Precise aspheric part profile measurement method

Abstract

The invention discloses a precision aspheric part profile measurement method. The method comprises the following steps: constructing a measurement system; point cloud data acquisition: controlling relative movement of a spectrum confocal sensor and a rotatable workpiece table in the measurement system, and acquiring three-dimensional point cloud data of the surface of the aspheric part in a spiral scanning mode or a layered annular scanning mode; performing fusion processing on the collected point cloud data, and preliminarily estimating the optical axis direction based on principal component analysis (PCA); and based on the fused point cloud data, calculating parameters such as an optical axis position and an attitude of the aspheric part, determining a curved surface equation of the optical element, calculating a transformation matrix, and performing point cloud coordinate transformation. According to the method, the spectrum confocal measurement technology is utilized, the high-precision position information aspheric part appearance measurement technology is fused, the three-dimensional appearance data of the whole surface of the aspheric part can be obtained in a non-contact and high-precision mode, and key parameters such as the optical axis of the aspheric part can be determined.

Description

Technical Field

[0001] This application belongs to the field of precision optical component measurement and three-dimensional shape detection technology, and relates to a non-aspherical part shape measurement technology that can integrate high-precision position information, specifically a precision non-aspherical part shape measurement method. Background Technology

[0002] Aspherical optical components have important applications in high-end optical systems, and their shape accuracy directly affects system performance. However, current methods for measuring aspherical surface shapes mainly include probe-based profilometry, interferometry, and structured light 3D scanning. While these methods have a broad application base in measuring aspherical parts, they also have many limitations.

[0003] (1) Contact profilometry method Contact profilometry uses a coordinate measuring machine (CMM) equipped with a stylus to acquire three-dimensional coordinate points by contacting the surface of the object being measured, thereby reconstructing the three-dimensional shape of the part. The basic principle of this method is to move the measuring probe along a predetermined path to contact the part surface point by point, measuring the coordinates of each contact point, and calculating the geometry of the part surface based on these coordinates. These measurement points are then processed by software to generate a complete model of the part surface.

[0004] The advantages of contact measurement lie in its wide applicability, capable of measuring almost all shapes of parts, especially providing a reliable solution when the part shape is complex and cannot be measured by optical methods. The equipment is relatively mature and easy to operate, making it suitable for high-precision single-point measurements. However, contact measurement also has significant disadvantages. First, the measurement speed is relatively slow, especially in mass production, resulting in low efficiency. Second, due to the contact involved in the measurement process, surface damage can easily occur, particularly on high-precision optical components, which may affect the final measurement results. Furthermore, contact measurement cannot fully acquire complete data on the surface of aspherical parts, especially the edge areas, which may be difficult to collect due to limitations in the probe's movement path.

[0005] (2) Interferometry Interferometry utilizes the principle of interferometers to measure the surface morphology of an object through the interference of light. Its basic principle is to obtain the object's surface position information by comparing the phase difference between a reference beam and a reflected beam using precise optical interferometry.

[0006] Interferometry boasts extremely high measurement accuracy, enabling nanoscale surface topography detection, making it particularly suitable for measuring high-precision optical components. Its non-contact nature avoids damage to the measurement surface, making it suitable for quality control of high-precision optical lenses, mirrors, and other optical parts. However, interferometry also has some significant drawbacks. First, the equipment is very expensive, requiring specialized technicians for operation and maintenance, and is typically highly sensitive to environmental conditions (such as temperature and vibration), resulting in poor stability in production environments. Second, the measurement range of interferometers is relatively limited, especially for large-area or complex-shaped parts, and it is difficult to obtain complete three-dimensional point cloud data. Furthermore, the interferometric measurement process demands extremely strict adjustments to the optical system; even slight misalignment or minor changes in the optical path can lead to unstable measurement results.

[0007] (3) Structured light three-dimensional scanning method Structured light 3D scanning projects a known optical pattern (such as stripes or Gray code) onto the surface of the object being measured using a projector. A camera captures the pattern reflected or deformed by the object's surface, and the object's 3D coordinates are calculated based on the deformation of the pattern. This method relies on the principle of triangulation, calculating the relative positional relationship between the light beam and the object's surface to obtain the object's surface morphological data.

[0008] The biggest advantage of structured light 3D scanning is its extremely fast measurement speed, making it suitable for rapid scanning of large-area surfaces. Its non-contact nature and high efficiency make it particularly suitable for applications such as reverse engineering, rapid prototyping, and quality control. Compared to other methods, structured light scanning equipment is relatively affordable, and the measurement process is relatively simple, adaptable to various production environments. Nevertheless, structured light scanning also has certain limitations. First, it has high requirements for surface gloss and reflectivity, which may lead to measurement errors on highly reflective or transparent materials. Second, lighting conditions and the environment have a significant impact; strong ambient light may interfere with the measurement results. Finally, structured light scanning typically requires scanning from multiple perspectives to fully cover the entire part surface, necessitating data stitching during the scanning process, which may lead to stitching errors and affect measurement accuracy.

[0009] Therefore, the following improvements are needed in the shape measurement of aspherical parts: (1) Improve measurement speed and efficiency: Existing methods are inefficient in practical applications, and a technology that can quickly and accurately complete large-scale surface scanning is needed.

[0010] (2) Improve measurement accuracy and reliability: Existing methods are poorly adaptable to complex surfaces and highly reflective, transparent materials. A measurement technology that can maintain high accuracy and high stability on various materials is needed.

[0011] (3) Enhance the integrity of non-contact measurement: Existing technologies cannot fully acquire complete data of the surface of aspherical parts, especially in the measurement of the edge area of ​​the parts, there are blind spots. A technology that can ensure comprehensive and high-precision surface acquisition is needed.

[0012] By improving existing technologies, interference from external environmental factors can be significantly reduced, providing more stable and reliable measurement results, meeting the needs of high precision and large-scale production, and promoting the development of high-precision optical measurement technology. Summary of the Invention

[0013] To address the shortcomings or deficiencies of the existing technologies, the technical problem to be solved by this application is to provide a precision aspherical part shape measurement method. This method utilizes spectral confocal measurement technology to achieve high-precision measurement of aspherical parts shape by fusing position information. It can acquire the three-dimensional topographic data of the entire surface of the aspherical part non-contactly and with high precision, and determine key parameters such as its optical axis pose based on this data.

[0014] To solve the above-mentioned technical problems, this application provides the following technical solution: This application proposes a method for measuring the shape of precision aspherical parts, including: Component measurement system; Point cloud data acquisition includes: controlling the relative motion between the spectral confocal sensor and the rotatable workpiece stage in the measurement system, and acquiring three-dimensional point cloud data of the surface of the aspherical part through a spiral scanning method or a layered ring scanning method. The collected point cloud data is fused and processed, and the optical axis direction is initially estimated based on principal component analysis (PCA). Based on the fused point cloud data, the optical axis position and orientation parameters of the aspherical part are calculated. The calculation also includes: determining the surface equation of the optical element and calculating the transformation matrix and performing point cloud coordinate transformation.

[0015] The measurement system includes: A spectral confocal sensor is used for non-contact, high-precision measurement of the surface morphology of aspherical parts. A rotatable workpiece stage is used to fix and drive aspherical parts to rotate about their axis; A linear motion platform is used to drive the spectral confocal sensor to move in the radial and vertical directions; A control unit is used to synchronously control the rotational motion of the rotatable workpiece stage and the radial feed of the linear motion platform; And a data processing unit, used to perform fusion processing and optical axis fitting calculation on the collected point cloud data.

[0016] Alternatively, the spectral confocal sensor can be integrated with the linear motion platform to form a multi-track scanning data acquisition device.

[0017] Specifically, a scheme for acquiring point cloud data of the aspherical part surface is formulated. The relative motion between the spectral confocal sensor and the part under test is controlled: preferably, a scanning method is adopted in which the part rotates around its axis and the probe feeds along the radial direction to achieve a spiral scanning pattern covering the entire aspherical surface; or the measurement area is layered by height, and a circular scan is performed in each layer to achieve tomographic surface shape acquisition. During the scanning process, the step distance is adaptively adjusted based on the curvature changes of the measured surface. In areas with large curvature changes, the sampling interval is reduced to obtain sufficient detail, and in flat areas, the step distance is increased to improve efficiency. Through the planned scanning motion, high-density three-dimensional point cloud data covering the entire aspherical surface is acquired.

[0018] Alternatively, the point cloud data acquisition described above may also include: a spiral scanning method and a layered circular scanning method. The spiral scanning method includes: controlling the rotatable workpiece stage to rotate continuously around its axis, while simultaneously controlling the spectral confocal sensor in the measurement system to feed radially, forming a spiral scanning trajectory, the equation of which satisfies:

[0019] in,

[0020] x(t), y(t), and z are the three-dimensional coordinates of the current scanning trajectory, respectively; z is a function based on x and y, and f(x,y) is the mathematical model of the surface of the optical element, which is an explicit equation. Let the initial radius be , Radial moving speed, ω is the angular velocity, and t is the time. The layered circular scanning method includes: dividing the measurement area of ​​the aspherical part into layers according to height, and performing a circumferential scan in each layer, wherein the scanning path satisfies:

[0021] in, Let be the radius of the optical element in the current layer, where , Angular velocity, x represents the current layer height. i (t), y i (t), z i These are the three-dimensional coordinates of the current layered scanning trajectory; The curvature-based adaptive step size adjustment method specifically involves using the minimum step size in regions with high curvature. The maximum step size is used in areas with small curvature. The formula for calculating the step size is:

[0022] in, This represents the maximum step size (the region with small curvature). This is the minimum step size (for regions with high curvature). The curvature at the current point, This represents the global maximum curvature.

[0023] The collected point cloud data undergoes fusion processing to improve the completeness and accuracy of the measurement results. First, positional confidence weights are assigned to the measurement points in the point cloud based on indicators such as the intensity of the sensor-returned signal, filtering out discrete outliers with low confidence levels and improving data reliability. Second, the global point cloud is fused with local high-density texture information: higher weights or detail enhancement algorithms are used for point clouds in key regions (such as optical edges or high-curvature areas) to ensure that local texture features in these key regions are accurately represented in the reconstructed shape. Interpolation and fitting methods are used to unify data with different sampling densities into a consistent model, achieving the fusion and reconstruction of macroscopic shape and microscopic details.

[0024] Further, optionally, the above-mentioned fusion processing of the collected point cloud data also includes: Statistical filtering or radius filtering is applied to point cloud data to remove outliers. Statistical filtering removes outliers by calculating the mean and standard deviation of points in the neighborhood, while radius filtering removes isolated noise points by setting a minimum number of neighbors within the radius. Principal Component Analysis (PCA) is used to extract the principal orientation of the point cloud and initially estimate the optical axis orientation. In the point cloud data center computation, the point cloud dataset is assumed to be:

[0025] in, For the total number of points in the point cloud, each point... Includes three-dimensional coordinates ; The center point of point cloud data can be calculated using the following formula:

[0026] In calculating the covariance matrix of a point cloud, based on the coordinates of the points in the point cloud data center, these coordinates can be substituted into the following formula to construct the covariance matrix of the point cloud data:

[0027] In solving for the eigenvalues ​​and eigenvectors of the covariance matrix, the covariance matrix... Perform eigenvalue decomposition:

[0028] in, For eigenvalues, according to Arranged in order, For the corresponding feature vectors; in a 3D point cloud, Corresponding minimum eigenvalue That is, the direction of the third principal component (the direction of minimum variance), which can be regarded as the preliminary estimated direction of the optical axis; Based on the preliminary estimated points and preliminary estimated directions of the optical axis obtained from the point cloud above, the preliminary estimated direction of the optical axis can be expressed as follows:

[0029]

[0030] in, Preliminary estimate of points for the center of the point cloud. equal , is the unit vector along the optical axis. for The length of the module.

[0031] Optionally, based on the fused point cloud data and preliminary estimations, the rigid body transformation parameters are iteratively optimized using the least squares method to align the measured point cloud with the ideal aspherical model, ultimately determining the linear equation and spatial orientation of the actual optical axis. Based on the fused 3D point cloud, the optical axis position and orientation parameters of the aspherical part are calculated. Principal component analysis (PCA) is used to initially estimate the principal axis direction of the point cloud, obtaining the initial position of the optical axis. Then, using the ideal design axis as a reference, the rigid body transformation is iteratively optimized using the least squares method to align the measured point cloud with the ideal aspherical model, obtaining the optimal alignment transformation parameters. Finally, the ideal optical axis is mapped to the measurement coordinate system through this optimized transformation, thus obtaining the linear equation and spatial orientation of the actual part's optical axis.

[0032] Further optionally, the above-mentioned calculation of parameters such as the optical axis position and orientation of the aspherical part based on the fused point cloud data also includes: determining the surface equation of the optical element and calculating the transformation matrix and performing point cloud coordinate transformation.

[0033] Further, optionally, the above calculation of the transformation matrix and the point cloud coordinate transformation include: Rotation: Changes the orientation of an object without altering its shape or size; rotation transformations around different axes can be represented using different rotation matrices. The rotation matrices around the x, y, and z axes are as follows:

[0034]

[0035]

[0036] in, It is the rotation angle about the x-axis. It is the rotation angle about y. It is the rotation angle about z; assuming the rotation order is first about the x-axis, then about the y-axis, and finally about the z-axis, then the combined rotation matrix is:

[0037] Translation: Moves an object without changing its shape or orientation; it can be represented using translation vectors.

[0038] Then, any point in the point cloud The transformed coordinates can be represented as:

[0039] The optimization objective of this task is to minimize the sum of the distances between the point cloud and the ideal surface after coordinate transformation. Therefore, the objective function can be expressed as:

[0040] in, For the total number of point clouds, This represents the distance from each point in the point cloud to the ideal surface after coordinate transformation. It can be represented by the shortest distance from a point to the surface. The optimization objective for optimizing variables is:

[0041] First, we confirm that the linear equation of the ideal optical axis can be expressed in parametric form:

[0042] in, It is a point on the ideal optical axis. It is the direction vector of the optical axis; Then, coordinate transformations are performed on a point on the ideal optical axis and the optical axis direction vector, respectively: Transformation of a point on a straight line:

[0043] Transformation of direction vectors:

[0044] Therefore, the transformed optical axis equation is: .

[0045] Compared with the prior art, this application has the following technical effects: This application achieves the acquisition of the complete three-dimensional shape of the entire surface of aspherical parts, including complete point cloud data of the central and edge regions, ensuring comprehensive and reliable measurement results. Secondly, through nanometer-level resolution measurement using a spectral confocal sensor and strict calibration error control, combined with the evaluation and screening of the confidence level of each measurement point's position information, high accuracy and reliability of the obtained data are guaranteed, reducing the impact of noise interference on the results. Furthermore, the data processing method that integrates local texture information allows for the preservation and accurate reconstruction of subtle features and variations in the local optical surface while ensuring overall morphological accuracy, improving the measurement's ability to resolve details of complex curved surfaces. This is of great significance for evaluating the surface quality and morphological errors of aspherical parts. In summary, the measurement technology provided by this invention can fit the complete three-dimensional morphology and optical axis pose of aspherical parts in a high-precision, non-contact manner, effectively improving the quality and efficiency of optical part inspection. Attached Figure Description

[0046] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 : An overall technical flow diagram of an embodiment of this application; Figure 2 A schematic diagram of the components of an embodiment of an aspherical part shape measurement system according to this application; Figure 3 A schematic diagram of the spiral scanning measurement trajectory on the surface of an aspherical optical element based on a spectral confocal measuring instrument; Figure 4 A schematic diagram of the layered circular scanning measurement trajectory on the surface of an aspherical optical element based on a spectral confocal measuring instrument. Detailed Implementation

[0047] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0048] like Figure 1 As shown, in one embodiment of this application, a method for measuring the shape of a precision aspherical part includes: Construct a measurement system; Point cloud data acquisition includes: controlling the relative motion between the spectral confocal sensor and the rotatable workpiece stage in the measurement system, and acquiring three-dimensional point cloud data of the surface of the aspherical part through a spiral scanning method or a layered ring scanning method. The collected point cloud data is fused and processed, and the optical axis direction is initially estimated based on principal component analysis (PCA). Based on the fused point cloud data, the optical axis position and orientation parameters of the aspherical part are calculated. The calculation also includes: determining the surface equation of the optical element and calculating the transformation matrix and performing point cloud coordinate transformation.

[0049] The measurement system includes: Spectral confocal sensor 1 is used for non-contact, high-precision measurement of the surface morphology of aspherical parts; A rotatable workpiece stage 2 is used to fix and drive the aspherical part to rotate about its axis. Linear motion platform 3 is used to drive the spectral confocal sensor 1 to move in the radial and vertical directions; The control unit is used to synchronously control the rotational motion of the rotatable workpiece stage 2 and the radial feed of the linear motion platform; And a data processing unit, used to perform fusion processing and optical axis fitting calculation on the collected point cloud data.

[0050] Among them, reference Figure 1 and Figure 2 As shown, the spectral confocal sensor 1 is integrated with the linear motion platform 3 to form a multi-track scanning data acquisition device. The aspherical optical component under test is fixed on the rotatable workpiece stage 2, and the spectral confocal sensor 1 is mounted on the linear motion platform 3. The control unit synchronously controls the workpiece stage rotation angle θ and the probe radial displacement r to achieve scanning of the surface shape information of the aspherical component, such as... Figure 2 As shown.

[0051] The point cloud data acquisition described above includes: controlling the relative motion between the spectral confocal sensor 1 and the rotatable workpiece stage 2 in the measurement system, and acquiring three-dimensional point cloud data of the aspherical part surface through a helical scanning method or a layered circular scanning method. The measurement process of the spectral confocal sensor relies on the relative motion between the sensor probe and the optical elements to ensure complete and efficient acquisition of point cloud data. The measurement principle of spectral confocal technology is as follows: Figure 3-4 For optical elements of different shapes, reasonable motion trajectories need to be designed to meet the requirements of measurement accuracy, efficiency, and coverage. The typical trajectory planning methods and corresponding implementation methods applicable to the aspherical lenses included in this embodiment (using polynomial, elliptical, or hyperbolic equations as cross-sectional profile curve equations) are as follows: The point cloud data acquisition also includes: spiral scanning and layered circular scanning methods. Helical scanning is a highly efficient measurement method suitable for rotationally symmetric optical components such as lenses and mirrors. The probe moves gradually outward from the center of the optical component along a helical path, achieving uniform sampling. Compared to traditional radial or circular scanning, helical scanning reduces the switching of measurement paths, improves measurement efficiency, and reduces errors caused by frequent system starts and stops. The specific technical approach is as follows: First, initial alignment is performed to ensure that the rotation axis of the optical element is aligned with the coordinate system. Based on axis error measurement and compensation technology, the initial position of the probe in the machine tool coordinate system (or world coordinate system) is ensured.

[0052] Then, determine the scanning path and set the step distance of the spiral path. and angular velocity In the XY plane (where the XYZ axes satisfy the right-hand rule and the Z-axis is along the principal axis), the rotatable workpiece stage is controlled to rotate continuously around its axis, while the spectral confocal sensor in the measurement system is controlled to feed radially, forming a spiral scanning trajectory. The equation of the scanning trajectory satisfies: (1) in, (2) x(t), y(t), and z are the three-dimensional coordinates of the current scanning trajectory, respectively; z is a function based on x and y, and f(x,y) is the mathematical model of the optical element surface, which is an explicit equation. The initial radius is set to be the same as the radius of the optical element in this embodiment. Radial moving speed, ω is the angular velocity, and t is the time. and The density of the scanned point cloud is determined by these factors, and it needs to be combined with subsequent point cloud data processing algorithms to achieve a balance between accuracy and time cost (including mechanical scanning time and data processing time).

[0053] To ensure convenient measurement, the optical element is fixed on a rotatable workpiece stage. Rotation drives the lens to move around its axis. Simultaneously, a linear motion platform controls the radial movement of the confocal probe, allowing for the measurement of the relative distances between multiple locations on the element's surface and the confocal probe. Finally, scanning yields point cloud data resembling a spiral shape, used to characterize the surface pose of the optical element, such as... Figure 3 As shown.

[0054] Layered circular scanning is suitable for complex freeform optical components. This method divides the measurement area into layers along the height direction, performing a circular scan on each layer to obtain discrete three-dimensional topographic data. This method is applicable to complex components such as freeform optical mirrors and aspherical lenses, avoiding the difficulty of complete coverage with a single-planar scan. The specific implementation scheme is as follows: First, determine the layering strategy. Based on the curvature variations of the optical elements and other measurement requirements, set the layer spacing. And calculate the number of measurement layers. : (3) in and These are the z-axis coordinates of the highest and lowest points of the component, respectively. Then, the circular scan path is determined. Within a layer height... Set the circular scan path.

[0055] (4) in , The angular velocity determines the point cloud density at that altitude. The radius of the optical element in this layer is... x represents the current layer height. i (t), y i (t), z i These are the three-dimensional coordinates of the current layered scan trajectory, such as... Figure 4 As shown. To ensure convenient measurement, it is proposed to control the confocal probe to achieve intermittent radial movement and control the spindle to achieve the rotational movement of the optical element. The relative position and relative movement of the confocal probe and the optical element are similar to those of helical scanning. The main difference is whether the radial movement of the confocal probe is continuous.

[0056] Furthermore, the adaptive trajectory of the curvature adaptive step size adjustment When measuring the surface of optical components, the curvature varies in different regions, and the required point cloud density may differ. To improve efficiency while ensuring measurement accuracy, an adaptive step size adjustment method based on curvature can be used. Specifically: for optical component surfaces with large curvature (such as steeply changing regions), a smaller step size is used to increase the sampling density and accurately acquire surface details; for surfaces with smaller curvature (such as gently changing regions), the step size is increased to reduce redundant data and improve measurement efficiency.

[0057] First, calculate the surface curvature at each location on the surface: Suppose the mathematical model of the optical element surface is an explicit equation: (5) Its first-order partial derivative is: (6) Its second-order partial derivative is: (7) Principal curvature , Calculated using Gaussian curvature and mean curvature:

[0058] (8) Principal curvature: (9) Regions with greater curvature require denser sampling. The adaptive step size is then calculated using the following formula: (10) in, This represents the maximum step size (the region with small curvature). This is the minimum step size (for regions with high curvature). The curvature at the current point, This represents the global maximum curvature.

[0059] By substituting the calculated step size into the Z value of the layered ring scanning strategy, an adaptive curvature scanning strategy can be achieved.

[0060] Furthermore, the above-mentioned fusion processing of the collected point cloud data also includes: Data preprocessing: The main goal of point cloud data preprocessing is to remove noise, standardize the data, and prepare it for subsequent optical axis fitting. Key steps include noise filtering. Point cloud data typically contains noise such as measurement errors and environmental interference, requiring noise reduction to improve data quality. Common noise reduction methods include statistical filtering and radius filtering.

[0061] Statistical filtering removes outliers based on the mean and standard deviation of the local neighborhood of a point cloud. First, for each point, the mean and standard deviation of its neighborhood are calculated. The mean Euclidean distance of the nearest neighbors Then, a standard deviation threshold is set. If the neighborhood distance of a certain point satisfy: (11) If so, the point is considered an outlier and is removed.

[0062] Radius filtering determines and removes noise points based on the number of neighbors within a certain radius of the point cloud. (Set radius) and minimum number of neighbors If point exist Number of neighbors satisfy (12) If so, the point is considered an outlier and is removed.

[0063] Furthermore, optical axis estimation based on principal component analysis: The core objective of preliminary optical axis estimation is to quickly obtain the approximate direction of the optical axis using point cloud data, providing a good initial value for subsequent optimization and fitting. As mentioned above, principal component analysis (PCA) is typically used for preliminary estimation. This method can extract the main direction of point cloud data with relatively low computational cost. The process mainly includes steps such as point cloud data center calculation, point cloud covariance matrix calculation, solving for eigenvalues ​​and eigenvectors of the covariance matrix, and optical axis determination, as detailed below: In point cloud data center computing, the point cloud dataset is assumed to be: (13) in, For the total number of points in the point cloud, each point... Includes three-dimensional coordinates .

[0064] The center point of point cloud data can be calculated using the following formula: (14) In calculating the covariance matrix of a point cloud, based on the coordinates of the points in the point cloud data center, these coordinates can be substituted into the following formula to construct the covariance matrix of the point cloud data: (15) In solving for the eigenvalues ​​and eigenvectors of the covariance matrix, the covariance matrix... Perform eigenvalue decomposition: (16) in, For eigenvalues, according to Arranged in order, This represents the corresponding feature vector. In a 3D point cloud, Corresponding minimum eigenvalue The direction of the third principal component (the direction with the minimum variance) can be considered as the preliminary estimated direction of the optical axis attitude.

[0065] Based on the preliminary estimated points of the point cloud and the preliminary estimated direction of the optical axis attitude obtained above, the preliminary estimated direction of the optical axis can be expressed as:

[0066] (17) in, Preliminary estimate of points for the center of the point cloud. equal , is the unit vector along the optical axis. for The length of the module.

[0067] Furthermore, in this embodiment, the optical axis is optimized based on least-squares fitting, specifically, The ideal position of an optical element (where the optical element and the mirror mount are coaxial) can be considered as the result of a rigid body transformation of the actual position of the optical element. All points on its surface and the optical axis follow the same rigid body transformation criterion (or rigid body transformation matrix). Based on the known equation of the profile curve of the central cross-section of the optical element (generally represented by a high-order polynomial), we can further obtain the surface equation. The points in the point cloud obtained by scanning at the actual position are then transformed to the surface of the optical element at the ideal position using the same coordinate transformation. At this point, the sum of the distances from the transformed points to the ideal surface should be minimized.

[0068] The specific approach includes determining the surface equations of optical elements, designing rigid body transformation matrices and transforming point cloud coordinates, determining optimization objectives, and solving optimization problems, as detailed below: Surface equation confirmed: In determining the surface equations of optical elements, the cross-sectional profile curve of an aspherical optical element can generally be explicitly characterized as follows: (18) in, The axis is a radial direction. The axis is the direction of the optical axis. Since optical elements are typical axisymmetric rotational structures, their surface equations can be expressed as: (19) in, This is the distance from a point in the XY plane to the origin.

[0069] Furthermore, the design of the rigid body transformation matrix and the point cloud coordinate transformation are as follows: Rigid transformations are used to implement, among other things: Rotation: Changes the orientation of an object without altering its shape or size. Rotation transformations about different axes can be represented using different rotation matrices; the rotation matrices about the x, y, and z axes are as follows:

[0070]

[0071] (20) in, It is the rotation angle about the x-axis. It is the rotation angle about y. It is the rotation angle around the z-axis. Assuming the rotation order is first around the x-axis, then around the y-axis, and finally around the z-axis, the combined rotation matrix is: (twenty one) Translation: Moves an object without changing its shape or orientation. It can be represented using translation vectors. (twenty two) Then, any point in the point cloud The transformed coordinates can be represented as: (twenty three) Further, optimize target confirmation: As mentioned earlier, the optimization objective of this task is to minimize the sum of the distances between the point cloud and the ideal surface after coordinate transformation. Therefore, the objective function can be expressed as: (twenty four) in, For the total number of point clouds, This represents the distance from each point in the point cloud to the ideal surface after coordinate transformation. It can be represented by the shortest distance from a point to the surface: (25) Then The optimization objective for the optimized variables is: (26) Furthermore, optimize the solution: In the optimization solution process, the rigid body transformation parameters, including rotation angles, are first initialized. and displacement Here, the preliminary optical axis estimation result obtained based on principal component analysis as described above is used. Subsequently, the coordinates of the transformed point cloud are calculated based on the current parameters, and the minimum distance from all points to the ideal optical surface is solved to calculate the value of the optimization objective function. Next, the partial derivatives of the objective function with respect to each optimization variable are calculated using numerical or analytical methods to obtain gradient information. Based on optimization algorithms such as gradient descent, Newton's method, or Levenberg-Marquardt, the rigid body transformation parameters are gradually updated to continuously reduce the objective function value. The optimization process continues until a convergence condition is met, such as the change in the objective function between two iterations being less than a set threshold. Finally, the optimal rigid body transformation parameters are obtained.

[0072] In optical axis fitting, as mentioned earlier, the point cloud on the surface of the optical element, the optical element as a whole, and the optical axis follow the same transformation criterion and unified transformation matrix during rigid body transformation. Based on the known linear equation of the optical axis in the ideal position of the optical element, the actual linear equation of the optical axis can be obtained by performing coordinate transformation on this equation, thus realizing the fitting of the optical axis and the calculation of spatial pose. The specific steps are as follows.

[0073] First, we confirm that the linear equation of the ideal optical axis can be expressed in parametric form: (27) in, It is a point on the ideal optical axis. It is the direction vector of the optical axis. These are parameters. Then, coordinate transformations are performed on a point on the ideal optical axis and the optical axis direction vector, respectively: Transformation of a point on a straight line: (28) Transformation of direction vectors: Since rotation in a rigid body transformation does not affect the length of the direction vector, the direction vector is only affected by the rotation matrix. The effect, that is, the transformed direction vector, is: (29) The transformed optical axis equation is: (30) The precision aspherical part shape measurement method provided by this invention has significant advantages. First, by integrating a spectral confocal sensor with a precision motion platform, it solves the problems of low efficiency and easy damage to the part surface associated with contact measurements, achieving non-contact high-speed scanning and high-precision data acquisition, significantly improving measurement efficiency and avoiding surface damage. Second, by introducing path planning methods for helical scanning and tomographic scanning, and curvature-based adaptive step size adjustment technology, it solves the problems of incomplete coverage and numerous edge blind spots in traditional scanning trajectories, as well as the problem of uneven sampling density on complex curved surfaces, balancing measurement accuracy and efficiency. Through a data processing method that integrates global point clouds and local textures, it improves the problems of noise interference and loss of local details, significantly enhancing data reliability and accurately restoring the surface micro-morphological features, providing a reliable basis for optical component quality assessment. Finally, by using a principal component analysis (PCA) combined with a least squares iteratively optimized optical axis fitting algorithm, it solves the problem of traditional optical axis calculation relying on manual experience and error accumulation, achieving automated high-precision calculation of optical axis pose, reducing surface measurement errors, and meeting the stringent testing requirements of high-end optical systems. Therefore, this application has good market application prospects.

[0074] In the description of this application, unless otherwise expressly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0075] In this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0076] In the description of this embodiment, the terms "upper," "lower," "left," "right," etc., refer to the orientation or positional relationship shown in the accompanying drawings. They are used only for ease of description and simplification of operation, 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 application. In addition, the terms "first" and "second" are used only for distinction in description and have no special meaning.

[0077] The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. The preferred embodiments have been described in detail. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this application without departing from the spirit and scope of the technical solutions of this application, and all such modifications and substitutions should be covered within the scope of the claims of this application.

Claims

1. A method for measuring the shape of a precision aspherical part, characterized in that, include: Construct a measurement system; Point cloud data acquisition includes: controlling the relative motion between the spectral confocal sensor and the rotatable workpiece stage in the measurement system, and acquiring three-dimensional point cloud data of the surface of the aspherical part through a spiral scanning method or a layered ring scanning method. The collected point cloud data is fused, including statistical filtering or radius filtering to remove outliers. Statistical filtering removes outliers by calculating the mean and standard deviation of points in the neighborhood, while radius filtering removes isolated noise points by setting a minimum number of neighbors within the radius. Then, the initial optical axis direction is estimated based on principal component analysis to extract the principal direction of the point cloud. Based on the fused point cloud data, the optical axis position and orientation parameters of the aspherical part are calculated. The calculation also includes: determining the surface equation of the optical element and calculating the transformation matrix and performing point cloud coordinate transformation.

2. The method for measuring the shape of precision aspherical parts according to claim 1, characterized in that, The measurement system includes: A spectral confocal sensor is used for non-contact, high-precision measurement of the surface morphology of aspherical parts. A rotatable workpiece stage is used to fix and drive aspherical parts to rotate about their axis; A linear motion platform is used to drive the spectral confocal sensor to move in the radial and vertical directions; A control unit is used to synchronously control the rotational motion of the rotatable workpiece stage and the radial feed of the linear motion platform; And a data processing unit, used to perform fusion processing and optical axis fitting calculation on the collected point cloud data.

3. The method for measuring the shape of precision aspherical parts according to claim 2, characterized in that, The spectral confocal sensor is integrated with the linear motion platform to form a multi-track scanning data acquisition device.

4. The method for measuring the shape of precision aspherical parts according to claim 1, characterized in that, The point cloud data acquisition mentioned above also includes: The spiral scanning method includes: controlling the rotatable workpiece stage to rotate continuously around its axis, while simultaneously controlling the spectral confocal sensor in the measurement system to feed radially, forming a spiral scanning trajectory, the equation of which satisfies: in, x(t), y(t), and z are the three-dimensional coordinates of the current scanning trajectory, respectively; z is a function based on x and y, and f(x,y) is the mathematical model of the surface of the optical element, which is an explicit equation. Let the initial radius be , Radial moving speed, ω is the angular velocity, and t is the time. The layered circular scanning method includes: dividing the measurement area of ​​the aspherical part into layers according to height, and performing a circumferential scan in each layer, wherein the scanning path satisfies: in, Let be the radius of the optical element in the current layer, where , Angular velocity, x represents the current layer height. i (t), y i (t), z i These are the three-dimensional coordinates of the current layered scanning trajectory; The curvature-based adaptive step size adjustment method specifically involves using the minimum step size in regions with high curvature. The maximum step size is used in areas with small curvature. The formula for calculating the step size is: in, For the maximum step size, For the minimum step size, The curvature at the current point, This represents the global maximum curvature.

5. The method for measuring the shape of precision aspherical parts according to claim 1, characterized in that, The above-mentioned method of extracting the principal orientation of the point cloud through principal component analysis to initially estimate the optical axis orientation also includes: In point cloud data center computing, the point cloud dataset is assumed to be: in, For the total number of points in the point cloud, each point... Includes three-dimensional coordinates ; The center point of point cloud data can be calculated using the following formula: In calculating the covariance matrix of a point cloud, based on the coordinates of the points in the point cloud data center, these coordinates can be substituted into the following formula to construct the covariance matrix of the point cloud data: In solving for the eigenvalues ​​and eigenvectors of the covariance matrix, the covariance matrix... Perform eigenvalue decomposition: in, For eigenvalues, according to Arranged in order, For the corresponding feature vectors; in a 3D point cloud, Corresponding minimum eigenvalue That is, the direction of the third principal component, which can be considered as the preliminary estimated direction of the optical axis; Based on the preliminary estimated points and preliminary estimated directions of the optical axis obtained from the point cloud above, the preliminary estimated direction of the optical axis can be expressed as follows: in, Preliminary estimate of points for the center of the point cloud. equal , is the unit vector along the optical axis. for The length of the module.

6. The method for measuring the shape of precision aspherical parts according to claim 1, characterized in that, Based on the fused point cloud data, and through preliminary estimation and iterative optimization of rigid body transformation parameters using the least squares method, the measured point cloud is aligned with the ideal aspherical model, and finally the linear equation and spatial attitude of the actual optical axis are determined.

7. The method for measuring the shape of precision aspherical parts according to claim 1 or 6, characterized in that, The above calculation of parameters such as the optical axis position and orientation of aspherical parts based on the fused point cloud data also includes: determining the surface equation of the optical element and calculating the transformation matrix and performing point cloud coordinate transformation.

8. The method for measuring the shape of precision aspherical parts according to claim 7, characterized in that, The above calculation of the transformation matrix and the point cloud coordinate transformation include: Rotational transformation: changes the orientation of an object without altering its shape or size; rotational transformations about different axes can be represented using different rotation matrices. The rotation matrices about the x, y, and z axes are as follows: in, It is the rotation angle about the x-axis. It is the rotation angle around y. It is the rotation angle about z; assuming the rotation order is first about the x-axis, then about the y-axis, and finally about the z-axis, then the combined rotation matrix is: Translation transformation: moves an object without changing its shape or orientation; it can be represented using translation vectors. Then, any point in the point cloud The transformed coordinates can be represented as: The optimization objective of this task is to minimize the sum of the distances between the point cloud and the ideal surface after coordinate transformation. Therefore, the objective function can be expressed as: in, For the total number of point clouds, This represents the distance from each point in the point cloud to the ideal surface after coordinate transformation. It can be represented by the shortest distance from a point to the surface. The optimization objective for optimizing variables is: First, we confirm that the linear equation of the ideal optical axis can be expressed in parametric form: in, It is a point on the ideal optical axis. This is the direction vector of the optical axis; then, coordinate transformations are performed on a point on the ideal optical axis and the direction vector of the optical axis, respectively: Transformation of a point on a straight line: Transformation of direction vectors: Therefore, the transformed optical axis equation is: 。

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