A parameter space based non-uniform b-spline inflection measurement universal reconstruction method

Abstract

The application discloses a non-uniform B-spline deflection measurement general reconstruction method based on a parameter space, belongs to the field of optical measurement, and provides a general deflection measurement framework integrating calibration and measurement, wherein a parameter space is defined by camera pixels, and the corresponding relationship among display pixels, measurement points of a measured element and the camera pixels is represented by non-uniform B-spline surfaces. When inputting calibration and measurement data, the geometric measurement of a measured surface shape can be completed by adjusting the control points of the non-uniform B-spline surfaces in the measurement framework to approximate the input data. The application establishes the corresponding relationship through parameter space mapping, avoids a large number of intersection point calculation operations based on ray tracing in deflection measurement, uses a non-uniform B-spline model to describe the measured surface shape, and can not only represent a more complex surface shape relative to a common Zernike model, but also effectively avoids the diffusion of local errors due to the local support property. In addition, the robustness of the application is improved through adaptive node adjustment.

Description

Technical Field

[0001] This invention relates to the field of deflection measurement technology, and in particular to a general reconstruction method for deflection measurement based on non-uniform B-spline in parameter space. Background Technology

[0002] With the continuous development of modern optical technology, it has been widely used in major equipment and advanced instruments in various fields such as astronomy, medicine, military, and aerospace. As photoelectric performance continues to improve, the requirements for the geometric quality of optical components are also becoming increasingly stringent, thus necessitating more precise detection of the geometry of optical components.

[0003] Interferometry has long been a primary method for inspecting optical components due to its superior measurement accuracy. However, this method has high requirements for the operating environment and is difficult to adapt to harsh production environments. In addition, its dynamic range is limited, and the measurement of freeform surfaces requires compensation mirrors or computer-generated holograms to compensate for the optical path, which is expensive and lacks flexibility.

[0004] Phase measurement deflection is a highly efficient, flexible, and robust technique for measuring complex curved surfaces, developed in recent years. Its dynamic measurement range is 1000 times that of traditional interferometry. Furthermore, it boasts advantages such as strong anti-interference capability, high sensitivity, and low cost. In terms of measurement accuracy, it is a strong competitor to interferometry in the sub-micron range and holds immense potential in various application fields.

[0005] Phase measurement deflection is based on the fundamental principle of ray tracing in geometrical optics. Its apparatus consists of a camera and a screen. A series of fringe patterns are displayed on the screen, and these patterns are captured by the camera after reflection from the device under test (DUT). The camera is treated as a pinhole model, and ray tracing is used to determine the correspondence between camera pixels, screen pixels, and the measured point on the DUT. The normal to the measured point is then calculated using the law of reflection, and finally, the surface shape of the DUT is reconstructed through gradient integration.

[0006] Gradient integration algorithms are a crucial component of phase deflection, primarily categorized into four-dimensional global integration, region-based methods, and pattern-based methods. The four-dimensional global integration method transforms a noisy, non-integrable gradient field into a combination of integrable fundamental functions in the frequency domain, enabling height field reconstruction. The accuracy of this method for reconstructing edge data depends entirely on whether the boundary data satisfies the periodic extension condition. The region-based method utilizes the local relationship between height and slope to establish a connection between measured gradient data and unknown height, finally estimating the height using least squares. However, this method suffers from low accuracy or even errors in reconstructing non-uniform grids, is susceptible to noise, and has a slow reconstruction speed. The pattern-based method describes the surface shape and gradient data using a mathematical model, estimating the height distribution using coefficients from the measured gradient. The Zernike model is the most widely used. This method is insensitive to noise but has a smoothing effect on high-frequency components, and the influence of each term in the polynomial extends to the entire reconstruction region.

[0007] However, in existing technologies, deflection measurement involves a large number of intersection point calculations based on ray tracing, which are computationally intensive and time-consuming. Meanwhile, the most commonly used Zernike orthogonal basis integral algorithm is only suitable for reconstructing simple surfaces and cannot represent complex curved surfaces. Furthermore, when local errors occur, they are averaged out to other locations, leading to error propagation. Summary of the Invention

[0008] To address the problems in existing deflection measurement methods, such as the large number of computational operations based on ray tracing intersections, the inability of Zernike models to describe complex surfaces and error propagation during integral reconstruction, and the misalignment of measurement data formats with processing standards, this invention proposes a general reconstruction method for deflection measurement based on non-uniform B-splines in parameter space, which can effectively solve the above problems.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] In a first aspect, the present invention provides a general reconstruction method for non-uniform B-spline deflection measurement based on parameter space. The method is applied to the surface shape measurement of a measured component using a deflection measurement system including a screen, a camera, and a calibration plate. The calibration plate has marked points. The method includes the following steps:

[0011] S1. Determine the position and pixel size of the screen and camera in the global coordinate system through system calibration, and record the height h of a certain feature point on the measured component in the global coordinate system;

[0012] S2. A series of phase-shifted sinusoidal fringes in both horizontal and vertical directions are displayed sequentially on the screen. The image of the phase-shifted sinusoidal fringes captured by the camera and reflected by the measured element is obtained. The phase Sp and Sv in both horizontal and vertical directions of the acquired image are obtained by using a phase-shifting algorithm. The correspondence between screen pixels and camera pixels is established based on the phase Sp and Sv.

[0013] S3. Based on the surface complexity of the measured component, determine the initial number of nodes n of the non-uniform B-spline surface, and generate the node vector. Where k is the degree of the spline function; and the parameter space is established based on the camera pixel coordinates: assuming the number of camera pixels is M×N, then the spline parameter coordinates corresponding to the (i, j)th camera pixel are... And calculate the basis functions for each B-spline interval.

[0014] S4. Set up a non-uniform B-spline surface Bsurf_S to represent the spatial coordinates of the corresponding screen pixels under the parameter coordinates (u, v). The parameter coordinates of each screen pixel are obtained according to the phase correspondence obtained in S2. Using the spatial coordinates of each screen pixel as the fitting object, calculate the control points in the surface Bsurf_S.

[0015] S5. Initialize the non-uniform B-spline surface Bsurf_M to represent the spatial coordinates on the measured surface under the parameter coordinates (u, v); connect each camera pixel to the camera optical center, and calculate the parameter coordinates corresponding to each measurement point by intersecting the current surface; use the spatial coordinates of each measurement point on the current surface as the fitting object to calculate the control points in the surface Bsurf_M.

[0016] S6. Establish a cost function F with the constraints of consistent light propagation direction ||cross(i1,i2)||, consistent normal direction ||cross(n1,n2)||, and consistent feature point height ||hG(Bsurf_M)||, where i1 is the direction vector of the line connecting a pixel on the camera image plane to the corresponding measurement point on Bsurf_M, i2 is the direction vector of the line connecting the pixel on the camera image plane to the camera optical center, r1 is the direction vector of the line connecting the measurement point on Bsurf_M to the corresponding pixel on Bsurf_S, n1 is the angular line direction vector determined by i1 and r1, n2 is the normal of the corresponding measurement point on Bsurf_M, and G(Bsurf_M) represents the height of the measurement point;

[0017] S7. Using automatic differentiation and the Levenberg-Marquardt optimization algorithm, the control points of Bsurf_M are iterated according to the cost function F until convergence, thereby obtaining the surface shape data Bsurf_M representing the component under test; including: using the cost function F as an index, detecting regions {Area} in Bsurf_M that are larger than the user-defined threshold, and if the ratio of a single detected closed region to the measured region Ratio(Area) is considered... i If the number of nodes in the region exceeds the user-defined threshold, return to S3, increase the number of nodes in that region, update the node vector, and repeat S4-S7 until Bsurf_M iterates to convergence.

[0018] In a preferred embodiment, in S3, the initial number of nodes n is determined by the surface complexity of the element under test, wherein... r is the number of pixels of the camera along this direction, i.e., M or N, and c is the number of inflection points of the surface shape of the measured element.

[0019] In a preferred embodiment, in S5, if the nominal surface shape of the measured element is known, Bsurf_M is initialized using the nominal surface shape of the measured element; if there is no nominal surface shape, a plane or a sphere is used as the initial surface shape.

[0020] In a preferred embodiment, the deflection measurement system includes two cameras, uses the pixel coordinates of one of the cameras as the parameter space and performs steps S1-S7, and adds a non-uniform B-spline surface to represent the correspondence between the pixels of the two cameras;

[0021] Furthermore, in S6, the cost function F is modified to be the consistency of the light propagation direction between the two cameras ||cross(i1,i2)|| and ||cross(i3,i4)||, and the consistency of the normal direction between the two cameras ||cross(n1,n3)|| and ||cross(n2,n3)||, where i1 and i2 are the direction vectors of the line connecting a pixel on the image plane of one camera to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; i3 and i4 are the direction vectors of the line connecting a corresponding pixel on the image plane of the other camera to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; n1 is the angular line direction vector of i1 and r2; n2 is the angular line direction vector of i3 and r1; n3 is the normal of Bsurf_M; and r1 and r2 are the direction vectors of the line connecting the corresponding measurement point on Bsurf_M to two corresponding pixels on Bsurf_S, respectively.

[0022] In a second aspect, the present invention provides an electronic device, including a memory storing executable program code and a processor coupled to the memory; wherein the processor calls the executable program code stored in the memory to execute the method described above.

[0023] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the method described above.

[0024] By employing the above technical solution, this invention provides a universal measurement framework for phase measurement deflection. Utilizing camera pixels as the parameter space, two non-uniform B-spline surfaces are initialized. After inputting calibration measurement data, the measurement is completed by adjusting control points to approximate the input data. Specifically, the correspondence between the screen, camera, and measurement points is established through the non-uniform B-spline parameter space, eliminating the need for extensive ray-tracing-based intersection point calculations. Furthermore, using non-uniform B-splines to represent the measured surface shape can effectively represent more complex surfaces and detailed information. Additionally, due to their local support, error propagation can be effectively prevented. Moreover, Non-uniform Rational B-Splines (NURBS) are an industry standard used for shape representation, design, and data exchange in computer processing of geometric information, playing a significant role in CAD / CAM / CAE design and manufacturing fields. The proposed method aligns the measurement data format with internationally accepted industry standards, further enhancing the applicability and robustness of deflection measurements. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the structure of a deflection measurement system according to the present invention;

[0026] Figure 2 This is a schematic diagram of the calibration plate used in Embodiment 1 of the present invention;

[0027] Figure 3 This is a flowchart of the method according to Embodiment 1 of the present invention;

[0028] Figure 4 This is a schematic diagram of the geometric constraint relationship in Embodiment 1 of the present invention;

[0029] Figure 5 The measurement data is from Embodiment 1 of the present invention;

[0030] Figure 6 This is a schematic diagram of the geometric constraint relationship in Embodiment 2 of the present invention;

[0031] Figure 7 This is a schematic diagram of the structure of Embodiment 3 of the present invention. Detailed Implementation

[0032] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that these descriptions are for the purpose of aiding understanding the present invention, but do not constitute a limitation thereof. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0033] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "front", "rear", etc., indicate the orientation or positional relationship based on the description of the structure of this invention shown in the accompanying drawings. They are only for the convenience of describing this invention and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0034] The terms "first" and "second" in this technical solution are merely designations for corresponding structures that are identical or similar, or that perform similar functions. They do not represent an arrangement of the importance of these structures, nor do they imply any ranking, comparison of size, or other meaning.

[0035] Furthermore, unless otherwise explicitly specified and limited, the terms "installation" and "connection" should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two structures. Those skilled in the art can understand the specific meaning of the above terms in this invention by considering the overall concept of the invention and the specific context of the solution.

[0036] Example 1

[0037] A general reconstruction method for non-uniform B-spline deflection measurement based on parameter space is proposed. This method is used for applications such as... Figure 1 The deflection measurement system shown is used to measure the surface shape of a component under test. The system includes a screen, a camera, and a calibration plate, which is a plane mirror. The plane mirror has multiple markers with known positional relationships, such as... Figure 2 The circle of black dots shown.

[0038] like Figure 3 As shown, the method provided in this embodiment includes the following steps:

[0039] S1. Determine the position and pixel size of the screen and camera in the global coordinate system through system calibration, and record the height h of a certain feature point on the measured component in the global coordinate system;

[0040] S2. Display a series of phase-shifted sinusoidal fringes in both horizontal and vertical directions on the screen in sequence. Obtain the image of the phase-shifted sinusoidal fringes after reflection by the measured element, which is captured by the camera. Solve the phase Sp and Sv in both horizontal and vertical directions of the captured image through the phase-shifting algorithm. Establish the correspondence between screen pixels and camera pixels based on the phase Sp and Sv.

[0041] S3. Based on the surface complexity of the component under test, determine the initial number of nodes n of the non-uniform B-spline surface, and generate the node vector. Where k is the degree of the spline function, usually set to 3 by default; and the parameter space is established based on the camera pixel coordinates: assuming the number of camera pixels is M×N, then the spline parameter coordinates corresponding to the (i, j)th camera pixel are... And calculate the basis functions for each B-spline interval.

[0042] S4. Set up a non-uniform B-spline surface Bsurf_S to represent the spatial coordinates of the corresponding screen pixels under the parameter coordinates (u, v). The parameter coordinates of each screen pixel are obtained according to the phase correspondence obtained in S2. Using the spatial coordinates of each screen pixel as the fitting object, calculate the control points in the surface Bsurf_S.

[0043] S5. Initialize the non-uniform B-spline surface Bsurf_M to represent the spatial coordinates on the measured surface under the parameter coordinates (u,v); connect each camera pixel to the camera optical center, and calculate the parameter coordinates corresponding to each measurement point by intersecting the current surface; use the spatial coordinates of each measurement point on the current surface as the fitting object to calculate the control points in the surface Bsurf_M.

[0044] S6, such as Figure 4 As shown, a cost function F is established with the following constraints: consistency of light propagation direction ||cross(i1,i2)||, consistency of normal direction ||cross(n1,n2)||, and consistency of feature point height ||hG(Bsurf_M)||. Here, i1 is the direction vector of the line connecting a pixel on the camera image plane to the corresponding measurement point on Bsurf_M, i2 is the direction vector of the line connecting the pixel on the camera image plane to the camera optical center, r1 is the direction vector of the line connecting the measurement point on Bsurf_M to the corresponding pixel on Bsurf_S, n1 is the angular line direction vector determined by i1 and r1, n2 is the normal of the corresponding measurement point on Bsurf_M, and G(Bsurf_M) represents the height of the measurement point.

[0045] S7. Using automatic differentiation and the Levenberg-Marquardt optimization algorithm, the control points of Bsurf_M are iterated according to the cost function F until convergence, thereby obtaining the surface shape data Bsurf_M representing the component under test; including: using the cost function F as an index, detecting regions {Area} in Bsurf_M that are larger than the user-defined threshold, and if the ratio of a single detected closed region to the measured region Ratio(Area) is considered... i If the number of nodes in the region exceeds the user-defined threshold, return to S3, increase the number of nodes in that region, update the node vector, and repeat S4-S7 until Bsurf_M iterates to convergence.

[0046] This embodiment also conducts a simulation experiment on the above method steps. A measurement system is constructed using a camera with a focal length of 35mm, a resolution of 1024×1280, and a pixel size of 0.005mm, and a screen with a resolution of 1536×2048 and a pixel size of 0.0784mm. For ease of simulation calculation, the coordinate system of the measured element is set as the global coordinate system. That is, the above coordinate system is transformed into a unified global coordinate system, and the global coordinate system can be specified according to requirements. The positional relationship between the camera and the global coordinate system is as follows:

[0047]

[0048] The positional relationship between the screen and the global coordinate system is as follows:

[0049]

[0050] Simulated measurements were performed on an aspherical mirror and a spherical mirror, respectively, and their surface equations were obtained as follows:

[0051] Z=α(1)(x 2 +y 2 )+α(2)(x 2 +y 2 ) 2 +α(3)(x 2 +y 2 ) 3 +α(4)(x 2 +y 2 ) 4 +α(5)(x 2 +y 2 ) 5 +α(6)(x 2 +y 2 ) 6 (x-β(1)) 2 +(y-β(2)) 2 +(z-β(3)) 2 =0

[0052] The aspherical mirror surface shape parameter α is:

[0053] α=[-3.257711e-4,6.273373e-9,-1.167982e-12,7.699833e-17,-7.971233e-21,7.349457e-26]

[0054] The surface shape parameter β of the sphere is:

[0055] β = [0, 0, 300]

[0056] Generate three-frequency, four-step phase-shifting fringes in both horizontal and vertical directions on the screen. The fringe equations are as follows:

[0057] I h =a+bcos(2pifx+2pi / 4(step-1))

[0058] I v =a+bcos(2pify+2pi / 4(step-1))

[0059] Where a is the background light intensity, b is the stripe contrast, f is the stripe frequency, and step is the phase shift step number. In this experiment, a = b = 127.5.

[0060] Based on the reconstruction process described above, aspherical and spherical surfaces were reconstructed within a 100×100 ROI. The measurement results and errors are as follows: Figure 5 As shown, where, Figure 5 (a) and (b) show the results and error distribution of the spherical mirror simulation measurement, respectively. Figure 5 (c) and (d) show the results and errors of the simulation measurement of the high-order freeform surface mirror, respectively. It can be seen that the error distribution is within 10... -9 The results, measured in milliseconds, demonstrate the effectiveness of this method.

[0061] Example 2

[0062] This embodiment provides a dual-view parameter space non-uniform B-spline deflection measurement method, which is a variation of the method steps disclosed in Embodiment 1. Specifically, the deflection measurement system includes two cameras. This method uses the pixel coordinates of one camera as the parameter space and performs steps S1-S7, and adds a non-uniform B-spline surface to represent the correspondence between the pixels of the two cameras.

[0063] In S6, such as Figure 6As shown, the cost function F is modified to be the consistency of the light propagation direction between the two cameras ||cross(i1,i2)|| and ||cross(i3,i4)||, and the consistency of the normal direction between the two cameras ||cross(n1,n3)|| and ||cross(n2,n3)||. Here, i1 and i2 are the direction vectors of a pixel on the image plane of one camera connected to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; i3 and i4 are the direction vectors of the corresponding pixel on the image plane of the other camera connected to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; n1 is the angular line direction vector of i1 and r2; n2 is the angular line direction vector of i3 and r1; n3 is the normal of Bsurf_M; and r1 and r2 are the direction vectors of the lines connecting the corresponding measurement point on Bsurf_M to two corresponding pixels on Bsurf_S, respectively. Other steps are described in Example 1 and will not be repeated here.

[0064] It is readily understood that, with slight modifications to the method steps disclosed in Embodiment 1, various variations can be constructed for various deflection measurement structures, such as a deflection measurement system consisting of a single camera and two screens.

[0065] Example 3

[0066] An electronic device, such as Figure 7 As shown, the system includes a memory storing executable program code and a processor coupled to the memory; wherein the processor calls the executable program code stored in the memory to execute the method steps disclosed in the above embodiments. The processor can be any conventional processor, such as a CPU, FPGA, etc.; the storage module can be any conventional storage device, such as a memory card, hard drive, cloud server, etc.

[0067] In addition, such as Figure 7 As shown, when used as a commercial measuring device, this equipment also includes a data acquisition module, a display module, and a power supply module. The data acquisition module transmits measurement data to a memory via a network cable or similar means. The memory then inputs the received measurement data and pre-stored executable program code into a processor. After processing by the processor, the measurement results are sent back to the storage module and displayed on the display module. The power supply module provides power to the other modules.

[0068] Example 4

[0069] A computer storage medium storing a computer program, wherein the computer program is executed by a processor to perform the method steps disclosed in the above embodiments.

[0070] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0071] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0072] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0073] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A general reconstruction method for non-uniform B-spline deflection measurement based on parameter space, the method being applied to the surface shape measurement of a measured component in a deflection measurement system including a screen, a camera, and a calibration plate, wherein the calibration plate has marked points, characterized in that: Includes the following steps: S1. Determine the position and pixel size of the screen and camera in the global coordinate system through system calibration, and record the height h of a certain feature point on the measured component in the global coordinate system; S2. A series of phase-shifted sinusoidal fringes in both horizontal and vertical directions are displayed sequentially on the screen. The image of the phase-shifted sinusoidal fringes captured by the camera and reflected by the measured element is obtained. The phase Sp and Sv in both horizontal and vertical directions of the acquired image are obtained by using a phase-shifting algorithm. The correspondence between screen pixels and camera pixels is established based on the phase Sp and Sv. S3. Based on the surface complexity of the measured component, determine the initial number of nodes n of the non-uniform B-spline surface, and generate the node vector. Where k is the degree of the spline function; and establish the parameter space based on the camera pixel coordinates: assuming the number of camera pixels is M×N, then the spline parameter coordinates corresponding to the (i, j)th camera pixel are... And calculate the basis functions for each B-spline interval; S4. Set up a non-uniform B-spline surface Bsurf_S to represent the spatial coordinates of the corresponding screen pixels under the parameter coordinates (u, v). The parameter coordinates of each screen pixel are obtained according to the phase correspondence obtained in S2. Using the spatial coordinates of each screen pixel as the fitting object, calculate the control points in the surface Bsurf_S. S5. Initialize the non-uniform B-spline surface Bsurf_M to represent the spatial coordinates on the measured surface under the parameter coordinates (u, v); connect each camera pixel to the camera optical center to form a line, and calculate the parameter coordinates corresponding to each measurement point by intersecting the current surface; use the spatial coordinates of each measurement point on the current surface as the fitting object to calculate the control points in the surface Bsurf_M. S6. Establish a cost function F with the constraints of consistent light propagation direction ||cross(i1, i2)||, consistent normal direction ||cross(n1, n2)||, and consistent feature point height ||hG(Bsurf_M)||, where i1 is the direction vector of the line connecting a pixel on the camera image plane to the corresponding measurement point on Bsurf_M, i2 is the direction vector of the line connecting the pixel on the camera image plane to the camera optical center, r1 is the direction vector of the line connecting the measurement point on Bsurf_M to the corresponding pixel on Bsurf_S, n1 is the angular line direction vector determined by i1 and r1, n2 is the normal of the corresponding measurement point on Bsurf_M, and G(Bsurf_M) represents the height of the measurement point; S7. Using automatic differentiation and the Levenberg-Marquardt optimization algorithm, the control points of Bsurf_M are iterated according to the cost function F until convergence, thereby obtaining the surface shape data Bsurf_M representing the component under test; including: using the cost function F as an index, detecting regions {Area} in Bsurf_M that are larger than the user-defined threshold, and if the ratio of a single detected closed region to the measured region Ratio(Area) is considered... i If the number of nodes in the region exceeds the user-defined threshold, return to S3, increase the number of nodes in that region, update the node vector, and repeat S4-S7 until Bsurf_M iterates to convergence.

2. The method according to claim 1, characterized in that: In S3, the initial number of nodes n is determined by the surface complexity of the measured element, wherein... r is the number of pixels of the camera along this direction, i.e., M or N, and c is the number of inflection points of the surface shape of the measured element.

3. The method according to claim 1, characterized in that: In S5, if the nominal surface shape of the measured element is known, Bsurf_M is initialized using the nominal surface shape of the measured element; if there is no nominal surface shape, a plane or a sphere is used as the initial surface shape.

4. The method according to any one of claims 1-3, characterized in that: The deflection measurement system includes two cameras. The pixel coordinates of one of the cameras are used as the parameter space and steps S1-S7 are executed. A non-uniform B-spline surface is added to represent the correspondence between the pixels of the two cameras. Furthermore, in S6, the cost function F is modified to be the consistency of the light propagation direction between the two cameras ||cross(i1,i2)|| and ||cross(i3,i4)||, and the consistency of the normal direction between the two cameras ||cross(n1, n3)|| and ||cross(n2, n3)||, where i1 and i2 are the direction vectors of the line connecting a pixel on the image plane of one camera to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; i3 and i4 are the direction vectors of the line connecting a corresponding pixel on the image plane of the other camera to the corresponding measurement point on Bsurf_M and the optical center of the camera, respectively; n1 is the angular line direction vector of i1 and r2; n2 is the angular line direction vector of i3 and r1; n3 is the normal of Bsurf_M; and r1 and r2 are the direction vectors of the line connecting the corresponding measurement point on Bsurf_M to two corresponding pixels on Bsurf_S, respectively.

5. An electronic device, characterized in that: The method includes a memory storing executable program code and a processor coupled to the memory; wherein the processor invokes the executable program code stored in the memory to perform the method as described in any one of claims 1-4.

6. A computer-readable storage medium storing a computer program, characterized in that: The computer program is executed by the processor to perform the method as described in any one of claims 1-4.

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