Coordinate unified calibrator and calibration method for micro-nanoscale composite measurement

Abstract

The present invention discloses a coordinate unified calibrator and calibration method for micro-nano composite measurement. A micro-nano three-coordinate machine and a white light interferometer are used for composite measurement. The calibrator is set as a triangular prism body with four measuring surfaces that are all planes. The three-coordinate machine and the interferometer are used to measure the four measuring surfaces respectively, and the coordinates of each vertex on the upper end face of the triangular prism body are fitted. The unit quaternion method is used to process the coordinates of each vertex to achieve the unification of the coordinate system of the three-coordinate machine and the interferometer. The calibrator of the present invention has simple geometric features, and the plane processing accuracy can be guaranteed. The calibrator of the present invention not only solves the problem that the existing calibrator is not suitable for the calibration of the micro-nano composite measurement system, but also fully reflects the Z-direction accuracy of the white light interferometer and gives full play to the advantages of the micro-nano three-coordinate measuring machine and the white light interferometer in being suitable for measuring planes, effectively ensuring the coordinate unified accuracy.

Description

Technical Field

[0001] The present invention relates to a coordinate unified calibrator and a calibration method for micro-nano composite measurement, and more specifically to a coordinate unified calibrator and a calibration method for micro-nano composite measurement using a micro-nano three-coordinate measuring machine and a white light interferometer. Background Art

[0002] With the continuous improvement of the level of scientific and technological development, the requirements for workpiece accuracy and measurement efficiency in the fields of aerospace, precision manufacturing and military industry are constantly increasing, so people have put forward higher requirements for measurement technology. The use of a single sensor measurement system can no longer fully meet the needs of society in terms of measurement accuracy and work efficiency. Multi-sensor combined measurement has emerged, which has the advantages of flexibility in the joint use of multiple probes, increased measurement space dimensions, improved accuracy and stability of the measurement system, and increased measurement range. For example, when measuring micro parts with holes or grooves, a white light interferometer can be used to scan the surface of the micro parts, and a micro-nano three-coordinate measuring machine can perform precise measurements of the holes or grooves while roughly measuring the surface. Finally, high-precision coordinate measurement data of micro parts can be obtained through coordinate unification.

[0003] The existing multi-sensor integrated measurement systems can be divided into two categories: one is the multi-vision sensor integrated system, and the other is the vision sensor and contact sensor integrated system. Among them, the measurement results of the multi-vision sensor integrated system are still the data output by the vision sensor, so it cannot solve the problems of low accuracy and large amount of measurement data in the vision sensor measurement process. The measurement accuracy of the existing vision sensor and contact sensor integrated system is mostly no more than 5 microns, which is used to measure relatively large workpieces. The horizontal size is usually greater than 20mm×20mm. For micro parts with geometric features such as deep holes, curved surfaces, grooves and bosses, the measurement accuracy is usually required to be nanometer level, but the existing combined measurement system cannot meet this accuracy requirement.

[0004] There are already micro-nano coordinate measuring machines with a resolution of 1nm and white light interferometers with a vertical resolution of 0.1nm. Both micro-nano coordinate measuring machines and white light interferometers can measure the size and morphology of ultra-precision machining surfaces, micro-components, and micro-electromechanical systems, but white light interferometers cannot be used to measure deep holes or grooves, and the measurement efficiency of micro-nano coordinate measuring machines is far inferior to that of white light interferometers. Therefore, the combination of micro-nano coordinate measuring machines and white light interferometers complements each other and is used to measure tiny and complex parts with horizontal dimensions less than 20mm×20mm, realizing micro-nano composite measurement, which can solve the problems of measurement accuracy and efficiency of existing systems.

[0005] How to design a standard to unify the coordinate systems of each sensor directly affects the accuracy of the part reconstruction model. The coordinate unification of multiple sensors usually uses a certain geometric feature calibrator or a combination of multiple geometric features, such as the commonly used standard sphere and cylinder, frustum, and sphere. However, in high-precision micro-nano composite measurements, the use of a standard sphere as a calibrator is insufficient: when the angle between the white light interferometer probe and the measuring surface exceeds a certain value, the probe will lose its ability and can only measure a small area on the top of the standard sphere, thus losing the Z-axis display performance, and the white light interferometer should most display the measurement advantage of the Z-axis. At the same time, the processing of tiny spheres is also very difficult, and their roundness cannot be guaranteed. There are designs of a combined calibrator that processes a coaxial truncated table on a cylinder and a combined calibrator that installs standard balls and standard circles at the four corners of the base, but they have errors in coaxiality, roundness, cylindricity and spatial measurement, and each sensor cannot guarantee the same point of measurement. The geometric features are not suitable for the measurement of white light interferometers. Therefore, these two combined calibrators are not suitable for the coordinate unification of micro-nano composite measurement systems. So far, there has been no public report on a calibrator for unifying the coordinate system of micro-nano coordinate measuring machines and white light interferometers.

[0006] In the composite measurement at the micro-nano level, there are many problems to be solved, such as how to unify the coordinate systems of the micro-nano three-dimensional coordinate measuring machine and the white light interferometer into one coordinate system with high precision; how to solve the inadaptability of the white light interferometer in measuring the traditional standard ball and the inherent error of the combined calibrator; how to provide the best measurement object for the micro-nano three-dimensional coordinate measuring machine and the white light interferometer, etc. Summary of the invention

[0007] The present invention aims to avoid the deficiencies of the above-mentioned prior art and to provide a unified coordinate calibrator and calibration method for micro-nano composite measurement, so as to realize micro-nano high-precision composite measurement of a micro-nano three-coordinate measuring machine and a white light interferometer.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The present invention provides a unified coordinate calibrator for micro-nano composite measurement, wherein the micro-nano composite measurement refers to composite measurement using a three-coordinate machine and an interferometer, wherein the three-coordinate machine is a micro-nano three-coordinate measuring machine, and the interferometer is a white light interferometer;

[0010] The coordinate unified calibrator for micro-nano-level composite measurement of the present invention is characterized in that: the calibrator is set as a triangular prism body, and is made of a quartz block suitable for interferometer measurement; the triangular prism body is formed with four measuring surfaces, namely the upper end surface of the triangular prism body and the three side surfaces of the triangular prism body; the three side surfaces are respectively: a first side surface, a second side surface and a third side surface.

[0011] The unified coordinate calibrator for micro-nanoscale composite measurement of the present invention is also characterized in that: by setting the sizes of the four measuring surfaces in the triangular prism body, the four measuring surfaces of the triangular prism body can be completely measured in both the three-coordinate machine and the interferometer; by setting the angles between the three side surfaces and the bottom surface of the triangular prism body, the sizes of the angles between the three side surfaces and the bottom surface of the triangular prism body are within the angle range of the interferometer measurement.

[0012] The unified coordinate calibrator for micro-nanoscale composite measurement of the present invention is also characterized in that the flatness errors of the four measuring surfaces of the triangular prism body are all no greater than 2 microns.

[0013] The coordinate unified calibrator for micro-nano-level composite measurement of the present invention is also characterized in that a triangular prism is integrally supported at the bottom of the triangular prism body, and the triangular prism serves as the calibrator base. The weight of the triangular prism serving as the calibrator base is utilized to keep the relative position of the calibrator unchanged when being measured.

[0014] The coordinate unified calibration method for micro-nano composite measurement of the present invention is characterized in that the coordinate unified calibrator for micro-nano composite measurement is used for calibration in the following method: a three-coordinate machine and an interferometer are used to measure the four measuring surfaces of the triangular prism respectively to obtain measurement data; the measurement data are used for fitting to obtain fitting equations of the four measuring surfaces respectively; the three vertex coordinates of the upper end surface of the triangular prism are obtained according to the fitting equations of the four measuring surfaces; the three vertex coordinates obtained by measuring and fitting by the three-coordinate machine and the three vertex coordinates obtained by measuring and fitting by the interferometer are used to obtain three pairs of corresponding point coordinates of the three vertices, and the unit quaternion method is used to process the three pairs of corresponding point coordinates to achieve the unification of the two coordinate systems, that is, the unification of the coordinate systems of the three-coordinate machine and the interferometer is achieved.

[0015] The coordinate unified calibration method for micro-nano composite measurement of the present invention is carried out according to the following steps:

[0016] Step 1: Use a three-coordinate machine and an interferometer to measure the calibrator as follows:

[0017] Measurement 1: The spatial rectangular coordinate system of the three-coordinate machine is recorded as O-XYZ. The upper end surface of the triangular prism is measured by the three-coordinate machine. Nine measuring points are set, and the nine measuring points are evenly distributed on three parallel straight lines on the upper end surface. Each measuring point is recorded as P. n , with P n (X n ,Y n ,Z n ) Characterization point P n Coordinates of, n = 1, 2…9;

[0018] Measurement 2: Use a three-coordinate machine to measure the three sides of the triangular prism one by one in the same way as measurement 1; set 9 measuring points on each side, each measuring point is marked as P in , with P in (X in ,Y in ,Z in ) Characterization point P in , and i=1, 2, 3 represent the first side surface, the second side surface and the third side surface in sequence;

[0019] Thus, a first array of four measurement surfaces measured by a three-coordinate machine is obtained;

[0020] Measurement 3: The spatial rectangular coordinate system of the interferometer is recorded as o-xyz; the upper end face of the triangular prism is measured using the interferometer for a total of 9 times. The central coordinates of all the data in each measurement are evenly distributed on three parallel straight lines on the upper end face. The point cloud data set of each measurement is recorded as W n , n=1,2…9;

[0021] Measurement 4: Use the interferometer to measure the three sides of the triangular prism one by one in the same way as measurement 3. Each side is measured 9 times. The point cloud data set of each measurement is recorded as W in , and i=1, 2, 3 represent the first side surface, the second side surface and the third side surface in sequence;

[0022] Thus, a second array of four measurement surfaces measured by the interferometer is obtained;

[0023] Step 2: Fit the plane equations of the four measurement surfaces;

[0024] The first arrays of the four measuring surfaces are used for equation fitting to obtain the first parameter equations of the four measuring surfaces in the three-coordinate machine coordinate system O-XYZ represented by equation (1):

[0025] Z=aX+bY+c (1)

[0026] a, b and c are the fitting coefficients of each parameter equation in the first parameter equation group;

[0027] The coordinate values ​​of the three vertices of the upper end surface of the triangular prism in the coordinate system O-XYZ are calculated using the first parametric equation group and recorded as first coordinate values;

[0028] The second arrays of the four measuring surfaces are used to perform equation fitting, and the second parameter equations of the four measuring surfaces in the interferometer coordinate system o-xyz represented by equation (2) are obtained respectively:

[0029] z=dx+ey+f (2)

[0030] d, e and f are the fitting coefficients of each parameter equation in the second parameter equation group;

[0031] The coordinate values ​​of the three vertices of the upper end surface of the triangular prism in the coordinate system o-xyz are calculated by using the second parameter equation group, and recorded as the second coordinate values;

[0032] Step 3: Take three pairs of corresponding points in the first coordinate value and the second coordinate value as standard points for coordinate unification;

[0033] The standard point coordinates of the three standard points in the first coordinate value are marked as P j , P j =P j (X j , Y j , Z j );

[0034] The standard point coordinates of the three standard points in the second coordinate value are marked as W j , W j =W j (x j ,y j , z j );

[0035] The three standard points are represented by j=1, 2, 3 in one-to-one correspondence;

[0036] Step 4: Using the one-to-one corresponding three pairs of standard point coordinates, the unit quaternion method is used to solve the rotation matrix R and translation matrix T between the three-coordinate machine space rectangular coordinate system O-XYZ and the interferometer space rectangular coordinate system o-xyz, so as to unify the coordinates of the three-coordinate machine and the interferometer and complete the calibration.

[0037] The characteristic of the coordinate unified calibration method for micro-nanoscale composite measurement of the present invention is also that the rotation matrix R and the translation matrix T are obtained according to the following steps:

[0038] Step 7.1: Construct unit quaternion;

[0039] The unit quaternion q consists of a real part and three imaginary parts, as represented by formula (3):

[0040] q=q0+q1u+q2v+q3w (3)

[0041] In formula (3), q0, q1, q2 and q3 are all real numbers and satisfy formula (4):

[0042]

[0043] u, v and w are imaginary units and satisfy equation (5):

[0044]

[0045] Follow steps 7.2 to 7.5 to solve and obtain the optimal unit quaternion, thereby obtaining the rotation matrix R;

[0046] Step 7.2: Calculate the centroid coordinates of the three standard points in the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz respectively:

[0047] The coordinates of the three standard points P in the three-coordinate machine coordinate system O-XYZ are calculated by formula (6): j The centroid coordinates ρ P :

[0048]

[0049] The coordinates W of the three standard points in the interferometer coordinate system o-xyz are calculated by formula (7): j The barycentric coordinates p W :

[0050]

[0051] Step 7.3: Construct the covariance matrix R(c) according to formula (8):

[0052]

[0053] In formula (8), T represents the transpose of the matrix;

[0054] Step 7.4: Construct a 4×4 symmetric matrix R(q) from the covariance matrix R(c) as shown in formula (9):

[0055]

[0056] In formula (9):

[0057] tr(R(c)) is the trace of the covariance matrix R(c);

[0058] I3 is a 3×3 unit matrix; Δ is a matrix represented by equation (10):

[0059] Δ=[A 23 A 31 A 12 ] (10)

[0060] A st represents the element in the s-th row and t-th column of matrix A, s,t=1,2,3;

[0061] The matrix A is constructed from the covariance matrix R(c). The elements A of the matrix A are st It is represented by formula (11):

[0062] Ast =(R(c)-R(c) T ) st (11)

[0063] Step 7.5: Calculate the eigenvalues ​​and eigenvectors of the symmetric matrix R(q). The eigenvector corresponding to the maximum eigenvalue in the symmetric matrix R(q) is the optimal unit quaternion.

[0064] Then the rotation matrix R is represented by equation (12):

[0065]

[0066] In formula (12):

[0067] R 12 =2(q1q2-q0q3); R 13 =2(q1q3+q0q2);

[0068] R 21 =2(q1q2+q0q3); R 23 =2(q2q3-q0q1);

[0069] R 31 =2(q1q3-q0q2); R 32 =2(q2q3+q0q1);

[0070] Then the translation matrix T is represented by equation (13):

[0071] T=ρ P -Rρ W (13)

[0072] According to the rotation matrix R and the translation matrix T, the positional relationship between the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz is obtained, thereby completing the coordinate unification of the three-coordinate machine and the interferometer, that is, completing the calibration.

[0073] The characteristic of the coordinate unified calibration method for micro-nano composite measurement of the present invention is also to verify the calibration accuracy according to the following steps:

[0074] Step 8.1: Get measurement data:

[0075] Set the area C1 in the surface B as the measured area, and the size of the area C1 is equal to the size of the interferometer's one-time measurement range;

[0076] The region C1 is measured using an interferometer to obtain an interferometer measurement data set W for the region C1. C1 ;

[0077] The three coordinate machine is used to measure the three measuring points evenly distributed in the area C1 respectively, and the three coordinate machine measurement data set P about the three measuring points is obtained. C1 ;

[0078] Step 8.2, get the conversion data:

[0079] The interferometer measurement data set W is transformed using the rotation matrix R and the translation matrix T. C1 Convert to the coordinate system O-XYZ of the three-coordinate machine to obtain the interferometer conversion data set W under the coordinate system O-XYZ CC1 ;

[0080] Step 8.3: Calculate the residual value

[0081] The interferometer transformation data set W CC1 The coordinate machine measurement data set P C1 The points whose measured data are closest to each other are regarded as corresponding points, and the residual value V between corresponding points is calculated according to formula (14): 3×3 :

[0082]

[0083] g represents the number of measuring points of the three-dimensional coordinate machine, g = 1, 2, 3; V 1g represents the X-direction residual of the g-th pair of corresponding points;

[0084] V 2g represents the Y-direction residual of the g-th pair of corresponding points, V 3g represents the Z-direction residual of the g-th pair of corresponding points;

[0085] Step 8.4, calculate the residual root mean square:

[0086] The residual root mean square RMSR1 of a measurement is calculated according to formula (15):

[0087]

[0088] Step 8.5: Follow the same method as steps 8.1 to 8.4 to correct the area C in surface B. K Continue to measure and obtain the residual root mean square RMSRk, k = 2, 3, ..., 10; calculate the mean RMSR of the sum of the residual root mean squares of 10 measurements according to formula (16):

[0089]

[0090] If the mean value RMSR of the root mean square sum of the residuals does not exceed the set value, it means that the calibration method meets the accuracy requirements of micro-nano composite measurement.

[0091] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0092] 1. The geometric features of the calibrator of the present invention are simple, and the plane processing accuracy can be guaranteed. There are no errors in coaxiality, roundness, cylindricity and space measurement of the combined calibrator composed of cylinders, spheres, frustums and standard circles, and there is no inadaptability problem of traditional calibrators such as white light interferometer measurement of standard spheres;

[0093] 2. The flatness error of each measuring surface in the calibrator of the present invention is less than 2 microns. When using a white light interferometer to measure the side of a prism with a small inclination angle, the Z-direction accuracy of the white light interferometer (its Z-direction resolution is 0.1nm) can be fully utilized to compensate for the accuracy in the X and Y directions, thereby improving the measurement accuracy of the three standard points; at the same time, the plane is the best measurement object for the white light interferometer. Similarly, the micro-nano coordinate measuring machine is also very effective in measuring planes. The calibrator of the present invention not only solves the problem that the existing calibrator is not suitable for calibration of micro-nano composite measurement systems, but also fully reflects the Z-direction accuracy of the white light interferometer and gives play to the advantages of the micro-nano coordinate measuring machine and the white light interferometer in measuring planes, effectively ensuring the unified accuracy of coordinates.

[0094] 3. The present invention is based on the premise that a single sensor has been calibrated, that is, it can independently complete the measurement of the workpiece, and use a calibrator to realize the coordinate system of contact sensors and non-contact sensors in pairs or in pairs of more than two. The method is simple and the efficiency of coordinate unification is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 This is a flow chart of the calibration method in the present invention;

[0096] Figure 2 It is a schematic diagram of the three-dimensional structure of the calibrator in the present invention;

[0097] Figure 3 It is a schematic diagram of the top view structure of the calibrator in the present invention;

[0098] Figure 4 It is a schematic diagram of the main structure of the calibrator in the present invention;

[0099] Figure 5 It is a schematic diagram of the side view structure of the calibrator in the present invention;

[0100] Figure 6 This is a schematic diagram of the measurement of the micro-nano coordinate measuring machine in the present invention;

[0101] Figure 7 It is a schematic diagram of the measurement of the white light interferometer in the present invention;

[0102] Numbers in the figure: 1 triangular prism, 2 triangular prism, 3 upper end surface, 4 first side surface, 5 second side surface, 6 third side surface, 7 three-coordinate machine Z axis, 8 three-coordinate machine X axis, 9 calibrator, 10 workbench, P is the three-coordinate machine probe, 11 interferometer Z axis, W is the interferometer probe; DETAILED DESCRIPTION

[0103] In this embodiment, the micro-nano composite measurement refers to composite measurement using a three-coordinate machine and an interferometer, wherein the three-coordinate machine is a micro-nano three-coordinate measuring machine, and the interferometer is a white light interferometer.

[0104] See also Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 In this embodiment, the coordinate unified calibrator for micro-nanoscale composite measurement is a triangular prism body 2, which is made of a quartz block suitable for interferometer measurement; the triangular prism body 2 has four measuring surfaces, namely the upper end surface 3 of the triangular prism body 2 and the three side surfaces of the triangular prism body 2; the three side surfaces are: a first side surface 4, a second side surface 5 and a third side surface 6; by setting the sizes of the four measuring surfaces in the triangular prism body 2, the four measuring surfaces of the triangular prism body 2 can be completely measured in both the three-coordinate machine and the interferometer; by setting the angle between the three side surfaces and the bottom surface of the triangular prism body 2 to be less than 10 degrees, the three side surfaces of the triangular prism body 2 can meet the angle measurement limit of the inclined surface in the interferometer; the flatness errors of the four measuring surfaces of the triangular prism body 2 are all set to be no more than 2 microns. The smaller the flatness error, the better the quality of the measurement data, thereby obtaining a higher calibration accuracy.

[0105] like Figure 2 As shown, in this embodiment, a triangular prism body 1 is integrally supported at the bottom of the triangular prism body 2, and the triangular prism body 1 is used as the base of the calibrator. The weight of the triangular prism body 1 as the base of the calibrator is used to keep the relative position of the calibrator unchanged when being measured.

[0106] In this embodiment, the following unified coordinate calibration method is provided for micro-nanoscale composite measurement:

[0107] The four measuring surfaces of the triangular prism body 2 are measured respectively by using a three-coordinate machine and an interferometer to obtain measurement data; the measurement data are used for fitting to obtain fitting equations of the four measuring surfaces respectively; the three vertex coordinates of the upper end surface 3 of the triangular prism body 2 are obtained according to the fitting equations of the four measuring surfaces;

[0108] The three pairs of corresponding point coordinates of the three vertices are obtained by using the three vertex coordinates obtained by measuring and fitting with a three-coordinate machine and the three vertex coordinates obtained by measuring and fitting with an interferometer. The three pairs of corresponding point coordinates are processed using the unit quaternion method to achieve the unification of the two coordinate systems, that is, the unification of the coordinate systems of the three-coordinate machine and the interferometer.

[0109] Based on the measurement range of the coordinate machine, the measurement range of the interferometer, the processing difficulty and the processing price, the range of each edge of the bottom surface of the triangular prism body 2 can be set to 20 to 80 mm, the range of each edge of the upper end surface 3 of the triangular prism body 2 can be set to 4 to 16 mm, and the angle between each side surface and the bottom surface of the triangular prism body 2 can be set to 0 to 10 degrees.

[0110] See also Figure 1 , the calibration method in this embodiment is performed as follows:

[0111] Step 1: Use a three-coordinate machine and an interferometer to measure the calibrator as follows:

[0112] Measurement 1: The spatial rectangular coordinate system of the three-coordinate machine is recorded as O-XYZ, such as Figure 6 As shown, the calibrator 9 is placed on the workbench 10, the three-dimensional coordinate machine is first reset to zero, and then the three-dimensional coordinate machine probe P is aligned with the upper end surface 3 of the triangular prism body 2 by moving the three-dimensional coordinate machine X-axis 8, the three-dimensional coordinate machine Z-axis 7 and the three-dimensional coordinate machine Y-axis. Then, the three axes of the three-dimensional coordinate machine are adjusted to measure the upper end surface 3 of the triangular prism body 2. The upper end surface 3 is a processed high-precision plane. In order to improve the accuracy of the measuring point fitting plane, 9 measuring points are set with reference to the number of measuring points and the distribution of measuring points recommended by the British standard BS7172, and the 9 measuring points are evenly distributed on three parallel straight lines in the upper end surface 3. Each measuring point is recorded as P n , with P n (X n ,Y n ,Z n ) Characterization point P n Coordinates of, n = 1, 2…9;

[0113] Measurement 2: Use a three-coordinate machine to measure the three sides of the triangular prism 2 one by one in the same way as in Measurement 1; set 9 measuring points on each side, each measuring point is denoted by P in , with P in (X in ,Y in ,Z in ) Characterization point P inThe coordinates of the first side surface 4, the second side surface 5 and the third side surface 6 are represented by i=1, 2, 3 in sequence. The four measuring surfaces are all high-precision planes. The three-coordinate machine has good performance in the process of measuring the planes. Thus, the first array of four measuring surfaces measured by the three-coordinate machine is obtained;

[0114] Measurement 3: The spatial rectangular coordinate system of the interferometer is recorded as o-xyz, such as Figure 7 As shown, the interferometer is first reset to zero. Each time a measurement is performed, the interferometer workbench and the interferometer Z axis 12 are adjusted to align the interferometer probe W with the upper end surface 3 of the triangular prism body 2. Then, the interference fringes are found by adjusting the interferometer Z axis 12. The scanning range is set to scan and measure the upper end surface 3 of the triangular prism body 2. The upper end surface 3 is a high-precision plane. In order to improve the accuracy of the measurement point fitting plane, the number of measurement points and the distribution of measurement points recommended by the British standard BS7172 are referred to. A total of 9 measurements are performed. Each time the center coordinates of all the data are evenly distributed on three parallel straight lines in the upper end surface 3. The point cloud data set of each measurement is recorded as W. n , n=1,2…9;

[0115] Measurement 4: Use the interferometer to measure the three sides of the triangular prism 2 one by one in the same way as in measurement 3. When the interferometer measures the three sides that form an 8-degree angle with the bottom surface of the triangular prism 2, its Z-direction accuracy can be fully utilized to improve the accuracy of the measuring points. Each side is measured 9 times, and the point cloud data set of each measurement is recorded as W in , and i=1, 2, 3 are used to represent the first side surface 4, the second side surface 5 and the third side surface 6 in sequence, the four measuring surfaces are all high-precision planes, and the interferometer has good performance in the process of measuring the planes; thereby obtaining the second array of four measuring surfaces measured by the interferometer;

[0116] Step 2: Fit the plane equations of the four measurement surfaces;

[0117] The first arrays of the four measuring surfaces are used for equation fitting to obtain the first parameter equations of the four measuring surfaces in the three-coordinate machine coordinate system O-XYZ represented by equation (1):

[0118] Z=aX+bY+c (1)

[0119] a, b and c are the fitting coefficients of each parameter equation in the first parameter equation group;

[0120] In this embodiment, the bottom surface of the triangular prism body 2 is set to be an equilateral triangle with a side length of 50 mm, and the angle between each side surface and the bottom surface of the triangular prism body 2 is set to 8 degrees. Then, the first parameter equation group of the four measuring surfaces under the three-coordinate machine coordinate system O-XYZ represented by equation (1) is equation (1.1), equation (1.2), equation (1.3) and equation (1.4):

[0121] Z = 2.4266 × 10 -4 X-4.6280×10 -4 Y-8.218463 (1.1)

[0122] Z=-1.1950×10 -1 X-6.9810×10 -2 Y-2.296533 (1.2)

[0123] Z=1.2021×10 -1 X-6.9901×10 -2 Y-16.393592 (1.3)

[0124] Z=4.5702×10 -4 X+1.3740×10 -1 Y-4.859813 (1.4)

[0125] Among them, formula (1.1), formula (1.2), formula (1.3) and formula (1.4) correspond one by one to represent the fitting equations of the upper end surface 3, the first side surface 4, the second side surface 5 and the third side surface 6.

[0126] The coordinate values ​​of the three vertices of the upper end surface 3 of the triangular prism body 2 in the coordinate system O-XYZ are calculated using the first parametric equation group and recorded as the first coordinate values;

[0127] The second arrays of the four measuring surfaces are used to perform equation fitting, and the second parameter equations of the four measuring surfaces in the interferometer coordinate system o-xyz represented by equation (2) are obtained respectively:

[0128] z=dx+ey+f (2)

[0129] d, e and f are the fitting coefficients of each parameter equation in the second parameter equation group;

[0130] In this embodiment, the second parameter equations of the four measuring surfaces in the interferometer coordinate system o-xyz represented by equation (2) are equations (2.1), (2.2), (2.3) and (2.4):

[0131] z = -8.3103 × 10 -4 x+6.9285×10 -3 y+12.475860 (2.1)

[0132] z=-1.1922×10 -1 x+7.8123×10 -2 y+17.022983 (2.2)

[0133] z=1.1884×10 -1 x+7.3209×10 -2 y+1.52070713 (2.3)

[0134] z=-2.6771×10 -3 x-1.2471×10 -1 y+19.751809 (2.4)

[0135] Among them, formula (2.1), formula (2.2), formula (2.3) and formula (2.4) correspond one by one to represent the fitting equations of the upper end surface 3, the first side surface 4, the second side surface 5 and the third side surface 6.

[0136] The coordinate values ​​of the three vertices of the upper end surface 3 of the triangular prism body 2 in the coordinate system o-xyz are calculated using the second parametric equation group and recorded as the second coordinate values;

[0137] Step 3: Take three pairs of corresponding points in the first coordinate value and the second coordinate value as standard points for coordinate unification;

[0138] In this embodiment, the coordinates P1, P2 and P3 of the three standard points in the first coordinate value obtained in step 2 are respectively:

[0139] P1(58.802679,-16.139934,-8.196724);

[0140] P2(53.994925, -24.446220, -8.194047);

[0141] P3(63.619767,-24.461186,-8.191704);

[0142] The coordinates W1, W2 and W3 of the three standard points in the second coordinate value obtained in step 2 are:

[0143] W1(66.068643, 45.996188, 12.739640);

[0144] W2(61.408037, 54.411023, 12.801815);

[0145] W3(71.047701, 54.275839, 12.792867);

[0146] The unit of coordinate value is mm; and: P1 and W1 are the corresponding standard point coordinates, P2 and W2 are the corresponding standard point coordinates, P3 and W3 are the corresponding standard point coordinates;

[0147] Step 4: Using the one-to-one corresponding three pairs of standard point coordinates, the unit quaternion method is used to solve the rotation matrix R and translation matrix T between the three-coordinate machine space rectangular coordinate system O-XYZ and the interferometer space rectangular coordinate system o-xyz, so as to unify the coordinates of the three-coordinate machine and the interferometer and complete the calibration.

[0148] There are many matrix transformation algorithms. Among the existing matrix transformation algorithms, the unit quaternion method has a slight advantage in performance over other algorithms. Therefore, the unit quaternion method is used to obtain the rotation matrix R and the translation matrix T in the following steps:

[0149] Step 7.1: Construct unit quaternion;

[0150] The unit quaternion q consists of a real part and three imaginary parts, as represented by formula (3):

[0151] q=q0+q1u+q2v+q3w (3)

[0152] In formula (3), q0, q1, q2 and q3 are all real numbers and satisfy formula (4):

[0153]

[0154] u, v and w are imaginary units and satisfy equation (5):

[0155]

[0156] Follow steps 7.2 to 7.5 to solve and obtain the optimal unit quaternion, thereby obtaining the rotation matrix R;

[0157] Step 7.2: Calculate the centroid coordinates of the three standard points in the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz respectively:

[0158] The coordinates of the three standard points P in the three-coordinate machine coordinate system O-XYZ are calculated by formula (6): j The centroid coordinates ρ P :

[0159]

[0160] The coordinates W of the three standard points in the interferometer coordinate system o-xyz are calculated by formula (7): j The barycentric coordinates p W :

[0161]

[0162] Step 7.3: Construct the covariance matrix R(c) according to formula (8):

[0163]

[0164] In formula (8), T represents the transpose of the matrix;

[0165] Step 7.4: Construct a 4×4 symmetric matrix R(q) from the covariance matrix R(c) as shown in formula (9):

[0166]

[0167] In formula (9):

[0168] tr(R(c)) is the trace of the covariance matrix R(c);

[0169] I3 is a 3×3 unit matrix; Δ is a matrix represented by equation (10):

[0170] Δ=[A 23 A 31 A 12 ] (10)

[0171] A st represents the element in the s-th row and t-th column of matrix A, s,t=1,2,3;

[0172] The matrix A is constructed from the covariance matrix R(c). The elements A of the matrix A are st It is represented by formula (11):

[0173] A st =(R(c)-R(c) T ) st (11)

[0174] Step 7.5: Calculate the eigenvalues ​​and eigenvectors of the symmetric matrix R(q). The eigenvector corresponding to the maximum eigenvalue in the symmetric matrix R(q) is the optimal unit quaternion.

[0175] Then the rotation matrix R is represented by equation (12):

[0176]

[0177] In formula (12):

[0178] R 12 =2(q1q2-q0q3); R 13 =2(q1q3+q0q2);

[0179] R 21 =2(q1q2+q0q3); R 23 =2(q2q3-q0q1);

[0180] R31 =2(q1q3-q0q2); R 32 =2(q2q3+q0q1);

[0181] Then the translation matrix T is represented by equation (13):

[0182] T=ρ P -Rρ W (13)

[0183] In this embodiment, the rotation matrix R and the translation matrix T calculated according to equation (12) and equation (13) are:

[0184]

[0185] T=[-6.471736 31.091881 4.241141]

[0186] According to the rotation matrix R and the translation matrix T, the positional relationship between the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz is obtained, thereby completing the coordinate unification of the three-coordinate machine and the interferometer, that is, completing the calibration.

[0187] In order to illustrate that the calibration method of the coordinate unified calibrator for micro-nano composite measurement meets the requirements of micro-nano composite measurement, the calibration accuracy is verified according to the following steps:

[0188] Step 8.1: Get measurement data:

[0189] Set the area C1 in the surface B as the measured area, and the size of the area C1 is equal to the size of the interferometer's one-time measurement range;

[0190] The interferometer is used to measure the area C1, and the interferometer measurement data set W of the area C1 is obtained. C1 ;

[0191] The three coordinate machine is used to measure the three measuring points evenly distributed in the area C1, and the three-coordinate machine measurement data set P of the three measuring points is obtained. C1 ;

[0192] Step 8.2, get the conversion data:

[0193] The interferometer measurement data set W is transformed using the rotation matrix R and the translation matrix T. C1 Convert to the coordinate system O-XYZ of the three-coordinate machine to obtain the interferometer conversion data set W under the coordinate system O-XYZ CC1 ;

[0194] Step 8.3, calculate the residual root mean square:

[0195] The interferometer transformation data set W CC1 The coordinate machine measurement data set P C1 The points whose measured data are closest to each other are regarded as corresponding points, and the residual value V between corresponding points is calculated according to formula (14): 3×3 :

[0196]

[0197] g represents the number of measuring points of the three-dimensional coordinate machine, g = 1, 2, 3; V 1g represents the X-direction residual of the g-th pair of corresponding points;

[0198] V 2g represents the Y-direction residual of the g-th pair of corresponding points, V 3g represents the Z-direction residual of the g-th pair of corresponding points;

[0199] Step 8.4, calculate the residual root mean square:

[0200] The residual root mean square RMSR1 of a measurement is calculated according to formula (15):

[0201]

[0202] Step 8.5: Follow the same method as steps 8.1 to 8.4 to correct the area C in surface B. K Continue to measure and obtain the residual root mean square RMSRk, k = 2, 3, ..., 10; multiple measurements are performed to obtain the mean RMSR of the sum of the root mean square of the residuals of each measurement, which can effectively reduce the accidental error. The mean RMSR of the sum of the root mean square of the residuals of 10 measurements is calculated according to formula (16):

[0203]

[0204] In this embodiment, the residual root mean square RMSR calculated by formula (16) is sub-micron level 0.0003 mm, and the calibration method meets the accuracy requirements of micro-nano composite measurement.

[0205] In order to conduct a more accurate calibration method accuracy verification experiment, the experiment uses area C on surface B. k The marking point is made of super high reflective material, and the size of each marking point is equal to the size of the interferometer's measurement range at one time.

[0206] The geometric features of the calibrator of the present invention are simple, and the plane processing accuracy can be guaranteed. There are no errors in the coaxiality, roundness, cylindricity and space measurement of the combined calibrator composed of cylinders, spheres, truncated cones and standard circles, and there is no problem of inadaptability of traditional calibrators such as white light interferometers measuring standard spheres. The flatness error of each measuring surface in the calibrator of the present invention is less than 2 microns. When using a white light interferometer to measure the side of a prism with a small inclination angle, the Z-direction accuracy of the white light interferometer (its Z-direction resolution is 0.1nm) can be fully utilized to compensate for the accuracy in the X and Y directions, thereby improving the measurement accuracy of the three standard points. At the same time, the plane is the best measurement object for the white light interferometer. Similarly, the micro-nano three-dimensional coordinate measuring machine is also very effective in measuring planes. The calibrator of the present invention not only solves the problem that the existing calibrator is not suitable for the calibration of micro-nano composite measurement systems, but also fully reflects the Z-direction accuracy of the white light interferometer and gives play to the advantages of the micro-nano three-dimensional coordinate measuring machine and the white light interferometer in measuring planes, effectively ensuring the unified accuracy of coordinates. The specific implementation case shows that the calibration method meets the requirements of micro-nano composite measurement.

[0207] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A coordinate unified calibration method for micro-nano composite measurement, characterized by: A coordinate unified calibrator for micro-nano composite measurement is provided. The micro-nano composite measurement refers to composite measurement using a three-coordinate machine and an interferometer. The three-coordinate machine is a micro-nano three-coordinate measuring machine, and the interferometer is a white light interferometer. The calibrator is characterized in that: the calibrator is a triangular prism body (2) made of a quartz block suitable for interferometer measurement; the triangular prism body (2) has four measuring surfaces, namely, an upper end surface (3) of the triangular prism body (2) and three side surfaces of the triangular prism body (2); the three side surfaces are: a first side surface (4), a second side surface (5 ) and a third side surface (6); by setting the sizes of the four measuring surfaces of the triangular prism body (2), the four measuring surfaces of the triangular prism body (2) can be completely measured in a three-coordinate machine and an interferometer; by setting the angles between the three side surfaces and the bottom surface of the triangular prism body (2), the sizes of the angles between the three side surfaces and the bottom surface of the triangular prism body (2) are within the angle range of interferometer measurement; the flatness errors of the four measuring surfaces of the triangular prism body (2) are all no greater than 2 microns; using the micro-nano composite measurement coordinate unified calibrator, calibration is performed according to the following method: A three-coordinate machine and an interferometer are used to measure the four measuring surfaces of the triangular prism (2) respectively to obtain measurement data; the measurement data are used to perform fitting to obtain fitting equations of the four measuring surfaces respectively; three vertex coordinates of the upper end surface (3) of the triangular prism (2) are obtained according to the fitting equations of the four measuring surfaces; three pairs of corresponding point coordinates of the three vertices are obtained by using the three vertex coordinates obtained by measuring and fitting the three-coordinate machine and the three vertex coordinates obtained by measuring and fitting the interferometer, and the three pairs of corresponding point coordinates are processed by the unit quaternion method to achieve the unification of the two coordinate systems, that is, to achieve the unification of the coordinate systems of the three-coordinate machine and the interferometer; the calibration method is performed according to the following steps: Step 1: Use a three-coordinate machine and an interferometer to measure the calibrator as follows: Measurement 1: The spatial rectangular coordinate system of the three-coordinate machine is recorded as O-XYZ. The upper end surface (3) of the triangular prism (2) is measured by the three-coordinate machine. Nine measuring points are set, and the nine measuring points are evenly distributed on three parallel straight lines in the upper end surface (3). Each measuring point is recorded as P. n , with P n (X n ,Y n ,Z n ) Characterization point P n Coordinates of, n = 1, 2…9; Measurement 2: Use a three-coordinate machine to measure the three sides of the triangular prism (2) one by one in the same way as in Measurement 1; set 9 measuring points on each side, each measuring point is denoted by P in , with P in (X in ,Y in ,Z in ) Characterization point P in , and i=1, 2, 3 represent the first side surface (4), the second side surface (5) and the third side surface (6) in sequence; Thus, a first array of four measurement surfaces measured by a three-coordinate machine is obtained; Measurement 3: The spatial rectangular coordinate system of the interferometer is recorded as o-xyz; the upper end surface (3) of the triangular prism (2) is measured by using the interferometer, and the measurement is performed 9 times in total. The central coordinates of all the data in each measurement are evenly distributed on three parallel straight lines in the upper end surface (3). The point cloud data set of each measurement is recorded as W n , n=1,2…9; Measurement 4: Using an interferometer, the three sides of the triangular prism (2) are measured one by one in the same way as in Measurement 3. Each side is measured 9 times. The point cloud data set of each measurement is recorded as W. in , and i=1, 2, 3 represent the first side surface (4), the second side surface (5) and the third side surface (6) in sequence; Thus, a second array of four measurement surfaces measured by the interferometer is obtained; Step 2: Fit the plane equations of the four measurement surfaces; The first arrays of the four measuring surfaces are used to perform equation fitting, and the first parameter equations of the four measuring surfaces under the three-coordinate machine coordinate system O-XYZ represented by equation (1) are obtained respectively: Z=aX+bY+c (1) a, b and c are the fitting coefficients of each parameter equation in the first parameter equation group; The coordinate values ​​of the three vertices of the upper end surface (3) of the triangular prism (2) in the coordinate system O-XYZ are calculated using the first parameter equation group and recorded as first coordinate values; The second arrays of the four measuring surfaces are used to perform equation fitting, and the second parameter equations of the four measuring surfaces in the interferometer coordinate system o-xyz represented by equation (2) are obtained respectively: z=dx+ey+f (2) d, e and f are the fitting coefficients of each parameter equation in the second parameter equation group; The coordinate values ​​of the three vertices of the upper end surface (3) of the triangular prism (2) in the coordinate system o-xyz are calculated using the second parameter equation group and recorded as second coordinate values; Step 3: Take three pairs of corresponding points in the first coordinate value and the second coordinate value as standard points for coordinate unification; The standard point coordinates of the three standard points in the first coordinate value are marked as P j , P j =P j (X j , Y j , Z j ); The standard point coordinates of the three standard points in the second coordinate value are marked as W j , W j =W j (x j ,y j , z j ); The three standard points are represented by j=1, 2, 3 in one-to-one correspondence; Step 4: Using the one-to-one corresponding three pairs of standard point coordinates, the unit quaternion method is used to solve the rotation matrix R and translation matrix T between the three-coordinate machine space rectangular coordinate system O-XYZ and the interferometer space rectangular coordinate system o-xyz, so as to unify the coordinates of the three-coordinate machine and the interferometer and complete the calibration; Follow the steps below to get the rotation matrix R and translation matrix T: Step A.1: Construct unit quaternion; The unit quaternion q consists of a real part and three imaginary parts, as represented by formula (3): q=q0+q1u+q2v+q3w (3) In formula (3), q0, q1, q2 and q3 are all real numbers and satisfy formula (4): u, v and w are imaginary units and satisfy equation (5): Solve according to steps A.2 to A.5 to obtain the optimal unit quaternion, thereby obtaining the rotation matrix R; Step A.2: Calculate the centroid coordinates of the three standard points in the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz respectively: The coordinates of the three standard points P in the three-coordinate machine coordinate system O-XYZ are calculated by formula (6): j The centroid coordinates ρ P : The coordinates W of the three standard points in the interferometer coordinate system o-xyz are calculated by formula (7): j The barycentric coordinates p W : Step A.3: Construct the covariance matrix R(c) according to formula (8): In formula (8), T represents the transpose of the matrix; Step A.4: Construct a 4×4 symmetric matrix R(q) from the covariance matrix R(c) as shown in formula (9): In formula (9): tr(R(c)) is the trace of the covariance matrix R(c); I3 is a 3×3 unit matrix; Δ is a matrix represented by equation (10): Δ=[A 23 A 31 A 12 ] (10) A st represents the element in the s-th row and t-th column of matrix A, s,t=1,2,3; The matrix A is constructed from the covariance matrix R(c). The elements A of the matrix A are st It is represented by formula (11): A st =(R(c)-R(c) T ) st (11) Step A.5: Calculate the eigenvalues ​​and eigenvectors of the symmetric matrix R(q). The eigenvector corresponding to the maximum eigenvalue in the symmetric matrix R(q) is the optimal unit quaternion. Then the rotation matrix R is represented by equation (12): In formula (12): Then the translation matrix T is represented by equation (13): T=ρ P -Rp W (13) According to the rotation matrix R and the translation matrix T, the positional relationship between the three-coordinate machine coordinate system O-XYZ and the interferometer coordinate system o-xyz is obtained, thereby completing the coordinate unification of the three-coordinate machine and the interferometer, that is, completing the calibration; Follow the steps below to verify the calibration accuracy: Step B.1, obtain measurement data: Set the area C1 in the surface B as the measured area, and the size of the area C1 is equal to the size of the interferometer's one-time measurement range; The region C1 is measured using an interferometer to obtain an interferometer measurement data set W for the region C1. C1 ; The three coordinate machine is used to measure the three measuring points evenly distributed in the area C1 respectively, and the three coordinate machine measurement data set P about the three measuring points is obtained. C1 ; Step B.2: Obtain conversion data: The interferometer measurement data set W is transformed using the rotation matrix R and the translation matrix T. C1 Convert to the coordinate system O-XYZ of the three-coordinate machine to obtain the interferometer conversion data set W under the coordinate system O-XYZ CC1 ; Step B.3: Calculate the residual value The interferometer transformation data set W CC1 The coordinate machine measurement data set P C1 The points whose measured data are closest to each other are regarded as corresponding points, and the residual value V between corresponding points is calculated according to formula (14): 3×3 : g represents the number of measuring points of the three-dimensional coordinate machine, g = 1, 2, 3; V 1g represents the X-direction residual of the g-th pair of corresponding points; V 2g represents the Y-direction residual of the g-th pair of corresponding points, V 3g represents the Z-direction residual of the g-th pair of corresponding points; Step B.4, calculate the residual root mean square: The residual root mean square RMSR1 of a measurement is calculated according to formula (15): Step B.5: Follow the same method as steps 8.1 to 8.4 to correct the area C in surface B. K Continue to measure and obtain the residual root mean square RMSRk, k = 2, 3, ..., 10; calculate the mean RMSR of the sum of the residual root mean squares of 10 measurements according to formula (16): If the mean value RMSR of the root mean square sum of the residuals does not exceed the set value, it means that the calibration method meets the accuracy requirements of micro-nano composite measurement.

2. The coordinate unified calibration method for micro-nanoscale composite measurement according to claim 1 is characterized in that: The bottom of the triangular prism body (2) is integrally supported by a triangular prism body (1), and the triangular prism body (1) is used as a base of the calibrator. The weight of the triangular prism body (1) as the base of the calibrator is used to keep the relative position of the calibrator unchanged when being measured.

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