JP4964691B2 - Measuring method of measured surface - Google Patents

Description

  The present invention relates to a method for measuring a surface to be measured.

  The need to measure long straight shapes and large area planar shapes with high precision is increasing due to the increase in the length of precision coating tools, the enlargement of wafers, and the increase in the area of LCD screens. The certainty of the metrics given is no longer limited. What is particularly symbolic is that the interference shape measuring machine that has been used as a plane measurement standard cannot sufficiently meet the current requirements for the size and accuracy of the reference plane as the measurement standard. Therefore, there is a need for a measurement method based on mathematically given standards that does not rely on physical standards for the correctness of planes and straight lines. In addition, if the measurement object is a two-dimensional or three-dimensional object, the Abbe's principle cannot be satisfied structurally, which is a big barrier to improving the accuracy. For this reason, the necessity of measuring and correcting the pitching error and the rolling error is remarkable in the high-precision measurement of the stage motion error. In order to satisfy this need, a reliable measurement method such as a reference plane is indispensable. Needs related to these linear motions have arisen for rotary tables as well. In the rotational motion, when the tilting motion error of the rotating shaft is observed along the circle generatrix, it corresponds to the pitching error and rolling error in the linear motion.

Conventionally, in the measurement of straight motion error, a straight ruler that guarantees straightness of the cross-section straight line is used as a reference, and the error of straight motion is calculated from the displacement meter output in the longitudinal direction of the straight ruler and the relative movement of the displacement meter. It was going to be detected. It is known that pitching can be measured theoretically based on the local inclination angle in the longitudinal direction. However, when a straight ruler is used as a reference, the difference between the displacements of two points arranged in the longitudinal direction at regular intervals is used. The method to obtain is used. It is also known to place two corner cubes on a moving object and read the relative displacement with a laser interferometer to measure pitching or yawing. However, due to the effects of air fluctuations, the movement straightness of a very long distance Stable measurement is difficult. Therefore, each of the moving stage, the rotating stage of the machine tool, the x-, y-, and z-axis moving mechanism, and the r, z, and θ-axis moving mechanism of the three-dimensional measuring machine are each equipped with a positioning encoder along the moving direction. Linear motion error (including translation error from a straight line, pitching error, yawing error, rolling error) and rotational motion error (inclination motion error in two directions of the rotational axis corresponding to pitching error, rolling error) (Including axial entry / exit errors and two radial translation errors) were detected and not controlled. However, with the improvement in accuracy required for machines, the establishment of a highly accurate and simple measurement method for linear motion has become an issue. Japanese Patent Application Laid-Open No. 2004-228688 discloses a technique for removing the pitching error due to the change in posture of the displacement sensor in the sequential two-point method and taking it into sensor data to improve the accuracy of surface shape measurement. As for the rotational motion error, a circular ruler in which the roundness of the end surface and side surface of the ring-shaped ruler is calibrated is used as a reference, but a good reference ruler is not known for the tilting motion.
JP 2005-114549 A

  However, the technique of Patent Document 1 irradiates the sensor unit with a laser from a distant location and reads the pitching angle, so that a space for providing a laser length measuring device is required, and the apparatus becomes large. is there. There was no direct measurement method for rolling. Moreover, it cannot be a method for measuring the motion of a machine tool having a poor measurement environment.

  In addition, the standard that has been supplied to measure the motion error is guaranteed only the maximum value of the standard error, such as straightness and roundness, and a fine inspection of the currently required motion accuracy. Cannot play a sufficient role. Of course, it cannot be used to measure motion errors in a rotational motion in which the object of laser reflection changes direction. In addition, the interference shape measuring machine, which is another method used to guarantee a standard such as a straight ruler, is not sufficiently large in size and accuracy to be covered.

  The present invention has been made in view of the problems of the prior art, and provides a reference plane by accurately pricing the uneven shape and the surface normal angle shape, and consequently, pitching error and rolling error. An object of the present invention is to provide a measuring method of a surface to be measured that can extract a signal and perform highly accurate measurement. It also provides zero-point calibration standards for various multipoint methods known as the three-point method.

The method of measuring a surface to be measured according to claim 1, wherein a member having the surface to be measured is rotatably supported,
Disposing a first two-dimensional angle sensor at a position where the first measurement point on the rotation axis of the surface to be measured can be measured;
A zero point relating to the detection of the linear pitching angle is calibrated with respect to the first two-dimensional angle sensor at a position where the second measurement point on the measurement surface with a predetermined radius R from the rotation axis can be measured. Disposing a second two-dimensional angle sensor,
The surface normal angle of the first measurement point is measured two-dimensionally by the first two-dimensional angle sensor while rotating the member having the surface to be measured, and the second two-dimensional angle sensor is used to measure the surface normal angle. Measuring the surface normal angle of the second measurement point in two dimensions;
Arranging the first two-dimensional angle sensor and the second two-dimensional angle sensor on the same circumference to calibrate a zero point related to detection of a linear rolling angle;
Removing a linear pitching error and a linear rolling error from the measurement value of the second two-dimensional angle sensor based on the measurement value of the first two-dimensional angle sensor;
The surface normal angle between the point on the rotation axis and the point on the circumference of the radius R is interpolated by changing the interval between the first two-dimensional angle sensor and the second two-dimensional angle sensor. It has the step to perform.

  According to the present invention, it is possible to eliminate the linear pitching error and the linear rolling error from the measurement value of the second two-dimensional angle sensor, and the surface normal of the first measurement point (the rotation center point of the surface to be measured). It can be related to the direction as a reference, whereby a highly accurate surface normal angle shape measurement can be performed.

Furthermore, the present invention provides
The interval between the first two-dimensional angle sensor and the second two-dimensional angle sensor is reduced from the initial R to R / N (where N> 1), and the two two-dimensional angle sensors are Disposing at any measurable position on one radius including the first measurement point on the rotation axis of the surface to be measured;
While rotating the member having the surface to be measured, surface normal angles on two circumferences having different radii measured by the two two-dimensional angle sensors are measured in two dimensions, and the two different radii are measured. Measuring in two dimensions the difference between surface normal angles on two circumferences without being affected by surface deflection associated with rotation of the surface to be measured;
A difference between surface normal angles on the two circumferences is obtained at a plurality of points on the one radius, and then evaluated by integration in the radial direction. The difference between the surface normal angle at the measurement point and the second measurement point of the radius R, and the first measurement point on the rotation axis of the previous measurement surface that is first known at the previous sensor interval R And the difference between the surface normal angles at the second measurement point of the radius R to calibrate the zero deviation caused when the interval between the two two-dimensional angle sensors is changed. It is characterized by correcting the data of the surface normal angle difference obtained at the interval R / N.
When the interval R / N between the two two-dimensional angle sensors is selected, an integer such as N = 10 is used, and the position of the first two-dimensional angle sensor is R · K / N (where K = 0 , 1, 2, N, N + 1,...) In many cases, the accuracy when calibrating the deviation of zero is increased. Therefore, it is preferable to include the case where N is an integer in the sensor interval.

  Furthermore, the present invention is a measuring apparatus used in the above-described method for measuring a surface to be measured, which includes a rotary table that rotatably supports the surface to be measured, two two-dimensional angle sensors, and a predetermined two-dimensional angle sensor. It has a holding tool held at intervals.

  Furthermore, the present invention is a flat plate having a measured surface measured by the above-described measuring method of the measured surface.

  Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a diagram showing coordinate axes used in the present specification. The direction of the rotation axis of the measurement surface CP is the Z axis, the direction orthogonal to the origin O on the measurement surface CP is the X axis, and the direction orthogonal to the Z axis and the X axis is the Y axis. An arbitrary point on the measurement surface CP is represented by a radius r from the rotation axis and an angle θ from the origin O. If the angle of the surface normal of the surface CP to be measured is obtained, the surface shape can be obtained by integrating the angle. Here, the two-dimensional angle sensor refers to a sensor that can measure the inclination of the surface normal of the measurement point in two dimensions.

FIG. 2 is a diagram for explaining the calibration of the zero point related to the detection of the linear pitching angle between the first two-dimensional angle sensor and the second two-dimensional angle sensor. First, as shown in FIG. 2A, a test piece TP having an upper surface having a shape of f (x) and a lower surface having a shape of g (x) when the longitudinal direction is the X direction is prepared. . Next, the first two-dimensional angle sensor SA that measures the shape of the upper surface of the test piece TP and the second two-dimensional angle sensor SB that measures the shape of the lower surface of the test piece TP are supported by the arm AM. The specimen TP is moved in the longitudinal direction (X direction). Here, when the output from the first two-dimensional angle sensor SA is μ _A (x) and the output from the second two-dimensional angle sensor SB is μ _B (x), the following (1), (2) The formula holds.

  Next, as shown in FIG. 2B, the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB are fixed to the lower arm AM, and the shape of the lower surface of the test piece TP is changed. (3) Formula is obtained by measuring. Further, as shown in FIG. 2C, while maintaining the relationship between the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB (for example, the arm AM is turned upside down), each of the test pieces is tested. By measuring the shape of the upper surface of TP, equation (4) is obtained. From the expressions (1) to (4), the zero point α (error in the pitching direction) relating to the detection of the linear pitching angle between the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB is calibrated. It will be. However, at such a stage, the zero point relating to the detection of the linear rolling angle is not calibrated, and the error in the rolling direction remains.

  Next, as shown in FIG. 3, with the two-dimensional angle sensors SA and SB attached to the holder HL (without changing the mutual distance), the first two-dimensional angle sensor SA is moved to the first position on the rotation axis AX. One measurement point p1 is arranged at a measurable position, and the second two-dimensional angle sensor is arranged at a position where the second point p2 on the circumference of the radius R can be measured. Here, while rotating the rotary table RT, the first measurement point p1 is measured by the first two-dimensional angle sensor SA, and the second measurement point p2 is measured by the second two-dimensional angle sensor SB. The rotation angle for each measurement is arbitrary, but a finer one is preferable.

  Here, in the above-described process, the zero point regarding the detection of the linear pitching angle is calibrated between the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB. Since the zero point relating to the detection of the angle is calibrated, the rotational axis AX is obtained from the outputs of the two-dimensional angle sensors SA and SB obtained simultaneously by rotating the measurement surface CP together with the rotary table RT and at one or more rotational positions. Therefore, the surface normal angle shape on the circumference of the surface CP to be measured with a predetermined radius R can be obtained with high accuracy.

  FIG. 4 is a diagram for explaining the zero point calibration relating to the detection of the linear rolling angle between the first two-dimensional angle sensor and the second two-dimensional angle sensor. A member (circular flat plate) M whose upper surface is the surface CP to be measured is disposed on a rotary table RT driven by a driving device (not shown). Further, the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB are connected by a straight plate-shaped holder HL fixed to a rigid body (not shown) obtained by removing a part of the arm AM of FIG. Hold. The measured values of the two-dimensional angle sensors SA and SB are stored in a memory (not shown). Here, the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB are arranged on one diameter on a circle having a radius R / 2. Further, the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB maintain the relationship at the time of measurement shown in FIG. 2C, so that the zero point calibration relating to the detection of the linear pitching angle can be performed. Shall be made. For a two-dimensional angle sensor, for example, by irradiating a light beam, the angle of the surface normal on the measured surface with respect to the XZ plane and YZ based on the position where the reflected light from the measured surface is received by the CCD or the like. It is known to obtain an angle with respect to a plane in two dimensions, and details are not described below.

  Here, while rotating the rotary table RT, the third measurement point p3 is measured by the first two-dimensional angle sensor SA, and the fourth measurement point p4 is measured by the second two-dimensional angle sensor SB. The rotation angle for each measurement is arbitrary, but a finer one is preferable.

  At this time, the measurement points p3. For the tilt motion around the diameter connecting p4, the same values are included in the first and second two-dimensional angle sensors SA and SB. Further, the average value of one rotation of the linear rolling angle shape along the circumference is theoretically zero. Therefore, the difference in the average value over one rotation of the outputs of the two sensors SA and SB gives the difference in the zero point of the linear rolling angle of both sensors. As a result, the zero point relating to the detection of the linear rolling angle between the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB can be calibrated.

This can be expressed by equations (5) to (6). ν _A (θ) and ν _B (θ) are outputs (measured values) of the tilt angles in the X-axis direction of the two-dimensional angle sensors SA and SB, respectively, and φ _y (θ) is y of the tilt motion of the rotation axis. It is an axial component, and f ′ _θ (R / 2, θ) indicates a linear rolling angle shape (circumferential pitching angle shape) along a circle having a radius R / 2. Also, β represents the zero difference between the two sensors for the linear rolling angle.

  As a result of the above measurement, the surface normal angle shape on the circumference of the radius R from the rotation axis AX on the measured surface CP becomes known with reference to the value of the point on the rotation axis AX, and from the integration, from the rotation axis AX The shape on the circumference of the radius R is known. Here, for the first time, the relationship between the two-dimensional angle sensors SA and SB is broken, and the distance between the two is changed and fixed on the holder HL.

  When the sensor interval is determined as R / N, concentric circles of the interval are sequentially measured by the sequential method. The positions of the first two-dimensional angle sensor SA and the second two-dimensional angle sensor SB are (r = 0, r = R / N), (r = R / N, r = 2R / N), (r = (2R / N, r = 3R / N), (r = (N−1) R / N, r = NR / N). Measurement is performed and stored as data.

  When the measurement is performed in this way, finally, the two-dimensional angle sensors SA and SB measure the measurement points on the measurement surface CP with the radius R from the rotation axis AX. This is nothing but the measurement of the second measurement point p2 on the measured surface CP with the radius R from the rotation axis AX measured before breaking the relationship between the two-dimensional angle sensors SA and SB. Therefore, the two-dimensional surface normal angle shape data on the circumference of the radius R from the rotation axis AX and the 2 of the circumference of the circumference of the same radius R obtained by the sensor interval R / N, measured directly by the above method. Comparing with the dimensional surface normal angle shape data, the accumulated accidental error can be found. By correcting the error by interpolation or the like, two-dimensional surface normal angle shape data of all measurement points in the radius R / N to R range from the rotation axis AX can be acquired, and the entire upper surface of the measured surface CP can be obtained. A two-dimensional surface normal angle shape can be obtained. Of course, if necessary, this sequential method can be extended to the measurement of positions where r> R. Further, a method called a general two-point method in which r is a position that does not become an integral multiple of R / N may be employed instead of the sequential method.

  In this way, the flat plate member M having the measured surface CP whose two-dimensional normal angle shape is accurately measured can be used as a ruler serving as a calibration reference for the measuring apparatus.

  According to the present invention described above, an operation such as reversing a member to be measured, which is necessary in a so-called reversal method, is unnecessary, and the circumferential rolling angle shape and the circumferential angle pitching shape of the surface to be measured, and those The uneven shape of the surface obtained by integration can be measured with high accuracy. In addition, since the origin adjustment in the first two-dimensional angle sensor and the second two-dimensional angle sensor can be performed at any time with respect to the surface to be measured, it is possible to perform high-precision measurement while avoiding problems such as accumulation of errors. Can do. In addition, the shape of a large-area surface can be measured with high accuracy by using it as a measured surface reference surface or a reference straight ruler once measured.

  In addition, according to the present invention, not only can the zero point adjustment of the angle two-point method with any sensor interval be performed, but also a three-point method in which three displacement sensors are arranged in a straight line in order to measure a straight shape, a displacement A mixing method in which two sensors and three angle sensors are arranged in a straight line, a three-angle method in which three angle sensors for measuring a planar shape are arranged two-dimensionally, and a four-dimensional displacement sensor It can be used for zero point calibration of all multipoint methods for shape measurement, such as a four-point displacement method and a two-dimensional mixed method in which an angle sensor and a displacement sensor are two-dimensionally arranged.

  In the above-described mixing method, a mixing sensor capable of detecting the angle and displacement of the same point is effective. FIG. 5 is a schematic diagram illustrating an example of a mixing sensor having both a displacement sensor and an angle sensor for realizing this. is there. In FIG. 5, the light beam emitted from the light source OS, which is a semiconductor laser, is reflected by the prism PS1, travels toward the surface to be measured, and the reflected light indicated by the dotted line passes through the prism PS1 and enters the prism PS2. Passes through and enters the interferometer IM1. The interferometer IM1 can measure the distance to the surface to be measured by the principle of interference. On the other hand, the remainder of the light beam is reflected by the prism PS2, collected by the lens L, and incident on the light receiving surface of a quadrant photodiode PSD (or CCD) that detects the spot position of the light. The angle of the surface to be measured can be measured based on the position of the received spot. In this example, a part of the light beam emitted from the light source OS passes through the prism PS1, is reflected by the prism PS3, and is received by the interferometer IM2, thereby the light beam emitted from the light source OS. Wavelength can be monitored.

It is a figure which shows the coordinate axis used in this specification. It is a figure for demonstrating the calibration of the zero point regarding the detection of the linear pitching angle between the 1st two-dimensional angle sensor and the 2nd two-dimensional angle sensor. It is a figure which shows the state which measures the shape of to-be-measured surface CP using a 1st two-dimensional angle sensor and a 2nd two-dimensional angle sensor. It is a figure for demonstrating the calibration of the zero point regarding the detection of the linear rolling angle between the 1st two-dimensional angle sensor and the 2nd two-dimensional angle sensor. It is the schematic which shows an example of the mixing sensor which has both a displacement sensor and an angle sensor.

Explanation of symbols

AM arm AX rotation axis CP surface to be measured HL holder IM1 interferometer IM2 interferometer L lens OS light source PS1 prism PS2 prism PS3 prism RT rotation table SA first two-dimensional angle sensor SB second two-dimensional angle sensor PSD4 divided photo Diode TP test piece

Claims (1)

A step of rotatably supporting a member having a surface to be measured;
Disposing a first two-dimensional angle sensor at a position where the first measurement point on the rotation axis of the surface to be measured can be measured;
A zero point relating to the detection of the linear pitching angle is calibrated with respect to the first two-dimensional angle sensor at a position where the second measurement point on the measurement surface with a predetermined radius R from the rotation axis can be measured. Disposing a second two-dimensional angle sensor,
The surface normal angle of the first measurement point is measured two-dimensionally by the first two-dimensional angle sensor while rotating the member having the surface to be measured, and the second two-dimensional angle sensor is used to measure the surface normal angle. Measuring the surface normal angle of the second measurement point in two dimensions;
Arranging the first two-dimensional angle sensor and the second two-dimensional angle sensor on the same circumference to calibrate a zero point related to detection of a linear rolling angle;
Removing a linear pitching error and a linear rolling error from the measurement value of the second two-dimensional angle sensor based on the measurement value of the first two-dimensional angle sensor;
By changing the interval between the first two-dimensional angle sensor and the second two-dimensional angle sensor, the relationship between the surface normal angle measured for the first measurement point and the second measurement point is used as a reference. A method for measuring a surface to be measured, comprising the step of interpolating a surface normal angle of a point between the first measurement point and the second.