A stitching method for complex transparent curved surfaces in a deflection measurement system

Abstract

The present invention belongs to the field of precision measurement technology, and specifically relates to a splicing method for complex transparent curved surfaces in a deflection measurement system. The present invention uses a deflection measurement system to measure a transparent component, obtaining surface-related information such as point clouds and gradients to be spliced; uses the KD-tree nearest neighbor point search method to obtain the overlapping regions of sub-regions, uses the multiple singular value decomposition method to calculate the pose between adjacent sub-regions, makes the target sub-region continuously move closer to the source sub-region through rigid body transformation, and ensures the correctness of the solution through the correlation constraint between the point cloud and the gradient. The upper and lower surfaces of the transparent component are subjected to rigid body transformation as a whole, and the pose is solved by iteratively constraining the corresponding points on the upper and lower surfaces, so as to achieve the motion consistency of the upper and lower surfaces in the splicing measurement, and ensure the splicing accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of precision measurement, and particularly relates to a splicing method for deflectometry measurement of complex transparent surfaces. Background Art

[0002] With the rapid development of technology, optical free-form surfaces are increasingly widely used in fields such as manufacturing, aerospace, etc. It is crucial to improve the imaging performance and processing accuracy of optical elements. For large-sized complex optical surfaces, it is difficult to complete the full-area measurement at one time. First, different sub-regions are collected separately and then spliced, which has become a common method for large-sized surface measurement.

[0003] Deflectometry is a non-contact measurement method with high dynamic range, low cost, and strong anti-interference ability. This method is based on the law of light reflection. A uniformly arranged sine stripe pattern is displayed on the screen, and the stripe changes after being reflected by the surface to be measured are captured at the camera end. After using methods such as stripe phase shift to solve the phase to obtain the pixel correspondence between the screen and the camera, the surface gradient field of the component can be measured, and the surface shape measurement can be realized through gradient integration. In recent years, with the gradually increasing requirements for complex optical surface measurement, this method has received extensive attention.

[0004] Currently, in the splicing methods implemented using deflectometry, the method of first reconstructing the surface shape after calculating the gradients of the measurement sub-regions and then performing surface shape splicing is mainly used. However, the method of directly using the surface shape for splicing will result in a relatively long error transmission chain, thus affecting the splicing accuracy, and there is a lack of feature constraint conditions. Some relevant research scholars have proposed using gradient data for splicing, which can reduce the transmission error, but the accuracy of splicing using only one feature is far from sufficient.

[0005] In addition, for smooth transparent components, while requiring the corresponding points on the upper and lower surfaces to achieve motion consistency, it is also necessary to reduce the transmission of lateral positioning errors. The existing methods do not solve the problem of the consistency of the rigid body transformation of the corresponding point positions on the upper and lower surfaces of the transparent component during the splicing process, and rely on external features to provide constraints during splicing, increasing the measurement complexity. Summary of the Invention

[0006] Aiming at the problem of splicing measurement of smooth transparent surfaces in the existing deflectometry system, the purpose of the present invention is to provide a splicing method for deflectometry measurement of complex transparent surfaces, so as to achieve high-precision splicing without introducing external features and markers during the measurement of transparent components.

[0007] The splicing method for deflectometry measurement of complex transparent surfaces provided by the present invention specifically includes the following steps:

[0008] S1. Set up a deflection measurement system. The system includes a transparent component to be measured, a screen for displaying a fringe pattern, and a camera for capturing a reflected pattern. Fix the transparent component.

[0009] S2. Suppose the upper and lower surface shape point cloud data and gradient data of the sub-region to be spliced are obtained by using the deflection measurement method. The point cloud data are denoted as M (1) (M (1) 1 ,M (1) 2 ,…,M (1) n ) and M (2) (M (2) 1 ,M (2) 2 ,…,M (2) n ), and the gradient data are denoted as Gx (1) (Gx (1) 1 ,Gx (1) 2 ,…,Gx (1) n ), Gy (1) (Gy (1) 1 ,Gy (1) 2 ,…,Gy (1) n ), and Gx (2) (Gx (2) 1 ,Gx (2) 2 ,…,Gx (2) n ), Gy (2) (Gy (2) 1 ,Gy (2) 2 ,…,Gy (2) n ), where n is the number of data points.

[0010] S3. For two adjacent upper surface point clouds of M (1) i and M (1) i+1 , suppose M (1) i is the source point cloud and M (1) i+1 is the target point cloud. Use the KD-tree nearest neighbor search method to obtain M (1) i and M (1)i+1 Overlapping region, calculate the three-dimensional point cloud data M (1) i Variance, take the dimension with the maximum variance as the splitting axis; for M (1) i Retrieve the median data according to the splitting axis dimension, put it on the current node, the values less than the median are divided into the left branch, and the values greater than or equal to the median are divided into the right branch; update the splitting axis to determine the left and right nodes. In M (1) i Find M (1) i+1 The nearest neighbor points of, the point pairs with a point spacing greater than three times are eliminated, and the remaining point pairs are the overlapping regions of the two. The target point cloud M (1) i+1 The overlapping region point cloud data M (1) si And the gradient data Gx (1) si 、Gy (1) si Perform a rigid body transformation with a rotation amount of R i And a translation amount of T i So that the relative poses of two adjacent sub-regions obtain multiple constraints and achieve the best registration effect;

[0011] S4. According to the method described in S3, construct the following objective function:

[0012]

[0013] In the formula, α, β, and γ respectively represent the weight coefficients of point cloud stitching and gradient stitching; p i,j Represents the j-th data point of the overlapping part M (1) si Between the i-th sub-region and the i + 1-th sub-region, q i,j Represents the nearest projection point of p i,j On the point set after transformation of the i + 1-th sub-region; Gx pi,j Is the x-direction gradient corresponding to p i,j Gy pi,j Is the y-direction gradient corresponding to p i,j ; Gx qi,j Is the x-direction gradient corresponding to q i,j Gy qi,j Is the y-direction gradient corresponding to q i,j ; NP represents the total number of sub-regions, N i Represents p i,j The total number of feature points corresponding to; R i And T i Respectively represent the rotation matrix and translation vector in the rigid body transformation of the i + 1-th sub-region;

[0014] The objective function (1) can be solved by the singular value decomposition method.

[0015] The specific process for solving the objective function (1) is as follows:

[0016] (1) Calculate the means P and Q of p i,j and q i,j and the covariance matrix H. Perform singular value decomposition on the covariance matrix such that H = UDV T , where D is a diagonal matrix, and V and U are orthogonal matrices. The rotation matrix R i and the translation vector T i are respectively R i = VU T , T i = P - R×Q. Perform the rigid body transformation in the objective function on the (i + 1)-th sub-region, and replace the (i + 1)-th sub-region of the initial value with the transformed (i + 1)-th sub-region. Among them, the processing methods of Gx pi,j and Gx qi,j , Gx pi,j and Gy qi,j are the same as the processing methods of p i,j and q i,j ;

[0017] (2) Use process (1) again for the i-th sub-region and the transformed (i + 1)-th sub-region to calculate the rotation matrix R i and the translation vector T i , and iterate and replace until the objective function converges to obtain the optimal rotation matrix R i and the translation vector T i .

[0018] S5. Use the mutual constraints of the corresponding points on the upper and lower surfaces to iteratively solve for the same pose of the upper and lower surfaces to achieve the splicing of the transparent components; the specific process is as follows:

[0019] (1) Optimize and splice the relative poses of the sub-regions on the upper and lower surfaces of the transparent component separately. Use the optimal rotation matrix R i (1) and the translation vector T i (1) obtained in steps S3 and S4 as the first pose transformation and assign them to the (i + 1)-th sub-region of the corresponding lower surface;

[0020] (2) Use steps S3 and S4 to solve for the optimal rotation matrix R i (2) and the translation vector T i (2), and obtain the (i + 1)-th lower surface sub-region after rigid body transformation.

[0021] (3) Assign the optimal rotation matrix R i (2) and translation vector T i (2) obtained in process (2) to the upper surface sub-region that has completed the first pose transformation in process (1), and repeat the steps of process (2) for iterative replacement until the rotation matrix and translation vector approach 0. At this time, the sum of the squared projection distances of the corresponding points on the upper and lower surfaces of the transparent element is the smallest;

[0022] (4) Through cumulative iterative calculation of poses, complete the splicing of the i-th and (i + 1)-th upper and lower surface sub-regions;

[0023] (5) Regard the spliced upper and lower surfaces as an integral sub-region and substitute it into the splicing of the next i + 2 sub-region;

[0024] (6) Repeat steps S3 to S5 until the splicing of all regions is completed.

[0025] In step S3 of the present invention, compare whether the distance from point to point between adjacent sub-regions exceeds a threshold. If it exceeds the threshold, first perform rough registration splicing, which can improve the splicing accuracy of step S5; the threshold is taken as 3 times the root mean square value of all point pair distances.

[0026] In the present invention, in the objective function for solving the poses of adjacent sub-regions, the accuracy of the component gradient obtained by the deflection measurement system is higher than the accuracy of the component point cloud. In the objective function, it is necessary to control the weight coefficients corresponding to the gradient and the point cloud respectively, that is, both β and γ are greater than α.

[0027] The splicing method of the present invention makes good use of the advantages of the deflection measurement system with precise gradient and the advantages of the mutual correlation between the upper and lower surfaces of the transparent element, provides more feature constraints for the splicing process, prevents the situation of local optimality of relative poses during the splicing process, shortens the error transfer chain in the splicing of optical elements, and overcomes the problem of lateral splicing misalignment caused by inconsistent motion during the splicing of transparent elements. The present invention has important application value for the splicing of transparent elements. Description of the Drawings

[0028] Figure 1 It is a sub-region diagram of the transparent element to be spliced in the present invention.

[0029] Figure 2 It is a flowchart of the method of the present invention.

[0030] Figure 3 It is a schematic diagram of the splicing method of the present invention.

[0031] Figure 4 This is the splicing result diagram of the present invention.

[0032] In the figure, reference numeral 1.1 is the upper surface of the source sub-region, 1.2 is the upper surface of the target sub-region, 2.1 is the lower surface of the source sub-region, and 2.2 is the lower surface of the target sub-region. Specific embodiments

[0033] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0034] The splicing method for complex transparent curved surface deflection measurement of the present invention has a process as Figure 2 shown, and the specific steps are as follows:

[0035] The specific steps are as follows:

[0036] S1. Set up a deflection measurement system, the system includes a transparent element, a screen and a camera, and fix the transparent element;

[0037] S2. Assume that the upper and lower surface sub-region surface point cloud data obtained by the deflection measurement method are M (1) (M (1) 1 , M (1) 2 , …, M (1) n ) and M (2) (M (2) 1 , M (2) 2 , …, M (2) n ), the gradient data are Gx (1) (Gx (1) 1 , Gx (1) 2 , …, Gx (1) n ), Gy (1) (Gy (1) 1 , Gy (1) 2 , …, Gy (1) n ) and Gx (2) (Gx (2) 1 , Gx (2) 2 , …, Gx (2) n ), Gy (2) (Gy (2) 1 , Gy (2) 2,…,Gy (2) n );

[0038] S3. Taking M (1) i and M (1) i+1 as examples of these two adjacent sub-regions on the upper surface, let M (1) i be the source point cloud and M (1) i+1 be the target point cloud. Using the KD-tree nearest neighbor search method, obtain the overlapping region of M (1) i and M (1) i+1 . Calculate the variance of the three-dimensional point cloud data M (1) i . Take the dimension with the maximum variance as the splitting axis; retrieve the median data according to the splitting axis dimension for M (1) i . Place it on the current node. Values less than the median are divided into the left branch, and values greater than or equal to the median are divided into the right branch; update the splitting axis to determine the left and right nodes. Search for the nearest neighbor of M (1) i in M (1) i+1 . Eliminate the point pairs with a point spacing greater than three times. The remaining point pairs are the overlapping regions of the two. For the overlapping region point cloud data M (1) i+1 corresponding to the target point cloud M (1) si and the gradient data Gx (1) si and Gy (1) si perform a rigid body transformation with a rotation amount of R i and a translation amount of T i simultaneously, so that the relative poses of the two adjacent sub-regions are constrained by multiple eigenvalues and the best registration effect is achieved between the two. Use the method of pose compensation to eliminate the position deviation between the two adjacent sub-regions;

[0039]

[0039] S4. For the method described in S3, construct the following objective function:

[0040]

[0041] In the formula, α, β, and γ respectively represent the weight coefficients of point cloud stitching and gradient stitching; p i,j represents the j-th data point of the overlapping part M (1) si between the i-th sub-region and the (i + 1)-th sub-region, and q i,j represents p i,jThe nearest projection point on the point set after transformation of the (i + 1)-th sub-region; Gx pi,j is p i,j The corresponding gradient in the x direction, Gy pi,j is p i,j The corresponding gradient in the y direction; Gx qi,j is q i,j The corresponding gradient in the x direction, Gy qi,j is q i,j The corresponding gradient in the y direction; NP represents the total number of sub-regions, N i represents the total number of feature points corresponding to p i,j ; R i and T i respectively represent the rotation matrix and the translation vector in the rigid body transformation of the (i + 1)-th sub-region;

[0042] The specific process of solving and optimizing the objective function is as follows:

[0043] (1) Calculate the means P and Q of p i,j and q i,j and the covariance matrix H. Perform singular value decomposition on the covariance matrix so that H = UDV T , D is a diagonal matrix, and V and U are orthogonal matrices. The rotation matrix R i and the translation vector T i are respectively R i = VU T , T i = P - R×Q. Perform the rigid body transformation in the objective function on the (i + 1)-th sub-region, and replace the (i + 1)-th sub-region of the initial value with the transformed (i + 1)-th sub-region. Among them, the processing methods of Gx pi,j and Gx qi,j , Gx pi,j and Gy qi,j are the same as the processing methods of p i,j and q i,j ;

[0044] (2) Use the process (1) again for the i-th sub-region and the transformed (i + 1)-th sub-region to calculate the rotation matrix R i and the translation vector T i , and iterate and replace until the objective function converges. At this time, the optimal rotation matrix R i and the translation vector T i are obtained.

[0045] S5. Use the corresponding points on the upper and lower surfaces to mutually constrain, and iteratively solve for the same pose of the upper and lower surfaces to achieve the splicing of the transparent components; the specific process is as follows:

[0046] (1) Optimize the splicing of the relative poses of the upper and lower surface sub-regions of the transparent component separately, and use the optimal rotation matrix R of the upper surface sub-region obtained in step S3 and step S4 i (1) and the translation vector T i (1) as the first pose transformation, assign it to the (i + 1)-th sub-region of the corresponding lower surface, and through M (2) i+1_0 = R i (1) × M (2) i+1 + T i (1) , Gx (2) i+1_0 = R i (1) × Gx (2) i+1 + T i (1)、 and Gy (2) i+1_0 = R i (1) × Gy (2) i+1 + T i (1) , the obtained M (2) i+1_0 , Gx (2) i+1_0 and Gy (2) i+1_0 are used as the initial values of the (i + 1)-th sub-region in the lower surface pose optimization;

[0047] (2) Use step S3 and step S4 to solve the optimal rotation matrix R i (2) and the translation vector T i (2) for the transformed i-th sub-region and (i + 1)-th sub-region of the lower surface, and through M (2) i+1_1 = R i (2) × M (2) i+1_0 + T i (2) , Gx (2) i+1_1 = R i (2) × Gx (2) i+1_0 + T i (1)、 and Gy (2) i+1_1 = Ri (2) ×Gy (2) i+1_0 +T i (2) , the obtained M (2) i+1_1 , Gx (2) i+1_1 and Gy (2) i+1_1 are the feature values of the (i + 1)-th lower surface sub-region respectively;

[0048] (3) Assign the optimal rotation matrix R i (2) and the translation vector T i (2) obtained in process (2) to the upper surface sub-region that has completed the first pose transformation in (1) according to the method in process (1), and continue to be used as the initial value of the upper surface pose optimization. Repeat step (2) for iterative replacement until the rotation matrix and the translation vector approach 0. At this time, the sum of the squared projection distances of the corresponding points on the upper and lower surfaces of the transparent component is the smallest;

[0049] (4) Through multiple cumulative iterative calculations of the poses from (1) to (3), complete the splicing of the i-th and (i + 1)-th upper and lower surface sub-regions;

[0050] (5) Regard the spliced upper and lower surfaces as a whole sub-region and substitute it into the splicing of the next i + 2 sub-region;

[0051] (6) Repeat step S3 to step S5 until the splicing of all regions is completed.

[0052] Example:

[0053] Use a smooth transparent component with a plano-concave surface for splicing, with a diameter of 200 mm. Taking two corresponding upper and lower surface sub-regions as an example, as Figure 1 shown, divide the transparent component in the same coordinate system obtained by deflection measurement into different sub-regions: the upper surface 1.1 of the source sub-region, the upper surface 1.2 of the target sub-region, the lower surface 2.1 of the source sub-region, and the lower surface 2.2 of the target sub-region.

[0054] Among them, the workpiece point cloud and gradient are known data obtained by deflection measurement.

[0055] The preset pose between adjacent sub-regions is:

[0056]

[0057] The unit of the above vectors is all mm, and the poses of the upper and lower surfaces are the same. At this time, the measurement error between the surface shapes of the two sub-regions and the theoretical surface shape is 0.2785 mm.

[0058] First, use adjacent upper surface sub-regions for registration, and use the k-D tree and the normal vector angle constraint to perform feature point matching to obtain the overlapping region. Then, minimize the projection distance of the point cloud and the gradient value in the overlapping region between the 1.1 source sub-region and 2.1, as Figure 2 shown, to obtain the relative pose of the upper surface. The obtained result is:

[0059]

[0060] Take R 0 and T 0 as the initial pose values between the adjacent lower surface sub-regions 2.1 and 2.2, and perform cumulative iteration of the pose. When the objective function is minimized, the overall pose of the transparent component is obtained as:

[0061]

[0062] The obtained overall pose result of the transparent component is consistent with the above preset value, as Figure 4 shown. The measurement error between the spliced surface shape and the theoretical surface shape is 1.8481×10 -14 mm, realizing the splicing with consistent movement of two adjacent upper and lower surfaces.

Claims

1. A splicing method for complex transparent curved surfaces in a deflection measurement system, characterized in that, the specific steps are as follows: S1. Set up a deflection measurement system, the system includes a transparent element, a screen and a camera, and fix the transparent element; S2. Use the deflection measurement method to obtain the surface point cloud data and gradient data of the upper and lower surfaces of the sub-region to be spliced; the point cloud data are respectively denoted as M (1) (M (1) 1 , M (1) 2 , …, M (1) n ) and M (2) (M (2) 1 , M (2) 2 , …, M (2) n ), and the gradient data are respectively denoted as Gx (1) (Gx (1) 1 , Gx (1) 2 , …, Gx (1) n ), Gy (1) (Gy (1) 1 , Gy (1) 2 , …, Gy (1) n ) and Gx (2) (Gx (2) 1 , Gx (2) 2 , …, Gx (2) n ), Gy (2) (Gy (2) 1 , Gy (2) 2 , …, Gy (2) n ), where n is the number of data points; S3. For M (1) i and M (1) i+1 For two adjacent point clouds on the upper surfaces, let M (1) i be the source point cloud and M (1) i+1 be the target point cloud. Use the KD-tree nearest neighbor search method to obtain the overlapping region of M (1) i and M (1) i+1 Calculate the variance of the three-dimensional point cloud data M (1) i Take the dimension with the maximum variance as the splitting axis; Retrieve the median data according to the splitting axis dimension for M (1) i Put it on the current node. Values less than the median are divided into the left branch, and values greater than or equal to the median are divided into the right branch; Update the splitting axis to determine the left and right nodes; Search for the nearest neighbor of M (1) i in M (1) i+1 Eliminate the point pairs with a point spacing greater than three times. The remaining point pairs are the overlapping regions of the two; For the overlapping region point cloud data M (1) i+1 corresponding to the target point cloud M (1) si and the gradient data Gx (1) si and Gy (1) si Perform a rigid body transformation with a rotation amount of R i and a translation amount of T i simultaneously, so that the relative poses of the two adjacent sub-regions obtain multiple constraints and achieve the best registration effect; S4. According to the method in S3, construct the following objective function: where α, β, and γ respectively represent the weight coefficients of point cloud stitching and gradient stitching; p i,j represents the j-th data point of the overlapping part M (1) si between the i-th sub-region and the (i + 1)-th sub-region, and q i,j represents the nearest projection point of p i,j on the point set after transformation of the (i + 1)-th sub-region; Gx pi,j is the x-direction gradient corresponding to p i,j , Gy pi,j is the y-direction gradient corresponding to p i,j ; Gx qi,j is the x-direction gradient corresponding to q i,j , Gy qi,j is the y-direction gradient corresponding to q i,j ; NP represents the total number of sub-regions, and N i represents the total number of feature points corresponding to p i,j . R i and T i respectively represent the rotation matrix and the translation vector in the rigid body transformation of the (i + 1)-th sub-region; The objective function (1) is solved by the singular value decomposition method; S5. Use the corresponding points on the upper and lower surfaces to constrain each other, and iteratively solve the same pose of the upper and lower surfaces to achieve the splicing of the transparent element; the specific process is: (1) Optimize the splicing of the relative poses of the sub-regions on the upper and lower surfaces of the transparent component separately, and assign the optimal rotation matrix R i (1) and translation vector T i (1) of the upper surface sub-region obtained in steps S3 and S4 as the first pose transformation to the (i + 1)-th sub-region corresponding to the lower surface; (2) Solve for the optimal rotation matrix \(R\) and translation vector \(T\) of the lower surface sub-region for the \(i\)-th lower surface sub-region and the new \((i + 1)\)-th sub-region using steps S3 and S4, and obtain the \((i + 1)\)-th lower surface sub-region after rigid body transformation; i (2) and translation vector \(T\) i (2) ; and obtain the \((i + 1)\)-th lower surface sub-region after rigid body transformation. (3) Assign the optimal rotation matrix R corresponding to the lower surface obtained in process (2) i (2) and the translation vector T i (2) to the upper surface sub-region that has completed the first pose transformation in process (1), and repeat the steps of process (2) for iterative replacement until the rotation matrix and the translation vector approach 0. At this time, the sum of the squared projection distances of the corresponding points on the upper and lower surfaces of the transparent component is the smallest; (4) Through the iterative calculation of the pose accumulation, complete the splicing of the i-th and i+1-th upper and lower surface sub-regions; (5) Regard the spliced upper and lower surfaces as a whole sub-region and substitute it into the splicing of the next i+2 sub-region; (6) Repeat steps S3 to S5 until all regions are spliced.

2. The splicing method according to claim 1, characterized in that, in step S3, compare whether the distance between points of adjacent sub-regions exceeds a threshold. If it exceeds the threshold, first perform rough registration splicing to improve the splicing accuracy of step S5.

3. The splicing method according to claim 1, characterized in that, in the objective function described in step S4, since the accuracy of the gradient information in the deflection measurement system is higher than the accuracy of the point cloud information, control the weights β and γ to be greater than α.

4. The splicing method according to claim 3, characterized in that, the specific process of solving the objective function (1) is: (1) Calculate p i,j and q i,j to obtain the means P and Q and the covariance matrix H. Perform singular value decomposition on the covariance matrix such that H = UDV T , where D is a diagonal matrix, and V and U are orthogonal matrices; the rotation matrix R i and the translation vector T i are respectively R i = VU T , T i = P - R×Q. Perform the rigid body transformation in the objective function on the i + 1 sub-region, and replace the i + 1 sub-region of the initial value with the transformed i + 1 sub-region; where the processing methods of Gx pi,j and Gx qi,j , Gx pi,j and Gy qi,j are the same as the processing methods of p i,j and q i,j ; (2) Reuse process (1) to calculate the rotation matrix R for the i-th sub-region and the transformed (i + 1)-th sub-region i and the translation vector T i , and iterate cyclically until the objective function converges to obtain the optimal rotation matrix R i and the translation vector T i .

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