Heterodyne laser interferometer rotation tilt error calibration method based on redundancy characteristics

Abstract

The invention provides a method for calibrating a rotation tilt error of a heterodyne laser interferometer based on redundancy characteristics, which comprises the following steps of: respectively and independently planning a moving path of a workbench in a horizontal direction X or Y direction, selecting a reference measurement point, setting maximum and minimum values of Rx, Ry and Rz at each measurement position, and setting the rest degrees of freedom to be zero; measuring at a reference point according to a set path, calculating Rz and Ry rotation inclination angles of the workpiece table through a six-degree-of-freedom measurement model and obtaining a deviation value between different measurement axes, then establishing a relation equation between the deviation value and an error coupling coefficient deviation value according to a Taylor expansion formula, and finally calculating an error coupling coefficient; substituting the updated and compensated error coupling coefficient into the model to calculate the rotation gradient of the workbench; and therefore, the purpose of calibrating the rotation and inclination postures of the heterodyne laser interferometer with redundant characteristics can be achieved. The method can be used for reducing the rotation tilt error of the heterodyne laser interferometer.

Description

(I) Technical field

[0001] The invention relates to a method for calibrating a rotation tilt error of a heterodyne laser interferometer based on redundant features, which can be used to calibrate the rotation tilt posture of the heterodyne laser interferometer and improve the measurement accuracy of the heterodyne laser interferometer, and belongs to the technical field of precision displacement measurement. (II) Background technology

[0002] With the continuous progress of science and technology, especially the development of nanotechnology, precision manufacturing, optical instruments and other fields, the requirements for the accuracy of displacement measurement are getting higher and higher. Although traditional displacement measurement methods, such as vernier calipers and micrometer screw micrometers, are suitable for some rough measurement tasks, they are difficult to meet the needs of modern high-precision measurement due to their limited accuracy and real-time performance. Therefore, precision displacement measurement technology came into being and became one of the key technologies to ensure the normal operation of high-precision equipment, processes and control systems.

[0003] Compared with traditional laser interferometers, heterodyne laser interferometers have the advantages of strong anti-noise ability, high measurement accuracy, high stability and low drift. Since its development, many scholars at home and abroad have conducted a lot of research and achieved fruitful results from the perspectives of nonlinear error sources, detection and compensation to improve its measurement accuracy. At present, the nonlinear error of heterodyne laser interferometers has been basically eliminated. However, there are relatively few studies on installation error and environmental error compensation model algorithms. The research on these two mainly focuses on multi-degree-of-freedom decoupling algorithms and calibration measurement model coordinate systems.

[0004] First, based on the characteristics of the linear laser interferometer system, the relationship between the optical path of the plane mirror interferometer system and the position of the workbench is derived. Secondly, the relationship between the optical path and the interferometer reading is established through the basic principle of interference and the change of fringes. Then, based on the above-derived relationship, the global model expressions of the measurement axes in the three directions of X, Y and Z are derived respectively, and the model expressions composed of the laser interferometer readings, the workpiece stage position coordinates and a large number of parameters will be obtained. The spatial geometric relationship in the heterodyne laser interferometer measurement system is then obtained through the coordinate system conversion expression. Therefore, the position of the workbench can be solved directly by obtaining the laser interferometer readings.

[0005] Under ideal circumstances, when the worktable performs translation or rotational tilting motion, the rotational tilting postures Rz and Ry are not affected by the other degrees of freedom. However, due to factors such as installation errors and processing errors, there is a deviation between the two degrees of freedom Rz and Ry measured by different measuring axes.

[0006] When the workbench is at different reference positions, different rotation and tilt postures are set, and the Rz and Ry degrees of freedom results calculated by different directions are inconsistent. Consider whether it is possible to use the X and Y direction measurement axes to measure the workbench position under different reference points, calculate the deviation values ​​of the two, and then solve the error coupling coefficient, reduce the difference between Rz and Ry calculated by the two measurement axes, eliminate the coupling effect of the remaining degrees of freedom caused by installation errors and processing errors on the workbench rotation and tilt, and finally complete the calibration of the rotation and tilt of the heterodyne laser interferometer based on redundant characteristics. (III) Summary of the invention

[0007] In order to improve the measurement accuracy of a heterodyne laser interferometer, the present invention provides a method for calibrating a rotation tilt error of a heterodyne laser interferometer based on redundant features.

[0008] The present invention discloses a method for calibrating a rotation tilt error of a heterodyne laser interferometer based on redundant features, which specifically comprises the following steps:

[0009] In the method: step S1 sets the X or Y position of the motion stage individually, and at each measurement position, sets the maximum and minimum values ​​of Rx, Ry and Rz of the motion stage, and keeps other degrees of freedom zero.

[0010] In the method: Step S2 reads the measurement value of the laser interferometer at each sampling point, substitutes the X and Y positions and the rotation tilt angle into the global measurement model for calculation, and obtains the degree of freedom position measured by each measurement axis.

[0011] In the method: Step 3, due to the measurement layout and system design of the heterodyne laser interferometer, the results of Rz and Ry are affected by the changes in the remaining degrees of freedom. According to the set reference measurement points, the values ​​of Rzx, Rzy and Ryx, Ryz are measured and calculated, and finally the differences of Rz and Ry when Rx, Ry, and Rz are at the maximum and minimum values ​​at different X and Y positions can be observed. Where s represents the six-degree-of-freedom information, and p represents the coupling coefficient. Rzx=Rzx(s,p (Rzx) ) Rzy=Rzy(s,p (Rzy) ) ΔRz(s,p (Rzx) ,p (Rzy) )=Rzx(s,p (Rzx) )-Rzy(s,p (Rzy) )=-Rz diff Ryx=Ryx(s,p (Rzx) ) Ryz=Ryz(s,p (Rzy) ) ΔRy(s,p(Ryx) ,p (Ryz) )=Ryx(s,p (Ryx) )-Ryz(s,p (Ryz) )=-Ry diff

[0012] In the method, step S4 introduces the global measurement model according to the difference relationship of the rotation inclination of the laser interferometer obtained in step 3, and then performs a first-order Taylor expansion to obtain the relationship between the deviation value of the coupling coefficient and the six degrees of freedom and the difference; wherein the six degrees of freedom and the difference are both known quantities, and it can be obtained that: Among them, δp (Rz) and δp (Ry) is the quantity to be determined. According to the above relationship, δp can be obtained by the least square method. (Rz) and δp (Ry) , which represents the deviation value of the error coupling coefficient, and its update method is as follows:

[0013] In the method, step S5 substitutes the updated error coupling coefficient into the global measurement model of the laser interferometer to recalculate the Rz and Ry rotation tilt angles of the workbench, and repeats step S3 to obtain the updated compensated error value, thereby completing the rotation tilt calibration of the heterodyne laser interferometer.

[0014] In summary, the method for calibrating the rotation and tilt error of a heterodyne laser interferometer based on redundant features of the present invention has the following beneficial results:

[0015] The present invention can effectively improve the measurement accuracy of the heterodyne laser interferometer displacement measurement system, reduce the error value of the rotation tilt of the heterodyne laser interferometer based on redundant characteristics, and provide a theoretical basis and technical support for the compensation of subsequent heterodyne laser interferometer measurement model errors. (IV) Description of the drawings

[0016] Figure 1 The present invention is a flow chart of a rotation tilt error calibration method of a heterodyne laser interferometer based on redundant features.

[0017] Figure 2 The workbench path planning diagram of the rotation and tilt error calibration method of heterodyne laser interferometer based on redundant features

[0018] Figure 3 The invention relates to a rotation tilt error calibration method of a heterodyne laser interferometer based on redundant characteristics, which sets reference measurement points in X and Y directions and sets maximum and minimum values ​​of different rotation tilt postures at different measurement points. (V) Specific implementation methods

[0019] The present invention is further described below with reference to specific examples.

[0020] See also Figure 1-3 The present invention discloses a method for calibrating a rotation tilt error of a heterodyne laser interferometer based on redundant features, which can be specifically divided into the following five steps.

[0021] Step S1: Plan the measurement path such as Figure 2 As shown, the X and Y positions of the workbench are set separately from -10mm to 6mm, and reference measurement points are selected at intervals of 2mm. The maximum and minimum values ​​of the motion table Rx, Ry and Rz ± 3.5mm are set at each measurement point. When setting the rotation and tilt posture, keep other degrees of freedom zero. The specific reference point and rotation and tilt posture settings are as follows Figure 3 shown.

[0022] Step S2: According to the set reference point, on the basis of the global measurement model of the heterodyne laser interferometer, an initial error coupling term is substituted into the model; during measurement, the coupling error term is set to the maximum or minimum value within the range, and the remaining errors are taken as zero, and the measurement results of each measurement axis of a total of 84 points in different rotation and tilt postures at different measurement points are calculated.

[0023] Step S3: According to the calculated value of the measurement model, the difference between Rzx, Rzy and Ryx, Ryz is obtained. The difference between Rz and Ry has a large correlation with other degrees of freedom. The rotation and tilt postures at each horizontal position are separated. The influence of different rotation and tilt postures on the difference between Rz and Ry is different, but the change trend with X and Y is consistent, and the influence of X and Y position changes on the difference between Rz and Ry is greater. In this way, it can be more intuitive to see the influence of different X and Y positions on the difference between the two degrees of freedom of Rz and Ry when they are in different tilt postures, so as to obtain the influence deviation value of each position separately.

[0024] Step S4: Solve the deviation value of the workbench at different X, Y positions and different rotation and tilt postures. According to the Taylor expansion formula, the deviation value and the measurement model expression are combined to obtain the correlation equations about the Rzy, Rzx and Ryx, Ryz deviation values ​​and the error coupling coefficient. Then, the partial derivative matrix of the error coupling coefficient is obtained. The equation is subjected to Taylor first-order expansion to obtain the relationship between the change value of the error coupling coefficient and the partial derivative matrix. Substitute the known quantity to obtain the specific deviation value of the error coupling coefficient. Finally, it is added to the initial coupling coefficient to obtain the updated and compensated coupling coefficient.

[0025] Step S5: Substitute the updated error coupling coefficient obtained in step 4 into the global measurement model to recalculate the compensated Rz and Ry, compare the difference before and after, and complete the rotation and tilt calibration of the heterodyne laser interferometer based on redundant features.

Claims

1. A method for calibrating rotation and tilt errors of a heterodyne laser interferometer based on redundancy characteristics. The method comprises: Select reference points on the separately planned X and Y paths, and set the maximum and minimum values ​​of Rx, Ry, and Rz at each set reference position; and calculate the worktable position according to the global measurement model of the laser interferometer in the X, Y, and Z directions; solve the deviation values ​​between Rzx, Rzy and Ryx, Ryz respectively, and use Taylor's first-order expansion formula to establish the correlation equation between the deviation value and the error coupling coefficient; then solve the updated error coupling coefficient according to the known equation and known value, and substitute the compensated error coupling coefficient into the global measurement model to calculate the new worktable position, so as to achieve the purpose of calibrating the rotation and tilt error of the heterodyne laser interferometer.

2. The method for calibrating the rotation and tilt error of a heterodyne laser interferometer based on redundant features according to claim 1 is characterized by: At each reference measurement position in the X and Y directions, the maximum or minimum value of the Rx, Ry, and Rz rotation tilt of the workbench is set separately, and the remaining degrees of freedom are zero at the same time.

3. The method for calibrating the rotation and tilt error of a heterodyne laser interferometer based on redundant features according to claim 1, characterized in that: The reference position measurement points with different rotation and tilt postures are substituted into the global measurement model, and the Rz and Ry rotation and tilt angles measured by the measurement axes in the X, Y and Z directions are obtained by calculation, thereby obtaining the rotation and tilt error value of the laser interferometer.

4. The method for calibrating the rotation and tilt error of a heterodyne laser interferometer based on redundant features according to claim 1, characterized in that: When establishing the correlation equation between the deviation value and the error coupling coefficient, the coupling coefficient should first be regarded as an unknown variable, then the equation is Taylor expanded, and then the known variables are substituted to obtain the change value of the coupling coefficient.

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