A large bandwidth high sensitivity optical acceleration sensor and measurement method

Abstract

The application relates to the technical field of optical acceleration sensors, and particularly relates to a large-bandwidth high-sensitivity optical acceleration sensor and a measuring method, the sensor comprising a signal generator, a narrow-line-width laser, a circulator, a beam splitter and combiner, an optical fiber A, an optical fiber B, a photoelectric detector, an oscilloscope, an upper computer and a sensitive unit, the sensitive unit comprising a substrate, small containing holes and large containing holes are respectively hollowed out on the surface of the substrate, a small double cascade spring resonator is arranged in the small containing hole, a large double cascade spring resonator is arranged in the large containing hole, a signal output end of the signal generator is connected with a voltage tuning end of the narrow-line-width laser, and an exit end of the narrow-line-width laser is connected with a first port of the circulator. The application effectively solves the problem that the existing optical acceleration sensor cannot simultaneously consider large bandwidth and high sensitivity, and is suitable for fields such as earthquake prediction and monitoring, structure health detection, inertial navigation, vector hydrophone detection and the like.

Description

Technical Field

[0001] This invention relates to the field of optical acceleration sensor technology, specifically a high-bandwidth, high-sensitivity optical acceleration sensor and its measurement method. Background Technology

[0002] Optical accelerometers are sensors that measure acceleration based on optical principles. They possess advantages such as resistance to electromagnetic interference, fast response speed, and suitability for long-distance transmission, and are widely used in fields such as earthquake prediction and monitoring, structural health detection, inertial navigation, and vector hydrophone detection. However, in practical applications, existing optical accelerometers, due to their use of single-degree-of-freedom spring resonators as the sensing element, suffer from a trade-off between operating bandwidth and sensitivity (increasing the operating bandwidth requires decreasing the sensitivity; conversely, increasing the sensitivity requires decreasing the operating bandwidth). This makes it impossible to simultaneously achieve large bandwidth and high sensitivity, thus limiting their applicability. Therefore, it is necessary to invent a high-bandwidth, high-sensitivity optical accelerometer and measurement method to solve the problem of existing optical accelerometers being unable to balance large bandwidth and high sensitivity. Summary of the Invention

[0003] To address the problem that existing optical accelerometers cannot simultaneously achieve both large bandwidth and high sensitivity, this invention provides a large bandwidth and high sensitivity optical accelerometer and a measurement method.

[0004] This invention is achieved using the following technical solution:

[0005] A high-bandwidth, high-sensitivity optical accelerometer includes a signal generator, a narrow-linewidth laser, a circulator, a beam splitter and combiner, fiber A, fiber B, a photodetector, an oscilloscope, a host computer, and a sensing unit.

[0006] The sensitive unit includes a substrate; the surface of the substrate is hollowed out with a small receiving hole and a large receiving hole; a small double-cascaded spring resonator is installed in the small receiving hole; a large double-cascaded spring resonator is installed in the large receiving hole.

[0007] The signal output terminal of the signal generator is connected to the voltage tuning terminal of the narrow linewidth laser; the output terminal of the narrow linewidth laser is connected to the first port of the circulator; the second port of the circulator is connected to the first port of the beam splitter / combiner; the second port of the beam splitter / combiner is connected to the beginning of fiber A; the end face of fiber A is opposite to a small double-cascaded spring resonator; the third port of the beam splitter / combiner is connected to the beginning of fiber B; the end face of fiber B is opposite to a large double-cascaded spring resonator; the third port of the circulator is connected to the incident terminal of the photodetector; the signal output terminal of the photodetector is connected to the signal input terminal of the host computer via an oscilloscope.

[0008] Furthermore, the beam splitter / combiner is a 50:50 beam splitter / combiner.

[0009] Furthermore, a slit A is provided between the wall of the small receiving hole and the outer surface of the substrate, and the tail end of the optical fiber A is inserted into the slit A; a slit B is provided between the wall of the large receiving hole and the outer surface of the substrate, and the tail end of the optical fiber B is inserted into the slit B.

[0010] Furthermore, the small double-cascaded spring resonator includes several spring beams A fixed to the wall of a small receiving hole; a small resonant frame is fixed to the tail end of each spring beam A; a notch A is opened on the small resonant frame opposite to the slit A; several spring beams B are fixed to the inner side of the small resonant frame; a small resonant block is fixed to the tail end of each spring beam B; the tail end face of the optical fiber A is opposite to the side of the small resonant block. The large double-cascaded spring resonator includes several spring beams C fixed to the wall of a large receiving hole; a large resonant frame is fixed to the tail end of each spring beam C; a notch B is opened on the large resonant frame opposite to the slit B; several spring beams D are fixed to the inner side of the large resonant frame; a large resonant block is fixed to the tail end of each spring beam D; the tail end face of the optical fiber B is opposite to the side of the large resonant block.

[0011] A method for measuring high-bandwidth, high-sensitivity optical acceleration, based on a high-bandwidth, high-sensitivity optical accelerometer as described in this invention, is implemented through the following steps:

[0012] First, control the sensor to enter the working mode; the working mode is as follows:

[0013] The signal generator outputs a signal, which is transmitted to a narrow-linewidth laser, causing the narrow-linewidth laser to emit narrow-linewidth laser light. The narrow-linewidth laser light passes through a circulator and is incident on a beam splitter and combiner, where it is split into two optical signals of equal power. The first optical signal passes sequentially through fiber A and notch A to a small resonator, and is reflected by the small resonator to form the first reflected optical signal. The first reflected optical signal passes sequentially through notch A and fiber A to the beam splitter and combiner. The second optical signal passes sequentially through fiber B and notch B to a large resonator, and is reflected by the large resonator to form the second reflected optical signal. The second reflected optical signal passes sequentially through notch B and fiber B to the beam splitter and combiner. The two reflected optical signals interfere in the beam splitter and combiner to form a beat frequency optical signal. The beat frequency optical signal passes through a circulator to a photodetector, and is converted into a beat frequency electrical signal by the photodetector and transmitted to an oscilloscope. The beat frequency electrical signal is displayed on the oscilloscope and transmitted to a host computer.

[0014] In the working mode, the end face of the tail of fiber A and the side of the small resonator together form the first FP resonant cavity, and the end face of the tail of fiber B and the side of the large resonator together form the second FP resonant cavity.

[0015] When there is no acceleration input, the cavity lengths of the first FP resonant cavity and the second FP resonant cavity remain unchanged, the phases of the first reflected light signal and the second reflected light signal remain unchanged, and the waveform of the beat frequency electrical signal remains unchanged.

[0016] When acceleration is input, it acts on two aspects: firstly, on the small double-cascaded spring resonator, causing displacement of the small resonant frame and small resonant block relative to the substrate; secondly, it acts on the large double-cascaded spring resonator, causing displacement of the large resonant frame and large resonant block relative to the substrate. This causes changes in the cavity lengths of both the first and second FP resonant cavities, resulting in changes in the phases of both the first and second reflected light signals, and consequently, changes in the waveform of the beat frequency electrical signal. Then, the host computer uses a white light interference phase demodulation algorithm to read the phase changes of the first and second reflected light signals from the beat frequency electrical signal. These phase changes are then substituted into the sensor's first and second acceleration measurement equations, respectively, to obtain the first and second measurement results of acceleration. Finally, based on these first and second measurement results, the final acceleration measurement result is calculated.

[0017] Furthermore, the first acceleration measurement equation and the second acceleration measurement equation of the sensor are respectively expressed as follows:

[0018] ;

[0019] ;

[0020] In the formula: The first type of measurement result representing acceleration; The second measurement result representing acceleration; Indicates the wavelength of a narrow-linewidth laser; Represents the refractive index of the end face of the fiber optic cable; This indicates the displacement sensitivity of the small resonant block; This indicates the displacement sensitivity of the large resonant block; This represents the phase change of the first reflected light signal; This indicates the amount of phase change in the second reflected light signal.

[0021] Furthermore, the final calculation formula for acceleration is as follows:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] In the formula: The final measurement result representing acceleration; The first type of measurement result representing acceleration; The second measurement result representing acceleration; , All represent weighting coefficients; This indicates the natural frequency of a small double-cascaded spring resonator. This indicates the natural frequency of a large double-cascaded spring resonator. This indicates the flat region range of a small double-cascaded spring resonator. This indicates the flat region range of a large double-cascaded spring resonator. This represents the elastic modulus of spring beam A; This represents the elastic modulus of spring beam B; This represents the elastic modulus of the spring beam C; This represents the elastic modulus of the spring beam D; This indicates the mass of the small resonant frame; This indicates the mass of the small resonator. This indicates the mass of the large resonant frame; This indicates the mass of the large resonant block.

[0028] Compared with existing optical accelerometers, this invention no longer uses a single-degree-of-freedom spring resonator as the sensing unit, but instead uses two double-cascaded spring resonators of different sizes as the sensing unit. This breaks the constraint between operating bandwidth and sensitivity, thus achieving both large bandwidth and high sensitivity, and making the application range no longer limited.

[0029] This invention effectively solves the problem that existing optical accelerometers cannot simultaneously achieve large bandwidth and high sensitivity, and is applicable to fields such as earthquake prediction and monitoring, structural health detection, inertial navigation, and vector hydrophone detection. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the structure of the present invention.

[0031] Figure 2 This is a schematic diagram of the planar structure of the sensitive unit in this invention.

[0032] Figure 3 yes Figure 2 A magnified view of a portion of point A in the middle.

[0033] Figure 4 yes Figure 2 A magnified view of a section at point B in the middle.

[0034] Figure 5 yes Figure 2 A magnified view of a section at point C.

[0035] Figure 6 yes Figure 2 A magnified view of a section at point D.

[0036] Figure 7 This is a three-dimensional structural diagram of the sensitive unit in this invention.

[0037] In the diagram: 1-Signal generator, 2-Narrow linewidth laser, 3-Circulator, 4-Beam splitter and combiner, 5-Fiber A, 6-Fiber B, 7-Photodetector, 8-Oscilloscope, 9-Host computer, 10-Substrate, 10.1-Small receiving aperture, 10.2-Large receiving aperture, 10.3-Slit A, 10.4-Slit B, 11-Spring beam A, 12-Small resonant frame, 12.1-Notch A, 13-Spring beam B, 14-Small resonant block, 15-Spring beam C, 16-Large resonant frame, 16.1-Notch B, 17-Spring beam D, 18-Large resonant block. Detailed Implementation

[0038] A high-bandwidth, high-sensitivity optical accelerometer includes a signal generator 1, a narrow-linewidth laser 2, a circulator 3, a beam splitter and combiner 4, an optical fiber A 5, an optical fiber B 6, a photodetector 7, an oscilloscope 8, a host computer 9, and a sensing unit.

[0039] The sensitive unit includes a substrate 10; the surface of the substrate 10 is respectively hollowed out with a small receiving hole 10.1 and a large receiving hole 10.2; a small double-cascaded spring resonator is disposed in the small receiving hole 10.1; a large double-cascaded spring resonator is disposed in the large receiving hole 10.2.

[0040] The signal output terminal of signal generator 1 is connected to the voltage tuning terminal of narrow linewidth laser 2; the output terminal of narrow linewidth laser 2 is connected to the first port of circulator 3; the second port of circulator 3 is connected to the first port of beam splitter / combiner 4; the second port of beam splitter / combiner 4 is connected to the beginning end of fiber A5; the end face of the end of fiber A5 is opposite to a small double-cascaded spring resonator; the third port of beam splitter / combiner 4 is connected to the beginning end of fiber B6; the end face of the end of fiber B6 is opposite to a large double-cascaded spring resonator; the third port of circulator 3 is connected to the incident end of photodetector 7; the signal output terminal of photodetector 7 is connected to the signal input terminal of host computer 9 through oscilloscope 8.

[0041] The beam splitter / combiner 4 is a 50:50 beam splitter / combiner.

[0042] A slit A10.3 is formed between the wall of the small receiving hole 10.1 and the outer surface of the substrate 10, and the tail end of the optical fiber A5 is inserted into the slit A10.3; a slit B10.4 is formed between the wall of the large receiving hole 10.2 and the outer surface of the substrate 10, and the tail end of the optical fiber B6 is inserted into the slit B10.4.

[0043] The miniature double-cascaded spring resonator includes several spring beams A11 fixed to the wall of the small receiving hole 10.1; a small resonant frame 12 is fixed to the tail end of each spring beam A11; a notch A12.1 opposite to the slit A10.3 is opened on the small resonant frame 12; several spring beams B13 are fixed to the inner side of the small resonant frame 12; a small resonant block 14 is fixed to the tail end of each spring beam B13; the tail end face of the optical fiber A5 is opposite to the side of the small resonant block 14. The large double-cascaded spring resonator includes several spring beams C15 fixed to the wall of the large receiving hole 10.2; the tail ends of each spring beam C15 are jointly fixed to a large resonant frame 16; the large resonant frame 16 has a notch B16.1 opposite to the slit B10.4; several spring beams D17 are fixed to the inner side of the large resonant frame 16; the tail ends of each spring beam D17 are jointly fixed to a large resonant block 18; the tail end face of the optical fiber B6 is opposite to the side of the large resonant block 18.

[0044] A method for measuring high-bandwidth, high-sensitivity optical acceleration, based on a high-bandwidth, high-sensitivity optical accelerometer as described in this invention, is implemented through the following steps:

[0045] First, control the sensor to enter the working mode; the working mode is as follows:

[0046] Signal generator 1 outputs a signal, which is transmitted to narrow-linewidth laser 2, causing narrow-linewidth laser 2 to emit narrow-linewidth laser light. The narrow-linewidth laser light passes through circulator 3 and is incident on beam splitter / combiner 4, where it is split into two optical signals of equal power. The first optical signal passes through fiber A5 and notch A12.1 sequentially and is incident on small resonator 14, where it is reflected to form the first reflected optical signal. The first reflected optical signal passes through notch A12.1 and fiber A5 sequentially and is incident on beam splitter / combiner 4. The second optical signal passes through fiber A5 and notch A12.1 sequentially and is incident on small resonator 14. The light is incident on the large resonator 18 through fiber B6 and notch B16.1, and after being reflected by the large resonator 18, a second reflected light signal is formed. The second reflected light signal is then incident on the beam splitter and combiner 4 through notch B16.1 and fiber B6. The two reflected light signals interfere in the beam splitter and combiner 4 to form a beat frequency light signal. The beat frequency light signal is incident on the photodetector 7 through the circulator 3, and after being converted into a beat frequency electrical signal by the photodetector 7, it is transmitted to the oscilloscope 8. The beat frequency electrical signal is displayed on the oscilloscope 8 and transmitted to the host computer 9.

[0047] In the working mode, the tail end face of optical fiber A5 and the side of small resonator 14 together form the first FP resonant cavity, and the tail end face of optical fiber B6 and the side of large resonator 18 together form the second FP resonant cavity.

[0048] When there is no acceleration input, the cavity lengths of the first FP resonant cavity and the second FP resonant cavity remain unchanged, the phases of the first reflected light signal and the second reflected light signal remain unchanged, and the waveform of the beat frequency electrical signal remains unchanged.

[0049] When acceleration is input, the acceleration acts on two aspects: firstly, on the small double-cascaded spring resonator, causing the small resonant frame 12 and the small resonant block 14 to displace relative to the substrate 10; secondly, it acts on the large double-cascaded spring resonator, causing the large resonant frame 16 and the large resonant block 18 to displace relative to the substrate 10. This causes changes in the cavity lengths of both the first and second FP resonant cavities, resulting in changes in the phases of both the first and second reflected light signals, and consequently, changes in the waveform of the beat frequency electrical signal. Then, the host computer 9 uses a white light interference phase demodulation algorithm to read the phase changes of the first and second reflected light signals from the beat frequency electrical signal, and substitutes these phase changes into the sensor's first and second acceleration measurement equations, respectively, to obtain the first and second measurement results of the acceleration. Finally, based on the first and second measurement results of the acceleration, the final measurement result of the acceleration is calculated.

[0050] The first and second acceleration measurement equations of the sensor are expressed as follows:

[0051] ;

[0052] ;

[0053] In the formula: The first type of measurement result representing acceleration; The second measurement result representing acceleration; Indicates the wavelength of a narrow-linewidth laser; Represents the refractive index of the end face of the fiber optic cable; This indicates the displacement sensitivity of the small resonator 14; This indicates the displacement sensitivity of the large resonant block 18; This represents the phase change of the first reflected light signal; This indicates the amount of phase change in the second reflected light signal.

[0054] The final calculation formula for acceleration is as follows:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] In the formula: The final measurement result representing acceleration; The first type of measurement result representing acceleration; The second measurement result representing acceleration; , All represent weighting coefficients; This indicates the natural frequency of a small double-cascaded spring resonator. This indicates the natural frequency of a large double-cascaded spring resonator. This indicates the flat region range of a small double-cascaded spring resonator. This indicates the flat region range of a large double-cascaded spring resonator. This represents the elastic modulus of spring beam A11; This represents the elastic modulus of spring beam B13; This indicates the elastic modulus of spring beam C15; This represents the elastic modulus of spring beam D17; This represents the mass of the small resonant frame 12; This indicates the mass of the small resonator 14; This indicates the mass of the large resonant frame 16; This indicates the mass of the large resonant block 18.

[0061] In practice, spring beams A11, B13, C15, and D17 are all serpentine spring beams. There are four spring beams A11, arranged symmetrically in a rectangle. There are four spring beams B13, arranged symmetrically in a rectangle. There are four spring beams C15, arranged symmetrically in a rectangle. There are four spring beams D17, arranged symmetrically in a rectangle.

[0062] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A high-bandwidth, high-sensitivity optical accelerometer, characterized in that: Includes a signal generator (1), a narrow linewidth laser (2), a circulator (3), a beam splitter and combiner (4), fiber A (5), fiber B (6), a photodetector (7), an oscilloscope (8), a host computer (9), and a sensing unit; The sensitive unit includes a substrate (10); the surface of the substrate (10) is hollowed out with a small receiving hole (10.1) and a large receiving hole (10.2); a small double-cascaded spring resonator is installed in the small receiving hole (10.1); a large double-cascaded spring resonator is installed in the large receiving hole (10.2); The signal output terminal of the signal generator (1) is connected to the voltage tuning terminal of the narrow linewidth laser (2); the output terminal of the narrow linewidth laser (2) is connected to the first port of the circulator (3); the second port of the circulator (3) is connected to the first port of the beam splitter and combiner (4); the second port of the beam splitter and combiner (4) is connected to the head end of the fiber A (5); the tail end face of the fiber A (5) is opposite to the small double cascade spring resonator; the third port of the beam splitter and combiner (4) is connected to the head end of the fiber B (6); the tail end face of the fiber B (6) is opposite to the large double cascade spring resonator; the third port of the circulator (3) is connected to the incident end of the photodetector (7); the signal output terminal of the photodetector (7) is connected to the signal input terminal of the host computer (9) through the oscilloscope (8).

2. The high-bandwidth, high-sensitivity optical accelerometer according to claim 1, characterized in that: The beam splitter and combiner (4) is a 50:50 beam splitter and combiner.

3. A high-bandwidth, high-sensitivity optical accelerometer according to claim 1 or 2, characterized in that: A slit A (10.3) is provided between the wall of the small receiving hole (10.1) and the outer side of the base (10), and the tail end of the optical fiber A (5) is inserted into the slit A (10.3); a slit B (10.4) is provided between the wall of the large receiving hole (10.2) and the outer side of the base (10), and the tail end of the optical fiber B (6) is inserted into the slit B (10.4).

4. The high-bandwidth, high-sensitivity optical accelerometer according to claim 3, characterized in that: The small double-cascaded spring resonator includes several spring beams A (11) fixed to the wall of the small receiving hole (10.1); a small resonant frame (12) is fixed to the tail end of each spring beam A (11); a notch A (12.1) is opened on the small resonant frame (12) opposite to the slit A (10.3); several spring beams B (13) are fixed to the inner side of the small resonant frame (12); a small resonant block (14) is fixed to the tail end of each spring beam B (13); the tail end face of the optical fiber A (5) is opposite to the side of the small resonant block (14); The large double-cascaded spring resonator includes several spring beams C (15) fixed to the wall of the large receiving hole (10.2); the tail ends of each spring beam C (15) are jointly fixed to a large resonant frame (16); the large resonant frame (16) has a notch B (16.1) opposite to the slit B (10.4); several spring beams D (17) are fixed to the inner side of the large resonant frame (16); the tail ends of each spring beam D (17) are jointly fixed to a large resonant block (18); the tail end face of the optical fiber B (6) is opposite to the side of the large resonant block (18).

5. A method for measuring high-bandwidth, high-sensitivity optical acceleration, the method being implemented based on a high-bandwidth, high-sensitivity optical accelerometer as described in claim 4, characterized in that: This method is implemented using the following steps: First, control the sensor to enter the working mode; the working mode is as follows: The signal generator (1) outputs a signal, which is transmitted to the narrow linewidth laser (2), causing the narrow linewidth laser (2) to emit a narrow linewidth laser. The narrow linewidth laser is incident on the beam splitter and combiner (4) through the circulator (3), and is split into two optical signals of equal power by the beam splitter and combiner (4). The first optical signal is incident on the small resonator (14) through the fiber A (5) and the notch A (12.1) in sequence, and is reflected by the small resonator (14) to form the first reflected optical signal. The first reflected optical signal is incident on the beam splitter and combiner (4) through the notch A (12.1) and the fiber A (5) in sequence. The second optical signal is incident on the beam splitter and combiner (4) through the notch A (12.1) and the fiber A (5) in sequence. Optical fiber B (6) and notch B (16.1) are incident on the large resonator (18) and reflected by the large resonator (18) to form a second reflected light signal; the second reflected light signal is incident on the beam splitter (4) through notch B (16.1) and optical fiber B (6) in sequence; the two reflected light signals interfere in the beam splitter (4) to form a beat frequency light signal; the beat frequency light signal is incident on the photodetector (7) through the circulator (3) and converted into a beat frequency electrical signal by the photodetector (7) and transmitted to the oscilloscope (8); the beat frequency electrical signal is displayed on the oscilloscope (8) and transmitted to the host computer (9) on the other hand. In the working mode, the tail end face of fiber A (5) and the side of small resonator (14) together form the first FP resonant cavity, and the tail end face of fiber B (6) and the side of large resonator (18) together form the second FP resonant cavity. When there is no acceleration input, the cavity lengths of the first FP resonant cavity and the second FP resonant cavity remain unchanged, the phases of the first reflected light signal and the second reflected light signal remain unchanged, and the waveform of the beat frequency electrical signal remains unchanged. When there is an acceleration input, the acceleration acts on the small double-cascaded spring resonator, causing the small resonant frame (12) and the small resonant block (14) to be displaced relative to the substrate (10). On the other hand, it acts on the large double-cascaded spring resonator, causing the large resonant frame (16) and the large resonant block (18) to be displaced relative to the substrate (10). This causes the cavity length of the first FP resonant cavity and the cavity length of the second FP resonant cavity to change, thereby causing the phase of the first reflected light signal and the phase of the second reflected light signal to change, which in turn causes the waveform of the beat frequency electrical signal to change. Then, the host computer (9) uses the white light interference phase demodulation algorithm to read the phase change of the first reflected light signal and the phase change of the second reflected light signal from the beat frequency electrical signal, and substitutes the phase change of the first reflected light signal and the phase change of the second reflected light signal into the first acceleration measurement equation and the second acceleration measurement equation of the sensor, respectively, thereby obtaining the first measurement result and the second measurement result of the acceleration. Then, based on the first measurement result and the second measurement result of the acceleration, the final measurement result of the acceleration is calculated.

6. The method for measuring high-bandwidth, high-sensitivity optical acceleration according to claim 5, characterized in that: The first and second acceleration measurement equations of the sensor are expressed as follows: ； ； In the formula: The first type of measurement result representing acceleration; The second measurement result representing acceleration; Indicates the wavelength of a narrow-linewidth laser; Represents the refractive index of the end face of the fiber optic cable; This indicates the displacement sensitivity of the small resonant block (14); This indicates the displacement sensitivity of the large resonant block (18); This represents the phase change of the first reflected light signal; This indicates the amount of phase change in the second reflected light signal.

7. The method for measuring optical acceleration with a large bandwidth and high sensitivity according to claim 6, characterized in that: The final calculation formula for acceleration is as follows: ； ； ； ； ； In the formula: The final measurement result representing acceleration; The first type of measurement result representing acceleration; The second measurement result representing acceleration; , All represent weighting coefficients; This indicates the natural frequency of a small double-cascaded spring resonator. This indicates the natural frequency of a large double-cascaded spring resonator. This indicates the flat region range of a small double-cascaded spring resonator. This indicates the flat region range of a large double-cascaded spring resonator. The elastic modulus of spring beam A (11) is represented; The elastic modulus of spring beam B (13) is represented; The elastic modulus of spring beam C(15) is represented; The elastic modulus of spring beam D(17) is represented; This represents the mass of the small resonant frame (12); This represents the mass of the small resonant block (14); This represents the mass of the large resonant frame (16); This represents the mass of the large resonant block (18).

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