Method for Measuring the Surface Shape of Large-Aperture Optical Elements Based on Multi-Camera Mosaic Deflectometry

Abstract

The present invention proposes a method for measuring the surface shape of a large-aperture optical element by multi-camera stitching deflectometry. This method combines multi-camera synchronous optimization calibration, stereo iterative surface shape reconstruction, and global optimization stitching. It can not only measure the surface shape of a large-aperture optical element, but also has the advantages of simple device, fast measurement speed, and low cost. The proposal of multi-camera synchronous optimization calibration enables this method to complete the calibration of the cameras and the measurement system by simply calibrating all the cameras simultaneously using a planar calibration target and then calibrating the attitude relationship between one of the cameras and the display using a high-quality planar mirror, solving the problem of error accumulation caused by multiple calibrations of multiple cameras in the existing methods; the adopted stereo iterative surface shape reconstruction and global optimization stitching algorithms enable this method to avoid the use of a reference element, the introduction of reset errors, and the errors caused by multiple stitching conversions.

Description

Technical Field

[0001] The present invention relates to the technical field of high-precision non-contact measurement of the surface shape of optical elements, and in particular to a method for measuring the surface shape of large-aperture optical elements based on multi-camera stitching deflectometry. Background Art

[0002] Inertial Confinement Fusion (ICF) devices use multiple high-power lasers to bombard deuterium-tritium target pellets to achieve controlled inertial confinement fusion, and then achieve "ignition" to release fusion energy. Such devices can be used to solve the energy crisis faced by humanity. Currently, the world's three major ICF devices are the National Ignition Facility (NIF) in the United States, the Laser Megajoules (LMJ) in France, and the Shenguang-Ⅲ laser device in China. These system devices contain tens of thousands of square optical elements with a diameter of more than 400 mm. As the core of large-scale laser devices, the surface shape accuracy of these large-aperture optical elements will directly affect the comprehensive performance of the system. Moreover, due to their large quantity, while efficient batch processing is required, a fast and effective high-precision surface shape detection method is needed to guide the processing.

[0003] Traditional measurement of the surface shape of optical elements is usually completed using an interferometer with high-precision detection capabilities. However, the high detection cost, limited dynamic range, and sensitivity to environmental impact noise of this method make it difficult to quickly complete the surface shape detection task. In recent years, Phase Measuring Deflectometry (PMD), as an optical element surface shape measurement method with a simple device, fast measurement speed, large dynamic range, and detection accuracy comparable to that of an interferometer, has received extensive attention from researchers. The general measurement process of phase measuring deflectometry is to display a set of sinusoidal fringe patterns on a display after calibrating the camera and the measurement system, and then use the camera to collect the fringe images reflected by the surface of the element to be measured. After obtaining the corresponding phase distribution through phase shift and phase unwrapping algorithms, the surface shape information of the element to be measured can be calculated by combining the calibration data of the camera and the measurement system.

[0004] To implement the surface shape measurement of large - aperture optical elements using deflectometry, a sub - aperture stitching detection method for the surface shape of large - aperture planar optical elements was disclosed in Patent CN106989689B. This technology uses a calibration method of machine vision to roughly obtain the coordinates of reflection points on the measured surface in advance, and then uses a reference element with higher surface shape accuracy to deduct systematic errors. However, the implementation of these two steps requires a mechanical device to adjust the positions of the calibration target surface, the reference element, and the measured element to make them coincide. This not only increases the complexity of the experimental measurement steps, but also, the inevitable reset error will directly affect the experimental measurement accuracy. In addition, Wang et al. (R. Wang, D. Li, X. Zhang, W. Zheng, L. Yu, and R. Ge, "Marker - free stitching deflectometry for three - dimensional measurement of the specular surface," Opt Express 29(25), 41851(2021).) proposed marker - free stitching deflectometry based on a stereoscopic deflectometry measurement device. This method obtains the point cloud within each sub - aperture through a stereoscopic search and iterative algorithm, and then uses a stitching algorithm to obtain the surface shape of the full aperture. This method realizes the stitching of measurement data of the subsystem composed of two cameras. However, when using this method with multiple cameras to implement the surface shape measurement of larger - aperture optical elements, problems of error accumulation will occur due to the need for multiple camera calibrations and data stitching. Summary of the Invention

[0005] To overcome the problems existing in the above - mentioned technologies, the present invention combines multi - camera synchronous optimization calibration, stereoscopic iterative surface shape reconstruction, and global optimization stitching to propose a method for measuring the surface shape of large - aperture optical elements using multi - camera stitching deflectometry. The proposed multi - camera synchronous optimization calibration enables this method to complete the calibration of the cameras and the measurement system by only calibrating all cameras simultaneously using a planar calibration target and then calibrating the attitude relationship between one camera and the display using a high - quality planar mirror, solving the problem of error accumulation caused by multiple calibrations of multiple cameras in the existing methods; the adopted stereoscopic iterative surface shape reconstruction and global optimization stitching algorithms enable this method to avoid the use of reference elements, the introduction of reset errors, and the errors caused by multiple stitching conversions.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A method for measuring the surface shape of a large-aperture optical element by multi-camera stitching deflectometry, including: two displays, which are used to display sine fringe patterns as structured light sources during calibration and measurement respectively; six cameras, which are used to collect fringe images reflected from different regions on the surface of the element to be measured. Among them, the six cameras and the displays respectively form six sub-detection systems, and their corresponding measurement regions on the surface of the element to be measured are Region 1, Region 2, Region 3, Region 4, Region 5, and Region 6, and there are overlapping regions between the measurement regions of adjacent sub-detection systems. The specific measurement steps are as follows:

[0008] Step 1: Calibration of cameras and measurement system

[0009] After installing and fixing the cameras and the displays used for measurement in the multi-camera stitching deflectometry measurement system, using the display for calibration as a planar calibration target, the sine fringe pattern displayed on the display for calibration as a feature pattern, while changing the attitude of the calibration target, using the six cameras to collect the feature patterns on the calibration target. To ensure the camera calibration accuracy, use the cameras to photograph 30 planar calibration targets with different attitudes; at this time, use the pinhole camera model and the lens distortion model to solve the internal parameters, external parameters, and distortion coefficients of the cameras, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; then select Camera 1 as the main camera, use the obtained external parameters to calculate the pose relationship between the coordinate systems of other cameras and the coordinate system of Camera 1, and use this as a constraint condition to synchronously optimize the internal parameters and distortion coefficients of all cameras, and the pose relationship between the coordinate system of Camera 1 and the coordinate system where the control points on the calibration target are located; then, using the display for measurement as a planar calibration target, use a high-quality planar mirror to complete the calibration of the attitude relationship between the coordinate system of Camera 1 and the coordinate system where the control points on the display for measurement are located. Similarly, to ensure the calibration accuracy, place the planar mirror in 30 different attitudes, and then use Camera 1 to photograph the feature patterns reflected by the planar mirror; then, use the pinhole camera model and the lens distortion model to solve the external parameters of Camera 1, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; after completion of the optimization, select the coordinate system where the control points on the display for measurement are located as the world coordinate system, use the calibrated external parameters of Camera 1, and the pose relationship between the coordinate systems of other cameras and the coordinate system of Camera 1 to obtain the pose relationship between all camera coordinate systems and the world coordinate system, and thus complete the calibration of the cameras and the measurement system;

[0010] Step 2: Stereo iterative surface shape reconstruction

[0011] After calibrating the camera and the measurement system, fix the component to be measured. Two sets of mutually orthogonal sine stripe patterns are sequentially displayed on the monitor used for measurement, and six cameras synchronously collect the stripe images reflected from the surface of the component to be measured; the phase-shifting and phase-unwrapping algorithms are used to obtain the corresponding phase distribution, and then the relationship between the stripe phase period and the number of monitor pixels, as well as the monitor pixel size, are used to obtain the coordinates of the monitor light source points; then, a reflection point is respectively determined in all overlapping regions by using the stereo search algorithm commonly used in stereo deflectometry For the sub-detection system composed of Camera 1 and the monitor used for measurement. Its measurement area on the surface of the component to be measured is Area 1. Assume that the surface of the component to be measured is the ideal plane where the reference point is located, and its height Then, the initial coordinates of the reflection point can be calculated using Equation (1): :

[0012]

[0013] The slope at the reflection point can be calculated using Equation (2):

[0014]

[0015] where d m2c and d m2s are respectively the distances from the reflection point M c1 to the projection center of Camera 1 and the monitor light source point After calculating the slope, the relative height is reconstructed using the Chebyshev polynomial-based modal method

[0016]

[0017] In the formula, a i and respectively represent the i-th coefficient and the polynomial; the coefficient a i is obtained by solving using the modal method. And this process belongs to an indefinite integral, and there is a constant that is uncertain. Therefore, it is necessary to use the reference point RP to determine the constant C, and then obtain the absolute height

[0018]

[0019] In the formula, is the absolute height of the reference point in the world coordinate system; is the relative height of the reference point, which is the x and y direction coordinates of the reference point It is calculated by substituting into formula (3). After the calculation of the absolute height is completed, it is used as the new surface of the component under test, and the corrected reflection point coordinates are calculated using formula (5).

[0020]

[0021] The corrected reflection point coordinates are substituted into formula (2) to obtain new slope data, and the surface shape reconstruction is carried out again using the pattern method, so as to obtain the new absolute height z and the reflection point coordinates M c1 , and after multiple cyclic iterations until the following formula is satisfied, the calculation of the reflection point coordinates in Region 1 can be completed :

[0022]

[0023] In the formula, j is the number of cyclic iterations; ε is the threshold. The same processing is carried out for the sub-detection systems composed of other cameras and displays respectively, and the reflection point coordinates in Regions 2, 3, 4, 5 and 6 can be obtained and

[0024] Step 3: Global optimization and stitching

[0025] The x and y direction coordinates of the reflection points on each region calculated in Step 2 are used to determine the coordinate range of the overlapping part of the measurement regions of two adjacent sub-detection systems on the xoy plane of the surface of the component under test, and re-sampling is carried out on the xoy plane. Then, substituting into formulas (3) and (4), the z direction coordinates of the reflection points of the newly sampled points in all adjacent region overlapping parts can be obtained. Then, taking the sub-detection system composed of Camera 1 and the display used for measurement as the main measurement system, formula (7) is used to calculate the surface shape height stitching conversion coefficients of the five sub-detection systems composed of other cameras and the display used for measurement:

[0026]

[0027] where TC i is the surface shape height stitching conversion coefficient corresponding to the measurement region of the i-th sub-detection system, and it is a 3×1 column vector;

[0028]

[0029] where x ij and y ij are the coordinates in the x and y directions after re-sampling of the overlapping part of the measurement regions of the i-th and j-th adjacent sub-detection systems; n ij is the number of sampled points after re-sampling of the overlapping part of the measurement regions of the i-th and j-th adjacent sub-detection systems; (xmi , y mi ), and (x mj , y mj ) are the coordinates in the x and y directions after resampling in the overlapping part of the measurement areas of the i-th and j-th sub-detection systems that have an adjacent relationship with the m-th sub-detection system; z m , z i and z j The z-direction coordinates calculated after resampling in the overlapping part of the corresponding measurement areas of the m-th, i-th, and j-th sub-detection systems.

[0030] Using formula (9), convert the z-direction coordinates of the reflection points in the measurement areas of the other five sub-detection systems except the main detection system to the main detection system:

[0031]

[0032] z mci The z-direction coordinate of the i-th sub-detection system in the corresponding measurement area; z all is the surface height information after the splicing conversion is completed. Description of the Drawings

[0033] Figure 1 is the schematic diagram of the method for measuring the surface shape of a large-aperture optical element based on multi-camera stitching deflectometry in the present invention;

[0034] Figure 2 is the schematic diagram of measuring a 400 mm 2 square optical element based on multi-camera stitching deflectometry in the present invention;

[0035] Figure 3 is the diagram of the display and the sine stripe pattern used for calibration in the present invention. Detailed Embodiments

[0036] To make the objectives and solutions of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings through examples. It is necessary to point out here that the following embodiments are only used to further illustrate the present invention and cannot be construed as limiting the protection scope of the present invention. Those skilled in the art make some non-essential improvements and adjustments to the present invention based on the above content of the present invention, and still fall within the protection scope of the present invention.

[0037] Refer to Figures 1 to 3 , a method for measuring the surface shape of a large-aperture optical element based on multi-camera stitching deflectometry, including two displays 7 and 9, which are respectively used to display the sine stripe pattern 10 as a structured light source during calibration and measurement; six cameras 1, 2, 3, 4, 5, and 6, which are used to collect the stripe images reflected from different areas on the surface of the element to be measured. Among them, the six cameras 1, 2, 3, 4, 5, and 6 respectively form six sub-detection systems with the displays, asFigure 2 As shown, their corresponding measurement areas on the surface of the device under test are Area One, Area Two, Area Three, Area Four, Area Five, and Area Six respectively, and there are overlapping areas between the measurement areas of adjacent sub-detection systems. The specific measurement steps are as follows:

[0038] Step 1: Calibration of the cameras and the measurement system

[0039] After installing and fixing cameras 1, 2, 3, 4, 5, and 6 and the measurement monitor 7 in the multi-camera stitching deflectometry measurement system, using the calibration monitor 9 as a planar calibration target and the sine fringe pattern 10 displayed on the monitor 9 as a feature pattern, while changing the attitude of the calibration target, collect the feature patterns on the calibration target using the six cameras 1, 2, 3, 4, 5, and 6. To ensure the calibration accuracy of cameras 1, 2, 3, 4, 5, and 6, take pictures of the planar calibration target in 30 different attitudes using the cameras; at this time, use the pinhole camera model and the lens distortion model to solve the internal parameters, external parameters, and distortion coefficients of cameras 1, 2, 3, 4, 5, and 6, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; then select Camera One 1 as the main camera, use the obtained external parameters to calculate the pose relationships between the other camera coordinate systems 2, 3, 4, 5, and 6 and the coordinate system of Camera One 1, and use this as a constraint condition to synchronously optimize the internal parameters and distortion coefficients of all cameras 1, 2, 3, 4, 5, and 6, as well as the pose relationship between the coordinate system of Camera One 1 and the coordinate system where the control points on the calibration target are located; then, using the measurement monitor 7 as a planar calibration target, use a high-quality planar mirror to complete the calibration of the attitude relationship between the coordinate system of Camera One 1 and the coordinate system where the control points on the measurement monitor 7 are located. Similarly, to ensure the calibration accuracy, place the planar mirror in 30 different attitudes, and then use Camera One 1 to take pictures of the feature patterns reflected by the planar mirror; then, use the pinhole camera model and the lens distortion model to solve the external parameters of Camera One 1, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; after completion of the optimization, select the coordinate system where the control points on the measurement monitor 7 are located as the world coordinate system, and use the calibrated external parameters of Camera One 1 and the pose relationships between the other camera coordinate systems 2, 3, 4, 5, and 6 and the coordinate system of Camera One 1 to obtain the pose relationships between all camera coordinate systems 1, 2, 3, 4, 5, and 6 and the world coordinate system, thereby completing the calibration of the cameras and the measurement system;

[0040] Step 2: Stereo iterative surface reconstruction

[0041] After calibrating the camera and the measurement system, the element 8 to be measured is fixed. Two sets of mutually orthogonal sine fringe patterns 10 are sequentially displayed on the monitor 7 used for measurement, and six cameras 1, 2, 3, 4, 5, and 6 synchronously collect the fringe images reflected from the surface of the element 8 to be measured; the phase shift and phase unwrapping algorithms are used to obtain the corresponding phase distribution, and then the relationship between the fringe phase period and the number of pixels of the monitor, as well as the pixel size of the monitor 7, are used to obtain the coordinates of the light source points of the monitor; then, a reflection point is respectively determined in all overlapping regions by using the stereo search algorithm commonly used in stereo deflectometry For the sub-detection system composed of the first camera 1 and the monitor 7 used for measurement. Its measurement area on the surface of the element 8 to be measured is Figure 2 the area 1 shown in. Assume that the surface of the element 8 to be measured is an ideal plane where the reference point is located, and its height Then, the initial coordinates of the reflection point can be calculated using formula (1):

[0042]

[0043] The slope at the reflection point can be calculated using formula (2):

[0044]

[0045] where d m2c and d m2s are respectively the distances from the reflection point M c1 to the projection center of the first camera 1 and the light source point of the monitor After calculating the slope, the relative height

[0046]

[0047] In the formula, a i and respectively represent the i-th coefficient and the polynomial; the coefficient a i is obtained by solving using the pattern method. And this process belongs to an indefinite integral, and there is a constant that is uncertain. Therefore, it is necessary to use the reference point RP to determine the constant C, and then obtain the absolute height

[0048]

[0049] In the formula, is the absolute height of the reference point in the world coordinate system; is the relative height of the reference point, which is the x and y direction coordinates of the reference point It is calculated by substituting into formula (3). After the calculation of the absolute height is completed, it is used as the new surface of the component under test, and the corrected reflection point coordinates are calculated using formula (5).

[0050]

[0051] Substitute the corrected reflection point coordinates into formula (2) to obtain new slope data, and then use the modal method for surface shape reconstruction again to obtain the new absolute height z and reflection point coordinates M c1 , and iterate multiple times until the following formula is satisfied to complete the calculation of the reflection point coordinates in Region 1 as shown in Figure 2 : :

[0052]

[0053] where j is the number of loop iterations; ε is the threshold. Perform the same processing on the sub-detection systems composed of other cameras and displays respectively to obtain the reflection point coordinates in Regions 2, 3, 4, 5, and 6 in Figure 2 : and

[0054] Step 3: Global optimization and stitching

[0055] Use the x and y direction coordinates of the reflection points on each region calculated in Step 2 to determine the coordinate range of the overlapping part of the measurement regions of two adjacent sub-detection systems on the xoy plane of the surface of the component under test 8, and resample on the xoy plane. Then, substitute into formulas (3) and (4) to obtain the z direction coordinates of the reflection points of the newly sampled points in all adjacent region overlapping parts. Then, take the sub-detection system composed of Camera 1 and the display 7 used for measurement as the main measurement system, and use formula (7) to calculate the surface shape height stitching conversion coefficients of the five sub-detection systems composed of other cameras 2, 3, 4, 5, and 6 and the display 7 used for measurement:

[0056]

[0057] where TC i is the surface shape height stitching conversion coefficient corresponding to the measurement region of the i-th sub-detection system, and it is a 3×1 column vector;

[0058]

[0059] where x ij and y ij are the coordinates in the x and y directions after resampling the overlapping part of the measurement regions of the i-th and j-th adjacent sub-detection systems; nij is the number of resampled points in the overlapping part of the measurement areas of the \(i\)-th and \(j\)-th adjacent sub-detection systems; \((x mi , y mi ) and \((x mj , y mj ) are the coordinates in the \(x\) and \(y\) directions after resampling in the overlapping part of the measurement areas of the \(i\)-th and \(j\)-th sub-detection systems adjacent to the \(m\)-th sub-detection system; \(z m , \(z i and \(z j are the \(z\)-direction coordinates calculated after resampling in the corresponding overlapping part of the measurement areas of the \(m\)-th, \(i\)-th, and \(j\)-th sub-detection systems.

[0060] Use formula (9) to convert the \(z\)-direction coordinates of the reflection points in the measurement areas of the other five sub-detection systems except the main detection system to the main detection system:

[0061]

[0062] \(z mci is the \(z\)-direction coordinate of the \(i\)-th sub-detection system in the corresponding measurement area; \(z all is the surface height information after the splicing conversion is completed.

Claims

1. A method for measuring the surface shape of a large-aperture optical element by multi-camera stitching deflectometry, characterized in that It includes two monitors, which are used to display sine fringe patterns as structured light sources during calibration and measurement respectively; six cameras, which are used to collect fringe images reflected from different regions on the surface of the component to be measured; among which the six cameras and the monitors respectively form six sub-detection systems, and the measurement regions on the surface of the component to be measured are Region 1, Region 2, Region 3, Region 4, Region 5 and Region 6 respectively, and there are overlapping regions between the measurement regions of two adjacent sub-detection systems; the specific measurement steps are as follows: Step 1: Calibration of cameras and measurement system After installing and fixing the cameras and the monitors used for measurement in the multi-camera stitching deflectometry measurement system, using the monitor for calibration as a planar calibration target, the sine fringe pattern displayed on the monitor for calibration as a feature pattern, while changing the attitude of the calibration target, using the six cameras to collect the feature patterns on the calibration target. To ensure the camera calibration accuracy, use the cameras to photograph the planar calibration target in 30 different attitudes; at this time, use the pinhole camera model and the lens distortion model to solve the internal parameters, external parameters and distortion coefficients of the cameras, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; then select Camera 1 as the main camera, use the obtained external parameters to calculate the pose relationship between the coordinate systems of other cameras and the coordinate system of Camera 1, and use this as a constraint condition to synchronously optimize the internal parameters and distortion coefficients of all cameras, and the pose relationship between the coordinate system of Camera 1 and the coordinate system where the control points on the calibration target are located; then, using the monitor for measurement as a planar calibration target, use a high-quality planar mirror to complete the calibration of the attitude relationship between the coordinate system of Camera 1 and the coordinate system where the control points on the monitor for measurement are located. Similarly, to ensure the calibration accuracy, place the planar mirror in 30 different attitudes, and then use Camera 1 to photograph the feature patterns reflected by the planar mirror; then, use the pinhole camera model and the lens distortion model to solve the external parameters of Camera 1, and use bundle adjustment to optimize the obtained parameters and the world coordinates of the control points; after optimization, select the coordinate system where the control points on the monitor for measurement are located as the world coordinate system, use the calibrated external parameters of Camera 1, and the pose relationship between the coordinate systems of other cameras and the coordinate system of Camera 1 to obtain the pose relationship between the coordinate systems of all cameras and the world coordinate system, and thus complete the calibration of the cameras and the measurement system; Step 2: Stereo iterative surface reconstruction After calibrating the camera and the measurement system, fix the component to be measured. On the monitor used for measurement, two sets of mutually orthogonal sine fringe patterns are sequentially displayed, and six cameras synchronously collect the fringe images reflected from the surface of the component to be measured. Use the phase-shifting and phase-unwrapping algorithms to obtain the corresponding phase distribution, and then use the correspondence between the fringe phase period and the number of pixels on the monitor, as well as the pixel size of the monitor, to obtain the coordinates of the light source points on the monitor. Then, use the stereo search algorithm commonly used in stereo deflectometry to determine a reflection point in each of all overlapping regions For the sub-detection system composed of Camera 1 and the monitor used for measurement; its measurement area on the surface of the component to be measured is Area 1; assume that the surface of the component to be measured is the ideal plane where the reference point is located, and its height Then, the initial coordinates of the reflection point can be calculated using Equation (1): are: Reflection point The slope at can be calculated by Equation (2): where d m2c and d m2s are the distances from the reflection point M c1 to the projection center of Camera 1 and the light source point of the display respectively; after calculating the slope, the relative height is reconstructed using the Chebyshev polynomial-based modal method where a i and represent the i-th coefficient and polynomial respectively; the coefficient a i is obtained by using the pattern method; and this process belongs to indefinite integral, and there is a constant that is uncertain; therefore, it is necessary to use the reference point RP to determine the constant C, and then obtain the absolute height In the formula, is the absolute height of the reference point in the world coordinate system; is the relative height of the reference point, which is obtained by substituting the x and y direction coordinates of the reference point into formula (3); after the calculation of the absolute height is completed, it is used as the new surface of the component to be measured, and the corrected reflection point coordinates Substitute the corrected reflection point coordinates into formula (2) to obtain new slope data, and then use the modal method again for surface shape reconstruction to further obtain the new absolute height z and reflection point coordinates M c1 , and perform multiple loop iterations until the following formula is satisfied to complete the calculation of the reflection point coordinates in Region 1 : In the formula, j is the number of loop iterations; ε is the threshold; by performing the same processing on the sub-detection systems composed of other cameras and displays respectively, the reflection point coordinates of regions two, three, four, five, and six can be obtained and Step 3: Global optimization for stitching Use the x and y direction coordinates of the reflection points on each region calculated in Step 2 to determine the coordinate range of the overlapping part of the measurement regions of two adjacent sub-detection systems on the xoy plane of the surface of the component to be measured, and resample on the xoy plane. Then, substituting into Formulas (3) and (4), the z direction coordinates of the reflection points of the newly sampled points in all adjacent region overlapping parts can be obtained; then, taking the sub-detection system composed of Camera 1 and the monitor for measurement as the main measurement system, use Formula (7) to calculate the surface height stitching conversion coefficients of the five sub-detection systems composed of other cameras and the monitor for measurement: Among them, TC i is the surface height splicing conversion coefficient of the corresponding measurement area of the i-th sub-detection system, which is a 3×1 column vector; where x ij and y ij are the coordinates in the x and y directions after resampling the overlapping part of the measurement areas of the i-th and j-th adjacent sub-detection systems; n ij is the number of sampling points after resampling the overlapping part of the measurement areas of the i-th and j-th adjacent sub-detection systems; (x mi , y mi ) and (x mj , y mj ) are the coordinates in the x and y directions after resampling the overlapping part of the measurement areas of the i-th and j-th sub-detection systems that have an adjacent relationship with the m-th sub-detection system; z m , z i and z j are the z-direction coordinates calculated after resampling the overlapping parts of the corresponding measurement areas of the m-th, i-th, and j-th sub-detection systems; Using formula (9), convert the z-direction coordinates of the reflection points in the measurement areas of the other five sub-detection systems except the main detection system to the main detection system: z mci The z-direction coordinate of the i-th sub-detection system in the corresponding measurement area; z all is the surface height information after the stitching conversion is completed.

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