Broadband vibration calibration heterodyne laser interferometry and its measuring device

Abstract

This invention discloses a broadband vibration calibration heterodyne laser interferometry method. First, a vibration table is used to provide vibration excitation of a specific amplitude within a wide frequency range to the accelerometer under test (AUT), and the excitation acceleration of the AUT is measured using a heterodyne laser interferometer. Second, the original laser interference signal and reference signal are transformed into a low-carrier-frequency interference signal and a low-frequency reference signal using two identical analog mixers and low-pass filters, respectively. Then, a data acquisition card is used to simultaneously acquire the transformed interference signal, reference signal, and AUT output signal, and these are processed to obtain the AUT's excitation acceleration. Finally, by calculating the amplitude and initial phase of the excitation acceleration and output signal, the sensitivity amplitude and phase of the AUT are determined. This method has advantages such as low cost, flexibility, high efficiency, and simplicity. It can measure the sensitivity amplitude and phase of accelerometers within a wide frequency range, significantly eliminates additional phase delay, and improves the sensitivity and phase calibration accuracy at high frequencies.

Description

Technical Field

[0001] This invention relates to a broadband vibration calibration heterodyne laser interferometry method and its measuring device, particularly a broadband vibration calibration heterodyne laser interferometry method and its measuring device based on symmetric differential demodulation. Background Technology

[0002] Piezoelectric, optomechanical, and microelectromechanical system (MEMS) accelerometers have wide applications in earthquake early warning, civil structure health monitoring, track and machinery health monitoring, and medical diagnostics. In these applications, the accelerometer's sensitivity is considered a precisely known value, directly determining the validity of its measurement data. To ensure performance in these applications, the accelerometer must be accurately calibrated. Therefore, developing a suitable vibration calibration method to determine the accelerometer's sensitivity over a wide frequency range is particularly important.

[0003] Currently, the laser interferometry (LI) method recommended by the International Organization for Standardization (ISO) is the preferred method for accelerometer calibration. Depending on the interferometer used, laser interferometry can be divided into two types: null-difference laser interferometer (MLI) and heterodyne laser interferometer (TLI). MLI uses two mutually orthogonal signals containing the excitation displacement to calibrate the accelerometer, achieving relatively high accuracy over a wide frequency range, with its low-frequency range easily below 1 Hz. Compared to MLI, TLI uses a laser interferometric signal with a high carrier frequency to measure the excitation displacement, offering advantages such as high displacement measurement accuracy, wide dynamic range, and low nonlinearity, making it increasingly widely used in broadband vibration calibration. In the past two years, TLI has been gradually applied to the calibration of digital accelerometers, achieving scaling factor and phase shift calibration accuracies as high as 0.2% and 0.1°, respectively. Although TLI can perform vibration calibration over a wide frequency range, its calibration accuracy and frequency range are often contradictory. The calibration performance of TLI depends on its excitation measurement accuracy, which is related to the acquisition and demodulation of the heterodyne laser interferometric signal. Currently, commonly used data acquisition methods include Nyquist sampling (NS), bandpass sampling (BPS), and mixer-and-low-pass filter sampling (MLPFS). The NS method is easy to implement for high-precision high-frequency vibration calibration, but its frequency range is limited. While the BPS method can achieve wideband calibration without any additional analog equipment, it requires complex sampling rate calculation methods and a dedicated acquisition card. The MLPFS method utilizes analog equipment to perform wideband vibration calibration, offering a suitable balance of accuracy and efficiency. However, when the frequency exceeds 5kHz, its sensitivity and phase are significantly affected by the analog low-pass filter. Furthermore, the phase expansion and sine approximation methods used for demodulation are optimal, as proven by multiple related publications.

[0004] Therefore, how to solve the current accelerometer calibration methods, which suffer from complex calibration systems, poor flexibility, high costs, and limited measurement range, especially the inadequacy of sensitivity phase calibration at higher frequencies, has become an urgent technical problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a broadband vibration calibration heterodyne laser interferometry method and its measurement device. This calibration method, by incorporating symmetrical differential demodulation technology, enables calibration frequencies below 1 Hz to reach tens of kHz. Compared with many current mainstream calibration methods, the studied method exhibits better overall performance in terms of calibration accuracy, efficiency, and frequency range.

[0006] The technical solution of this invention is a broadband vibration calibration heterodyne laser interferometry method, which mainly includes: first, using a vibration table to provide vibration excitation of a specific amplitude within a wide frequency range to the accelerometer under test, and using a heterodyne laser interferometer to measure the excitation acceleration of the accelerometer under test; second, using two identical types of analog mixers and low-pass filters to transform the original laser interference signal and reference signal into a low-carrier-frequency interference signal and a low-frequency reference signal, respectively; then, using a data acquisition card to simultaneously acquire the transformed interference signal, reference signal, and output signal of the accelerometer under test, and processing them to obtain the excitation acceleration of the accelerometer under test; finally, by calculating the amplitude and initial phase of the excitation acceleration and output signal, the sensitivity amplitude and phase of the accelerometer under test are determined.

[0007] In the aforementioned broadband vibration calibration heterodyne laser interferometry method, the measurement method includes the following steps:

[0008] S1: The accelerometer under test is fastened to the center of the worktable surface of the vibration table. The accelerometer under test and the worktable surface have the same excitation. The laser beam of the heterodyne laser interferometer, which can simultaneously and directly output the original laser interference signal and the reference signal, is vertically focused on the center of the surface of the accelerometer under test to measure the excitation acceleration of the accelerometer under test.

[0009] S2: The original laser interference signal and reference signal generated by the heterodyne laser interferometer are transformed into a low-carrier frequency interference signal and a low-frequency reference signal by two identical types of analog mixers and low-pass filters, respectively.

[0010] S3: Use a data acquisition card to acquire the transformed low-carrier frequency interference signal, low-frequency reference signal, and output signal of the accelerometer under test, and process them to obtain the excitation acceleration of the accelerometer under test.

[0011] S4: By combining the calculated excitation acceleration and the amplitude and initial phase of the output signal, the sensitivity amplitude and phase of the accelerometer under test are obtained.

[0012] In the aforementioned broadband vibration calibration heterodyne laser interferometry method, the vibration table can provide the accelerometer under test with vibration excitation of a specific amplitude within a wide frequency range. Since the vibration table is excited by a sinusoidal signal, the original laser signal U of the heterodyne laser interferometer... HRF (t) and reference signal U HREF (t) is:

[0013]

[0014] Wherein, modulation phase φ Mod The excitation displacements s(t) and s(t) have the following forms:

[0015]

[0016] In the formula: U HRF f c and They are U HRF The amplitude, carrier frequency, and initial phase of (t), U HREF It's U HREF The magnitude of (t), s p f v and These are the amplitude, frequency, and initial phase of s(t), respectively, and λ is the laser wavelength = 632.8 nm.

[0017] U HRF The bandwidth of (t) depends on the corresponding excitation speed, which is typically much lower than f. c Therefore, an analog mixer and a low-pass filter are used to implement U. HRF (t) and U HREF The downconversion of (t) is performed to significantly reduce the required sampling rate.

[0018] In the aforementioned broadband vibration calibration heterodyne laser interferometry method, the low carrier frequency interference signal U LRF (t), low-frequency reference signal U LREF The signals V(t) and the output signal V(t) of the accelerometer under test are synchronously acquired by the data acquisition card, and can be expressed as:

[0019]

[0020] In the formula: U LRF and U LREF They are U LRF (t) and U LREF The magnitude of (t), f LO1 and f LO2 These are the local frequencies of the mixer. It is the initial phase affected by the low-pass filter delay, V p and These are the amplitude and initial phase of V(t), where t is the amplitude and initial phase of V(t). j This is the sampling time, j = 1, 2, ..., N, where N is the number of samples;

[0021] f LO2 It can get infinitely close to f c This makes U LREF The frequency of (t) is much lower than the cutoff frequency of the low-pass filter, therefore the low-pass filter has a lower frequency for U. LREF The time delay of (t) is negligible.

[0022] In the aforementioned broadband vibration calibration heterodyne laser interferometry method, the sensitivity calibration accuracy of the accelerometer under test depends on the measurement accuracy of the vibration excitation demodulated from the interference signal. This accuracy is related to the phase modulation of the sinusoidal excitation displacement from the collected interference signal. The acquisition of can be expressed as:

[0023]

[0024] In the formula: kπ is an additional phase used to avoid U L1 (t j Arctan calculation at the zero-point intersection The resulting unevenness, and the value of k belongs to the set {0,1,2,…} of integers;

[0025] The amplitude and initial phase of s(t) can be obtained as follows:

[0026]

[0027] In the formula: ω v It is the angular frequency, parameter A s B s C s and D s The corresponding N overdetermined equations can be solved using the least squares method.

[0028] A measurement device for a broadband vibration calibration heterodyne laser interferometer, the device mainly includes: two vibration tables, a low-frequency accelerometer under test, an embedded accelerometer under test, a laser head, a heterodyne laser interferometer, an analog mixer, a low-pass filter, a data acquisition card and a program processing unit;

[0029] Two vibration tables provide sinusoidal excitation in the range of 0.1Hz to 20kHz; the low-frequency accelerometer under test and the embedded accelerometer under test are fixed to the center of the vibration table's working surface, both having consistent sinusoidal excitation; the laser head provides a vertical beam to the low-frequency accelerometer under test and the embedded accelerometer under test; a heterodyne laser interferometer is used to measure the excitation acceleration; an analog mixer and a low-pass filter are used to convert the original laser interference signal and the reference signal; a data acquisition card is used to simultaneously acquire the signals transformed by the analog mixer and low-pass filter, as well as the output signals of the low-frequency accelerometer under test and the embedded accelerometer under test; the program processing unit processes the acquired signals, calculates and saves the fitted amplitude and initial phase of each signal.

[0030] The beneficial effects of this invention are as follows: Compared with the prior art, the broadband vibration calibration heterodyne laser interferometry method based on symmetric differential demodulation has the following advantages:

[0031] (1) The method of the present invention is stable, reliable and practical, and can be applied to the measurement of the sensitivity amplitude and phase of accelerometers in a wide frequency range, especially at high frequencies.

[0032] (2) The method of the present invention is simple, flexible, efficient and low cost. For vibration calibration of accelerometer, only an analog mixer, an analog low-pass filter and a data acquisition card are needed.

[0033] (3) The method of the present invention determines the sensitivity amplitude and phase by applying a symmetric MLPFS consisting of an analog mixer and an analog low-pass filter. The MLPFS can significantly eliminate additional phase delay by utilizing their differential mode.

[0034] (4) Comparative experiments between the method of the present invention and the commonly used MV and EG methods in the range of 0.1 to 10 Hz, and the traditional MLPFS-TLI and NS-TLI methods in the range of 10 Hz to 20 kHz, show that SDD-TLI can achieve satisfactory calibration accuracy for the sensitivity, amplitude and phase of the accelerometer.

[0035] (5) The method of the present invention evaluates the uncertainty of the main error sources in the calibration process, indicating that the SDDTLI method has good calibration performance. Attached Figure Description

[0036] Appendix Figure 1 This is a schematic diagram of a specific implementation apparatus for the method of the present invention;

[0037] Appendix Figure 2 This is a schematic diagram of a broadband vibration calibration heterodyne laser interferometry system based on symmetric differential demodulation.

[0038] Appendix Figure 3This is a flowchart of sensitivity, amplitude, and phase calibration for a wide-frequency-range accelerometer based on SDD-TLI;

[0039] Appendix Figure 4 Sensitivity amplitude and phase of low-frequency AUTs calibrated for SDD-TLI, MV, and EG methods in the range of 0.1–10 Hz;

[0040] Appendix Figure 5 Sensitivity amplitude and phase of mid-to-high frequency AUTs calibrated for SDD-TLI, MLPFS-TLI and NS-TLI MV methods in the range of 10 Hz to 20 kHz.

[0041] Figure labels: 1-Vibration table, 2-Low-frequency accelerometer under test, 3-Embedded accelerometer under test, 4-Laser head, 5-Heterodyne laser interferometer, 6-Analog mixer, 7-Low-pass filter, 8-Data acquisition card, 9-Program processing unit. Detailed Implementation

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0043] Embodiments of the present invention: To address the problems of existing calibration methods for accelerometer calibration, such as system complexity, high cost, poor flexibility, and limited calibration range and accuracy, the present invention provides a broadband vibration calibration heterodyne laser interferometry method based on symmetrical differential demodulation, which is used to measure the sensitivity amplitude and phase of accelerometers over a wide frequency range. The present invention will be described in detail below with reference to the accompanying drawings and specific implementation examples.

[0044] refer to Figure 1 The following is a schematic diagram of an implementation example of the method of the present invention. The device mainly includes: two vibration tables 1, including an ESZ185-400 with a frequency of 0.01 to 100 Hz and a PCB 396C11 with a frequency of 5 Hz to 20 kHz; a low-frequency accelerometer under test 2 (MSV3000); an embedded accelerometer under test 3 (PCB 396C11); a laser head 4; a Polytec heterodyne laser interferometer 5 (OFV-5000); an analog mixer 6 (MC ZAD-1-1+, with a frequency of 0.5 to 500 MHz); a low-pass filter 7 (MC BLP-2.5+, with a cutoff frequency of 2.5 MHz); a data acquisition card 8 (ADLINK 9846, with a maximum sampling rate of 40 MHz); and a program processing unit (9).

[0045] Two vibration tables 1 provide sinusoidal excitation in the range of 0.1Hz to 20kHz; the low-frequency accelerometer under test 2 and the embedded accelerometer under test 3 are fixed to the center of the work surface of the vibration table 1, and both have the same sinusoidal excitation; the laser head 4 provides a vertical beam for the low-frequency accelerometer under test 2 and the embedded accelerometer under test 3; the heterodyne laser interferometer 5 is used to measure the excitation acceleration; the analog mixer 6 and the low-pass filter 7 are used to convert the original laser interference signal and the reference signal; the data acquisition card 8 is used to simultaneously acquire the signal converted by the analog mixer 6 and the low-pass filter 7 as well as the output signal of the low-frequency accelerometer under test 2 and the embedded accelerometer under test 3; the program processing unit 9 processes the acquired signals, calculates and saves the fitted amplitude and initial phase of each signal.

[0046] refer to Figure 2 This is a schematic diagram of a broadband vibration calibration heterodyne laser interferometry system based on symmetrical differential demodulation. The measurement method of this invention mainly includes the following steps:

[0047] Step S1: Obtaining the excitation acceleration of the accelerometer under test (AUT), which includes: fixing the AUT to the center of the vibration table's working surface, ensuring the AUT and the working surface have the same excitation, and using a heterodyne laser interferometer to vertically focus its laser beam onto the center of the AUT's surface to obtain the original laser signal U from the heterodyne laser interferometer. HRF (t) and reference signal U HREF (t) Then the excitation acceleration of the AUT is measured;

[0048] The vibration table can provide vibration excitation of a specific amplitude over a wide frequency range for the AUT. Since the vibration table is excited by a sinusoidal signal, the original laser signal U of the heterodyne laser interferometer... HRF (t) and reference signal U HREF (t) is:

[0049]

[0050] Among them, modulation phase The excitation displacement s(t) has the following form:

[0051]

[0052] In the formula: U HRF ,f c and They are U HRF The amplitude, carrier frequency, and initial phase of (t), U HREF It's U HREF The magnitude of (t), s p ,f v and λ represents the amplitude, frequency, and initial phase of s(t), respectively, and λ is the laser wavelength (632.8 nm).

[0053] Step S2: Low carrier frequency interference signal U LRF (t) and low-frequency reference signal U LREF The acquisition of (t) includes: due to U HRF The bandwidth of (t) depends on the corresponding excitation speed, which is typically much lower than f. c Therefore, an analog mixer and a low-pass filter are used to implement U. HRF (t) and U HREF The down-conversion of (t) is performed to significantly reduce the required sampling rate. The original laser interference signal and reference signal generated by the heterodyne laser interferometer are converted into low-carrier-frequency interference signal and low-frequency reference signal, respectively, using an analog mixer and low-pass filter. Then, the U signal is processed by a data acquisition card. LRF (t), U LREF The output signal V(t) of the AUT and the output signal V(t) are synchronously acquired for subsequent processing;

[0054] Low carrier frequency interference signal U LRF (t), low-frequency reference signal U LREF The AUT's output signal V(t) and the AUT's output signal V(t) are synchronously acquired by the data acquisition card, and can be expressed as:

[0055]

[0056] In the formula: U LRF and U LREF They are U LRF (t) and U LREF The magnitude of (t), f LO1 and f LO2 These are the local frequencies of the mixer. It is the initial phase affected by the low-pass filter delay, V p and These are the amplitude and initial phase of V(t), where t is the amplitude and initial phase of V(t). j This is the sampling time (j = 1, 2, ..., N, where N is the number of samples). f LO2 It can get infinitely close to f c This makes U LREF The frequency of (t) is much lower than the cutoff frequency of the low-pass filter, therefore the low-pass filter has a lower frequency for U. LREF The time delay of (t) is negligible.

[0057] Step S3: Demodulation of the sensitivity amplitude and phase of the AUT, which includes: firstly, obtaining the phase modulated by sinusoidal excitation displacement from the collected interference signal. phase It can be represented as:

[0058]

[0059] In the formula: kπ is an additional phase used to avoid U L1 (t j Arctan calculation at the zero-point intersection The non-uniformity caused by (t) and the value of k belongs to the set {0,1,2,…}.

[0060] The amplitude and initial phase of s(t) can be obtained as follows:

[0061]

[0062] In the formula: ω v It is the angular frequency, parameter A s B s C s and D s The corresponding N overdetermined equations can be solved using the least squares method.

[0063] Will U LRF (t j ) divided into orthogonal bases<I,Q> Two orthogonal signals can be represented as:

[0064]

[0065] Where I and Q can be represented as:

[0066]

[0067] In the formula: f or For the frequencies of I and Q. U is eliminated by a digital low-pass filter. L1 (t j ) and U L2 (t j After removing the high-frequency components, it can be simplified to:

[0068]

[0069] In the formula: f c '1 and f c '2 are U L1 (t) and U L2 The carrier frequency of (t) can be equal to f. c -f LO1 -f or and f c -f LO2 -f or Then, the phase expansion method was used to obtain U. L1 (t j ) and UL2 (t j The modulation phase of two orthogonal signals.

[0070] Next, the calculated phase is fitted using a sine approximation method with four parameters. and the corresponding sampling time series {t j To obtain the amplitude and initial phase of s(t), we have N phases. and the corresponding time series {t j This constitutes an overdetermined system of equations (N is much greater than 4), expressed in matrix form as follows:

[0071]

[0072] A s B s C s and D s The least squares method can be used to solve for s(t). The fitted amplitude and initial phase of s(t) can be obtained by solving for A. s and B s Calculate using the following formula:

[0073]

[0074] In the formula: The phase delay is caused by the time delay of the low-pass filter. Then, the corresponding excitation acceleration amplitude 'a' is calculated using the second derivative. p and initial phase

[0075]

[0076] In the formula: s p and By using parameter A s and B s The solution is then performed. Similarly, for the collected reference signal U... LREF (t j initial phase and V(t) j The fitted amplitude V p and initial phase They can be represented as:

[0077]

[0078] The time delay caused by the low-pass filter inevitably affects the initial phase of the excitation acceleration, especially reducing the calibration accuracy of the sensitivity phase at high frequencies. This delay can be determined using the proposed symmetric differential method.

[0079]

[0080] In the formula: The solution parameter D in formula (5) s .

[0081] Step S4: Adjusting the calibration accuracy of the sensitivity phase at high frequencies, which includes: calculating the fitted amplitude and initial phase of the signal based on the least squares method and second derivative; improving the calibration accuracy of the sensitivity phase at high frequencies through the proposed symmetric differentiation method; and utilizing S... mag The relative standard deviation (S) m,RStd ) and S pha Standard deviation (S p,Std The calibration repeatability of the studied method can be described by the following formula:

[0082]

[0083] Where S mag and S pha They can be represented as:

[0084]

[0085] refer to Figure 3 This is a flowchart illustrating the sensitivity, amplitude, and phase calibration of a wide-frequency-range accelerometer based on SDD-TLI. The measurement method of this invention includes the following steps:

[0086] Step S1: Use the data acquisition card to read the low carrier frequency interference signal and low frequency reference signal transformed by the analog mixer and low-pass filter, as well as the AUT output signal;

[0087] Step S2: By U LRF (t j ) divided into orthogonal bases<I,Q> Two orthogonal signals are used to obtain their modulation phases using the phase expansion method;

[0088] Step S3: Use the sinusoidal approximation method with four parameters to fit the calculated phase and the corresponding sampling time series to obtain the amplitude and initial phase of s(t);

[0089] Step S4: Fit the amplitude and initial phase of s(t) based on the least squares principle, and improve the calibration accuracy of the sensitivity phase caused by time delay by using the proposed symmetric differentiation method;

[0090] Step S5: Select a similar method, i.e., fit the amplitude and initial phase of the collected reference signal and AUT output signal based on the least squares principle;

[0091] Step S6: The calibration repeatability of the method of the present invention is described by the ratio of the fitted amplitude of the AUT output signal to the fitted amplitude of the excitation acceleration, and the difference between the initial phase of the output signal and the excitation acceleration.

[0092] The specific parameters of the device in this embodiment are as follows: two vibration tables, ESZ185-400 with a frequency range of 0.01 to 100 Hz and PCB 396C11 with a frequency range of 5 Hz to 20 kHz, respectively; the accelerometers under test are MSV 3000 and PCB 396C11, respectively; an analog mixer with a frequency range of 0.5 to 500 MHz; a low-pass filter with a cutoff frequency of 2.5 MHz; and a data acquisition card with a maximum sampling rate of 40 MHz.

[0093] To verify the performance of the broadband vibration calibration heterodyne laser interferometry method based on symmetric differential demodulation of this invention in calibrating accelerometers at low frequencies, calibration was performed within the frequency range of 0.1–10 Hz using the method of this invention. The test frequencies were selected based on 1 / 3 octave bands, and each test frequency was calibrated 10 times. To fully verify the calibration accuracy of the method of this invention, the sensitivity amplitude and phase of the embedded AUT were calibrated within the frequency range of 10 Hz–20 kHz using the method of this invention. At each test frequency within this range, the sensitivity amplitude and phase were calibrated 10 times. Table 1 shows the repeatability of the accelerometer sensitivity amplitude and phase calibration in the range of 0.1–20 kHz using the SDD-TLI, MLPFS-TLI, EG, and MV methods of this invention.

[0094] Table 1. Repeatability of accelerometer sensitivity amplitude and phase calibration in the 0.1–20 kHz range using SDD-TLI, MLPFS-TLI, EG, and MV methods.

[0095]

[0096] Figure 4 Sensitivity amplitude and phase measurement results of low-frequency AUTs calibrated for SDD-TLI, MV, and EG methods in the range of 0.1–10 Hz. Throughout the range, the maximum differences between SDD-TLI and the EG and MV methods are 0.067° and 0.183°, respectively, although SDD-TLI shows a smaller difference in Ssensitivity at frequencies below 0.4 Hz. p,Std Slightly larger than the EG and MV methods, but similar to the EG and MV methods at other higher frequencies; Figure 5 Sensitivity amplitude and phase measurement results of mid-to-high frequency AUTs calibrated for SDD-TLI, MLPFS-TLI, and NS-TLI MV methods in the range of 10 Hz to 20 kHz. Throughout the range, the SDD-TLI S... m,RStdThe maximum value was 0.086%, slightly lower than MLPFS-TLI's 0.112% and NS-TLI's 0.101%, and the maximum difference between SDD-TLI and NS-TLI was S. p,Ave Approximately 0.1°, less than the corresponding difference of 0.811° between MLPFS-TLI and NS-TLI, and the SDD-TLI's S p,Std Highly similar to NS-TLI and MLPFS-TLI, except for a few higher frequencies, all are less than 0.1°.

[0097] The foregoing description provides a detailed account of embodiments of the present invention and is not intended to limit the invention in any way. Those skilled in the art can make various optimizations, improvements, and modifications based on this invention. Therefore, the scope of protection of this invention should be defined by the appended claims.

Claims

1. A broadband vibration calibration heterodyne laser interferometry method, characterized by: The method includes the following steps: S1: The accelerometer under test is fastened to the center of the worktable surface of the vibration table. The accelerometer under test and the worktable surface have the same excitation. The laser beam of the heterodyne laser interferometer, which simultaneously outputs the original laser interference signal and the reference signal, is vertically focused on the center of the surface of the accelerometer under test, so as to measure the excitation acceleration of the accelerometer under test. S2: Set up 2 analog mixers and 2 low-pass filters. One analog mixer and one low-pass filter form one group, for a total of 2 groups. Both groups of analog mixers and low-pass filters are used to transform the original laser interference signal and reference signal generated by the heterodyne laser interferometer into a low-carrier frequency interference signal and a low-frequency reference signal. The two analog mixers and two low-pass filters are of the same type and have the same parameters. The purpose of setting up two groups of analog mixers and low-pass filters is to cancel out the phase delay introduced by the analog mixer through differential. S3: Use a data acquisition card to acquire the transformed low-carrier frequency interference signal, low-frequency reference signal, and output signal of the accelerometer under test, and process them to obtain the excitation acceleration of the accelerometer under test. S4: By combining the calculated excitation acceleration and the amplitude and initial phase of the output signal, the sensitivity amplitude and phase of the accelerometer under test are obtained; The vibration table provides the measured accelerometer with vibration excitation of specific amplitude in wide frequency range. Since the excitation signal of the vibration table is sinusoidal, the original laser interference signal U HRF (t) of the heterodyne laser interferometer is: HREF (t) is respectively: （1）， where the modulation phase φ Mod (t) and the excitation displacement s(t) have the following forms: （2）， where: U HRF , f c and are the amplitude, carrier frequency and initial phase of U HRF (t), respectively, U HREF is the amplitude of U HREF (t), s p , f v and are the amplitude, frequency and initial phase of s(t), respectively, and λ is the laser wavelength = 632.8 nm; the bandwidth of U HRF (t) depends on the corresponding excitation velocity; The low carrier frequency interference signal U LRF The low frequency reference signal U LREF The output signal V(t) of the accelerometer under test is acquired simultaneously by a third channel of the data acquisition card, indicated as: （3）， In the formula: U LRF and U LREF They are U LRF (t) and U LREF The magnitude of (t), f LO1 and f LO2 These are the local oscillator frequencies of the analog mixer. It is the initial phase affected by the low-pass filter delay, V p and These are the amplitude and initial phase of V(t), where t is the amplitude and initial phase of V(t). j This is the sampling time, j = 1, 2, …N, where N is the number of sampling points; The sensitivity calibration accuracy of the accelerometer under test depends on the vibration excitation measurement accuracy demodulated from the acquired raw laser interferometer signal. This accuracy is related to the phase modulated by the sinusoidal excitation displacement in the acquired raw laser interferometer signal. It can be solved using the following formula: （4）， In the formula: It is an additional phase used to avoid U L1 (t j Arctan calculation at the zero-point intersection The resulting unevenness, and the value of k belongs to the set {0, 1, 2, …} of integers; For the amplitude and initial phase of s(t), the following formula is used to fit different sampling times {t}. j } and the corresponding phase { Obtain the parameters: （5）， In the formula: It is the angular frequency, parameter A s B s C s and D s Solve using the least squares method; U L1 (t j ) and U L2 (t j ) for U LRF (t j ) divided into orthogonal bases<I, Q> Two orthogonal signals can be represented as: （6）， Where I and Q represent the orthogonal sine and cosine components, respectively: （7）， where: f or frequencies for I and Q; The amplitude and initial phase of s(t) are found by solving A s and B s are calculated with the following equation: （8）， In the formula: The phase delay is caused by the time delay of the low-pass filter.

2. A measuring device for broadband vibration calibration heterodyne laser interferometry as described in claim 1, characterized in that: The device mainly includes: a vibration table (1), an accelerometer under test, a laser head (4), a heterodyne laser interferometer (5), an analog mixer (6), a low-pass filter (7), a data acquisition card (8), and a program processing unit (9); The vibration table (1) provides sinusoidal excitation in the range of 0.1 Hz to 20 kHz; the accelerometer under test is fixed to the center of the working surface of the vibration table (1), and the vibration table (1) and the accelerometer under test have the same sinusoidal excitation; the laser head (4) provides a vertical beam to the accelerometer under test; the heterodyne laser interferometer (5) is used to measure the excitation acceleration; the analog mixer (6) and the low-pass filter (7) are used to convert the original laser interference signal and the reference signal; the data acquisition card (8) is used to simultaneously acquire the signal transformed by the analog mixer (6) and the low-pass filter (7) as well as the output signal of the accelerometer under test; the program processing unit (9) processes the acquired signals, calculates and saves the fitted amplitude and initial phase of each signal.

3. The measuring device for broadband vibration calibration heterodyne laser interferometry according to claim 2, characterized in that: The vibration table (1) and the accelerometer under test are each set to 2, one vibration table provides sinusoidal excitation of 0.01 to 100 Hz, and the other vibration table provides sinusoidal excitation of 5 Hz to 20 kHz.

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