A laser interference linear / angular vibration synchronous measurement device and decoupling method

Abstract

A laser interference linear / angular vibration synchronous measurement device and decoupling method belong to the field of laser interference measurement. The linear / angular vibration synchronous measurement device comprises an optical system, a precision adjusting support, a controller, a data acquisition system, a linear / angular vibration comprehensive calibration software and an integrated connecting cable. The optical system is used for emitting three measurement lights and focusing on the surface of a vibrator, and receiving the light energy reflected from the surface of the vibrator and converting into photoelectric signals. The precision adjusting support is used for accurately adjusting the measurement posture of the optical system. The linear / angular vibration upper computer is used for decoupling the collected signals and respectively acquiring linear vibration and angular vibration parameters, realizing real-time tracking display of time-frequency domain curves, and automatically fitting and quickly displaying the space running vector trajectory of the motion target. The three-beam symmetric differential Mach-Zehnder heterodyne interference method is adopted, the linear vibration and angular vibration parameters of the measured target can be synchronously acquired, and the comprehensive calibration of the calibrated sensor can be realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser interferometry, and relates to a laser interferometry linear / angular vibration synchronous measurement device and a decoupling method. BACKGROUND

[0002] Patents CN221649712U and CN105547454.A mainly focus on improving the measurement accuracy and range of linear vibration by improving the optical path design and signal processing algorithm. Although the patent has achieved certain results in linear vibration measurement, it does not involve angular vibration measurement.

[0003] Patent CN200610152126.6 mainly focuses on the measurement and analysis of angular vibration of a rotating table, and collimated laser is incident on a grating to demodulate the angular vibration of the rotor by using the laser Doppler principle.

[0004] This limitation is particularly prominent in the fields of aerospace, precision machinery, and earthquake monitoring, because these fields often need to analyze linear and angular vibrations in a complex vibration environment simultaneously to accurately evaluate the dynamic performance of the system. SUMMARY

[0005] The purpose of the application is to provide a laser interferometry linear / angular vibration synchronous measurement device and a decoupling method, which uses a three-beam symmetric differential Mach-Zehnder heterodyne interference method to synchronously obtain linear and angular vibration parameters of a measured target, and realizes comprehensive calibration of a calibrated sensor.

[0006] The purpose of the application is achieved by the following technical solutions:

[0007] The laser interferometry linear / angular vibration synchronous measurement device disclosed by the application comprises an optical system, a precision adjustment support, a controller, a data acquisition system, linear / angular vibration comprehensive calibration software installed on an upper computer, and an integrated connection cable.

[0008] The optical system is used to emit three measurement beams and focus them on the surface of a vibrator, simultaneously receive reflected light energy from the surface of the vibrator, and convert the light energy into photoelectric signals.

[0009] The precision adjustment support is used to accurately adjust the measurement posture of the optical system, so that the incident light accurately aims at the surface of the measured columnar grating.

[0010] The controller is used to control power supply of the optical system, drive of an acousto-optic modulator, and preprocessing of original photoelectric signals, and transmit the preprocessed three-way original photoelectric signals and the acousto-optic modulator drive signals to the data acquisition system in the form of analog signals.

[0011] The data acquisition system is used to acquire signals output by the controller.

[0012] Line / angle vibration host computer, for decoupling the collected signals and obtaining line vibration and angle vibration parameters respectively, realizing real-time tracking display of time-frequency domain curves, and automatically fitting and quickly displaying the spatial running vector trajectory of the moving target;

[0013] Integrated connecting cable, for power supply and signal transmission between the optical system and the controller, the signal transmission including transmission of high-frequency signals, low-frequency signals, DC signals and control signals, and the cable shielding structure isolates the crosstalk between signals.

[0014] The optical system emits three beams of measurement light and focuses on the surface of the vibrator, while receiving the reflected light energy from the surface of the vibrator, converting it into an optical signal and transmitting it to the controller. The controller is used to control the power supply of the optical system, the driving of the acousto-optic modulator, the preprocessing of the original optical signal, and transmit the preprocessed three-way original optical signal and the acousto-optic modulator driving signal (reference signal) to the data acquisition system in the form of analog signals (BNC cable). Through the line / angle vibration comprehensive calibration software installed on the host computer, the line vibration and angle vibration parameters are decoupled and obtained respectively, that is, the real-time tracking display of the line vibration and angle vibration parameter time-frequency domain curves is realized, and at the same time, the spatial running vector trajectory of the moving target is further automatically fitted and quickly displayed. The data acquisition system also synchronously collects the output of the calibrated sensor, taking the optical system measurement result as the reference value, and through comparison with the line / angle vibration values obtained by the optical system, the line / angle vibration comprehensive calibration of the calibrated sensor is realized, that is, the separate calibration of the line vibration magnitude and the angle vibration magnitude is realized synchronously, and then the comprehensive running trajectory calibration is realized.

[0015] The optical system adopts a single helium-neon laser as a light source; the laser emitted by the laser passes through a collimating mirror group and a lambda / 2 wave plate, and is divided into three beams by a light splitting prism: one as a linear vibration measurement beam—middle, directly incident on a spherical cat-eye mirror located at the center of the angular vibration workbench surface; the other two as angular vibration measurement beams—left and right, respectively incident on the lateral columnar surface of the angular vibration workbench from the symmetrical positions on both sides, the columnar surface being processed with a columnar grating; by controlling the incident angle of the measurement beam—middle, the first-order diffracted light is made to coincide with the incident light beam, so as to realize the accurate alignment of the measurement beam—middle; the measurement beam—middle is returned to the original direction through the spherical cat-eye mirror, passes through the wave plate, is reflected by the light splitting prism, the reference light is reflected by the right side of the light splitting prism, is transmitted by the light splitting prism, and then is reflected by the right angle reflecting prism, the two beams are combined and interfered at the light splitting prism, and then are received by a photoelectric detector after passing through the wave plate; the measurement beam—middle is modulated by an acousto-optic modulator to form a heterodyne interference signal of the carrier after interference; the left angular vibration measurement light is incident on the columnar grating surface of the lateral columnar surface, and by controlling the incident angle to be 1 / 2 of the initial diffraction angle, the first-order diffracted light is made to coincide with the incident light beam, i.e., returned to the original direction, and is combined and interfered with the light reflected by the light splitting prism, the light splitting prism and the right angle reflecting prism at the light splitting prism, and finally is received by the photoelectric detector to obtain and output the original photoelectric signal; similarly, the right angular vibration measurement light is combined and interfered with the light reflected by the light splitting prism, the light splitting prism and the right angle reflecting prism at the light splitting prism, and finally is received by the photoelectric detector to obtain and output the original photoelectric signal.

[0016] The controller comprises an optical head power supply module, an acousto-optic modulator driving module, a photoelectric signal energy display module, a signal preprocessing module and a function expansion module.

[0017] The optical head power supply module provides power supply driving for the optical head and the optical devices and electronic devices in the controller.

[0018] The acousto-optic modulator driving module provides a high-power driving signal for the acousto-optic modulator in the optical head, and outputs a synchronous reference signal to the data acquisition system.

[0019] The photoelectric signal energy display module acquires and displays the current photoelectric signal amplitude in real time based on the logarithmic amplifier detection function.

[0020] The signal preprocessing module comprises adaptive amplitude modulation, adjustable signal gain and phase-locked amplification functions of the photoelectric signal, and is used to improve the signal quality and the accuracy of the demodulation process.

[0021] The function expansion module reserves a function expansion module installation position.

[0022] This invention discloses a method for synchronous measurement and decoupling of laser interferometric normal / angular vibration, which is implemented based on a laser interferometric normal / angular vibration synchronous measurement device. The method includes the following steps:

[0023] Step 1: Decouple the normal / angular vibration. The laser measurement system emits three measurement beams, defined as measurement beam-left, measurement beam-middle, and measurement beam-right. Measurement beam-middle is directly incident on the spherical cat's eye mirror located at the center of rotation. Measurement beam-left and measurement beam-right are incident on the lateral cylindrical surfaces of the angular vibration stage from symmetrical positions on both sides. By controlling the incident angle of the measurement beams, the first-order diffracted light is made to coincide with the incident beam.

[0024] For linear vibration measurement, since the center of the angular vibration stage only experiences linear vibration and not angular vibration, the measurement beam directly measures the center position of the stage. A spherical cat's-eye reflector is used to avoid beam swaying caused by stage rotation and large-amplitude vibration, maintaining the stability of the reflected beam direction during angular vibration and thus ensuring measurement signal quality. Linear vibration measurement follows the same principle as traditional heterodyne laser vibrometers, utilizing the proportional relationship between Doppler frequency shift and the measured velocity to measure the target velocity.

[0025] For the measurement of angular vibration, during the vibration process, the measurement beam—the left measurement point—measures the linear vibration velocity ν(t) and the angular vibration velocity v. 左 At the coupling point of (t), in order to decouple the angular vibration magnitude, the reflected light from the measurement beam -left and the measurement beam - is interfered with (i.e., subtracted) to obtain the photoelectric signal -left. This interference is the subtraction. Since the reflected light from the measurement beam -left contains both linear vibration velocity ν(t) and angular vibration velocity v... 左 The reflected light in the measurement beam contains only the linear vibration velocity ν(t). Therefore, the photoelectric signal obtained after the two interfere and beat only contains v(t). 左 (t) information, that is, to achieve decoupling of angular vibration and linear vibration.

[0026] Similarly, it is also possible to achieve ν 右 The acquisition of (t), v 左 (t) and ν 右 (t) represents two linear velocity values ​​at symmetrical positions around the center of the platform. These values ​​should be equal if the radii are the same. To improve the accuracy of angular vibration measurements, by adjusting v... 左 (t) and ν 右 The final angular vibration measurement result is obtained by averaging (t). The laser vibrometer measures the displacement change at the equivalent radius R of the rotation axis of the angular vibration worktable, which is the displacement amplitude.

[0027] According to the laser Doppler formula:

[0028] v 左 (t)=g×Δf 左 (t)

[0029]

[0030] Similarly, we obtain

[0031]

[0032] Where: v 左 (t) represents the angular vibration velocity of the measurement beam at the left measurement point, g is λ / 2, and Δf 左 (t) is the Doppler frequency of the measurement beam at the left measurement point, ω 左 (t) represents the rotational speed of the measurement beam at the left measurement point. ω 右 (t) Similarly.

[0033] The angular velocity can be calculated using the known grating constant, the radius of the measuring point on the platform, and the Doppler frequency shift measured by the optical system.

[0034] For the same vibration table surface, the measuring points have the same radius, and the angular velocities at any position on the surface are equal. In order to improve the accuracy of angular velocity measurement, the average angular velocity value is obtained by taking the average value through symmetrical measurement.

[0035]

[0036] Step 2: The decoupled linear / angular vibration laser interferometric signal is transmitted to the host computer. By demodulating the amplitude and phase of the output signal, the peak values ​​of displacement, velocity, or acceleration are analyzed. The sinusoidal approximation demodulation method described above is used to analyze the peak values ​​of displacement, velocity, or acceleration. The two photoelectric signals are converted from two continuous signals to two discrete sequences u1(t) by A / D conversion. i ) and u2(t i Perform a division operation on the two signals, then perform an arctangent operation on the quotient to obtain the sequence.

[0037]

[0038] In the formula:

[0039]

[0040] Since the arctangent function is a multivalued and discontinuous function, a phase expansion algorithm is used to obtain a definite value, so that the obtained phase value is continuous. After phase expansion and appropriate calculations, a discrete sequence with continuous phase values ​​can be obtained.

[0041]

[0042] In the formula: k i These are the values ​​obtained through the phase expansion algorithm, where ω is the angular velocity, φ0 is the initial phase, and l0 is a constant.

[0043] The waveform of the vibration signal to be measured can be reproduced by calculating this discrete sequence, thus obtaining the amplitude and initial phase. However, the obtained amplitude and phase are not accurate. To improve measurement accuracy, [further details are needed]. Further processing is performed using a sine fitting algorithm. The sine fitting method is to... Write it as follows:

[0044]

[0045] In the formula:

[0046] i = 1, 2, ..., n;

[0047]

[0048] Through data series By fitting a sinusoidal function with a DC component and calculating A, B, and C in the above equation using the least squares method, the vibration displacement d and the initial phase φ0 are obtained as follows:

[0049]

[0050] The velocity and acceleration of the measured object are obtained by performing first and second derivatives on the displacement data.

[0051]

[0052] In the formula, u i (t) is the input signal of the differentiator; u o (t) is the output signal of the differentiator.

[0053] When the noise bandwidth is greater than the signal bandwidth, the signal-to-noise ratio after differentiation will deteriorate. Differentiation operations must take into account the impact of noise on the calculation results. The data before processing must limit the signal and noise bandwidths, and low-pass filtering must be performed after processing.

[0054] Step 3: In actual measurement, factors such as stage vibration, large-amplitude vibration guidance errors, installation deviations of the cat's-eye reflector, and processing quality inevitably cause amplitude modulation of the original photoelectric signal related to the vibration phase. Although this phenomenon can be reduced through high-precision structural design, optical system optimization, and photoelectric signal preprocessing circuits, it cannot be completely eliminated. To further improve the accuracy of the measurement system and reduce the uncertainty of the device, an adaptive optimization modulation based on a correlation algorithm is used in the photoelectric signal demodulation process to improve the signal-to-noise ratio of the original photoelectric signal. The specific implementation method is as follows:

[0055] The key challenge in adaptive optimization modulation of non-stationary optoelectronic signals lies in the accuracy of frequency and initial phase estimation. Frequency and initial phase estimation methods are easily affected by low signal-to-noise ratios and poor signal quality, leading to significant errors. Therefore, optimization and improvement of frequency and initial phase estimation methods are necessary.

[0056] In the improved frequency estimation method, the autocorrelation detection method is used to reduce the signal-to-noise ratio. Since there is no correlation between the signal and the noise, an autocorrelation function with the same frequency as the original signal is calculated, and then FFT frequency estimation is performed on the autocorrelation function.

[0057] The improved method for initial phase estimation utilizes the independence of signal and noise, employs a cross-correlation function combined with the least squares parameter estimation method, and establishes a set of parameter estimation equations when the sum of squared errors between the estimated and true values ​​is minimized. By solving the set of equations, a high-precision estimate of the phase is obtained.

[0058] The process of transforming noisy Doppler signals into smooth Doppler signals commonly employs methods such as low-pass filtering, neighborhood smoothing filtering, and wavelet filtering. Of these three methods, low-pass filtering causes the greatest distortion to the Doppler signal and its filtering effect is inferior to the other two, therefore it is not used. Neighborhood smoothing filtering and wavelet filtering have comparable processing effects. Wavelet filtering has the advantage of causing the least distortion to the Doppler signal; neighborhood smoothing filtering allows for flexible processing of Doppler signals modulated by any frequency band by changing the smoothing coefficients, while wavelet filtering requires appropriate adjustments to its wavelet basis function, decomposition scale, and threshold processing method based on different types of Doppler signals to achieve optimal results. Since this invention is a real-time signal demodulation scheme, neighborhood smoothing filtering is used to better suit real-time requirements.

[0059] ① Autocorrelation detection frequency estimation method

[0060] The autocorrelation detection method utilizes the uncorrelated property between signal and noise to perform autocorrelation analysis on the input signal in order to improve the signal-to-noise ratio.

[0061] A single-frequency real sinusoidal signal mixed with Gaussian white noise is

[0062]

[0063] Where z(n) is white noise.

[0064] N sample values ​​are obtained by sampling the signal.

[0065]

[0066] Define the correlation function based on time averaging as follows:

[0067]

[0068] Where τ represents the delay.

[0069] Then the autocorrelation function R of the signal x(n) xy (τ) is

[0070] R XX (τ)=R SS (τ)+R SZ (τ)+R ZS (τ)+R ZZ (τ)

[0071] Among them, R ss (τ) and R zz (τ) are the autocorrelation functions of the sinusoidal signal s(n) and the white noise z(n), respectively, and R sz (τ) and R zs (τ) are the cross-correlation functions of the sinusoidal signal s(n) and the noise z(n), respectively. The white noise z(n) is random and has no correlation with the sinusoidal signal s(n), so R... sz (τ) and R zs The (τ) terms all approach zero.

[0072] The autocorrelation function of Gaussian white noise has an expected value of 0 at all locations except for zero.

[0073] R ZZ (τ)=σ 2 δ(τ)

[0074] Where δ(τ) is the unit sampled signal.

[0075] When the sample value N is large enough, the autocorrelation function R of the sinusoidal signal s(n) SS (τ) is

[0076]

[0077] When N is sufficiently large, the autocorrelation function of a sinusoidal signal is a sinusoidal signal with the same frequency. Preprocessing the input signal with autocorrelation can reduce noise, thereby improving the accuracy of frequency estimation algorithms for sinusoidal signals.

[0078] ② Cross-correlation combined with least squares parameter estimation algorithm

[0079] Least squares estimation is essentially parameter estimation, which involves establishing a system of equations about the parameters and solving the system of equations to find the parameters.

[0080] The observed signal mixed with Gaussian white noise is

[0081]

[0082] In the formula, s(n) is a real sine wave signal and z(n) is Gaussian white noise.

[0083] Let Φ be the parameter estimates of the amplitude and phase of the sinusoidal signal, respectively. Examine the sum of squared errors between the parameter estimates and the true values.

[0084]

[0085] When the signal-to-noise ratio is high, the parameter estimate can be obtained directly using the least squares solution of the above equation. However, when the signal-to-noise ratio is low, the accuracy of obtaining the parameter estimate by directly using the least squares solution of the above equation is not high, or even impossible.

[0086] To ensure the effectiveness of the parameter estimation equations, it is necessary to remove noise interference. This paper utilizes the uncorrelation between the signal s(n) = cos(ω0n) and the noise z(n) to reduce noise interference, and employs a method combining cross-correlation and least quadratic parameter estimation to establish the parameter estimation equations.

[0087] Given cross-correlation function

[0088]

[0089] z(n)=x(n)-[a1 cos(w0n)-a2 cos(w0t)]

[0090] The amplitude component

[0091] When the sum of squared errors between the parameter estimates and the true values ​​reaches its minimum, based on the uncorrelated relationship between the signal s(n) = cos(ω0n) and the noise z(n), the above equation can be expressed as follows:

[0092]

[0093] The following formula is true

[0094]

[0095] The expansion yields the parameter estimation equations.

[0096]

[0097] Solving the system of equations yields a1 and a2, which in turn provides estimates of the amplitude and initial phase.

[0098]

[0099] The resulting initial phase estimation is more reliable and stable than that obtained by directly using the least squares estimation method, thus enabling automatic acquisition of the initial phase of the reference signal and real-time signal processing of photoelectric signals.

[0100] Beneficial effects:

[0101] 1. This invention discloses a laser interferometric normal / angular vibration synchronous measurement device and decoupling method. It emits three measurement beams (measurement beam-left, measurement beam-middle, and measurement beam-right). The measurement beam-middle is directly incident on a spherical cat's-eye mirror located at the center of rotation, while the measurement beams-left and-right are incident from symmetrical positions on either side onto the lateral cylindrical surfaces of the angular vibration stage. By controlling the incident angle, the first-order diffracted light is made to overlap with the incident beam and return in the original direction, interfering with the light reflected by the beam splitter. The resulting photoelectric signal is received and output by a photodetector. Since all three measurement channels are based on the same laser source and the same reference clock, the time synchronization of linear and angular vibration measurements can be guaranteed, thereby improving the accuracy of the laser interferometric normal / angular vibration synchronous measurement. Compared to using two independent systems to obtain angular velocity and linear velocity separately, the measurement device and method used in this patent can quickly, synchronously, and with high precision acquire linear / angular velocity.

[0102] 2. This invention discloses a laser interferometric normal / angular vibration synchronous measurement device and decoupling method, which subtracts the reflected light from the measurement beam -left from the measurement beam - to obtain the photoelectric signal -left. Since the reflected light from the measurement beam -left contains v... 左 The reflected light in the measurement beam contains only v(t) information, and therefore, the photoelectric signal obtained after the two interfere and beat at the same frequency contains only v(t) information. 左 (t) information, that is, the decoupling of angular vibration and linear vibration is achieved. Similarly, v can also be achieved. 右 The acquisition of (t). ν 左 (t) and ν 右 (t) represents two linear velocity values ​​at a centrally symmetrical position on the platform, which are equal when the radii are the same. This is determined by considering ν. 左 (t) and ν右 The final angular vibration measurement result is obtained by averaging (t), which improves the accuracy of angular vibration measurement. This method can decouple linear vibration and angular vibration, thereby enabling the synchronous acquisition of high-precision linear velocity and angular velocity in subsequent signal processing. Attached Figure Description

[0103] Figure 1 Laser Interferometric Normal / Angular Vibration Integrated Measurement System

[0104] Figure 2 This is a schematic diagram of the optical system;

[0105] Among them, 1 is a helium-neon laser, 2 is a collimating lens group, 3-1 is a waveplate, 3-2 is a waveplate, 3-3 is a waveplate, 4-1 is a right-angle reflecting prism, 4-2 is a right-angle reflecting prism, 4-3 is a right-angle reflecting prism, 5-1 is a beam splitter, 5-3 is a beam splitter, 5-4 is a beam splitter, 5-5 is a beam splitter, 5-6 is a beam splitter, 5-7 is a beam splitter, 5-8 is a beam splitter, 6 is an acousto-optic modulator, 7-1 is the measurement beam—left, 7-2 is the measurement beam—middle, 7-3 is the measurement beam—right, 8-1 is a photodetector, 8-2 is a photodetector, 8-3 is a photodetector, 13 is a spherical cat's eye reflector, 14 is an angular vibration worktable, and 15 is a lateral cylindrical surface.

[0106] Figure 3 This is a schematic diagram of an embedded reflector;

[0107] Figure 4 Schematic diagram of a cylindrical grating with a lateral cylindrical surface.

[0108] Figure 5 This is a schematic diagram of the controller principle based on a serial bus.

[0109] Figure 6 This is a typical circuit schematic of a logarithmic amplifier;

[0110] Figure 7 This is a schematic diagram of an LED array-type energy bar (front panel of the controller);

[0111] Figure 8 A larger diagram showing the components of the conditioning section;

[0112] Figure 9 Schematic diagram of decoupling principle for linear / angular vibration;

[0113] Figure 10 This is a flowchart of the orthogonal phase solution based on arctangent;

[0114] Figure 11 This is a flowchart of data processing for the sine approximation method. Detailed Implementation

[0115] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0116] Example 1:

[0117] like Figure 1 As shown, this embodiment discloses a laser interferometric normal / angular vibration synchronous measurement device, including an optical system, a precision adjustment bracket, a controller, a data acquisition system, line / angular vibration comprehensive calibration software installed on a host computer, and an integrated connecting cable;

[0118] The optical system is used to emit three beams of measurement light and focus them on the surface of the oscillator, while simultaneously receiving the light energy reflected back from the surface of the oscillator and converting it into photoelectric signals.

[0119] A precision adjustment bracket is used to precisely adjust the measurement posture of the optical system so that the incident light is accurately aimed at the surface of the cylindrical grating being measured.

[0120] The controller is used to control the power supply of the optical system, drive the acousto-optic modulator, and preprocess the raw photoelectric signals. It then transmits the preprocessed three raw photoelectric signals and the acousto-optic modulator drive signal to the data acquisition system in the form of analog signals.

[0121] A data acquisition system is used to acquire signals output by the controller.

[0122] The linear / angular vibration host computer is used to decouple the acquired signals and obtain the linear vibration and angular vibration parameters separately, realize the real-time tracking and display of time-frequency domain curves, and automatically fit and quickly display the spatial running vector trajectory of the moving target;

[0123] The integrated connecting cable is used for power supply and signal transmission between the optical system and the controller. The signal transmission includes the transmission of high-frequency signals, low-frequency signals, DC signals and control signals. The cable shielding structure isolates crosstalk between signals.

[0124] The optical system emits three beams of measurement light and focuses them onto the surface of the oscillator. Simultaneously, it receives the light energy reflected from the oscillator surface, converts it into photoelectric signals, and transmits them to the controller. The controller controls the power supply to the optical system, drives the acousto-optic modulator, and preprocesses the raw photoelectric signals. It then transmits the three preprocessed raw photoelectric signals and the acousto-optic modulator drive signal (reference signal) to the data acquisition system in analog signal form (BNC cable). Linear and angular vibration comprehensive calibration software installed on the host computer decouples and separately acquires the linear and angular vibration parameters, enabling real-time tracking and display of the time-frequency domain curves of the linear and angular vibration parameters. Furthermore, it automatically fits and quickly displays the spatial trajectory of the moving target. The data acquisition system also simultaneously acquires the output of the sensor under calibration, using the measurement results from the optical system as a reference value. By comparing these values ​​with the linear and angular vibration values ​​obtained from the optical system, it achieves comprehensive calibration of the linear and angular vibration of the sensor under calibration, simultaneously calibrating the linear and angular vibration values ​​separately, thereby calibrating the overall trajectory.

[0125] The optical system uses a single helium-neon laser 1 as the light source, with a wavelength of 632.8 nm and a peak power of 3.3 mW. The laser emitted by laser 1 is collimated by collimating lens group 2 and λ / 2 waveplate 3-1, and then split into three beams by beam splitter prism 5-1: one beam, serving as the linear vibration measurement beam—center 7-2, is directly incident on the spherical cat's-eye mirror 13 located at the center of the angular vibration stage 14; the other two beams, serving as the angular vibration measurement beam—left 7-1 and the angular vibration measurement beam—right 7-3, are incident from symmetrical positions on the lateral cylindrical surface 15 of the angular vibration stage 14, which is fabricated with a 1200 L / mm cylindrical grating. By controlling the incident angle of the measurement beam—center 7-2, the first-order diffracted light coincides with the incident beam, achieving precise alignment of the measurement beam—center 7-2. The measuring beam 7-2 is reflected back in the original direction through the spherical cat's eye mirror 13, passes through the wave plate 3-2, and is reflected by the beam splitter prism 5-8. The reference beam is reflected by the right side of the beam splitter prism 5-1, transmitted through the beam splitter prism 5-1, and then passes through the right-angle reflecting prism 4-2. The two beams meet and interfere at the beam splitter prism 5-5. After passing through the wave plate 3-3, they are received by the photodetector 8-2. The measurement beam 7-2 carries a 40MHz carrier wave applied by the acousto-optic modulator 6, thus forming a heterodyne interference signal with a 40MHz carrier wave after interference. The left-side angular vibration measurement beam 7-1 is incident on the surface of the cylindrical grating 15 on the lateral cylindrical surface. By controlling its incident angle to be 1 / 2 of the initial diffraction angle, the first-order diffracted beam can be made to coincide with the incident beam, that is, return in the original direction. It then merges and interferes with the light reflected by the beam splitter 5-8, beam splitter 5-3 and right-angle reflecting prism 4-4 at the beam splitter 5-7. Finally, it is received by the photodetector 8-1 to obtain the original photoelectric signal and output it. Similarly, the right-side angular vibration measurement beam 7-3 merges and interferes with the light reflected by the beam splitter 5-8, beam splitter 5-4 and right-angle reflecting prism 4-3 at the beam splitter 5-6. Finally, it is received by the photodetector 8-3 to obtain the original photoelectric signal and output it.

[0126] The controller includes an optical head power supply module, an acousto-optic modulator drive module, a photoelectric signal energy display module, a signal preprocessing module, and a function expansion module.

[0127] The optical head power supply module provides power to drive the optical and electronic components in the optical head and controller.

[0128] The acousto-optic modulator driver module provides a high-power drive signal for the acousto-optic modulator in the optical head and outputs a synchronization reference signal to the data acquisition system.

[0129] The photoelectric signal energy display module, based on the logarithmic amplifier detection function, acquires and displays the current photoelectric signal amplitude in real time.

[0130] The signal preprocessing module includes functions such as adaptive amplitude modulation of photoelectric signals, adjustable signal gain, and phase-locked amplification, which are used to improve signal quality and the accuracy of the demodulation process.

[0131] Functional expansion module, with reserved installation space for functional expansion module.

[0132] This embodiment discloses a method for synchronous measurement and decoupling of laser interferometric normal / angular vibration, which is implemented based on the aforementioned laser interferometric normal / angular vibration synchronous measurement device. The method for synchronous measurement and decoupling of laser interferometric normal / angular vibration disclosed in this invention includes the following steps:

[0133] Step 1: Decouple the normal / angular vibration. The laser measurement system emits three measurement beams, defined as measurement beam-left, measurement beam-middle, and measurement beam-right. Measurement beam-middle is directly incident on the spherical cat's eye mirror located at the center of rotation. Measurement beam-left and measurement beam-right are incident on the lateral cylindrical surfaces of the angular vibration stage from symmetrical positions on both sides. By controlling the incident angle of the measurement beams, the first-order diffracted light is made to coincide with the incident beam.

[0134] For linear vibration measurement, since the center of the angular vibration stage only experiences linear vibration and not angular vibration, the measurement beam directly measures the center position of the stage. A spherical cat's-eye reflector is used to avoid beam swaying caused by stage rotation and large-amplitude vibration, maintaining the stability of the reflected beam direction during angular vibration and thus ensuring measurement signal quality. Linear vibration measurement follows the same principle as traditional heterodyne laser vibrometers, utilizing the proportional relationship between Doppler frequency shift and the measured velocity to measure the target velocity.

[0135] For the measurement of angular vibration, during the vibration process, the measurement beam—the left measurement point—measures the linear vibration velocity ν(t) and the angular vibration velocity v. 左 At the coupling point of (t), in order to decouple the angular vibration magnitude, the reflected light in the measurement beam -left is interfered with (i.e., subtracted) to obtain the photoelectric signal -left. This interference is the subtraction. Since the reflected light from the measurement beam -left contains both linear vibration velocity v(t) and angular vibration velocity v... 左 The reflected light in the measurement beam contains only the linear vibration velocity v(t). Therefore, the photoelectric signal obtained after the two interfere and beat only contains v(t). 左 (t) information, that is, achieving decoupling between angular vibration and linear vibration. Similarly, it is also possible to achieve ν. 右 The acquisition of (t), v 左 (t) and v 右 (t) represents two linear velocity values ​​at symmetrical positions around the center of the platform. These values ​​should be equal if the radii are the same. To improve the accuracy of angular vibration measurements, by adjusting v... 左(t) and ν 右 The final angular vibration measurement result is obtained by averaging (t). The laser vibrometer measures the displacement change at the equivalent radius R of the rotation axis of the angular vibration worktable, which is the displacement amplitude.

[0136] According to the laser Doppler formula:

[0137] v 左 (t)=g×Δf 左 (t)

[0138]

[0139] Similarly, we obtain

[0140]

[0141] Where: v 左 (t) represents the angular vibration velocity of the measurement beam at the left measurement point, g is λ / 2, and Δf 左 (t) is the Doppler frequency of the measurement beam at the left measurement point, ω 左 (t) represents the rotational speed of the measurement beam at the left measurement point. ω 右 (t) Similarly.

[0142] The angular velocity can be calculated using the known grating constant, the radius of the measuring point on the platform, and the Doppler frequency shift measured by the optical system.

[0143] For the same vibration table surface, the measuring points have the same radius, and the angular velocities at any position on the surface are equal. In order to improve the accuracy of angular velocity measurement, the average angular velocity value is obtained by taking the average value through symmetrical measurement.

[0144]

[0145] Step 2: The decoupled linear / angular vibration laser interferometric signal is transmitted to the host computer. By demodulating the amplitude and phase of the output signal, the peak values ​​of displacement, velocity, or acceleration are analyzed. The sinusoidal approximation demodulation method described above is used to analyze the peak values ​​of displacement, velocity, or acceleration. The two photoelectric signals are converted from two continuous signals to two discrete sequences u1(t) by A / D conversion. i ) and u2(t i Perform a division operation on the two signals, then perform an arctangent operation on the quotient to obtain the sequence.

[0146]

[0147] In the formula:

[0148]

[0149] Since the arctangent function is a multivalued and discontinuous function, a phase expansion algorithm is used to obtain a definite value, so that the obtained phase value is continuous. After phase expansion and appropriate calculations, a discrete sequence with continuous phase values ​​can be obtained.

[0150]

[0151] In the formula: k i These are the values ​​obtained through the phase expansion algorithm, where ω is the angular velocity, φ0 is the initial phase, and l0 is a constant.

[0152] The waveform of the vibration signal to be measured can be reproduced by calculating this discrete sequence, thus obtaining the amplitude and initial phase. However, the obtained amplitude and phase are not accurate. To improve measurement accuracy, [further details are needed]. Further processing is performed using a sine fitting algorithm. The sine fitting method is to... Write it as follows:

[0153]

[0154] In the formula:

[0155] i = 1, 2, ..., n;

[0156]

[0157] Through data series By fitting a sinusoidal function with a DC component and calculating A, B, and C in the above equation using the least squares method, the vibration displacement d and the initial phase φ0 are obtained as follows:

[0158]

[0159] The velocity and acceleration of the measured object are obtained by performing first and second derivatives on the displacement data.

[0160]

[0161] In the formula, u i (t) is the input signal of the differentiator; u o (t) is the output signal of the differentiator.

[0162] When the noise bandwidth is greater than the signal bandwidth, the signal-to-noise ratio after differentiation will deteriorate. Differentiation operations must take into account the impact of noise on the calculation results. The data before processing must limit the signal and noise bandwidths, and low-pass filtering must be performed after processing.

[0163] Step 3: In actual measurement, factors such as stage vibration, large-amplitude vibration guidance errors, installation deviations of the cat's-eye reflector, and processing quality inevitably cause amplitude modulation of the original photoelectric signal related to the vibration phase. Although this phenomenon can be reduced through high-precision structural design, optical system optimization, and photoelectric signal preprocessing circuits, it cannot be completely eliminated. To further improve the accuracy of the measurement system and reduce the uncertainty of the device, an adaptive optimization modulation based on a correlation algorithm is used in the photoelectric signal demodulation process to improve the signal-to-noise ratio of the original photoelectric signal. The specific implementation method is as follows:

[0164] The key challenge in adaptive optimization modulation of non-stationary optoelectronic signals lies in the accuracy of frequency and initial phase estimation. Frequency and initial phase estimation methods are easily affected by low signal-to-noise ratios and poor signal quality, leading to significant errors. Therefore, optimization and improvement of frequency and initial phase estimation methods are necessary.

[0165] In the improved frequency estimation method, the autocorrelation detection method is used to reduce the signal-to-noise ratio. Since there is no correlation between the signal and the noise, an autocorrelation function with the same frequency as the original signal is calculated, and then FFT frequency estimation is performed on the autocorrelation function.

[0166] The improved method for initial phase estimation utilizes the independence of signal and noise, employs a cross-correlation function combined with the least squares parameter estimation method, and establishes a set of parameter estimation equations when the sum of squared errors between the estimated and true values ​​is minimized. By solving the set of equations, a high-precision estimate of the phase is obtained.

[0167] The process of transforming noisy Doppler signals into smooth Doppler signals commonly employs methods such as low-pass filtering, neighborhood smoothing filtering, and wavelet filtering. Of these three methods, low-pass filtering causes the greatest distortion to the Doppler signal and its filtering effect is inferior to the other two, therefore it is not used. Neighborhood smoothing filtering and wavelet filtering have comparable processing effects. Wavelet filtering has the advantage of causing the least distortion to the Doppler signal; neighborhood smoothing filtering allows for flexible processing of Doppler signals modulated by any frequency band by changing the smoothing coefficients, while wavelet filtering requires appropriate adjustments to its wavelet basis function, decomposition scale, and threshold processing method based on different types of Doppler signals to achieve optimal results. Since this invention is a real-time signal demodulation scheme, neighborhood smoothing filtering is used to better suit real-time requirements.

[0168] ① Autocorrelation detection frequency estimation method

[0169] The autocorrelation detection method utilizes the uncorrelated property between signal and noise to perform autocorrelation analysis on the input signal in order to improve the signal-to-noise ratio.

[0170] A single-frequency real sinusoidal signal mixed with Gaussian white noise is

[0171]

[0172] Where z(n) is white noise.

[0173] N sample values ​​are obtained by sampling the signal.

[0174]

[0175] Define the correlation function based on time averaging as follows:

[0176]

[0177] Where τ represents the delay.

[0178] Then the autocorrelation function R of the signal x(n) xy (τ) is

[0179] R XX (τ)=R SS (τ)+R SZ (τ)+R ZS (τ)+R ZZ (τ)

[0180] Among them, R ss (τ) and R zz (τ) are the autocorrelation functions of the sinusoidal signal s(n) and the white noise z(n), respectively, and R sz (τ) and R zs (τ) are the cross-correlation functions of the sinusoidal signal s(n) and the noise z(n), respectively. The white noise z(n) is random and has no correlation with the sinusoidal signal s(n), so R... sz (τ) and R zs The (τ) terms all approach zero.

[0181] The autocorrelation function of Gaussian white noise has an expected value of 0 at all locations except for zero.

[0182] R ZZ (τ)=σ 2 δ(τ)

[0183] Where δ(τ) is the unit sampled signal.

[0184] When the sample value N is large enough, the autocorrelation function R of the sinusoidal signal s(n) SS (τ) is

[0185]

[0186] When N is sufficiently large, the autocorrelation function of a sinusoidal signal is a sinusoidal signal with the same frequency. Preprocessing the input signal with autocorrelation can reduce noise, thereby improving the accuracy of frequency estimation algorithms for sinusoidal signals.

[0187] ② Cross-correlation combined with least squares parameter estimation algorithm

[0188] Least squares estimation is essentially parameter estimation, which involves establishing a system of equations about the parameters and solving the system of equations to find the parameters.

[0189] The observed signal mixed with Gaussian white noise is

[0190]

[0191] In the formula, s(n) is a real sine wave signal and z(n) is Gaussian white noise.

[0192] Let Φ be the parameter estimates of the amplitude and phase of the sinusoidal signal, respectively. Examine the sum of squared errors between the parameter estimates and the true values.

[0193]

[0194] When the signal-to-noise ratio is high, the parameter estimate can be obtained directly using the least squares solution of the above equation. However, when the signal-to-noise ratio is low, the accuracy of obtaining the parameter estimate by directly using the least squares solution of the above equation is not high, or even impossible.

[0195] To ensure the effectiveness of the parameter estimation equations, it is necessary to remove noise interference. This paper utilizes the uncorrelation between the signal s(n) = cos(ω0n) and the noise z(n) to reduce noise interference, and employs a method combining cross-correlation and least quadratic parameter estimation to establish the parameter estimation equations.

[0196] Given cross-correlation function

[0197]

[0198] z(n)=x(n)-[a1 cos(w0n)-a2 cos(w0t)]

[0199] The amplitude component

[0200] When the sum of squared errors between the parameter estimates and the true values ​​reaches its minimum, based on the uncorrelated relationship between the signal s(n) = cos(ω0n) and the noise z(n), the above equation can be expressed as follows:

[0201]

[0202] The following formula is true

[0203]

[0204] The expansion yields the parameter estimation equations.

[0205]

[0206] Solving the system of equations yields a1 and a2, which in turn provides estimates of the amplitude and initial phase.

[0207]

[0208] The resulting initial phase estimation is more reliable and stable than that obtained by directly using the least squares estimation method, thus enabling automatic acquisition of the initial phase of the reference signal and real-time signal processing of photoelectric signals.

[0209] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for synchronous measurement and decoupling of laser interferometric normal / angular vibration, characterized in that, Includes the following steps: Step 1: Decouple the normal / angular vibration; The laser measurement system emits three measurement beams, which are defined as measurement beam-left, measurement beam-middle, and measurement beam-right, respectively. Measurement beam-middle is directly incident on the spherical cat's eye mirror located at the center of rotation. Measurement beam-left and measurement beam-right are incident on the lateral cylindrical surfaces of the angular vibration table from symmetrical positions on both sides. By controlling the incident angle of the measurement beams, the first-order diffracted light is made to coincide with the incident beam. For linear vibration measurement, since the center of the angular vibration table only experiences linear vibration and not angular vibration, the measurement beam directly measures the center position of the table. The measurement target mirror uses a spherical cat's eye reflector to avoid beam swaying caused by table rotation and large-amplitude vibration, maintaining the stability of the reflected beam direction during angular vibration, thus ensuring the quality of the measurement signal. Linear vibration measurement follows the same principle as traditional heterodyne laser vibrometer, using the proportional relationship between Doppler frequency shift and the measured velocity to measure the target velocity. For the measurement of angular vibration, during the vibration process, the measurement beam—the left measurement point—measures the linear vibration velocity ν(t) and the angular vibration velocity v. 左 At the coupling point of (t), in order to decouple the angular vibration magnitude, the reflected light in the measurement beam -left is interfered with to obtain the photoelectric signal -left. The interference is subtraction. Since the reflected light in the measurement beam -left contains the linear vibration velocity ν(t) and the angular vibration velocity v 左 The reflected light in the measurement beam contains only the linear vibration velocity ν(t). Therefore, the photoelectric signal obtained after the two interfere and beat only contains v(t). 左 (t) information, that is, to achieve decoupling of angular vibration and linear vibration; Similarly, to achieve ν 右 The acquisition of (t), v 左 (t) and ν 右 (t) represents two linear velocity values ​​at symmetrical positions around the center of the platform. These values ​​should be equal if the radii are the same. To improve the accuracy of angular vibration measurements, by adjusting v... 左 (t) and ν 右 (t) The final angular vibration measurement result is obtained by averaging; the laser vibration meter measures the displacement change at the equivalent radius R of the rotation axis of the angular vibration worktable, and the displacement change is the displacement amplitude; According to the laser Doppler formula: v 左 (t)=g×Δf 左 (t) Similarly, we obtain Where: v 左 (t) represents the angular vibration velocity of the measurement beam at the left measurement point, g is λ / 2, and Δf 左 (t) is the Doppler frequency of the measurement beam at the left measurement point, ω 左 (t) represents the rotational speed of the measurement beam at the left measurement point; ω 右 (t) is determined similarly; The angular velocity can be calculated using the known grating constant, the radius of the measuring point on the platform, and the Doppler frequency shift measured by the optical system. For the same vibration table surface with the same measuring point radius, the angular velocity at any position on the surface is equal. In order to improve the accuracy of angular velocity measurement, the average angular velocity value is obtained by taking the average value through symmetrical measurement. Step 2: The decoupled linear / angular vibration laser interferometric signal is transmitted to the host computer; by demodulating the amplitude and phase of the signal output, the peak values ​​of displacement, velocity, or acceleration are analyzed; a sinusoidal approximation demodulation method is used to analyze the peak values ​​of displacement, velocity, or acceleration; the two photoelectric signals are converted from two continuous signals into two discrete sequences u1(t) i ) and u2(t i Perform division on the two signals, then perform arctangent operation on the quotient to obtain the sequence. In the formula: Since the arctangent function is a multivalued and discontinuous function, a phase expansion algorithm is used to obtain a definite value, so that the obtained phase value is continuous. After phase expansion and appropriate calculations, a discrete sequence with continuous phase values ​​can be obtained. In the formula k i The values ​​obtained through the phase expansion algorithm are: ω is the angular velocity, φ0 is the initial phase, and l0 is a constant. The waveform of the vibration signal to be measured can be reproduced by calculating this discrete sequence, thus obtaining the amplitude and initial phase; however, the obtained amplitude and phase are not accurate. To improve the measurement accuracy, [further details are needed]. Further processing is performed using a sine fitting algorithm; the sine fitting method is to... Write it as follows: In the formula: i = 1, 2, ..., n; Through data series By fitting a sinusoidal function with a DC component and calculating A, B, and C in the above equation using the least squares method, the vibration displacement d and the initial phase φ0 are obtained as follows: The velocity and acceleration of the measured object are obtained by performing first and second derivatives on the displacement data; the differential equation of the differentiator is: In the formula, u i (t) is the input signal of the differentiator; u o (t) is the output signal of the differentiator; When the noise bandwidth is greater than the signal bandwidth, the signal-to-noise ratio after differentiation will deteriorate; the differentiation operation must take into account the impact of noise on the calculation result, the data before processing must limit the signal and noise bandwidth, and low-pass filtering must be performed after processing; Step 3: During the demodulation of the photoelectric signal, an adaptive optimization modulation based on a correlation algorithm is used to improve the signal-to-noise ratio of the original photoelectric signal. The specific implementation method is as follows: In the improved frequency estimation method, the autocorrelation detection method is used to reduce the signal-to-noise ratio. Since there is no correlation between the signal and the noise, an autocorrelation function with the same frequency as the original signal is calculated, and then FFT frequency estimation is performed on the autocorrelation function. The improved method for initial phase estimation utilizes the independence of signal and noise, and adopts a cross-correlation function combined with the least squares parameter estimation method. When the sum of squared errors between the estimated value and the true value is minimized, a set of parameter estimation equations is established. By solving the set of equations, a high-precision estimate of the phase is obtained. The noisy Doppler signal is processed into a smooth Doppler signal by using a neighborhood smoothing filter method. ① Autocorrelation detection frequency estimation method The autocorrelation detection method utilizes the characteristic that there is no correlation between signal and noise to perform autocorrelation analysis on the input signal in order to improve the signal-to-noise ratio. A single-frequency real sinusoidal signal mixed with Gaussian white noise is Where z(n) is white noise; N sample values ​​are obtained by sampling the signal. Define the correlation function based on time averaging as follows: Where τ is the delay; Then the autocorrelation function R of the signal x(n) xy (τ) is R XX (τ)=R SS (t)+R SZ (t)+R ZS (t)+R ZZ (t) Among them, R ss (τ) and R zz (τ) are the autocorrelation functions of the sinusoidal signal s(n) and the white noise z(n), respectively, and R sz (τ) and R zs (τ) are the cross-correlation functions of the sinusoidal signal s(n) and the noise z(n), respectively; where the white noise z(n) is random and has no correlation with the sinusoidal signal s(n), so R sz (τ) and R zs The terms (τ) all approach zero; The autocorrelation function of Gaussian white noise has an expected value of 0 at all locations except for zero. R ZZ (t)=s 2 d(t) Where δ(τ) is the unit sampled signal; When the sample value N is large enough, the autocorrelation function R of the sinusoidal signal s(n) SS (τ) is When N is large enough, the autocorrelation function of a sinusoidal signal is a sinusoidal signal with the same frequency. Autocorrelation preprocessing of the input signal can reduce noise, thereby improving the accuracy of frequency estimation algorithm for sinusoidal signal frequency estimation. ② Cross-correlation combined with least squares parameter estimation algorithm Least squares estimation is essentially parameter estimation, which involves establishing a system of equations about the parameters and solving the system of equations to find the parameters. The observed signal mixed with Gaussian white noise is In the formula, s(n) is a real sine wave signal, and z(n) is Gaussian white noise; Let Φ be the parameter estimates of the amplitude and phase of the sinusoidal signal, respectively. Examine the sum of squared errors between the parameter estimates and the true values. When the signal-to-noise ratio is high, the parameter estimate can be obtained directly using the least squares solution of the above equation; however, when the signal-to-noise ratio is low, the accuracy of obtaining the parameter estimate by directly using the least squares solution of the above equation is not high, or even impossible. The noise interference is reduced by utilizing the uncorrelation between the signal s(n)=cos(ω0n) and the noise z(n). The parameter estimation equations are established by using the method of cross-correlation combined with minimum quadratic parameter estimation. Given cross-correlation function z(n)=x(n)-[a1 cos(w0n)-a2 cos(w0t)] The amplitude component When the sum of squared errors between the parameter estimates and the true values ​​reaches its minimum, based on the uncorrelated relationship between the signal s(n) = cos(ω0n) and the noise z(n), the above equation can be expressed as follows: The following formula is true The expansion yields the parameter estimation equations. Solving the system of equations yields a1 and a2, which in turn provides estimates of the amplitude and initial phase. This enables the automatic acquisition of the initial phase of the reference signal, and thus enables real-time signal processing of the photoelectric signal.

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