JPH1183450A - Error correcting method for optical probe type shape measuring machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To separate error components into a probe-originating error component and an orthoganality error component, and estimate and correct the probe error at optional inclination accurately. SOLUTION: An object to be measured 1 is disposed and fixed to a stage 4, which is scanned in the X-axis direction under such a control that the light convergence point of a light probe 7 matches with the surface of the object 1 in the Z-axis direction, and the surface shape of the object 1 is read in the form of coordinates from the output value of laser length measuring machines 5 and 6. Two reference spherical surfaces having different radii are used as the object to be measured 1, and their surface shapes are measured, and the measuring errors at different measuring points are extracted. The acquired measuring errors are separated into the probe-originating error component and an error component originating from the degree of orthogonal intersection, followed by storing in memory the relationship between the inclination of each measuring point and the probe-originating error component, and the inclination of each measuring point is determined from the measured data for an arbitrary plane, and the probe-originating error component is calculated from the inclinations of the measuring points, and a subtraction is made from the measurements so that necessary correction for the error takes place.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an error correction method for an optical stylus type shape measuring instrument, and more particularly to a method for correcting a probe error and an orthogonality error of an optical stylus type shape measuring instrument. It can be applied to error correction of a three-dimensional shape measuring machine.

[0002]

2. Description of the Related Art A shape measuring apparatus using an optical probe is used for measuring a shape of an aspheric surface or the like with high accuracy.
FIG. 1 is a diagram showing an example of the shape measuring device as described above,
As is well known, the DUT 1, the X-axis reference mirror 2, and the Z-axis reference mirror 3 are fixedly arranged. At this time, the reference mirrors 2 and 3 are arranged as orthogonal as possible. X, Z 2
An X-axis laser length measuring device 5, a Z-axis laser length measuring device 6, and an optical probe 7 are attached to the stage 4 that can move in the axial direction. Here, the stage 4 is scanned in the X-axis direction while controlling the focal point of the optical probe 7 and the surface of the DUT 1 in the Z-axis direction. The readings of 5 and 6 are stored as coordinate values. as a result,
The contour shape of the DUT 1 is measured as a point sequence of coordinate data. A three-dimensional shape measuring machine can be realized by the same principle.

[0003]

As described above, the measurement result of the optical stylus type shape measuring instrument includes an error (probe error) depending on the inclination of the measured surface of the DUT 1 as a characteristic of the optical probe 7. There is an error (orthogonality error) caused because the orthogonality of the reference mirrors 2 and 3 is not sufficient.

According to the present invention, there is provided an optical stylus type shape measuring instrument as described above, wherein: an error component is separated, a probe error is corrected, and an orthogonality error is corrected by a simpler method; To improve the correction accuracy by separating the measurement error component from the data at high speed and accurately. ・ Applying the relationship between the inclination and the probe error to the model formula to accurately estimate the probe error amount at an arbitrary inclination. It is intended to increase the correction accuracy by quickly and accurately estimating the orthogonality error amount from the measured value of the reference spherical surface including the orthogonal error component, and so on.

[0005]

According to a first aspect of the present invention, there is provided a stage movable in two orthogonal axes (X axis and Z axis).
An X-axis reference mirror and a Z-axis reference mirror fixed and disposed orthogonal to the stage; an X-axis laser length measuring device, a Z-axis laser length measuring device, and an optical probe disposed on the stage Having a fixedly arranged object to be measured with respect to the stage, while controlling the stage such that the focal point of the optical probe coincides with the surface of the object to be measured in the Z-axis direction, In the measurement error correction method in the optical stylus type shape measuring instrument that scans in the X-axis direction and reads the surface shape of the object as coordinate values from readings of the laser length measuring devices, the object to be measured has a different radius. Using two reference spheres,
A means for measuring the surface shape of each of these reference spheres having different radii of curvature, extracting a measurement error at each measurement point, a means for separating the measurement error into a probe error component and an orthogonality error component, A means for storing the relationship between probe error components, a means for calculating the slope of each measurement point from measurement data on any surface, and a probe error component calculated from the slope of each measurement point, and subtraction from the measured value to correct errors Means for correcting the probe error by means of
By using a simple method to separate a probe error and an orthogonality error and use them for probe error correction, more accurate correction can be performed.

According to a second aspect of the present invention, two orthogonal axes (X axis,
A stage movable in the (Z-axis) direction, an X-axis reference mirror and a Z-axis reference mirror fixedly disposed perpendicular to the stage, an X-axis laser length measuring device disposed on the stage, A Z-axis laser length measuring device, and an optical probe, wherein an object to be measured is fixedly arranged with respect to the stage, and the focal point of the optical probe and the object to be measured are arranged in the Z-axis direction. Scanning in the X-axis direction while controlling the surfaces so that they coincide with each other, and correcting the measurement error in the optical stylus type shape measuring instrument that reads the surface shape of the object as coordinate values from readings of the laser length measuring devices. In the method, two reference spheres having different radii are used as the object to be measured, a surface shape of each of the reference spheres having a different radius of curvature is measured, and a measurement error at each measurement point is extracted. Two reference spheres and the reference sphere Means for extracting a measurement error of each measurement point from the measurement data, means for separating the measurement error into a probe error component and an orthogonality error component, means for storing the relationship between the inclination of each measurement point and the probe error component, Means for calculating the slope of each measurement point from the measurement data of the surface, means for calculating the probe error component from the slope of each measurement point, and correcting the error by subtracting from the measurement value; and The probe error and the orthogonality error are corrected by means for estimating the angle deviation of the reference mirror, means for storing the estimated angle deviation, and means for correcting coordinates based on the stored estimated value of the angle deviation. Thus, the probe error and the orthogonality error are separated by a simple method, and by using each of them for correction, it is possible to perform more accurate correction.

According to a third aspect of the present invention, in the first or second aspect, the means for extracting the measurement error of each measurement point from the measurement data of the reference spherical surface is a model formula.

[0008]

(Equation 4)

A means for performing a least-squares approximation to a non-linear model using as parameters the shift amounts x ₀ and z ₀ from the coordinate origin of the measuring machine to the coordinate origin of the reference spherical surface; And a means for calculating the difference between the measurement error components, so that the measurement error component can be extracted at high speed and with high accuracy. Note that the approximate similarity of the orthogonality error cannot be established unless the measurement error component is accurately separated, but the approximate correlation has been confirmed by the present invention.

According to a fourth aspect of the present invention, in the first or second aspect, the means for storing the relationship between the inclination of each of the measurement points and the probe error component is a polynomial approximation of the point sequence data indicating the relationship between the inclination and the error. Means for calculating the probe error component from the slope of each measurement point described above, and subtracting the measured value from the measured value to correct the error. It is characterized in that it is a means for solving an error by solving a polynomial and subtracting it, so that it is possible to estimate a probe error amount at an arbitrary inclination with high accuracy and stability. is there. Further, by performing a polynomial approximation, it is possible to cancel a random error component such as a tracking error component that occurs because the stage cannot follow the surface of the measured object.

According to a fifth aspect of the present invention, in the first or second aspect of the present invention, the means for estimating the angle deviation of the reference mirror from the extracted orthogonality error data includes a model formula.

[0012]

(Equation 5)

In the above, the angle deviation C is estimated by performing a least squares approximation to a nonlinear model using the shift amounts x ₀ and z ₀ from the coordinate origin of the measuring instrument to the coordinate origin of the reference spherical surface and the angle deviation C as parameters. The present invention is characterized in that the angle deviation C can be obtained at high speed and with high accuracy by a simple method.

According to a sixth aspect of the present invention, there is provided a reference sphere having a sufficiently small radius of curvature, a means for extracting a probe error of each measurement point from measurement data of the reference sphere, and a relation between a slope of each measurement point and a probe error component. A means for storing, a means for calculating a slope of each measurement point from measurement data of an arbitrary surface, and a means for calculating a probe error component from a slope of each measurement point and subtracting the measured value from the measured value to correct the error. It is characterized by correcting the error, so that only one reference sphere is measured,
Only the probe error can be separated and corrected.

According to a seventh aspect of the present invention, in the first or second aspect, the means for extracting the measurement error of each measurement point from the measurement data of the reference spherical surface is represented by the following model formula:

[0016]

(Equation 6)

Means for performing a least-squares approximation to a non-linear model using the shift amounts x ₀ , y ₀ , and z ₀ from the coordinate origin of the measuring instrument to the coordinate origin of the reference spherical surface as:
The present invention is characterized in that it has means for calculating the difference between the model formula and each of the measurement points, so that the invention of claim 3 is adapted to three-dimensional measurement.

[0018]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the present invention, the shape of an object to be measured is measured using an optical stylus type shape measuring instrument having the structure shown in FIG. 1. As described above, FIG. The measurement results of the optical stylus type shape measuring instrument having the configuration shown include an error (probe error) depending on the inclination of the measured surface of the DUT 1 as a characteristic of the optical probe 7 and the orthogonality of the reference mirrors 2 and 3. There is an error (orthogonality error) caused by insufficient degrees. First, the probe error will be described. The probe error is an error that depends on the optical stylus displacement sensor, and is an error that depends on the inclination between the optical axis of the objective lens and the normal vector of the measured surface at each measurement point. Therefore, for the measurement results of two reference spheres having different radii of curvature R, x ′ = x /
When converted to R, the slope at the same x 'is the same, and the probe error is also the same.

Next, the orthogonality error will be described. Here, a two-dimensional (x, z) coordinate system is considered. FIG. 2 shows a coordinate system (x′-z) having an angular deviation C with respect to an ideal spherical surface.
FIG. 6 is a diagram showing a relationship between coordinates P when measured in a coordinate system (coordinate system). In this case, (x,
The point P in z) is represented by (x / cos C, z + x × sin C) in a coordinate system having an angle deviation C (x′-z coordinate system). Here, since C is close to 0 for several seconds, sin
It can be approximated as C ≒ C, cos C ≒ 1. Therefore,
Point P is approximately represented as (x, z + xxC) in the x'-z coordinate system.

Here, the influence of the measurement result when the reference sphere is measured by a measuring machine having an angular deviation will be considered. FIG.
Is a diagram showing a comparison between measured values of an ideal spherical surface (curve A) and a spherical surface (curved surface B) containing an error. In the figure, the angle deviation is exaggerated to C = 0.1 [rad]. It is plotted. Here, the deviation of the measured value from the ideal spherical surface is called an orthogonality error. From FIG. 3, it can be seen that, for the same angular deviation C, the geometrical similarity is maintained in the orthogonality error even if the radius of curvature R changes.

Here, with respect to two spherical surfaces (here, R = 10 mm and 100 mm) having different radii of curvature, reference spherical surface data is created within a specific range (here, ± 30 [deg]). The coordinate transformation described above (here, C
= 0.0001 [rad] for about 20 seconds). The actual measurement data is the shift amount (x ₀ ,
Since z ₀ ) is not known, x ₀ , z ₀ ) was optimized so that the sum of squares of the difference from the ideal sphere was minimized, and then the difference from the reference sphere was obtained. Here, when x / R is plotted on the horizontal axis and (error) / R is plotted on the vertical axis, the results shown in FIG. 4 are obtained. The error components overlapped with an error of 1.0E-11 [mm]. Therefore, if the orthogonality error is on the order of a few seconds,
When x '= x / R is converted in the same manner as the probe error, the orthogonality error at the same x' can be considered to be proportional to the radius of curvature.

(Inventions of Claims 1 and 2) First, in the optical stylus type shape measuring instrument as shown in FIG. 1, the orthogonality error is adjusted to an accuracy of several seconds by a four-right angle master or the like. Next, two calibration spherical surfaces (here, R = 10 and R = 100) are measured. Then, for the measurement results of the two reference spheres, an error component is extracted by calculating the difference between the curvature radius R of each of the reference spheres and the ideal spherical model having the same R.

For the extracted error component, x '= x / R
Expressing the point sequence data E (R) converted into E (R) as a probe error Ep and an orthogonality error Es (R), E (10) Ep + Es (10) E (100) = Ep + Es (100) Here, Es is approximately Es from the relationship described above.
(100) = 10 Es (10). Therefore, Es (10) = (E (100) -E (10)) / 9, and thus Ep = E (10)-(E (100) -E (10)) / 9. Here, since the x-axis is x ′ = x / R = sin θ, by converting to θ = arcsin x ′, the converted data indicates the relationship between the inclination and the probe error. This data is stored in such a way that the probe error can later be estimated from the slope.

Next, the inclination of each measurement point of the actual measurement result is estimated. This is obtained, for example, by extracting several pieces of data in the vicinity and performing linear approximation on the data. In addition, it is also possible to obtain the data of the whole or the vicinity by polynomial approximation and the differential value thereof. Then, a probe error is estimated from the estimated inclination. By subtracting this from the measured value, probe error correction is performed. Although the probe error separation method shown here has been described in a two-dimensional plane, the probe error can be separated in the same way in three dimensions.

(Invention of Claim 2) As described above, a probe error is separated and a correction parameter is created. Next, the probe error is corrected for the measurement result of the reference spherical surface having the larger radius of curvature. Here, the parameter of the angle deviation C is estimated such that the sum of squares of the shape error when the error is corrected is minimized. The angle deviation C is stored. When measuring an arbitrary measurement target, z '= z + C
By performing x conversion, the orthogonality error of the measuring instrument can be corrected.

(Invention of Claim 3) The sum of squares of the difference between the following translational movement (x ₀ , z ₀ ) and the model equation of the spherical surface expressed with the radius of curvature R as a variable is minimized. Perform variable optimization.

[0027]

(Equation 7)

(Invention of Claim 4) As described above, since the relationship between the inclination at each measurement point and the probe error is given, this is approximated by a polynomial and the coefficients of each term are stored.
When estimating the probe error from the slope when taking an arbitrary shape, from the stored parameters and the slope,
Estimate the probe error by solving the polynomial.

Next, a specific method of estimating the angle deviation C will be described. First, a model equation of a spherical surface having an origin at an arbitrary position in a coordinate system having an angular deviation C is shown below.

[0030]

(Equation 8)

Here, the parameter C can be estimated by performing a least-squares approximation to a non-linear model using C, x ₀ , and z ₀ as parameters.

FIG. 4 is a diagram showing the relationship between x / R and (orthogonality error) / R. As is apparent from FIG. 4, when the angle deviation C is on the order of several seconds, The effect of the orthogonality error per mm is about 5 nm in PV. Therefore, for example, for a measuring instrument with a measurement accuracy of 0.1 μm, R
When a reference spherical surface of = 2 mm is measured, the influence of the orthogonality error is about 10 nm in PV, which is sufficiently small with respect to the measurement accuracy. Therefore, it can be considered that the measurement error of the reference spherical surface does not include the orthogonality error component.
Therefore, a probe error can be obtained by measuring one reference sphere and extracting an error from the ideal sphere.

(Invention of claim 7) The difference between the three-dimensional shape measurement result and the model expression of the spherical surface expressed by using the following translational movement (x ₀ , y ₀ , z ₀ ) as a variable is 2 Optimize variables to minimize sum of squares.

[0034]

(Equation 9)

[0035]

According to the first aspect of the present invention, there are provided two types having different curvature radii.
Two reference spheres, means for extracting a measurement error of each measurement point from the measurement data of the reference sphere, means for separating the measurement error into a probe error component and an orthogonality error component, a slope of each measurement point and a probe error component Means for storing the relationship between the two, and means for calculating the slope of each measurement point from the measurement data of an arbitrary surface, means for calculating a probe error component from the slope of each measurement point, and means for correcting the error by subtracting from the measured value. Thus, the probe error and the orthogonality error can be separated by a simple method, and the probe error can be corrected by using the probe error and the orthogonality error.

According to a second aspect of the present invention, there are provided two reference spheres having different radii of curvature, means for extracting a measurement error of each measurement point from measurement data of the reference sphere, and converting the measurement error into a probe error component and an orthogonality error component. Means for separating, means for storing the relationship between the inclination of each measurement point and the probe error component, means for obtaining the inclination of each measurement point from measurement data on an arbitrary surface, and calculation of the probe error component from the inclination of each measurement point Means for correcting the error by subtracting from the measured value, means for estimating the angle deviation of the reference mirror from the extracted orthogonality error data, means for storing the estimated angle deviation, and estimation of the stored angle deviation Since the probe error and the orthogonality error are corrected by the means for correcting the coordinates based on the values, the probe error and the orthogonality error are separated by a simple method, and by using each of them for correction, higher accuracy is achieved. Correction can be performed.

According to a third aspect of the present invention, in the first or second aspect, the means for extracting the measurement error of each measurement point from the measurement data of the reference sphere is a model formula.

[0038]

(Equation 10)

Means for performing a least-squares approximation to a non-linear model using the shift amounts x ₀ , z ₀ from the coordinate origin of the measuring machine to the coordinate origin of the reference spherical surface as a parameter, And means for calculating the difference between
The measurement error component can be extracted with high speed and high accuracy. Note that the approximate similarity of the orthogonality error cannot be established unless the measurement error component is accurately separated, but the approximate correlation was confirmed for the first time by the present invention.

According to a fourth aspect of the present invention, in the first or second aspect, the means for storing the relationship between the inclination of each measurement point and the probe error component is a polynomial approximation of the point sequence data indicating the relationship between the inclination and the error. Means for calculating the probe error component from the slope of each measurement point described above, and subtracting the measured value from the measured value to correct the error. Since the error is obtained by solving the polynomial and the error is subtracted, it is possible to stably and accurately estimate the probe error amount at an arbitrary inclination. Further, by performing the polynomial approximation, it is possible to cancel a random error component such as a tracking error component that occurs because the stage cannot follow the surface of the object to be measured.

According to a fifth aspect of the present invention, in the first or the second aspect of the present invention, the means for estimating the angle deviation of the reference mirror from the extracted orthogonality error data is a model formula.

[0042]

[Equation 11]

In the above, the least squares approximation to a non-linear model using the shift amounts x ₀ , z ₀ and the angle deviation C from the coordinate origin of the measuring instrument to the coordinate origin of the reference spherical surface as a parameter is performed.
Therefore, the angle deviation C can be obtained at high speed and with high accuracy by a simple method.

According to a sixth aspect of the present invention, there is provided a reference sphere having a sufficiently small radius of curvature, a means for extracting a probe error of each measurement point from measurement data of the reference sphere, and a relationship between a slope of each measurement point and a probe error component. Means for calculating the inclination of each measurement point from the measurement data of an arbitrary surface, and means for calculating the probe error component from the inclination of each measurement point and subtracting the error from the measurement value to correct the probe error. Is corrected,
With only one reference sphere measurement, only the probe error can be separated and corrected.

According to a seventh aspect of the present invention, in the first or second aspect, the means for extracting the measurement error of each measurement point from the measurement data of the reference sphere is represented by the following model formula:

[0046]

(Equation 12)

Means for performing least-squares approximation to a non-linear model using the shift amounts x ₀ , y ₀ , and z ₀ from the coordinate origin of the measuring instrument to the coordinate origin of the reference spherical surface as:
Since there is a means for calculating the difference between this model formula and each measurement point, the invention of claim 3 can be adapted to three-dimensional measurement.

[Brief description of the drawings]

FIG. 1 is a main part configuration diagram for explaining an example of a shape measuring apparatus using an optical probe.

FIG. 2 is a diagram of coordinates when measured in a coordinate system having an angle deviation C with respect to an ideal spherical surface.

FIG. 3 is a diagram comparing measured values of an ideal spherical surface and a spherical surface including an error.

FIG. 4 is a diagram illustrating a relationship between a coordinate error (orthogonality error) and a curvature R;

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... DUT, 2 ... X-axis reference mirror, 3 ... Z-axis reference mirror, 4 ... Stage, 5 ... X-axis laser length measuring device, 6 ... Z-axis laser length measuring device, 7 ... Optical probe.

Claims (7)

[Claims] 1. A stage movable in two orthogonal (X-axis, Z-axis) directions, an X-axis reference mirror and a Z-axis reference mirror fixed and disposed orthogonal to the stage, and the stage An X-axis laser length measuring device, a Z-axis laser length measuring device, and an optical probe are provided above, and an object to be measured is fixedly disposed on the stage. Is controlled in such a manner that the focal point of the optical probe coincides with the surface of the device under test, while scanning in the X-axis direction, and reading the surface shape of the device under test from the readings of the respective laser length measuring devices to coordinate values. In a method for correcting a measurement error in an optical stylus type shape measuring instrument which reads as two different reference spheres having different radii as the object to be measured, means for measuring the surface shapes of the reference spheres having different radii of curvature, respectively, Means for extracting the measurement error of the point; Means for separating the measurement error into a probe error component and an orthogonality error component, means for storing the relationship between the inclination of each measurement point and the probe error component, and means for obtaining the inclination of each measurement point from measurement data on an arbitrary surface An error correction method for an optical stylus type shape measuring device, wherein a probe error component is calculated from a slope of each measurement point, and the error is corrected by subtracting the probe error component from the measured value. 2. A stage movable in two orthogonal (X-axis, Z-axis) directions, an X-axis reference mirror and a Z-axis reference mirror fixedly disposed orthogonal to the stage, and the stage. An X-axis laser length measuring device, a Z-axis laser length measuring device, and an optical probe are provided above, and an object to be measured is fixedly disposed on the stage. Is controlled in such a manner that the focal point of the optical probe coincides with the surface of the device under test, while scanning in the X-axis direction, and reading the surface shape of the device under test from the readings of the respective laser length measuring devices to coordinate values. In a method for correcting a measurement error in an optical stylus type shape measuring instrument which reads as two different reference spheres having different radii as the object to be measured, means for measuring the surface shapes of the reference spheres having different radii of curvature, respectively, Means for extracting the measurement error of the point; Two reference spheres with different radii of curvature,
Means for extracting the measurement error of each measurement point from the measurement data of the reference sphere, means for separating the measurement error into a probe error component and an orthogonality error component, and stores the relationship between the inclination of each measurement point and the probe error component. Means, means for calculating the inclination of each measurement point from measurement data of an arbitrary surface, means for calculating a probe error component from the inclination of each measurement point, and subtraction from the measurement value to correct the error; and Means for estimating the angle deviation of the reference mirror from the degree error data, means for storing the estimated angle deviation, and means for correcting the coordinates based on the stored estimated value of the angle deviation, thereby correcting the probe error and the orthogonality error. An error correction method for an optical stylus type shape measuring instrument, characterized in that: 3. A means for extracting a measurement error at each measurement point from the measurement data of the reference spherical surface is obtained by a model equation Means for performing a least-squares approximation to a non-linear model using the shift amounts x ₀ and z ₀ from the coordinate origin of the measuring machine to the coordinate origin of the reference spherical surface as parameters, and calculating the difference between the model formula and each measurement point. 3. An error correction method for an optical stylus type shape measuring instrument according to claim 1, further comprising means for calculating. 4. The means for storing the relationship between the inclination of each measurement point and the probe error component is a means for polynomial approximating point sequence data indicating the relationship between the inclination and the error, and storing the parameters thereof. The means for calculating a probe error component from the slope of the point and subtracting the error from the measured value to correct the error is a means for solving the polynomial to find the error and subtracting the error from the parameter and the slope of each measurement point. 3. The error correction method for an optical stylus type shape measuring instrument according to claim 1 or 2, wherein: 5. A method for estimating an angle deviation of a reference mirror from the extracted orthogonality error data, comprising: A means for estimating the angle deviation C by performing a least squares approximation to a nonlinear model using the shift amounts x ₀ , z ₀ from the coordinate origin of the measuring instrument to the coordinate origin of the reference spherical surface and the angle deviation C as parameters. 3. The error correction method for an optical stylus type shape measuring instrument according to claim 1 or 2, wherein: 6. A reference sphere having a sufficiently small radius of curvature, means for extracting a probe error of each measurement point from measurement data of the reference sphere, means for storing a relationship between the inclination of each measurement point and a probe error component, Correcting the probe error by means for calculating the inclination of each measurement point from the measurement data of an arbitrary surface, and means for calculating the probe error component from the inclination of each measurement point and subtracting from the measured value to correct the error An error correction method for an optical stylus type shape measuring instrument, characterized in that: 7. A means for extracting a measurement error at each measurement point from the measurement data of the reference spherical surface is represented by the following model formula: Means for performing a least-squares approximation to a non-linear model using the shift amounts x ₀ , y ₀ , and z ₀ from the coordinate origin of the measuring machine to the coordinate origin of the reference spherical surface, and this model formula and each measurement point 3. An error correction method for an optical stylus type three-dimensional shape measuring instrument according to claim 1, further comprising means for calculating a difference between the two.