JP2007232649A - Method and device for measuring flat plate flatness - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and a device for measuring the flatness of a flat plate while minimizing errors by having the inherent errors of equipment being scaling errors and spatial torsion in a non-contact three-dimensional measuring instrument. <P>SOLUTION: The method for measuring the flat plate flatness comprises installing a calibration plate arranging a known sphere as a known measured point in a coordinate by center coordinates and radiuses of at least three points at positions for measuring the flatness for instance, storing calibration values of the inherent measuring errors in the three-dimensional measuring instrument on the basis of results measuring the calibration plate by the three-dimensional measuring instrument, and measuring the flatness of a specimen by calibrating the measured result of the specimen by the calibration values stored to a storing means. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a flat plate flatness measuring method and apparatus, and more particularly, to a flat plate flatness measuring method and apparatus capable of measuring the flatness of a large flat plate with high accuracy.

  For example, FIG. 17A is a partially cutaway schematic perspective view, and FIG. 17B is a schematic cross-sectional structural view. In the integrated laminated fuel cell 90, the interconnector 91 and the power generation film 92 used are ceramic. The sealing material 93 is provided with a fuel inlet 94 and an air inlet 95. The power generation performance of the fuel cell is achieved by controlling the gap between the interconnector 91 and the power generation film 92. If the interconnector 91 and the power generation film 92 have warpage or unevenness, the gap The problem arises that the power generation performance does not come out due to the increase or decrease in the size.

  Therefore, there is a demand for improving the power generation performance by measuring, classifying, and sorting the flatness of the interconnector 91. The flatness of such a flat plate is measured by, for example, in Patent Document 1 by relatively moving a measurement point displacement meter that detects a distance from a measurement point on the surface of the measurement object and the measurement object. A three-dimensional surface shape measuring apparatus is shown that relatively scans the surface of an object and detects a change in distance from a measurement point on the scanning locus by a measurement point displacement meter to measure the surface shape of the measurement object. Yes.

  Further, Patent Document 2 discloses an installation surface with which a surface to be measured comes into contact, a plurality of contact-type displacement detectors disposed relative to the surface to be measured, and measured values of the surface to be measured obtained from the displacement detector. There is shown a shape measuring apparatus including an arithmetic unit that calculates an approximate plane related to a surface to be measured based on the calculated plane and calculates flatness of the surface to be measured based on the approximate plane.

  Further, Patent Document 3 includes a probe that scans the surface of the sample, and a displacement detection unit that detects a displacement related to the distance between the sample and the probe, and a relative position between the sample and the probe along the sample surface. A surface measuring device is shown that measures surface characteristics while controlling the relationship between the sample and the probe to be maintained in a constant state.

  However, the interconnector 91 used in a large fuel cell is so large that the contact-type three-dimensional measuring device as shown in these Patent Documents 1 to 3 takes time and cannot perform in-process measurement. It was. In addition, since it takes time to measure the planar shape, it cannot be reflected in the lamination process, so that a combination is tried and assembled.

  Therefore, for example, Patent Document 4 discloses a technique shown as an absolute flatness measurement method using an interferometer, and Patent Document 5 shows a slit projection method (also referred to as an optical cutting method) called a range finder. 18, such as the technique shown in FIG. 18 and the method shown in FIG. 19A in which the subject is scanned with a laser beam or the like and the reflection time of the laser beam is measured. It is desired to measure with a contact type three-dimensional measuring device.

  In FIG. 18, reference numeral 100 denotes a slit laser projector, 101 denotes a driving source for rotating or rotating the galvano mirror 102, 103 denotes an imaging device, 104 denotes an image input means for a subject imaged by the imaging device, and 105 denotes a slit. This is a means for extracting the image position of the light. As shown by 106, the slit light extracted from the image is measured by measuring the step as a step occurs if there is a warp or unevenness on the subject (not shown). It is possible to detect how much warpage or unevenness is present.

  In FIG. 19A, 110 is a projector such as a laser, 111 and 113 are reflection mirrors that are rotated or rotated by drive sources 112 and 114, and 115 is a scanning position of a subject (not shown). Then, while the laser beam is swung and scanned in the horizontal direction in the subject, for example, the reflection mirror 113 is swung in the vertical direction and the unevenness of the subject is measured by the reflection time from the subject.

JP 2002-250620 A Japanese Patent Laid-Open No. 2003-214843 Japanese Patent No. 3667143 JP 11-37742 A JP-A-10-124646

  However, in the non-contact type three-dimensional measuring device as shown in FIGS. 18 and 19A, the reflecting mirrors 102, 111, and 113 shown in FIGS. For example, as shown in FIG. 19B, the degree of error is low, the distortion of the drive system of the drive sources 101, 112, and 114 that drive these mirrors, the error in image recognition of the measurement screen by the imaging device, or the like. There is a problem that a scaling error that becomes larger or smaller with respect to the distance and a spatial distortion in which a plane as shown in FIG.

  That is, in the graph of FIG. 19B, the horizontal axis is the rotation angle command value, the vertical axis is the actual rotation angle, and the actual rotation angle is larger than the input rotation angle. In this case, the actual distance Results in a smaller measurement result. Further, FIG. 20A shows a case where the plane indicated by 120 appears to wave as indicated by 121, and this corresponds to the command rotation angle as shown in FIG. 20B. On the other hand, when the actual rotation angle changes linearly, it is recognized as a plane as indicated by 120, but a function having a rotation angle θ with respect to the command value x as shown in FIG. In the case of changing according to θ = F (x)), it indicates that the wave is recognized as indicated by 121. In the graphs of FIGS. 20B and 20C, the horizontal axis is the command value of the rotation angle, and the vertical axis is the actual rotation angle.

  In addition, the technique shown in Patent Document 4 uses a three-surface alignment method, and is not suitable for measuring the flatness of a large flat plate such as the interconnector of the present application. A method for dealing with such a scaling error and spatial distortion is not shown.

  Therefore, in the present invention, a flatness measuring method and apparatus capable of measuring flatness while using a non-contact type three-dimensional measuring instrument and having a simple configuration while minimizing errors due to scaling errors and spatial distortions are provided. It is a problem to do.

In order to solve the above problems, the flatness measuring method according to the present invention is as follows.
A flat plate flatness measuring method in which a flat specimen is set at a measurement position and measured with a non-contact type three-dimensional measuring instrument to measure flatness,
A calibration plate having measurement points whose known coordinates are at least three or more is set in advance at the measurement position, and the measurement points are measured by the three-dimensional measuring device to calibrate inherent measurement errors in the three-dimensional measuring device. Then, the object is placed at the measurement position and the flatness is measured.

In addition, the flatness measuring apparatus according to the present invention for carrying out this method,
A flat plate flatness measuring device comprising a non-contact type three-dimensional measuring instrument for measuring an object comprising a flat plate installed at a measurement position,
In the three-dimensional measuring instrument, the flatness measuring apparatus is provided with a calibration plate having at least three known measurement points at the measurement position, and calculated based on the measured coordinates of the measurement points. It has a storage means for storing a calibration value of an inherent measurement error, and measures the flatness of the subject by calibrating the measurement result of the subject with the calibration value stored in the storage means.

  In this way, after the calibration plate is set in advance at the measurement position and measured by a three-dimensional measuring instrument, and the inherent measurement error such as scaling error and spatial distortion in the three-dimensional measuring instrument is calibrated, the subject is By measuring the flatness by installing the flatness, it is possible to measure the flatness with few errors.

  The calibration plate is arranged with a sphere whose center coordinates and radius are known as the measurement point, the sphere is arranged diagonally with the center of the calibration plate, and above, below, left and right of the center, and the calibration is performed By calibrating the scaling error caused by the nonlinearity of the driving mechanism in the three-dimensional measuring device from the distance between the center coordinates of different spheres by obtaining the center coordinates of the spheres, the center coordinates can be easily obtained if the surface coordinates are known. Therefore, if the distance between the center coordinates of the two spheres is obtained, the scaling error can be calibrated. Further, by arranging this sphere on the diagonal line with the center of the calibration plate and on the top, bottom, left and right of the center, the interconnector of the fuel cell is likely to warp in a plane, and the three-dimensional coordinates are shown in FIGS. Since the θ according to the rotation angle shown in FIG. 20 is easily changed, the flatness measurement method and apparatus can reliably calibrate these errors by arranging them one by one 90 degrees axisymmetrically from the center. Can be provided.

  The calibration plate is provided with a cylinder whose center axis coordinates and radius are known as the measurement point. At least three cylinders are prepared, and each center axis intersects with the center axis of another cylinder. In the calibration, the center axis coordinates of the cylinder and the intersection coordinates of the center axes are obtained, and the scaling error due to the nonlinearity of the driving mechanism in the three-dimensional measuring device is calculated from the distance between the intersection coordinates. By calibrating with the coordinates of the central axis, if the surface coordinates of the cylinder are known, the central axis coordinates and intersections can be easily calculated, thereby providing a flatness measuring method and apparatus that can calibrate both scaling error and spatial distortion. can do.

  Further, the calibration plate has a sphere having a known center coordinate and a radius as the measurement point on a plane having a known plane coordinate, and the sphere is diagonal to the center of the calibration plate and above and below the center. The calibration is performed on the left and right, and the calibration obtains the coordinates of the center of the sphere and the coordinates of the plane, and the scaling error due to the nonlinearity of the driving mechanism in the three-dimensional measuring device is determined from the distance between the coordinates of the centers of the different spheres. By calibrating the distortion by obtaining the value of the arbitrary direction coordinate in the plane, the sphere can easily determine the center coordinate if the surface coordinate is known, and thereby by determining between the center coordinates of the two spheres, A flat plate flatness measuring method and apparatus capable of calibrating both scaling error and spatial distortion can be provided.

  The three-dimensional measuring device is prepared corresponding to each of the front and back sides of the subject, and after calculating a coordinate conversion parameter that unifies the measurement coordinate system of both the three-dimensional measuring devices by measuring the calibration plate, the measurement position The object is placed on the surface and the flatness is measured. For this purpose, the three-dimensional measuring devices are arranged corresponding to the front and back of the subject, and the measurement of both the three-dimensional measuring devices calculated by measuring the calibration plate is performed. Coordinate transformation parameters that unify the coordinate system are stored in the storage means, and the measurement result of the subject is calibrated with the coordinate transformation parameters stored in the storage means to measure the flatness of the subject. A flat plate flatness measuring method and apparatus capable of accurately measuring the front and back surfaces can be provided.

  In addition, a rotation stage is prepared by holding the subject or the calibration plate at the measurement position and rotating it so that the front and back can be measured with a single three-dimensional measuring instrument. The calibration plate is attached to the rotation stage. After calibrating the inherent measurement error in the three-dimensional measuring instrument, the subject is attached to the rotating stage and rotated to measure the front and back, and for that purpose, the subject or calibration plate is held and rotated, By providing a rotating stage that can measure the front and back of the subject by rotation, the front and back of the subject can be measured with a single three-dimensional measuring instrument, and the flatness measurement device can be configured at a low cost. can do.

  Further, the calibration plate has a plane having a known plane coordinate attached to a cylinder having a known radius and a sphere having a known center coordinate and a radius on the plane, which can be mounted around the rotation axis of the rotary stage. In the calibration, the center axis coordinates of the cylinder, the center coordinates of the sphere, and the coordinates of the plane are obtained, and the scaling error due to the non-linearity of the driving mechanism in the three-dimensional measuring instrument is determined. From the above, it is possible to provide a flatness measuring method and apparatus capable of calibrating both a scaling error and a spatial distortion by obtaining and calibrating a spatial distortion by obtaining a value of a central axis coordinate of the cylinder and an arbitrary direction coordinate in the plane. it can.

  The non-contact type three-dimensional measuring instrument has an imaging device, and the measurement position is on an extension of the optical axis of the imaging device and is arranged at the measurement position symmetrically across the optical axis of the imaging device. A reflection mirror for sending light from the front and back of the subject to the imaging device is prepared, and the flatness is measured. For this purpose, the flat plate flatness measuring device includes a non-contact type three-dimensional measuring instrument having an imaging device, A reflection mirror that is provided symmetrically across the optical axis of the imaging apparatus and that transmits light from the front and back of the subject placed at the measurement position on the extension of the optical axis of the imaging apparatus to the imaging apparatus Therefore, it is possible to provide a flatness measuring method and apparatus capable of simultaneously measuring both the front and back surfaces of a subject with a single three-dimensional measuring instrument.

  Further, the non-contact type three-dimensional measuring device further includes a projector positioned on the optical axis of the imaging device and a mirror that swings light emitted from the projector, and is emitted from the projector and is swung by the mirror. A second reflecting mirror provided symmetrically across the optical axis of the imaging device that sends the measured light to the measurement position is prepared, so that the non-contact type three-dimensional measuring device is positioned on the optical axis of the imaging device And a mirror for oscillating the light emitted from the projector, and provided symmetrically across the optical axis of the imaging device that sends the light emitted from the projector and oscillated by the mirror to the measurement position. Flatness measurement that can measure both front and back surfaces of a subject at the same time with a single three-dimensional measuring device, even with a three-dimensional measuring device using a light cutting method, etc. Methods and apparatus can be provided

And in order to solve the said subject, the flatness flatness measuring method which becomes this invention is the following.
A flat plate flatness measuring method in which a flat specimen is set at a measurement position and measured with a non-contact type three-dimensional measuring instrument to measure flatness,
When the subject is a regular polygon, the subject is rotated around the center of the regular polygon so that each corner is overlapped, and measured by the non-contact type three-dimensional measuring device, and measured at each measurement point. The average value is calculated by adding the results, and the difference between the maximum value and the minimum value among the values obtained by subtracting the average value from each measurement result is defined as the flatness of the measurement point.

In addition, the flatness measuring apparatus according to the present invention for carrying out this method,
A flat plate flatness measuring device comprising a non-contact type three-dimensional measuring instrument for measuring an object comprising a flat plate installed at a measurement position,
A mechanism for rotating the subject; storage means for storing the measurement result of the non-contact type three-dimensional measuring instrument measured by rotating the subject; and adding the measurement results stored in the storage means to obtain an average value And calculating means for calculating the flatness of the measurement point as a difference between a maximum value and a minimum value of values obtained by subtracting the average value from the measurement results.

  By rotating the subject in this way and processing it using each measurement result, each actual measurement result contains spatial distortion components and information about the measurement target, of which spatial distortion components Therefore, it is possible to provide a method and apparatus for easily measuring the flatness of a subject without using a calibration plate or the like.

  Further, the non-contact type is configured such that the regular polygonal object is rotated at an angle formed by connecting an adjacent corner of the regular polygon to the center of the object with a center point connecting a center and a corner of the object as a center. When measuring with a three-dimensional measuring device is performed for all corners and measuring the flatness of the subject, a certain offset is placed on the subject surface, for example, the four corners bend in the same direction. Even for a test object that is known, it is possible to cancel the spatial distortion component described above with respect to the center point connecting the center and the corner of the test object of a regular polygon. A method and apparatus for easily measuring the flatness of a subject without using a calibration plate or the like can be provided.

Moreover, in order to solve the above problems, the flatness measuring method according to the present invention is as follows.
A flat plate flatness measuring method in which a flat specimen is set at a measurement position and measured with a non-contact type three-dimensional measuring instrument to measure flatness,
When the subject is a regular polygon, a calibration plate having a size that includes a circle circumscribing the regular polygon is prepared in advance, and measured with the non-contact type three-dimensional measuring device while rotating the calibration plate. The measurement results are added for each measurement point, an average value is calculated, and the average value is stored as a distortion component of the three-dimensional measuring device. Then, the subject is measured by the non-contact type three-dimensional measuring device. The distortion component is removed from the measurement result, and the obtained result is used as the flatness of the subject.

  Before measuring the subject in this way, a calibration plate having a size including a circle circumscribing the subject is prepared, and the distortion component in the three-dimensional measuring device is stored, so that the subject is not rotated. Therefore, it is possible to provide a method for easily measuring the flatness of a subject in a short time.

  As described above, the flatness measurement method and apparatus according to the present invention have a simple configuration and flatness of the flat plate while minimizing errors caused by scaling errors and spatial distortions when using a non-contact type three-dimensional measuring instrument. A flat plate flatness measuring method and apparatus capable of measurement can be provided, and a great effect can be obtained by using it for flatness measurement of an interconnector of a fuel cell.

  Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the drawings. However, the dimensions, materials, shapes, relative arrangements, and the like of the components described in this embodiment are not intended to limit the scope of the present invention unless otherwise specified, but are merely illustrative examples. Not too much.

  FIG. 1 is a diagram showing a configuration for carrying out a first embodiment of a flat plate flatness measuring method and apparatus according to the present invention. In FIG. 1, reference numerals 1 and 4 denote an object (flat plate) by a light cutting method or laser light. The non-contact type three-dimensional measuring device that scans and measures the flatness of the subject based on the reflection time of the laser beam and has a scaling error and a spatial distortion as described above, 2 and 5 are measurement result storage devices, 3 , 6 is a control device having a calculation stage, and 7 is a subject (flat plate) or a calibration plate. In the flatness measuring method according to the present invention, the front and back of the subject 7 are basically measured simultaneously as described above, but the front and back may be measured separately.

  FIG. 2 is a first embodiment of a calibration plate for calibrating the three-dimensional measuring device indicated by 1 and 4 in FIG. 1, in which 20 is a calibration plate, 21 to 29 are known in the center coordinates and the radius R, respectively. Since the fuel cell interconnector 91 is a true sphere, plane warpage is likely to occur, and θ in the three-dimensional coordinates is easily changed by the rotation angle. These errors are reliably calibrated by arranging them one by one every 90 degrees in axial symmetry.

  In the present invention, as shown in FIG. 2, the calibration plate 20 having at least three known measurement points is positioned at the measurement position indicated by 7 in FIG. The surface coordinates of each sphere (measurement point) are measured by the three-dimensional measuring devices 1 and 4. Then, the measurement result is stored in the storage devices 2 and 5, the error is calculated by the calculation means included in the control devices 3 and 6 using the result, and a coordinate transformation matrix for calibrating the error is calculated and the storage device 2. 5, and thereafter, the interconnector 91 as the subject is installed at the measurement position to measure the flatness.

  Among them, FIG. 3 shows a flow for calibrating the three-dimensional measuring device shown by 1 and 4 in FIG. 1 using the calibration plate 20 shown in FIG. 2, and FIG. 3A shows the main flow of the calibration process. , (B) is a flow of the calibration processing part.

  First, when the calibration process of the coordinate transformation matrix T is started in step S1 of the main flow in FIG. 3A, the calibration process of the three-dimensional measuring device 1 is performed in step S2, so the process is step S10 of FIG. 3B. go to. In step S11, the calibration plate 20 is measured by the three-dimensional measuring devices 1 and 4 that measure the flatness of the subject. This measurement is performed by using a light cutting method as described above, scanning a subject (flat plate) with a laser beam or the like, and reflecting the reflection time of the laser beam from the subject. Three-dimensional coordinates are calculated and stored in the storage devices 2 and 5.

In step S12, the calibration plate 20 is divided into several regions using the measurement results stored in the storage devices 2 and 5, and the spherical surface in each region divided in the next step S13 is determined. In step S14, the spherical surface is fitted based on the known radius, the center coordinates are calculated, and in step S15, the error function e1 of the three-dimensional measuring device ₁ is calculated.

This error function e ₁ is
n: number of spheres used Pn: center coordinates of spherical surface calculated from measurement results
⁰ Pn: When the corrected true value of the center coordinate of the sphere is assumed,

となる。

It becomes.

Therefore, evaluation of the error function e ₁ in the next step S16 is carried out, and the results of evaluation, correction of calibration curve parameters using nonlinear least-squares method proceeds to step S17 if the value is not valid performed, If valid, the process proceeds to step S18 and ends.

The calibration curve parameters used here are, for example, the three-dimensional coordinates (X _i , Y _i , Z _i ) of the measurement point Q _i on the sphere from the slit light image position (I, J) in the light cutting method shown in FIG. , When the actual mirror rotation angle is represented by a high-order polynomial represented by θ = F (x), as shown in FIG. 20C, with respect to the mirror rotation angle command value x at that time, The coefficient included in the following formula (2).

Therefore, in “correction of calibration curve parameters using the nonlinear least square method” in step S17, first, parameters such as the slit light image position (I, J) and the mirror rotation angle θ are used, as in step S11. The three-dimensional coordinates are calculated from the data of the spherical area, and the center coordinates of the sphere that minimize the error e _{0 of the} following equation from the three-dimensional coordinates Q _i determined as the measurement points on the spherical surface by area division (step S12). P _n (X ₀ , Y ₀ , Z ₀ ) _n is obtained by a nonlinear least square method using the known Levenberg-Marquardt method, the Powell method, or the like (same as step S14). However, R is a value calibrated in advance.

e ₀ = Σ | (X ₀ −X _i ) ² + (Y ₀ −Y _i ) ² + (Z ₀ −Z _i ) ² −R ² | (3)
Then, an error function e ₁ between the calibrated inter-spherical distance and the obtained inter-spherical distance is calculated (same as step S15).

When the calibration process of the three-dimensional measuring instrument 1 is completed in this way, the process of step S2 in FIG. 3A is completed. Next, the process proceeds to the calibration process of the three-dimensional measuring instrument 2 in step S3. Similar to the calibration process of FIG. 3, the process goes to step S10 in FIG. 3B, and the error function e2 of the three-dimensional measuring instrument ₂ is calculated using the equation (1) as described above.

The following three-dimensional measuring instrument error function e ₂ of 2 is computed processed using Proceeding to FIG. 3 (A) step S4, to match the coordinate system of the three-dimensional measuring device 1 and 4, the nonlinear least square method The coordinate transformation matrix T is calculated according to the equation (2), and is stored and stored in the storage devices 2 and 5 in step S5, and the process ends in step S6.

  After the coordinate transformation matrix T is stored in the storage devices 2 and 5 in this way, a flat plate as the subject is then placed at the position indicated by 7 in FIG. The coordinates are measured and converted by the coordinate transformation matrix T stored in the storage devices 2 and 5 to measure the flatness of the subject 7.

  As described above, after the calibration plate 20 is installed in the measurement position in advance and measured by the three-dimensional measuring devices 1 and 4, the inherent measurement error such as the scaling error as described above in the three-dimensional measuring devices 1 and 4 is calibrated. By installing the subject 7 and measuring the flatness, the flatness measurement with less error can be performed.

  FIG. 4 is a second embodiment of the calibration plate for calibrating the scaling error and the spatial distortion in the three-dimensional measuring instrument indicated by 1 and 4 in FIG. 1 used in the flatness measuring method and apparatus according to the present invention. In the figure, 30 is a calibration plate, 31, 33, and 35 are cylinders whose coordinates and radius R of each of the center axes 32, 34, and 36 are known, and each of the center axes 32, 34, and 36 is mutually different from the other center axis. It is arranged to cross. In the example shown in FIG. 4, the number of cylinders 31, 33, and 35 is three. However, this number is required to calibrate both the scaling error and the spatial distortion. You may do it.

  FIG. 5 is a flow chart for calibrating the three-dimensional measuring instrument indicated by 1 and 4 in FIG. 1 using the calibration plate 30 of the embodiment 2 shown in FIG. 4, and has been described with reference to FIG. This corresponds to the detailed calibration processing flow. Note that the flow described in FIG. 3A is omitted for common purposes.

  As in the case of the calibration plate 20 of the first embodiment shown in FIG. 2, first, when the calibration process of the coordinate transformation matrix T is started in step S1 of the main flow in FIG. 3A, a three-dimensional measuring device is obtained in step S2. In order to perform the calibration process 1, the process goes to step S <b> 20 in FIG. 5. In step S21, the calibration plate 30 is measured by the three-dimensional measuring devices 1 and 4 that measure the flatness of the subject. This measurement is performed by using the light cutting method as described above, or by scanning the subject (flat plate) with laser light or the like, and performing the reflection time of the laser light from the subject to measure the flatness of the subject. The measurement is performed by the three-dimensional measuring devices 1 and 4 as described above, and the three-dimensional coordinates of the calibration plate 30 and the cylinders 3, 33, and 35 are calculated and stored in the storage devices 2 and 5.

  In step S22, the calibration plate 30 is divided into several regions using the measurement results stored in the storage devices 2 and 5, and the cylindrical surface in each region divided in the next step S23 is determined. In step S24, the cylindrical surface is fitted based on the known radius, the central coordinates are calculated, the intersection of the central axes 32, 34, and 36 is calculated in step S25, and the error function of the three-dimensional measuring instrument 1 is further calculated in step S26. e is calculated.

This error function e is
e = e ₁ + e ₂ ………………………………………… (5)
Where e ₁ is the same as above Pn: intersection of the central axes of the cylindrical surfaces

とすると、

Then,

で、ｅ_２は、
Ｐｋ：円筒表面に属する点の３次元座標
Ｄ（Ｐｋ）：円筒面との距離
とすると、

And e ₂ is
Pk: three-dimensional coordinates of a point belonging to the cylindrical surface D (Pk): a distance from the cylindrical surface,

となる。

It becomes.

  Therefore, the error function e is evaluated in the next step S27, and if the value is not valid as a result of the evaluation, the process proceeds to step S28, and the calibration curve parameter is corrected using the nonlinear least squares method. If so, the process proceeds to step S29 and ends.

At this time, the calibration curve parameter is corrected in the same manner as described above, but only the data of the cylindrical surface region is obtained for the three-dimensional coordinate calculation. Therefore, in “correction of calibration curve parameters using nonlinear least square method” in step S28, first, parameters such as the slit light image position (I, J) and mirror rotation angle θ are used, as in step S21. The three-dimensional coordinates are calculated from the data of the cylindrical surface area, and the error e ₁ of the following equation (7) is minimized from the three-dimensional coordinates Q _i determined as the measurement points on the cylindrical surface by area division (step S22). The components of the coordinate transformation matrix T of 3 rows × 4 columns to be obtained are obtained by the nonlinear least square method using the known Levenberg-Marquardt method, the Powell method, or the like (same as step S24). _{However, t ij (i = 1~3,} j = 1~4) passes through the center point of the cylindrical surface, the components of the coordinate transformation matrix T central axis coincides with the Z axis, R represents the radius of the calibrated cylindrical surface It is.

e ₁ = Σ | (t ₁₁ X _i + t ₁₂ Y _i + t ₁₃ Z _i + t ₁₄ ) ² +
_{(t 21 X i + t 22} Y i + t 23 Z i + t 24) 2 -R 2 | ............ (7)

A straight line represented by the center coordinates (X ₀ , Y ₀ , Z ₀ ) of the cylindrical surface obtained by the following formula (8) and the unit direction vector (l, m, n) of the center axis from the obtained coordinate transformation matrix. The distance e ₂ between the intersections is calculated. This process is repeated while correcting the calibration curve parameters, and the obtained error function e ₁ + e ₂ is used as the evaluation function.

  When the calibration process of the three-dimensional measuring instrument 1 is completed in this way, the process of step S2 in FIG. 3A is completed. Next, the process proceeds to the calibration process of the three-dimensional measuring instrument 2 in step S3. Similar to the calibration process of FIG. 5, the process goes to step S20 in FIG. 5, and the error function e of the three-dimensional measuring instrument 2 is calculated using the equations (1), (5), and (6) as described above.

  Then, when the processing proceeds to step S4 in FIG. 3A, the coordinate transformation matrix T according to the following equation (4) using the nonlinear least square method is used as described above to match the coordinate systems of the three-dimensional measuring instruments 1 and 4. Is calculated and stored in the storage devices 2 and 5 in step S5, and the process ends in step S6.

  After the coordinate transformation matrix T is stored in the storage devices 2 and 5 in this way, a flat plate as the subject is then placed at the position indicated by 7 in FIG. As described with reference to FIG. 3, the coordinates are measured and converted by the coordinate transformation matrix T stored in the storage devices 2 and 5 to measure the flatness of the subject 7.

  As described above, after the calibration plate 20 is installed in the measurement position in advance and measured by the three-dimensional measuring devices 1 and 4, the inherent measurement error such as the scaling error as described above in the three-dimensional measuring devices 1 and 4 is calibrated. By installing the subject 7 and measuring the flatness, the flatness measurement with less error can be performed.

  FIG. 6 is a third embodiment of the calibration plate for calibrating the scaling error and the spatial distortion in the three-dimensional measuring instrument shown by 1 and 4 in FIG. 1 used in the flatness measuring method and apparatus according to the present invention. In the figure, reference numeral 40 denotes a calibration plate. The calibration plate 40 has known coordinates, and as described above, the calibration plate 40 is symmetrical with respect to the center of the calibration plate 40 and diagonally with respect to the center of the calibration plate 40. A true sphere whose center coordinates and radius R are known, one by one every 90 degrees, is fitted, so that both scaling error and spatial distortion can be calibrated.

  FIG. 7 is a flow chart for calibrating the three-dimensional measuring instrument indicated by 1 and 4 in FIG. 1 using the calibration plate 40 of Example 3 shown in FIG. 6, and has been described with reference to FIG. This corresponds to the detailed calibration processing flow. Note that the flowchart described with reference to FIG. 3A is omitted because it is the same as that in the second embodiment.

  As in the first embodiment shown in FIG. 2 and the second embodiment shown in FIG. 4, first, when the calibration process of the coordinate transformation matrix T is started in step S1 of the main flow in FIG. 3A, 3 in step S2. In order to perform the calibration process of the dimension measuring instrument 1, the process goes to step S30 in FIG. In step S31, the calibration plate 40 is measured by the three-dimensional measuring instruments 1 and 4 that measure the flatness of the subject. This measurement is performed by using the light cutting method as described above, or by scanning the subject (flat plate) with laser light or the like, and performing the reflection time of the laser light from the subject to measure the flatness of the subject. The measurement is performed by the three-dimensional measuring devices 1 and 4 as described above, and the three-dimensional coordinates of the calibration plate 40 and the spheres 41 to 49 are calculated and stored in the storage devices 2 and 5.

In step S32, the calibration plate 40 is divided into several regions using the measurement results stored in the storage devices 2 and 5, and in the next step S33, the calibration plate 40 is calibrated with a spherical surface or the calibration plate 40 itself is flat. or calibration is selected in, for example, in the case of calibration sphere the same spherical surface fitted to the case of example 1 performed step S34, the error function e ₁ is calculated in step S35. In the case of calibration the calibration plate 40 itself planes planes fitted proceeds to step S36, the error function e ₂ is calculated in step S37.

The error function e is e = e ₁ + e ₂ as described above.
First, e ₁ is
Pn: spherical center coordinates
⁰ Pn: When the true value of the center coordinate of the sphere is calibrated, the same as above

となる。また、
Ｐｋ：平面領域に属する点の３次元座標
Ｄ（Ｐｋ）：平面との距離
とするとｅ_２は、

It becomes. Also,
Pk: three-dimensional coordinates of a point belonging to a plane area D (Pk): e ₂

となる。

It becomes.

  Therefore, the error function e is evaluated in the next step S38, and if the value is not valid as a result of the evaluation in the next step S39, the process proceeds to step S40 to correct the calibration curve parameter using the nonlinear least square method. If yes, go to step S41 and end.

At this time, the calibration curve parameters are corrected in the same manner as described above, but the three-dimensional coordinate calculation is the data of the spherical region and the planar region. For this reason, the “calibration curve using the nonlinear least square method” in step S40. In the “parameter correction”, first, parameters such as the slit light image position (I, J) and the mirror rotation angle θ are used to calculate the three-dimensional coordinates with the data of the spherical area as in the case of step S31, and to divide the area (step The center coordinate P _n (X ₀ , Y ₀ , Z ₀ ) _n of the sphere that minimizes the error e _{0 of the} following equation is known from the three-dimensional coordinate Q _i determined as the measurement point on the spherical surface by S32). The Levenberg-Marquardt method, the Powell method, or the like is used to obtain the nonlinear least square method (same as step S35). However, R is a value calibrated in advance.

_{e 0 = Σ | (X 0} -X i) 2 + (Y 0 -Y i) 2 + (Z 0 -Z i) 2 -R 2 | ...... (3)

Then, an error function e ₁ between the calibrated inter-spherical distance and the obtained inter-spherical distance is calculated (same as step S15). Similarly to steps S36 and S37, e ₂ is calculated by the formula (6) using a least square method such as a Gaussian elimination method for the three-dimensional coordinates Q _i determined as the measurement point on the plane.

  When the calibration process of the three-dimensional measuring instrument 1 is completed in this way, the process of step S2 in FIG. 3A is completed. Next, the process proceeds to the calibration process of the three-dimensional measuring instrument 2 in step S3. As in the calibration process of FIG. 7, the process goes to step S30 in FIG. 7, and the error function e of the three-dimensional measuring instrument 2 is calculated using the equations (1), (5), and (6) as described above.

  Then, when the error function e of the three-dimensional measuring instrument 2 is calculated and the process proceeds to step S4 in FIG. 3A, the following (using the nonlinear least square method is used to match the coordinate systems of the three-dimensional measuring instruments 1 and 4 ( 4) The coordinate transformation matrix T is calculated according to the equation. In step S5, it is stored and stored in the storage devices 2 and 5, and the process ends in step S6.

  After the coordinate transformation matrix T is stored in the storage devices 2 and 5 in this way, a flat plate as the subject is then placed at the position indicated by 7 in FIG. As described with reference to FIG. 3, the coordinates are measured and converted by the coordinate transformation matrix T stored in the storage devices 2 and 5 to measure the flatness of the subject 7.

  In this way, the calibration plate 40 is set in advance at the measurement position and measured by the three-dimensional measuring devices 1 and 4, and the inherent measurement errors such as the scaling error and the spatial distortion as described above in the three-dimensional measuring devices 1 and 4 are measured. After calibration, the flatness measurement with few errors can be performed by installing the subject 7 and measuring the flatness.

  FIG. 8 is a fourth embodiment of the flatness measuring method and apparatus according to the present invention. In the first to third embodiments so far, two two-dimensional measuring instruments are used to simultaneously measure the front and back of the subject. However, in the fourth embodiment, a rotation stage 58 that can hold and rotate a calibration plate and a flat plate that is a subject is prepared, and a single three-dimensional measuring device 59 can measure the front and back sides.

  Further, the calibration plate 50 used in the fourth embodiment can be attached with the rotation axis of the rotary stage 58 as the rotation center, and the plane coordinates attached to the cylinder 57 with the known radius are the known plane, and further to the plane. The spheres 51 to 56 whose center coordinates and radius are known are arranged, and in the calibration, the scaling error due to the non-linearity of the driving mechanism in the three-dimensional measuring device 59 is determined from the distance between the center coordinates of the different spheres 51 to 56. The spatial distortion is calibrated by the values of the central axis coordinates of the cylinder 57 and the arbitrary direction coordinates on the plane.

  FIG. 9 is a flowchart for performing the calibration process of the rotating shaft in order to calibrate the three-dimensional measuring instrument 59 shown in FIG. 3 using the calibration plate 50 of the fourth embodiment shown in FIG. This corresponds to the detailed flow of the calibration process described above. The flow chart described in FIG. 3A is omitted because it is the same as in the second and third embodiments, except that step S3 is not necessary.

  As in the first to third embodiments shown in FIGS. 2, 4, and 6, first, when the calibration process of the coordinate transformation matrix T is started in step S1 of the main flow in FIG. In order to perform the calibration process of the measuring instrument 1, first, the process goes to step S50 in FIG. 9 to perform the calibration process of the rotating shaft. In step S51, for example, when the rotation angle of the rotary stage 58 is φ, φ = 0 ° is set, and in the next step S52, φ + Δφ is replaced with φ, and the three-dimensional measuring instrument 59 uses the calibration plate 50. The three-dimensional coordinates of the cylinder 57 are calculated and stored in a storage device (not shown).

In step S53, the calibration plate 50 is divided into several regions using the measurement result stored in the storage device, the cylindrical surface is fitted in the next step S54, and the central axis _Lφ is calculated in step S55. Is done.

Calculation of the center axis L _phi of the cylinder 57 is the same as the case of obtaining the center coordinates of the cylinder 31, 33, 35 in the second embodiment shown in FIG. 4, first, the slit light image position (I, J) And the parameters such as the mirror rotation angle θ are used to calculate the three-dimensional coordinates from the cylindrical surface area data, and from the three-dimensional coordinates Q _i determined as the measurement points on the cylindrical surface by the area division, the components of the coordinate transformation matrix T of 3 rows × 4 columns of the error _{e 1} minimizes using known Levenberg-Marquardt method, Powell method, or the like obtained by a nonlinear least-squares method. Where t _ij (i = 1 to 3, j = 1 to 4) is a component of the coordinate transformation matrix T that passes through the center point of the cylindrical surface and the center axis coincides with the Z axis, and R is the radius of the calibrated cylindrical surface It is.

e ₁ = Σ | (t ₁₁ X _i + t ₁₂ Y _i + t ₁₃ Z _i + t ₁₄ ) ² +
_{(t 21 X i + t 22} Y i + t 23 Z i + t 24) 2 -R 2 | ............ (7)

Then, from the obtained coordinate transformation matrix, the center coordinates (X ₀ , Y ₀ , Z ₀ ) of the cylindrical surface obtained by the following formula (8) and the unit direction vector (l, m, n) of the center axis are obtained and shown in FIG. Store in a storage device not shown. When the center coordinates of the cylinder at φ + Δφ are obtained in this way, in the next step S56, it is determined whether or not the angle φ is φmax (for example, 360 °). If it is not φmax, the process returns to step S52 and the same processing is performed. Repeated.

If the angle φ is φmax, the intersection position (X _c , Y _c , Z _c ) of each central line group calculated for each Δφ between φ _i = 0 and φ in step S57 is minimized. A direction vector that is calculated by the square method or the like, passes through the intersection point position, and minimizes the variance of the inner product value with each straight line group is calculated as an orientation vector of the rotation axis using an algorithm such as the Powell method.

And saved it in step S58, the one ends the calculation of the center axis L _phi cylinder 57, as further described in Example 3, or to calibrate a spherical, calibrated with the calibration plate 50 itself planes For example, when calibrating with a spherical surface, the spherical function is fitted as in the first embodiment, and the error function e ₁ is calculated. In the case of calibration the calibration plate 50 itself planes error function e ₂ are fitting plane are computed.

The error function e is e = e ₁ + e ₂ as described above.
Therefore, the error function e is evaluated, and if this value is not valid, the calibration curve parameter is corrected using the nonlinear least squares method. Not stored in storage device and saved and exit.

  As described above, the flat plate of the subject is installed instead of the calibration plate 50, the plane coordinates of the surface are measured by the three-dimensional measuring device 59, and the flatness of the subject is measured. By using this, the front and back of the subject can be measured with a single three-dimensional measuring device 59, and the flatness measuring apparatus can be configured at a low cost.

  FIGS. 10 and 11 show a fifth embodiment of the flatness measuring method and apparatus according to the present invention. In the first to fourth embodiments so far, a three-dimensional measuring instrument is used to simultaneously measure the front and back of the subject. Two are used, or a calibration plate and a subject are attached to a rotary stage for measurement, but in this Example 5, the subject and the optical axis of the imaging device used for the three-dimensional measuring instrument are extended on the extension. A calibration plate is placed, and a reflection mirror that sends images of the front and back of the subject to the imaging device is provided symmetrically across the subject and the calibration plate, and the front and back of the subject can be measured at once with a single three-dimensional measuring instrument. It is what I did.

  First, the configuration of FIG. 10 will be described. In the figure, reference numeral 60 denotes a subject or calibration plate, 61 denotes a three-dimensional measuring device using an imaging device, and 62 and 63 denote reflections that send an image of the subject or calibration plate 60 to the imaging device 61. 61A and 61B are positions of the virtual three-dimensional measuring device formed by the reflection mirrors 62 and 63.

The relationship between each component is as follows: the distance from the subject to the virtual three-dimensional measuring devices 61A and 61B is H, the distance from the center of the reflecting mirror 62 to the subject is L ₁ , and the virtual three-dimensional from the center of the reflecting mirror 62 is also the same. The distance from the measuring devices 61A and 61B is L ₂ , the distance from the three-dimensional measuring device 61 to the subject 60 is L ₃ , the angle at which the subject 60 is viewed from the virtual three-dimensional measuring devices 61A and 61B is τ, the reflection mirror 62, The angle formed by the straight line drawn from the virtual three-dimensional measuring devices 61A and 61B to the subject 60 through the center of the 63 with the subject 60 is θ, the optical axis of the three-dimensional measuring device 61, the three-dimensional measuring device 61, and the reflection mirror. If the angle between the line connecting the centers of 62 and 63 is δ, the angle between the reflection mirrors 62 and 63 and the subject 60 is φ, the length of the subject 60 is W, and the length of the reflection mirror is B,
H = W (cosτ−cos2θ) / sinτ
L ₂ = (H / sin θ) −L ₁
δ = sin ⁻¹ (L ₁ sin θ / L ₂ )
φ = 0.5 (180−θ−δ)

となる。

It becomes.

  Therefore, a calibration plate is first placed at the position 60 as described in the first, second, and third embodiments, and the inherent error such as the scaling error and spatial distortion of the three-dimensional measuring device 61 is calibrated. By placing and measuring, the front and back of the subject can be measured at once.

  In addition to the configuration of FIG. 10, the configuration of FIG. 11 further includes the subject 70 of the three-dimensional measuring device 71 on the optical axis of the imaging device that configures the three-dimensional measuring device 71 so that the light cutting method or the like can be used. On the opposite side, a projector 72 is installed with the opposite direction to the subject 70, and a mirror for scanning the subject 70 such as a galvanometer mirror 77 that shakes light from the projector is provided, and the light Are provided with second reflecting mirrors 75 and 76 for sending the image to the subject 70 side. In FIG. 11, 73 and 74 are first reflecting mirrors for sending an image of the subject 70 to the three-dimensional measuring device 72, 71A and 71B are virtual three-dimensional measuring devices, and 72A and 72B are virtual projectors. It is.

  As described above, the light projector 72 for the subject 70 is provided on the optical axis of the imaging device constituting the three-dimensional measuring device 71 and is shaken by the galvano mirror 77 so that the front and back of the subject 70 are simultaneously scanned. The flatness of the front and back of the subject 70 can be measured at a time using the method. It should be noted that the calibration method of the three-dimensional measuring device 71 may be the method of the first to third embodiments, and the galvano mirror 77 may be a scanning mirror of another type, such as a polygon mirror. Of course.

  FIGS. 12, 13 and 14 are Embodiment 6 of the flatness measuring method and apparatus according to the present invention. In the embodiments described so far, in order to calibrate the scaling error and spatial distortion of the three-dimensional measuring instrument, a calibration plate is placed at the measurement position, and the three-dimensional measuring instrument is used to measure these errors. It has been explained that the flatness of a flat plate is actually measured after calibration. However, in the sixth embodiment, when the subject is a regular polygon such as a square, for example, each corner is overlapped with the center of the regular polygon and measured with a three-dimensional measuring device. The average value is calculated by adding the measurement results, and the difference between the maximum and minimum values obtained by subtracting the average value from each measurement result is taken as the flatness of the measurement point. The present invention provides a method for measuring the flatness of a flat plate that does not require measurement.

  FIG. 12A is a diagram for explaining the flat plate flatness measuring method and apparatus of the sixth embodiment. Z (i, j) indicated by 82 is a measurement of the subject measured with a three-dimensional measuring instrument. When the result is an N × N array, the measurement result 82 is obtained by measuring the actual warp or uneven component T (i, j) of the target surface of the subject indicated by 80 and the subject indicated by 81. This is a result of adding the spatial distortion component D (i, j) of the sensor (three-dimensional measuring instrument) such as the above-described scaling error and spatial distortion of the three-dimensional measuring instrument. Note that i of these components is a horizontal index, and j is a vertical index.

Therefore, in this sixth embodiment, when the actual warpage or unevenness of the target surface in the subject is randomly generated, for example, N × N of the result 82 obtained by measuring a square subject with a three-dimensional measuring instrument. The array is stored in the storage device, and the subject is measured while being rotated at a 90-degree pitch, and each measurement result is stored in the storage device. Then, the measurement result of M × N ² (M = 2 to 4 in the case of a square) is obtained, and the following M × N ² relational expressions are obtained.

Results of measurement with the opposite (0 °): ¹ Z (i, j) = T (i, j) + D (i, j)
Measurement result after rotating 90 °: ² Z (i, j) = T (i, j) + D (i, j)
Result measured by rotating 180 °: ³ Z (i, j) = T (i, j) + D (i, j)
270 ° ……………
……………

  Therefore, as described above, when it is assumed that the subject is warped or uneven randomly, the average value of the measured values at each measurement point

を作成し、各測定結果^ｍＺ（ｉ，ｊ）から差し引いた値^ｍΔＺ（ｉ，ｊ）の最大値と最小値との差を、その測定ポイントにおける局所的な平面度Δ（ｉ，ｊ）とする。

And the difference between the maximum value and the minimum value of the value ^m ΔZ (i, j) subtracted from each measurement result ^m Z (i, j) is used as the local flatness Δ (i, j at the measurement point. ).

  That is,

として、平面度Δを測定ポイントにおける局所的な平面度の最大値として次式で評価し、合否を判定する。

Then, the flatness Δ is evaluated as the maximum value of the local flatness at the measurement point by the following formula, and pass / fail is determined.

        Δ = max | Δ (i, j |

  This process is shown in the flowchart of FIG. First, when the flatness evaluation process is started in step S60, a control device (not shown) of the three-dimensional measuring device uses a mechanism 86 for holding the subject 80 as shown in FIG. The center is grasped, and if the shape is a square as described above, the I / F of the control device that rotates at a pitch of 90 degrees is instructed to set the subject at a predetermined angle. In FIG. 14, the gripping position of the subject 80 is depicted as being shifted from the center of the subject 80, but the center position may be gripped in the same manner.

を算出する。そして前記した式に基づき、局所的な平面度Δ（ｉ，ｊ）を作成する。そしてステップＳ６９で前記式に基づき、平面度Δの評価を行い、その合否をステップＳ７０で外部に表示すると共に、不合格の場合はステップＳ６１に戻り、合格の場合はステップＳ７１で終了する。 In step S63, the entire object is measured by the three-dimensional measuring device, and stored in the storage device in step S64. The above processing is repeated three more times, for example, while rotating the subject by 90 °. When that is done, pre-process in step S66, and in step S67, the average value of the measured values

Is calculated. Based on the above formula, a local flatness Δ (i, j) is created. In step S69, the flatness Δ is evaluated based on the above expression, and the pass / fail result is displayed to the outside in step S70. If it fails, the process returns to step S61, and if it passes, the process ends in step S71.

  By doing so, the spatial distortion component of the three-dimensional measuring device included in each actual measurement result can be canceled, and a flat plate surface that can easily measure the flatness of the subject without using a calibration plate or the like. A degree measuring method and apparatus can be provided.

  When a certain offset is placed on the surface of the object, for example, when it is known that the four corners of the square flat plate bend in the same direction, the above method cannot remove the spatial distortion. In that case, as shown in FIG. 12B, the rotation center 84 of the subject 83 is a midpoint connecting the center and the corner of the subject, and the method described above covers a quarter range including the rotation center. In this case, it is possible to measure the flatness of the flat area of all the areas by repeating the measurement in (1) as shown in 83A and 83B for each 1/4 area.

  FIGS. 15 and 16 are diagrams for explaining a seventh embodiment of the flatness measuring method and apparatus according to the present invention, and FIG. 15 is a diagram showing a measurement region of a subject to be evaluated for flatness in the seventh embodiment. FIG. 16 is a flowchart of the flatness evaluation process.

  In the sixth embodiment described above, each regular polygonal subject is rotated so that the corners of the subject overlap each other and measured with a three-dimensional measuring instrument, and the measurement results are added at each measurement point to obtain an average value. After the calculation, the average value was subtracted from each measurement result to measure the flatness of the flat plate.A specimen prepared with the same material and surface treatment as the specimen to be evaluated for flatness was prepared in advance as a calibration plate. In the seventh embodiment, the distortion component D (i, j) of the three-dimensional measuring instrument is obtained from the average value of the measurement results measured by rotating at an angular pitch of 6 to eliminate the need for rotational measurement for each subject. It is.

  In other words, rotate the subject as a calibration plate created with the same material and surface treatment as the subject to be evaluated for flatness at an arbitrary angular pitch at the measurement position, and average the measurement results.

を算出し、この値が、３次元測定器の歪み成分Ｄ（ｉ，ｊ）と同一であるとして保存しておくことで、平面度評価する被検体の測定結果Ｚ（ｉ，ｊ）からこの歪み成分Ｄ（ｉ，ｊ）を差し引けば、その結果Ｚ’（ｉ，ｊ）は被検体の反りや凹凸の成分であるとすることができるから、それによって平面度を評価することが可能となり、校正板の測定以後は、被検体を回転させることなく平面度評価が可能となる。

And this value is stored as being the same as the distortion component D (i, j) of the three-dimensional measuring instrument, so that this is obtained from the measurement result Z (i, j) of the subject to be evaluated for flatness. If the distortion component D (i, j) is subtracted, as a result, Z ′ (i, j) can be regarded as a component of warping or unevenness of the subject, so that the flatness can be evaluated. Thus, after the measurement of the calibration plate, the flatness can be evaluated without rotating the subject.

  FIG. 15 is a diagram showing the measurement region of the subject to be evaluated for flatness in Example 7, as described above. In Example 7, the measurement region 80 for the subject to be evaluated for flatness is rotated by an arbitrary angle. However, in order to enable measurement, a disk 87 having the same size as a circle circumscribing the measurement region 80 of the subject or a flat plate 88 inscribed in the circle 87 is used as a calibration plate.

  Then, the calibration plate 87 or 88 is attached to the object gripping apparatus shown in FIG. 14 as described above, and measured as described above to calculate the distortion component D (i, j) of the three-dimensional measuring instrument. . The flowchart is the flowchart shown in FIG. In the flowchart of FIG. 16, the same numbers are assigned to the flows having the same contents as those in the sixth embodiment shown in FIG.

  When the processing starts in step S80, first, a distortion component D (i, j) of the three-dimensional measuring device is calculated. That is, the control device (not shown) of the three-dimensional measuring instrument grips the center of the calibration plate as the test object in step S62, for example, with the mechanism 86 that holds the test object 80 as shown in FIG. Thus, in the case of a square, the subject is set at a predetermined angle by instructing the I / F of the control device to rotate at a pitch of 90 degrees.

  Then, in step S63, the entire subject is measured by the three-dimensional measuring instrument, and after preprocessing in step S66, the measured value is added according to the following equation (9) in step S81.

そしてこの処理を例えば被検体（校正板）が正方形や長方形の場合は９０°ずつ回転させて実施し、ステップＳ６７で測定値の平均値

For example, if the subject (calibration plate) is square or rectangular, this process is performed by rotating 90 ° at a time. In step S67, the average value of the measured values is measured.

を算出する。そしてこの値をステップＳ８２でステップＳ８４に示したように歪み成分データとして保存し、ステップＳ８３で校正板の計測と歪み成分の算出を終了する。

Is calculated. This value is stored as distortion component data in step S82 as shown in step S84, and calibration plate measurement and distortion component calculation are terminated in step S83.

  When the distortion component of the three-dimensional measuring device is calculated and stored in this manner, the flatness of the subject is evaluated from step S60. In this process, the whole object is measured by the three-dimensional measuring device in step S63 as described above, and after preprocessing in step S66, the distortion correction process of the measured value is performed in accordance with the following equation (10) in step S85.

そしてその値によって局所的な平面度Δ（ｉ，ｊ）を作成する。そしてステップＳ６９で下記式（１１）に基づいて平面度Δの評価を行い、ステップＳ８６で終了する。

Then, a local flatness Δ (i, j) is created based on the value. In step S69, the flatness Δ is evaluated based on the following equation (11), and the process ends in step S86.

        Δ = max (Z ′) − min (Z ′) (11)

  By doing so, since the spatial distortion component of the three-dimensional measuring device is known in advance, it is possible to provide a flatness measuring method that can measure the flatness simply by measuring the object. .

  As described above, according to the present invention, flatness can be measured using a non-contact type three-dimensional measuring device with a simple configuration while minimizing a scaling error and a spatial distortion error of the three-dimensional measuring device. Therefore, the flatness of the flat plate can be easily measured, and in-process measurement can be performed, so that a great effect can be obtained.

It is the figure which showed the structure which implements the flat-plate flatness measuring method and apparatus which become this invention. 5 is a calibration plate used for calibration of a three-dimensional measuring instrument in Example 1 in the flatness measuring method and apparatus according to the present invention. FIG. 2 is a flowchart of calibration processing according to the first embodiment, where (A) is a main flow of calibration processing, and (B) is a flowchart of only the calibration processing portion. It is a calibration board used for the calibration of a three-dimensional measuring device in Example 2 in the flatness measuring method and apparatus which become this invention. FIG. 10 is a flowchart of only the calibration processing part of the second embodiment. It is a calibration board used for the calibration of a three-dimensional measuring device in Example 3 in the flatness measuring method and apparatus which become this invention. FIG. 10 is a flowchart of only the calibration processing part of the third embodiment. It is a structure outline of Example 4 of the flatness flatness measuring method and apparatus which become this invention. FIG. 10 is a flowchart of a calibration process of a rotation axis of a rotation stage in Embodiment 4. FIG. 6 is a schematic configuration diagram of Embodiment 5 of the flatness measuring method and apparatus according to the present invention, and is a schematic configuration in which both front and back surfaces of a subject are simultaneously measured with a single three-dimensional measuring device. In addition to the configuration of FIG. 10, it is an outline of a configuration in which a projector and a galvanometer mirror are arranged on the optical axis of a three-dimensional measuring device so that a light cutting method or the like can be used. It is a figure for demonstrating Example 6 of the flatness measuring method and apparatus which become this invention. FIG. 10 is a flowchart illustrating a flatness evaluation process according to the sixth embodiment. FIG. 10 is a schematic perspective view of an example of a subject grasping apparatus used in Example 6; FIG. 10 is a diagram illustrating a measurement region of a subject to be evaluated for flatness in Example 7. FIG. 10 is a flowchart of flatness evaluation processing according to the seventh embodiment. FIG. 2 is a partially broken schematic perspective view (A) and a schematic cross-sectional structure diagram (B) in an integrated stacked fuel cell. It is a figure for demonstrating the outline of the measuring method by an optical cutting method, (A) is the figure which showed one structure outline which implements an optical cutting method, (B) is a figure for demonstrating a measuring method. (A) is a diagram showing an outline of the configuration of a non-contact type three-dimensional measuring device that scans a subject by oscillating a laser beam, and (B) is a graph showing a scaling error. (A) It is a figure for demonstrating a spatial distortion, (B) is a graph which showed the relationship between the command value when a spatial distortion generate | occur | produces, and the rotation angle of a mirror when a spatial distortion occurs.

Explanation of symbols

1, 4 3D measuring device 2, 5 Storage device 3, 6 Control device 7 Subject (flat plate) or calibration plate 20 Calibration plate 21-29 True sphere with known radius and center coordinates

Claims (32)

A flat plate flatness measuring method in which a flat specimen is set at a measurement position and measured with a non-contact type three-dimensional measuring instrument to measure flatness,
A calibration plate having measurement points whose known coordinates are at least three or more is set in advance at the measurement position, and the measurement points are measured by the three-dimensional measuring device to calibrate inherent measurement errors in the three-dimensional measuring device. Then, the flatness is measured by installing a subject at the measurement position and measuring the flatness.   The flatness measuring method according to claim 1, wherein the calibration plate is prepared by arranging a sphere having a known center coordinate and radius as the measurement point.   The flatness measuring method according to claim 2, wherein the spheres are prepared by being arranged diagonally with respect to the center of the calibration plate and on the top, bottom, left and right of the center.   4. The calibration according to claim 2, wherein the calibration obtains a center coordinate of the sphere and calibrates a scaling error caused by nonlinearity of a driving mechanism in the three-dimensional measuring device from a distance between center coordinates of different spheres. The flat plate flatness measuring method described.   2. The flat plate flatness measuring method according to claim 1, wherein the calibration plate is prepared by arranging a cylinder whose center axis coordinate and radius are known as the measurement point.   The flatness measuring method according to claim 5, wherein at least three cylinders are prepared, and each center axis is prepared so as to intersect with a center axis of another cylinder.   The calibration obtains a center axis coordinate of the cylinder and an intersection coordinate of the center axis, and determines a scaling error caused by nonlinearity of a drive mechanism in the three-dimensional measuring device from a distance between the intersection coordinates, and a spatial distortion as the center. The flatness measuring method according to claim 5 or 6, wherein calibration is performed based on the coordinates of the axis.   2. The flatness measuring method according to claim 1, wherein the calibration plate is prepared by arranging a sphere having a known center coordinate and radius as the measurement point on a plane having a known plane coordinate.   The flatness measuring method according to claim 8, wherein the spheres are prepared by being arranged diagonally with respect to the center of the calibration plate and on the top, bottom, left and right of the center.   In the calibration, the center coordinates of the sphere and the coordinates of the plane are obtained, and the scaling error due to the non-linearity of the driving mechanism in the three-dimensional measuring device is calculated from the distance between the center coordinates of different spheres, and the spatial distortion is calculated in the plane. The flatness measuring method according to claim 8 or 9, wherein a value of an arbitrary direction coordinate is obtained and calibrated.   The three-dimensional measuring device is prepared corresponding to each of the front and back sides of the subject, and after calculating coordinate conversion parameters that unify the measurement coordinate system of both the three-dimensional measuring devices by measuring the calibration plate, the three-dimensional measuring device is measured at the measurement position. The flatness measurement method according to claim 1, wherein the flatness is measured by installing a specimen.   A rotating stage is prepared by holding the subject or the calibration plate at the measurement position and rotating it so that the front and back can be measured with a single three-dimensional measuring device. The calibration plate is attached to the rotating stage and the 3 2. The flatness measurement method according to claim 1, wherein after the measurement error inherent in the dimension measuring instrument is calibrated, the object is attached to the rotating stage and rotated to measure the front and back sides.   The calibration plate is prepared by attaching a plane having a known plane coordinate attached to a cylinder having a known radius and a sphere having a known center coordinate and a radius on the plane, which can be attached around the rotation axis of the rotary stage. The flat plate flatness measuring method according to claim 12.   The calibration obtains the center axis coordinates of the cylinder, the center coordinates of the sphere, and the coordinates of the plane, and the scaling error due to the non-linearity of the drive mechanism in the three-dimensional measuring device is determined from the distance between the center coordinates of different spheres. 14. The flat plate flatness measuring method according to claim 13, wherein the spatial distortion is calibrated by obtaining a value of a central axis coordinate of the cylinder and an arbitrary direction coordinate in the plane.   The non-contact type three-dimensional measuring instrument has an imaging device, and the subject is placed at the measurement position symmetrically across the optical axis of the imaging device while the measurement position is on an extension of the optical axis in the imaging device The flatness measurement method according to claim 1, wherein a reflection mirror that sends light from the front and back of the image sensor to the imaging device is prepared and the flatness is measured.   The non-contact type three-dimensional measuring device further includes a projector positioned on the optical axis of the imaging device, and a mirror that swings light emitted from the projector, and light emitted from the projector and swung by the mirror 16. The flat plate flatness measuring method according to claim 15, wherein a second reflecting mirror provided symmetrically with respect to the optical axis of the image pickup device is prepared. A flat plate flatness measurement method in which a flat specimen is set at a measurement position and measured by a non-contact type three-dimensional measuring instrument to measure flatness,
When the subject is a regular polygon, the subject is rotated around the center of the regular polygon so that each corner is overlapped, and measured by the non-contact type three-dimensional measuring device, and measured at each measurement point. An average value is calculated by adding the results, and the flatness of the measurement point is defined as the difference between the maximum value and the minimum value among the values obtained by subtracting the average value from the measurement results. Degree measurement method.   The non-contact type three-dimensional object is rotated by an angle formed by an adjacent corner of the regular polygon and the center of the subject around a midpoint connecting a center and a corner of the subject of the regular polygon. The flatness measurement method according to claim 17, wherein the flatness of the subject is measured by performing measurement with a measuring instrument on all corners. A flat plate flatness measuring method in which a flat specimen is set at a measurement position and measured with a non-contact type three-dimensional measuring instrument to measure flatness,
When the subject is a regular polygon, a calibration plate having a size that includes a circle circumscribing the regular polygon is prepared in advance, and measured with the non-contact type three-dimensional measuring device while rotating the calibration plate. The measurement results are added for each measurement point, an average value is calculated, and the average value is stored as a distortion component of the three-dimensional measuring device. Then, the subject is measured by the non-contact type three-dimensional measuring device. A flat plate flatness measuring method, wherein the distortion component is removed from the measurement result, and the obtained result is used as the flatness of the subject. A flat plate flatness measuring device comprising a non-contact type three-dimensional measuring instrument for measuring an object comprising a flat plate installed at a measurement position,
In the three-dimensional measuring instrument, the flatness measuring apparatus is provided with a calibration plate having at least three known measurement points at the measurement position, and calculated based on the measured coordinates of the measurement points. A flat plate plane having storage means for storing a calibration value of an inherent measurement error, and measuring the flatness of the object by calibrating the measurement result of the object with the calibration value stored in the storage means Degree measuring device.   20. The flatness measuring apparatus according to claim 19, wherein the calibration plate is provided with a sphere having a known center coordinate and radius as the measurement point.   21. The flatness measuring apparatus according to claim 20, wherein the spheres are arranged diagonally with respect to the center of the calibration plate and on the top, bottom, left and right of the center.   The flatness measuring apparatus according to claim 19, wherein the calibration plate is provided with a cylinder whose center axis coordinate and radius are known as the measurement point.   The flatness measuring apparatus according to claim 22, wherein at least three cylinders are prepared, and each central axis is arranged to intersect with a central axis of another cylinder.   The flatness measuring apparatus according to claim 19, wherein the calibration plate has a sphere with a known center coordinate and radius as the measurement point on a plane with a known plane coordinate.   25. The flatness measuring apparatus according to claim 24, wherein the spheres are arranged diagonally to the center of the calibration plate and on the top, bottom, left and right of the center.   The three-dimensional measuring device is arranged corresponding to each of the front and back sides of the subject, and coordinate conversion parameters that unify the measurement coordinate system of both the three-dimensional measuring devices calculated by measuring the calibration plate are stored in the storage means, 26. The flatness measuring apparatus according to claim 19, wherein the flatness of the subject is measured by calibrating the measurement result of the subject using the coordinate conversion parameter stored in the storage means.   The flatness measuring apparatus according to claim 19, further comprising a rotation stage that holds and rotates the subject or the calibration plate so that the front and back of the subject can be measured by the rotation.   The calibration plate includes a cylinder with a known radius that is calibrated so as to be attachable around the rotation axis of the rotary stage, a plane with a known plane coordinate attached to the cylinder, and a center coordinate and a radius known to the plane. A flatness measuring apparatus according to claim 27, wherein a sphere is arranged.   The flatness measuring device is provided symmetrically with a non-contact type three-dimensional measuring device having an imaging device, the measurement position provided on the extension of the optical axis of the imaging device, and the optical axis of the imaging device. The flatness measuring apparatus according to any one of claims 19 to 25, further comprising: a reflection mirror that transmits light from the front and back of the subject arranged at the measurement position to the imaging apparatus.   The non-contact type three-dimensional measuring device further includes a projector positioned on the optical axis of the imaging device, and a mirror that swings light emitted from the projector, and light emitted from the projector and swung by the mirror 30. The flatness measuring apparatus according to claim 29, further comprising a second reflection mirror provided symmetrically across the optical axis of the imaging apparatus that sends the image to the measurement position. A flat plate flatness measuring device comprising a non-contact type three-dimensional measuring instrument for measuring an object comprising a flat plate installed at a measurement position,
A mechanism for rotating the subject; storage means for storing the measurement result of the non-contact type three-dimensional measuring instrument measured by rotating the subject; and adding the measurement results stored in the storage means to obtain an average value A flatness measurement of flatness, comprising: an arithmetic means for calculating and calculating a difference between a maximum value and a minimum value among values obtained by subtracting the average value from each measurement result. apparatus.

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