An apparatus and method for measuring the surface potential of a test mass based on a milligram-level torsion balance

Abstract

This application belongs to the field of precision measurement, and specifically discloses a device and method for measuring the surface potential of a test mass based on a milligram-level torsion balance. Through this application, a milligram-level torsion balance is used instead of the traditional torsion balance. Compared with the traditional torsion balance, the milligram-level torsion balance has a smaller moment of inertia, lower torque-sensing thermal noise, and a torque detection level better than 10<supgt;‑18< / supgt> Nm / Hz<supgt;0.5< / supgt>, with extremely high detection sensitivity; a micrometer-level charged microsphere is used instead of the source conductor probe as the excitation source, and the spatial resolution can reach the micrometer level. Since the charged microsphere in suspension has a small charge amount and a small volume, the influence on the surface potential of the test mass to be measured is small and can be ignored, taking into account a relatively high spatial resolution; an optical module is used instead of the micro-displacement platform to provide the optical trap gradient force for the suspension of the charged microsphere and change the position of the suspended charged microsphere so that it faces different regions of the test mass surface. The suspended microsphere only interacts with photons, reducing the mechanical contact between the microsphere and other objects, reducing the friction effect, and improving the detection accuracy.

Description

Technical Field

[0001] This application belongs to the field of precision measurement, and more specifically, relates to a device and method for measuring the surface potential of a test mass based on a milligram-level torsion balance. Background Art

[0002] In the past two decades, with the need for gravitational experiments, the measurement of the surface potential of conductors has received increasing attention. Currently, the mainstream surface potential measurement methods mainly include electron microscopy technology, Kelvin probe technology, torsion balance technology, and probe technology based on optically levitated particles.

[0003] The traditional torsion balance scheme suspends the test mass with a suspension wire, and drives the source conductor probe to move through a micro-displacement platform. There is an electric potential difference between the source conductor probe and the surface of the torsion balance. The torsion balance will deflect under the action of the electrostatic torque. By measuring the electrostatic torque received by the torsion balance through capacitive displacement sensing, the electric potential situation of the sample can be reflected.

[0004] However, the size of the source conductor probe is on the order of millimeters, and its spatial resolution can only reach the sub-millimeter level. Reducing the size of the source conductor probe will reduce the electrostatic force between the probe and the sample, resulting in a decrease in the sensitivity of electric potential measurement.

[0005] The probe technology based on optically levitated particles uses a laser to levitate a solid medium as a sensitive unit, and obtains the magnitude of the external force field by measuring the change in the motion state of the sensitive unit after being affected by an external force. The size of the optically levitated particles is generally on the order of micrometers or sub-micrometers. For example, in the paper "Experimental Study on Measuring the Surface Potential of a Test Mass Based on Levitated Particles", only by measuring the offset of the particle equilibrium position and the stiffness of the optical trap in the direction, the electrostatic force received by the particle can be calculated, and then the electric potential difference between the test mass and the particle can be obtained. However, this method requires building a complex position detection optical path to measure the position offset of the levitated particle. The theoretical calculation of the stiffness of the optical trap in the direction is relatively complex and there is a certain deviation from the actual situation. The measurement of many parameters in the theoretical calculation is also difficult. Summary of the Invention

[0006] Aiming at the defects of the existing technology, the purpose of this application is to provide a device and method for measuring the surface potential of a test mass based on a milligram-level torsion balance, aiming to solve the problem that the existing technology cannot simultaneously achieve high sensitivity and high spatial resolution in the measurement of the surface potential of the test mass.

[0007] The first aspect of this application relates to a device for measuring the surface potential of a test mass based on a milligram-level torsion balance, including: an optical module, a charged microsphere, a milligram-level torsion balance, a signal monitoring module, and a processing unit;

[0008] The optical module is used to provide the optical trap gradient force for suspending charged microspheres and change the positions of the suspended charged microspheres so that they face different regions of the surface of the test mass;

[0009] The suspended charged microspheres serve as an excitation source for electrostatic interaction with the charges in the regions facing the surface of the test mass;

[0010] The milligram-level torsion balance is composed of a milligram-level test mass suspended by a suspension wire;

[0011] The test mass is used to undergo a torsional motion under the action of an electrostatic torque when the suspended charged microspheres approach;

[0012] The signal monitoring module is used to monitor the torsional angle of the test mass and send it to the processing unit;

[0013] The processing unit is used to calibrate the electrostatic charge of the charged microspheres, calculate the electrostatic torque received by the test mass by combining the change in the torsional angle of the test mass and the transfer function; and inversely calculate the electric potential and overall distribution of each region on the surface of the test mass by integrating the electrostatic charge of the charged microspheres and the electrostatic torque received by the test mass.

[0014] Preferably, the device further includes: capacitor plates for applying a horizontal harmonic alternating electric field to the suspended charged microspheres during the calibration process of the electrostatic charge of the charged microspheres;

[0015] The optical module is also used to transfer the motion information of the charged microspheres into optical signals and send the motion power spectrum of the microspheres to the processing unit;

[0016] The processing unit is also used to calibrate the electrostatic charge of the charged microspheres according to the first motion power spectrum without the harmonic alternating electric field and the second motion power spectrum driven by the harmonic alternating electric field.

[0017] Preferably, the device further includes: an electromagnetic shielding cover for shielding the influence of the harmonic alternating electric field on the milligram-level torsion balance.

[0018] Preferably, the suspension wire is a quartz wire with a diameter in the micron range, and the connection between the quartz wire and the milligram-level test mass is made by laser non-destructive welding.

[0019] Preferably, the electrostatic charge of the charged microspheres is dozens of electrons, the diameter does not exceed the micron range; and the distance between the suspended microspheres and the test mass is in the micron range.

[0020] Preferably, the length of the vacuum optical trap generated by the optical module is not less than twice the length of the test mass.

[0021] Preferably, the signal monitoring module is a light lever signal monitoring module.

[0022] The second aspect of the present application relates to a method for measuring the surface potential of a test mass based on a milligram torsion balance, including:

[0023] Step 1: Calibrate the electrostatic charge of the charged microsphere.

[0024] Step 2: Move the position of the suspended charged microsphere to make it close to and directly face a region of the test mass until the test mass undergoes a torsional movement.

[0025] Step 3: Fit the curve of the change in the torsional angle during the torsion process of the test mass to obtain the quality factor, and combine it with the angle-electrostatic torque transfer function to calculate the electrostatic torque received by the test mass.

[0026] Step 4: According to the theoretical model of the electrostatic force action between the sphere and the plate, and by comprehensively considering the electrostatic charge of the charged microsphere and the electrostatic torque received by the test mass, inversely calculate the potential of the region on the surface of the test mass directly facing the suspended charged microsphere.

[0027] Preferably, the method further includes:

[0028] Step 5: Change the position of the suspended charged microsphere to make it directly face another region on the surface of the test mass, and repeat Steps 3-4 until all regions on the surface of the test mass are scanned, thereby obtaining the surface potential distribution of the test mass.

[0029] Preferably, the inversion of the potential of a certain region on the surface of the test mass is specifically as follows:

[0030]

[0031] where, represents the electrostatic torque, represents the torsional angle of the test mass, represents the capacitance between the suspended charged microsphere and the test mass, represents the electrostatic charge of the suspended charged microsphere, represents the potential of a certain region on the surface of the test mass.

[0032] It can be understood that the beneficial effects of the above second aspect can be referred to the relevant descriptions in the above first aspect, and will not be elaborated here.

[0033] Generally speaking, compared with the prior art, the above technical solution conceived by the present application has the following beneficial effects:

[0034] (1) The present application proposes a device for measuring the surface potential of a test mass based on a milligram torsion balance. The milligram torsion balance is used instead of the traditional torsion balance. Compared with the traditional torsion balance, the milligram torsion balance has a smaller moment of inertia, lower thermal noise of torque sensing, and a torque detection level better than 10 -18 Nm / Hz 0.5, it has extremely high detection sensitivity; moreover, the milligram-level torsion balance has a relatively high intrinsic frequency, which can supplement the high-frequency detection range not covered by the large-mass torsion balance; using micron-level charged microspheres instead of source conductor probes as the excitation source, the spatial resolution can reach the micron level. Since the charged microspheres in suspension have a small charge and a small volume, the influence on the potential of the surface of the test mass to be measured is small and can be ignored, taking into account a relatively high spatial resolution; using an optical module instead of a micro-displacement platform to provide the optical trap gradient force for the suspension of the charged microspheres and changing the position of the suspended charged microspheres so that they face different regions of the surface of the test mass. The suspended microspheres only interact with photons, reducing the mechanical contact between the microspheres and other objects, reducing the friction effect, and improving the detection accuracy.

[0035] (2) The present application proposes a device for measuring the surface potential of a test mass based on a milligram-level torsion balance. When calculating the electrostatic torque, what is changed is the equilibrium position of the suspended charged microspheres, and what is measured is the torsional motion information of the test mass. In essence, it still belongs to the torsion balance technology. Compared with the scheme based on optically suspended particles, what is changed is the position of the test mass, and what is measured is the displacement offset of the charged microspheres. Since what is changed in the present application is the equilibrium position of the suspended charged microspheres, the additional interference factors introduced to the test mass to be measured are reduced, and the electrostatic torque can be calculated more accurately; since what is measured in the present application is the torsional motion information of the test mass, compared with the scheme based on optically suspended particles, a complex position detection optical path needs to be built to measure the position offset of the suspended particles. In the case of achieving the same measurement accuracy, the measurement optical path of the present application is simpler and the operation is more convenient. In both measurement schemes, the test mass and the suspended particles as the measurement objects are both in a vacuum container, and the space inside the container is limited. The measurement optical path can only be set outside the container. The optical path of the present application is simple and can save space. Brief Description of the Drawings

[0036] Figure 1 is a schematic structural diagram of a device for measuring the surface potential of a test mass based on a milligram-level torsion balance provided by an embodiment of the present application.

[0037] Figure 2 is a flowchart of a method for measuring the surface potential of a test mass based on a milligram-level torsion balance provided by an embodiment of the present application.

[0038] In all the drawings, the same reference numerals are used to denote the same elements or structures, where:

[0039] 1 - milligram-level torsion balance; 2 - test mass; 3 - signal monitoring module; 4 - charged microsphere; 5 - optical module; 6 - capacitor plate; 7 - electromagnetic shielding cover. Detailed Description of the Embodiments

[0040] In order to make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0041] The embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application.

[0042] As Figure 1 shown, the present application provides a device for measuring the surface potential of a test mass based on a milligram-level torsion balance, including: an optical module 5, a charged microsphere 4, a milligram-level torsion balance 1, a signal monitoring module 3, and a processing unit (not shown).

[0043] The optical module 5 is used to provide an optical trap gradient force for suspending the charged microsphere 4 and change the position of the suspended charged microsphere so that it faces different regions on the surface of the test mass 2.

[0044] The suspended charged microsphere serves as an excitation source and is used to have an electrostatic interaction with the charges in the region facing the surface of the test mass.

[0045] The milligram-level torsion balance 1 is composed of a milligram-level test mass suspended by a suspension wire; the test mass is used to undergo a torsional motion under the action of an electrostatic torque when the suspended charged microsphere approaches.

[0046] The signal monitoring module 3 is used to monitor the torsional angle of the test mass 2 and send it to the processing unit.

[0047] The processing unit is used to calibrate the electrostatic charge of the charged microsphere, calculate the electrostatic torque received by the test mass by combining the change in the torsional angle of the test mass and the transfer function; and inversely calculate the potential and overall distribution of each region on the surface of the test mass by integrating the electrostatic charge of the charged microsphere and the electrostatic torque received by the test mass.

[0048] Preferably, the suspension wire is a quartz wire with a diameter in the micron range, and the connection method between the quartz wire and the milligram-level test mass is laser non-destructive welding.

[0049] It should be noted that the present application preferably uses a quartz wire at the micron level, which has a higher quality factor and lower heat dissipation, and can effectively improve the sensitivity of the milligram-level torsion balance; the present application preferably uses laser non-destructive welding, which can effectively reduce the connection loss between the suspension wire and the test mass.

[0050] In an illustrated embodiment, the milligram-level torsion balance 1 is composed of a test mass suspended by an ultra-fine quartz wire with a diameter of 3 μm and a length of 100 mm. The test mass 2 has a diameter of 3 mm and a thickness of 0.5 mm, and is gold-plated on the surface of the test mass to make it a conductor and act as a mirror. The total mass of the milligram-level torsion balance is within 100 mg, and the moment of inertia is at 10 -5kg·m 2 In the order of magnitude, the Q value of the torsion mode of the milligram-level torsion balance can reach 10 -5 In the order of magnitude, theoretically, the torque detection sensitivity can reach 10 -18 Nm / HZ 0.5 , which is at least three orders of magnitude higher than the torque detection sensitivity of the large-mass torsion balance.

[0051] Fabrication of the milligram-level torsion balance:

[0052] 1) Suspension wire: In the torsion pendulum system, the commonly selected suspension wire material is quartz. Compared with metal wires, quartz wires have a higher quality factor and lower heat dissipation. In this application, an ultra-fine quartz wire with a diameter of 3 μm and a length of 100 mm is selected.

[0053] 2) Test mass: The test mass uses quartz with a low coefficient of thermal expansion as the substrate, and a layer of gold film is plated on the surface to make it a conductor and act as a mirror. The smaller the thickness of the mirror, the smaller the moment of inertia. Therefore, the designed thickness of the test mass is 0.5 mm, the diameter of the test mass is 3 mm, and the total mass is within 100 mg.

[0054] 3) Welding: The quartz wire and the milligram-level test mass are welded together to form a milligram-level torsion balance. However, the dissipation at the connection between the quartz wire and the test mass will also affect the torque detection sensitivity of the torsion balance. The beam generated by a carbon dioxide laser can effectively melt quartz and achieve a good welding effect. Parameters such as the power of the laser and the shape of the beam can be controlled, and no additional air flow will be generated. Therefore, in this application, a carbon dioxide laser is used to weld the quartz wire and the test mass together. The amplitude provided by the laser is 0 - 4.6 V, the frequency is 5 KHZ, the duty cycle is 1.5% - 50%, the power adjustment range is 10 W - 150 W, and the greater the duty cycle, the greater the output power.

[0055] The test mass in the milligram-level torsion balance undergoes a torsional motion under the action of the electrostatic torque between it and the suspended microsphere. That is, in this application, the magnitude of the electrostatic torque is reflected by the torsional motion of the test mass. The signal monitoring module detects the torsional motion of the test mass and can detect the change in the torsional angle. Then, the Q value of the milligram-level torsion balance is fitted through the amplitude of the change in the torsional angle, and further the magnitude of the electrostatic torque is obtained.

[0056] Preferably, the device further includes: a capacitor plate 6 for applying a horizontal harmonic alternating electric field to the suspended charged microsphere during the electrostatic charge calibration process of the charged microsphere; the optical module is further used to transmit the motion information of the charged microsphere into an optical signal and send the motion power spectrum of the microsphere to the processing unit; the processing unit is further used to calibrate the electrostatic charge of the charged microsphere according to the first motion power spectrum without the harmonic alternating electric field and the second motion power spectrum driven by the harmonic alternating electric field.

[0057] Preferably, the capacitor plates are fixed on the lifting platform, and the position of the capacitor plates relative to the microspheres can be changed by adjusting the lifting platform.

[0058] In the initial state, the milligram torsion balance and the suspended microspheres are already located in the vacuum chamber. When calibrating the static electricity of the suspended microspheres, adjust the lifting platform to move the electromagnetic shielding cover and cover the milligram torsion balance with the electromagnetic shielding cover. When there is no harmonic AC electric field, the capacitor plates are below the suspended microspheres; when a harmonic AC electric field needs to be applied, adjust the lifting platform to move the capacitor plates to both sides of the suspended microspheres and apply a harmonic AC electric field between the capacitor plates. After the calibration of the static electricity of the suspended microspheres is completed, adjust the lifting platform to remove the capacitor plates and also remove the electromagnetic shielding cover, and then adjust the optical path to move the suspended charged microspheres near the test mass.

[0059] Preferably, the device further includes: an electromagnetic shielding cover 7 for shielding the influence of the harmonic AC electric field on the milligram torsion balance. The electromagnetic shielding cover 7 is fixed on the lifting platform, and the position of the electromagnetic shielding cover can be changed by adjusting the lifting platform.

[0060] It should be noted that this application preferably introduces an electromagnetic shielding cover to exclude the influence of the harmonic AC electric field on the milligram torsion balance, and at the same time reduce the influence of the milligram torsion balance on the calibration result of the static electricity of the charged microspheres, so as to more accurately calibrate the static electricity of the charged microspheres.

[0061] Preferably, the static electricity of the charged microspheres is dozens of electrons, and the diameter does not exceed the micron level; the distance between the suspended microspheres and the test mass is at the micron level.

[0062] It should be noted that the interaction force between the suspended microspheres as the excitation source and the test mass to be measured is the electrostatic force, and the static electricity of the microspheres will affect the electric potential on the surface of the test mass to be measured. This application preferably has the static electricity of the suspended microspheres as dozens of electrons and the diameter does not exceed the micron level. Due to the small charge amount and small volume, the influence on the electric potential on the surface of the test mass to be measured is small and can be ignored, improving the accuracy.

[0063] Preferably, the length of the vacuum optical trap generated by the optical module is not less than twice the test mass.

[0064] It should be noted that this application preferably has the above design to ensure that there is enough space for the suspended microspheres to move to measure the electric potential of each region on the surface of the test mass and prevent the influence on the electric potential on the surface of the test mass.

[0065] In an illustrated embodiment, the optical module includes a light source of suspended microspheres and its optical path, an acousto-optic modulator AOM (used to adjust the power of the suspended microsphere beam), a photodetector and its optical path (for detecting the position change of the microsphere). Specifically, after the light trap capture light emitted by the light source enters the vacuum chamber, it is focused by a focusing lens, and a light trap is formed near the focal position to stably capture charged microspheres. The light trap structure can be a vertical light trap or a horizontal light trap. In order to reduce the influence of environmental thermal noise on detection, it is necessary to reduce the air pressure in the vacuum chamber. The captured charged microspheres are spherical in shape and made of silica.

[0066] Preferably, the signal monitoring module is a light-lever signal monitoring module.

[0067] It should be noted that this application preferably measures the torsion angle of the test mass based on the light-lever principle. This method is a non-contact measurement, does not require direct contact with the test mass, will not affect the electric potential on the surface of the test mass, and this method has a high measurement accuracy, reaching the sub-microarcsecond level.

[0068] In an illustrated embodiment, the signal monitoring module is used to monitor the torsional motion of the test mass. It is composed of a laser, a chopper, a position detector PSD, a lock-in amplifier, a signal acquisition system and a computer. The position detector is located about 1 m outside the window of the vacuum container corresponding to the test mass, and is used to receive the reflected light from the surface of the test mass and convert the reflected light signal into a voltage signal, that is, convert the angular change of the test mass into a voltage signal and output it as a voltage signal. The PSD is connected to the lock-in amplifier in the signal acquisition system, and the lock-in amplifier extracts and amplifies the voltage signal output by the PSD. The signal acquisition system is connected to the computer and is used to convert the voltage signal output by the PSD into a digital signal and store it in the computer, that is, extract the electrical signal converted from the motion angle change of the test mass.

[0069] The working process of the signal monitoring module: A He-Ne laser with a wavelength of 633 nm and a power of about 1 mW is used as the light source. The light emitted by it becomes a light wave with a certain frequency after passing through a chopper, and then passes through a pentaprism and a focusing system and is incident on the coating on the surface of the test mass and reflected back, and finally focused on the surface of the position sensor PSD. Through the photoelectric effect, a current proportional to the light intensity is generated at the incident point on the surface of the PSD, and after passing through the conversion circuit, it becomes two voltages and outputs the two voltages to the lock-in amplifier in the signal acquisition system. The lock-in amplifier extracts and amplifies the voltage The signal is extracted and amplified, and the amplified signal is converted into a digital signal by a signal acquisition circuit and stored in a computer. When the deflection angle for inspecting the quality changes, the reflected light of the optical lever will deflect accordingly, and thus the incident point of the reflected light on the position sensor will also change. To reduce the influence of factors such as the laser power, the difference signal of two voltages is selected to give the angular change of the inspection mass.

[0070] The entire measuring device is in an environment where a modulation electric field can be applied for calibrating the charge quantity of the microsphere. The charged microsphere and the optical module together constitute an optically levitated auxiliary system. In the levitated micro auxiliary system, except that the microsphere is located near the inspection mass to be measured, the rest of the optical components are located at positions far from the inspection mass to be measured.

[0071] As Figure 2 shown, the present application discloses a method for measuring the surface potential of an inspection mass based on a milligram-level torsion balance, including:

[0072] Step 1: Calibrate the electrostatic quantity of the charged microsphere.

[0073] S11. Adjust the optical path to form a double-beam potential well to levitate the charged microsphere.

[0074] Specifically, a single beam of light emitted by the light source passes through a half-wave plate and a beam splitter to be divided into two beams with perpendicular polarization directions. After the two beams are converged by an acousto-optic modulator, a beam expander, and an objective lens, finally, a counter-propagating double-beam potential well is formed in the vacuum chamber to capture the charged microsphere, so that the charged microsphere is stably levitated in the vacuum chamber.

[0075] S12. Obtain the first motion power spectrum of the levitated microsphere without the action of a simple harmonic alternating electric field, and the motion power spectrum includes the power intensity of the levitated microsphere at different motion frequencies.

[0076] Record the motion of the levitated microsphere without the action of a simple harmonic alternating electric field, and this situation is used for comparison when an alternating electric field acts.

[0077] S13. Apply a simple harmonic alternating electric field to the levitated microsphere and obtain the second motion power spectrum of the levitated microsphere driven by the alternating electric field force .

[0078] Specifically, adjust the lifting table to move the capacitor plates to both sides of the levitated microsphere, and apply a simple harmonic alternating electric field between the capacitor plates.

[0079] The motion equation of the levitated charged microsphere driven by the alternating electric field force:

[0080]

[0081] Where represents the displacement of the levitated charged microsphere, , respectively represent the first derivative and the second derivative with respect to time, represents the velocity damping of the microsphere, represents the eigenfrequency of the microsphere, represents the background field force in which the microsphere is located, represents the time of the microsphere's movement, represents the mass of the charged microsphere, represents the electrostatic charge of the charged microsphere, alternating electric field , represents the amplitude of the alternating electric field, represents the driving frequency of the alternating electric field.

[0082] Convert the above formula into a displacement power spectral density expression:

[0083]

[0084] where, represents the total power spectral density of the microsphere, represents the angular frequency of the microsphere, represents the Boltzmann constant, represents the environmental temperature, represents the sampling time of the photodetector for the optical signal containing the movement information of the microsphere, represents the sinc function, represents the power spectral density of random thermal noise in the background environment, represents the power spectral density caused by the electric field drive.

[0085] S14. Calculate the ratio of the two motion power spectra at the driving frequency of the alternating electric field to calibrate the electrostatic charge of the suspended microsphere.

[0086] Denote as the magnitude of the random noise power spectral density at the driving frequency, as the magnitude of the power spectral density at the driving frequency under the action of the alternating electric field force, and the above formula can be converted to:

[0087]

[0088] Preferably, the electrostatic charge of the suspended microsphere is calculated as follows:

[0089]

[0090] where, represents the Boltzmann constant, represents the environmental temperature, represents the velocity damping of the suspended microsphere, represents the ratio of two motion power spectra at the driving frequency of the simple harmonic alternating electric field, represents the mass of the suspended charged microsphere, represents the amplitude of the alternating electric field, represents the sampling time.

[0091] Step 1 further includes:

[0092] S15. Build a milligram-level torsion balance unit in the vacuum chamber, adjust the lifting platform to raise the electromagnetic shielding cover to an appropriate height so that it completely covers the milligram-level torsion balance.

[0093] Specifically, the milligram-level torsion balance unit consists of a milligram-level torsion balance and a light lever signal monitoring module. Determine parameters such as the upper flange position and window position of the vacuum container to determine parameters such as the length of the suspension wire, connect the suspension wire and the test mass, and fabricate a milligram-level torsion balance. The milligram-level torsion balance uses vacuum guidance for suspension. The vacuum guide is connected to the suspension wire below, and the suspension wire suspends the test mass. The height of the test mass in the vacuum chamber can be changed by rotating the side of the vacuum guide, and the deflection angle of the test mass can be changed by rotating the knob at the top. Adjust the height and angle of the test mass through the vacuum guide. Adjust the optical path of the signal monitoring module to monitor the motion signal of the test mass.

[0094] Step 2: Move the position of the suspended charged microsphere so that it approaches and faces a region of the test mass until the test mass undergoes a torsional motion.

[0095] Step 3: Fit the curve of the change in the torsional angle during the torsion process of the test mass to obtain the quality factor, and combine it with the angle-electrostatic torque transfer function to calculate the electrostatic torque received by the test mass.

[0096] Specifically, a beam of laser is incident on the surface of the test mass and reflected back, and finally converges on the surface of the position sensor PSD. Through the photoelectric effect, a current proportional to the light intensity is generated at the incident point, and then flows through the substrate to the electrodes at both ends and becomes two voltage signals after passing through the conversion circuit 、 . To reduce the influence of factors such as laser power fluctuation, the division signal of the two voltage signals is selected to give the angle change of the test mass. The division signal of the two voltages can be written as follows:

[0097]

[0098] The angle change of the test mass The expression can be written as:

[0099]

[0100] Among them, represents the distance between the test mass and the detector, Indicates the distance between two detector electrodes. After a period of accumulation, the change curve of the test mass angle is obtained. Indicates The change amount of.

[0101] Fitting the change curve of the test mass angle to obtain Values and other parameters, combined with the transfer function, calculate the electrostatic torque received by the test mass.

[0102] Considering the structural damping, the motion equation of the test mass can be written as follows:

[0103]

[0104] Among them, Indicates the motion angle of the test mass, Indicates the second derivative of the motion angle of the test mass, Indicates the moment of inertia of the test mass, Indicates the torsional elastic coefficient of the suspension wire, Indicates the imaginary unit, Indicates the structural damping dissipation factor, , Indicates the electrostatic torque.

[0105] Performing Fourier transform on the above formula, in the frequency domain, there is:

[0106]

[0107] Among them, the torsional elastic coefficient Can be expressed by the natural frequency And the moment of inertia As . The above formula can be written as:

[0108]

[0109] Preferably, the relationship between the motion angle Of the test mass and the electrostatic torque Is as follows:

[0110]

[0111]

[0112] Among them, Indicates the angle-electrostatic torque transfer function, Indicates the torsional elastic coefficient of the suspension wire, Indicates the natural frequency of the test mass motion, Indicates the quality factor of the milligram-level torsion balance.

[0113] Step 4: According to the theoretical model of the electrostatic force between the sphere and the plate, by synthesizing the electrostatic charge of the charged microsphere and the electrostatic torque exerted on the test mass, the electric potential of the area on the test mass surface facing the suspended charged microsphere is inversely calculated.

[0114] Preferably, the method for inversely calculating the electric potential of a certain area on the test mass surface is as follows:

[0115]

[0116] where, represents the electrostatic torque, represents the torsional angle of the test mass, represents the capacitance between the suspended charged microsphere and the test mass, represents the electrostatic charge of the suspended charged microsphere, represents the electric potential of a certain area on the test mass surface.

[0117] Preferably, the method further includes:

[0118] Step 5: Change the position of the suspended charged microsphere so that it faces another area on the test mass surface, and repeat Steps 3-4 until all areas on the test mass surface are scanned, thereby obtaining the electric potential distribution on the test mass surface.

[0119] This application realizes the electric potential measurement within a large dynamic range by moving the position of the microsphere:

[0120]

[0121] where, represents the electric potential distribution on the test mass surface, represents the difference between the electric potential of a certain area on the th block on the test mass surface and the electric potential of a certain area on the th block on the surface, represents the displacement between the two small areas.

[0122] It should be understood that expressions such as "including" and "may include" that can be used in this application indicate the existence of the disclosed functions, operations, or constituent elements, and do not limit the existence of one or more additional functions, operations, and constituent elements. In this application, terms such as "including" and / or "having" can be interpreted as indicating specific characteristics, numbers, operations, constituent elements, components, or combinations thereof, but cannot be interpreted as excluding the existence or possibility of addition of one or more other characteristics, numbers, operations, constituent elements, components, or combinations thereof.

[0123] In the description and claims of this application, terms such as "first" and "second" are used to distinguish different objects, rather than to describe a specific order of the objects. For example, a first response message and a second response message are used to distinguish different response messages, rather than to describe a specific order of the response messages.

[0124] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate an example, illustration, or explanation. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0125] In the description of the embodiments of this application, unless otherwise specified, the meaning of "a plurality of" refers to two or more. For example, a plurality of processing units refers to two or more processing units; a plurality of elements refers to two or more elements.

[0126] In addition, in this application, the expression "and / or" includes any and all combinations of the associated listed words. For example, the expression "A and / or B" may include A, may include B, or may include both A and B.

[0127] In the description of the embodiments of this application, it should be noted that, unless otherwise clearly specified and limited, the term "connection" should be understood in a broad sense. For example, "connection" may be a detachable connection or a non-detachable connection; it may be a direct connection or an indirect connection through an intermediate medium. Among them, "fixed connection" means that the two are connected and the relative position relationship after connection remains unchanged. "Rotational connection" means that the two are connected and can rotate relative to each other after connection. "Sliding connection" means that the two are connected and can slide relative to each other after connection. The orientation terms mentioned in the embodiments of this application, such as "top", "bottom", "inner", "outer", "left", "right", etc., are only references to the direction of the drawings. Therefore, the orientation terms used are for better and clearer description and understanding of the embodiments of this application, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation on the embodiments of this application.

[0128] In addition, in the embodiments of the present application, mathematical concepts such as symmetry, equality, parallelism, and perpendicularity are mentioned. These definitions are all based on the current technological level, rather than the absolutely strict definitions in the mathematical sense. A small deviation is allowed, and approximate symmetry, approximate equality, approximate parallelism, approximate perpendicularity, etc. are all acceptable. For example, when it is stated that A is parallel to B, it means that A is parallel to B or approximately parallel to B, and the included angle between A and B can be between 0 degrees and 10 degrees. When it is stated that A is perpendicular to B, it means that A is perpendicular to B or approximately perpendicular to B, and the included angle between A and B can be between 80 degrees and 100 degrees.

[0129] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should all be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A device for measuring the surface potential of a test mass based on a milligram-level torsion balance, characterized in that, Comprising: An optical module, charged microspheres, a milligram-level torsion balance, a signal monitoring module, and a processing unit; The optical module is used to provide an optical trap gradient force for suspending the charged microspheres and change the position of the suspended charged microspheres so that they face different regions of the surface of the test mass; The suspended charged microspheres serve as an excitation source and are used to have an electrostatic interaction with the charges in the region of the test mass surface facing them; The milligram-level torsion balance is composed of a milligram-level test mass suspended by a suspension wire; The test mass is used to undergo a torsional motion under the action of an electrostatic torque when the suspended charged microspheres approach; The signal monitoring module is used to monitor the torsional angle of the test mass and send it to the processing unit; The processing unit is used to calibrate the electrostatic charge of the charged microspheres; fit the curve of the change in the torsional angle during the torsional process of the test mass to obtain a quality factor, and combine the quality factor with the transfer function of the test mass torsional angle - electrostatic torque to calculate the electrostatic torque received by the test mass; Based on the electrostatic charge of the charged microspheres and the electrostatic torque received by the test mass, the electric potential and its overall distribution of each region on the surface of the test mass are inversely calculated.

2. The device according to claim 1, characterized in that, The device further includes: capacitor plates, which are used to apply a horizontal harmonic alternating electric field to the suspended charged microspheres during the calibration process of the electrostatic charge of the charged microspheres; The optical module is further used to transfer the motion information of the charged microspheres into an optical signal and send the motion power spectrum of the microspheres to the processing unit; The processing unit is further used to calibrate the electrostatic charge of the charged microspheres according to the first motion power spectrum without a harmonic alternating electric field and the second motion power spectrum driven by a harmonic alternating electric field.

3. The device according to claim 2, wherein The device further includes: an electromagnetic shielding cover, which is used to shield the influence of the harmonic alternating electric field on the milligram-level torsion balance.

4. The device according to claim 1, characterized in that, The suspension wire is a quartz wire with a diameter in the micron range, and the connection method between the quartz wire and the milligram-level test mass adopts laser non-destructive welding.

5. The device according to claim 1, characterized in that, The electrostatic charge of the charged microspheres is dozens of electrons, and the diameter does not exceed the micron range; the distance between the charged microspheres and the test mass is in the micron range.

6. The device according to claim 1, wherein The length of the vacuum optical trap generated by the optical module is not less than twice that of the test mass.

7. The device according to claim 1, wherein The signal monitoring module is an optical lever signal monitoring module.

8. A method for measuring the surface potential of a test mass based on a milligram-level torsion balance, characterized in that, Including: Step 1, calibrate the electrostatic charge of the charged microspheres; Step 2, move the position of the suspended charged microspheres to make them approach and face a region of the test mass until the test mass undergoes a torsional motion; Step 3, fit the curve of the change in the torsional angle during the torsional process of the test mass to obtain a quality factor, and combine the quality factor with the transfer function of the test mass torsional angle - electrostatic torque to calculate the electrostatic torque received by the test mass; Step 4, according to the theoretical model of the electrostatic force action between the sphere and the plate, based on the electrostatic charge of the charged microspheres and the electrostatic torque received by the test mass, inversely calculate the electric potential of the region on the surface of the test mass facing the suspended charged microspheres.

9. The method according to claim 8, wherein, The method further includes: Step 5, change the position of the suspended charged microspheres to make them face another region of the surface of the test mass, and repeat Steps 3 - 4 until all regions of the surface of the test mass are scanned, thereby obtaining the electric potential distribution on the surface of the test mass.

10. The method according to claim 8, wherein, The inverse calculation of the electric potential of a certain region on the surface of the test mass is specifically as follows: Among them, represents the electrostatic torque, represents the torsional angle of the test mass, represents the capacitance between the suspended charged microsphere and the test mass, represents the electrostatic charge of the suspended charged microsphere, represents the electric potential of a certain area on the surface of the test mass.

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