CN114280327A - High-sensitivity acceleration measuring method and sensor based on optical fiber tweezers - Google Patents

High-sensitivity acceleration measuring method and sensor based on optical fiber tweezers Download PDF

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CN114280327A
CN114280327A CN202111525384.5A CN202111525384A CN114280327A CN 114280327 A CN114280327 A CN 114280327A CN 202111525384 A CN202111525384 A CN 202111525384A CN 114280327 A CN114280327 A CN 114280327A
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microfluidic channel
optical fiber
groove
laser
tweezers
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CN114280327B (en
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张武
王子煌
张梦
朱必锋
陈洪彬
高钰淞
林佳翰
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Guangzhou University
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Abstract

The invention discloses a high-sensitivity acceleration measuring method and a sensor based on optical fiber tweezers, wherein a certain fluid traction force is applied to a polystyrene microsphere captured by the optical tweezers, the displacement of the polystyrene microsphere is measured by a four-quadrant photoelectric detector, and the relationship between the displacement of the microsphere and the light receiving force is calibrated; when the micro-sphere is placed in an acceleration environment, the micro-sphere displacement caused by the environmental acceleration obtains the light force corresponding to the deviation displacement caused by the environmental acceleration according to the relationship between the displacement of the calibrated micro-sphere and the light receiving force, and then the light force is divided by the mass of the micro-sphere to obtain the environmental acceleration. The invention uses the optical fiber optical tweezers technology and the micro-fluidic technology to stably capture the microspheres in the micro-fluidic channel in a non-contact way, and selects the proper tapered optical fiber based on the finite difference numerical calculation of the time domain, thereby realizing the measurement of the acceleration of the microspheres with miniaturization, high sensitivity, high precision and low cost.

Description

High-sensitivity acceleration measuring method and sensor based on optical fiber tweezers
Technical Field
The invention belongs to the technical field of acceleration measurement, and particularly relates to a high-sensitivity acceleration measurement method and a sensor based on optical fiber tweezers.
Background
Light has energy and momentum, classical optics mainly takes electromagnetic radiation as a research object, and the development of modern optics takes the interaction of light and substances as important research content. The invention of laser in the 60 s of the 20 th century also made the optical tweezers technology. The optical tweezers technology is mainly used for actively controlling particles, capturing micro particles, measuring micro acting force, micro devices and the like in modern practical application. The optical tweezers technology utilizes the radiation pressure effect of laser, and a three-dimensional potential well formed by a beam of highly-converged laser realizes non-contact and nondestructive precise control on peer-to-peer tiny particles (with the size ranging from submicron to tens of microns). At present, the method is widely applied to the fields of physics, chemistry, medicine, life science, material science, nanotechnology and the like. The optical tweezers technology is mainly used for actively controlling particles, capturing micro particles, measuring micro acting force, micro devices and the like in modern practical application.
Microfluidics refers to science and technology related to systems for processing or manipulating micro fluids by using microchannels with dimensions of tens of to hundreds of micrometers, different micromachining methods are selected according to different materials used, the main machining methods are lithography techniques from the microelectronics industry and soft lithography techniques for surface patterning, and after microchannels are etched on materials by the two methods, two pieces of materials are generally bonded by a high-temperature, high-pressure or high-voltage method to manufacture a complete microfluidic microchannel. Microfluidic technology is playing an increasingly important role in the application fields of organic synthesis, microreactors, chemical analysis, biomedicine and the like.
In the measurement and study of atomic acceleration by scientists based on the optical force action, the conventional scientists adopt a complicated optical path structure, and are difficult to realize the miniaturization and the low cost of a sensor. When the acceleration of the atom is detected, the acceleration generated by the unbalanced force applied to the atom is difficult to accurately measure due to the fact that the mass and the volume of the atom are too small.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art and provide a high-sensitivity acceleration measuring method based on optical fiber tweezers.
Another object of the present invention is to provide a high-sensitivity acceleration sensor based on fiber optical tweezers, which applies the above-mentioned high-sensitivity acceleration measuring method based on fiber optical tweezers.
In order to achieve the purpose, the invention adopts the following technical scheme:
in one aspect of the present invention, a high-sensitivity acceleration measurement method based on fiber optical tweezers is provided, which is characterized by comprising the following steps:
introducing the polystyrene microsphere suspension into a microfluidic channel groove through a liquid injection device;
forming optical tweezers by laser through a tapered optical fiber, and capturing the polystyrene microspheres flowing through the microfluidic channel groove;
stopping the liquid injection device, and enabling the polystyrene microspheres to form light spots on the center of the target surface of the four-quadrant photoelectric detector under the action of the imaging system;
starting the liquid injection device and setting a flow rate within a certain range, and applying fluid traction force to the polystyrene microsphere, wherein the polystyrene microsphere deviates from the center of the target surface of the four-quadrant photoelectric detector;
obtaining the magnitude of the corresponding fluid traction force according to the flow velocity, determining the deviation displacement of the polystyrene microsphere according to the relation coefficient of the output voltage, the voltage and the position of the known quadrant photoelectric limit detector, and calibrating the corresponding relation between different deviation displacements and the magnitude of the fluid traction force or the light force;
stopping the liquid injection device, and returning the polystyrene microspheres to the initial equilibrium position;
when the device is in an acceleration environment, the polystyrene microspheres deviate from the initial equilibrium position under the action of the environmental acceleration, the light force corresponding to the deviation displacement caused by the environmental acceleration is obtained according to the corresponding relation between the different deviation displacements and the fluid traction force or the light force, and the light force is divided by the mass of the polystyrene microspheres to obtain the environmental acceleration.
In another aspect of the present invention, a high-sensitivity acceleration sensor based on fiber optical tweezers is provided, which is applied to the above high-sensitivity acceleration measuring method based on fiber optical tweezers, and includes a microfluidic channel substrate, a microfluidic channel top plate, a tapered fiber, a laser, a liquid injection device, a catheter, an imaging system, and a four-quadrant photodetector;
the microfluidic channel substrate is fixedly connected with the microfluidic channel top plate; the microfluidic channel substrate is provided with an optical fiber groove and a microfluidic channel groove, and the tail end of the optical fiber groove is communicated with the microfluidic channel groove;
the liquid injection device is connected with an inlet of the microfluidic channel groove through a conduit, and polystyrene microsphere suspension is arranged in the liquid injection device;
the laser is connected with a tapered optical fiber, the tapered optical fiber is arranged in the optical fiber groove, and one end of the taper is close to the microfluidic channel groove;
the imaging system is used for imaging the polystyrene microspheres in the micro-flow channel groove to the target surface of the four-quadrant photoelectric detector;
the four-quadrant photoelectric detector is used for measuring the displacement of the polystyrene microspheres in the microfluidic channel groove.
As a preferred technical scheme, the microfluidic channel top plate is connected with the microfluidic channel substrate in a hot press pressing mode.
As a preferable technical scheme, the microfluidic channel top plate is provided with microfluidic holes serving as inlet and outlet of the microfluidic channel at positions corresponding to two ends of the microfluidic channel groove, and the liquid injection device is connected with the microfluidic holes through a conduit.
As a preferred technical scheme, an optical fiber groove and a microfluidic channel groove are arranged on the microfluidic channel substrate, and the tail end of the optical fiber groove is communicated with the microfluidic channel groove, specifically:
the microfluidic channel substrate is etched with two intersecting microfluidic channel grooves and an optical fiber groove in a laser engraving manner, the optical fiber groove is arranged on an angular bisector of the intersecting microfluidic channel grooves, and one end of the optical fiber groove is communicated with an intersection point of the microfluidic channel grooves; the thickness of the microfluidic channel substrate is 1mm, and the depths of the optical fiber groove and the microfluidic channel groove are 125 micrometers.
The device also comprises an LED light source and a CCD imaging system which are used for observing the capture condition of the polystyrene microspheres in the groove of the microfluidic channel.
As a preferred technical scheme, the tapered optical fiber and the laser are used for forming optical tweezers; the conical end face of the tapered optical fiber is formed by a curve
Figure BDA0003410168970000041
The diameter of the bottom surface of the conical end surface is 125 mu m, and the height is 1562.5 mu m; the wavelength of the laser output by the laser is 980 nm.
As a preferable technical scheme, the flow speed range of the liquid output by the liquid injection device in the microfluidic channel groove is set to be 20-2000 mu m/s.
As a preferred technical scheme, the refractive index of the polystyrene microsphere is 1.615, and the diameter of the polystyrene microsphere is 50 μm.
As a preferred technical solution, the imaging system comprises a 780nm laser and an imaging optical path; the 780nm laser is used for outputting laser with the wavelength of 780nm and irradiating the polystyrene microspheres to generate scattered light; the imaging light path is used for focusing the scattered light spots and imaging the scattered light spots onto a target surface of the four-quadrant photoelectric detector. Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the invention uses the fiber optical tweezers technology and the microfluidic technology to stably capture the microspheres in the microfluidic channel in a non-contact manner, thereby realizing the measurement of the acceleration of the microspheres with miniaturization, high sensitivity, high precision and low cost.
(2) The method is based on finite difference time domain numerical calculation, selects a proper tapered optical fiber, captures the target microsphere by combining an optical fiber technology and an optical tweezers technology, and improves the measurement precision value by using the weak and high precision of the optical power.
(3) The invention utilizes the optical tweezers technology to capture the microspheres at a balance position. The accuracy value of the light force is higher than that of other means, so that the measurement accuracy of the invention is obviously higher than that of other existing products;
drawings
FIG. 1 is a flow chart of a high-sensitivity acceleration measurement method based on fiber optical tweezers according to an embodiment of the present invention;
FIG. 2 is a flow chart of tapered fiber draw according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the structure of the tapered end face of a tapered optical fiber according to an embodiment of the present invention;
FIG. 4 is a schematic view of a microfluidic channel substrate according to an embodiment of the present invention;
FIG. 5 is a schematic view of a micro flow channel substrate and a micro flow channel cover plate according to an embodiment of the invention;
FIG. 6 is a schematic diagram of an embodiment of the present invention in which polystyrene microspheres are captured by fiber optical tweezers in a microfluidic channel slot;
FIG. 7 is a schematic diagram of an embodiment of the present invention in which polystyrene microspheres are captured by fiber optical tweezers and imaged on a target surface of a four-quadrant photodetector by an imaging device;
the reference numbers illustrate: 11. an optical fiber; 12. the optical fiber fusion splicer discharges the pointed end; 13. a tapered optical fiber; 21. a microfluidic channel substrate; 22. a fiber groove; 23. a microfluidic channel groove; 24. a laser engraving machine; 31. a microfluidic channel top plate; 41. a liquid injection device; 42. a conduit; 43. a micro-orifice; 44. polystyrene microspheres; 45. a 980nm laser; 51. an LED light source; 52. a CCD imaging system; 53. a four quadrant photodetector; 54. a 780nm laser; 55. a beam splitter prism A; 56. a first lens; 57. a filter plate; 58. a beam splitter prism II; 59. a lens II; 60. a lens three; 61. a lens four; .
Detailed Description
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Examples
As shown in fig. 1, the present embodiment provides a high-sensitivity acceleration measurement method based on fiber optical tweezers, which includes the following steps:
s1, starting an LED light source and a CCD imaging system, and observing the environment in the microfluidic channel groove in real time;
s2, introducing the polystyrene microsphere suspension into a microfluidic channel groove through a liquid injection device (in the embodiment, a syringe pump is adopted);
in this example, the initial flow rate was set to 100 μm/s and the diameter of the polystyrene microspheres was set to 50 μm.
S3, passing laser through a tapered optical fiber to form optical tweezers, and capturing the polystyrene microspheres flowing through the microfluidic channel groove;
in this example, a tapered optical fiber, which is drawn from the end face of a single-mode optical fiber having a diameter of 125 μm by a discharge tip of an optical fiber fusion splicer and tapered to form a tapered end face as shown in fig. 4, was connected using a laser having an output laser wavelength of 980nm and a fixed power of 20 mW. The end face is obtained by FDTD simulation optimization, and the end face is a curve
Figure BDA0003410168970000061
Rotated about the x-axis. In the curve, the value range of x is 0-1562.5 mu m, the value range of y is 0-62.5 mu m, the end face can focus laser with 980nm wavelength, and an optical tweezers potential well is formed at the focus.
S4, stopping the injection pump, enabling the polystyrene microspheres to be in an initial balance position, and enabling the polystyrene microspheres to form light spots on the center of the target surface of the four-quadrant photoelectric detector under the action of an imaging system;
in the embodiment, a laser with the power fixed at 10 μ W and the output laser wavelength of 780nm is used as detection light, a four-quadrant photoelectric detector receives 780nm laser scattered from a microsphere, and the position of the four-quadrant photoelectric detector is finely adjusted, so that a scattered 780nm laser spot is positioned at the center of the four-quadrant photoelectric detector;
s5, starting the injection pump and setting a flow rate in a certain range, and applying fluid traction to the polystyrene microsphere, wherein the polystyrene microsphere deviates from the center of the target surface of the four-quadrant photoelectric detector;
in this embodiment, the flow rate of the liquid injection device is set to be in the range of 20 μm/s to 2000 μm/s, the polystyrene microsphere suspension is slowly pushed to apply a fluid pulling force to the polystyrene microspheres, the fluid pulling force makes the polystyrene microspheres deviate from the initial equilibrium position, the magnitude of the fluid pulling force is equal to the optical force applied to the polystyrene microspheres by the optical tweezers, and the range of the pulling force is 8.55pN to 855.14pN according to the Stokes equation.
S6, 780nm laser scattered by the polystyrene microsphere is received and measured through a four-quadrant photoelectric detector, the illumination received by each quadrant and the output current form the center to the periphery in a direct proportion relation, the deviation displacement of the polystyrene microsphere can be measured according to the known relation coefficient of the output voltage, the voltage and the position of the four-quadrant photoelectric limit detector, and the corresponding relation between different deviation displacements and the fluid traction force or the light force is calibrated; the light force range is the same as the traction force range and is 8.55 pN-855.14 pN;
s7, stopping the injection pump to make the fluid in a static state, and the polystyrene microsphere is still captured by the optical tweezers and returns to the initial balance position;
s8, when the whole device is in an acceleration environment, the polystyrene microspheres deviate from the initial equilibrium position under the action of the environmental acceleration, the light force corresponding to the deviation displacement caused by the environmental acceleration is obtained according to the corresponding relation between the different deviation displacements and the fluid traction force or the light force, the light force is divided by the mass of the polystyrene microspheres to obtain the environmental acceleration, and the environmental acceleration is obtained according to the calculation of the mass of the polystyrene microspheres at 0.12m/S2~12.45m/s2Between
As shown in fig. 2, fig. 3, fig. 4, fig. 5, fig. 6, and fig. 7, in another embodiment of the present invention, there is provided a high-sensitivity acceleration sensor based on fiber optical tweezers, to which the high-sensitivity acceleration measuring method based on fiber optical tweezers of the above-mentioned embodiment can be applied, including a microfluidic channel substrate 21, a microfluidic channel top plate 31, a tapered optical fiber 13, a 980nm laser 45, a liquid injection device 41 (in this embodiment, an injection pump is used), a conduit 42, an imaging system, a four-quadrant photodetector 53, a 780nm laser 54, a CCD imaging system 52, and an LED light source 51;
the microfluidic channel substrate 21 is fixedly connected with the microfluidic channel top plate 31 in a hot press pressing mode; two intersecting microfluidic channel grooves 23 and an optical fiber groove 22 are etched on the microfluidic channel substrate 21 through a laser engraving machine 24, the optical fiber groove 22 is arranged on an angular bisector of the intersecting microfluidic channel grooves 23, and one end of the optical fiber groove 22 is communicated with an intersection point of the microfluidic channel grooves 23, as shown in fig. 5;
the thickness of the microfluidic channel substrate 21 is 1mm, and the depths of the optical fiber groove 22 and the microfluidic channel groove 23 are 125 μm;
the microfluidic channel top plate 31 is provided with microfluidic holes 43 serving as inlet and outlet of the microfluidic channel at positions corresponding to the two ends of the microfluidic channel groove 23, and the liquid injection device 41 is connected with the microfluidic holes 43 at the inlet of the microfluidic channel groove 23 through a conduit. The liquid injection device 41 is internally provided with polystyrene microsphere suspension liquid; the flow speed range of the liquid output by the liquid injection device 41 in the microfluidic channel groove 23 is set to be 20-2000 μm/s; the refractive index of the polystyrene microspheres 44 is 1.615, and the diameter of the polystyrene microspheres 44 is 50 μm.
The output power of the 980nm laser 45 is fixed to be 20mW and is connected with the tapered optical fiber 13, the tapered optical fiber 13 is arranged in the optical fiber groove 22, and one end of the cone is close to the microfluidic channel groove 23; as shown in fig. 4, the tapered optical fiber 13 is obtained by drawing an end face of a single-mode optical fiber 11 having a diameter of 125 μm by using a discharge tip 12 of an optical fiber fusion splicer, and the end face is tapered to form a tapered end face as shown in fig. 3. The end face is obtained by FDTD simulation optimization, and the end face is a curve
Figure BDA0003410168970000081
Rotated about the x-axis. In the curve, the value range of x is 0-1562.5 μm, the value range of y is 0-62.5 μm, the end face can focus laser with the wavelength of 980nm, an optical tweezers potential well is formed at the focus, and the polystyrene microsphere 44 is captured, as shown in fig. 6.
As shown in fig. 7, the CCD imaging system 52 and the LED light source 51 image the polystyrene particle microspheres 44 in the microfluidic channel groove 23 to the CCD imaging system 52 by using a beam splitter prism two 58, a lens two 59, a lens three 60 and a lens four 61, so as to observe the microsphere capture in real time.
The output power of the 780nm laser 54 is fixed to 10 μ W, and the 780nm laser is used for outputting laser with the wavelength of 780nm and irradiating the polystyrene microspheres 44 to generate scattered light, and the scattered light is used for observing the positions of the polystyrene microspheres 44; as shown in FIG. 7, an imaging optical path constructed by a beam splitter first 55, a lens first 56 and a filter 57 is used for focusing scattered light onto the target surface of a four-quadrant photodetector 53, wherein the four-quadrant photodetector 53 is used for collecting and detecting 780nm laser light scattered from polystyrene microspheres 44 and measuring the displacement of the polystyrene microspheres 44 in the microfluidic channel groove 23.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (10)

1. The high-sensitivity acceleration measuring method based on the optical fiber tweezers is characterized by comprising the following steps of:
introducing the polystyrene microsphere suspension into a microfluidic channel groove through a liquid injection device;
forming optical tweezers by laser through a tapered optical fiber, and capturing the polystyrene microspheres flowing through the microfluidic channel groove;
stopping the liquid injection device, and enabling the polystyrene microspheres to form light spots on the center of the target surface of the four-quadrant photoelectric detector under the action of the imaging system;
starting the liquid injection device and setting a flow rate within a certain range, and applying fluid traction force to the polystyrene microsphere, wherein the polystyrene microsphere deviates from the center of the target surface of the four-quadrant photoelectric detector;
obtaining the magnitude of the corresponding fluid traction force according to the flow velocity, determining the deviation displacement of the polystyrene microsphere according to the relation coefficient of the output voltage, the voltage and the position of the known quadrant photoelectric limit detector, and calibrating the corresponding relation between different deviation displacements and the magnitude of the fluid traction force or the light force;
stopping the liquid injection device, and returning the polystyrene microspheres to the initial equilibrium position;
when the device is in an acceleration environment, the polystyrene microspheres deviate from the initial equilibrium position under the action of the environmental acceleration, the light force corresponding to the deviation displacement caused by the environmental acceleration is obtained according to the corresponding relation between the different deviation displacements and the fluid traction force or the light force, and the light force is divided by the mass of the polystyrene microspheres to obtain the environmental acceleration.
2. The high-sensitivity acceleration sensor based on the optical fiber optical tweezers is characterized by being applied to the high-sensitivity acceleration measuring method based on the optical fiber optical tweezers, which comprises a microfluidic channel substrate, a microfluidic channel top plate, a tapered optical fiber, a laser, a liquid injection device, a catheter, an imaging system and a four-quadrant photoelectric detector, wherein the microfluidic channel substrate is arranged on the microfluidic channel top plate;
the microfluidic channel substrate is fixedly connected with the microfluidic channel top plate; the microfluidic channel substrate is provided with an optical fiber groove and a microfluidic channel groove, and the tail end of the optical fiber groove is communicated with the microfluidic channel groove;
the liquid injection device is connected with an inlet of the microfluidic channel groove through a conduit, and polystyrene microsphere suspension is arranged in the liquid injection device;
the laser is connected with a tapered optical fiber, the tapered optical fiber is arranged in the optical fiber groove, and one end of the taper is close to the microfluidic channel groove;
the imaging system is used for imaging the polystyrene microspheres in the micro-flow channel groove to the target surface of the four-quadrant photoelectric detector;
the four-quadrant photoelectric detector is used for measuring the displacement of the polystyrene microspheres in the microfluidic channel groove.
3. The high-sensitivity acceleration sensor based on optical tweezers of claim 2, wherein the microfluidic channel top plate is connected with the microfluidic channel substrate by means of pressing of a hot press.
4. The high-sensitivity acceleration sensor based on fiber optical tweezers of claim 2, wherein the microfluidic channel top plate is provided with microfluidic holes as the inlet and outlet of the microfluidic channel groove at positions corresponding to the two ends of the microfluidic channel groove, and the liquid injection device is connected with the microfluidic holes through a conduit.
5. The high-sensitivity acceleration sensor based on fiber optical tweezers of claim 2, wherein the microfluidic channel substrate is provided with a fiber groove and a microfluidic channel groove, and the tail end of the fiber groove is communicated with the microfluidic channel groove, specifically:
the microfluidic channel substrate is etched with two intersecting microfluidic channel grooves and an optical fiber groove in a laser engraving manner, the optical fiber groove is arranged on an angular bisector of the intersecting microfluidic channel grooves, and one end of the optical fiber groove is communicated with an intersection point of the microfluidic channel grooves; the thickness of the microfluidic channel substrate is 1mm, and the depths of the optical fiber groove and the microfluidic channel groove are 125 micrometers.
6. The high-sensitivity acceleration sensor based on optical tweezers of claim 2, wherein the high-sensitivity acceleration sensor further comprises an LED light source and a CCD imaging system for observing the trapping condition of the polystyrene microspheres in the groove of the microfluidic channel.
7. The highly sensitive acceleration sensor based on fiber optical tweezers of claim 2, wherein the tapered fiber and laser are used to form optical tweezers; the conical end face of the tapered optical fiber is formed by a curve
Figure FDA0003410168960000021
The diameter of the bottom surface of the conical end surface is 125 mu m, and the height is 1562.5 mu m; the wavelength of the laser output by the laser is 980 nm.
8. The high-sensitivity acceleration sensor based on optical tweezers of claim 2, wherein the flow rate of the liquid output by the liquid injection device in the micro-flow channel groove is set to be in the range of 20 μm/s to 2000 μm/s.
9. The highly sensitive acceleration sensor based on fiber optical tweezers of claim 2, wherein the refractive index of the polystyrene microsphere is 1.615, and the diameter of the polystyrene microsphere is 50 μm.
10. The highly sensitive acceleration sensor based on fiber optical tweezers of claim 2, wherein the imaging system comprises a 780nm laser and an imaging optical path; the 780nm laser is used for outputting laser with the wavelength of 780nm and irradiating the polystyrene microspheres to generate scattered light; the imaging light path is used for focusing the scattered light spots and imaging the scattered light spots onto a target surface of the four-quadrant photoelectric detector.
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CN114720722A (en) * 2022-04-06 2022-07-08 中国人民解放军国防科技大学 Method and device for stabilizing scale factor of optical suspension acceleration sensor
CN114859076A (en) * 2022-07-06 2022-08-05 之江实验室 Acceleration measurement method and device based on optical suspension multi-microsphere array
CN114859076B (en) * 2022-07-06 2022-10-21 之江实验室 Acceleration measurement method and device based on optical suspension multi-microsphere array

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