WO2010053229A1

WO2010053229A1 - Method and system of measuring motion error in precision linear stage

Info

Publication number: WO2010053229A1
Application number: PCT/KR2009/000415
Authority: WO
Inventors: Changsoo Han; Dongik Shin; Weijun Wang; Yunggi Lee; Indong Kim
Original assignee: Industry University Cooperation Foundation IUCF HYU
Current assignee: Industry University Cooperation Foundation IUCF HYU
Priority date: 2008-11-06
Filing date: 2009-01-28
Publication date: 2010-05-14
Anticipated expiration: 2011-05-06
Also published as: KR20100050877A; KR101016229B1

Abstract

Disclosed herein is a method of measuring an error of a linear stage that moves in a straight line. The linear stage moves in a straight line along an x-axis, and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error. The method includes obtaining measurement values represented by vector sums of components including some components of the errors in various directions with a sensor, and calculating the errors using the obtained measurement values. Accordingly, the method indirectly measures errors of the linear stage, and allows a single measurement system alone to measure any error of the linear stage, thereby ensuring convenient installation and operation of the measurement system, while determining accuracy of a measured error. Further, the system can be configured with only a relatively inexpensive electrostatic capacity sensor, thereby providing superior economic effects.

Description

METHOD AND SYSTEM OF MEASURING MOTION ERROR IN PRECISION LINEAR STAGE

The present invention relates to a method of measuring an error in a linear stage that moves along a straight line, and more particularly to a method of indirectly measuring an error through various measurement values.

With recent industrial development, products and components have a tendency toward high-performance and ultra-compactness. Further, development in information technology (IT), biotechnology (BT), and nano technology (NT) demands industrial technology with nano level precision. Among production systems following such a tendency, an ultra-precision linear stage has been consistently developed to provide improved precision to a linear stage that moves along a straight line.

Although the linear stage is a production system configured to move in a straight line, the linear stage undergoes various errors including an error in a motion direction. Fig. 12 shows errors in the linear stage. For example, assuming a motion direction of a movable unit 800 is in an x-axis in a state that the linear stage moves along a linear guide 810, the linear stage undergoes a translational motion error, such as a horizontal motion error (e_h) that occurs in a y-axis direction and a vertical motion error (e_v) that occurs in a z-axis direction, a roll error based on rotational motions in the x-axis, y-axis and z-axis, a pitch error, and a yaw error.

Such errors become significant to the ultra-precision linear stage, and it is very important to ensure the precision of the linear stage through measurement of the errors.

Conventionally, various devices such as laser interferometers, autocollimators, electrostatic capacity sensors, etc. are simultaneously employed to measure such errors.

Since conventional measurement requires simultaneous use of various devices, however, a user is burdended not only with complex installation of the devices and severe difficulty in operation of the devices for measurement, but also with installation errors during installation. Further, even though the errors have to be measured with respect to an original position, the use of many devices generally makes it difficult to determine a correct original position.

Further, although the conventional measurement is highly likely to provide such errors, it is very difficult to confirm accuracy of a measurement value.

Moreover, among the devices used in the conventional measurement, the laser interferometer and the autocollimator are very expensive, thereby providing an economic burden when installing both of them.

The present invention is conceived to solve the problems as described above, and an aspect of the present invention is to provide a method of indirectly measuring an error of a linear stage with measurement values obtained from a single measurement system.

In accordance with an aspect of the present invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: obtaining measurement values represented by vector sums of components including some components of the errors in various directions with a sensor; and calculating values of the errors using the obtained measurement values. Here, the sensor may include an electrostatic capacity sensor. Additionally, the method may further include determining accuracy of error measurement by comparing the same kind of error values obtained by different processes among the calculated values of the errors after calculating the values of the errors.

According to an embodiment of the present invention, a basic principle of indirectly measuring the error is based on a relationship between distance measurement values that have the same error components but differ in measuring direction.

In accordance with another aspect of the invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: obtaining a first measurement value represented by a sum of components including the vertical motion error, the roll error, and a shape error on a measuring surface; obtaining a second measurement value and a third measurement value each represented by a sum of components including the vertical motion error, the roll error, and another shape error on the measuring surface at a position where a measuring direction for the first measurement value is reversed with respect to the y-axis or the z-axis; and calculating the vertical motion error, the roll error and the shape errors on the measuring surface based on the first to third measurement values.

In this regard, the obtaining the measurement value by the sum of components including the vertical motion error, the roll error and the shape error on the measuring surface may include measuring a distance in the z-axis using a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face upward or downward. Further, the sensor may include an electrostatic capacity sensor. Hereinafter, this method will be referred to as a vertical reverse method.

In accordance with a further aspect of the invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: obtaining a fourth measurement value represented by a sum of components including the horizontal motion error, the roll error, and a shape error on a measuring surface; obtaining a fifth measurement value represented by a sum of components including the horizontal motion error, the roll error and another shape error on the measuring surface at a position where a measuring direction for the fourth measurement value is reversed with respect to the z-axis; and calculating the shape errors on the measuring surface and the horizontal motion error based on the fourth and fifth measurement values and a separately measured roll error.

The obtaining the measurement value represented by the sum of components including the horizontal motion error, the roll error and the shape error on the measuring surface may include measuring a distance in the y-axis using a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face laterally. Further, the sensor may include an electrostatic capacity sensor, and the separately measured roll error may be obtained by the vertical reverse method. Hereinafter, this method will be referred to as a horizontal reverse method.

In accordance with yet another aspect of the invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: obtaining a first measurement value measured at a first measuring position and represented by a sum of components including the vertical motion error, the roll error, and a shape error on a measuring surface; obtaining a sixth measurement value measured at a second measuring position and represented by a sum of components including the vertical motion error and the roll error of the first measurement value, a component including the pitch error at the first measuring position, and a component including a shape error at the second measuring position on the measuring surface, the second measuring position being spaced a predetermined distance from the first measuring position in the x-axis; and calculating the pitch error based on the first and sixth measurement values and the shape errors separately measured at the first and second measuring positions on the measuring.

At this time, the obtaining the first measurement value may include measuring a distance along the z-axis with a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face upward or downward, and the obtaining the sixth measurement value may include measuring a distance in the z-axis with the sensor at the second measuring position spaced the predetermined distance from the first measuring axis in the x-axis in a state that the straight ruler is secured. Here, the sensor may include an electrostatic capacity sensor. Further, the separately measured shape errors at the first and second measuring positions on the measuring surface may be obtained by the vertical or horizontal reverse method. Hereinafter, this method will be referred to as a pitch error measuring method.

In accordance with a yet another aspect of the invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: obtaining a fourth measurement value represented by a sum of components including the horizontal motion error, the roll error, and a shape error on a measuring surface at a third measuring position; obtaining a seventh measurement value measured at a fourth measuring position and represented by a sum of components including the horizontal motion error and the roll error of the fourth measurement value, a component including the yaw error at the third measuring position, and a component including a shape error at the fourth measuring position on the measuring surface, the fourth measuring position being spaced a predetermined distance from the third measuring position in the x-axis; and calculating the yaw error based on the fourth and seventh measurement values and the shape errors separately measured at the third and fourth measuring positions on the measuring surface.

The obtaining the fourth measurement value may include measuring a distance in the y-axis with a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face laterally, and the obtaining the seventh measurement value may include measuring a distance in the y-axis with the sensor at the fourth measuring position spaced the predetermined distance from the third measuring position in the x-axis in a state that the straight ruler is secured. Further, the sensor may include an electrostatic capacity sensor. Also, the separately measured shape errors at the third and fourth measuring positions on the measuring surface may be obtained by the vertical or horizontal reverse method. Hereinafter this method will be referred to as a yaw error measuring method.

In accordance with yet another aspect of the invention, there is provided a method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method including: calculating the vertical motion error, the roll error, and a shape error on a measuring surface using the vertical reverse method; calculating a shape error on the measuring surface, and the horizontal motion error based on the roll error calculated by the vertical reserve method, using the horizontal reverse method; calculating the pitch error based on the shape error on the measuring surface calculated by the vertical or horizontal reverse method, using the pitch error measuring method; and calculating the yaw error based on the shape error on the measuring surface calculated by the vertical or horizontal reverse method, using the yaw error measuring method. Here, the method may further include determining accuracy in error measurement by comparing the shape errors on the measuring surface obtained by the horizontal reverse method and the vertical reverse method.

In accordance with yet another aspect of the invention, there is provided a system of measuring an error in an ultra-precision linear stage including a movable unit and a stationary unit, the system including: a sensor jig including a jig column standing on the movable unit, and a jig arm hingably coupled to an upper portion of the jig column and having an end to which a sensor is rotatably coupled; an adjustment stage installed at a side of the ultra-precision linear stage and adjustable with respect to x-, y- and z-axes and a yaw; and a rotatable straight ruler installed in the adjustment stage and having a measuring surface. Here, the sensor installed in the sensor jig may include an electrostatic capacity sensor.

The jig arm of the sensor jig may include an arm hingably coupled to the jig column, and a sensor unit rotatably coupled to the arm, and the sensor unit may include two sensors and a single pointer which are arranged in a line. The sensor unit may include a ball plunger to rotate by 90 degrees. The pointer may be adjustable in a forward and rearward direction.

The adjustment stage may include a lower stage configured to allow adjustment in the x- and y-axes and the yaw, and an upper stage configured to allow adjustment in the z-axis. The straight ruler may include a reference groove formed on the measuring surface. The straight ruler may be modularized into a straight ruler module including a stationary body having a coupling portion to be coupled to the adjustment stage, and a straight body rotatably coupled to the stationary body and having a measuring surface at one side thereof. Further, the straight body may comprise a ball plunger to rotate by 90 degrees.

According to an embodiment of the present invention, the method of indirectly measuring an error of a linear stage allows a single measurement system alone to measure any error. Accordingly, the method ensures convenient installation and operation of the measurement system, while providing a method of evaluating accuracy of a measured error. Further, according to another embodiment of the present invention, the system may be configured with only a relatively inexpensive electrostatic capacity sensor, thereby providing superior economic effects.

The above and other aspects, features and advantages of the present invention will become apparent from the following description of exemplary embodiments given in conjunction with the accompanying drawings, in which:

Fig. 1 is a perspective view of an error measurement system according to an embodiment of the present invention;

Fig. 2 is a perspective view of a sensor jig;

Fig. 3 is a perspective view of an adjustment stage;

Fig. 4 is a perspective view of a straight ruler module;

Fig. 5(a) is a perspective view of arrangement of the measurement system for measuring a first measurement value, and Fig. 5(b) is a view for explaining vector components of the first measurement value;

Fig. 6(a) is a perspective view of arrangement of the measurement system for measuring a second measurement value, and Fig. 6(b) is a view for explaining vector components of the second measurement value;

Fig. 7(a) is a perspective view of arrangement of the measurement system for measuring a third measurement value, and Fig. 7(b) is a view for explaining vector components of the third measurement value;

Fig. 8(a) is a perspective view of an arrangement of a measurement system for measuring a fourth measurement value, and Fig. 8(b) is a view for explaining vector components of the fourth measurement value;

Fig. 9(a) is a perspective view of an arrangement of a measurement system for measuring a fifth measurement value, and Fig. 9(b) is a view for explaining vector components of the fifth measurement value;

Fig. 10 is a view for explaining a method of measuring a pitch error;

Fig. 11 is a view for explaining a method of measuring a yaw error; and

Fig. 12 shows errors in a linear stage.

Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

First, an error measurement system according to an embodiment of the present invention will be described, and then a method of measuring an error using this error measurement system will be described.

Referring to Fig. 1, which shows an error measurement system according to an embodiment of the present invention, the error measurement system according to this embodiment is used for an ultra-precision linear stage that includes a movable unit 800 movable along a linear guide 810, and a stationary unit 900. The system includes a sensor jig 100, an adjustment stage 200 and a straight ruler module 300.

Referring to Fig. 2, the sensor jig 100 includes a jig column 110 and a jig arm 120.

The jig column 110 is formed at an upper portion thereof with a hinge shaft 112 for hinge coupling, and stands on the movable unit 800 such that the hinge shaft 112 is in parallel with a moving axis (i.e. an x-axis) of the movable unit 800.

The jig arm 120 includes an arm 122 and a sensor unit 126. The arm 122 is hingably coupled at one end thereof to the hinge shaft 112 located at the upper portion of the jig column 110 to rotate by 180 degrees, and is formed at the other end thereof with a rotation shaft 124 which is parallel with the hinge shaft 112. The sensor unit 126 is coupled to the rotation shaft 124 formed at the other end part of the arm 122, and includes a sensor 127 and a pointer 128 arranged side by side in a direction of the rotation shaft 124. In this embodiment, the sensor 127 includes two sensors 127(a) and 127(b) arranged in a line. The sensor unit 126 is rotatable with respect to the rotation shaft 124, so that the sensor 127 and the pointer 128 can be oriented in different directions. Here, a ball plunger 129 is used to stop the sensor unit 126 at intervals of 90 degrees, so that the sensor 127 and the pointer 128 can be accurately oriented in lateral, upward, downward directions. Although any sensor can be used for the sensor 127 so long as it can measure a distance, a relatively inexpensive electrostatic capacity sensor may be advantageously used as the sensor 127. Further, the pointer 128 is configured to have an adjustable extent of protrusion.

Fig. 3 shows the adjustment stage of the linear stage.

The adjustment stage 200 is disposed at one side of the linear stage, and is configured to permit yaw adjustment as well as position adjustment in x-, y- and z-axes so as to adjust a position of the straight ruler module 300 corresponding to a position of the sensor 127.

In this embodiment, the adjustment stage 200 includes a lower stage 210 and an upper stage 220, which are coupled via a magnetic base 230. The lower stage 210 is configured to adjust a position of the upper stage 220 located thereon in the x- and y-axes and a yaw direction. The upper stage 220 is provided with a stage member 222 to which the straight ruler module 300 is coupled. The upper stage 220 is configured to adjust a position of the stage member 222 in the z-axis. Here, the adjustment stage 200 may have any typical adjustment structure without limitation.

Fig. 4 shows the straight ruler module of the linear stage.

The straight ruler module 300 is a modularized straight ruler, which will be subject to measurement according to an embodiment of the present invention. By modularizing the straight ruler, the straight ruler modules 300 fabricated corresponding to various lengths can be replaced in accordance with the size of the linear stage.

The straight ruler module 300 includes a stationary body 310 and a straight body 320. The stationary body 310 is formed with a coupling portion 312 to be coupled to the stage member 222, and includes a rotation shaft 314 arranged in parallel with the x-axis. The straight body 320 is rotatably coupled to the rotation shaft 314 and has a measuring surface 322. In this embodiment, the measuring surface 322 is a surface to be detected by the sensor 127, and can be oriented in various directions as the straight body 320 rotates. Here, a ball plunger 326 is used to stop at intervals of 90 degrees, so that the measuring surface 322 can be accurately oriented in lateral, upward, downward directions.

The straight ruler module 300 is coupled to the adjustment stage 200 so that the position of the straight ruler module 300 can be adjusted corresponding to the position of the sensor 127 of the sensor jig 100. Further, the measuring surface 322 is formed with a reference groove 324. The adjustment stage 200 is adjusted such that an end point of the pointer 128 faces the reference groove 324. Thus, even if a sensing direction of the sensor jig 100 is changed, the measurement system can be easily adjusted to measure the same point.

A method of indirectly measuring an error in an ultra-precision linear stage with the measurement system as described above will be given. According to an embodiment of the present invention, a basic principle of indirectly measuring the error is based on a relationship between distance measurement values that have the same error components but differ in measuring direction. The error components of the distance measurement values depend on the measuring direction due to arrangement of the measuring surface and the sensor, and thus the method is classified into a vertical reverse method, a horizontal reverse method, and a rotational error measuring method.

- Vertical reverse method

The vertical reverse method is a method of indirectly measuring an error on the basis of a relationship between a basic measurement value having a vertical motion error component and measurement values obtained by reversing the measuring direction or position with respect to the y- and z-axes. The measurement of an error using the vertical reverse method is as follows.

First, a first measurement value is obtained by adjusting the measurement system. Fig. 5(a) is a perspective view of arrangement of the measurement system for measuring the first measurement value, and Fig. 5(b) is a view for explaining vector components of the first measurement value.

For this purpose, the sensor jig 100 is installed on the movable unit 800 of the linear stage such that the hinge shaft 112 of the jig column 110 is in parallel with the x-axis, and the angle of the sensor unit 126 is adjusted to cause the sensor 127 to face downward. Further, the adjustment stage 200 is installed at a side of the linear stage, with its position and direction selected corresponding to the position of the sensor unit 126. Finally, with the measuring surface 322 disposed to face upward, the adjustment stage 200 is adjusted such that the reference groove 324 is aligned with the end point of the pointer 128.

In this state, the first measurement value M₁(x) is obtained by measuring a distance to the measuring surface 322 with the sensor 127. Here, the first measurement value can be represented together with the error of the linear stage as follows.

[Corrected under Rule 26 13.04.2009]

Here, r(x) indicates an error value due to the shape of the measuring surface, y indicates a distance between a motion axis of the linear stage and the y-axis, and a rotational error of the motion axis is a roll error. The motion axis of the linear stage is varied according to the kind of the linear stage. Hereinafter, a linear stage where the movable unit 800 moves along the linear guide 810 will be described. In this case, the motion axis of the linear stage is the center of the linear guide 810.

Then, a second measurement value is obtained in a measuring direction where the measuring direction for the first measurement value is reversed with respect to the y-axis. Fig. 6(a) is a perspective view of arrangement of the measurement system for measuring the second measurement value, and Fig. 6(b) is a view for explaining vector components of the second measurement value.

First, in the state that the direction of the sensor jig 100 and the installation position of the adjustment stage 200 are maintained without change, the sensor unit 126 is rotated by 180 degrees such that the sensor 127 faces upward. Further, with the measuring surface 322 disposed to face downward, the adjustment stage 200 is adjusted such that the reference groove 324 is aligned with the end point of the pointer 128.

In this state, the second measurement value M₂(x) is obtained by measuring a distance to the measuring surface 322 with the sensor 127. Here, the second measurement value can be represented together with the error of the linear stage as follows.

[Corrected under Rule 26 13.04.2009]

Then, a third measurement value is obtained in a measuring direction where the measuring direction for the first measurement value is reversed with respect to the z-axis. Fig. 7(a) is a perspective view of arrangement of the measurement system for measuring a third measurement value, and Fig. 7(b) is a view for explaining vector components of the third measurement value.

First, the arm 122 of the sensor jig 100 is rotated by 180 degrees and the sensor 127 is disposed to face downward. Further, the adjustment stage 200 is moved to an opposite side of the linear stage and installed facing the sensor jig 100. Last, with the measuring surface 322 disposed to face upward, the adjustment stage 200 is adjusted such that the reference groove 324 is aligned with the end point of the pointer 128.

In this state, the third measurement value M₃(x) is obtained by measuring a distance to the measuring surface 322 with the sensor 127. Here, the third measurement value can be represented together with the error of the linear stage as follows.

[Corrected under Rule 26 13.04.2009]

Finally, the following equations can be obtained by solving the above simultaneous equations.

[Corrected under Rule 26 13.04.2009]

Accordingly, it is possible to calculate a roll error, a shape error on the measuring surface, and a motion error in the vertical direction.

- Horizontal reverse method

The horizontal reverse method is a method of indirectly measuring an error on the basis of a relationship between a basic measurement value having a horizontal motion error component and a measurement value obtained by reversing the measuring position for the basic measurement value with respect to the z-axes. The method of measuring an error using the horizontal reverse method is as follows.

First, a fourth measurement value is obtained by adjusting the measurement system. Fig. 8(a) is a perspective view of arrangement of the measurement system for measuring the fourth measurement value, and Fig. 8(b) is a view for explaining vector components of the fourth measurement value.

For this purpose, the sensor jig 100 is installed on the movable unit 800 of the linear stage such that the hinge shaft 112 of the jig column 110 is in parallel with the x-axis, and the angle of the sensor unit 126 is adjusted to cause the sensor 127 to face laterally. Further, the adjustment stage 200 is installed at a side of the linear stage, with its position and direction selected corresponding to the position of the sensor unit 126. Finally, with the measuring surface 322 disposed to face laterally, the adjustment stage 200 is adjusted such that the reference groove 324 is aligned with the end point of the pointer 128.

In this state, the fourth measurement value M₄(x) is obtained by measuring a distance to the measuring surface 322 with the sensor 127. Here, the fourth measurement value can be represented together with the error of the linear stage asfollows.

[Corrected under Rule 26 13.04.2009]

Here, z indicates a distance between a motion axis of the linear stage and the z-axis.

Then, a fifth measurement value is obtained in a measuring direction where the measuring direction for the fourth measurement value is reversed with respect to the z-axis. Fig. 9(a) is a perspective view of arrangement of the measurement system for measuring the fifth measurement value, and Fig. 9(b) is a view for explaining vector components of the fifth measurement value.

First, the arm 122 of the sensor jig 100 is rotated by 180 degrees and the sensor 127 is disposed to face laterally. Further, the adjustment stage 200 is moved to an opposite side of the linear stage and installed facing the sensor jig 100. Last, with the measuring surface 322 disposed to face laterally, the adjustment stage 200 is adjusted such that the reference groove 324 is aligned with the end point of the pointer 128.

In this state, the fifth measurement value M₅(x) is obtained by measuring a distance to the measuring surface 322 with the sensor 127. Here, the fifth measurement value can be represented together with the error of the linear stage as follows.

[Corrected under Rule 26 13.04.2009]

With the fourth and the fifth measurement values, it is possible to calculate the shape error on the measuring surface. If the roll error is given, it is also possible to calculate even the horizontal motion error. In this regard, the roll error can be measured by a separate method, but may be easily calculated by the foregoing vertical reverse method when using the measurement system according to the embodiment of the invention.

- Rotational error measuring method

The rotational error measuring method is a method of indirectly measuring an error on the basis of a relationship between a basic measurement value having a vertical motion error component or a horizontal motion error component and a measurement value at a position moved a predetermined distance from a measuring position for the basic measurement value in the x-axis. Here, two sensors spaced a predetermined distance from each other may be used to easily obtain a desired value. A method using the measurement value having the vertical motion error component will be referred to as a pitch error measuring method, and a method using the measurement value having the horizontal motion error component will be referred to as a yaw error measuring method. The method of measuring an error on the basis of the rotational error measuring method is as follows.

-Pitch error measuring method

First, the measurement system is adjusted to implement measurement. Fig. 10 is a view for explaining a method of measuring a pitch error. An arrow of Fig. 10 indicates a moving direction of the linear stage.

The sensor jig 100 and the adjustment stage 200 have the same position and direction as in the vertical reverse method, and a description will be given particularly with respect to the arrangement for obtaining the first measurement value. According to an embodiment of the invention, the measurement system includes two sensors 127 spaced a predetermined distance Δx from each other along the x-axis. Hereinafter, a position measured by a first sensor 127 and a position measured by a second sensor 127 will be referred to as a first measuring position and a second measuring position, respectively. A value obtained at the first measuring position is equal to the first measurement value M₁(x), but can be represented as follows to distinguish the measuring positions.

[Corrected under Rule 26 13.04.2009]

In the second measuring position, a sixth measurement value M₆(x) is obtained. The sixth measurement value M₆(x) can be represented as follows.

[Corrected under Rule 26 13.04.2009]

Finally, the following equation can be obtained by solving the above simultaneous equations.

[Corrected under Rule 26 13.04.2009]

Accordingly, if the shape errors on the measuring surface at the first measuring position and the second measuring position are given, the pitch error can be calculated from the first and sixth measurement values. In this regard, the shape errors on the measuring surface can be measured by a separate method, but may be easily calculated by the aforementioned vertical or horizontal reverse method.

-Yaw error measuring method

First, the measurement system is adjusted to implement measurement. Fig. 11 is a view for explaining a method of measuring a yaw error. An arrow in Fig. 11 indicates a moving direction of the linear stage.

The sensor jig 100 and the adjustment stage 200 have the same position and direction as in the vertical reverse method, and a description will be given particularly with respect to the arrangement for obtaining the fourth measurement value. According to an embodiment of the present invention, the measurement system includes two sensors 127 spaced a predetermined distance Δx from each other along the x-axis. Hereinafter, a position measured by a first sensor 127 and a position measured by a second sensor 127 will be referred to as a third measuring position and a fourth measuring position, respectively. A value obtained at the third measuring position is equal to the fourth measurement value M₄(x), but can be represented as follows to distinguish the measuring positions.

[Corrected under Rule 26 13.04.2009]

In the fourth measuring position, a seventh measurement value M₇(x) is obtained. The seventh measurement value M₇(x) can be represented as follows.

[Corrected under Rule 26 13.04.2009]

Accordingly, if the shape errors on the measuring surface at the third and fourth measuring positions are given, the yaw error can be calculated from the fourth and seventh measurement values. In this regard, the shape error on the measuring surface can be measured by a separate method, but may be easily calculated by the aforementioned vertical or horizontal reverse method.

With the above methods, any error of the linear stage can be indirectly measured by a single measurement system using a relatively inexpensive electrostatic capacity sensor. Further, accuracy of the measured error can be determined through the measurement system and method according to the embodiment of the present invention. As apparent from the above description, the shape errors on the measuring surface can be separately calculated by the vertical and horizontal reverse methods, respectively. Thus, it is possible to indirectly evaluate the accuracy of the indirectly measured error by comparing the shape error r^v(x) calculated by the vertical reverse method and the shape error r^h(x) calculated by the horizontal reverse method. It can be judged that the smaller the difference between the two shape errors, the more accurate the indirectly measure derror.

Although the present invention has been described with reference to the embodiments and the accompanying drawings, it will be apparent to those skilled in the art that the embodiments are given by way of illustration, and that various modifications and equivalent embodiments can be made without departing from the spirit and scope of the present invention. Accordingly, the scope of the present invention should be limited only by the accompanying claims.

Claims

A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

obtaining measurement values represented by vector sums of components comprising some components of the errors in various directions with a sensor; and

calculating values of the errors using the obtained measurement values.
The method according to claim 1, wherein the sensor comprises an electrostatic capacity sensor
The method according to claim 1, after the step of calculating the values of errors, further comprising: determining accuracy of error measurement by comparing the same kind of error values obtained by different processes among the calculated values of the errors.
A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

obtaining a first measurement value represented by a sum of components including the vertical motion error, the roll error, and a shape error on a measuring surface;

obtaining a second measurement value and a third measurement value each represented by a sum of components including the vertical motion error, the roll error, and another shape error on the measuring surface at a position where a measuring direction for the first measurement value is reversed with respect to the y-axis or the z-axis; and

calculating the vertical motion error, the roll error, and the shape errors on the measuring surface based on the first to third measurement values.
The method according to claim 4, wherein the obtaining the measurement value by the sum of components including the vertical motion error, the roll error and the shape error on the measuring surface comprises measuring a distance in the z-axis using a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face upward or downward.
The method according to claim 5, wherein the sensor comprises an electrostatic capacity sensor.
A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

obtaining a fourth measurement value represented by a sum of components including the horizontal motion error, the roll error, and a shape error on a measuring surface;

obtaining a fifth measurement value represented by a sum of components including the horizontal motion error, the roll error and another shape error on the measuring surface at a position where a measuring direction for the fourth measurement value is reversed with respect to the z-axis; and

calculating the shape errors on the measuring surface and the horizontal motion error based on the fourth and fifth measurement values and a separately measured roll error.
The method according to claim 7, wherein the obtaining the measurement value represented by the sum of components including the horizontal motion error, the roll error and the shape error on the measuring surface comprises measuring a distance in the y-axis using a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face laterally.
The method according to claim 8, wherein the sensor comprises an electrostatic capacity sensor.
The method according to claim 7, wherein the separately measured roll error is obtained by the method according to claim 4.
A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

obtaining a first measurement value measured at a first measuring position and represented by a sum of components including the vertical motion error, the roll error, and a shape error on a measuring surface;

obtaining a sixth measurement value measured at a second measuring position and represented by a sum of components comprising the vertical motion error and the roll error of the first measurement value, a component comprising the pitch error at the first measuring position, and a component comprising a shape error at the second measuring position on the measuring surface, the second measuring position being spaced a predetermined distance from the first measuring position in the x-axis; and

calculating the pitch error based on the first and sixth measurement values and the shape errors separately measured at the first and second measuring positions on the measuring surface.
The method according to claim 11, wherein the obtaining the first measurement value comprises measuring a distance in the z-axis with a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face upward or downward, and the obtaining the sixth measurement value comprises measuring a distance in the z-axis with the sensor at the second measuring position spaced the predetermined distance from the first measuring axis in the x-axis in a state that the straight ruler is secured.
The method according to claim 12, wherein the sensor comprises an electrostatic capacity sensor.
The method according to claim 11, wherein the separately measured shape errors at the first and second measuring positions on the measuring surface are obtained by the method according to claim 4 or 7.
A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

obtaining a fourth measurement value measured at a third measuring position and represented by a sum of components including the horizontal motion error, the roll error, and a shape error on a measuring surface;

obtaining a seventh measurement value measured at a fourth measuring position and represented by a sum of components comprising the horizontal motion error and the roll error of the fourth measurement value, a component comprising the yaw error at the third measuring position, and a component comprising a shape error at the fourth measuring position on the measuring surface, the fourth measuring position being spaced a predetermined distance from the third measuring position in the x-axis; and

calculating the yaw error based on the fourth and seventh measurement values and the shape errors separately measured at the third and fourth measuring positions on the measuring surface.
The method according to claim 15, wherein the obtaining the fourth measurement value comprises measuring a distance in the y-axis with a sensor in a state that the measuring surface of a straight ruler arranged in parallel with the x-axis is disposed to face laterally, and the obtaining the seventh measurement value comprises measuring a distance in the y-axis with the sensor at the fourth measuring position spaced the predetermined distance from the third measuring position in the x-axis in a state that the straight ruler is secured.
The method according to claim 16, wherein the sensor comprises an electrostatic capacity sensor.
The method according to claim 15, wherein the separately measured shape errors at the third and fourth measuring positions on the measuring surface are obtained by the method according to claim 4 or 7.
A method of measuring an error in an ultra-precision linear stage that moves in a straight line along an x-axis and has a horizontal motion error of a y-axis, a vertical motion error of a z-axis, a roll error, a yaw error and a pitch error, the method comprising:

calculating the vertical motion error, the roll error, and a shape error on a measuring surface using the method according to claim 4;

calculating a shape error on the measuring surface and the horizontal motion error on the basis of the roll error calculated by the method of claim 4, using the method according to claim 7;

calculating the pitch error on the basis of the shape error on the measuring surface calculated by the method according to claim 4 or 7, using the method according to claim 11; and

calculating the yaw error on the basis of the shape error on the measuring surface calculated by the method according to claim 4 or 7, using the method according to claim 15.
The method according to claim 19, further comprising: determining accuracy in error measurement by comparing the shape errors on the measuring surface respectively calculated using the methods according to claims 4 and 7.
A system of measuring an error in an ultra-precision linear stage including a movable unit and a stationary unit, the system comprising:

a sensor jig comprising a jig column standing on the movable unit, and a jig arm hingably coupled to an upper portion of the jig column and having an end to which a sensor is rotatably coupled;

an adjustment stage installed at a side of the ultra-precision linear stage and adjustable with respect to x-, y- and z-axes and a yaw; and

a rotatable straight ruler installed in the adjustment stage and having a measuring surface.
The system according to claim 21, wherein the sensor installed in the sensor jig comprises an electrostatic capacity sensor.
The system according to claim 21, wherein the jig arm of the sensor jig comprises an arm hingably coupled to the jig column, and a sensor unit rotatably coupled to the arm, the sensor unit comprising two sensors and a single pointer which are arranged in a line.
The system according to claim 23, wherein the sensor unit comprises a ball plunger to rotate by 90 degrees.
The system according to claim 23, wherein the pointer is adjustable in a forward and rearward direction.
The system according to claim 21, wherein the adjustment stage comprises a lower stage configured to allow adjustment in the x- and y-axes and the yaw, and an upper stage configured to allow adjustment in the z-axis.
The system according to claim 21, wherein the straight ruler comprises a reference groove formed on the measuring surface.
The system according to claim 21, wherein the straight ruler is modularized into a straight ruler module comprising a stationary body having a coupling portion to be coupled to the adjustment stage, and a straight body rotatably coupled to the stationary body and having a measuring surface at one side thereof.
The system according to claim 28, wherein the straight body comprises a ball plunger to rotate by 90 degrees.