Nanometer grating pose calibration system based on laser interferometer

Through the nano-grating posture calibration system based on laser interferometer, the nano-grating posture error problem is solved using a four-axis displacement stage and signal processing system, and the accuracy and reliability of the grating displacement measurement system are improved.

CN119268563APending Publication Date: 2025-01-07SHANGHAI METROLOGY & TESTING TECHNOLOGY RESEARCH INSTITUTE CO LTD +1
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Patent Information

Application Number
CN202411599697.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-11
Publication Date
2025-01-07

AI Technical Summary

Technical Problem

The existing nanograting posture calibration methods have problems such as large installation error, high adjustment difficulty and low accuracy, resulting in low measurement accuracy of the grating displacement measurement system.

Method used

Design a nano-grating posture calibration system based on laser interferometer. Using the stability and high sensitivity of laser interferometer, the feedback information of the photodetector is collected through the signal processing system. After the algorithm is processed, the four-axis displacement stage is driven to adjust the nano-grating bracket. , reduce pose error.

Benefits of technology

The measurement accuracy of the grating displacement measurement system is improved, labor and time costs are reduced, and the accuracy and reliability of the optical path system signal is ensured.

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Abstract

The invention relates to a nano grating pose calibration system based on a laser interferometer, which comprises a light path system and a displacement table driving system, the displacement table driving system comprises a four-axis displacement table, a nano grating support for mounting a nano grating and the laser interferometer are arranged on a mounting table surface of the four-axis displacement table, and the laser interferometer is arranged on the mounting table surface of the four-axis displacement table. The three-axis direction angles of the nano grating are sequentially corrected through the four-axis displacement table, wherein the three-axis direction angles comprise free rotation in three degrees of freedom of pitching, rolling and deflection and linear displacement in the axis direction of the grating. The measurement value of the laser interferometer is used as the correction feedback of the grating attitude, the measurement value of the grating displacement measurement system is compared with the measurement value, the adjustment direction of each axis of the four-axis displacement table is judged, finally, the four-axis displacement table is driven for many times, the nano grating support is adjusted to the ideal position, and the problem of the nano grating attitude error is solved.
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Description

Technical Field

[0001] The invention relates to an optical device for a grating displacement measurement system, and in particular discloses a nano grating position calibration system based on a laser interferometer, belonging to the technical field of optical devices. Background Art

[0002] Nano gratings are key components for precision displacement measurement in the integrated circuit industry, ultra-precision machining, precision scientific instruments and other fields. With the widespread application of nano gratings in various instruments, the requirements for grating instruments are gradually increasing. For grating displacement measurement systems, there are five inevitable errors: environmental error, model error, installation error, switching error and instrument error. The installation error of nano gratings is a major factor. Minimizing the nano grating posture error to ensure the reliability of the grating measurement system optical path is the key to ensuring the accuracy of precision measurement results.

[0003] The grating period is usually determined by optical diffraction or metrological atomic force microscopy. The optical diffraction method is the most commonly used grating period measurement method in the laboratory, and its measurement principle is based on the grating equation. When the laser is incident at the Littrow angle, ,in is the Littrow angle, λ is the wavelength of the laser, n is the refractive index of air, d is the period of the grating, and k is the diffraction order. The incident light is a 405nm semiconductor laser. The wavelength of the incident light is known, and the incident angle is measured. And the refractive index of air can be used to obtain the period of the grating.

[0004] The coupling error between the grating and the workpiece stage is the main factor causing the installation error. The workpiece stage on which the grating is installed has nonlinearity and straightness errors, which will cause the two diffracted light beams returning along the original path in the Littrow structure to deviate from the ideal position, greatly reducing the signal-to-noise ratio of the interference signal, and even introducing additional phase differences, causing measurement errors. The most important factor causing the above errors is the installation posture of the nano-grating, that is, the positional relationship between the pitch, roll and yaw degrees of freedom between the grating and the translation stage.

[0005] Therefore, solving the problem that causes the nano-grating posture error can effectively improve the overall accuracy of the grating displacement measurement system.

[0006] The traditional nano-grating calibration method usually uses a multi-degree-of-freedom clamping bracket, and verifies the perfection of the grating posture adjustment through the output waveform feedback of the overall optical system, which has strong uncertainty. And because most of its brackets are mechanical structures, they are usually adjusted manually, and cannot achieve arc-second-level micro-movements. Therefore, it is difficult to adjust, and the adjustment time and adjustment effect basically depend on the user's experience. Therefore, when adjusting the optical path, a lot of manpower and time costs will be wasted, and the adjustment accuracy cannot be guaranteed. At the same time, it is also impossible to further quantify the relationship between the nano-grating posture and the output signal of the optical path system, which causes inconvenience to calibrate the nano-grating posture. Summary of the invention

[0007] The purpose of the present invention is to solve the defects of the prior art and design a nano-grating posture calibration system based on laser interferometer. The stability and high sensitivity of the laser interferometer are used as the correction feedback of the grating posture. The feedback information of the photodetector is collected by the signal processing system, and the correction value is obtained after algorithm processing. The nano-grating bracket is then adjusted to the ideal position by driving the four-axis translation stage, so as to minimize the posture error caused by the nano-grating during installation, solve the problem of nano-grating posture error, and improve the measurement accuracy of the overall grating displacement measurement system.

[0008] The present invention is implemented as follows: a nano-grating position calibration system based on a laser interferometer, characterized in that it includes an optical path system and a displacement stage drive system, the displacement stage drive system includes a four-axis displacement stage, a nano-grating bracket and a laser interferometer are arranged on the mounting table of the four-axis displacement stage, a nano-grating is installed on the nano-grating bracket, the optical path system includes a laser, a wave plate I, a wave plate II, a wave plate III, a polarization beam splitter prism, a polarizer, an interferometer measurement light reflector, a plane reflector I and a plane reflector II, the wave plate I and the polarization beam splitter prism are sequentially arranged on the laser emission light path, the wave plate III and the plane reflector II are sequentially arranged on the horizontal polarized light path of the polarization beam splitter prism, the wave plate II and the plane reflector I are sequentially arranged on the vertical polarized light path of the polarization beam splitter prism, the nano-grating is arranged on the reflection light path of the plane reflector II and the plane reflector I, and the nano-grating is respectively for the plane reflector II and the plane reflector I. The reflected light forms a corresponding diffracted light path, and forms a diffracted light path after being combined through a polarization beam splitter prism. Polarizers and photodetectors are sequentially arranged on the diffracted light path. The interferometer measuring light reflector is arranged on a laser interferometer. The four-axis translation stage performs a four-axis displacement motion consisting of rotational motion in the three-axis directions of x, y, and z and linear motion in the direction of x-axis.

[0009] In the optical path system, the emitted light of the laser is incident on the polarization beam splitter prism through the wave plate I, and is divided into a vertical polarization light path and a horizontal polarization light path in equal proportion after passing through the polarization beam splitter prism. The two diffracted light paths formed by the vertical polarization light path and the horizontal polarization light path after being incident on the nano-grating surface at the Littrow angle return to the polarization beam splitter prism along the original light paths respectively and then are combined. The combined diffracted light is filtered by a polarizer and then received by a photodetector.

[0010] The nano grating is fixed on the four-axis displacement stage through the nano grating bracket, and the four-axis displacement stage drives the free rotation in the three degrees of freedom of pitch, roll and yaw, and the linear displacement in the direction of the grating axis, so as to correct the grating posture, and the linear motion in the x-axis direction of the four-axis displacement stage is parallel to the axis of the nano grating as much as possible. The four-axis displacement stage is controlled by the host computer and driven by the driving module to perform displacement motion.

[0011] The laser interferometer measurement light reflector required by the laser interferometer is installed on the side of the nano grating support, and the normal line of the plane mirror is orthogonal to the normal line of the nano grating support.

[0012] The wave plate I is a half wave plate, and the wave plates II and III are quarter wave plates respectively.

[0013] After the nano-grating bracket and the four-axis translation stage are installed, the center position of the translation stage is calibrated by a three-coordinate machine or by adding a vertical auxiliary bracket. The four-axis translation stage is calibrated for orthogonality by installing an orthogonal bracket between the laser interferometer measurement light reflector and the nano-grating bracket.

[0014] The correction of the nano-grating posture is to correct the angles of the three axes of the nano-grating in turn. The movement direction of the nano-grating, the laser incident direction of the laser interferometer and the movement direction of the four-axis translation stage are kept consistent. The display value of the laser interferometer is a reference for the actual displacement of the nano-grating after being driven by the four-axis translation stage. The interference signal collected by the photoelectric detector is converted into a current signal and transmitted to the signal processing system. Through the signal processing system, the displacement of the grating displacement measurement system is obtained based on the light intensity and grating displacement formula, which is compared with the laser interferometer display value. When the single-axis rotation angle is corrected until the actual displacement displayed by the photoelectric detector is closest to the reference displacement, it is used as a sign that the correction of the axis is completed.

[0015] The signal processing flow of the signal processing system in the nano-grating posture calibration system: The processing flow of the signal processing system for photoelectric signals in the nano-grating posture calibration system: The laser light source emitted by the laser is adjusted by the system optical path, and is received by the photoelectric detector to convert the optical signal into an electrical signal, and then passes through the signal amplifier, and then the corresponding electrical signal is received by the acquisition card, and is transmitted to the host computer together with the electrical signal of the laser interferometer collected by the acquisition card at the same time for data processing. The driving module in the displacement stage driving system drives the four-axis displacement stage to perform correction work according to the displacement obtained after processing by the host computer.

[0016] The beneficial effects of the present invention are as follows: the present invention uses data collected by a laser interferometer as a reference, realizes numerical control calibration of a nano-grating by adjusting the angle of a four-axis translation stage, utilizes the characteristics of good stability and high sensitivity of the laser interferometer as correction feedback for the grating posture, and simultaneously uses a host computer to collect feedback information from a photoelectric detector, and obtains a correction value after algorithm processing, and finally adjusts the nano-grating bracket to an ideal position by driving the four-axis translation stage, thereby minimizing the posture error caused by the nano-grating during installation and improving the measurement accuracy of the overall grating displacement measurement system.

[0017] In terms of industrial production, the application of the present invention can enable manufacturers to achieve more accurate dimensional measurement and quality control during the production process, thereby reducing product defect rates, improving production efficiency, and reducing the cost of unqualified products, thereby achieving cost control effects.

[0018] At the same time, since the present invention introduces a laser interferometer, the nano-grating position calibration can be traced back to the laser wavelength of the laser interferometer, which greatly improves its traceability and improves the accuracy and reliability of the measurement results. Therefore, in scientific research and experiments, the application of the present invention can reduce the measurement error of the grating displacement measurement system, make the experimental results more reliable and repeatable, help verify research hypotheses, ensure the accuracy of experimental data, and provide support for the verification of scientific theories.

[0019] The system of the present invention can be widely used in various high-tech industries such as medical treatment, aerospace, semiconductors, and environmental testing, and contributes to the comprehensive promotion of the intelligent development of the industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the overall composition of the system and the optical path system of the present invention.

[0021] Figure 2 It is a schematic diagram of the pitch angle adjustment of the nano grating bracket in the system of the present invention.

[0022] Figure 3 It is a schematic diagram of the roll angle adjustment of the nano-grating bracket in the system of the present invention.

[0023] Figure 4 It is a schematic diagram of the adjustment of the deflection angle of the nano-grating bracket in the system of the present invention.

[0024] Figure 5 It is a schematic diagram of the working process of the system of the present invention for performing single-axis direction angle correction on the nano grating.

[0025] Figure 6 It is a schematic diagram of the installation position structure of the four-axis translation platform and the components on the installation table in the system of the present invention.

[0026] Figure 7 It is a schematic block diagram of the photoelectric signal processing flow of the signal processing system in the system of the present invention.

[0027] In the figure: 1. Laser; 21. Wave plate I; 22. Wave plate II; 23. Wave plate III; 24. Polarization beam splitter prism; 25. Polarizer; 3. Transmission stage drive system; 31. Interferometer measurement light reflector; 32. Nano grating bracket; 33. Four-axis translation stage; 41. Plane reflector I; 42. Plane reflector II; 5. Laser interferometer; 6. Photoelectric detector. DETAILED DESCRIPTION

[0028] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0029] According to the attached Figure 1-Figure 4 and Figure 6The present invention is a nano-grating position calibration system based on a laser interferometer, comprising an optical path system and a displacement stage driving system 3, wherein the displacement stage driving system 3 comprises a four-axis displacement stage 33, wherein a nano-grating bracket 32 ​​and a laser interferometer 5 are arranged on the mounting surface of the four-axis displacement stage 33, wherein a nano-grating bracket 32 ​​is mounted with a nano-grating, wherein the optical path system comprises a laser 1, a wave plate I 21, a wave plate II 22, a wave plate III 23, a polarization beam splitter prism 24, a polarizer 25, an interferometer measurement light reflector 31, a plane reflector I 41 and a plane reflector II 42, wherein the wave plate I 21 and the polarization beam splitter prism 24 are sequentially arranged on the optical path of the emitted light of the laser 1, the wave plate III 23 and the plane reflector II 42 are sequentially arranged on the optical path of the horizontally polarized light of the polarization beam splitter prism 24, the wave plate II 22 and the plane reflector I 41 are sequentially arranged on the optical path of the vertically polarized light of the polarization beam splitter prism 24, and the nano-grating is arranged on the plane reflector II 42 and the reflected light path of the plane reflector I 41, the nano grating forms corresponding diffraction light paths for the reflected light from the plane reflector II 42 and the plane reflector I 41 respectively, and forms a diffraction light path after beam combining through the polarization splitter prism 24, a polarizer 25 and a photodetector 6 are sequentially arranged on the diffraction light path, the interferometer measurement light reflector 31 is arranged on the laser interferometer 5, wherein the wave plate I 21 adopts a half wave plate, and the wave plate II 22 and the wave plate III 23 adopt a quarter wave plate respectively.

[0030] In the optical path system, the emitted light of the laser 1 is incident on the polarization splitter prism 24 through the wave plate I 21, and is divided into a vertical polarization light path and a horizontal polarization light path in equal proportion after passing through the polarization splitter prism 24. The two diffracted light paths formed by the vertical polarization light path and the horizontal polarization light path after being incident on the nano-grating surface at the Littow angle return to the polarization splitter prism 24 along the original light paths respectively and then are combined. The combined diffracted light is filtered by the polarizer 25 and then received by the photodetector 6.

[0031] The nano-grating is fixed on the four-axis translation stage 33 through the nano-grating bracket 32, and the linear motion of the four-axis translation stage 33 in the x-axis direction should be as parallel as possible to the axis of the nano-grating.

[0032] The four-axis displacement stage 33 adopts a high-precision four-axis displacement stage, which is controlled by the host computer and driven by the driving module to perform displacement movement. It can realize rotational movement in the three axes of x, y, and z and linear movement in the x-axis direction, that is, it can realize free rotation in the three degrees of freedom of pitch, roll, and yaw, and linear displacement in the direction of the grating axis, so as to realize the correction of the grating posture. The displacement range of its x-axis displacement is ±6.5mm, and the resolution reaches 5μm. Its three degrees of freedom parameters are: pitch range: ±2.5°, pitch resolution: 29.3''; roll range: ±4°, roll resolution: 33''; yaw range: ±2.5°, yaw resolution: 27.8''.

[0033] The display value of the laser interferometer 5 is a reference for the actual displacement of the nano-grating after being driven by the four-axis translation stage 33. If a traceable single-wavelength laser interferometer is used, the system can make the overall nano-grating posture repair system traceable and realize the calibration of the system.

[0034] like Figure 6 As shown, the laser interferometer measurement light reflector 31 required by the laser interferometer 5 is installed on the side of the nano grating support 32, and the normal line of the plane mirror is orthogonal to the normal line of the nano grating support 32.

[0035] According to the attached Figure 5 During correction, the angles of the three axes of the nano-grating are corrected in turn until the posture correction of the three axes is completed.

[0036] Single-axis correction process: First, set the adjustment axis, displacement direction and total rotation value of the four-axis translation stage to zero, determine the rotation step amount, set a larger rotation step amount first, and drive the four-axis translation stage to rotate and displace a specified distance in a single direction. Observe whether the rotation step amount data is close to the change trend of the actual displacement data shown by the laser interferometer 5. If the change trend is opposite to the demand, determine that the rotation direction is reverse, and drive the reverse rotation of the current step amount again. After each drive is completed, according to the positive and reverse directions of the current rotation step amount, add or subtract the current rotation step amount to the total rotation value, and set the four-axis translation stage to zero along the displacement direction. If the rotation step amount data is close to the change trend of the actual displacement data shown by the laser interferometer 5, observe whether it is the minimum step amount. If so, it can be regarded as completing the correction of the axis, that is, reading the total rotation value as the correction value of the four-axis translation stage this time. Otherwise, reduce the rotation step amount, and repeat until the rotation angle step length is equal to the minimum step amount of the four-axis translation stage.

[0037] The correction of the other two axes is the same as the above steps. Due to the existence of the nano-grating posture error, the actual displacement will be slightly smaller than the reference displacement. The correction of the single-axis rotation angle is taken as the sign that the axis correction is completed when the photoelectric detector 6 shows that the actual displacement is closest to the reference displacement.

[0038] In order to minimize the three-axis coupling effect produced during correction, the nano-grating bracket 32 ​​and the four-axis translation stage 33 should be calibrated after installation. Before the correction begins, the three-coordinate machine calibration should be performed at the center of the four-axis translation stage or a vertical auxiliary bracket should be installed to minimize the correction error caused by the coupling between the two and reduce the installation error produced when the nano-grating bracket is installed.

[0039] During correction, the entire system of the present invention should be placed on a horizontal table. An inclined table or ground will affect the incident angle of the laser 1, causing the incident light on the nano-grating surface to be inconsistent with the theory. This situation should be avoided as much as possible.

[0040] First, the orthogonality calibration of the four-axis translation stage 33 should be completed. The calibration can be achieved by using a collimator to calibrate the angles of the interferometer measurement light reflector 31 and the nano-grating support 32. Figure 1 As shown, the optical path system of the system optical platform is completed.

[0041] During correction, the moving direction of the nano-grating, the incident direction of the laser interferometer 5 and the moving direction of the four-axis translation stage 33 should be kept consistent.

[0042] The interference signal collected by the photodetector 6 is converted into a current signal and transmitted to the signal processing system, which processes the interference signal based on the light intensity and grating displacement formula. Convert to obtain the displacement, where I is the interference signal intensity, I0 is the laser output intensity, is the displacement of the stage, and d is the grating period of the grating used.

[0043] Then, the displacement obtained after conversion is compared with the actual displacement data shown by the laser interferometer 6 to see whether the data are consistent. If not, Figure 5 The single-axis correction process shown is used to correct the three-axis angles (pitch, roll, and yaw) of the nano-grating.

[0044] According to the attached Figure 7 The signal processing system in the nano-grating posture calibration system processes the photoelectric signal as follows: the laser light source emitted by the laser 1 is adjusted by the system optical path and then received by the photodetector 6 to convert the optical signal into an electrical signal. The optical signal is then passed through a signal amplifier and then received by an acquisition card, and the corresponding electrical signal is transmitted to the host computer together with the electrical signal of the laser interferometer 5 collected by the acquisition card at the same time for data processing. The driving module in the translation stage driving system 3 drives the four-axis translation stage 33 to perform correction work according to the displacement obtained after processing by the host computer.

[0045] The above describes in detail the preferred specific embodiments of the present invention. It should be understood that the optical path system described in the present invention is not unique, and any system that can use nano-gratings to achieve the purpose of displacement measurement can apply the posture calibration system described in the present invention. Ordinary technicians in this field can make many equivalent or equivalent changes based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the existing technology in the field should be included in the protection scope determined by the claims of the present invention.

Claims

1. A nano-grating position calibration system based on laser interferometer, characterized in that: The invention comprises an optical path system and a displacement stage driving system, wherein the displacement stage driving system comprises a four-axis displacement stage, a nano-grating bracket and a laser interferometer are arranged on the mounting table of the four-axis displacement stage, a nano-grating is installed on the nano-grating bracket, the optical path system comprises a laser, a wave plate I, a wave plate II, a wave plate III, a polarization beam splitter prism, a polarizer, an interferometer measurement light reflector, a plane reflector I and a plane reflector II, wherein the wave plate I and the polarization beam splitter prism are arranged in sequence on the optical path of the laser emission light, the wave plate III and the plane reflector II are arranged in sequence on the optical path of the horizontal polarized light of the polarization beam splitter prism, the wave plate II and the plane reflector I are arranged in sequence on the optical path of the vertical polarized light of the polarization beam splitter prism, the nano-grating is arranged on the reflected optical path of the plane reflector II and the plane reflector I, and the nano-grating respectively reflects the reflected light from the plane reflector II and the plane reflector I The reflected light forms a corresponding diffracted light path, and forms a diffracted light path after being combined through a polarization beam splitter prism. Polarizers and photodetectors are sequentially arranged on the diffracted light path. The interferometer measuring light reflector is arranged on a laser interferometer. The four-axis translation stage performs a four-axis displacement motion consisting of rotational motion in the three-axis directions of x, y, and z and linear motion in the direction of x-axis.

2. The laser interferometer-based nano-grating position calibration system according to claim 1, characterized in that: In the optical path system, the emitted light of the laser is incident on the polarization beam splitter prism through the wave plate I, and is divided into a vertical polarization light path and a horizontal polarization light path in equal proportion after passing through the polarization beam splitter prism. The two diffracted light paths formed by the vertical polarization light path and the horizontal polarization light path after being incident on the nano-grating surface at the Littrow angle return to the polarization beam splitter prism along the original light paths respectively and then are combined. The combined diffracted light is filtered by a polarizer and then received by a photodetector.

3. The laser interferometer-based nano-grating position calibration system according to claim 1, characterized in that: The nano grating is fixed on a four-axis translation stage through a nano grating bracket, and is driven by the four-axis translation stage to realize free rotation in three degrees of freedom, namely pitch, roll and yaw, as well as linear displacement in the direction of the grating axis, so as to realize the correction of the grating posture, and the linear motion in the x-axis direction performed by the four-axis translation stage is parallel to the axis of the nano grating as much as possible.

4. The laser interferometer-based nano-grating position calibration system according to claim 1, characterized in that: The laser interferometer measurement light reflector required by the laser interferometer is installed on the side of the nano grating support, and the normal line of the plane mirror is orthogonal to the normal line of the nano grating support.

5. The laser interferometer-based nano-grating position calibration system according to claim 1 or 2, characterized in that: The wave plate I is a half wave plate, and the wave plates II and III are quarter wave plates respectively.

6. The nano-grating position calibration system based on laser interferometer according to claim 1, characterized in that: After the nano-grating bracket and the four-axis translation stage are installed, the center position of the four-axis translation stage is calibrated by a three-coordinate machine or by adding a vertical auxiliary bracket. The four-axis translation stage realizes orthogonality calibration by calibrating between the laser interferometer measurement light reflector and the nano-grating bracket through a collimator.

7. The nano-grating position calibration system based on laser interferometer according to any one of claims 1 to 3, characterized in that: The correction of the nano-grating posture is to correct the angles of the three axes of the nano-grating in turn. The movement direction of the nano-grating, the laser incident direction of the laser interferometer and the movement direction of the four-axis translation stage are kept consistent. The display value of the laser interferometer is a reference for the actual displacement of the nano-grating after being driven by the four-axis translation stage. The interference signal collected by the photoelectric detector is converted into a current signal and transmitted to the signal processing system. Through the signal processing system, the displacement of the grating displacement measurement system is obtained based on the light intensity and grating displacement formula, which is compared with the laser interferometer display value. When the single-axis rotation angle is corrected until the actual displacement displayed by the photoelectric detector is closest to the reference displacement, it is used as a sign that the correction of the axis is completed.

8. The nano-grating position calibration system based on laser interferometer according to any one of claims 1 to 3, characterized in that The signal processing flow of the signal processing system in the nano-grating posture calibration system: The processing flow of the signal processing system for photoelectric signals in the nano-grating posture calibration system: The laser light source emitted by the laser is adjusted by the system optical path, and is received by the photoelectric detector to convert the optical signal into an electrical signal, and then passes through the signal amplifier, and then the corresponding electrical signal is received by the acquisition card, and is transmitted to the host computer together with the electrical signal of the laser interferometer collected by the acquisition card at the same time for data processing. The driving module in the displacement stage driving system drives the four-axis displacement stage to perform correction work according to the displacement obtained after processing by the host computer.

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