurement target, and A e is the amplitude of the multipath interference, and θ e (t) is the Doppler phase change brought by the multipath interference;

[0087] The original reference signal I a (t) detected by the photodetector 2 is:

[0088] I a (t) = A a cos(2πf AOM t),

[0089] where A a is the amplitude of the reference signal.

[0090] When not considering multipath interference, it is necessary to calculate the phase θ(t) to obtain Δd, and its calculation process is as Figure 2 shown,

[0091] Figure 3 shows the unwanted reflections that usually occur due to interference during the actual measurement process, such as the back reflection of a lens or a quarter-wave plate.

[0092] Furthermore, as shown in Figure 2 by performing quadrature demodulation on the original measurement signal and the reference signal, the expressions for the quadrature signal I(t) and the quadrature signal Q(t) obtained are:

[0093]

[0094]

[0095] For simplicity of representation, in the formula

[0096] the demodulated phase θ c ′ al (t) is calculated as:

[0097]

[0098] θ c ′ al (t) is not equal to θ(t), and the deviation between these two terms is usually referred to as the nonlinear error. Figure 4 and Figure 5Shows the simulation and demodulation results at different ratios of the main reflection intensity to the multipath reflection intensity. The vibration frequency and amplitude of the target are 300 Hz and 1 μm respectively. The ideal Lissajous curve is a circle centered at the origin of the coordinate system. If the multipath interference is stable, the Lissajous curve will be a circle with the center deviated from the origin.

[0099] However, the multipath interference in the industrial environment is dynamic. In this case, the Lissajous curve is not a circle. Figure 4 Shows that when there is vibration in the multipath interference, the Lissajous curve is a helix. As the ratio of the main reflection intensity to the multipath reflection intensity decreases, the Lissajous curve deviates more and more from the origin. The calculated target vibration is as Figure 5 shown, the dynamic nonlinear error increases as the ratio of the main reflection intensity to the multipath reflection intensity decreases. That is to say, when the backscatter of the target is weaker than the multipath interference, the influence of the dynamic nonlinear error is greater, which is very common in the measurement of rough non-cooperative targets.

[0100] According to Figure 4 it can be known that under the influence of the dynamic nonlinear error, the Lissajous curve is a helix. In this case, the existing calibration method based on ellipse fitting is no longer applicable. And, θ e (t) is related to the environmental vibration and cannot be determined by pre-calibration.

[0101] Furthermore, as shown in Figure 3 , the multipath interference terms in the expressions of the quadrature signal I(t) and the quadrature signal Q(t) are defined as follows:

[0102] I e (t) = B cos[θ e (t)],

[0103] Q e (t) = B sin[θ e (t)],

[0104] where I e (t) is the multipath interference term in the quadrature signal I(t), and Q e (t) is the multipath interference term in the quadrature signal Q(t);

[0105] Performing Taylor expansion on I e (t) and Q e (t) in the range of (t0 = 0, |t - t0| < 1), the Taylor expansion formula of the multipath interference term is obtained:

[0106] I e (t) = B * cos[θ e (0)] - B * θ e '(0) * sin[θ e(0)]*t - 0.5*B*{[θ e '(0)] 2 *cos[θ e (0)] + θ e ”(0)*sin[θ e (0)]}*t 2 +R In (t),

[0107] Q e (t) = B*sin[θ e (0)] + B*θ e '(0)*cos[θ e (0)]*t - 0.5*B*{[θ e '(0)] 2 *sin[θ e (0)] - θ e ”(0)*cos[θ e (0)]}*t 2 +R Qn (t),

[0108] where R In (t) is the remainder term of the Taylor expansion of I e (t), and R Qn (t) is the remainder term of the Taylor expansion of Q e (t).

[0109] The specific expression of the Taylor expansion remainder term R In (t) is:

[0110]

[0111] The specific expression of the Taylor expansion remainder term R Qn (t) is:

[0112]

[0113] In practical applications, the frequency of environmental vibration is often on the order of hundreds of hertz. When the time t is on the order of milliseconds, the first three terms of the Taylor expansion in the Taylor expansion of the multipath interference term are much larger than the corresponding Taylor expansion remainder terms. Then, the Taylor expansion of the multipath interference term is simplified to:

[0114]

[0115]

[0116] where the six set variables include: a 1 is the quadratic term coefficient of the orthogonal signal I(t), b 1 is the linear term coefficient of the orthogonal signal I(t), c1 is the constant term of the orthogonal signal I(t); a 2 is the quadratic term coefficient of the orthogonal signal Q(t), b 2 is the linear term coefficient of the orthogonal signal Q(t), c 2 is the constant term of the orthogonal signal Q(t).

[0117] Furthermore, based on the simplified expression of the multipath interference term, the orthogonal signal expression containing the multipath interference term is transformed to obtain the transformed orthogonal signal expression:

[0118] I(t) = A cos[θ(t)] + a 1 t 2 + b 1 t + c 1 ,

[0119] Q(t) = A sin[θ(t)] + a 2 t 2 + b 2 t + c 2 .

[0120] According to the transformed orthogonal signal expression, the Lissajous curve expression is obtained as follows:

[0121] [I(t) - a 1 t 2 - b 1 t - c 1 2 + [Q(t) - a 2 t 2 - b 2 t - c 2 2 - A 2 = 0;

[0122] According to the orthogonal signal expression containing the multipath interference term, the demodulation phase θ c ′ al (t):

[0123]

[0124] Using the least squares method, a 1 , b 1 , c 1 , a 2 , b 2 , c 2 These 6 parameters can be calculated.

[0125] According to the calculation results of the 6 set variables, the multipath interference term is removed to obtain the demodulation phase θ cal (t):​​

[0126]

[0127] Furthermore, in combination with Figure 1 as shown, the structure of the laser Doppler vibrometer adopted by the method of the present invention includes:

[0128] The output of the single-frequency laser is split by the beam splitter 1 into two beams of light with an intensity ratio of 99:1, which respectively enter the acousto-optic modulator 1 and the acousto-optic modulator 2 to generate frequency shifts; the frequency shifts generated by the acousto-optic modulator 1 and the acousto-optic modulator 2 are different;

[0129] The light passing through the acousto-optic modulator 1 is split by the beam splitter 2 into two beams of light with an intensity ratio of 99:1. Among them, 99% of the light is used as the measurement light and passes through the collimating mirror 1, the polarization beam splitter, the converging mirror and the 1 / 4 wave plate to hit the measurement target; the light reflected by the measurement target carries the Doppler frequency shift generated by the vibration of the measurement target, passes through the 1 / 4 wave plate and the converging mirror again, and enters the collimating mirror 2 through the reflection of the polarization beam splitter and the mirror;

[0130] The light passing through the acousto-optic modulator 2 is split by the beam splitter 3 into two beams of light with an intensity ratio of 50:50; one of the beams of light and the beam of light output by the collimating mirror 2 enter the photodetector 1 through the coupler 1 for interference to generate the original measurement signal;

[0131] 1% of the light generated by the beam splitter 2 and the other beam of light output by the beam splitter 3 enter the photodetector 2 through the coupler 2 for interference to generate the reference signal.

[0132] Based on the above principle, the method of the present invention corrects the dynamic nonlinear error by fitting the helix of the orthogonal signal and is used in combination with the quadrature demodulation algorithm. The whole process is as Figure 6 shown.

[0133] Figures 7 to 10 shows the simulation results of the helix fitting correction method. In the simulation, the vibration frequency of the measured target is 300 Hz, the amplitude is 1 μm, and f AOM is 5 MHz. The ratio of the main reflection intensity to the multipath reflection intensity is set to 0.5, the vibration frequency of the multipath interference is 15 Hz, and the amplitude is 0.25 μm.

[0134] Figure 7 shows the Lissajous curves before and after correction using two methods. Although most of the nonlinear errors have been eliminated using the segmented Heydemann correction method, the Lissajous curve still shows residual nonlinearity. The helix fitting correction method of the present invention corrects the Lissajous curve into a circle centered on the origin of the coordinate system. Figure 8 shows that the amplitude and phase of the uncorrected demodulation signal are severely distorted due to dynamic multipath interference. Figure 9 and Figure 10The demodulated signals corrected by two methods are shown. Although the traditional method compensates for most of the nonlinear errors, the distortion of some segments makes the compensated demodulated signals inconsistent with the original signals. Applying the method proposed by the present invention makes the amplitudes of the demodulated signals and the original signals consistent.

[0135] In the simulation of dynamic multipath interference, compared with the performance of the traditional method, the compensation ability of this method for nonlinear errors has been significantly improved. Therefore, the method of the present invention can improve the accuracy of LDV measurement in industrial environments and shows excellent performance in correcting the residual nonlinearity of Lissajous curves and compensating for the nonlinear errors of demodulated signals.

[0136] Although the present invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed, as long as they do not depart from the spirit and scope of the present invention as defined by the appended claims. It should be understood that different dependent claims and the features described herein can be combined in a manner different from that described in the original claims. It should also be understood that the features described in connection with a separate embodiment can be used in other described embodiments.

Claims

1. A method for correcting dynamic nonlinear errors in a laser Doppler vibrometer, characterized in that it includes using a laser Doppler vibrometer to measure a measurement target to determine the original measurement signal and the reference signal under multipath interference; performing quadrature demodulation on the original measurement signal and the reference signal to obtain an expression of the quadrature signal containing multipath interference terms; performing Taylor expansion on the multipath interference terms in the quadrature signal expression to obtain a Taylor expansion formula of the multipath interference terms; removing the Taylor expansion remainder from the Taylor expansion formula to obtain a simplified expression of the multipath interference terms; deforming the quadrature signal expression containing multipath interference terms according to the simplified expression of the multipath interference terms to obtain a deformed quadrature signal expression; the deformed quadrature signal expression includes six set variables; obtaining a Lissajous curve expression according to the deformed quadrature signal expression; performing spiral correction fitting on the Lissajous curve expression by using the least squares method to obtain the calculation results of the six set variables in the Lissajous curve expression; calculating the calculation result of the demodulation phase after eliminating multipath interference from the calculation results of the six set variables, and obtaining the distance change caused by the vibration of the measurement target from the calculation result of the demodulation phase to realize the nonlinear correction of the original measurement signal.

2. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 1, characterized in that, Original measurement signal I of a laser Doppler vibrometer under multipath interference m (t) is as follows: I m y(t) = A m cos[2πft AOM + θ(t)] + A e [2πf AOM t + θ e (t)], where t is the time, A m is the amplitude of the measurement signal, f AOM is the frequency difference between two acousto-optic modulators in the laser Doppler vibrometer, θ(t) is the Doppler phase change caused by the vibration of the measurement target, A e is the amplitude of the multipath interference, θ e (t) is the Doppler phase change brought by the multipath interference; Original reference signal I a (t) is as follows: I a (t) = A a cos(2πf AOM t), where A a is the amplitude of the reference signal.

3. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 1, characterized in that, The expressions of the quadrature signal I(t) and the quadrature signal Q(t) obtained by performing quadrature demodulation on the original measurement signal and the reference signal are: In the formula 4. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 3, characterized in that, The definitions of the multipath interference terms in the expressions of the quadrature signal I(t) and the quadrature signal Q(t) are as follows: I e I(t) = B cos[θ e (t)], Q e (t) = Bsin[θ e (t)], where I e (t) is the multipath interference term in the quadrature signal I(t), Q e (t) is the multipath interference term in the quadrature signal Q(t); For I e (t) and Q e (t) is Taylor-expanded in the range of (t0 = 0, |t - t0| < 1) to obtain the Taylor expansion of the multipath interference term: I e (t) = B * cos[θ e (0)] - B * θ e '(0) * sin[θ e (0)] * t -0.5*B*{[θ e '(0)] 2 *cos[θ e (0)]+θ e ”(0)*sin[θ e (0)]}*t 2 +R In (t), Q e (t) = B * sin[θ e (0)] + B * θ e '(0) * cos[θ e (0)] * t -0.5*B*{[θ e '(0)] 2 *sin[θ e (0)]-θ e ”(0)*cos[θ e (0)]}*t 2 +R Qn (t), where R In (t) is the remainder of the Taylor expansion of I e (t), and R Qn (t) is the remainder of the Taylor expansion of Q e (t).

5. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 4, characterized in that, Taylor expansion remainder R In (t) has the following specific expression: Taylor expansion remainder R Qn (t) has the following specific expression: According to the frequency of environmental vibration being in the order of hundreds of hertz, when the time t is in the order of milliseconds, the first three terms of the Taylor expansion in the Taylor expansion formula of the multipath interference terms are much larger than the corresponding Taylor expansion remainder, so the Taylor expansion formula of the multipath interference terms is simplified as: Among the six set variables in the formula are: a 1 which is the quadratic term coefficient of the quadrature signal I(t), b 1 which is the linear term coefficient of the quadrature signal I(t), c 1 which is the constant term of the quadrature signal I(t); a 2 which is the quadratic term coefficient of the quadrature signal Q(t), b 2 which is the linear term coefficient of the quadrature signal Q(t), c 2 which is the constant term of the quadrature signal Q(t).

6. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 5, characterized in that, Based on the simplified expression of the multipath interference terms, deforming the quadrature signal expression containing multipath interference terms to obtain a deformed quadrature signal expression: I(t) = Acos[θ(t)] + a 1 t 2 + b 1 t + c 1 , Q(t) = Asin[θ(t)] + a 2 t 2 + b 2 t + c 2 。 7. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 6, characterized in that, According to the deformed quadrature signal expression, the Lissajous curve expression is as follows: [I(t) - a 1 t 2 - b 1 t - c 1 2 + [Q(t) - a 2 t 2 - b 2 t - c 2 2 - A 2 = 0,​​ Using the least squares method to calculate and obtain the values of the six set variables.

8. The method for correcting dynamic nonlinear errors in a laser Doppler vibrometer according to claim 7, characterized in that, According to the orthogonal signal expression containing multipath interference terms, the demodulation phase θ when there are multipath interference terms is obtained c ′ al (t): Based on the calculation results of six set variables, the multipath interference terms are removed to obtain the demodulation phase θ after removing the multipath interference terms cal (t):

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