Micro-nano multi-sensor measurement machine coordinate unification method

Abstract

The application discloses a kind of micro-nano multi-sensor measuring machine coordinate unified calibration methods, setting calibrator, using micro-nano white light interferometer and three coordinate measuring machines are measured respectively to each measuring surface of calibrator, obtain the space equation of each measuring surface in corresponding coordinate system and the space coordinates and direction vector of the upper end surface center point of calibrator, the translation matrix and rotation matrix between two coordinates are calculated using the obtained data, to determine the spatial position relationship between white light interferometer and three coordinate measuring machine coordinate system and unify the data measured by three coordinate measuring machine to white light interferometer coordinate system, to realize the coordinate of micro-nano multi-sensor measuring machine unified.

Description

Technical Field

[0001] This invention relates to coordinate unification for micro / nano-scale multi-sensor measuring machines, and more specifically to a coordinate unification calibrator and calibration method for composite measurements using a nano-scale coordinate measuring machine and a white light interferometer probe. Background Technology

[0002] As the requirements for workpiece precision, structural intricacy, geometric complexity, and measurement efficiency become increasingly stringent, single-contact sensor systems often struggle to meet all measurement needs. Consequently, multi-sensor combined measurement systems have emerged, offering advantages such as high flexibility and measurement efficiency, increased measurement space dimension, and high precision, accuracy, and stability.

[0003] In existing technologies, both white light interferometers and micro / nano coordinate measuring machines can measure the dimensions and morphology of ultra-precision machined surfaces and micro-sized parts. White light interferometers have high measurement efficiency and large data volume, and their Z-axis measurement accuracy can reach the nanometer level, but their X and Y-axis accuracy is relatively insufficient. Micro / nano coordinate measuring machines have excellent accuracy in the X, Y, and Z axes, and can measure geometric parts with deep holes or grooves that white light interferometers cannot measure, but their measurement efficiency and data volume are inferior to those of white light interferometers.

[0004] Therefore, this patent employs coordinate unification technology to integrate a white light interferometer and a micro / nano coordinate measuring machine into a multi-sensor measurement system, forming a complementary advantage to achieve micro / nano-level composite measurement and improve the system's measurement accuracy and efficiency. The purpose of this invention is to provide a technical method for coordinate unification to achieve multi-sensor composite measurement. Using this method, data measured by different sensors in different coordinate systems can be unified into the same coordinate system. Physical objects with different geometric combinations are used as the medium for coordinate unification between the white light interferometer and the micro / nano coordinate measuring machine sensors. The measurement data from both the white light interferometer and the micro / nano coordinate measuring machine are processed separately to bring the two coordinate systems into the same coordinate system. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a coordinate unification calibrator and coordinate unification method for a micro / nano-scale multi-sensor measuring machine, aiming to achieve high-precision composite measurement at the micro / nano level using a micro / nano coordinate measuring machine and a white light interferometer.

[0006] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0007] This invention discloses a unified coordinate calibration method for a micro / nano-level multi-sensor measuring machine. The micro / nano-level multi-sensor measuring machine is a combination of a coordinate measuring machine and an interferometer. The coordinate measuring machine is a micro / nano-level coordinate measuring machine, and the interferometer is a white light interferometer. A calibrator is set up, which consists of two cylinders of equal size fixed on the same plane. Each cylinder contains two different measurement surfaces: a cylindrical surface serving as the calibration elevation and an upper cylindrical surface serving as the calibration end face. Each calibration end face has at least two trace lines passing through the center point, which bisect the calibration end face equally. The trace lines are indentations or convexities formed on the calibration end face.

[0008] The calibration method is set up by following these steps:

[0009] Step 1: Denote the interferometer coordinate system O1-XYZ as coordinate system O1. Use the interferometer to measure the calibration end face and obtain the interferometer measurement data for the calibration end face and the trace lines. Use the interferometer measurement data to fit and obtain the spatial plane equations A1 and A2 of the calibration end faces of the two cylinders in coordinate system O1, and obtain the set of spatial straight line equations B1 and B2 of the trace lines of the two cylinders in coordinate system O1. By calculating the intersection of the straight lines, obtain the center points P1 and P2 of the calibration end faces of the two cylinders in coordinate system O1 respectively.

[0010] Step 2: Denote the coordinate system O2-XYZ of the coordinate measuring machine as coordinate system O2. Use the coordinate measuring machine to measure the calibration elevation and calibration end face to obtain the coordinate measuring machine measurement data for the calibration elevation and calibration end face. Use the coordinate measuring machine measurement data to fit and obtain the measurement surface space equation of the two cylindrical targets in coordinate system O2. Use the measurement surface space equation to calculate the center point Q1 and center point Q2 of the calibration end of the two cylinders in coordinate system O2.

[0011] Step 3: Use center point P1 and center point Q1 to obtain the translation matrix T between coordinate system O1 and coordinate system O2;

[0012] Step 4: Construct a spatial vector belonging to coordinate system O1 using the center point P1 under coordinate system O1 and the normal vector of the calibration end face. Construct a spatial vector belonging to coordinate system O2 from the center point Q1 in coordinate system O2 and the normal vector of the calibration end face. Using the space vector and Construct the Rodriguez rotation equation and solve for the spatial rotation matrix R1 of the rotational degrees of freedom in the X and Y directions between the constrained coordinate systems O1 and O2;

[0013] Construct a spatial vector belonging to coordinate system O1 from the center points P1 and P2 in coordinate system O1. Construct a spatial vector belonging to coordinate system O2 from the center points Q1 and Q2 in coordinate system O2. Using spatial vectors and Construct the Rodriguez rotation equation and solve for the spatial rotation matrix R2 of the rotational degrees of freedom in the Z-axis direction between constrained coordinate systems O1 and O2.

[0014] Therefore, the spatial rotation matrix R between coordinate systems O1 and O2 is: R = R1R2;

[0015] Step 5: Based on the translation matrix T and the spatial rotation matrix R, unify coordinate system O2 into coordinate system O1 to achieve coordinate unification.

[0016] Step 1 of the micro / nano-scale multi-sensor measurement machine coordinate unified calibration method of the present invention is performed as follows:

[0017] 1.1: An interferometer was used to measure the calibration end faces of the two cylinders in the calibrator, and a set of three-dimensional point cloud data of each calibration end face was obtained in a one-to-one correspondence.

[0018] 1.2: For one of the cylinders, the best plane equation is fitted using its three-dimensional point cloud data to obtain the spatial plane equation A1 of its calibrated end face in coordinate system O1 as shown in equation (1), and the normal vector of the spatial plane equation A1 is obtained. As in equation (2):

[0019] a0X0+b0Y0+c0Z0+d0=0 (1)

[0020]

[0021] in:

[0022] a0, b0, c0, d0 are all coefficients of the spatial plane equation A1;

[0023] Let X0, Y0, and Z0 characterize the variables of the plane equation A1 under coordinate system O1;

[0024] Using the trace line data in its three-dimensional point cloud data, spatial straight line equations are fitted to obtain a set of spatial straight line equations B1 in coordinate system O1. The intersection point of each trace line in the set of spatial straight line equations B1 is obtained by simultaneous calculation. The intersection point is the center point P1. Let (x1, y1, z1) represent the spatial coordinates of the center point P1 in coordinate system O1, that is: P1 = (x1, y1, z1).

[0025] 1.3: For the other cylinder, obtain the coordinates of the center point P2 using the same method as in step 1.2. Let (x2, y2, z2) represent the spatial coordinates of the center point P2 in coordinate system O1, i.e., P2 = (x2, y2, z2).

[0026] In the micro / nano-scale multi-sensor measurement machine coordinate unified calibration method of the present invention, step 2 is performed as follows:

[0027] 2.1: For one of the cylinders, the coordinate measuring machine measurement data is fitted to obtain the spatial plane equation C of the upper end face in coordinate system O2 represented by equation (3), the cylindrical equation D of the side elevation represented by equation (4), and the normal vector of the spatial plane equation C of the upper end face represented by equation (5).

[0028] a1X1+b1Y1+c1Z1+d1=0 (3)

[0029] (X2-x0) 2 +(Y2-y0) 2 +(Z2-z0) 2 -[l(X2-x0)+m(Y2-y0)+n(Z2-z0) 2 ] 2 =r 2 (4)

[0030]

[0031] in:

[0032] a1, b1, c1, and d1 are all coefficients of the spatial plane equation C.

[0033] Let X1, Y1, and Z1 characterize the variables of the plane equation C under coordinate system O2;

[0034] Let X2, Y2, and Z2 characterize the variables of the cylindrical equation D in coordinate system O2;

[0035] Let (x0, y0, z0) represent the coordinates of point q0 on the axis of the cylinder, that is: q0 = (x0, y0, z0)

[0036] Let (l,m,n) represent the axis vector of the cylinder. Right now:

[0037] r is the radius of the cylinder;

[0038] By solving the spatial plane equation C and the side elevation cylinder equation D, the center point Q1 is obtained:

[0039] The point q0 on the axis and the ray vector of the cylinder axis are obtained from the equation D of the side elevation cylinder. The parametric equation for the ray N0 along the axis of the cylinder, originating from point q0, is as follows:

[0040]

[0041] Where: t is a constant, and t∈[0,+∞);

[0042] Different points on the ray are obtained based on different values ​​of t. The intersection point is obtained by simultaneously solving the equations of the ray N0 along the cylinder's axis and the spatial plane C, and this intersection point is the center point Q1. This represents the spatial coordinates of the center point Q1 in coordinate system O2, i.e.: Q1=(x1′,y1′,z1′);

[0043] 2.2: For the other cylinder, obtain the coordinates of the center point Q2 using the same method as in step 2.1. Let (x′2,y′2,z′2) represent the spatial coordinates of the center point Q2 in coordinate system O2, that is: Q2=(x′2,y′2,z′2).

[0044] In the micro / nano-scale multi-sensor measurement machine coordinate unified calibration method of the present invention, step 3 is performed as follows:

[0045] Calculate the coordinate differences dx, dy, and dz between the two points P1 and Q1 based on the coordinates (x1, y1, z1) and Q1 respectively. This will give us the translation matrix T between coordinate systems O1 and O2.

[0046] Introduce homogenized coordinates w for center points P1 and Q1 respectively, and set w to 1. Construct the translation matrix T accordingly:

[0047]

[0048] in:

[0049] dx=x1-x1′, dy=y1-y1′, dz=z1-z1′.

[0050] In the micro / nano-scale multi-sensor measurement machine coordinate unified calibration method of the present invention, step 4 is performed as follows:

[0051] 4.1: Obtain the spatial rotation matrix R1:

[0052] The center point P1 and normal vector in coordinate system O1 Determine spatial vectors The space vector Starting from the center point P1, and using the normal vector Its direction;

[0053] In coordinate system O2, the center point Q1 and the normal vector Determine spatial vectors The space vector Starting from the center point Q1, with the normal vector ξo2 Its direction;

[0054] According to spatial vectors and Construct the Rodrigues rotation equation and solve for the rotation matrix R1 to obtain the space vector. Spatial correspondence between them.

[0055] 4.2: Obtain the spatial rotation matrix R2:

[0056] Construct a spatial vector from the center points P1 and P2 in coordinate system O1.

[0057] Construct a spatial vector from the center points Q1 and Q2 in coordinate system O2.

[0058] Obtain the spatial vector using the same method as in step 4.1. and space vectors The rotation matrix R2 between them.

[0059] In the micro / nano-scale multi-sensor measurement machine coordinate unified calibration method of the present invention, step 4.1 is performed as follows:

[0060] The center point P1 of coordinate system O1 has been determined as: P1 = (x1, y1, z1), and the normal vector is... for:

[0061] And determine the center point Q1 of coordinate system O2 as: Q1=(x1′,y1′,z1′), and the normal vector ξ. o2 for:

[0062] 4.1.1: Calculating Vectors with vector The axis of rotation between:

[0063] The vectors are obtained by normalizing the vectors. unit vector sum vector unit vector

[0064]

[0065] The unit vector is obtained by calculating the cross product. and rotation axis vector

[0066] Rotate axis vector Standardization yields the unit vector of the rotation axis.

[0067] 4.1.2: Calculating Vectors and The cosine of the rotation angle θ, cosθ, is:

[0068]

[0069] 4.1.3: Obtain the spatial rotation matrix R1:

[0070] The Rodriguez rotation equation is established as shown in equation (6):

[0071]

[0072] Define the unit vector of the rotation axis The cross product matrix is Equation (6) can be transformed into matrix form as shown in equation (7):

[0073]

[0074] Then the rotation matrix R1 is:

[0075]

[0076] in:

[0077] E 3×3 It is a third-order identity matrix. Unit vector of rotation axis The cross product matrix.

[0078] The calibration accuracy of this invention is verified in the following manner:

[0079] (1) Use an interferometer to perform n measurements on the curved surface, stitch the measurement data together to obtain the dataset W in coordinate system O1 of the n measurements. sum ;

[0080] (2) Use a coordinate measuring machine to measure the curved surface within the scanning area of ​​the interferometer, and obtain the dataset P in coordinate system O2 containing m measurement points. sum ;

[0081] (3) Transform the dataset in coordinate system O2 into P using translation matrix T and rotation matrix R. sum The dataset W′ converted to coordinate system O1 is:

[0082]

[0083] in: For Kronecker product;

[0084] (4) For each point in the dataset W′, retrieve its corresponding position in the dataset W′. sum The closest points in the matrix are paired as corresponding points. The residual matrix V between all corresponding points is calculated as follows:

[0085]

[0086] Elements V in the residual matrix V 1i V 2i V 3i Let i represent the residuals of each pair of corresponding points in the X, Y, and Z directions, respectively, i = 1, 2, 3…m;

[0087] (5) The root mean square residual (RMSR) is calculated as follows:

[0088]

[0089] The root mean square residual (RMSR) is used as the basis for evaluating the error of coordinate unification. The larger the RMSR value, the lower the accuracy of coordinate unification, and vice versa.

[0090] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0091] 1. The calibrator of this invention has a simple geometric structure, high reliability, small size, low cost, and is easy to integrate for online measurement;

[0092] 2. The planar machining accuracy of this invention can be guaranteed. It makes full use of the high precision of the white light interferometer in the Z direction (its Z direction resolution is 0.1nm) to compensate for the lack of precision in the X and Y directions, and does not have the problem of incompatibility with traditional calibrators such as the white light interferometer measuring standard ball;

[0093] 3. This invention enables measurement by combining contact and non-contact probes, while allowing each sensor to complete the measurement independently without the need to fix the two probes together. This results in high measurement freedom, unified coordinates, and high efficiency. Attached Figure Description

[0094] Figure 1 This is a three-dimensional structural diagram of the calibrator in this invention;

[0095] Figure 2a , Figure 2b and Figure 2c A one-to-one correspondence is shown in the top, front, and side views of the calibrator;

[0096] Figure 3 This is a schematic diagram of the calibration measurement of the calibrator in the white light interferometer of the present invention;

[0097] Figure 4This is a schematic diagram of the calibration measurement of the calibrator in the micro-nano coordinate measuring machine of the present invention;

[0098] The numbers in the diagram are: 1. Base, 2. Calibration elevation, 3. Calibration end face, 4. Trace line, 5. Micro-nano coordinate measuring machine frame, 6. White light interferometer frame, 7. Calibrator, 8. Worktable, N is the micro-nano coordinate measuring machine contact probe, and M is the white light interferometer probe. Detailed Implementation

[0099] In this embodiment, the micro-nano-scale multi-sensor measuring machine uses a combination of a coordinate measuring machine and an interferometer for measurement. The coordinate measuring machine is a micro-nano coordinate measuring machine, and the interferometer is a white light interferometer.

[0100] The method for unified coordinate calibration of the micro / nano-scale multi-sensor measuring machine in this embodiment is as follows:

[0101] First, set as follows Figure 1 , Figure 2a , Figure 2b and Figure 2c The calibrator shown consists of two cylinders of equal size fixed on the same plane of the base 1. Each cylinder contains two different measuring surfaces: a cylindrical surface that serves as the calibration elevation 2 and an upper cylindrical surface that serves as the calibration end face 3. Each calibration end face 3 has at least two trace lines 4 passing through the center point. The trace lines 4 divide the calibration end face into equal parts. The trace lines 4 are indentations or convexities formed on the calibration end face 3.

[0102] In this embodiment, the calibration method is performed according to the following steps:

[0103] Step 1: Denote the interferometer coordinate system O1-XYZ as coordinate system O1. Use the interferometer to measure the calibration end face 3 and obtain the interferometer measurement data for the calibration end face 3 and the trace line 4. Use the interferometer measurement data to fit and obtain the spatial plane equations A1 and A2 of the calibration end face 3 of the two cylinders in coordinate system O1, and obtain the set of spatial straight line equations B1 and B2 of the trace line 4 of the two cylinders in coordinate system O1. By calculating the intersection of the straight lines, obtain the center point P1 and center point P2 of the calibration end face of the two cylinders in coordinate system O1.

[0104] Step 2: Denote the coordinate system O2-XYZ of the coordinate measuring machine as coordinate system O2. Use the coordinate measuring machine to measure the calibration elevation 2 and calibration end face 3 to obtain the coordinate measuring machine measurement data for calibration elevation 2 and calibration end face 3. Use the coordinate measuring machine measurement data to fit and obtain the measurement surface space equation of the two cylindrical bodies in coordinate system O2. Use the measurement surface space equation to calculate the center point Q1 and center point Q2 of the calibration end of the two cylinders in coordinate system O2.

[0105] Step 3: Use center point P1 and center point Q1 to obtain the translation matrix T between coordinate system O1 and coordinate system O2, and use the translation matrix T to determine the translation relationship between the interferometer coordinate system and the coordinate machine coordinate system.

[0106] Step 4: Construct a spatial vector belonging to coordinate system O1 using the center point P1 under coordinate system O1 and the normal vector of the calibration end face. Construct a spatial vector belonging to coordinate system O2 from the center point Q1 in coordinate system O2 and the normal vector of the calibration end face. Using spatial vectors and Construct the Rodriguez rotation equation and solve for the spatial rotation matrix R1 of the rotational degrees of freedom in the X and Y directions between the constrained coordinate systems O1 and O2;

[0107] Construct a spatial vector belonging to coordinate system O1 from the center points P1 and P2 in coordinate system O1. Construct a spatial vector belonging to coordinate system O2 from the center points Q1 and Q2 in coordinate system O2. Using spatial vectors and Construct the Rodriguez rotation equation and solve for the spatial rotation matrix R2 of the rotational degrees of freedom in the Z-axis direction between the constrained coordinate systems O1 and O2. Then, the spatial rotation matrix R between coordinate systems O1 and O2 is: R = R1R2. The rotational relationship between coordinate systems O1 and O2 is determined by the spatial rotation matrix R.

[0108] Step 5: Unify coordinate system O2 into coordinate system O1 based on the translation matrix T and the spatial rotation matrix R to achieve coordinate unification.

[0109] In practice, the corresponding technical measures also include:

[0110] Step 1 is performed as follows:

[0111] 1.1: See Figure 3 Place the calibrator 7 on the worktable 8 in the interferometer, and adjust the white light interferometer measuring machine frame 6 so that the white light interferometer probe M is in the set position. Use the interferometer to measure the calibration end faces 3 of the two cylinders in the calibrator respectively, and obtain a set of three-dimensional point cloud data of each calibration end face 3. The three-dimensional point cloud data includes the three-dimensional shape of the calibration end face 3 and the trace line 4.

[0112] 1.2: For one of the cylinders, the best plane equation is fitted using its three-dimensional point cloud data to obtain its spatial plane equation A1 of the calibrated end face 3 in coordinate system O1 as shown in equation (1), and the normal vector of the spatial plane equation A1 is obtained. As in equation (2):

[0113] a0X0+b0Y0+c0Z0+d0=0 (1)

[0114]

[0115] in:

[0116] a0, b0, c0, d0 are all coefficients of the spatial plane equation A1;

[0117] Let X0, Y0, and Z0 characterize the variables of the plane equation A1 under coordinate system O1;

[0118] Using the trace line 4 data in its 3D point cloud data, spatial straight line equations are fitted to obtain the set of spatial straight line equations B1 in coordinate system O1. The intersection point of each trace line in the set of spatial straight line equations B1 is obtained by simultaneous calculation. The intersection point is the center point P1. Let (x1,y1,z1) represent the spatial coordinates of the center point P1 in coordinate system O1, that is: P1=(x1,y1,z1).

[0119] 1.3: For the other cylinder, obtain the coordinates of the center point P2 using the same method as in step 1.2. Let (x2, y2, z2) represent the spatial coordinates of the center point P2 in coordinate system O1, i.e., P2 = (x2, y2, z2).

[0120] Step 2 is performed as follows:

[0121] 2.1: See Figure 4 Place the calibrator 7 on the worktable 8 of the micro-nano coordinate measuring machine, adjust the frame 5 of the micro-nano coordinate measuring machine so that the contact probe N of the micro-nano coordinate measuring machine is in the set position, and for one of the cylinders, use its coordinate measuring machine measurement data to fit, and obtain the upper end face spatial plane equation C in coordinate system O2 represented by equation (3), the side elevation cylinder equation D represented by equation (4), and the normal vector of the upper end face spatial plane equation C represented by equation (5).

[0122] a1X1+b1Y1+c1Z1+d1=0 (3)

[0123] (X2-x0) 2 +(Y2-y0) 2 +(Z2-z0) 2 -[l(X2-x0)+m(Y2-y0)+n(Z2-z0) 2 ] 2 =r 2 (4)

[0124]

[0125] in:

[0126] a1, b1, c1, and d1 are all coefficients of the spatial plane equation C.

[0127] Let X1, Y1, and Z1 characterize the variables of the plane equation C under coordinate system O2;

[0128] Let X2, Y2, and Z2 characterize the variables of the cylindrical equation D in coordinate system O2;

[0129] Let (x0, y0, z0) represent the coordinates of point q0 on the axis of the cylinder, that is: q0 = (x0, y0, z0)

[0130] Let (l,m,n) represent the axis vector of the cylinder. Right now:

[0131] r is the radius of the cylinder;

[0132] By solving the spatial plane equation C and the side elevation cylinder equation D, the center point Q1 is obtained:

[0133] The point q0 on the axis and the ray vector of the cylinder axis are obtained from the equation D of the side elevation cylinder. The parametric equation for the ray N0 along the axis of the cylinder, originating from point q0, is as follows:

[0134]

[0135] Where: t is a constant, and t∈[0,+∞);

[0136] Different points on the ray are obtained by taking different values ​​of t. Solve for t by combining the equations of the cylinder axis ray N0 and the space plane C to obtain the intersection point. The intersection point is the center point Q1. Let (x1′,y1′,z1′) represent the spatial coordinates of the center point Q1 in the coordinate system O2, that is: Q1=(x1′,y1′,z1′).

[0137] 2.2: For the other cylinder, obtain the coordinates of the center point Q2 using the same method as in step 2.1. Let (x′2,y′2,z′2) represent the spatial coordinates of the center point Q2 in coordinate system O2, that is: Q2=(x′2,y′2,z′2).

[0138] Step 3 is performed as follows:

[0139] Calculate the coordinate differences dx, dy, and dz between the two points P1 and Q1 based on the coordinates (x1, y1, z1) and Q1 respectively. This will give us the translation matrix T between coordinate systems O1 and O2.

[0140] Introduce homogenized coordinates w for center points P1 and Q1 respectively, and set w to 1. Construct the translation matrix T accordingly:

[0141]

[0142] in:

[0143] dx=x1-x1′, dy=y1-y1′, dz=z1-z1′.

[0144] Step 4 is performed as follows:

[0145] 4.1: Obtaining the spatial rotation matrix R1:

[0146] The center point P1 and normal vector in coordinate system O1 Determine spatial vectors Space vector Starting from the center point P1, and using the normal vector Its direction;

[0147] In coordinate system O2, the center point Q1 and the normal vector Determine spatial vectors Space vector Starting from the center point Q1, with the normal vector ξ o2 Its direction;

[0148] According to spatial vectors and Construct the Rodrigues rotation equation and solve for the rotation matrix R1 to obtain the space vector. Spatial correspondence between them.

[0149] This step 4.1 is performed as follows:

[0150] The center point P1 of coordinate system O1 has been determined as: P1 = (x1, y1, z1), and the normal vector is... for:

[0151] And determine the center point Q1 of coordinate system O2 as: Q1=(x1′,y1′,z1′), and the normal vector ξ. o2 for:

[0152] 4.1.1: Calculating Vectors with vector The axis of rotation between:

[0153] The vectors are obtained by normalizing the vectors. unit vector sum vector unit vector

[0154]

[0155] The unit vector is obtained by calculating the cross product. and rotation axis vector

[0156] Rotate axis vector Standardization yields the unit vector of the rotation axis.

[0157] 4.1.2: Calculating Vectors and The cosine of the rotation angle θ, cosθ, is:

[0158]

[0159] 4.1.3: Obtaining the spatial rotation matrix R1:

[0160] The Rodriguez rotation equation is established as shown in equation (6):

[0161]

[0162] Define the unit vector of the rotation axis The cross product matrix is Equation (6) can be transformed into matrix form as shown in equation (7):

[0163]

[0164] Then the rotation matrix R1 is:

[0165]

[0166] in:

[0167] E 3×3 It is a third-order identity matrix. Unit vector of rotation axis The cross product matrix.

[0168] 4.2: Obtaining the spatial rotation matrix R2:

[0169] Construct a spatial vector from the center points P1 and P2 in coordinate system O1.

[0170] Construct a spatial vector from the center points Q1 and Q2 in coordinate system O2.

[0171] Obtain the spatial vector using the same method as in step 4.1. and space vectors The rotation matrix R2 between them.

[0172] Verify the calibration accuracy as follows:

[0173] The curved surface is measured n times using a white light interferometer. The measurement data are then stitched together to obtain the dataset W in coordinate system O1 for the n measurements. sum ;

[0174] The curved surface within the scanning area of ​​the white light interferometer was measured using a micro-nano coordinate measuring machine, and a dataset P containing m measurement points in coordinate system O2 was obtained. sum ;

[0175] The dataset in coordinate system O2 is P, defined by translation matrix T and rotation matrix R. sum The dataset W′ converted to coordinate system O1 is:

[0176]

[0177] in: For Kronecker product;

[0178] For each point in dataset W′, retrieve its representation in dataset W. sum The closest points in the matrix are paired as corresponding points. The residual matrix V between all corresponding points is calculated as follows:

[0179]

[0180] Elements V in the residual matrix V 1i V 2i V 3i Let i represent the residuals of each pair of corresponding points in the X, Y, and Z directions, respectively, i = 1, 2, 3…m;

[0181] The calculated root mean square residual (RMSR) is:

[0182]

[0183] The root mean square residual (RMSR) is used as the basis for evaluating the error of coordinate unification. The larger the RMSR value, the lower the accuracy of coordinate unification, and vice versa.

[0184] This invention can be used in coordinate unification in multi-sensor combined measurements using micro-nano coordinate measuring machines and white light interferometers, providing a prerequisite for achieving high-precision composite measurements, and providing a method for verifying the accuracy of coordinate unification.

Claims

1. A unified calibration method for the coordinates of a micro-nano multi-sensor measuring machine, wherein the micro-nano multi-sensor measuring machine is a combination of a coordinate measuring machine and an interferometer, wherein the coordinate measuring machine is a micro-nano coordinate measuring machine and the interferometer is a white light interferometer, characterized in that: a calibrator is set, which consists of two cylinders of equal size fixedly set on the same plane, each cylinder containing two different measuring surfaces, namely a cylindrical surface as a calibration elevation (2) and an upper cylindrical surface as a calibration end face (3), wherein each calibration end face (3) has at least two trace lines (4) passing through the center point, the trace lines (4) dividing the calibration end face equally, and the trace lines (4) are concave or convex marks formed on the calibration end face (3); the calibration method is set according to the following steps: Step 1: Denote the interferometer coordinate system O1-XYZ as coordinate system O1. Use the interferometer to measure the calibration end face (3) to obtain the interferometer measurement data for the calibration end face (3) and the trace line (4). Use the interferometer measurement data to fit and obtain the spatial plane equations A1 and A2 of the calibration end face (3) of the two cylinders in coordinate system O1, and obtain the set of spatial straight line equations B1 and B2 of the trace line (4) of the two cylinders in coordinate system O1. By calculating the intersection of the straight lines, obtain the center point of the calibration end face of the two cylinders in coordinate system O1. and center point Step 1 is performed as follows: 1.1: An interferometer was used to measure the calibration end faces (3) of the two cylinders in the calibrator respectively, and a set of three-dimensional point cloud data of each calibration end face (3) was obtained one by one; 1.2: For one of the cylinders, the best plane equation is fitted using its three-dimensional point cloud data to obtain the spatial plane equation A1 of its calibrated end face (3) in coordinate system O1 as shown in equation (1), and the normal vector of the spatial plane equation A1 is obtained. As shown in equation (2): （1）； （2）； in: All are coefficients of the spatial plane equation A1; X0, Y0 and Z0 represent the variables of the plane equation A1 under coordinate system O1; Using the trace lines (4) data in its three-dimensional point cloud data, spatial straight line equations are fitted to obtain a set of spatial straight line equations B1 in coordinate system O1. The intersection points of the trace lines in the set of spatial straight line equations B1 are obtained by simultaneous calculation. The intersection points are the center points. ,by( () indicates the center point The spatial coordinates in coordinate system O1 are: ; 1.3: For the other cylinder, obtain the center point using the same method as in step 1.

2. The coordinates, with ( () indicates the center point Spatial coordinates in coordinate system O1, i.e. ; Step 2: Denote the coordinate system O2-XYZ of the coordinate measuring machine as coordinate system O2. Use the coordinate measuring machine to measure the calibration elevation (2) and calibration end face (3) to obtain the coordinate measuring machine measurement data for the calibration elevation (2) and calibration end face (3). Use the coordinate measuring machine measurement data to fit and obtain the measurement surface space equation of the two cylinders in coordinate system O2. Use the measurement surface space equation to calculate the center point of the calibration end of the two cylinders in coordinate system O2. and center point Step 2 is performed as follows: 2.1: For one of the cylinders, the coordinate measuring machine measurement data is used for fitting to obtain the spatial plane equation C of the upper end face in coordinate system O2 represented by equation (3), the cylindrical equation D of the side elevation represented by equation (4), and the normal vector of the spatial plane equation C of the upper end face represented by equation (5). : （3）； （4）； （5）； in: All are coefficients of the spatial plane equation C, with X1, Y1, and Z1 representing the variables of the plane equation C in coordinate system O2; and X2, Y2, and Z2 representing the variables of the cylinder equation D in coordinate system O2; Points on the axis of the cylinder The coordinates, that is: ;by Characterizing the axis vector of the cylinder ,Right now: ; Let C be the radius of the cylinder; by solving the spatial plane equation C and the side elevation cylinder equation D, the center point Q1 is obtained; the point on its axis is obtained from the side elevation cylinder equation D. and the ray vector of the cylinder axis , constructing a point The axis of the cylinder from which the ray originates. The parametric equation is: ； in: It is a constant, and ;according to Different values ​​of the ray yield different points on the ray, and the ray along the axis of the cylinder is combined with the ray. Solving the equation C of the space plane The intersection point is obtained, and the intersection point is the center point. ,by Indicates the center point Spatial coordinates in coordinate system O2, i.e.: ; 2.2: For the other cylinder, obtain the center point using the same method as in step 2.

1. The coordinates, with Indicates the center point Spatial coordinates in coordinate system O2, i.e.: ; Step 3: Using the center point and center point Obtain the translation matrix between coordinate systems O1 and O2. ; Step 4: From the center point in coordinate system O1 Construct a spatial vector belonging to coordinate system O1 using the calibration end face normal vector. From the center point of coordinate system O2 Construct a spatial vector belonging to coordinate system O2 using the calibration end face normal vector. Using the space vector and Construct the Rodrigues rotation equations and solve for the spatial rotation matrix of the rotational degrees of freedom in the X and Y directions between constrained coordinate systems O1 and O2. From the center point in coordinate system O1 and Construct a spatial vector belonging to coordinate system O1 From the center point in coordinate system O2 and Construct a spatial vector belonging to coordinate system O2 Using spatial vectors and Construct the Rodrigues rotation equations and solve for the spatial rotation matrix of the rotational degrees of freedom in the Z-axis direction between constrained coordinate systems O1 and O2. Then, the spatial rotation matrix between coordinate systems O1 and O2 is... R for: ; Step 5: Based on the translation matrix and spatial rotation matrix Unify coordinates by unifying coordinate system O2 into coordinate system O1.

2. The micro / nano-scale multi-sensor measurement machine coordinate unified calibration method according to claim 1, characterized in that: step 3 is performed according to the following process: based on the center point coordinates ( ) and center point coordinates Find the coordinate difference between two points This yields the translation matrix between coordinate systems O1 and O2. ; for the center point and center point Introducing homogenized coordinates respectively and will Set it to 1, and construct the translation matrix accordingly. T for: ； in: , , .

3. The micro / nano-scale multi-sensor measurement machine coordinate unified calibration method according to claim 2, characterized in that: Step 4 is performed as follows: 4.1: Obtain the spatial rotation matrix : From the center point of coordinate system O1 and normal vector Determine spatial vectors The space vector Based on the center point Starting from the normal vector Its direction; In coordinate system O2, from the center point and normal vector Determine spatial vectors The space vector Based on the center point Starting from the normal vector Its direction; According to spatial vectors and Construct the Rodriguez rotation equation and solve for the rotation matrix. To obtain spatial vectors , Spatial correspondence between them; 4.2: Obtain the spatial rotation matrix. : From the lower center point of coordinate system O1 and center point Constructing spatial vectors , ; From the center point of coordinate system O2 and center point Constructing spatial vectors , ; Obtain the spatial vector using the same method as in step 4.

1. and space vectors Rotation matrix between .

4. The method for unified coordinate calibration of a micro / nano-scale multi-sensor measuring machine according to claim 3, characterized in that, Step 4.1 is performed as follows: The center point of coordinate system O1 has been determined. for: normal vector for: ; And determine the center point under coordinate system O2. for: normal vector for: ; 4.1.1: Calculating Vectors with vector The axis of rotation between: The vectors are obtained by normalizing the vectors. unit vector , and vector unit vector : ， ； The unit vector is obtained by calculating the cross product. and rotation axis vector , Rotate the axis vector Standardization yields the unit vector of the rotation axis. ; 4.1.2: Calculating Vectors and Inter-rotation angle cosine value for: ； 4.1.3: Obtain the spatial rotation matrix. The Rodriguez rotation equation is established as shown in equation (6): (6)； Define the unit vector of the rotation axis The cross product matrix is Equation (6) can be transformed into matrix form as shown in equation (7): (7)； Then the rotation matrix for: ； in: It is a third-order identity matrix. Unit vector of rotation axis The cross product matrix.

5. The method for unified coordinate calibration of a micro / nano-scale multi-sensor measuring machine according to claim 1, characterized in that: Verify the calibration accuracy as follows: (1) Using an interferometer to examine the curved surface The measurement data is then stitched together to obtain... Dataset in coordinate system O1 of the second measurement ; (2) Use a coordinate measuring machine to measure the curved surface within the scanning area of ​​the interferometer to obtain the data containing... The dataset under coordinate system O2 for each measurement point is as follows: ; (3) Using translation matrix and rotation matrix The dataset in coordinate system O2 is Convert the dataset to coordinate system O1 for: ； in: For Kronecker product; (4) For the dataset Retrieving each point in the dataset The closest points in the matrix are paired up to form corresponding points, and the residual matrix between all corresponding points is calculated. for: ； residual matrix elements in These represent the residuals of each pair of corresponding points in the X, Y, and Z directions, respectively. i =1,2,3…m; (5) Calculate the root mean square of the residuals for: ； The root mean square of the residual As a basis for error assessment in coordinate unification, The larger the value, the lower the coordinate unification accuracy, and vice versa.

Images