Double-closed-loop optical accelerometer

Abstract

The invention provides a double-closed-loop optical accelerometer. The double-closed-loop optical accelerometer comprises a sensing head and a signal processing unit, the signal processing unit comprises a laser LD, a first photoelectric detector, a second photoelectric detector, a trans-impedance amplifier, an A / D conversion circuit, a lock-in amplifier, an FPGA, a cantilever beam phase locking controller, a light source power locking controller, a D / A conversion circuit, a linear amplification circuit and a constant current source circuit. The FPGA is used for generating two sinusoidal signals with the same frequency; on the basis that the cantilever beam is stabilized at a closed-loop working point through electromagnetic force driving, phase locking of the cantilever beam is realized through superposition of electromagnetic force modulation, so that the 1 / f noise of the system is reduced, and the influence of stray light interference is eliminated; in addition, closed-loop locking is carried out on the output power of the light source, and low-frequency fluctuation noise and relative intensity noise caused by light power drifting are reduced. The light emitting power of the light source is locked, and the detection precision of the whole optical acceleration is improved.

Description

Technical Field

[0001] This application belongs to the field of optical accelerometer design, and particularly relates to a dual-closed-loop optical accelerometer. Background Technique

[0002] With the progress of technology, the production and life of the people are increasingly inseparable from navigation technology. Accelerometers are one of the key components in inertial navigation systems and are widely used in various fields of national production and life. Traditional accelerometers are based on capacitive effects, piezoresistive effects, or tunnel electron effects. This sensing method has some inherent disadvantages, such as being susceptible to environmental temperature effects and cross-sensitivity effects of electromagnetic interference.

[0003] Compared with traditional accelerometers, optical accelerometers belonging to the MOMES category have strong anti-electromagnetic interference capabilities, small size, high precision, better sensitivity and linearity, and have better prospects and application values.

[0004] However, the weak optical signals of optical accelerometers are susceptible to various noises and uncertainties of optical parameters, which poses challenges to the theoretical high-precision signal processing of optical accelerometers.

[0005] As an accelerometer using an optical detection method, the optical accelerometer applies the sensitive principle of double-beam interference. The schematic diagram of the optical sensing working principle is as Figure 1 shown. When a part of the incident coherent light passes through the transparent medium and is reflected by the phase diffraction grating to form diffracted light; another part passes through the diffraction grating, is reflected by the mirror glued to the bottom of the detection mass block, and then passes through the diffraction grating again to form diffracted light. The two diffracted light beams interfere in the transparent medium similar to a Michelson interferometer, forming a diffraction interference field where the intensity of each fixed-order fringe changes with the distance d between the grating reflection surfaces. According to scalar diffraction theory, the intensity of the diffraction order can be expressed as a function of the gap distance d,

[0006]

[0007]

[0008] where I0 and I1 represent the intensities of the output light of the zeroth and first diffraction orders, and I in is the intensity of the incident light, and λ is the wavelength of the light source.

[0009]

[0010] Among them, m, b, and k represent the central mass, damping coefficient, and spring stiffness respectively, x is the relative displacement of the central detection mass block, and a is the input acceleration. When there is a static acceleration input, the above formula can be simplified to kx = ma. When there is an acceleration input from the outside world, the distance between the reflecting surface and the micro grating will change, resulting in a change in the intensity of the diffraction fringes at each order in the diffraction interference field. The voltage after being detected by the detector and amplified by the transimpedance amplifier can be used as the open-loop output of the micro grating accelerometer. Since the open-loop light intensity output and the spacing d satisfy the cosine function form shown in formula (1), the available open-loop linear measurement range of the actual system is less than λ / 4, and the corresponding acceleration detection range is only dozens of mg, which is difficult to meet the requirements of actual engineering practice.

[0011] In order to improve the dynamic detection range of the optical accelerometer, in the 4th article "Design of the Force Feedback System of Micro Grating Accelerometer" in the 15th volume of the Journal of Navigation and Control in 2016, a closed-loop detection scheme based on electrostatic force feedback was proposed. The sensitive head structure converts the external acceleration change into a light intensity change, the detector converts the light intensity signal into an electrical signal, which becomes the required voltage signal after passing through the conditioning circuit, is compared with the voltage at the closed-loop optimal working point, outputs a feedback control signal through the digital control circuit, and stabilizes the mass block at the closed-loop optimal working point through electrostatic force drive. The electrostatic force feedback signal is positively correlated with the acceleration. Experiments show that the dynamic detection range of the optical accelerometer is increased by 11.9 times compared with the open loop, which improves the dynamic detection range of the optical accelerometer. However, due to the introduction of a second-order nonlinear link by the electrostatic force drive, the actual detection accuracy will instead decrease, and the power consumption of the electrostatic force drive is relatively large, which is not conducive to engineering promotion.

[0012] Patent No. CN109870592 mentions an optical accelerometer based on electromagnetic force drive, which uses electromagnetic drive to achieve closed-loop control of the micro grating accelerometer. Through the electromagnetic force drive module, the position of the cantilever beam is always at the optimal working point, and the feedback signal is used as the closed-loop output signal of the accelerometer. The electromagnetic force has a linear relationship with the feedback voltage, reducing the power consumption and improving the detection linearity.

[0013] However, there is still room for improvement in the closed-loop detection accuracy of the grating accelerometer in the entire system. Summary of the Invention

[0014] The present invention proposes a dual-closed-loop optical accelerometer, which improves the closed-loop detection accuracy of the grating accelerometer considering optical power fluctuations, stray light interference, and 1 / f noise of the system.

[0015] The present invention proposes a dual-closed-loop optical accelerometer, including: a sensitive head and a signal processing unit;

[0016] The signal processing unit includes: a laser diode (LD), a first photodetector, a second photodetector, a transimpedance amplifier, an A / D conversion circuit, a lock-in amplifier, an FPGA, a cantilever beam phase-locking controller, a light source power-locking controller, a D / A conversion circuit, a linear amplifier circuit, and a constant current source circuit; wherein, the FPGA is used to generate a first high-frequency signal and a second high-frequency signal, and the first high-frequency signal and the second high-frequency signal are sinusoidal signals with the same frequency;

[0017] The first photodetector, the transimpedance amplifier, the A / D conversion circuit, the lock-in amplifier, the cantilever beam phase-locking controller, the FPGA, the D / A conversion circuit, the linear amplifier circuit, and the sensor head form an optical accelerometer cantilever beam phase-locking loop;

[0018] The laser diode (LD), the second photodetector, the transimpedance amplifier, the A / D conversion circuit, the light source power-locking controller, the D / A conversion circuit, and the constant current source circuit form an optical accelerometer light source locking loop.

[0019] Optionally, the first photodetector is used to convert the optical signal output by the sensor head into a first current signal and send it to the transimpedance amplifier; the first current signal is used to indicate the working position of the cantilever beam;

[0020] The transimpedance amplifier is used to convert the first current signal into an analog voltage signal containing acceleration detection information and send it to the lock-in amplifier through the A / D conversion circuit;

[0021] The lock-in amplifier is used to perform digital demodulation and low-pass filtering on the digital voltage signal according to the first high-frequency signal, and send the processed signal to the cantilever beam phase-locking controller;

[0022] The cantilever beam phase-locking controller is used to generate a first closed-loop error signal according to the received signal;

[0023] The D / A conversion circuit is used to receive the mixed signal of the second high-frequency signal and the first closed-loop error signal, convert it to obtain a first analog voltage signal, and send it to the linear amplifier circuit;

[0024] The linear amplifier circuit is used to perform impedance matching on the first analog voltage signal and load it onto the sensor head magnet torque actuator, adjust the working position of the cantilever beam, and make the cantilever beam stable at the closed-loop working point;

[0025] The second photodetector is packaged together with the laser diode (LD) and is used to send a second current signal to the transimpedance amplifier; the second current signal is used to indicate the optical power output backward by the laser diode (LD);

[0026] The transimpedance amplifier is also used to convert the second current signal into an analog voltage signal containing optical power information and send it to the light source power-locking controller through the A / D conversion circuit;

[0027] The light source power locking controller is used to generate a second closed-loop error signal according to a preset optical power and a received signal;

[0028] The D / A conversion circuit is further configured to convert the second closed-loop error signal to obtain a second analog voltage signal and send it to the constant current source circuit;

[0029] The constant current source circuit is used to load the received signal onto the laser LD, so that the output power of the light source tends to the preset optical power.

[0030] Optionally, the second closed-loop error signal is used to cancel the influence brought by the optical power fluctuation in the phase-locked loop of the optical accelerometer cantilever beam.

[0031] Optionally, the second high-frequency signal U m is expressed as: U m = Acosω0t;

[0032] The first high-frequency signal is expressed as: U s = Bcos(ω0Tk);

[0033] Wherein, A and B are amplitudes, ω0 is the modulation angular frequency, t is time, T is the sampling period, and k is the corresponding discrete time.

[0034] Optionally, the diffracted light intensity output by the sensing head detected by the first photodetector is expressed as U 0p (t);

[0035]

[0036] Wherein, I in is the light intensity of the incident light provided by the laser LD, R is the transimpedance gain of the first photodetector, α is the optical path loss, d0 is the initial position of the cantilever beam, I noise is the stray light interference without interference; Δx is the displacement change of the cantilever beam caused by the external input acceleration, Δx m is the displacement change of the cantilever beam caused by the modulation signal; λ is the wavelength of the incident light.

[0037] Optionally, the demodulation signal generated by the lock-in amplifier is expressed by the following formula:

[0038]

[0039] Wherein, U 0p (k) is the digital voltage before demodulation, k1 represents the gain of the transimpedance amplifier, k2 represents the gain of the A / D conversion circuit, J nIt represents the nth order coefficient of the first kind of Bessel function, where n = 1, 2, 3... ∞; ω1 corresponds to the angular frequency of the position change Δx of the cantilever beam.

[0040] Optionally, the output after low-pass filtering of the lock-in amplifier is expressed as U(k);

[0041]

[0042] K is the gain coefficient of the forward channel, and Δk is the gain fluctuation of I in of.

[0043] Optionally, the sensitive head includes: a mass block, a cantilever beam, a diffraction grating, a transparent medium, a coil, a yoke, a magnet, an electrode plate, and a mirror; among them,

[0044] The diffraction grating is adhered to the upper layer of the transparent medium, and a structure similar to an F-P resonant cavity is formed between the detection mass block and the diffraction grating; the mirror is arranged on the mass block and is opposite to the diffraction grating;

[0045] The coil, yoke, magnet, and electrode plate form a magnetic torque actuator mechanism for realizing the functions of phase modulation and feedback control of the cantilever beam.

[0046] The beneficial technical effects of this application:

[0047] The present invention proposes a double-closed-loop optical accelerometer, and the present invention improves the above-mentioned electromagnetic force-driven optical accelerometer. On the basis of driving the cantilever beam to be stable at the closed-loop working point by electromagnetic force, electromagnetic force modulation is superimposed to realize the phase locking of the cantilever beam, so as to reduce the 1 / f noise of the system and eliminate the influence of stray light interference; in addition, the output power of the light source is locked to reduce the low-frequency fluctuation noise and relative intensity noise caused by the drift of the light power. Through the closed-loop control of electromagnetic force drive, the working point of the cantilever beam is locked and the driving current is monitored and adjusted to lock the output light power of the light source, so as to improve the detection accuracy of the entire optical accelerometer on the premise of ensuring the dynamic detection range and linearity. Description of the Drawings

[0048] Figure 1 It is a schematic diagram of the sensing principle of the optical accelerometer;

[0049] Figure 2 It is a schematic diagram of the sensitive head of the optical accelerometer;

[0050] Figure 3 It is a schematic diagram of the signal processing unit. Detailed Embodiments

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0052] The features and exemplary embodiments of various aspects of the present invention will be described in detail below. In the following detailed description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to those of ordinary skill in the art that the present invention may be practiced without some of these specific details. The following description of the embodiments is only intended to provide a better understanding of the present invention by showing examples of the present invention. The present invention is in no way limited to any specific arrangements and methods set forth below, but covers any improvements, substitutions, and modifications of structures, methods, and devices without departing from the spirit of the present invention. Well-known structures and technologies are not shown in the drawings and the following description to avoid unnecessarily obscuring the present invention.

[0053] It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other, and each embodiment may be referred to and cited by each other. The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0054] The present invention will be further described in detail below in combination with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0055] Please refer to Figures 1-3 , the present invention provides a dual-closed-loop optical accelerometer.

[0056] The present invention proposes a dual-closed-loop optical accelerometer, which mainly includes two working loops: the optical accelerometer cantilever beam phase-locked loop and the optical accelerometer light source locked loop.

[0057] The dual-closed-loop optical accelerometer includes two parts: a sensitive head and a signal processing unit. The signal processing unit consists of a cantilever beam phase-locked loop and a light source locked loop.

[0058] The structure of the sensitive head is as Figure 2 shown, and it includes a mass block, a cantilever beam, a diffraction grating, a transparent medium, a coil, a yoke, a magnet, an electrode plate, and a mirror. Among them, the metal diffraction grating is adhered to the upper layer of the transparent medium, and a structure similar to an F-P resonant cavity is formed between the detection mass block and the diffraction grating. The coil, yoke, magnet, and electrode plate form a magnetic torque actuator mechanism for realizing the functions of cantilever beam phase modulation and feedback control. The voltage applied to the coil is the modulation voltage Um and the feedback voltage U f consists of two parts. U m is used to implement the phase modulation of the cantilever beam. The original closed-loop error signal is modulated to a high frequency by introducing a high-frequency carrier signal. U f Provides the feedback voltage to keep the accelerometer cantilever beam locked at the closed-loop operating point.

[0059] The signal processing unit is shown in Figure 3 and consists of a laser LD (light source), a photodetector PD1, a photodetector PD2, a transimpedance amplifier, an A / D conversion circuit, a lock-in amplifier, an FPGA, a D / A conversion circuit, a linear amplifier circuit, and a constant current source circuit.

[0060] The photodetector PD1 is used to convert the optical signal output by the sensing head into a current signal.

[0061] The transimpedance amplifier converts the current signal into an analog voltage signal containing the detected acceleration information.

[0062] The A / D conversion circuit converts the analog voltage signal into a digital voltage signal, which enters the lock-in amplifier for digital demodulation and low-pass filtering.

[0063] The FPGA generates a high-frequency sine signal of the same frequency, which is used for the phase modulation of the cantilever beam and the phase-sensitive demodulation of the lock-in amplifier respectively.

[0064] The cantilever beam phase-locking controller and the light source power controller are digital closed-loop controllers based on the FPGA, including but not limited to digital PID controllers.

[0065] The D / A conversion circuit converts the processed digital voltage signal into an analog signal.

[0066] The linear amplifier circuit performs impedance matching on the converted analog voltage signal and loads it onto the coil of the electromagnetic drive module.

[0067] The photodetector PD2 can be packaged together with the laser LD. PD2 is used to monitor the optical power output backward by the laser LD.

[0068] The current output by the photodetector PD2 is converted into an analog voltage signal through a transimpedance amplifier, digitized through an A / D conversion circuit, enters the light source power locking controller for arithmetic processing, and the output deviation signal is loaded onto the laser LD through a D / A conversion circuit and a constant current source circuit, making the light source output power tend to a steady-state value.

[0069] Working process of the cantilever beam phase-locked loop: The FPGA generates two high-frequency sine signals with the same frequency. One of them is used as the modulation signal, which is loaded onto the coil of the sensitive head magnet torque generator through the D / A conversion circuit and the linear amplification circuit to achieve the phase modulation of the cantilever beam. When an acceleration signal is input, the modulated light intensity signal is photoelectrically converted by the photodetector PD1, and then converted into a digital voltage signal with acceleration information through the transimpedance amplifier and the A / D conversion circuit. It is then subjected to phase-sensitive demodulation with another high-frequency sine signal generated by the FPGA to filter out the 1 / f noise and background stray light interference. The processed digital signal is sent to the cantilever beam phase-locked controller for arithmetic processing to obtain a feedback signal U that has a linear relationship with the external acceleration signal. f , on the one hand, it is the digital output of the closed-loop system, and on the other hand, it is loaded onto the magnet torque generator of the sensitive structure to achieve servo balance.

[0070] The modulation signal U m is expressed as:

[0071] U m = Acosω0t

[0072] A is the amplitude of the modulation signal, and ω0 is the modulation angular frequency. The diffracted light intensity detected by the photodetector PD1 can be expressed as U 0p (t);

[0073]

[0074] I in is the light intensity of the incident light, R is the transimpedance gain of the photodetector, α is the optical path loss, d0 is the initial position of the cantilever beam, I noise is the stray light interference without interference. Δx is the displacement change of the cantilever beam caused by the external input acceleration, and Δx m is the displacement change of the cantilever beam caused by the external input acceleration;

[0075] The process of phase-sensitive demodulation is as follows:

[0076]

[0077] is the demodulated digital voltage, U 0p (k) is the digital voltage before demodulation, B is the amplitude corresponding to the demodulation signal, T is the sampling period, k is the corresponding discrete time, k1 represents the gain of the transimpedance amplifier, k2 represents the gain of the A / D conversion circuit, and J n represents the nth order coefficient of the first kind of Bessel function, where n = 1, 2, 3... ω1 corresponds to the angular frequency of the cantilever beam position change Δx.

[0078] The output after the low-pass filtering of the lock-in amplifier is:

[0079]

[0080] k is the gain coefficient of the forward path, and Δk is the gain fluctuation of the laser power I in After introducing the cantilever beam phase modulation, it can be seen that the demodulated output effectively suppresses the I noise corresponding stray light interference and 1 / f noise. Compared with the electromagnetic force-driven optical accelerometer mentioned in the background technology, the closed-loop detection accuracy is optimized; however, there is still light source intensity noise within the filtering bandwidth of the lock-in amplifier, and the light source I in will generate low-frequency fluctuations Δk during long-term operation, which still restricts the detection accuracy and closed-loop stability of the entire optical accelerometer. To solve this problem, we introduce a light source locking loop to make the output power of the light source stable and tend to a constant value.

[0081] Working process of the light source locking loop: The photodetector PD2 is packaged with the laser LD. PD2 is used to monitor the optical power output backward by the laser LD. The output current is converted into a voltage signal through a transimpedance amplifier, and then converted into a digital voltage through an A / D conversion circuit. In the light source power locking controller, it is subtracted from the voltage reference value corresponding to the ideal optical power to generate a deviation signal. After arithmetic processing, it enters the constant current source circuit through the D / A conversion circuit and finally serves as the drive current of the laser LD to achieve a stable output of the laser LD power Δk≈0. By introducing the light source locking loop, a stable output laser power is obtained, the light source intensity noise of the laser is suppressed, and the problem of optical power drift with temperature change is solved, thereby effectively improving the detection accuracy and the closed-loop stability of the optical accelerometer.

[0082] The present invention introduces a cantilever beam phase locking loop into the traditional electromagnetic-driven optical accelerometer. On the one hand, in addition to using electromagnetic force for closed-loop control of the cantilever beam, the cantilever beam is also modulated at a high frequency. The demodulated output can effectively suppress the I noise corresponding stray light interference and the 1 / f noise of the system, and effectively improve the detection accuracy of the optical accelerometer on the premise of ensuring the dynamic range;

[0083] A light source locking loop is introduced into the electromagnetic-driven optical accelerometer. By real-time monitoring of the output power of the laser LD, the deviation amount is sent to the light source power locking controller for arithmetic processing, which speeds up the tracking speed of the loop and improves the dynamic characteristics of the loop. The steady-state output of the laser LD power can be achieved. The light source intensity noise of the laser is suppressed, and the problem of optical power drift with temperature change is solved, thereby further improving the closed-loop detection accuracy of the optical accelerometer.

[0084] As described above, it is only a further embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the scope disclosed by the present invention, according to the technical solution and concept of the present invention, making equivalent substitutions or changes, all belong to the protection scope of the present invention.

Claims

1. A dual closed-loop optical accelerometer, characterized in that, Comprising: A sensitive head and a signal processing unit; The signal processing unit includes: a laser LD, a first photodetector, a second photodetector, a transimpedance amplifier, an A / D conversion circuit, a lock-in amplifier, an FPGA, a cantilever beam phase-locking controller, a light source power-locking controller, a D / A conversion circuit, a linear amplifier circuit, and a constant current source circuit; wherein, the FPGA is used to generate a first high-frequency signal and a second high-frequency signal, and the first high-frequency signal and the second high-frequency signal are sine signals with the same frequency; The first photodetector, the transimpedance amplifier, the A / D conversion circuit, the lock-in amplifier, the cantilever beam phase-locking controller, the FPGA, the D / A conversion circuit, the linear amplifier circuit, and the sensitive head form an optical accelerometer cantilever beam phase-locking loop; The laser LD, the second photodetector, the transimpedance amplifier, the A / D conversion circuit, the light source power-locking controller, the D / A conversion circuit, and the constant current source circuit form an optical accelerometer light source locking loop.

2. The dual-closed-loop optical accelerometer according to claim 1, characterized in that The first photodetector is used to convert the optical signal output by the sensitive head into a first current signal and send it to the transimpedance amplifier; the first current signal is used to indicate the working position of the cantilever beam; The transimpedance amplifier is used to convert the first current signal into an analog voltage signal containing acceleration detection information and send it to the lock-in amplifier through the A / D conversion circuit; The lock-in amplifier is used to perform digital demodulation and low-pass filtering on the digital voltage signal according to the first high-frequency signal and send the processed signal to the cantilever beam phase-locking controller; The cantilever beam phase-locking controller is used to generate a first closed-loop error signal according to the received signal; The D / A conversion circuit is used to receive the mixed signal of the second high-frequency signal and the first closed-loop error signal, perform conversion to obtain a first analog voltage signal, and send it to the linear amplifier circuit; The linear amplifier circuit is used to perform impedance matching on the first analog voltage signal and load it onto the sensitive head magnet torque device to adjust the working position of the cantilever beam so that the cantilever beam is stabilized at the closed-loop working point; The second photodetector is packaged together with the laser LD and is used to send a second current signal to the transimpedance amplifier; the second current signal is used to indicate the optical power output backward by the laser LD; The transimpedance amplifier is also used to convert the second current signal into an analog voltage signal containing optical power information and send it to the light source power-locking controller through the A / D conversion circuit; The light source power-locking controller is used to generate a second closed-loop error signal according to the preset optical power and the received signal; The D / A conversion circuit is also used to convert the second closed-loop error signal to obtain a second analog voltage signal and send it to the constant current source circuit; The constant current source circuit is used to load the received signal onto the laser LD so that the light source output power tends to the preset optical power.

3. The double-closed-loop optical accelerometer according to claim 1, characterized in that The second closed-loop error signal is used to cancel the influence brought by the optical power fluctuation in the optical accelerometer cantilever beam phase-locking loop.

4. The double-closed-loop optical accelerometer according to claim 1, characterized in that, Second high-frequency signal U m It is expressed as: U m = Acosω0t; The first high-frequency signal is expressed as: U s = Bcos(ω0Tk); Wherein, A and B are amplitudes, ω0 is the modulation angular frequency, t is time, T is the sampling period, and k is the corresponding discrete time.

5. The dual-closed-loop optical accelerometer according to claim 4, wherein The diffracted light intensity output from the sensitive head detected by the first photodetector is expressed as U 0p (t); Among them, I in is the light intensity of the incident light provided to the laser LD, R is the transimpedance gain of the first photodetector, α is the optical path loss, d0 is the initial position of the cantilever beam, I noise is the stray light interference without interference; Δx is the displacement change of the cantilever beam caused by the externally input acceleration, Δx m is the displacement change of the cantilever beam caused by the modulation signal; λ is the wavelength of the incident light.

6. The double-closed-loop optical accelerometer according to claim 5, characterized in that The demodulation signal generated by the lock-in amplifier is expressed by the following formula: Among them, U 0p (k) is the digital voltage before demodulation, k1 represents the gain of the transimpedance amplifier, k2 represents the gain of the A / D conversion circuit, J n represents the nth order coefficient of the first kind of Bessel function, n = 1, 2, 3... ∞; ω1 corresponds to the angular frequency of the change in the position Δx of the cantilever beam.

7. The double-closed-loop optical accelerometer according to claim 6, characterized in that, The output after low-pass filtering by the lock-in amplifier is expressed as U(k); K is the gain coefficient of the forward channel, and Δk is the gain fluctuation of I in ​ 8. The dual-closed-loop optical accelerometer according to claim 1, wherein The sensitive head includes: a mass block, a cantilever beam, a diffraction grating, a transparent medium, a coil, a yoke, a magnet, an electrode plate, and a mirror; among them, the diffraction grating is adhered to the upper layer of the transparent medium, and a structure similar to an F-P resonant cavity is formed between the detection mass block and the diffraction grating; the mirror is arranged on the mass block and is opposite to the diffraction grating; the coil, the yoke, the magnet, and the electrode plate form a magnetic torque actuator mechanism for realizing the functions of phase modulation and feedback control of the cantilever beam.

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