A spatial light path detection system and method for anti-magnetic levitation resonator multi-dimensional motion

Abstract

The application discloses a kind of anti-magnetic suspension resonator multi-dimensional motion space optical path detection system and method.Firstly, the coordinates and parameters of space light source are drafted, and the basic parameters of resonator are drafted;Then, the path beam characteristic parameters of light beam on the incident and exit path of resonator are obtained by simulation calculation;Then, the suspension potential well device structure is designed according to the path beam characteristic parameters;After that, the space optical path is built according to the foregoing design, the potential well device carrying the resonator is placed in the space optical path and the position is adjusted, so that the resonator is finally located in the set coordinates in simulation, and the coaxial state of optical path and the non-volume collision state are maintained;Finally, the photoelectric detection system with multi-dimensional motion signal acquisition function is placed at the detection end of optical path, and the detection of resonator multi-dimensional motion is carried out.The optical path state of the application is good, which is beneficial to detection, and can be used as a reference for the first disclosed design paradigm.

Description

Technical Field

[0001] This invention belongs to the field of optical precision measurement technology, specifically relating to a spatial optical path detection system and method for antimagnetic levitation harmonic oscillators undergoing multidimensional motion. Background Technology

[0002] Antimagnetic levitation is an emerging cutting-edge technology. In an antimagnetic levitation system, the strong magnetic field generated by a permanent magnet causes a resonator made of diamagnetic material to levitate under the influence of magnetic force, forming a three-dimensional potential well for the resonator and thus stably capturing it. In the fields of acceleration and mechanics sensing, this system has proven to have ultra-high precision and has the potential to play an important role as a core device in applications such as vibration monitoring, gravity measurement, and fundamental physics research including non-Newtonian gravity, short-range forces, and the Standard Model.

[0003] The antimagnetic levitation system has the following unique technical advantages: the harmonic oscillator has no mechanical contact with the environment, avoiding mechanical losses such as clamping dissipation and stress relaxation, and is expected to achieve ultra-high sensing sensitivity and long-term stability; it adopts a passive levitation mechanism, which does not require harsh low temperature environment and complex motion cooling technology, resulting in low power consumption, low cost, and more stable system.

[0004] In this system, achieving high-precision mechanical sensing requires accurate measurement of the motion of the antimagnetically levitated resonator. Currently, the academic community generally uses optical precision measurement methods for detection. In the paper "Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator," the antimagnetically levitated resonator is a polyethylene sphere with a diameter of 2 μm. A 633 nm laser beam illuminates the sphere from above at an angle, and then a detector collects the scattered light from the sphere directly above. The motion information of the resonator is obtained based on the change in the intensity of the scattered light. In the paper "Lens-Free Optical Detection of Thermal Motion of a Submillimeter Sphere Diamagnetically Levitated in High Vacuum," the antimagnetically levitated resonator is an acrylic sphere with a diameter of 500 μm. An optical fiber is placed on each side of the resonator, parallel and offset by a certain distance. The detection beam exits from one optical fiber and illuminates the resonator. After being focused by the sphere resonator, it is transmitted to the other optical fiber and collected by a detector. The change in the collected light intensity reflects the motion information of the resonator.

[0005] The optical detection methods described in the aforementioned literature share a common problem: the horizontal and vertical motion information of the harmonic oscillator is mixed in the same signal, making it difficult to distinguish motion in different dimensional directions. It is known that to accurately and without crosstalk distinguish the motion of a suspended spherical harmonic oscillator in different dimensions, a high-quality, coaxial, collision-free, and highly efficient space detection optical path is required, coupled with a photoelectric detection system capable of acquiring multi-dimensional motion signals. Otherwise, volume collisions will lead to reduced signal-to-noise ratio, nonlinearity introduced by diffraction effects, and long-term drift introduced by thermal expansion. However, in the field of antimagnetic levitation, no such space detection optical path meeting these conditions has been found, nor has a description of the corresponding optical path design process or experimental paradigm been found. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a spatial optical path detection system and method for multidimensional motion of antimagnetic levitation harmonic oscillators, aiming to achieve the advantages of coaxiality, no volume collision, and high detection efficiency. The invention also describes in detail the design process of the corresponding optical path and the antimagnetic levitation potential well device in cooperation, providing a reference for research in the field of antimagnetic levitation as an experimental and design paradigm.

[0007] This invention is achieved through the following technical solution: A spatial optical path detection method for multidimensional motion of magnetically levitated harmonic oscillators: S1. Construct a spatial coordinate system in the computer, set up a spatial light source and determine the coordinates and initial spatial beam characterization parameters of the spatial light source, set up a harmonic oscillator and determine the basic parameters of the harmonic oscillator; S2. The spatial light source emits a spatial beam toward the harmonic oscillator. The spatial beam is incident on the harmonic oscillator and emitted after modulation. The spatial beam is simulated and calculated using the coordinates of the spatial light source and the initial spatial beam characterization parameters to obtain the spatial beam characterization parameters of the incident path and the path on the exit path of the spatial beam before and after modulation. S3. Based on the obtained path space beam characterization parameters, design an antimagnetic levitation potential well device for placing the resonator; perform magnetic field simulation on the antimagnetic levitation potential well device, calculate the magnetic potential energy of the resonator on the antimagnetic levitation potential well device, and then simulate the levitation of the resonator in the antimagnetic levitation potential well device; if the resonator is levitated and the antimagnetic levitation potential well device does not collide with the space beam in volume, output the antimagnetic levitation simulation parameters and proceed to step S4; otherwise, repeat steps S1-S3. S4. According to the antimagnetic levitation simulation parameters, place a spatial light source and build a spatial optical path; place the antimagnetic levitation potential well device carrying the resonator into the spatial optical path, so that the resonator is located in the coordinates specified in the basic parameters. S5. A photoelectric detection system is placed at the detection end of the spatial optical path. The harmonic oscillator undergoes multidimensional motion in the antimagnetic levitation potential well device. The photoelectric detection system is used to detect the multidimensional motion of the harmonic oscillator.

[0008] In step S1, the basic parameters of the harmonic oscillator include data such as the material, size, and coordinates of the harmonic oscillator in the spatial coordinate system.

[0009] The resonator is a spherical antimagnetic levitation resonator, which is made of antimagnetic material, and the antimagnetic material is one or more of the following: quartz, polystyrene, acrylic, and antimagnetic polymer.

[0010] In step S1, the spatial coordinate system is provided with X, Y, and Z directions in the translation direction. The X, Y, and Z directions are mutually orthogonal translational coordinate axes, and the direction of the centroid of the harmonic oscillator is taken as the Y direction.

[0011] In step S2, the spatial beam is a fundamental mode Gaussian beam, and the optical axis of the spatial beam is placed coaxially with the geometric symmetry axis of the harmonic oscillator 2. The characterization parameters of the spatial beam include the wavelength and q parameter of the fundamental mode Gaussian beam.

[0012] The path characteristics parameters of the spatial beam before and after modulation by the harmonic oscillator, including the incident and exit paths, are calculated as follows: After the spatial beam enters the resonator, it is modulated by the resonator. When the spatial beam meets the requirements of paraxial ray and geometric optics, the path q parameters at different positions on the incident and exit paths of the spatial beam before and after modulation by the resonator are calculated using the ray matrix method. The required path spatial beam characterization parameters are obtained through the path q parameters.

[0013] In step S3, the magnetic field simulation uses the finite element method to solve for the static magnetic induction field generated by the antimagnetic levitation potential well device. Then, calculate the total potential energy E, which consists of the magnetic potential energy of the harmonic oscillator and the gravitational potential energy. The formula for calculating the total potential energy E is as follows: ; Where mgy is gravitational potential energy. It is magnetic potential energy. Let be the spatial coordinates of the harmonic oscillator sphere. It is magnetic susceptibility. y is the vacuum permeability, y is the coordinate of the center of mass of the harmonic oscillator in the direction of gravity, m is the mass of the harmonic oscillator, g is the acceleration due to gravity, and d is the velocity of the oscillator. V It is a volumetric infinitesimal element.

[0014] In step S3, the design of the antimagnetic levitation potential well device for placing the resonator specifically includes: The antimagnetic levitation potential well device includes an upper permanent magnet and a lower permanent magnet. The upper permanent magnet is a triangular-like permanent magnet distributed circumferentially around the center. The lower permanent magnet is an extended triangular-like permanent magnet distributed circumferentially around the center.

[0015] The polarization directions of the triangular-like permanent magnet and the extended triangular-like permanent magnet both point towards or away from the geometric center of the upper or lower permanent magnet they are located in. The geometric centers of the upper and lower permanent magnets are vertically aligned, and the polarization directions of the triangular-like permanent magnet and the extended triangular-like permanent magnet are opposite.

[0016] An upper through hole is provided at the geometric center of the upper permanent magnet, and the upper through hole serves as the levitation region for carrying the resonator.

[0017] The aforementioned triangular-like extended permanent magnet is disposed at the lower end of the triangular-like permanent magnet. The end of the triangular-like extended permanent magnet closer to the geometric center is closer to the geometric center than the other end of the triangular-like permanent magnet.

[0018] The side of the triangular permanent magnet and the extended triangular permanent magnet that is away from the geometric center can be optionally connected to an extension segment, i.e., an additional quadrilateral permanent magnet can be added as an extension segment.

[0019] The aforementioned antimagnetic levitation potential well device is equipped with a light transmission channel for spatial optical path transmission.

[0020] When the light transmission channel is used for horizontal transmission of the spatial optical path: the upper permanent magnet is divided into two halves, and the two halves are separated by a light transmission channel parallel to the optical axis of the spatial optical path. The width of the light transmission channel is greater than the diameter of the light spot on the spatial optical path.

[0021] When the light-transmitting channel is used for vertical transmission in a spatial optical path: a lower through-hole is provided at the geometric center of the lower permanent magnet, and the upper through-hole and the lower through-hole together serve as the light-transmitting channel. The diameter of the inscribed circle of the light-transmitting channel is larger than the diameter of the light spot on the spatial optical path.

[0022] The method for calculating the spot diameter is as follows: Based on the path spatial beam characterization parameters calculated in step S2, the 1 / e spot radius at each position on the path is calculated using the path q parameter. The spot radius R(z) is calculated as follows: ; Where z is the position coordinate, and q(z) is the path parameter q of coordinate z.

[0023] In step S4, the antimagnetic levitation potential well device carrying the resonator is placed in the spatial optical path, so that the resonator is located in the coordinates set in the basic parameters, as follows: Before placing the antimagnetic levitation potential trap device into the spatial optical path, a beam cross-section analyzer is placed at the detection end of the spatial optical path to receive the spatial beam in the spatial optical path and record the optical axis position of the spatial beam. The antimagnetic levitation potential trap device is placed on a three-axis displacement stage, and then the three-axis displacement stage is moved to adjust the placement position of the antimagnetic levitation potential trap device. At the same time, the beam cross-section analyzer is observed to adjust the device so that after the spatial beam enters the resonator on the antimagnetic levitation potential trap device, it is modulated by the resonator and emitted to the recorded optical axis position, and there is no volume collision between the spatial beam and the antimagnetic levitation potential trap device.

[0024] In step S5, the photoelectric detection system includes a multi-dimensional motion signal acquisition function, and the photoelectric detection system is one or more of a four-quadrant detector and a D-shaped mirror-balanced detector.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes for the first time a detection scheme that sets up a light transmission channel for a spatial optical path in a double-layer antimagnetic levitation potential well device, uses a displacement stage to adjust the relative position of the potential well device and the optical path, and observes the beam cross-section to determine the state of the optical path. It has the advantages of being coaxial and having no volume collision, which is beneficial for crosstalk-free detection of the multidimensional motion of the harmonic oscillator, improving detection efficiency, enhancing the signal-to-noise ratio, avoiding nonlinearity introduced by diffraction effects, and avoiding signal drift introduced by thermal expansion.

[0026] This invention provides the first detailed description of a complete detection method design process involving optical path design, device structure design, and experimental adjustment methods, which can serve as an experimental and design paradigm to provide a reference for research in the field of antimagnetic levitation. Attached Figure Description

[0027] Figure 1 This is a flowchart of a spatial optical path detection method for multidimensional motion of an antimagnetic levitation harmonic oscillator according to the present invention; Figure 2 This is a simulation diagram of the beam transmission in the second step of an embodiment of the present invention; Figure 3 This is a diagram showing the beam simulation calculation results of the second step in an embodiment of the present invention; Figure 4 This is a structural diagram of the potential well device designed in the third step of Embodiment 1 of the present invention; Figure 5 This is a simulation result of the magnetic field of the potential well device designed in the third step of Embodiment 1 of the present invention; Figure 6 This is a diagram showing the calculation results of the potential well restoring force of the harmonic oscillator in the third step of Embodiment 1 of the present invention; Figure 7 This is an experimental schematic diagram of the fourth step of constructing the space detection optical path in Embodiment 1 of the present invention; Figure 8 This is a structural diagram of the potential well device designed in the third step of Embodiment 2 of the present invention; Figure 9 This is a simulation result of the magnetic field of the potential well device designed in the third step of Embodiment 2 of the present invention; Figure 10 This is a diagram showing the calculation results of the potential well restoring force of the harmonic oscillator in the third step of Embodiment 2 of the present invention; Figure 11 This is a schematic diagram of the experiment for constructing the space detection optical path in the fourth step of Embodiment 2 of the present invention; Figure 12 This is a structural diagram of the potential well device designed in the third step of Embodiment 3 of the present invention; Figure 13 This is a simulation result of the magnetic field of the potential well device designed in the third step of Embodiment 3 of the present invention; Figure 14 This is a diagram showing the calculation results of the potential well restoring force of the harmonic oscillator in the third step of Embodiment 3 of the present invention; Figure 15 This is an experimental schematic diagram of the fourth step of building a space detection optical path in Embodiment 3 of the present invention.

[0028] In the figure: 1-Focusing lens, 2-Resonator, 3-Antimagnetic levitation potential well device one, 4-Triaxial displacement stage, 5-Beam cross section analyzer, 6-Antimagnetic levitation potential well device two, 7-Antimagnetic levitation potential well device three, 8-Suspension area, 9-Light transmission channel, 10-Lower layer through hole. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It is readily understood that, based on the technical solutions of the present invention, those skilled in the art can propose various interchangeable structural methods and implementations without altering the essential spirit of the invention. Therefore, the following specific embodiments and accompanying drawings are merely illustrative examples of the technical solutions of the present invention and should not be considered as the entirety of the present invention or as limitations or restrictions on the technical solutions of the present invention.

[0030] Figure 1 This is a flowchart of a spatial optical path detection method for resisting the multidimensional motion of a magnetically levitated harmonic oscillator according to the present invention. As shown in the figure, the overall process is divided into two parts: design and experiment. First, the spatial optical path detection scheme is designed, and then the experimental system is built to guide the process. The following embodiments are performed according to the flowchart, and the specific implementation of each step will be described in detail.

[0031] Includes the following steps: S1. Construct a spatial coordinate system in the computer, set up a spatial light source in the spatial coordinate system and determine the coordinates of the spatial light source and the initial spatial beam characterization parameters, set up the harmonic oscillator 2 and determine the basic parameters of the harmonic oscillator 2. S2. A spatial light source emits a spatial beam toward the resonator 2. The beam transmission is simulated. The optical axis of the spatial beam and the geometric symmetry axis of the resonator 2 are placed coaxially, so that the emitted spatial beam passes through the resonator 2. The spatial beam is incident on the resonator 2 and modulated by the resonator 2 before being emitted. The spatial beam is simulated and calculated using the coordinates of the spatial light source and the initial spatial beam characterization parameters. The incident path and the path spatial beam characterization parameters of the spatial beam before and after modulation by the resonator 2 are obtained. S3. Based on the obtained path spatial beam characterization parameters, design the structure of the antimagnetic levitation potential well device for placing the resonator 2; this structure should avoid volume collision with the set spatial beam. Perform magnetic field simulation on the antimagnetic levitation potential well device, calculate the magnetic potential energy of the resonator 2 on the antimagnetic levitation potential well device, and then simulate the levitation of the resonator 2 in the antimagnetic levitation potential well device; if the resonator 2 can levitate and the antimagnetic levitation potential well device does not collide with the spatial beam, output the antimagnetic levitation simulation parameters and proceed to step S4; otherwise, repeat steps S1-S3. S4. Based on the simulation parameters of antimagnetic levitation obtained from the simulation results of steps S1-S3, place a spatial light source in the experimental platform to generate a spatial beam and build a spatial optical path; use a three-axis displacement stage 4 to place the antimagnetic levitation potential well device carrying the resonator 2 into the spatial optical path, and then use the three-axis displacement stage 4 to adjust the position of the device so that the resonator 2 is located in the coordinates specified in the basic parameters, that is, the resonator 2 is finally located in the set coordinates in the simulation, and the optical axis of the spatial beam and the geometric symmetry axis of the resonator 2 are placed coaxially. The spatial beam enters the resonator 2, is modulated and then emitted to form a new spatial optical path. There is no volume collision between the spatial optical path and the antimagnetic levitation potential well device. S5. At the detection end of the spatial optical path, a photoelectric detection system is placed. The harmonic oscillator 2 moves in multiple dimensions above the antimagnetic levitation potential well device. The photoelectric detection system is used to detect the multidimensional motion of the harmonic oscillator 2.

[0032] In simple terms, the invention first determines the coordinates and parameters of the spatial light source and the basic parameters of the resonator. Then, it simulates and calculates the path beam characteristics along the incident and exit paths of the beam through the resonator. Based on these path beam characteristics, a suspended potential well device structure is designed. Next, a spatial optical path is constructed according to the aforementioned design. The potential well device carrying the resonator is placed within the spatial optical path and its position is adjusted so that the resonator is ultimately located at the set coordinates in the simulation, maintaining the coaxiality and collision-free state of the optical path. Finally, a photoelectric detection system with multi-dimensional motion signal acquisition capabilities is placed at the optical path detection end to detect the multi-dimensional motion of the resonator. This invention features a good optical path state, facilitating detection, and can serve as a reference for a newly disclosed design paradigm.

[0033] In step S1, the basic parameters of the harmonic oscillator 2 include data such as the material, size, and coordinates of the harmonic oscillator 2 in the spatial coordinate system; Resonator 2 is a spherical antimagnetic levitation resonator made of a transparent antimagnetic material, which is one or more of the following: quartz, polystyrene (PS), acrylic, and antimagnetic polymers. The diameter of resonator 2 is on the sub-millimeter or millimeter scale.

[0034] In step S1, the spatial coordinate system is set with X, Y, and Z directions in the translation direction. The X, Y, and Z directions are mutually orthogonal translational coordinate axes, and the direction of the centroid of the harmonic oscillator 2 is taken as the Y direction.

[0035] In step S2, the spatial beam is a fundamental mode Gaussian beam, and the spatial beam characterization parameters include the wavelength and q-parameter of the fundamental mode Gaussian beam. The q-parameter (complex beam parameter) is a complex physical quantity used to uniformly describe two characteristics of the Gaussian beam when it propagates in free space or an optical system: the radius of curvature of the equiphase surface and the spot size.

[0036] In step S2, the path spatial beam characterization parameters on the incident and exit paths before and after modulation by the resonator 2 are calculated as follows: The harmonic oscillator 2 can be considered a spherical optical element, and its effect on the beam can be represented by a ray matrix related to its size and the refractive index of the material. After the spatial beam enters the harmonic oscillator 2, it is modulated. When the spatial beam meets the requirements of paraxial rays and geometric optics, the ray matrix method in the field of geometric optics is used to calculate the path q parameters at different positions on the incident and exit paths of the spatial beam before and after modulation by the harmonic oscillator 2. The required path spatial beam characterization parameters are obtained through the path q parameters.

[0037] Paraxial rays require that the angle between the ray and the optical axis is very small.

[0038] Specifically, geometric optics requires that the beam propagation aperture be much larger than the wavelength of light.

[0039] In step S3, during the magnetic field simulation, the static magnetic induction field generated by the antimagnetic levitation potential well device is solved using the finite element method. Then calculate the total potential energy E, which consists of the magnetic potential energy of harmonic oscillator 2 plus the gravitational potential energy. The formula for calculating the total potential energy E is: ; Where mgy is gravitational potential energy. It is magnetic potential energy. r Let the coordinates of the harmonic oscillator be the sphere in space. χ y is the magnetic susceptibility, μ0 is the free permeability, y is the coordinate of the center of mass of the harmonic oscillator 2 in the direction of gravity, i.e., the Y direction, m is the mass of the harmonic oscillator (2), g is the gravitational acceleration, and d is the magnetic susceptibility. V Let be a volumetric infinitesimal element. Calculate the total potential energy at each location in space. The spatial minimum value is the deepest point of the potential well, which is the stable levitation position of the harmonic oscillator 2.

[0040] In step S3, the structure of the antimagnetic levitation potential well device for placing the resonator 2 is specifically designed as follows: The antimagnetic levitation potential well device includes an upper permanent magnet and a lower permanent magnet. The upper permanent magnet is a triangular permanent magnet, which is distributed around the center along the circumference, so that the triangular permanent magnets are arranged symmetrically. The lower permanent magnet is an extended triangular permanent magnet, which is distributed around the center along the circumference, so that the quadrilateral permanent magnets are arranged symmetrically.

[0041] The polarization directions of the triangular-like permanent magnet and the extended triangular-like permanent magnet both point towards or away from the geometric center of the upper or lower permanent magnet on which they are located. The geometric centers of the upper and lower permanent magnets are vertically aligned, and the polarization directions of the triangular-like permanent magnet and the extended triangular-like permanent magnet are opposite, so as to form a stable levitation potential well at the geometric center of the device.

[0042] The end of the triangular-like extended permanent magnet closer to the geometric center is closer than the end of the triangular-like permanent magnet closer to the geometric center. The side of the triangular-like permanent magnet and the side of the triangular-like extended permanent magnet furthest from the geometric center may or may not be connected to an extension segment.

[0043] An upper through hole is provided at the geometric center of the upper permanent magnet. The upper through hole forms a constraint in the three-axis direction and forms an antimagnetic levitation potential well. The upper through hole serves as the levitation region 8 that carries the resonator 2.

[0044] The width of the light transmission channel is set to be greater than the diameter of the light spot on the spatial optical path. The light spot diameter is calculated as follows: Based on the path spatial beam characterization parameters obtained in step S2, the 1 / e spot radius at each position on the path is calculated using the path q parameter. The spot radius R(z) is calculated as follows: ; Where z is the position coordinate, and q(z) is the path parameter q of coordinate z.

[0045] Specifically, the spatial optical path is set to horizontal transmission, the upper permanent magnet is set to contain an even number of triangular permanent magnets, the upper layer is set to be divided into two halves, and the two halves are separated by a light-transmitting channel 9 parallel to the optical axis of the spatial optical path. The width of the channel is greater than the diameter of the light spot 2R(z) on the optical path.

[0046] Alternatively, the spatial optical path can be set as vertical transmission, with a through hole at the geometric center of the lower layer. The through holes in the upper and lower layers can be set together as the light transmission channel 9, and the diameter of the inscribed circle of the through hole is larger than the diameter of the light spot on the optical path 2R(z).

[0047] In step S4, the antimagnetic levitation potential well device carrying the resonator 2 is placed in the spatial optical path, and then the position of the device is adjusted using a displacement stage so that the resonator 2 is located in the coordinates set in the basic parameters, as follows: Before placing the antimagnetic levitation potential well device into the spatial optical path, a beam cross-section analyzer 5 is placed at the detection end of the spatial optical path to receive the spatial beam in the spatial optical path and record the optical axis position of the spatial beam. The antimagnetic levitation potential well device is placed on a three-axis displacement stage, and then the three-axis displacement stage is moved to adjust the placement position of the antimagnetic levitation potential well device. At the same time, the beam cross-section analyzer 5 is observed. The adjustment is made so that after the spatial beam enters the resonator 2 on the antimagnetic levitation potential well device, the output beam obtained after modulation by the resonator 2 is located at the recorded optical axis position, and there is no volume collision between the spatial beam and the antimagnetic levitation potential well device, and the spot radius of the spatial beam is consistent with the calculated value.

[0048] Among them, the presence or absence of a volume collision can be determined from the beam cross-section analyzer 5, and the instrument can also automatically calculate the radius of the beam spot.

[0049] In step S5, the photoelectric detection system includes a multi-dimensional motion signal acquisition function. The photoelectric detection system is one or more of the following: a four-quadrant detector (QPD) and a D-shaped mirror-balanced detector (D-BPD). Specific Implementation Example 1: Step 1. Determine the coordinates of the space source and the spatial beam characterization parameters. Specifically, the space source is determined to be a fundamental mode Gaussian beam with a wavelength of 1550nm. The beam characterization parameter q at the source is determined to be q1. It is known that when q1 is determined, the expression of the entire Gaussian beam of the source is uniquely determined, and its beam waist position, radius, divergence angle and other parameters can be calculated.

[0051] The material, size, and coordinates of the antimagnetic levitation resonator are determined. Specifically, the resonator is proposed to be spherical, made of antimagnetic material PS, with a diameter of 1.2 mm, and its center coordinates are selected near the waist of the light source beam.

[0052] The second step is to perform beam transmission simulation, in which the spatial beam and the antimagnetic levitation resonator are placed coaxially. The spatial beam is incident on the resonator and exits after being affected by the resonator.

[0053] Since the size of the proposed harmonic oscillator is much larger than the wavelength of the beam, and the Gaussian beam meets the requirements of paraxial rays, the ray matrix method (ABCD law) from the field of geometric optics is used to simulate and calculate the q parameters at different positions on the incident and exit paths.

[0054] like Figure 2 As shown, the ray matrix of the homogeneous medium is The harmonic oscillator can be considered as a spherical optical element. Its effect on a light beam can be viewed as passing through a sphere from air to a medium, propagating a distance of diameter 2R within the sphere, and then passing through another sphere from the medium to air. Ultimately, the spherical harmonic oscillator can be represented by a ray matrix that depends on its size and the refractive index of the material. ; Figure 2 At the light source, q1 becomes q2 before the incident harmonic oscillator after passing through a uniform medium. After passing through the harmonic oscillator, q2 becomes q3 at the exit point. Then, q3 is transmitted to a distant point and becomes q4. The q parameter at each position along the entire optical path can be calculated using the ray matrix method.

[0055] Figure 2 The solid and dashed lines illustrate the different effects of changing the position of the harmonic oscillator on the incident beam. Figure 2 The dimensions shown are for illustrative purposes only and do not reflect actual sizes. Changing the position of the resonator relative to the light source alters the propagation length in the uniform medium before incidence, thus changing the q-parameters along the subsequent path. A change in q1 at the light source changes the q-parameters throughout the entire path, specifically altering the 1 / e spot radius at each position along the path. The calculation method is as follows: ; In the beam propagation simulation, different values ​​of q1 were selected, and the beam spot diameter at 9.4 mm after emission was calculated when the resonator was at different positions relative to the beam waist of the source beam. The calculation results are as follows: Figure 3 As shown.

[0056] It should be noted that the ray matrix method used in this embodiment is only an example method in beam transmission simulation. In other embodiments, for the sake of convenience of analysis, ray tracing, wave optics and other methods can be used to simulate beam transmission under different applicable ranges of harmonic oscillator size. These methods can also calculate the spot radius at each position on the path without affecting the essential spirit of the present invention.

[0057] The third step is to design the structure of the antimagnetic levitation potential well device where the harmonic oscillator is located, based on the calculated characterization parameters of the spatial beam along the incident and exit paths. This structure should avoid volumetric collisions with the designated spatial beam.

[0058] Specifically, according to Figure 3 Based on the calculation results, q1 = -0.04 + 0.0007i is proposed, and the resonator is proposed to be located at 0.9 mm, corresponding to a beam diameter of 0.45 mm at 9.4 mm after emission. Under the above proposed parameters, the q parameters and beam diameter at each point on the incident and emission paths are further calculated to guide the subsequent structural design of the potential well device.

[0059] Designed potential well devices such as Figure 4 As shown, it consists of several N52 neodymium iron boron permanent magnets, divided into upper and lower layers, each layer consisting of 8 identical permanent magnets. Within each layer, the permanent magnets are symmetrically arranged. In the upper layer, the polarization direction points towards the geometric center; in the lower layer, the polarization direction points away from the geometric center. The polarization directions of the upper and lower layers are opposite to form a stable levitation potential well at the geometric center of the device. A through-hole is provided at the geometric center of the upper layer, forming a triaxial constraint and an antimagnetic levitation potential well. This through-hole serves as the levitation region 8 supporting the resonator.

[0060] The spatial optical path is set to horizontal transmission. The upper layer is divided into two halves, separated by a light-transmitting channel 9 parallel to the optical axis of the spatial optical path. The channel is 20mm long and 0.59mm wide, which is larger than the diameter of the light spot on the path in the beam transmission simulation. With this design, the spatial light path can pass through the potential well device almost unobstructed, which can be considered as avoiding volumetric collisions.

[0061] After designing the potential well device structure, magnetic field simulation and magnetic potential energy calculation of the harmonic oscillator are performed on the structure to simulate the levitation of the harmonic oscillator in the potential well device.

[0062] In the magnetic field simulation, the finite element method is used to solve for the static magnetic induction field generated by the potential well device. The solution results are as follows Figure 5 As shown.

[0063] Then, based on the magnetic field simulation results, the magnetic potential energy of the harmonic oscillator is calculated, and its gravitational potential energy is added to obtain the total potential energy. The calculation method is as follows: ; Where mgy is gravitational potential energy. It is magnetic potential energy. r Let the coordinates of the harmonic oscillator be the sphere in space. χ y is the magnetic susceptibility, μ0 is the free permeability, y is the coordinate of the center of mass of harmonic oscillator 2 in the direction of gravity, i.e., the Y-axis, m is the mass of harmonic oscillator 2, g is the acceleration due to gravity, and d is the magnetic susceptibility. V It is a volumetric infinitesimal element.

[0064] The total potential energy at each location in the calculation space is minimized; the point where the total potential energy is minimized indicates the deepest part of the potential well, which is the stable levitation position of the resonator. Specifically, by taking the partial derivative of the total potential energy at each location, the restoring force on the resonator at that location can be obtained. When the restoring force is zero, it indicates that the resonator is located at the deepest part of the potential well, which is the levitation position. The x and z axes are defined on a horizontal plane, with the z-axis along the light transmission channel 9, the y-axis at the geometric center, and the origin at the interface between the upper and lower magnets. Figure 6 The calculation results of the restoring force of the harmonic oscillator are shown. It can be seen that in the designed potential well device structure, the suspension position is (0 μm, 799 μm, 0 μm). The spherical harmonic oscillator can be suspended at this position, and the potential well device structure will not have a volume collision with the space beam. Therefore, we can proceed to the fourth step.

[0065] It should be noted that the potential well device structure set in this embodiment is only for illustrative purposes. In other embodiments, various designs can be made based on different application considerations. For example, linear quadrupole, cylindrical quadrupole, axisymmetric potential well structures can be adopted, or the number of permanent magnets (as shown in Embodiment 2 below) and materials can be changed. These designs will not change the principle of antimagnetic levitation and will not affect the essential spirit of the present invention.

[0066] Step 4. Construct the coaxial spatial optical path according to the aforementioned parameters. The experimental procedure is as follows: Figure 7 As shown, the arrow indicates the direction of beam transmission. Figure 7 The dimensions shown are for illustrative purposes only and do not reflect the actual sizes.

[0067] Specifically, the collimated Gaussian beam with a diameter of 2.1 mm is adjusted to coaxially pass through the focusing lens 1 with a focal length of 40 mm, so that when it exits from the focusing lens 1, q1 = -0.04 + 0.0007i.

[0068] Before placing the potential well device 3, a beam cross-section analyzer 5 was placed at the detection end of the optical path to receive the beam and record the optical axis position. Then, the antimagnetic levitation potential well device 3, carrying the resonator 2, was placed into the spatial optical path using a triaxial displacement stage 4. The position of the device 3 was adjusted using the displacement stage 4, while the beam cross-section analyzer 5 was observed simultaneously. The adjustment ensured that the emitted beam was located at the recorded optical axis position, without volume collision, and that the beam spot radius matched the calculated value. The presence or absence of volume collision can be determined from the beam spot image on the beam cross-section analyzer 5, which can also automatically calculate the beam spot radius.

[0069] Step 5. At the detection end of the spatial optical path, a photoelectric detection system with multi-dimensional motion signal acquisition function is placed to detect the multi-dimensional motion of the harmonic oscillator. The photoelectric detection system includes: a four-quadrant detector (QPD), a D-shaped mirror-balanced detector (D-BPD), etc. Specific Implementation Example 2 The first and second steps are the same as in Example 1.

[0071] The third step is to design the structure of the antimagnetic levitation potential well device where the harmonic oscillator is located, based on the calculated characterization parameters of the spatial beam along the incident and exit paths. This structure should avoid volumetric collisions with the designated spatial beam.

[0072] Specifically, according to Figure 3 Based on the calculation results, q1 = -0.04 + 0.0007i is proposed, and the resonator is proposed to be located at 0.9 mm, corresponding to a beam diameter of 0.45 mm at 9.4 mm after emission. Under the above proposed parameters, the q parameters and beam diameter at each point on the incident and emission paths are further calculated to guide the subsequent structural design of the potential well device.

[0073] Designed potential well devices such as Figure 8 As shown, it consists of several N52 neodymium iron boron permanent magnets, divided into upper and lower layers, each layer consisting of six identical permanent magnets. Within each layer, the permanent magnets are arranged symmetrically. In the upper layer, the polarization direction points towards the geometric center; in the lower layer, the polarization direction points away from the geometric center. The polarization directions of the upper and lower layers are opposite to form a stable levitation potential well at the geometric center of the device. A through-hole is provided at the geometric center of the upper layer, forming a triaxial constraint and an antimagnetic levitation potential well. This through-hole serves as the levitation region 8 supporting the resonator.

[0074] The spatial optical path is set to horizontal transmission. The upper layer is divided into two halves, separated by a light-transmitting channel 9 parallel to the optical axis of the spatial optical path. The channel is 20mm long and 0.64mm wide, which is larger than the diameter of the light spot on the path in the beam transmission simulation. With this design, the spatial light path can pass through the potential well device almost unobstructed, which can be considered as avoiding volumetric collisions.

[0075] After designing the potential well device structure, magnetic field simulation and magnetic potential energy calculation of the harmonic oscillator are performed on the structure to simulate the levitation of the harmonic oscillator in the potential well device.

[0076] In the magnetic field simulation, the finite element method is used to solve for the static magnetic induction field generated by the potential well device. The solution results are as follows Figure 9 As shown.

[0077] Then, based on the magnetic field simulation results, the magnetic potential energy of the harmonic oscillator is calculated, and its gravitational potential energy is added to obtain the total potential energy. The calculation method is as follows: Where mgy is gravitational potential energy. It is magnetic potential energy. r Let the coordinates of the harmonic oscillator be the sphere in space. χ y is the magnetic susceptibility, μ0 is the free permeability, y is the coordinate of the center of mass of the harmonic oscillator 2 in the direction of gravity, i.e., the Y direction, m is the mass of the harmonic oscillator (2), g is the gravitational acceleration, and d is the magnetic susceptibility. V It is a volumetric infinitesimal element.

[0078] The total potential energy at each location in the calculation space is minimized; the point where the total potential energy is minimized indicates the deepest part of the potential well, which is the stable levitation position of the resonator. Specifically, by taking the partial derivative of the total potential energy at each location, the restoring force on the resonator at that location can be obtained. When the restoring force is zero, it indicates that the resonator is located at the deepest part of the potential well, which is the levitation position. The x and z axes are defined on a horizontal plane, with the z-axis along the light transmission channel 9, the y-axis at the geometric center, and the origin at the interface between the upper and lower magnets. Figure 10 The calculation results of the restoring force of the harmonic oscillator are shown. It can be seen that in the designed potential well device structure, the suspension position is (0 μm, 740 μm, 6 μm). The spherical harmonic oscillator can be suspended at this position, and the potential well device structure will not have a volume collision with the space beam. Therefore, we can proceed to the fourth step.

[0079] Step 4. Construct the coaxial spatial optical path according to the aforementioned parameters. The experimental procedure is as follows: Figure 11 As shown, the arrow indicates the direction of beam transmission. Figure 11 The dimensions shown are for illustrative purposes only and do not reflect the actual sizes.

[0080] Specifically, the collimated Gaussian beam with a diameter of 2.1 mm is adjusted to coaxially pass through the focusing lens 1 with a focal length of 40 mm, so that when it exits from the lens 1, q1 = -0.04 + 0.0007i.

[0081] Before placing the potential well device 6, a beam cross-section analyzer 5 was placed at the detection end of the optical path to receive the beam and record the optical axis position. Then, the antimagnetic levitation potential well device 6, carrying the resonator 2, was placed into the spatial optical path using a triaxial displacement stage 4. The position of the device 6 was adjusted using the displacement stage 4, while the beam cross-section analyzer 5 was observed simultaneously. The adjustment ensured that the emitted beam was located at the recorded optical axis position, without volume collision, and that the beam spot radius matched the calculated value. The presence or absence of volume collision can be determined from the beam spot image on the beam cross-section analyzer 5, which can also automatically calculate the beam spot radius.

[0082] Step 5 is the same as in Example 1. Specific Implementation Example 3 The first and second steps are the same as in Example 1.

[0084] The third step is to design the structure of the antimagnetic levitation potential well device where the harmonic oscillator is located, based on the calculated characterization parameters of the spatial beam along the incident and exit paths. This structure should avoid volumetric collisions with the designated spatial beam.

[0085] Specifically, according to Figure 3 Based on the calculation results, q1 = -0.04 + 0.0007i is proposed, and the resonator is proposed to be located at 0.9 mm, corresponding to a beam diameter of 0.45 mm at 9.4 mm after emission. Under the above proposed parameters, the q parameters and beam diameter at each point on the incident and emission paths are further calculated to guide the subsequent structural design of the potential well device.

[0086] Designed potential well devices such as Figure 12 As shown, it consists of several N52 neodymium iron boron permanent magnets, divided into upper and lower layers, each layer consisting of 8 identical permanent magnets. Within each layer, the permanent magnets are symmetrically arranged. In the upper layer, the polarization direction points towards the geometric center; in the lower layer, the polarization direction points away from the geometric center. The polarization directions of the upper and lower layers are opposite to form a stable levitation potential well at the geometric center of the device. A through-hole is provided at the geometric center of the upper layer, forming a triaxial constraint and an antimagnetic levitation potential well. This through-hole serves as the levitation region 8 supporting the resonator.

[0087] The spatial optical path is set as a vertical transmission from bottom to top. A through-hole is set at the geometric center of the lower layer, and the through-holes of the upper and lower layers are set together as the light transmission channel 9. The lower through-hole 10 is set to have a height of 5mm and an inscribed circle diameter of 0.78mm; the upper through-hole is set to have a height of 1.5mm and an inscribed circle diameter of 1.5mm. The inscribed circle diameters of the through-holes are all set to be larger than the diameter of the light spot on the optical path. With this design, the spatial light path can pass through the potential well device almost unobstructed, which can be considered as avoiding volumetric collisions.

[0088] After designing the potential well device structure, magnetic field simulation and magnetic potential energy calculation of the harmonic oscillator are performed on the structure to simulate the levitation of the harmonic oscillator in the potential well device.

[0089] In the magnetic field simulation, the finite element method is used to solve for the static magnetic induction field generated by the potential well device. The solution results are as follows Figure 13 As shown.

[0090] Then, based on the magnetic field simulation results, the magnetic potential energy of the harmonic oscillator is calculated, and its gravitational potential energy is added to obtain the total potential energy. The calculation method is as follows: Where mgy is gravitational potential energy. It is magnetic potential energy. r Let the coordinates of the harmonic oscillator be the sphere in space. χ y is the magnetic susceptibility, μ0 is the free permeability, y is the coordinate of the center of mass of the harmonic oscillator 2 in the direction of gravity, i.e., the Y direction, m is the mass of the harmonic oscillator (2), g is the gravitational acceleration, and d is the magnetic susceptibility. V It is a volumetric infinitesimal element.

[0091] The total potential energy at each location in the calculation space is minimized; the point where the total potential energy is minimized indicates the deepest part of the potential well, which is the stable levitation position of the resonator. Specifically, by taking the partial derivative of the total potential energy at each location, the restoring force on the resonator at that location can be obtained. When the restoring force is zero, it indicates that the resonator is located at the deepest part of the potential well, which is the levitation position. The x and z axes are defined on a horizontal plane, both aligned with the edges of the magnets; the y-axis is located at the geometric center, with the origin at the interface between the upper and lower magnets. Figure 14 The calculation results of the restoring force of the harmonic oscillator are shown. It can be seen that in the designed potential well device structure, the suspension position is (-1 μm, 867 μm, 3 μm). The spherical harmonic oscillator can be suspended at this position, and the potential well device structure will not have a volume collision with the space beam. Therefore, we can proceed to the fourth step.

[0092] Step 4. Construct the coaxial spatial optical path according to the aforementioned parameters. The experimental procedure is as follows: Figure 15 As shown, the arrow indicates the direction of beam transmission. Figure 15 The dimensions shown are for illustrative purposes only and do not reflect the actual sizes.

[0093] Specifically, the collimated Gaussian beam with a diameter of 2.1 mm is adjusted to coaxially pass through the focusing lens 1 with a focal length of 40 mm, so that when it exits from the lens 1, q1 = -0.04 + 0.0007i.

[0094] Before placing the potential well device 7, a beam cross-section analyzer 5 was placed at the detection end of the optical path to receive the beam and record the optical axis position. Then, the antimagnetic levitation potential well device 7, carrying the resonator 2, was placed into the spatial optical path using a triaxial displacement stage 4. The position of the device 7 was adjusted using the displacement stage 4, while the beam cross-section analyzer 5 was observed simultaneously. The adjustment ensured that the emitted beam was located at the recorded optical axis position, without volume collision, and that the beam spot radius matched the calculated value. The presence or absence of volume collision can be determined from the beam spot image on the beam cross-section analyzer 5, which can also automatically calculate the beam spot radius.

[0095] Step 5 is the same as in Example 1.

[0096] As can be seen from the above embodiments, the present invention realizes a spatial optical path detection method for multidimensional motion of antimagnetic levitation harmonic oscillators through a series of steps, achieving the advantages of coaxiality, no volume collision, and high detection efficiency. The present invention also describes in detail the design process of the corresponding optical path and the antimagnetic levitation potential well device, which can serve as an experimental and design paradigm to provide a reference for research in the field of antimagnetic levitation.

[0097] The specific embodiments of the present invention have been described above with reference to the accompanying drawings. However, these descriptions should not be construed as limiting the scope of the present invention. The scope of protection of the present invention is defined by the appended claims. Any modifications based on the claims of the present invention are within the scope of protection of the present invention.

Claims

1. A spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator, characterized in that, S1. Construct a spatial coordinate system in the computer, set up a spatial light source and determine the coordinates and initial spatial beam characterization parameters of the spatial light source, set up the harmonic oscillator (2) and determine the basic parameters of the harmonic oscillator (2); S2. The spatial light source emits a spatial beam toward the resonator (2). The spatial beam is incident on the resonator (2) and emitted after modulation. The spatial beam is simulated and calculated by the coordinates of the spatial light source and the initial spatial beam characterization parameters to obtain the spatial beam characterization parameters of the incident path and the path on the exit path of the spatial beam before and after modulation. S3. Based on the obtained path space beam characterization parameters, design an antimagnetic levitation potential well device for placing the resonator (2); perform magnetic field simulation on the antimagnetic levitation potential well device, calculate the magnetic potential energy of the resonator (2) on the antimagnetic levitation potential well device, and then simulate the levitation of the resonator (2) in the antimagnetic levitation potential well device; if the resonator (2) is levitation and the antimagnetic levitation potential well device does not collide with the space beam in volume, output the antimagnetic levitation simulation parameters and proceed to step S4; otherwise, repeat steps S1-S3. S4. According to the antimagnetic levitation simulation parameters, place a spatial light source and build a spatial optical path; place the antimagnetic levitation potential well device carrying the resonator (2) into the spatial optical path so that the resonator (2) is located in the coordinates specified in the basic parameters. S5. At the detection end of the spatial optical path, a photoelectric detection system is placed. The resonator (2) moves in multiple dimensions in the antimagnetic levitation potential well device. The photoelectric detection system is used to detect the multidimensional motion of the resonator (2).

2. The spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S1, the basic parameters of the harmonic oscillator (2) include the material, size and coordinate data of the harmonic oscillator (2) in the spatial coordinate system; The resonator (2) is a spherical antimagnetic levitation resonator, which is made of antimagnetic material, and the antimagnetic material is one or more of the following: quartz, polystyrene, acrylic, and antimagnetic polymer.

3. The spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S1, the spatial coordinate system is provided with X, Y, and Z directions in the translation direction. The X, Y, and Z directions are mutually orthogonal translational coordinate axes, and the direction of the center of gravity of the harmonic oscillator (2) is taken as the Y direction.

4. The spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S2, the spatial beam is a fundamental mode Gaussian beam, the optical axis of the spatial beam and the geometric symmetry axis of the harmonic oscillator 2 are placed coaxially, and the characterization parameters of the spatial beam include the wavelength and q parameter of the fundamental mode Gaussian beam. The path spatial beam characterization parameters on the incident and exit paths before and after modulation by the resonator (2) are calculated as follows: After the spatial beam enters the resonator (2), it is modulated by the resonator (2). When the spatial beam meets the requirements of paraxial ray and geometric optics, the path q parameter at different positions on the incident path and the exit path of the spatial beam before and after modulation by the resonator (2) is calculated by the ray matrix method. The required path spatial beam characterization parameters are obtained through the path q parameter.

5. The spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S3, the magnetic field simulation uses the finite element method to solve for the static magnetic induction field generated by the antimagnetic levitation potential well device. Then calculate the total potential energy E formed by the magnetic potential energy of the harmonic oscillator (2) plus the gravitational potential energy. The formula for calculating the total potential energy E is as follows: ； Where mgy is gravitational potential energy. It is magnetic potential energy. Let the coordinates of the harmonic oscillator (2) be the spherical space coordinates. It is magnetic susceptibility. y is the vacuum permeability, y is the coordinate of the center of mass of the harmonic oscillator (2) in the direction of gravity, m is the mass of the harmonic oscillator (2), g is the gravitational acceleration, and d is the velocity of the oscillator. V It is a volumetric infinitesimal element.

6. The spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S3, the antimagnetic levitation potential well device designed for placing the resonator (2) is specifically as follows: The antimagnetic levitation potential well device includes an upper permanent magnet and a lower permanent magnet. The upper permanent magnet is a triangular permanent magnet distributed around the center along the circumference. The lower permanent magnet is an extended triangular permanent magnet distributed around the center along the circumference. The polarization directions of the triangular permanent magnet and the extended triangular permanent magnet both point towards or away from the geometric center of the upper or lower permanent magnet, the geometric centers of the upper and lower permanent magnets are vertically aligned, and the polarization directions of the triangular permanent magnet and the extended triangular permanent magnet are opposite. An upper through hole is provided at the geometric center of the upper permanent magnet, and the upper through hole serves as the suspension area (8) for carrying the resonator (2).

7. A spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 6, characterized in that, The aforementioned triangular-shaped extended permanent magnet is disposed at the lower end of the triangular-shaped permanent magnet; The end of the triangular-like extended permanent magnet that is closer to the geometric center is closer to the geometric center than the end of the triangular-like permanent magnet that is closer to the geometric center.

8. A spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 6, characterized in that, The aforementioned antimagnetic levitation potential trap device is equipped with a light transmission channel for spatial optical path transmission; When the light transmission channel (9) is used for horizontal transmission of the spatial optical path: the upper permanent magnet is divided into two halves, and the two halves are separated by a light transmission channel (9) parallel to the optical axis of the spatial optical path. The width of the light transmission channel (9) is greater than the diameter of the light spot on the spatial optical path. When the light transmission channel (9) is used for vertical transmission of the spatial optical path: a lower through hole (10) is set at the geometric center of the lower permanent magnet, and the upper through hole and the lower through hole (10) together serve as the light transmission channel (9). The diameter of the inscribed circle of the light transmission channel (9) is larger than the diameter of the light spot on the spatial optical path. The method for calculating the spot diameter is as follows: Based on the path spatial beam characterization parameters calculated in step S2, the 1 / e spot radius at each position on the path is calculated using the path q parameter. The spot radius R(z) is calculated as follows: ； Where z is the position coordinate, and q(z) is the path parameter q of coordinate z.

9. A spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S4, the antimagnetic levitation potential well device carrying the resonator (2) is placed in the spatial optical path, so that the resonator (2) is located in the coordinates set in the basic parameters, as follows: Before placing the antimagnetic levitation potential trap device into the spatial optical path, a beam cross section analyzer (5) is placed at the detection end of the spatial optical path to receive the spatial beam in the spatial optical path and record the optical axis position of the spatial beam. The antimagnetic levitation potential trap device is placed on a three-axis displacement stage. The three-axis displacement stage is then moved to adjust the placement position of the antimagnetic levitation potential trap device. At the same time, the beam cross section analyzer (5) is observed. The adjustment is made so that after the spatial beam enters the resonator (2) on the antimagnetic levitation potential trap device, it is modulated by the resonator (2) and emitted to the recorded optical axis position. The spatial beam does not collide with the antimagnetic levitation potential trap device in volume.

10. A spatial optical path detection method for multidimensional motion of an antimagnetically levitated harmonic oscillator according to claim 1, characterized in that, In step S5, the photoelectric detection system includes a multi-dimensional motion signal acquisition function, and the photoelectric detection system is one or more of a four-quadrant detector and a D-shaped mirror-balanced detector.

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