Ultraviolet camera optical axis calibration device and method based on multi-source error collaborative compensation

Abstract

The application discloses a multi-source error collaborative compensation-based ultraviolet camera optical axis calibration device, which comprises a laser tracker, a contact probe, a collimator, a reflecting ball base, a reflecting target ball, a high-precision electric linear guide rail, a camera fixing tool, an optical two-dimensional rotary table, a data processing and control module, an optical vibration isolation air floating platform and a distributed temperature sensor array. Low-frequency noise is inhibited through the optical vibration isolation air floating platform. Position measurement is carried out through the laser tracker, the normal vector of the light-emitting surface of the collimator, the actual movement axis of the high-precision electric linear guide rail and the camera optical axis are fitted, the included angle between the normal vector and the camera optical axis and the actual movement axis of the high-precision electric linear guide rail is calculated, the rotation angle of the optical two-dimensional rotary table and the slider position of the high-precision electric linear guide rail are adjusted, the camera optical axis is calibrated, and the requirement for the aperture of the collimator is reduced. Meanwhile, temperature data are combined to calculate mechanical errors, environmental errors and measurement errors, and adjustment instructions are corrected.

Description

Technical Field

[0001] This invention relates to the field of measurement and calibration technology, to optical precision measurement and ultraviolet detection calibration, and particularly to an ultraviolet camera optical axis calibration device and method based on multi-source error collaborative compensation. Background Technology

[0002] The optical axis calibration of an ultraviolet (UV) camera plays a decisive role in the performance of UV detection. Current technology has improved the measurement accuracy of UV cameras from the angular level to the sub-arcsecond level. Compared with traditional optical measurements, it has significant advantages in terms of cost, measurement speed, ease of use, and measurement accuracy.

[0003] The optical axis of an ultraviolet camera is mainly composed of the CMOS mounting accuracy, the lens optical axis, and the overall camera optical axis. The measurement of the overall optical axis relies primarily on the parallelism of the collimator and the mounting fixture. Traditional calibration methods depend on theodolites or autocollimators, whose accuracy is limited by imaging resolution, and are complex to operate, applicable to a limited range of measurement functions, making them unsuitable for high-precision coaxial measurements with multiple cameras. Using large-diameter collimators is costly and uneconomical, and cannot achieve dynamic error separation, nor can it correct for coupled mechanical errors, environmental thermal deformation, and measurement noise. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a device and method for calibrating the optical axis of an ultraviolet camera based on multi-source error collaborative compensation. It is applicable to optical calibration, spatial target positioning, multi-target coaxiality, and error compensation, and can improve measurement accuracy and efficiency while reducing equipment costs.

[0005] The ultraviolet camera optical axis calibration device based on multi-source error collaborative compensation includes a laser tracker, a contact probe, a collimator, a reflective sphere base, a reflective target sphere, a high-precision electric linear guide, a camera fixing fixture, an optical two-dimensional turntable, a data processing and control module, an optical vibration isolation air-bearing platform, and a distributed temperature sensor array.

[0006] The collimator is fixed to one side of the optical vibration isolation air-float platform. The laser tracker is set next to the optical vibration isolation air-float platform, with the laser emission position opposite to the light outlet of the collimator, and the contact probe is set near the light outlet of the collimator.

[0007] The high-precision electric linear guide is fixed on the optical vibration-isolation air-bearing platform, located between the collimator and the laser tracker. The optical two-dimensional turntable is used to fix the camera fixture on the slider of the high-precision electric linear guide.

[0008] The air-floating vibration isolation platform integrates an active tilt adjustment module, which dynamically adjusts the platform's levelness through air film pressure to suppress low-frequency vibrations below 10Hz.

[0009] The reflective ball base is used to fix the reflective target ball on a high-precision electric linear guide and camera mounting fixture.

[0010] The distributed temperature sensor array includes multiple temperature sensors fixed on a collimator, a high-precision motorized linear guide, and an optical two-dimensional turntable to measure the ambient or equipment temperature.

[0011] The data processing and control module acquires measurement data from the laser tracker and the distributed temperature sensor array, calculates multi-source error compensation values, and controls the movement of the high-precision electric linear guide and optical two-dimensional turntable.

[0012] The method for calibrating the optical axis of an ultraviolet camera based on multi-source error collaborative compensation uses the aforementioned device to calibrate the optical axis of the ultraviolet camera. The specific steps are as follows:

[0013] Step 1: Establish a global coordinate system with the laser tracker as the origin, use a contact probe to measure the coordinates of multiple points on the light-emitting surface of the collimator, and calculate the normal vector of the light-emitting surface of the collimator. The reflective target ball is moved by the slider of a high-precision electric linear guide, and the coordinates of the reflective target ball are measured to fit the actual motion axis of the high-precision electric linear guide. Calculate the angle θ between the high-precision electric linear guide and the collimator, and adjust the installation position of the high-precision electric linear guide until... .

[0014] Step 2: Fix the camera fixture onto the optical 2D turntable, then fix the optical 2D turntable onto the slider of the high-precision electric linear guide. Start the high-precision electric linear guide to move the camera fixture and the reflective target ball synchronously to multiple positions, reaching position p at the k-th position. k A fixed reflective target ball is used to measure the coordinates of m points at different angles, and the coordinates at position p are fitted. k The rotation axis vector of the camera fixture .

[0015] Step 3: Calculate the reference vector Rotational axis vector of the camera fixture The included angle and reference vector The actual motion axis of the high-precision electric linear guide. The angle between Adjust the rotation angle of the optical 2D turntable or the slider position of the high-precision electric linear guide to make... , .

[0016] Step 4: Acquire temperature data measured by a distributed temperature sensor array through the data processing and control module, and calculate the temperature difference based on historical data. Acquire the vibration acceleration of the optical vibration-isolated air-bearing platform through an accelerometer. The calculation device's mechanical errors, environmental errors, and measurement errors are assessed, and error compensation is performed.

[0017] Step 5: Return to Step 2, repeat coordinate measurement and vector fitting, and adjust the module's attitude until... The calibration is now complete.

[0018] The present invention has the following beneficial effects:

[0019] 1. The proposed method for calculating the deflection angle and the error compensation algorithm can guarantee a measurement accuracy of 1″. At the same time, the collimator used only needs to have a diameter larger than the size of the camera lens to achieve coaxial measurement of the optical axes of multiple cameras, which greatly reduces the cost of the collimator. Furthermore, since it only uses the coordinate system of the laser tracker globally, it reduces manual modeling errors, increases system bandwidth, and its system operation is simple and low-cost.

[0020] 2. By using an orthogonal error separation algorithm to decouple the multi-axis error chain, the coupled errors are decomposed into guide rail errors, turntable errors, and measurement errors, thereby mapping the errors to independent control channels for independent compensation.

[0021] 3. Air-float-laser coordinated control: The air-float platform is used to suppress low-frequency vibrations of <10Hz, and the laser tracker uses closed-loop correction to correct high-frequency errors of >10Hz, thereby improving system bandwidth.

[0022] 4. A nonlinear temperature compensation model is proposed. Through finite element thermal model calibration, compensation strategy learning is integrated with temperature gradient, temperature change rate and historical data to reduce manual modeling errors and achieve advanced compensation.

[0023] 5. A multi-point dynamic measurement method is proposed. By calculating the angle error between the rotation axis vector and the reference vector of the camera fixture at different positions when the slider moves, coaxial high-precision calibration of multiple ultraviolet cameras can be achieved, reducing the requirements for the aperture size of the collimator. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the calibration device;

[0025] Figure 2 Error separation algorithm flowchart;

[0026] Figure 3 This is a schematic diagram of the laser compensation signal;

[0027] Figure 4 For air flotation-laser coordinated control of vibration power spectral density;

[0028] Figure 5 The effect of laser compensation on high-frequency residuals.

[0029] 1. Laser tracker; 2. Contact probe; 3. Collimator; 4. Reflector sphere base; 5. Reflector target sphere; 6. High-precision electric linear guide; 7. Camera mounting fixture; 8. Optical 2D turntable; 9. Data processing and control module; 10. Optical vibration isolation air-bearing platform; 11. Temperature sensor. Detailed Implementation

[0030] The present invention will be further explained below with reference to the accompanying drawings;

[0031] like Figure 1 As shown, the ultraviolet camera optical axis calibration device based on multi-source error collaborative compensation includes a laser tracker 1, a contact probe 2, a collimator 3, a reflective sphere base 4, a reflective target sphere 5, a high-precision electric linear guide rail 6, a camera fixing fixture 7, an optical two-dimensional turntable 8, a data processing and control module 9, an optical vibration isolation air-bearing platform 10, and a distributed temperature sensor array 11.

[0032] The collimator 3 is fixed to one side of the optical vibration isolation air-float platform. The laser tracker 1 is set next to the optical vibration isolation air-float platform 10, with the laser emission position opposite to the light outlet of the collimator 3, and the contact probe 2 is set near the light outlet of the collimator 3.

[0033] The high-precision electric linear guide 6 is fixed on the optical vibration isolation air-bearing platform, located between the collimator 3 and the laser tracker 1. The optical two-dimensional turntable 8 is used to fix the camera fixture 7 on the slider of the high-precision electric linear guide 6.

[0034] The optical vibration isolation air-float platform 10 integrates an active tilt adjustment module, which dynamically adjusts the surface level through air film pressure to suppress low-frequency vibrations below 10Hz.

[0035] The reflective ball base 4 is used to fix the reflective target ball 5 on the high-precision electric linear guide rail 6 and the camera fixing fixture 7.

[0036] The distributed temperature sensor array includes multiple temperature sensors 11, which are fixed on a collimator 3, a high-precision electric linear guide rail 6, and an optical two-dimensional turntable 8 to measure the ambient or equipment temperature.

[0037] The data processing and control module 9 collects measurement data from the laser tracker 1 and the temperature sensor 11, calculates multi-source error compensation values, and controls the movement of the high-precision electric linear guide 6 and the optical two-dimensional turntable 8.

[0038] like Figure 2As shown, the method for calibrating the optical axis of an ultraviolet camera based on multi-source error collaborative compensation uses the above-mentioned device to calibrate the optical axis of the ultraviolet camera. The specific steps are as follows:

[0039] Step 1: Preheat the laser tracker to ensure its stability. Establish a global coordinate system with the laser tracker as the origin, and calculate the normal vector of the collimator's output surface. The actual motion axis of the high-precision electric linear guide. and the rotation axis vector of the camera fixture The specific steps are as follows:

[0040] s1.1 Use a contact probe to measure the three-dimensional coordinates of nine non-collinear points on the output surface of the collimator. , By fitting the spatial plane equation using the least squares method, the normal vector of the light-emitting surface of the collimator is calculated. , as the reference vector.

[0041] For the three-dimensional coordinates of the 9 non-collinear points First, calculate the centroid coordinates. :

[0042]

[0043] Then construct the covariance matrix. And expand:

[0044]

[0045] Where T denotes matrix transpose. , , .

[0046] Perform eigenvalue decomposition on the covariance matrix M:

[0047]

[0048] Then the reference vector This is the eigenvector corresponding to the smallest eigenvalue.

[0049] Based on the measurement error of the laser tracker The number of points selected can control the fitting residual. .

[0050] s1.2. Start the high-precision electric linear guide rail, which moves the reflective target ball via a slider. Use a laser tracker to measure the coordinates of the reflective target ball at different positions. Similarly, perform eigenvalue decomposition based on the covariance matrix. The eigenvector corresponding to the largest eigenvalue represents the main direction of the data point distribution, i.e., the actual motion axis of the high-precision electric linear guide rail. s.

[0051] The actual motion axis of the high-precision electric linear guide is calculated using the vector angle calculation formula. With reference vector The angle between Angle, when At that time, adjust the installation position of the high-precision electric linear guide until... .

[0052]

[0053] s1.3. Fix the camera fixture onto the optical 2D turntable, and then fix the optical 2D turntable onto the slider of the high-precision electric linear guide. Fix the reflective target ball onto the camera fixture via the reflective ball base. Start the high-precision electric linear guide to move the camera fixture and the reflective target ball synchronously. Each time it moves to a position p k The rotation and pitch angles are changed by an optical two-dimensional turntable, causing the turntable to rotate around the rotation axis of the camera fixture. A laser tracker records the coordinates L of the reflecting target ball at different rotation angles. m Let m = 1, 2, 3...M, and let m be the rotation axis vectors of the camera fixture. It is necessary to solve for the principal direction axis of the set of coordinate points of the reflecting target sphere, even if all coordinate points are to The sum of squared vertical distances is minimized:

[0054]

[0055] Where c represents the coordinates of the rotation center, and V represents the rotation axis vector of the camera fixture. The unit vector.

[0056] Eigenvalue decomposition is performed based on the covariance matrix, and the eigenvector corresponding to the smallest eigenvalue is used as the rotation axis vector of the camera fixture. .

[0057] Step 2: Calculate the position p of the camera fixture. k Lower reference vector Rotational axis vector of the camera fixture The included angle ,when At that time, correction commands are output through the inverse motion model of the turntable. Perform linear error compensation:

[0058]

[0059]

[0060] in, This indicates the angle that the optical two-dimensional turntable needs to be adjusted. This represents the cumulative error as the camera fixture moves from the first position to the kth position. It is the proportional gain coefficient, with a value of 0.5 and a unit of μrad / ″, used in the proportional control loop; It is the integral gain coefficient, with a value of 0.1 and a unit of μrad / (″·s), used in the integral control loop.

[0061] Calculate the rotation axis vector of the camera fixture The actual motion axis of the high-precision electric linear guide. The angle between ,when At that time, straightness compensation pulses are generated through the inverse motion model of the turntable. Further adjustments are made to the slider position of the high-precision electric linear guide until... :

[0062]

[0063]

[0064] in, This indicates the length of the guide rail, in mm. This indicates the distance the slider has moved, in mm.

[0065] Calculate the thermal expansion deformation of a high-precision electric linear guide. Perform pre-compensation for slider motion commands and calculate the theoretical target position after compensation. :

[0066]

[0067]

[0068] in, β represents the initial length of the high-precision electric linear guide, in mm. β is the coefficient of thermal expansion of the high-precision electric linear guide material, in °C. -1 Starget represents the pre-compensated actual target position of the high-precision electric linear guide, in mm. ΔT represents the difference between the actual temperature and the initial temperature, in °C. Zero point represents the zero point of the high-precision guide coordinate system.

[0069] Step 3: The data processing and control module acquires temperature data measured by a distributed temperature sensor array to obtain the ambient temperature T and the temperature gradient ΔT of the high-precision electric linear guide and optical two-dimensional turntable. The vibration acceleration of the optical vibration-isolated air-bearing platform is acquired using an accelerometer. The calculation device's mechanical errors, environmental errors, and measurement errors are assessed, and error compensation is performed. The specific steps are as follows:

[0070] s3.1 Calculate the rotation center drift of the optical two-dimensional turntable. :

[0071]

[0072] Where ΔO is in mm, γ1 represents the linearity error coefficient, and γ2 represents the nonlinearity error coefficient. Based on the rotation center drift... Rotation command of optical 2D turntable Dynamically corrected to :

[0073]

[0074] Where R is the rotation radius of the optical two-dimensional turntable, in mm.

[0075] s3.2. Based on the temperature data T measured by the distributed temperature sensor array, calculate the temperature drift of the laser tracker measurement value, and then calculate the coordinate measurement value P of the reflecting target sphere. 测 Make corrections:

[0076]

[0077]

[0078] in, The measurement is for coordinate correction, and the unit is mm. P represents the rate of temperature change, in °C / min; α1 and α2 are temperature compensation coefficients calibrated experimentally. 真 This represents the corrected coordinate values.

[0079] s3.3 Activate the optical vibration isolation air-float platform to suppress low-frequency vibrations below 10Hz, based on the vibration acceleration of the optical vibration isolation air-float platform. The tilt of the computing platform :

[0080]

[0081] in, This is the pressure feedback coefficient, in kPa·s. 2 / m. The platform's levelness is dynamically adjusted using air film pressure.

[0082]

[0083] Among them, P 气P0 is the reference air film pressure, which is the real-time adjusted air film pressure. This is the pressure feedback coefficient.

[0084] During laser tracker measurements, multipath reflection interference exists in the data. This can be addressed using the frequency response function. Real-time frequency domain filtering attenuates signals with frequencies above 10Hz, effectively correcting high-frequency errors and improving the accuracy of measurement data.

[0085]

[0086] Where h is the imaginary unit and f is the frequency of the input signal. , which represents the cutoff frequency.

[0087] By using real-time measurement data from a laser tracker to correct high-frequency errors above 10Hz through closed-loop control, air-float-laser coordinated control is achieved, thereby improving system bandwidth. Figures 3-5 The image shows the gain effect. From Figure 3 As can be seen, this method can separate high-frequency errors in real time, and the laser compensation signal can effectively compensate for high-frequency residuals. From... Figure 4 As can be seen, after initiating coordinated control, nonlinear harmonics at different frequencies can be effectively suppressed. From Figure 5 As can be seen, especially in the high-frequency region with frequencies >10Hz, after laser compensation, the suppression of structural functions at 60Hz reaches 45dB, while the suppression of high-frequency noise at 120Hz reaches 32dB, with an average suppression of over 30dB.

[0088] Step 4: Dynamic Temperature Compensation Model (DTCM), integrated into the data processing and control module, is based on the temperature data T measured at different times t by the distributed temperature sensor array. t Deformation of computing device :

[0089]

[0090] Where n represents the number of parts; This represents the coefficient of thermal expansion of the q-th component, in °C. -1 ; This represents the actual temperature of the q-th component measured at time t; This represents the initial geometric length of the q-th component, in meters (m).

[0091] Step 5: Based on the deformation obtained from the dynamic temperature compensation model, perform real-time correction on the laser tracker measurement data and calculate the pre-compensation for motion control commands. Return to Step 2 to re-perform vector fitting and module attitude adjustment until... The calibration is now complete.

Claims

1. An ultraviolet camera optical axis calibration device based on multi-source error collaborative compensation, comprising a laser tracker, a contact probe, a collimator, a camera fixing fixture, a reflective sphere base, a reflective target sphere, and a data processing and control module, characterized in that: It also includes high-precision electric linear guides, camera fixtures, optical two-dimensional turntables, optical vibration isolation air-bearing platforms, and distributed temperature sensor arrays. The collimator is fixed to one side of the optical vibration isolation air-float platform; the laser tracker is set next to the optical vibration isolation air-float platform, with the laser emission position opposite to the light outlet of the collimator, and the contact probe is set near the light outlet of the collimator. The high-precision electric linear guide is fixed on the optical vibration isolation air-bearing platform and is located between the collimator and the laser tracker; the optical two-dimensional turntable is used to fix the camera fixture on the slider of the high-precision electric linear guide. The optical vibration isolation air-bearing platform dynamically adjusts the platform's levelness through air film pressure to suppress low-frequency vibrations; The reflective ball base is used to fix the reflective target ball on a high-precision electric linear guide and camera fixing fixture; The distributed temperature sensor array includes multiple temperature sensors fixed on a collimator, a high-precision electric linear guide, and an optical two-dimensional turntable to measure the ambient or equipment temperature. The data processing and control module acquires measurement data from the laser tracker and the distributed temperature sensor array, calculates mechanical errors, environmental errors and measurement errors, controls the movement of the high-precision electric linear guide and optical two-dimensional turntable, and calibrates the camera optical axis.

2. A method for calibrating the optical axis of an ultraviolet camera based on multi-source error collaborative compensation, characterized in that: The specific steps for calibrating the optical axis of an ultraviolet camera using the apparatus described in claim 1 are as follows: Step 1: Establish a global coordinate system with the laser tracker as the origin, and fit the normal vector of the light-emitting surface of the collimator. The actual motion axis of the high-precision electric linear guide. The angle between the high-precision electric linear guide and the collimator was calculated. Adjust the installation position of the high-precision electric linear guide until... ; Step 2: Fix the camera fixture onto the slider of the high-precision electric linear guide using an optical 2D turntable. Start the high-precision electric linear guide to move the camera fixture and the reflective target ball synchronously to multiple positions, reaching position p at the k-th position. k Fix the reflective target sphere and rotate the optical two-dimensional turntable to different angles to fit the position p. k The rotation axis vector of the camera fixture ; Step 3: Calculate the normal vector Rotation axis vector of the camera fixture The included angle ,as well as The actual motion axis of the high-precision electric linear guide. Angle error between Adjust the rotation angle of the optical 2D turntable or the slider position of the high-precision electric linear guide to make... , ; Step 4: Obtain temperature data from the distributed temperature sensor array and calculate the temperature difference based on historical data; collect the vibration acceleration of the optical vibration isolation air-floating platform using an accelerometer. Mechanical errors, environmental errors, and measurement errors of the computing device; Step 5: Return to Step 2, and based on the error value obtained in Step 4, re-perform coordinate measurements and vector fitting, and adjust the module's attitude until... The calibration is now complete.

3. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2, characterized in that: The three-dimensional coordinates of multiple non-collinear points on the output surface of the collimator are measured using a contact probe, and then the centroid coordinates of these multiple non-collinear points are calculated. Construct the covariance matrix And expand: ； Where T denotes matrix transpose. , , , Represent the three-dimensional coordinates of the i-th non-collinear point; perform eigenvalue decomposition on the covariance matrix M, and select the eigenvector corresponding to the smallest eigenvalue as the normal vector of the light-emitting surface of the collimator. .

4. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2, characterized in that: A reflective target ball is fixed on the slider of a high-precision electric linear guide. The high-precision electric linear guide is started, and the slider moves the reflective target ball. A laser tracker is used to measure the coordinates of the reflective target ball at different positions. Eigenvalue decomposition is performed based on the covariance matrix, and the eigenvector corresponding to the largest eigenvalue is used as the actual motion axis of the high-precision electric linear guide. s.

5. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2, characterized in that: At position k, p k With the objective of minimizing the sum of the squared vertical distances from the coordinate points of the optical two-dimensional turntable at different angles to the center of rotation, the model at position p is fitted. k The rotation axis vector of the camera fixture .

6. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2, characterized in that: when At that time, the adjustment angle of the output optical two-dimensional turntable : ； in, This represents the cumulative error as the camera fixture moves from the first position to the kth position. It is the proportional gain coefficient. It is the integral gain coefficient; when At that time, output straightness compensation pulse Adjust the slider position of the high-precision electric linear guide: ； in, Indicates the length of the guide rail. Indicates the distance the slider moves; calculates the thermal expansion deformation of a high-precision electric linear guide. The actual target position S of the adjusted slider is obtained. 目标 : ； ； in, β is the initial length of the high-precision electric linear guide, β is the coefficient of thermal expansion of the high-precision electric linear guide material, and ΔT is the difference between the actual temperature and the initial temperature.

7. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2 or 6, characterized in that: Calculate the center of rotation drift of an optical two-dimensional turntable : ； Where γ1 represents the linear error coefficient and γ2 represents the nonlinear error coefficient; based on the rotation center drift... Rotation command of optical 2D turntable Dynamically corrected to : ； Where R is the rotation radius of the optical two-dimensional turntable.

8. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in any one of claims 2 to 5, characterized in that: Calculate the temperature drift of the laser tracker measurements. The coordinate measurement value P of the reflecting target sphere 测 Make corrections: ； ； in, The temperature change rate is represented by T, where T represents the temperature data measured by the distributed temperature sensor array, t represents time, and ΔT is the difference between the current temperature and the initial temperature; α1 and α2 are temperature compensation coefficients calibrated experimentally; P 真 This represents the corrected coordinate values.

9. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in claim 2, characterized in that: The vibration acceleration α of the optical vibration isolation air-floating platform was collected. 振动 Through frequency response function To suppress signals with frequencies above 10Hz, the tilt adjustment amount of the calculation platform is calculated. Adjust the air film pressure: ； ； in, P is the pressure feedback coefficient. 气 P0 is the reference air film pressure, which is the real-time adjusted air film pressure. This is the pressure feedback coefficient.

10. The ultraviolet camera optical axis calibration method based on multi-source error collaborative compensation as described in any one of claims 2 to 6, characterized in that: Based on the temperature data T measured at different times t by the distributed temperature sensor array t Deformation of computing device Used for temperature compensation of laser tracker measurement data and adjustment commands: ； Where n represents the number of parts; This represents the coefficient of thermal expansion of the q-th component; This represents the actual temperature of the q-th component measured at time t; This represents the initial geometric length of the q-th component.

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