JP3474448B2 - Calibration method of coordinate axis squareness error and three-dimensional shape measuring device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical element such as a lens, and more particularly to a method of calibrating a perpendicularity error of a coordinate axis when measuring the shape of an aspherical surface and a three-dimensional shape measuring apparatus.

[0002]

2. Description of the Related Art A typical method for measuring the shape of an aspherical lens is an object to be measured at a position facing a probe provided on a three-axis orthogonal stage having an X-axis stage, a Y-axis stage and a Z-axis stage. Is fixed, the three-axis orthogonal stage is driven, and the surface of the object to be measured is scanned by the probe.
The position of the probe during this scanning is successively measured using a laser length measuring device or the like to obtain the shape of the surface of the measured object as point sequence data.

The probe for measuring the shape can be roughly classified into a contact type and a non-contact type. As shown in the configuration diagram of FIG. 5, the contact-type probe 2a has a contactor 23 elastically supported in a thrust direction by a spring 22 with respect to a housing 21, and has a contactor 23 from the outside to suck air into a porous material 25 through an intake port 24. This constitutes the static pressure air guide of the contact 23. A true sphere 26 is fixed to the tip of the contactor 23 on the side in contact with the surface to be measured 28, and a displacement gauge 27 is provided at a position facing the end surface on the opposite side. And housing 2
1 is fixed to drive the 3-axis orthogonal stage, and the contact 23
When the true sphere 26 at the tip of is pressed against the surface of the object to be measured, the spring 22 deforms and the output of the displacement meter 27 changes. There 3
The surface to be measured 28 is scanned while controlling the output of the displacement meter 27 to be constant by driving the axis orthogonal stage, and at the same time, the position of the probe 2a being scanned is sequentially measured using a laser length measuring device or the like. The shape of the measured object is measured. Further, by adding a slight output fluctuation of the displacement meter 27 during scanning to the output of the laser length measuring device or the like, the measured surface 28
It is possible to correct the tracking error of the probe 2a with respect to the unevenness of, and it is possible to perform more accurate measurement.

An optical probe is used as a typical example of the non-contact type probe. In the optical probe 2b, as shown in the configuration diagram of FIG. 6, the light emitted from the light source 31 is sent from the half mirror 32 to the lens 33, and is condensed by the lens 33 on the measured surface 27 with a minute spot of about several μm. To be done. The light reflected by the measured surface 28 passes through the lens 33 and the half mirror 32 again and is guided to the focus detection system 34. For the focus detection system 34, for example, an optical system similar to a pickup of an optical disk drive is used, and an electric signal according to the distance to the measured surface 28 is output. The three-axis orthogonal stage to which the optical probe 2b is attached is driven to bring the optical probe 2b close to the surface 28 to be measured to capture the output signal, and the three-axis orthogonal stage is controlled so that the output signal becomes constant. The surface 28 is scanned, and the position of the optical probe 2b during scanning is sequentially measured using a laser length measuring device or the like to measure the shape of the measured object.

[0005]

When the contact type or non-contact type probe is used to scan the surface of the object to be measured to measure the shape as described above, for example, the document "Ultra High Precision Three-dimensional Measuring Machine" is used. Accuracy calibration method "(Keiichi Yoshizumi, Optics Vol.
20, No. 5 (1991)),
The orthogonality of the three axes x, y, and z of the measurement coordinate system affects the measurement accuracy, and a measurement error of a size that cannot be ignored occurs depending on the orthogonality of the three axes.

For example, as shown in FIG. 7, an actual coordinate system (X, Y, Z) including three coordinate axis orthogonality errors is converted into an ideal orthogonal coordinate system (X ₀ , Y) that does not include orthogonality errors. ₀ , Z ₀ )
When overlaid on top, the actual coordinate system (X, Y, Z)
Coordinates of the point P in (px, py, pz) and the coordinates of the point P in the ideal Cartesian coordinate system (X ₀ , Y ₀ , Z ₀ ) (p
x ₀ , py ₀ , pz ₀ ) has the relationship of the following expression (1).

[0007]

[Equation 1]

However, (is, js, ks) represents a unit vector in the s direction, and A is a coordinate conversion matrix.

At this time, in the ideal coordinate system, a set of points P at a distance R from the origin, that is, a spherical surface having a radius R is the inner product of the following equation (2) in the actual coordinate system (X, Y, Z). The curved surface is represented by.

[0010]

[Equation 2]

In general, the equation (2) represents an elliptical surface.
That is, the expression (2) indicates that the spherical surface will be measured as an elliptic surface unless the squareness of the measurement coordinate system is accurate. Then, assuming a spherical surface having a radius of 20 mm as the object to be measured, the results of trial calculation of the influence of the squareness error are shown in FIGS. FIG. 8 shows the measurement error when the squareness error between the Y axis and the Z axis is 5 seconds (2.42 × 10 ⁻⁵ rad),
FIG. 9 shows the measurement error when the squareness error between the Z axis and the X axis is 5 seconds, and FIG. 10 shows the measurement error when the squareness error between the X axis and the Y axis is 5 seconds. In either case, a measurement error occurs on the order of several hundred nm.

When measuring in the order of sub-μm, it is necessary to suppress the squareness error of the three coordinate axes on the order of seconds. Moreover, since the angular deviation of the second order is a problem, the change over time cannot be ignored, and regular calibration work is required. As this calibration work, conventionally, a method of actually measuring a squareness error is used, and a reference spherical surface for calibration is measured so that the measurement result as illustrated in FIGS. 8 to 10 is as flat as possible. The method of finding the angle error by trial and error is adopted. However, each method has a disadvantage that it requires a skilled worker and requires a very long time for the calibration work.

The present invention solves the above drawbacks and automatically estimates the correction parameters by a simple operation without requiring a particularly skilled worker, and in a short calculation processing time, the squareness error of the coordinate axes of the three axes. It is an object of the present invention to provide a method of calibrating a perpendicularity error of a coordinate axis for correcting the error and a three-dimensional shape measuring apparatus.

[0014]

A method of calibrating a perpendicularity error of a coordinate axis according to the present invention comprises:
Calibration of the coordinate axis squareness error that measures the coordinates of the scanning path as three-dimensional orthogonal coordinate point sequence data and performs coordinate conversion on the measured point sequence data to correct the distortion of the measurement data caused by the squareness error between the measurement coordinate axes. The measurement coordinate system is designed to minimize the difference between the measurement data of the reference spherical surface and the elliptical surface obtained by measuring the shape of the reference spherical surface and converting the ideal spherical surface into the coordinate system for measurement. Transformation from a to the ideal coordinate system
It is characterized in that a conversion matrix is estimated, and the three-dimensional orthogonal coordinate point sequence data of the object to be measured is subjected to coordinate conversion using the parameters of the estimated coordinate conversion matrix to correct the squareness error between the measurement coordinate axes.

Measurement reference points are set in the vicinity of the center of the measurement range of the reference spherical surface, and the point sequence data on a plurality of paths are radially arranged including the reference points, or a plurality of points are arranged concentrically with respect to the reference points. It is desirable to estimate the coordinate conversion matrix using point sequence data on the route or point sequence data on a plurality of routes arranged in a concentric polygonal shape with respect to the reference point.

The three-dimensional shape measuring apparatus of the present invention comprises a shape measuring probe provided on the three-axis orthogonal moving means, a moving amount measuring means for measuring the moving amount of each axis of the orthogonal moving means, a coordinate data calculating means, and The orthogonal movement means performs scanning following the shape measurement probe on the reference spherical surface and the surface of the object to be measured, and the movement amount measurement means measures the movement amount of each axis of the orthogonal movement means. The coordinate data calculation means calculates the coordinates of the scanning path of the shape measuring probe from the movement amount measured by the movement amount measurement means as three-dimensional orthogonal coordinate point sequence data, and the arithmetic processing means uses the ideal spherical surface as the measurement coordinate system. From the coordinate system for measurement to the ideal coordinate system so as to minimize the difference between the ellipsoid obtained by coordinate transformation and the measurement data of the reference sphere.
The coordinate transformation matrix to the 3D orthogonal coordinate point sequence data of the DUT is estimated by using the parameters of the estimated coordinate transformation matrix.
And performing the perpendicularity error correction between the measurement axes by performing coordinate transformation data.

The coordinate data calculating means sets a measurement reference point near the center of the measurement range of the reference spherical surface, and concentric circles with respect to the point sequence data or the reference points on a plurality of paths radially arranged including the reference point. It is desirable to send point sequence data on a plurality of paths arranged in a line or point sequence data on a plurality of paths arranged in a concentric polygonal shape to the reference point to the arithmetic processing means.

The moving amount measuring means is preferably a laser interferometer. Further, the laser interferometer of the movement amount measuring means and the shape measuring probe are installed on the same moving table, and the position of the tip of the shape measuring probe is always on the same straight line as each measuring optical path of the laser interferometer. It is advisable to dispose the laser interferometer lengthwise.

Further, a static pressure fluid guide may be used as the orthogonal moving means.

[0020]

BEST MODE FOR CARRYING OUT THE INVENTION The three-dimensional shape measuring apparatus of the present invention has a shape measuring probe, a movement amount measuring means, a coordinate data calculating section, an arithmetic processing section and an output section which are provided on a three-axis orthogonal stage. The shape measuring probe scans the surface of the object to be measured, which is fixed on the mounting table, by driving the three-axis orthogonal stage. The moving amount measuring means is, for example, a laser interferometer, and measures the moving amount of each axis of the three-axis orthogonal stage. The coordinate data calculation unit calculates the coordinates of the scanning path of the shape measuring probe from the movement amount measured by the movement amount measuring means as three-dimensional orthogonal coordinate point sequence data (hereinafter referred to as point sequence data). The arithmetic processing unit has a switching unit, a coordinate conversion matrix estimation unit, and a squareness error correction unit.

When measuring the shape of an object to be measured such as a lens with this three-dimensional shape measuring apparatus, first, the reference spherical surface is fixed to the mounting table, the triaxial orthogonal stage is driven, and the reference spherical surface is measured by the shape measuring probe. While following the profile scanning, the moving amount measuring means detects the moving amount of each axis of the three-axis orthogonal stage and sends it to the coordinate data calculating section. The coordinate data calculation unit calculates point sequence data of the scanning path of the reference spherical surface from the transmitted movement amount and sends it to the arithmetic processing unit. The switching unit of the arithmetic processing unit sends the point sequence data sent from the coordinate data calculation unit to the coordinate conversion matrix estimation unit during the contour scanning of the reference spherical surface. The coordinate transformation matrix estimation unit estimates the coordinate transformation matrix so as to minimize the difference between the elliptical surface obtained by coordinate transformation of the ideal sphere and the sent point sequence data of the reference sphere. Next, the object to be measured is fixed to a mounting table, and while driving the three-axis orthogonal stage to scan the surface of the object to be measured by the shape measuring probe, the movement amount measuring means is used to move each axis of the three-axis orthogonal stage. The amount of movement is detected and sent to the coordinate data calculation unit. The coordinate data calculation unit calculates point sequence data of the scanning path of the surface of the object to be measured from the sent movement amount and sends it to the arithmetic processing unit. The switching unit of the arithmetic processing unit sends the point sequence data sent from the coordinate data calculation unit to the squareness error correction unit during the contour scan of the measured object. The squareness error correction unit performs coordinate transformation of the sent point sequence data using the parameters of the coordinate transformation matrix estimated by the coordinate transformation matrix estimation unit, and transforms the point sequence data between the measurement coordinate axes into the shape data. And send it to the output section. The output unit outputs the sent shape data to a display device, a storage device, or the like.

[0022]

1 is a block diagram showing the configuration of an embodiment of the present invention. As shown in the figure, the three-dimensional shape measuring device has a three-axis orthogonal stage 1, a shape measuring probe 2, a movement amount measuring means 3, a coordinate data calculation unit 4, an arithmetic processing unit 5, and an output unit 6. As shown in FIG. 2, the three-axis orthogonal stage 1 has an X-axis stage 7, a Y-axis stage 8 and a Z-axis stage 9, and is a contact type or non-contact type shape measurement probe 2
And a mounting table 11 for fixing the object to be measured 10 is provided at a position facing the shape measuring probe 2. The shape measuring probe 2 scans the surface of the object to be measured 10 by driving the three-axis orthogonal stage 1. The movement amount measuring means 3 is, for example, a laser interferometer, and measures the movement amount of each axis of the triaxial orthogonal stage 1, that is, the movement amount of the shape measuring probe 2. The coordinate data calculation unit 4 uses the movement amount measured by the movement amount measuring means 3 to determine the shape measurement probe 2
3D Cartesian coordinate point sequence data (hereinafter,
It is calculated as point sequence data). The arithmetic processing unit 5 has a switching unit 12, a coordinate transformation matrix estimation unit 13, and a squareness error correction unit 14. The switching unit 12 switches the output destination of the point sequence data input from the coordinate data calculation unit 4 to the coordinate conversion matrix estimation unit 13 or the squareness error correction unit 14 depending on the processing mode. The coordinate transformation matrix estimation unit 13 estimates the coordinate transformation matrix so as to minimize the difference between the ellipsoidal surface obtained by coordinate transformation of the ideal sphere and the measurement data of the reference sphere. The squareness error correction unit 14 performs coordinate conversion on the point sequence data of the DUT 10 using the parameters of the estimated coordinate conversion matrix to correct the squareness error between the measurement coordinate axes. The output unit 6 outputs the shape data of the DUT 10 on which the squareness error correction between the measurement coordinate axes is performed by the squareness error correction unit 14 to a display device, a storage device, or the like.

In explaining the processing of the three-dimensional shape measuring apparatus configured as described above, first, the principle of estimating the parameters of the coordinate conversion matrix for correcting the squareness error will be described.

As shown in FIG. 3, the coordinate system of three axes with respect to an ideal Cartesian coordinate system (X _0, Y _0, Z ₀ ) which does not include the orthogonality error, the actual coordinate system (X, Y , Z) is defined by α, β, γ. In FIG. 3, an ideal orthogonal coordinate system (X ₀ , Y ₀ , Z ₀ ) with respect to the actual coordinate system (X, Y, Z) is selected so that the Z-axis direction and the ZX plane overlap. However, for example, it may be selected so that the X-axis direction and the XY plane overlap. Alternatively, only the Y-axis direction may be selected to be overlapped, or all of the X-axis, Y-axis, and Z-axis may be oriented in arbitrary directions. If all of the axes and the Z-axis are oriented in arbitrary directions, the solution becomes indefinite when a rotating object such as a reference spherical surface is used, so a constraint condition for preventing such a case is required.

When the squareness error is defined as shown in FIG. 3, when α << 1, β << 1, γ << 1, ideal orthogonality is obtained from the actual coordinate system (X, Y, Z). Coordinate system (X ₀ , Y _0, Z
The linear conversion matrix A to ₀ ) is expressed by the following equation (3).

[0026]

[Equation 3]

Substituting this conversion matrix A into the equation (2),
The following formula (4) is obtained.

[0028]

[Equation 4]

In equation (4), α << 1, β << 1,
Considering γ << 1 and ignoring high-order minute amounts, (4)
The equation is expressed by the following equation (5).

[0030]

[Equation 5]

The above equation (4) or equation (5) represents an ellipsoidal surface that is mapped onto a spherical surface of radius R by coordinate transformation by the transformation matrix A of equation (3). This equation (4) or (5)
(X-xs) and (y-y) are added to x, y, and z of the equation, respectively.
s), (z−zs) are used as model expressions, and α, β, as optimization problems that minimize the difference from the actual measurement data.
γ, xs, ys, zs are calculated. In this way, the squareness errors α, β, γ can be determined, and the actual coordinate system (X, Y,
The coordinate conversion matrix A from Z) to the ideal rectangular coordinate system (X ₀ , Y ₀ , Z ₀ ) can be obtained.

The process for correcting the squareness error of the shape data of the object to be measured based on this principle will be described with reference to the flowchart of FIG.

First, the reference spherical surface is fixed on the mounting table 11 of the three-dimensional shape measuring apparatus, the three-axis orthogonal stage 1 is driven, and the reference spherical surface is scanned by the shape measuring probe 2 (step S1). The measuring means 3 detects the amount of movement of each axis of the triaxial orthogonal stage 1, that is, the movement amount of the shape measuring probe 2, and sends it to the coordinate data calculating section 4. By using a laser interferometer as a movement amount calculating means 3 for measuring the movement amount of each axis of the three-axis orthogonal stage 1, a stabilized light wavelength is used as a measurement reference, and a relation with a squareness error is obtained. The amount of movement of each axis of the three-axis orthogonal stage 1 can be measured extremely accurately by eliminating a measurement error that is not present as much as possible, and the squareness error can be accurately determined on the order of seconds.

In order to accurately measure the movement amount of the triaxial orthogonal stage 1, it is necessary to pay sufficient attention to Abbe error. One method of eliminating the Abbe error is to measure the length coaxially with the object to be measured. Therefore, a laser interferometer is used as the movement amount measuring means 3, and the interferometer of the laser interferometer is placed on the same moving table as the shape measuring probe 2 so that the tip of the shape measuring probe 2 is always laser interferometer. It should be on the extension of the length measuring optical path of the long instrument. By arranging the laser interferometer in this way, the tip position of the shape measuring probe 2 can be accurately measured without being affected by the Abbe error even if the shape measuring probe 2 moves.

Another method for eliminating the Abbe error is to increase the straightness accuracy rather than the attitude accuracy of the three-axis orthogonal stage 1 which causes the Abbe error. Therefore, by using a hydrostatic fluid guide as the three-axis orthogonal stage 1, posture information and straightness accuracy can be improved, and the laser length measuring device of the movement amount measuring means 3 measures the length coaxially with the tip of the shape measuring probe 2. Even if it is difficult to do so, the Abbe error can be minimized.

The coordinate data calculation unit 4 calculates point sequence data of the scanning path of the reference spherical surface from the sent movement amount and sends it to the arithmetic processing unit 5 (step S2). Switching unit 12 of arithmetic processing unit 5
Is the coordinate conversion matrix estimation unit 1 based on the point sequence data sent from the coordinate data calculation unit 4 during the contour scanning of the reference spherical surface.
Send to 3. The coordinate transformation matrix estimation unit 13 substitutes the sent point sequence data of the reference sphere into x, y, and z of the equation (4) or (5), respectively, and transforms the ideal sphere into coordinates and the reference ellipsoid. The parameters α, β, γ of the coordinate transformation matrix that minimize the difference from the measured data of the spherical surface are estimated (step S3). Next, the object to be measured 10 is fixed to the mounting table 11 of the three-dimensional shape measuring apparatus, the three-axis orthogonal stage 1 is driven, and the surface of the object to be measured 10 is scanned by the shape measuring probe 2 (step S4). The movement amount measuring means 3 detects the movement amount of each axis of the three-axis orthogonal stage 1 and sends it to the coordinate data calculation section 4. The coordinate data calculation unit 4 calculates the point sequence data of the scanning path on the surface of the DUT 10 from the sent movement amount and sends it to the arithmetic processing unit 5 (step S5). Arithmetic processing unit 5
The switching section 12 sends the point sequence data sent from the coordinate data calculation section 4 to the squareness error correction section 14 while the object 10 is being scanned. The squareness error correction unit 14 performs coordinate conversion of the sent point sequence data using the parameters α, β, γ of the coordinate conversion matrix estimated by the coordinate conversion matrix estimation unit 13 (step S6), and the straight line between the measurement coordinate axes is corrected. The point sequence data with the corrected angle error is sent to the output unit 6 as shape data. The output unit 6 outputs the sent shape data to a display device, a storage device or the like (step S7).

In this way, the arithmetic processing unit 5 of the three-dimensional shape measuring apparatus automatically estimates the coordinate conversion matrix for correcting the squareness error between the measurement coordinate axes and corrects the squareness error, thereby correcting the lens etc. It is possible to accurately measure the shape of the optical element or the aspherical surface without any variation among operators and without performing troublesome and complicated calibration work.

When the parameters of the coordinate conversion matrix are estimated or the point sequence data of the object to be measured are coordinate-converted as described above, the number of data used for the calculation should be as small as possible from the viewpoint of shortening the calculation time. convenient. The measurement error due to the squareness error between the coordinate axes is as shown in FIGS.
Since an S-shaped surface along the Y-axis direction, an S-shaped surface along the X-axis direction, a saddle-shaped surface inclined by 45 degrees with respect to the X-axis and Y-axis directions, and a combination of these appear, measurement is made. Data arranged radially through the points near the center of the range, that is, X
If the data along the direction parallel to the axis and the Y-axis and the direction intersecting the X-axis and the Y-axis at 45 degrees are used, the number of data used for the calculation is reduced, and the ellipsoidal surface obtained by converting the coordinates of the ideal spherical surface. It is possible to stably estimate the parameter of the coordinate transformation matrix that minimizes the difference between the measured value of the reference spherical surface and the measured data of the reference spherical surface, and it is possible to shorten the calculation time for correcting the squareness error between coordinate axes.
Further, even if the data arranged in a concentric polygonal shape or the data arranged in a concentric circle with respect to the point near the center of the measurement range is extracted, the number of data used for the calculation can be reduced and the calculation time can be shortened. Therefore, the coordinate data calculation unit 4 can significantly reduce the processing time of the arithmetic processing unit 5 by selecting these data and sending them to the arithmetic processing unit 5.

[0039]

As described above, according to the present invention, the coordinate transformation matrix is estimated so as to minimize the difference between the measured data of the ellipsoidal surface obtained by coordinate transformation of the ideal spherical surface and the reference spherical surface. By using the parameters of the transformation matrix to perform coordinate transformation on the point sequence data of the DUT and automatically correct the squareness error between the measurement coordinate axes, it is possible to measure the shape of optical elements such as lenses and aspherical surfaces. Can be measured with high accuracy without any variation among operators and without performing a troublesome and complicated calibration work.

Further, the coordinate conversion matrix is estimated by using the data radially arranged passing through the points near the center of the measurement range of the reference spherical surface, thereby reducing the number of data used for the calculation and shortening the calculation time. You can

Further, by using a laser interferometer as a moving amount calculating means, which uses the wavelength of the stabilized light as a measurement reference, a measurement error unrelated to the squareness error is eliminated as much as possible, and the three axes are measured. The amount of movement of each axis of the orthogonal moving means can be measured extremely accurately, and the squareness error can be accurately determined on the order of seconds.

Further, the interferometer of the laser interferometer is placed on the same moving table as the shape measuring probe so that the tip of the shape measuring probe is always on the extension line of the measuring optical path of the laser interferometer. By doing so, even if the shape measuring probe moves, the tip position of the shape measuring probe can be accurately measured without being affected by the Abbe error, and a highly reliable squareness error estimated value can be obtained. it can.

Further, by using the hydrostatic fluid guide as the three-axis orthogonal moving means, the posture information and the straightness accuracy can be enhanced, and the length is measured coaxially with the tip of the shape measuring probe by the laser interferometer. Even if it is difficult to obtain, the Abbe error can be suppressed to the minimum.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of the present invention.

FIG. 2 is a configuration diagram of a three-axis orthogonal stage.

FIG. 3 is an explanatory diagram showing a squareness error of an actual coordinate system.

FIG. 4 is a flowchart showing the processing of the above embodiment.

FIG. 5 is a configuration diagram of a contact type probe.

FIG. 6 is a configuration diagram of a non-contact type probe.

FIG. 7 is an explanatory diagram showing an ideal rectangular coordinate system and an actual coordinate system.

FIG. 8 is an explanatory diagram showing a first result of trial calculation of an influence of a squareness error.

FIG. 9 is an explanatory diagram showing a second result of trial calculation of an influence of a squareness error.

FIG. 10 is an explanatory diagram showing a third result of trial calculation of influence of squareness error.

[Explanation of symbols]

1 3-axis orthogonal stage 2 Shape measurement probe 3 Moving amount measuring means 4 Coordinate data calculation unit 5 Arithmetic processing unit 6 Output section 10 DUT 12 Switching unit 13 Coordinate conversion matrix estimation unit 14 Squareness error correction unit

Claims (2)

(57) [Claims] 1. The surface of the object to be measured is traced and scanned, the coordinates of the scanning path are measured as three-dimensional orthogonal coordinate point sequence data, and the measured point sequence data is subjected to coordinate conversion to cause a squareness error between measurement coordinate axes. This is a method of calibrating the perpendicularity error of the coordinate axis to correct the distortion of the measured data.The shape of the reference sphere is measured and the ideal sphere is converted into the coordinate system for measurement. The ideal coordinate system for measurement should be used to minimize the difference from the measured data on the spherical surface.
Estimating the coordinate transformation matrix to the standard system, and using the parameters of the estimated coordinate transformation matrix, the three-dimensional orthogonal coordinate point sequence of the DUT
A method of calibrating a squareness error of a coordinate axis, which comprises performing coordinate transformation on data to correct a squareness error between measurement coordinate axes. 2. A shape measuring probe provided on a triaxial orthogonal moving means, a moving amount measuring means for measuring a moving amount of each axis of the orthogonal moving means, a coordinate data calculating means, and an arithmetic processing means, The orthogonal movement means performs scanning by moving the shape measurement probe on the reference spherical surface and the surface of the object to be measured, the movement amount measurement means measures the movement amount of each axis of the orthogonal movement means, and the coordinate data calculation means moves the movement amount. The coordinates of the scanning path of the shape measuring probe are calculated as three-dimensional orthogonal coordinate point sequence data from the movement amount measured by the measuring means, and the arithmetic processing means uses the ideal spherical surface as a measuring seat.
Ideal from the coordinate system for measurement so as to minimize the difference between the ellipsoid obtained by coordinate conversion to the standard system and the measurement data of the reference sphere.
Three-dimensional orthogonal locus coordinates with the coordinate transformation matrix estimates to system, the object to be measured by using the parameters of the estimated coordinate transformation matrix
A three-dimensional shape measuring apparatus characterized by performing coordinate conversion on the reference point string data to correct squareness error between measurement coordinate axes.