A verification device and method for picometer displacement resolution

Abstract

The application discloses a kind of verification device and method of picometer displacement resolution, comprising: the rigidity of the target mirror to be measured is fixed on the motion table of displacement generation module, precision controller is used to output voltage signal to drive the motion of displacement generation module;The same target mirror to be measured is detected by reference interferometer and near coaxial detection of displacement measurement system to be measured, and the displacement change of the target mirror to be measured is detected;Reference interferometer is used to calibrate the single-step displacement of displacement generation module;PD detection and filter amplification module receive the signal output by displacement measurement system to be measured, complete photoelectric conversion, band-pass filtering and linear amplification, improve the signal-to-noise ratio of signal;Displacement generation module drives the target mirror to be measured to do synchronous translation;Displacement generation module outputs controllable step displacement of pm to nm order;The measurement axis of reference interferometer, the measurement axis of displacement measurement system to be measured and the displacement direction of displacement generation module strictly coincide, ensure that the measurement optical axis is incident to the center of the target mirror to be measured along the motion axis, reduce cosine error and abbe error.

Description

Technical Field

[0001] This invention relates to the fields of ultra-precision displacement measurement and lasers, and particularly to a device and method for verifying picometer-level displacement resolution. Background Technology

[0002] With the rapid development of ultra-precision manufacturing, micro-nano fabrication, integrated circuit equipment (e.g., lithography machine workpiece stage positioning), and quantum metrology, industrial and scientific research equipment are placing higher demands on the accuracy, resolution, and long-term stability of displacement measurement. Displacement resolution, as a core indicator of the system, determines the minimum movement step distance that the equipment can identify and respond to, and is an important prerequisite for ensuring the processing and positioning accuracy of ultra-precision equipment.

[0003] Current displacement measurement technology is rapidly advancing from the nanometer level to the picometer level in terms of resolution, giving rise to various novel measurement schemes. For example, patent CN202210393703.X discloses a Michelson laser and displacement measurement system that detects displacement by converting displacement changes into changes in laser frequency, with a theoretical resolution reaching the picometer level. However, for such picometer-level displacement measurement systems, there is currently a lack of reliable and rigorous methods for verifying the resolution, which remains a pressing technical challenge.

[0004] Current displacement resolution verification generally employs the "direct comparison method": a displacement generating device produces minute step displacements, which are then read by the system under test to determine its resolvable limit step size. Regarding the generation of picometer-level displacements, relevant technologies have been reported. For example, patent CN119714082B proposes a testing method based on "optical equivalent displacement," which indirectly generates the required picometer-level step displacement by controlling the minute deflection of a glass plate in the optical path and altering the optical path using the principle of refraction. Additionally, some studies have directly used piezoelectric ceramics (PZT) to drive the generation of picometer-level mechanical step displacements. However, at extremely small step displacements, the accuracy of the above displacement generation schemes is difficult to guarantee due to environmental interference (e.g., thermal drift, mechanical micro-vibration) and the physical characteristics of the actuator itself (e.g., hysteresis, creep, and nonlinear effects of piezoelectric ceramics).

[0005] Therefore, synchronous measurement and calibration must be performed using reference instruments (e.g., laser interferometers). This raises a contradiction in current verification methods: the resolution limit of existing conventional reference instruments is typically in the sub-nanometer range (e.g., 0.1 nm). Due to the lack of reliable and traceable picometer-level reference measurement equipment, existing verification methods are trapped in the technical dilemma of "verifying high-resolution systems with low-resolution references," making it difficult to rigorously verify the picometer-level resolution performance of novel systems experimentally. Summary of the Invention

[0006] To address the technical challenge of lacking traceable picometer-level displacement benchmarks in existing technologies, making it difficult to rigorously verify the actual resolution of high-resolution displacement measurement systems, this invention provides a device and method for verifying picometer-level displacement resolution. Based on a common-path comparison testing platform, the core principle of this invention is the micro-step accumulation calibration method: picometer-level single-step displacements that cannot be directly resolved by benchmark instruments are accumulated through multiple unidirectional steps to a level resolvable by the reference interferometer. Then, the true value of the single-step displacement is inversely derived through linear fitting, achieving the transfer of picometer-level displacement values. Finally, the calibrated picometer-level displacement is used as input to verify the actual resolution capability of the displacement measurement system under test, as detailed below:

[0007] Firstly, a device for verifying picometer-level displacement resolution, the device comprising:

[0008] The target mirror under test is rigidly fixed on the motion stage of the displacement generation module, and the precision controller is used to output a precise voltage signal to drive the movement of the displacement generation module.

[0009] The measuring optical axis of the reference interferometer is aligned with the target mirror under test to detect the displacement, and the displacement is transmitted to the control and data acquisition module. The control and data acquisition module is used to acquire, store and display the displacement measurement data of the reference interferometer in real time.

[0010] The displacement measurement system and the reference interferometer are nearly coaxially probed by the same target mirror; the PD detection and filtering amplification module receives the signal output by the displacement measurement system, completes photoelectric conversion, bandpass filtering and linear amplification, and improves the signal-to-noise ratio of the signal;

[0011] The signal acquisition module acquires the processed signals; the data processing and visualization module is used for control, data operation and analysis, and display of result curves.

[0012] The displacement generation module drives the target mirror under test to perform synchronous translation; the displacement generation module adopts a closed-loop piezoelectric ceramic nano-positioning stage, which outputs controllable step displacement in the pm to nm range; the reference interferometer adopts a commercial zero-difference or heterodyne laser interferometer.

[0013] The measurement axis of the reference interferometer, the measurement axis of the displacement measurement system, and the displacement direction of the displacement generation module are coincident, ensuring that the measurement optical axis is incident on the center of the target mirror along the motion axis, thereby reducing cosine error and Abbe error.

[0014] The device further includes: an environmental control and vibration isolation module.

[0015] The environmental control and vibration isolation module includes an active vibration isolation platform, an acoustic shielding box, and a high-precision constant temperature cover.

[0016] Preferably, the displacement measurement system is a Michelson laser, a high-precision capacitive displacement sensor, or a grating interferometer.

[0017] Secondly, a method for verifying picometer-level displacement resolution, the method comprising:

[0018] A nanometer-scale large voltage step is applied to the displacement generation module by a precision controller to generate displacement steps that can be directly resolved by the reference interferometer. Each step is tested repeatedly.

[0019] Using the measurement data from the reference interferometer, the correspondence between the driving voltage and the output displacement is fitted to verify the linearity and hysteresis characteristics of the displacement output near the current clamping state and the working point, ensuring that the displacement generation module works in the quasi-linear range.

[0020] A small voltage step ΔV is applied to the displacement generation module by a precision controller to make its nominal single-step displacement in the picometer range; N small steps in the same direction are applied continuously, and the data collected by the reference interferometer and the displacement measurement system under test are recorded simultaneously.

[0021] After comparing the overall trend consistency of the two data streams, single-step displacement calibration is performed based on the measurement data from the reference interferometer. N consecutive steps correspond to N+1 displacement stability segments, and the average displacement of each stability segment is extracted. , , , …, Calculate the single-step displacement;

[0022] Using a small, cumulatively calibrated voltage step ΔV, the displacement generation module outputs a single-step picometer-level displacement step. Response data from the displacement measurement system is collected, and the mean displacement difference between the stable sections before and after the step is calculated. Calculate the standard deviation of the stable segment before and after the step. , ,Pick This allows us to determine whether the displacement measurement system can resolve displacements at the picometer level.

[0023] The determination of whether the displacement measurement system can distinguish picometer-level displacement resolution is as follows:

[0024] Single-test resolution criterion: If satisfied The displacement measurement system was determined to have effectively identified the picometer-level displacement step in this test.

[0025] Repeat the single-step step test described above, and statistically analyze the dispersion of the response quantities of all tests. If the relative standard deviation of the response quantities of all tests meets the metrological requirements, and combined with the single 3σ criterion, it is finally determined that the displacement measurement system under test can distinguish the physical step at the picometer level.

[0026] The method further includes: determining the limiting resolution of the displacement measurement system to be measured as follows:

[0027] Gradually reduce the small step size ΔV of the driving voltage output by the precision controller to the displacement generation module, and repeat the above calibration and verification process until the step response of the displacement measurement system under test just meets the resolution criterion. The corresponding calibrated single-step displacement is the ultimate displacement resolution of the displacement measurement system under test.

[0028] The beneficial effects of the technical solution provided by this invention are:

[0029] 1. This invention pioneers a "micro-step accumulation calibration" method, breaking through the resolution bottleneck of reference instruments. By continuously sending micro-drive steps to the displacement generation module, this invention accumulates and amplifies the picometer-level single-step displacement, which cannot be directly measured, to the reliable measurement range of conventional laser interferometers. Then, the true value of the single-step displacement is inversely derived through mean calculation or linear fitting. This provides a new solution to the technical dilemma of "verifying high-resolution systems with low-resolution references" caused by the lack of picometer-level reference instruments.

[0030] 2. This invention employs a testing method that combines static evaluation and dynamic testing. Static testing evaluates the background noise and equivalent displacement resolution of the displacement measurement system under test. After confirming that both the displacement measurement system under test and the reference interferometer are operating stably, picometer-level dynamic displacement step tests are further conducted. This combines the static noise level with the actual displacement response, improving the accuracy and reliability of the resolution determination.

[0031] 3. Near-coaxial, common-target alignment architecture ensures consistency and traceability of measurements. Using the same target mirror as the common target for both measurements, the near-coaxial optical path design ensures that the reference interferometer and the displacement measurement system sense the same displacement, minimizing system errors introduced by inconsistencies between the two displacement paths. The reference interferometer can be directly traced back to the national length metrology standard, providing a complete traceability chain for the picometer-level displacement obtained through calibration, and ensuring the metrological reliability of the verification results.

[0032] 4. Multi-stage error suppression and repeated verification mechanisms enhance the reliability of verification results. By pre-verifying linearity to screen the quasi-linear operating range of the displacement generation module, and by suppressing environmental interference through drift subtraction and outlier removal, combined with the single-step 3σ discrimination criterion and multiple repeated consistency checks, the system's ability to identify minute displacements is verified, while ensuring the accuracy of the verification results. The evaluation conclusions are rigorous and reliable.

[0033] 5. This invention expands the performance evaluation system for ultra-precision sensors. The verification mechanism of this invention is not only applicable to Michelson laser displacement measurement systems, but can also be extended to the limit resolution calibration of picometer or sub-nanometer precision measuring instruments such as high-precision capacitive displacement sensors and grating interferometers, and has broad prospects for industrial and scientific research applications. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of a device for verifying picometer-level displacement resolution.

[0035] in,

[0036] 1-Target mirror to be tested; 2-Displacement generation module;

[0037] 3-Precision controller; 4-Reference interferometer;

[0038] 5-Control and data acquisition module; 6-Displacement measurement system;

[0039] 7-PD detection and filtering amplification module; 8-Signal acquisition module;

[0040] 9-Data processing and visualization module; 10-Environmental control and vibration isolation module. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0042] Example 1

[0043] The embodiments of the present invention are constructed as follows Figure 1 The test platform shown uses the target mirror 1 under test as the common target for both the reference interferometer 4 and the displacement measurement system 6. The target mirror 1 is rigidly fixed to the motion stage of the displacement generation module 2, which drives the target mirror 1 to perform synchronous translation. The displacement generation module 2 can use a closed-loop piezoelectric ceramic nano-positioning stage to output controllable step displacement in the pm to nm range. The precision controller 3 is a matching high-resolution drive power supply used to output precise voltage signals to drive the movement of the displacement generation module 2. The reference interferometer 4 can be a commercial zero-difference or heterodyne laser interferometer. The measuring optical axis of the reference interferometer 4 is aligned with the target mirror 1 under test to detect the displacement and transmit the displacement to the control and data acquisition module 5. The control and data acquisition module 5 is used to collect, store, and display the displacement measurement data of the reference interferometer 4 in real time.

[0044] Among them, the displacement measurement system 6 and the reference interferometer 4 are nearly coaxial (i.e., the two sets of measurement optical paths of the displacement measurement system 6 and the reference interferometer 4 are approximately coincident) to detect the same target mirror 1; the PD detection and filtering amplification module 7 receives the signal output by the displacement measurement system 6, completes photoelectric conversion, bandpass filtering and linear amplification, and improves the signal-to-noise ratio; the signal acquisition module 8 performs high-precision acquisition of the processed signal; and the data processing and visualization module 9 is used for control, data operation and analysis and result curve display.

[0045] The optical path orientation is adjusted to ensure that the measurement axes of the reference interferometer 4, the displacement measurement system 6, and the displacement generation module 2 are strictly aligned, guaranteeing that the measuring optical axis is incident on the center of the target mirror 1 along the motion axis, minimizing cosine and Abbe errors. The entire optomechanical device is built within the environmental control and vibration isolation module 10, which includes an active vibration isolation stage, an acoustic shielding box, and a high-precision constant temperature enclosure. After assembly, the constant temperature enclosure is sealed, the active vibration isolation stage is activated, and the device is left to stand for a period of time until the background drift trends of the reference interferometer 4 and the displacement measurement system 6 become relatively flat.

[0046] Example 2

[0047] With no drive signal output from the precision controller 3 and the displacement generation module 2 remaining stationary, the displacement measurement system 6 and the reference interferometer 4 are reset to zero. The background displacement data corresponding to the fixed target mirror 1 is continuously acquired. After removing outliers using the 3σ criterion, the static time-domain displacement background data are obtained. and .

[0048] For reference interferometer 4, displacement background data is used. Determine if it is within the normal range specified by the factory. If it is, the reference interferometer 4 is considered to be working normally and the process continues. If not, the reference interferometer 4 is considered to be working abnormally, an alarm signal is output and the measurement task is terminated.

[0049] For the displacement measurement system 6 under test, data analysis is carried out in two ways: on the one hand, the static time-domain displacement background data obtained from the displacement measurement system 6 under test is analyzed. Allen bias is calculated, and the curve of Allen bias as a function of integration time τ is plotted. The white noise level of the displacement measurement system 6 under short-time integration and the drift characteristics under long-time integration are identified. The integration time corresponding to the minimum point of the Allen bias curve is selected as the optimal response window for subsequent single-step testing.

[0050] If the minimum value of the time-domain Allan deviation is on the order of pm, it is preliminarily determined that it has the potential to resolve displacement at the picometer level; on the other hand, for static time-domain displacement background data A fast Fourier transform is performed to obtain the displacement noise power spectral density, and then the noise level under different frequency components is obtained, realizing the frequency domain characterization of the resolution capability of the displacement measurement system under test.

[0051] I. Linearity Pre-verification of Displacement Generation Module 2

[0052] A precision controller 3 applies nanometer-scale large voltage steps to the displacement generation module 2, sequentially generating displacement steps of 1nm, 2nm, 5nm, and 10nm that can be directly resolved by the reference interferometer 4. Each step is repeated multiple times. Using the measurement data from the reference interferometer 4, the correspondence between the driving voltage and the output displacement is fitted to verify the linearity and hysteresis characteristics of the displacement output near the current clamping state and the operating point, ensuring that the displacement generation module 2 operates in the quasi-linear range.

[0053] II. Pictometer-level single-step displacement accumulation calibration

[0054] A small voltage step ΔV is applied to the displacement generation module 2 by the precision controller 3, so that its nominal single-step displacement (i.e., the nominal output value obtained based on the voltage-displacement calibration relationship given in the product manual of the displacement generation module 2) is in the picometer range; N small steps in the same direction are applied continuously, and the value of N is based on the total cumulative displacement reaching the reliable resolution range of the reference interferometer 4. At the same time, the data collected by the reference interferometer 4 and the displacement measurement system 6 are recorded synchronously.

[0055] After comparing the overall trend consistency of the two data streams, single-step displacement calibration is performed based on the measurement data from reference interferometer 4. N consecutive steps correspond to N+1 displacement stabilization segments (the initial zero position is level 0, and one new level is added after each step). The average displacement of each stabilization segment is extracted. , , , …, Single-step displacement can be calculated in two ways: the first-to-last average method, suitable for rapid estimation, and the formula is... ,in The mean of the initial zero-position stable segment, The mean value of the stable segment after step N; a linear fitting method, a more accurate calibration method, using the step number k (k=0,1,2,…,N) as the independent variable, the mean displacement of each stable segment. Using the variable as the dependent variable, a least-squares linear fit is performed to fit the mean of the N+1 level stable segment. The fitting equation is: The actual displacement in a single step is obtained by fitting the solution. This method utilizes data from all N+1 stable segments in the calculation, effectively suppressing the impact of single-step random fluctuations and slow drift on the calibration results.

[0056] III. Verification and Repeatability Test of Single-Step Step Resolution

[0057] Using a small, cumulatively calibrated voltage step ΔV, the displacement generation module 2 outputs a single-step picometer-level displacement step. Response data from the displacement measurement system 6 is collected, and the mean displacement difference between the stable sections before and after the step is calculated. This refers to the step response of the displacement measurement system 6; simultaneously, the standard deviation of the stable segment before and after the step is calculated. , ,Pick .

[0058] During the test, if there is obvious linear thermal drift before and after the step, the drift component is deducted by linear interpolation of adjacent zero segments; if there is abnormal data caused by sudden vibration or other interference, the data set is removed and the test is repeated.

[0059] Single-test resolution criterion: If satisfied If the displacement measurement system 6 can effectively identify the picometer-level displacement step in this test, then it is determined that the displacement measurement system 6 can effectively identify the displacement step in this test.

[0060] Repeat the single-step step test described above and statistically analyze the dispersion of the response quantities for all tests. If the relative standard deviation of the response quantities for all tests meets the metrological requirements (for example, not greater than 10%), then, based on the single 3σ criterion, it is finally determined that the displacement measurement system 6 under test can distinguish the picometer-level physical step.

[0061] To determine the limiting resolution of the displacement measurement system 6, the driving voltage step ΔV output by the precision controller 3 to the displacement generation module 2 can be gradually reduced, and the above calibration and verification process can be repeated until the step response of the displacement measurement system 6 just meets the resolution criterion. At this point, the corresponding calibrated single-step displacement is the limit displacement resolution of the displacement measurement system 6 to be measured.

[0062] Example 3

[0063] The present invention uses a Michelson laser displacement measurement system as a typical verification object. The Michelson laser displacement measurement system includes a measuring arm and a reference arm, wherein the frequency in the reference arm remains constant, and the length of the measuring arm is changed by the motion traction of the target mirror 1 under test.

[0064] Based on the principle of external cavity laser, the laser frequency variation The change in target mirror displacement Δx satisfies the following relationship: (in (where L is the laser center frequency, L is the laser cavity length, and n is the ambient refractive index of the Michelson laser). This allows for the mapping of minute displacements to frequency changes in a beat frequency signal, and the displacement information can be recovered by measuring the frequency fluctuations of the beat frequency signal.

[0065] The test platform on which the verification method is based includes: the target mirror under test 1, displacement generation module 2, precision controller 3, reference interferometer 4, control and data acquisition module 5, Michelson laser, PD detection and filtering amplification module 7, signal acquisition module 8, data processing and visualization module 9, and environmental control and vibration isolation module 10.

[0066] The control and data acquisition module 5 is used to acquire, store, and display the displacement measurement data of the reference interferometer 4; the Michelson laser and the reference interferometer 4 are nearly coaxial to detect the same target mirror 1 under test, converting the displacement change of the target mirror 1 under test into the frequency change of the laser beat frequency; the PD detection and filtering amplification module 7 is used to receive the beat frequency signal output by the Michelson laser, complete photoelectric conversion, filtering and amplification, and optimize the quality of the beat frequency signal; the signal acquisition module 8 is a frequency counter used to perform high-precision frequency counting and synchronous acquisition of the beat frequency signal.

[0067] The data processing and visualization module 9 is communicatively connected to the signal acquisition module 8, and is used for test process control, data processing and analysis, and result visualization output. This data processing and visualization module 9 integrates an Allan bias analysis module, a Kalman filter, and a polynomial baseline fitting algorithm module, used to accurately extract picometer-level step features from low-frequency thermal drift and broadband white noise. The aforementioned Allan bias analysis module, Kalman filter, and polynomial baseline fitting algorithm module are technical terms well-known to those skilled in the art, and will not be elaborated upon in this embodiment. The data processing and analysis is based on... The relationship is used to convert the frequency change data collected by the signal acquisition module 8 (here, the frequency counter) into displacement information.

[0068] The environmental control and vibration isolation module 10 includes an active vibration isolation table, an acoustic shielding box, and a high-precision constant temperature enclosure. Each functional module is enclosed inside the constant temperature enclosure, which suppresses ambient temperature fluctuations to the millikelvin level and shields against external airflow disturbances and micro-vibrations. This reduces interference from external mechanical vibrations, environmental refractive index fluctuations, and other factors, creating low-noise experimental conditions for picometer-level resolution verification and ensuring the accuracy of experimental test results.

[0069] The method for verification using the above-mentioned device specifically includes the following steps:

[0070] The first step is static resolution assessment. With displacement generation module 2 stationary, static output data (displacement background data) of Michelson laser and reference interferometer 4 are collected. For reference interferometer 4, the displacement background data is used to determine whether it is within the normal range specified by the factory, thereby confirming its working status. For Michelson laser, its equivalent displacement resolution and displacement noise power spectral density are evaluated respectively.

[0071] The second step is to accumulate displacement output. N picometer-level nominal step drive voltages in the same direction are continuously sent to the displacement generation module 2. After each step, a stable duration is maintained so that the total accumulated displacement reaches the order of magnitude that the reference interferometer 4 can reliably resolve.

[0072] The third step is single-step displacement calibration. Displacement data of each step is collected synchronously using the reference interferometer 4, the average displacement of each stable segment is extracted, and linear fitting is performed on the multi-level displacement data to calculate the actual displacement corresponding to a single drive command, thus completing the calibration of the picometer-level single-step displacement.

[0073] The fourth step is the single-step resolution test. Using the calibrated driving parameters, the displacement generation module 2 is controlled to output a single-step picometer-level physical displacement. The response data of the Michelson laser under test is collected, and the standard deviation of the response before and after the stable segment is observed. The resolution capability is preliminarily determined based on the 3σ criterion.

[0074] Step 5: Repeatability verification and final judgment. Repeat the above tests multiple times to verify the consistency of the response and comprehensively judge the Michelson laser's ability to resolve picometer-level displacements.

[0075] The above description is only a preferred embodiment of the present invention. It should be noted that this embodiment uses a Michelson laser displacement measurement system as an example to describe the verification method in detail. The core principles and method flow of the present invention are also applicable to other types of displacement measurement systems. Such equivalent effects should be considered within the scope of protection of the present invention. For those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

[0076] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0077] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A device for verifying picometer-level displacement resolution, characterized in that, The device includes: The target mirror under test is rigidly fixed on the motion stage of the displacement generation module, and the precision controller is used to output a precise voltage signal to drive the movement of the displacement generation module. The measuring optical axis of the reference interferometer is aligned with the target mirror under test to detect the displacement, and the displacement is transmitted to the control and data acquisition module. The control and data acquisition module is used to acquire, store and display the displacement measurement data of the reference interferometer in real time. The displacement measurement system and the reference interferometer are nearly coaxially probed by the same target mirror; the PD detection and filtering amplification module receives the signal output by the displacement measurement system, completes photoelectric conversion, bandpass filtering and linear amplification, and improves the signal-to-noise ratio of the beat frequency signal; The signal acquisition module acquires the processed signals; the data processing and visualization module is used for control, data operation and analysis, and display of result curves.

2. The device for verifying picometer-level displacement resolution according to claim 1, characterized in that, The displacement generation module drives the target mirror under test to perform synchronous translation; the displacement generation module adopts a closed-loop piezoelectric ceramic nano-positioning stage, which outputs controllable step displacement in the pm to nm range; the reference interferometer adopts a commercial zero-difference or heterodyne laser interferometer.

3. The device for verifying picometer-level displacement resolution according to claim 1, characterized in that, The measurement axis of the reference interferometer, the measurement axis of the displacement measurement system, and the displacement direction of the displacement generation module are coincident, ensuring that the measurement optical axis is incident on the center of the target mirror along the motion axis, thereby reducing cosine error and Abbe error.

4. The device for verifying picometer-level displacement resolution according to claim 1, characterized in that, The device also includes an environmental control and vibration isolation module. The environmental control and vibration isolation module includes an active vibration isolation platform, an acoustic shielding box, and a high-precision constant temperature cover.

5. A device for verifying picometer-level displacement resolution according to claim 1 or 3, characterized in that, The displacement measurement system consists of a Michelson laser, a high-precision capacitive displacement sensor, and a grating interferometer.

6. A method for verifying picometer-level displacement resolution, characterized in that, The method includes: A nanometer-scale large voltage step is applied to the displacement generation module by a precision controller to generate displacement steps that can be directly resolved by the reference interferometer. Each step is tested repeatedly. Using the measurement data from the reference interferometer, the correspondence between the driving voltage and the output displacement is fitted to verify the linearity and hysteresis characteristics of the displacement output near the current clamping state and the working point, ensuring that the displacement generation module works in the quasi-linear range. A small voltage step ΔV is applied to the displacement generation module by a precision controller to make its nominal single-step displacement in the picometer range; N small steps in the same direction are applied continuously, and the data collected by the reference interferometer and the displacement measurement system under test are recorded simultaneously. After comparing the overall trend consistency of the two data streams, single-step displacement calibration is performed based on the measurement data from the reference interferometer. N consecutive steps correspond to N+1 displacement stability segments, and the average displacement of each stability segment is extracted. , , ,…, Calculate the single-step displacement; Using a small, cumulatively calibrated voltage step ΔV, the displacement generation module outputs a single-step picometer-level displacement step. Response data from the displacement measurement system is collected, and the mean displacement difference between the stable sections before and after the step is calculated. Calculate the standard deviation of the stable segment before and after the step. , ,Pick This allows us to determine whether the displacement measurement system can resolve displacements at the picometer level.

7. The method for verifying picometer-level displacement resolution according to claim 6, characterized in that, The determination of whether the displacement measurement system can distinguish picometer-level displacement resolution is as follows: Single-test resolution criterion: If satisfied The system was determined to have effectively identified the picometer-level displacement step in this test. Repeat the single-step step test described above, and statistically analyze the dispersion of the response quantities of all tests. If the relative standard deviation of the response quantities of all tests meets the metrological requirements, and combined with the single 3σ criterion, it is finally determined that the displacement measurement system under test can distinguish the physical step at the picometer level.

8. The method for verifying picometer-level displacement resolution according to claim 6, characterized in that, The method further includes: determining the limiting resolution of the displacement measurement system to be measured as follows: Gradually reduce the small step size ΔV of the driving voltage output by the precision controller to the displacement generation module, and repeat the above calibration and verification process until the step response of the displacement measurement system under test just meets the resolution criterion. The corresponding calibrated single-step displacement is the ultimate displacement resolution of the displacement measurement system under test.

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