JP5545691B2 - Shape measuring method and shape measuring apparatus - Google Patents

Description

  The present invention relates to a shape measuring method and a shape measuring device.

Conventionally, various methods have been used as small sphere measuring methods (sphericity measuring methods), but there has been no decisive method. For example, one steel ball is measured with a roundness measuring device to measure the contour of the steel ball surface on two or three equator planes that are 90 ° to each other, and the radial distance from each minimum circumscribed circle to the steel ball surface is measured. Measure the maximum value as sphericity, or place one steel ball between the 90 ° and 120 ° V-grooves and the perpendicular probe, and change direction (10 times or more recommended) ), The value obtained by dividing the maximum value of the movement of the stylus by 2 is known as the sphericity (JIS standard (JIS B1501)). Deviation) cannot be taken as a surface. In particular, in the case of a small sphere (diameter of 1 to 2 mm or less), in order to measure the sphericity of the small sphere, a probe having a fine tip sphere is required, and a probe for processing such probe ( Measuring element) A processing method and a processing machine are considered (see Patent Document 1).
However, even if a probe having such a fine tip sphere can be processed, it cannot be performed until the sphericity of the fine tip sphere of the processed probe is measured. Sphericality measurement has been the key to improving the precision of minute probing systems that are expected to develop in the future.
As a method for measuring the sphericity of such a fine tip sphere, a plurality of cross-sectional shapes are measured from a sphere that is the object to be measured, and “the center of each cross-section ((part) circle) matches the center of the sphere”. Using this assumption, a method of numerically synthesizing the cross-sectional shape and measuring the sphericity based on the shape obtained by the synthesis is considered.
JP 2005-96033 A

  However, in the case of the method for measuring the sphericity of the above-mentioned fine tip sphere, the measurement is performed based on the assumption that the center of each cross section coincides with the center of the sphere. There was a problem that there was no guarantee that

  An object of the present invention is to provide a shape measuring method and a shape measuring apparatus capable of performing shape measurement with high accuracy and high reliability.

In order to solve the above problems, the invention described in claim 1
In the shape measuring method for measuring the cross-sectional shape of the measured object that is a rotationally symmetric body and measuring the shape of the measured object,
The object to be measured is a sphere,
Obtaining first information relating to a cross-sectional shape of the object to be measured parallel to the rotational symmetry axis of the object to be measured, each time the object to be measured is rotated by a predetermined angle around the rotational symmetry axis;
Obtaining second information relating to a cross-sectional shape of the measured object at an angle different from the rotational symmetry axis of the measured object;
By using a predetermined constraint condition between the cross-sectional shape of the measured object parallel to the rotational symmetry axis and the cross-sectional shape of the measured object at an angle different from the rotational symmetry axis, the first information and Calculating a relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis acquired in the step of acquiring the first information based on the second information;
Calculating the shape of the object to be measured based on the calculated relative position;
With
A Y axis parallel to the rotational symmetry axis, a Z axis parallel to the optical axis at the time of measurement, and an X axis orthogonal to the Y axis and the Z axis,
The predetermined constraint condition is such that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and the cross-sectional shape of the object to be measured at an angle different from the rotational symmetry axis coincide with the center of each measured cross-sectional shape. In the coordinate system at the time of measurement passing through the center of the measured object perpendicular to the optical axis at the time of measurement, performing only parallel movement in the direction connecting the intersection of the ideal rotational symmetry body and the straight line including the two cross-sectional shapes, Translation is performed only in a plane where z = 0, and the translation component of the entire object to be measured is constrained so that the center of the object to be measured comes to the origin on the coordinates.

The invention according to claim 2 is the shape measuring method according to claim 1,
The step of acquiring the first information includes the step of acquiring one-section shape information of the object to be measured parallel to the rotational symmetry axis, and the step of rotating the object to be measured around the rotational symmetry axis at a predetermined angle; By alternately repeating, the first information relating to the cross-sectional shape of the object to be measured is obtained,
The step of acquiring the second information includes the step of acquiring the cross-sectional shape information of the measured object after tilting the rotational symmetry axis to a predetermined angle and the measured object about the rotational symmetry axis before tilting. The second information relating to the cross-sectional shape of the object to be measured is acquired by alternately repeating the step of rotating at a predetermined angle.

The invention according to claim 3 is the shape measuring method according to claim 1,
The step of acquiring the first information includes the step of acquiring one-section shape information of the object to be measured parallel to the rotational symmetry axis, and the step of rotating the object to be measured around the rotational symmetry axis at a predetermined angle; By alternately repeating, the first information relating to the cross-sectional shape of the object to be measured is obtained,
The step of acquiring the second information includes the step of acquiring the cross-sectional shape information of the measured object after tilting the rotational symmetry axis to a predetermined angle and the measurement target around the rotational symmetry axis after tilting. The second information relating to the cross-sectional shape of the object to be measured is acquired by alternately repeating the step of rotating the object at a predetermined angle.

Invention of Claim 4 is the shape measuring method of Claim 2 or 3,
A step of attaching a stem to the object to be measured;
The step of rotating the object to be measured at a predetermined angle is characterized in that the object to be measured is rotated at a predetermined angle together with the stem.

Invention of Claim 5 is the shape measuring method as described in any one of Claims 1-4 ,
The first information and the second information relating to a cross-sectional shape of the object to be measured are measured and acquired by non-contact measurement.

The invention described in claim 6
In a shape measuring apparatus that measures the cross-sectional shape of a measurement object that is a rotationally symmetric body and measures the shape of the measurement object,
The object to be measured is a sphere,
Rotating means for rotating the object to be measured at a predetermined angle around the rotational symmetry axis;
Each time the object to be measured is rotated by a predetermined angle by the rotating means, a cross-sectional shape of the object to be measured parallel to the rotational symmetry axis of the object to be measured is calculated, and a first shape related to the cross-sectional shape of the object to be measured is calculated. First information acquisition means for acquiring one information;
Rotational symmetry axis holding means for holding the rotational symmetry axis at a predetermined angle;
Second information acquisition means for acquiring second information relating to a cross-sectional shape of the object to be measured, after the rotation symmetry axis is inclined at a predetermined angle by the rotation symmetry axis holding means;
The first information acquisition is performed by using a predetermined constraint condition between a cross-sectional shape of the measured object parallel to the rotational symmetry axis and a cross-sectional shape of the measured object at an angle different from the rotational symmetry axis. Based on the first information acquired by the means and the second information acquired by the second information acquisition means, the cross-sectional shape of the measured object parallel to the rotational symmetry axis acquired by the first information acquisition means Position calculating means for calculating a relative position between the cross-sectional shapes in each of them,
Shape measuring means for calculating the shape of the object to be measured based on the calculated relative position;
With
A Y axis parallel to the rotational symmetry axis, a Z axis parallel to the optical axis at the time of measurement, and an X axis orthogonal to the Y axis and the Z axis,
The predetermined constraint condition is such that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and the cross-sectional shape of the object to be measured at an angle different from the rotational symmetry axis coincide with the center of each measured cross-sectional shape. In the coordinate system at the time of measurement passing through the center of the measured object perpendicular to the optical axis at the time of measurement, performing only parallel movement in the direction connecting the intersection of the ideal rotational symmetry body and the straight line including the two cross-sectional shapes, Translation is performed only in a plane where z = 0, and the translation component of the entire object to be measured is constrained so that the center of the object to be measured comes to the origin on the coordinates.

The invention according to claim 7 is the shape measuring apparatus according to claim 6 ,
The second information acquisition means includes
After the rotationally symmetric axis is tilted to a predetermined angle by the rotationally symmetric axis holding unit, the measured object is rotated by the rotating unit around the rotationally symmetric axis before the tilting by a predetermined angle. Is calculated, and second information relating to the cross-sectional shape of the object to be measured is obtained.

The invention according to claim 8 is the shape measuring apparatus according to claim 6 ,
Second rotating means for rotating the object to be measured held by tilting the rotational symmetry axis at a predetermined angle by the rotational symmetry axis holding means at a predetermined angle around the rotational symmetry axis;
The second information acquisition means includes
Each time the rotationally symmetric axis is tilted to a predetermined angle by the rotationally symmetric axis holding means, the measured object is rotated at a predetermined angle by the second rotating means around the rotationally symmetric axis after tilting. One cross-sectional shape of the object to be measured is calculated, and second information relating to the cross-sectional shape of the object to be measured is acquired.

Invention of Claim 9 is the shape measuring apparatus as described in any one of Claims 6-8 ,
A light source unit for irradiating the object to be measured with light;
Imaging means for imaging a map formed by irradiating the object to be measured with light output from the light source unit;
With
The first information acquisition unit and the second information acquisition unit are:
One cross-sectional shape of the object to be measured is calculated based on the map imaged by the imaging means.

According to the first aspect of the present invention, the first information related to the cross-sectional shape of the measured object parallel to the rotational symmetry axis of the measured object and the first information related to the cross-sectional shape of the measured object at an angle different from the rotational symmetric axis. 2 information can be obtained, and a predetermined constraint condition between the cross-sectional shape of the measured object parallel to the rotational symmetry axis and the cross-sectional shape of the measured object at a different angle from the rotational symmetry axis is used. Based on the first information and the second information, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis acquired in the step of acquiring the first information is calculated. The shape of the object to be measured can be calculated based on the calculated relative position, and the predetermined constraint condition is that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and an angle different from the rotational symmetry axis. Disconnection of measured object The shape is translated only in the direction connecting the intersection of the ideal rotationally symmetric body matched with the center of each measured cross-sectional shape and the straight line including the two cross-sectional shapes, and is perpendicular to the optical axis at the time of measurement. In the coordinate system at the time of measurement passing through the center of the measurement object, the translation is performed only in the plane where z = 0, and the translation component of the entire measurement object is centered on the coordinate origin. Ru can be constrained to.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the invention described in claim 2, it is needless to say that the same effect as that of the invention described in claim 1 can be obtained, and the object to be measured parallel to the rotational symmetry axis is obtained by the step of acquiring the first information. The first information relating to the cross-sectional shape of the object to be measured can be obtained by alternately repeating the step of acquiring the cross-sectional shape information and the step of rotating the object to be measured at a predetermined angle around the rotational symmetry axis. In the step of acquiring the second information, after the rotational symmetry axis is inclined at a predetermined angle, the step of acquiring the cross-sectional shape information of the object to be measured and the object to be measured around the rotational symmetry axis before the inclination are determined. By alternately repeating the step of rotating at an angle, the second information relating to the cross-sectional shape of the object to be measured can be acquired.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the third aspect of the invention, it is needless to say that the same effect as that of the first aspect of the invention can be obtained, and the object to be measured parallel to the rotational symmetry axis is obtained by the step of acquiring the first information. The first information relating to the cross-sectional shape of the object to be measured can be obtained by alternately repeating the step of acquiring the cross-sectional shape information and the step of rotating the object to be measured at a predetermined angle around the rotational symmetry axis. In addition, the step of acquiring the second information is performed by tilting the rotational symmetry axis to a predetermined angle, and then acquiring the cross-sectional shape information of the object to be measured. The second information relating to the cross-sectional shape of the object to be measured can be acquired by alternately repeating the process of rotating at the angle of.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the invention described in claim 4, it is needless to say that the same effect as that of the invention described in claim 2 or 3 can be obtained, and a step of attaching a stem to the object to be measured is provided. By the step of rotating at an angle, the object to be measured can be rotated at a predetermined angle together with the stem.
Therefore, by attaching a stem to the object to be measured, it is possible to suitably position the object to be measured when performing shape measurement, and to improve handling performance when rotating the object to be measured at a predetermined angle. be able to.

According to the invention described in claim 5 , it is needless to say that the same effect as in the invention described in any one of claims 1 to 4 can be obtained, and the first information relating to the cross-sectional shape of the object to be measured and The second information can be obtained by measurement by non-contact measurement.
Therefore, the shape measurement can be suitably performed without scratching the surface of the object to be measured.

According to the sixth aspect of the present invention, the object to be measured can be rotated around the rotational symmetry axis by a predetermined angle by the rotating means, and the object to be measured is predetermined by the rotating means by the first information acquiring means. Each time the object is rotated at an angle, one cross-sectional shape of the object to be measured parallel to the rotational symmetry axis of the object to be measured can be calculated, and first information related to the cross-sectional shape of the object to be measured can be acquired, and the rotational symmetry axis can be maintained. The rotation symmetry axis can be held at a predetermined angle by the means, and the second information acquisition means can tilt the rotation symmetry axis to a predetermined angle by the rotation symmetry axis holding means, and then The second information related to the cross-sectional shape can be acquired, and the position calculation means allows the cross-sectional shape between the cross-sectional shape of the measured object parallel to the rotational symmetry axis and the cross-sectional shape of the measured object at a different angle from the rotational symmetry axis. Where Based on the first information acquired by the first information acquisition means and the second information acquired by the second information acquisition means, the rotational symmetry axis acquired by the first information acquisition means is used. The relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object can be calculated, and the shape of the measured object can be calculated based on the calculated relative position by the shape measuring means. The predetermined constraint condition is that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and the cross-sectional shape of the object to be measured at an angle different from the rotational symmetry axis are matched to the ideal rotational symmetry that matches the center of each measured cross-sectional shape. A coordinate system at the time of measurement that passes only in the direction connecting the intersection of the body and the straight line including the two cross-sectional shapes, passes through the center of the object to be measured, perpendicular to the optical axis at the time of measurement, and z = 0 In plane Only perform translation, the translation component of the entire object to be measured, can be the center of the object to be measured, restrained to come to the origin of the coordinates.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the seventh aspect of the invention, it is of course possible to obtain the same effect as that of the sixth aspect of the invention. By the second information acquisition means, the rotational symmetric axis holding means is predetermined by the rotational symmetric axis holding means. After being tilted at an angle, the cross-sectional shape of the object to be measured is calculated each time the object to be measured is rotated at a predetermined angle by the rotating means around the rotational symmetry axis before the tilt, and the cross-sectional shape of the object to be measured is calculated. The second information can be acquired.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the eighth aspect of the invention, it is possible to obtain the same effect as the sixth aspect of the invention, and the second rotational means causes the rotationally symmetric axis holding means to set the rotationally symmetric axis to a predetermined value. The object to be measured held at an angle can be rotated at a predetermined angle around the rotational symmetry axis, and the rotational symmetry axis is inclined at the predetermined angle by the rotational symmetry axis holding means by the second information acquisition means. After that, each time the object to be measured is rotated at a predetermined angle by the second rotating means around the rotationally symmetric axis after being tilted, one cross-sectional shape of the object to be measured is calculated, and the second cross-sectional shape of the object to be measured is calculated. 2 information can be acquired.
Therefore, by measuring a plurality of cross-sectional shapes of the object to be measured that intersect each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the object to be measured is rotated about the rotational symmetry axis. Even if it occurs, the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained. As a result, it is possible to perform shape measurement with high accuracy and high reliability.

According to the invention described in claim 9 , it is needless to say that the same effect as the invention described in any one of claims 6 to 8 can be obtained, and the light source unit can irradiate light, The imaging unit can capture a map formed by irradiating the object to be measured with the light output from the light source unit, and based on the map captured by the imaging unit by the first information acquisition unit and the second information acquisition unit. One cross-sectional shape of the object to be measured can be calculated.
Therefore, the shape measurement can be suitably performed without scratching the surface of the object to be measured.

  Hereinafter, specific embodiments of the shape measuring method and the shape measuring apparatus according to the present invention will be described with reference to the drawings. In the present embodiment, a spherical object will be described as an example of an object to be measured that is a rotationally symmetric body.

<First Embodiment>
As shown in FIG. 1, the shape measuring apparatus 100 according to the first embodiment includes a light source unit 10, a collimating lens 20, a rotating mechanism 30 that rotatably supports a sphere (object to be measured) 200, an objective lens 40, and imaging. A collimator lens 20, a sphere 200, an objective lens 40, and an imaging unit 50 are arranged in this order along the optical axis of the light emitted from the light source unit 10. ing.

  For example, as illustrated in FIG. 1, the light source unit 10 irradiates the sphere 200 with white light using a point light source that outputs white light. The light source unit 10 is not limited to such a point light source, and may be a surface light source, or may generate light using a discharge lamp, a light emitting diode, a laser, or the like.

  The collimating lens 20 is a lens that converts light emitted from the light source unit 10 into parallel light.

  For example, as illustrated in FIG. 1, the rotation mechanism 30 includes a grip portion 31, an angular position adjustment mechanism 32, and a rotation table 33.

The grip portion 31 grips the stem 201 attached to the sphere 200. As a configuration for gripping the stem 201, for example, a collet chuck is used. In addition, the center of the sphere 200 is formed on the extension line of the stem 201 attached to the sphere 200.

  For example, as shown in FIG. 4, the angular position adjustment mechanism 32 forms a concave slope, and is a mechanism that slides the grip portion 31 along the slope. Further, the slope has a substantially semicircular shape, and the center of curvature of the semicircle is formed to coincide with the center of the sphere 200. Therefore, when the grip portion 31 is slid, the stem 201 can be held at a predetermined angle without adjusting the center position of the sphere 200. As a result, the angular position adjusting mechanism 32 functions as a rotationally symmetric axis holding unit that holds the stem 201 held by the holding unit 31 at a predetermined angle.

As shown in FIG. 1, the rotary table 33 is configured so that the angular position adjusting mechanism 32 can be placed. For example, the drive motor 33 a has a stem 201 that is perpendicular to the optical axis of the light source unit 10 as a rotationally symmetric axis. The sphere 200 is rotated by driving. Further, the rotation table 33 controls the rotation angle by, for example, an encoder (not shown). Thereby, the rotary table 33 functions as a rotating means.

  For example, as shown in FIG. 1, the objective lens 40 is disposed between the sphere 200 and an imaging surface of an imaging unit 50 described later on the optical axis of the light emitted from the light source unit 10. Is used to form an image on the imaging surface of the imaging unit 50.

For example, a CCD camera is used as the imaging unit 50 and images a mapping through the objective lens 40.
Specifically, as shown in FIG. 2, a map formed by the light output from the light source unit 10 irradiating the sphere 200 through the collimator lens 20 is imaged through the objective lens 40.
The imaging unit 50 functions as an imaging unit by imaging a mapping using such a CCD camera.

  For example, as shown in FIG. 1, the image processing unit 60 includes a CPU (Central Processing Unit) 61, a RAM (Random Access Memory) 62, a storage unit 63, a display unit 64 that displays an image processing result, and the like. By executing a predetermined program stored in the storage unit 63, it has a function of performing operation control of each unit based on predetermined operation conditions set in advance in order to perform a predetermined operation.

  The CPU 61 reads out a processing program or the like stored in the storage unit 63, develops it in the RAM 62, and executes it to perform image processing of the sphere 200.

  The RAM 62 develops the processing program executed by the CPU 61 in the program storage area in the RAM 62, and stores the input data and the processing result generated when the processing program is executed in the data storage area.

  The storage unit 63 includes, for example, a recording medium (not shown) in which programs, data, and the like are stored in advance, and this recording medium is configured by, for example, a semiconductor memory. The storage unit 63 stores various data for the CPU 61 to perform image processing, various processing programs, data processed by executing these programs, and the like. More specifically, for example, as shown in FIG. 1, the storage unit 63 stores a first information acquisition program 63a, a second information acquisition program 63b, a position calculation program 63c, a shape measurement program 63d, and the like.

The first information acquisition program 63a is a program that causes the CPU 61 to realize a function of acquiring first information related to the cross-sectional shape of the sphere 200 parallel to the stem 201 attached to the sphere 200.
Specifically, for example, by executing the first information acquisition program 63a, the CPU 61 captures an image of one cross-sectional shape of the sphere 200 parallel to the stem 201 attached to the sphere 200 by the imaging unit 50, and FIG. As shown, edge detection is performed on the image of the cross-sectional shape of the captured sphere 200 to obtain first information related to the cross-sectional shape of the sphere 200. Then, the CPU 61 executes the first information acquisition program 63a to rotate the rotary table 33 at a predetermined angle, and then again captures one cross-sectional shape of the sphere 200 by the imaging unit 50, and the captured sphere The first information related to the cross-sectional shape of the sphere 200 is acquired by performing edge detection on the map having a cross-sectional shape of 200. Then, such a series of operations is repeated until one section of the first photographed sphere 200 is rotated by 180 °, and the first information is obtained as shown in FIG. 3 (a thin line representing a spherical shape).
The CPU 61 functions as a first information acquisition unit by executing the first information acquisition program 63a.

The second information acquisition program 63b is a program that causes the CPU 61 to realize a function of acquiring the second information related to the cross-sectional shape of the sphere 200 at an angle different from that of the stem 201 attached to the sphere 200.
Specifically, for example, by executing the second information acquisition program 63b, the CPU 61 slides the grip portion 31 by the angular position adjustment mechanism 32 and is gripped by the grip portion 31 as shown in FIG. The stem 201 is tilted to a predetermined angle. Then, by executing the second information acquisition program 63b, the CPU 61 captures an image of one cross-sectional shape of the sphere 200 by the imaging unit 50 in the same manner as when the first information acquisition program 63a is executed, and the captured sphere The second information (thick line representing the spherical shape in FIG. 3) related to the sectional shape of the sphere 200 is acquired by performing edge detection on the mapping of one sectional shape of the 200. Then, the CPU 61 executes the second information acquisition program 63b to rotate the rotary table 33 at a predetermined angle θ as shown in FIGS. The second information relating to the cross-sectional shape of the sphere 200 is acquired by performing image detection by the unit 50 and performing edge detection on the image of the cross-sectional shape of the captured sphere 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates by 180 °, and the second information is acquired.
The CPU 61 functions as a second information acquisition unit by executing the second information acquisition program 63b.

The position calculation program 63c causes the CPU 61 to realize a function of calculating a relative position between the cross-sectional shapes of the sphere 200 parallel to the stem 201 attached to the sphere 200 acquired by the execution of the first information acquisition program 63a. It is a program.
Specifically, for example, the CPU 61 executes the position calculation program 63c, so that the cross-sectional shape between the cross-sectional shape of the sphere 200 parallel to the stem 201 of the sphere 200 and the cross-sectional shape of the sphere 200 at an angle different from the stem 201 is determined. And the stem 201 of the sphere 200 based on the first information acquired by the execution of the first information acquisition program 63a and the second information acquired by the execution of the second information acquisition program 63b. The relative position between the cross-sectional shapes in the parallel sphere 200 is calculated.
The CPU 61 functions as a shape measuring unit by executing the shape measuring program 63d.

More specifically, for example, the CPU 61 executes the position calculation program 63c, thereby acquiring the first information acquired by the execution of the first information acquisition program 63a and the first information acquired by the execution of the second information acquisition program 63b. 2 Based on the information, the center of each measured cross-sectional shape is matched with the center of the nominal circle. At this time, the least square circle of each measured cross-sectional shape may be obtained, and the center (temporary center) of the least square circle may be matched with the center of the nominal circle.
At this time, if there are two nominal cross sections that intersect each other (the cross section of an ideal sphere), the circular shape of each cross section should have two intersections, but in reality, measurement errors are included, so Does not match.
Therefore, the circular shape is translated in the direction of the straight line connecting the circular intersections of the two nominal cross sections so that the positions of the same points are equal (the difference is minimized).
Then, based on the first information acquired by the execution of the first information acquisition program 63a and the second information acquired by the execution of the second information acquisition program 63b, this is considered a combination of all the obtained cross sections, The optimum adjustment amount is obtained by the method of least squares.

Here, for example, as shown in FIG. 7, the first information acquisition program 63 a executes the first cross section in the meridian direction of the sphere 200 while giving the rotation angle θ around the Y axis (around the stem 201). Get information. Next, by executing the second information acquisition program 63b, the second information related to the cross-sectional shape of the sphere 200 is acquired while the stem 201 is tilted at an angle φ with respect to the Y axis on the YZ plane and further given the rotation angle θ. To do. At this time, the rotation angle at the i-th (i = 1,..., N) measurement is θ _{i and the} inclination angle φ _i . However, when acquiring the cross-sectional shape in the meridian direction of the sphere 200 around the Y axis (around the stem 201), φ _i = 0.
Assume that n cross-sectional shapes C _i (i = 1, 2,..., N) are measured.
At this time, since the cross-sectional shape of the sphere 200 is measured from the Z-axis direction, the one having the largest intersection (circle) between the plane perpendicular to the Z-axis and the sphere 200 is measured. That is, the cross section is perpendicular to the Z axis and passes through the center of the sphere 200.
Therefore, any two measured cross sections pass through the center of the sphere 200. Therefore, an intersection line formed by a plane including two cross sections is a straight line passing through the center of the sphere 200, and this straight line intersects the sphere 200 at two points.

Specifically, for example, as shown in FIG. 8, two intersecting points (same points when an ideal circle is considered) of two arbitrary cross sections C _i and C _j (i ≠ j) measured are represented. Let P _{i, j} and Q _{i, j} .
At this time, the plane equation including the cross section of the i-th measurement is as follows.
(Sin θ _i cos φ _i ) x − (sin φ _i ) y + (cos θ _i cos φ _i ) z = 0 Equation (1)
When simplified, the following equation is obtained.
_{a i x + b i y +} c i z = 0 ··· Equation (2)
At this time, the normal vector of the plane is (a _i , b _i , c _i ).
Similarly, the equation of the plane including the j-th measurement cross section is as follows.
(Sin θ _j cos φ _j ) x − (sin φ _j ) y + (cos θ _j cos φ _j ) z = 0 Equation (3)
For simplification, it is expressed as follows.
a _j x + b _j y + c _j z = 0 Equation (4)
At this time, a linear equation including two cross sections C _i and C _j (i ≠ j) is expressed by the following equation.
(X, y, z) = k (c _j b _i −c _i b _j , c _i a _j −c _j a _i , a _i b _j −b _i a _j ) (5)
(K: any number)
To simplify, the equation of the straight line of the equation (5) is as follows.
(X, y, z) = k (a _{i, j} , b _{i, j} , c _{i, j} ) (6)
At this time, the direction vector of the straight line is (a _{i, j} , b _{i, j} , c _{i, j} ).
Also, the nominal sphere equation is expressed as:
x ² + y ² + z ² = r ² (7)
Then, the intersection of the nominal sphere and the straight line including the two cross sections C _i and C _j (i ≠ j) is obtained by the equation shown in Equation 1.

In Equation 1, P _{i, j} and Q _{i, j} are only the difference in sign, and the order is arbitrary.
At this time, this intersection is a point on the two measured cross sections, and the same point is measured, so the coordinate values of the measured values are theoretically equal.
However, (i) the calculation is performed on the assumption that the center of the cross section is the center coordinate of the sphere 200, and (ii) they do not necessarily match due to a measurement error. Therefore, in order to match the two as much as possible, based on the constraint conditions described below, the measurement data is translated to create spherical data. At this time, as a restraint condition,
(A) Only translation is performed in the direction connecting the intersections.
(B) The translation is performed only in a plane perpendicular to the optical axis at the time of measurement and passing through the center of the sphere. This plane is the coordinate system at the time of measurement, and z = 0.
Under this constraint condition, optimum solutions are obtained by the least square method for all effective combinations. However, the equation cannot always be solved only by these constraint conditions. This is because the component that translates the entire sphere becomes indefinite.
Therefore, the following constraint condition is added.
(C) The translation component of the entire sphere is constrained so that the center of the sphere is at the origin on the coordinates.
At this time, the measurement is generally discrete. Therefore, there is not always measurement data at the intersection. Therefore, the data of the nearest neighbor point is used or interpolated from the peripheral data. At this time, a filter may be used to remove measurement noise and spatial high frequency data.

Here, the constraint conditions (a) and (b) of the measurement data described above are formulated. Specifically, as shown in FIG. 7, a constraint on the i-th cross section C _i and the j-th cross section C _j is considered. The coordinate axes ξ _{i, i, j} are taken in the direction of the straight line connecting the intersections of the two cross sections. Further, the coordinate axis ζ _{i, i, j} is taken so as to be in a plane passing through the center of the circle, perpendicular to the coordinate axis ξ _{i, i, j} and including the cross section C _i . Also, let ω _{i, i, j} be an axis perpendicular to these two coordinate axes. As shown in FIG. 8, ω _{i, i, j} takes a positive direction in the optical axis direction at the time of measurement, and ξ _{i, i, j} , ζ _{i, i, j} forms a right-handed coordinate system. Determine as follows.
At this time, the constraint condition is expressed by the following equation.
ω _{i, i, j} = 0 (10)
ω _{j, j, i} = 0 (11)
ξ _{i, i, j} −ξ _{j, i, j} = δ _{i, j} Equation (12)

ξ _{j, i, j} is corrected in the ξ _{j, j, i} direction (the ζ _{i, i, j} , ζ _{j, j, i} direction is not constrained only by the constraint condition of two cross sections).
Further, δ _{i, j} is the difference in the position of the cross section in the straight line direction connecting the two nominal intersections (preferably using the average of the two points P _{i, j} and Q _{i, j} ).
Here, the movement amount (adjustment amount) vector represented by the original xyz coordinates of the cross section C _j is M _i = (x _i , y _i , z _i ).
The xyz coordinate system and ξ _{i, i, j} ζ _{i, i, j} ω _{i, i, j} coordinate system have a common origin and are related only by rotation. Therefore, in order to convert the vector M _i to ξ _{i, i, j} ζ _{i, i, j} ω _{i, i, j} coordinate system, it can be converted using the 3 × 3 matrix R _{i, j} , The value is expressed as:
R _{i, j} M _i = (α _{i, j} (x _i , y _i , z _i ), β _{i, j} (x _i , y _i , z _i ), γ _{i, j} (x _i , y _i , z _i ))... Formula (13)
R _{j, i} M _j = (α _{j, i} (x _j , y _j , z _j ), β _{j, i} (x _j , y _j , z _j ), γ _{j, i} (x _j , y _j , z _j )) ... Formula (14)
Since the vector of the coordinate system after the rotation is known from the equations (2) and (6), the rotation angle can be identified, and the transformation matrix R _{i, Find j} . At this time, the ω _{i, i, j} axis is obtained by rotating the z-axis by φ _i about the x-axis and further by θ _i about the y-axis, and further about the ω _{i, i, j-} axis. The x axis after the rotation of φ _i and θ _{i is} rotated so as to coincide with the ξ _{j, i, j} axis. The equation of rotation can be calculated by, for example, a reference document (Robot Manipulator, RP Paul, translated by Tsuneo Yoshikawa, Corona Publishing, 1984).

Then, the following constraint equation is obtained from the equations (10), (11), and (12).
α _{i, j} (x _i , y _i , z _i ) −α _{j, i} (x _j , y _j , z _j ) = δ _{i, j} (15)
γ _{i, j} (x _i , y _i , z _i ) = 0 (16)
γ _{j, i} (x _j , y _j , z _j ) = 0 Equation (17)
Here, α _{i, j} (x _i , y _i , z _i ), α _{j, i} (x _j , y _j , z _j ), γ _{i, j} (x _i , y _i , z _i ), γ _{j , i} (x _j , y _j , z _j ) is a linear combination of x _i , y _i , z _i , x _j , y _j , z _j , as is clear from equations (13) and (14). It is a formula expressed.
Therefore, it can be expressed in the form of the following equation.
D _{i, j} x _i + E _{i, j} y _i + F _{i, j} z _i + D _{j, i} x _j + E _{j, i} y _j + F _{j, i} z _j = δ _{i, j} (18)
G _{i, j} x _i + H _{i, j} y _i + I _{i, j} z _i = 0 (19)
G _{j, i} x _j + H _{j, i} y _j + I _{j, i} z _j = 0 (20)
These equations are applied for all possible cross-section combinations.

  Next, when the constraint condition (c) is formulated, the constraint of the entire sphere may be used, and therefore expressed by the following formula.

In Equation 2, (x _i , y _i , z _i ) that simultaneously satisfy the expressions (21) to (23) is the adjustment amount to be obtained.
However, since the above constraint conditions are generally over-constrained, there is no unique solution considering that there is measurement noise. Therefore, a solution is obtained by the least square method (generalized inverse matrix).
Therefore, when Expressions (18) to (23) are expressed in matrix, they are expressed by the following expression.

In Equation 3, the size of the matrix A is (3 _n C ₂ + 3n) × (3n) at the maximum, and B is a vector and has a size of (3 _n C ₂ + 3n) × 1. Note that the number of rows may be reduced by removing those that cannot contribute to the measurement due to the combination. It is also desirable to remove data sets with poor calculation conditions.
Moreover, Formula (24) is represented by the following formula using a generalized inverse matrix.

Then, based on the adjustment amounts (x _i , y _i , z _i ) (i = 1,..., N) obtained in Equation 4, the cross-sectional shapes in each of the cross-sectional shapes of the sphere 200 parallel to the stem 201 are relative to each other. The correct position is calculated.
The CPU 61 functions as a position calculation unit by executing the position calculation program 63c.

The shape measurement program 63d is a program that causes the CPU 61 to realize a function of calculating the shape of the sphere 200.
Specifically, for example, the CPU 61 executes the shape measurement program 63d, thereby adjusting amounts (x _i , y _i , z _i ) (i = 1,..., N) calculated by executing the position calculation program 63c. ), By parallelly moving and synthesizing each of the cross-sectional shapes of the sphere 200 parallel to the stem 201, map data of the shape of the sphere 200 can be obtained, and the sphere shape can be calculated. Further, sphericity (deviation from the least square sphere, difference between the maximum inscribed sphere and the minimum circumscribed sphere, etc.) can be calculated from this data.

  Next, a method for measuring the shape of the sphere 200 by the shape measuring apparatus 100 according to the first embodiment will be described with reference to the flowchart of FIG.

  First, in step S1, as shown in FIG. 1, in a state where the stem 201 is attached to the sphere 200 and the sphere 200 is arranged so that the axis of the stem 201 is perpendicular to the optical axis, the CPU 61 By executing the information acquisition program 63a, the imaging unit 50 captures one cross-sectional shape of the sphere 200 parallel to the stem 201 attached to the sphere 200, and edge detection is performed on the image of the one-cross-sectional shape of the captured sphere 200. As a result, the first information relating to the cross-sectional shape of the sphere 200 is acquired. Then, the CPU 61 executes the first information acquisition program 63a to rotate the rotary table 33 at a predetermined angle, and then again captures one cross-sectional shape of the sphere 200 by the imaging unit 50, and the captured sphere The first information related to the cross-sectional shape of the sphere 200 is acquired by performing edge detection on the map having a cross-sectional shape of 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates 180 °, and the first information is acquired.

  Next, in step S2, the CPU 61 executes the second information acquisition program 63b to slide the grip portion 31 by the angular position adjustment mechanism 32 as shown in FIG. Tilt 201 to a predetermined angle.

  Next, in step S3, the CPU 61 executes the second information acquisition program 63b to image one cross-sectional shape of the sphere 200 by the imaging unit 50 in the same manner as when the first information acquisition program 63a is executed. By performing edge detection on the image of the cross-sectional shape of the imaged sphere 200, second information relating to the cross-sectional shape of the sphere 200 is acquired. Then, the CPU 61 executes the second information acquisition program 63b to rotate the rotary table 33 at a predetermined angle, and then again captures one cross-sectional shape of the sphere 200 by the imaging unit 50, and the captured sphere The second information related to the cross-sectional shape of the sphere 200 is acquired by performing edge detection on the map having a cross-sectional shape of 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates by 180 °, and the second information is acquired.

  Next, in step S4, the CPU 61 executes the position calculation program 63c to match the provisional center of the circular shape in the measured cross section with the center of the nominal circle.

  Next, in step S5, the CPU 61 executes the position calculation program 63c to obtain intersection points for all cross-sectional combinations and calculate an adjustment amount.

  Next, in step S6, the CPU 61 executes the position calculation program 63c to create a matrix expression including all constraint conditions.

  Next, in step S7, the CPU 61 calculates an adjustment amount that simultaneously satisfies the determinant created in step S6 by executing the position calculation program 63c.

Next, in step S8, the CPU 61 executes the shape measurement program 63d, thereby adjusting amounts (x _i , y _i , z _i ) (i = 1,..., N) calculated by executing the position calculation program 63c. Based on the above, the cross-sectional shapes are translated and combined to obtain map data of the shape of the sphere 200, the sphere shape is calculated, and this processing is terminated.

In this way, the sphere 200 can be rotated around the stem 201 by a predetermined angle by the rotary table 33, and the CPU 61 executes the first information acquisition program 63a, thereby causing the sphere 200 to be predetermined by the rotary table 33. Each time the rotation is performed at an angle, one cross-sectional shape of the sphere 200 parallel to the stem 201 of the sphere 200 can be calculated, and first information relating to the cross-sectional shape of the sphere 200 can be acquired. 201 can be tilted and held at a predetermined angle, and the CPU 61 executes the second information acquisition program 63b to tilt the stem 201 to a predetermined angle by the angular position adjustment mechanism 32 and then before tilting. Each time the sphere 200 is rotated at a predetermined angle by the rotary table 33 around the stem 201, the sphere 200 The cross-sectional shape can be calculated and second information related to the cross-sectional shape of the sphere 200 can be acquired, and the CPU 61 executes the position calculation program 63c, whereby the cross-sectional shape of the sphere 200 parallel to the stem 201 and the stem 201 Obtained by executing the first information acquisition program 63b and the first information acquisition program 63b by using a predetermined constraint condition between the cross-sectional shapes of the sphere 200 and the cross-sectional shape of the sphere 200 at different angles. Based on the second information thus obtained, it is possible to calculate the relative position between the cross-sectional shapes in each of the cross-sectional shapes of the sphere 200 parallel to the stem 201 of the sphere 200 acquired by executing the first information acquisition program 63a. The CPU 61 executes the shape measurement program 63d, based on the calculated relative position. It can be calculated the shape of a sphere 200.
Therefore, when a plurality of cross-sectional shapes of the sphere intersect with each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the sphere is rotated around the rotational symmetry axis. Even in such a case, the relative position between the cross-sectional shapes in the sphere can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained, and the shape measurement can be performed with high accuracy and high reliability. Can do.
Further, the CPU 61 includes a light source unit for irradiating the sphere 200 with light and an imaging unit 50 for capturing a map formed by irradiating the sphere with light output from the light source unit, and the CPU 61 includes a first information acquisition program 63a. In addition, by executing the second information acquisition program 63b, it is possible to calculate one cross-sectional shape of the sphere based on the mapping imaged by the imaging unit 50.
Therefore, the shape measurement can be suitably performed without damaging the surface of the sphere.

Second Embodiment
Next, 2nd Embodiment which concerns on the shape measuring apparatus of this invention is described with reference to FIG. The basic configuration of the second embodiment is the same as that of the first embodiment, and parts different from the configuration of the first embodiment will be described.

  As shown in FIG. 10, the shape measuring apparatus 300 according to the second embodiment includes a light source unit 10, a collimating lens 20, a rotating mechanism 330 that rotates and supports a sphere (object to be measured) 200, an objective lens 40, and imaging. A collimator lens 20, a sphere 200, an objective lens 40, and an imaging unit 50 are arranged in this order along the optical axis of the light emitted from the light source unit 10. ing.

  For example, as illustrated in FIG. 10, the rotation mechanism 330 is configured to rotate the grip portion 31, the angular position adjustment mechanism 32, the rotary table 33, and the grip portion 31 attached to the angular position adjustment mechanism 32. 34.

As the second drive motor 34, a stepping motor or the like is used, and a rotary shaft (not shown) attached to the second drive motor 34 is connected to the grip portion 31. By rotating the rotary shaft, gripping is performed. The part 31 can be rotated. Thereby, for example, as shown in FIG. 11, the sphere 200 can be rotated around the stem 201 gripped by the grip portion 31.
Thereby, the 2nd drive motor 34 functions as the 2nd rotation means.

The second information acquisition program 363b is a program that causes the CPU 61 to realize a function of acquiring the second information related to the cross-sectional shape of the sphere 200 at an angle different from that of the stem 201 attached to the sphere 200.
Specifically, for example, by executing the second information acquisition program 363b, the CPU 61 slides the grip portion 31 by the angular position adjustment mechanism 32 and is gripped by the grip portion 31 as shown in FIG. The stem 201 is tilted to a predetermined angle. Then, by executing the second information acquisition program 363b, the CPU 61 captures an image of one cross-sectional shape of the sphere 200 by the imaging unit 50, and performs edge detection on the image of the cross-sectional shape of the imaged sphere 200. Second information relating to the cross-sectional shape of the sphere 200 is acquired. Then, the CPU 61 executes the second information acquisition program 363b to rotate the second drive motor 34 at a predetermined angle, and then again captures an image of one cross-sectional shape of the sphere 200 by the imaging unit 50. The second information relating to the cross-sectional shape of the sphere 200 is obtained by performing edge detection on the mapping of the cross-sectional shape of the sphere 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates by 180 °, and the second information is acquired.
The CPU 61 functions as a second information acquisition unit by executing the second information acquisition program 363b.

  Next, a method for measuring the shape of the sphere 200 by the shape measuring apparatus 300 according to the second embodiment will be described with reference to the flowchart of FIG.

  First, in step S11, as shown in FIG. 1, in a state where the stem 201 is attached to the sphere 200 and the sphere 200 is arranged so that the axis of the stem 201 is perpendicular to the optical axis, the CPU 61 By executing the information acquisition program 63a, the imaging unit 50 captures one cross-sectional shape of the sphere 200 parallel to the stem 201 attached to the sphere 200, and edge detection is performed on the image of the one-cross-sectional shape of the captured sphere 200. As a result, the first information relating to the cross-sectional shape of the sphere 200 is acquired. Then, the CPU 61 executes the first information acquisition program 63a to rotate the rotary table 33 at a predetermined angle, and then again captures one cross-sectional shape of the sphere 200 by the imaging unit 50, and the captured sphere The first information related to the cross-sectional shape of the sphere 200 is acquired by performing edge detection on the map having a cross-sectional shape of 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates 180 °, and the first information is acquired.

  Next, in step S <b> 12, as shown in FIG. 11, the CPU 61 executes the second information acquisition program 363 b to slide the grip portion 31 by the angular position adjustment mechanism 32, and the stem gripped by the grip portion 31. Tilt 201 to a predetermined angle.

  Next, in step S <b> 13, the CPU 61 executes the second information acquisition program 363 b to pick up an image of one cross-sectional shape of the sphere 200 by the imaging unit 50, and performs edge detection on the image of the single cross-sectional shape of the imaged sphere 200. As a result, the second information relating to the cross-sectional shape of the sphere 200 is acquired. Then, the CPU 61 executes the second information acquisition program 363b to rotate the second drive motor 34 at a predetermined angle, and then again captures an image of one cross-sectional shape of the sphere 200 by the imaging unit 50. The second information relating to the cross-sectional shape of the sphere 200 is obtained by performing edge detection on the mapping of the cross-sectional shape of the sphere 200. Then, such a series of operations is repeated until one section of the sphere 200 imaged first rotates by 180 °, and the second information is acquired.

  Next, in step S14, the CPU 61 executes the position calculation program 63c to match the temporary center of the circular shape in the measured cross section with the center of the nominal circle.

  Next, in step S15, the CPU 61 executes the position calculation program 63c to obtain intersections for all cross-sectional combinations and calculate adjustment amounts.

  Next, in step S16, the CPU 61 executes the position calculation program 63c to create a matrix expression including all constraint conditions.

  Next, in step S17, the CPU 61 calculates an adjustment amount that simultaneously satisfies the determinant created in step S16 by executing the position calculation program 63c.

Next, in step S18, the CPU 61 executes the shape measurement program 63d, thereby adjusting amounts (x _i , y _i , z _i ) (i = 1,..., N) calculated by executing the position calculation program 63c. Based on the above, the cross-sectional shapes are translated and combined to obtain map data of the shape of the sphere 200, the sphere shape is calculated, and this processing is terminated.

In this way, the sphere 200 can be rotated around the stem 201 by a predetermined angle by the rotary table 33, and the CPU 61 executes the first information acquisition program 63a, thereby causing the sphere 200 to be predetermined by the rotary table 33. Each time the rotation is performed at an angle, one cross-sectional shape of the sphere 200 parallel to the stem 201 of the sphere 200 can be calculated, and first information relating to the cross-sectional shape of the sphere 200 can be acquired. 201 can be held at a predetermined angle, and the sphere 200 held by tilting the stem 201 at a predetermined angle by the angular position adjusting mechanism 32 by the second drive motor 34 around the stem 201 at a predetermined angle. The CPU 61 executes the second information acquisition program 363b so that the angle can be rotated. After the stem 201 is tilted to a predetermined angle by the position adjusting mechanism 32, one cross-sectional shape of the sphere 200 is calculated each time the sphere 200 is rotated by the second drive motor 34 around the tilted stem 201. Then, the second information related to the cross-sectional shape of the sphere 200 can be acquired, and the CPU 61 executes the position calculation program 63c, so that the cross-sectional shape of the sphere 200 parallel to the stem 201 and the angle different from the stem 201 are obtained. By using a predetermined constraint condition between the cross-sectional shape and the cross-sectional shape of the sphere 200, the first information acquired by the execution of the first information acquisition program 63a and the second information acquired by the execution of the second information acquisition program 363b. A sphere parallel to the stem 201 of the sphere 200 acquired by executing the first information acquisition program 63a based on the information The relative positions between the cross-sectional shapes in each of the 200 cross-sectional shapes can be calculated, and the CPU 61 calculates the shape of the sphere 200 based on the calculated relative positions by executing the shape measurement program 63d. can do.
Therefore, when a plurality of cross-sectional shapes of the sphere intersect with each other based on a predetermined constraint condition between the cross-sectional shapes of the object to be measured, a rotation error occurs when the sphere is rotated around the rotational symmetry axis. Even in such a case, the relative position between the cross-sectional shapes in the sphere can be calculated by the constraint condition, and a more appropriate cross-sectional shape can be obtained, and the shape measurement can be performed with high accuracy and high reliability. Can do.
Further, the CPU 61 includes a light source unit for irradiating the sphere 200 with light and an imaging unit 50 for capturing a map formed by irradiating the sphere with light output from the light source unit, and the CPU 61 includes a first information acquisition program 63a. And by executing the second information acquisition program 363b, it is possible to calculate one cross-sectional shape of the sphere based on the mapping imaged by the imaging unit 50.
Therefore, the shape measurement can be suitably performed without damaging the surface of the sphere.

The present invention is not limited to the above embodiment, and the object to be measured may be a rotationally symmetric body, and may be an ellipse, a cylinder, or the like.
In this embodiment, by executing the second information acquisition program 363b, the angular position adjusting mechanism 32 tilts the stem 201 to a predetermined angle, and then rotates the stem 201 around the stem 201 before tilting. A design (first embodiment) for calculating one cross-sectional shape of the sphere 200 each time the sphere 200 is rotated by a predetermined angle and acquiring the second information related to the cross-sectional shape of the sphere 200, or the angular position adjustment mechanism 32 Then, each time the stem 201 is tilted to a predetermined angle by the second drive motor 34 around the tilted stem 201, the cross-sectional shape of the sphere 200 is calculated each time the sphere 200 is rotated by a predetermined angle. The second information related to the 200 cross-sectional shapes is designed to be acquired (second embodiment). However, the present invention is not limited to this. May, for example, the second information may be only one cross-sectional shape. That is, when acquiring the second information, it is not always necessary to rotate the stem 201 around the stem 201 before or after the stem 201 is tilted to a predetermined angle.
In addition, it is needless to say that other specific detailed structures can be appropriately changed.

It is the schematic which shows the structure of the shape measuring apparatus in 1st Embodiment which concerns on this invention. It is a figure which shows the mapping when light is irradiated from the light source part in the shape measuring apparatus which concerns on this invention, and light is irradiated to the spherical body. It is a figure which shows the cross-sectional shape of the sphere which concerns on the 1st information acquired in the shape measuring apparatus which concerns on this invention, and the cross-sectional shape of the sphere which concerns on 2nd information. It is a figure which shows angle position adjustment of the angle position adjustment mechanism which concerns on this invention. It is the schematic which shows the state which attached and rotated the spherical body to the rotation mechanism which concerns on this invention. It is a top view at the time of rotating by attaching a spherical body to the rotation mechanism in the shape measuring apparatus according to the present invention. It is a figure explaining the rotation angle at the time of rotating a spherical body in the shape measuring apparatus which concerns on this invention, and the inclination angle at the time of inclining a rotational symmetry axis. It is a figure explaining the process of calculating the relative position between cross-sectional shapes in the shape measuring apparatus which concerns on this invention. It is a flowchart figure which shows the shape measuring method of the shape measuring apparatus in 1st Embodiment which concerns on this invention. It is the schematic which shows the structure of the shape measuring apparatus in 2nd Embodiment which concerns on this invention. It is the schematic which shows the state which attached and rotated the spherical body to the rotation mechanism in 2nd Embodiment which concerns on this invention. It is a flowchart figure which shows the shape measuring method of the shape measuring apparatus in 2nd Embodiment which concerns on this invention.

Explanation of symbols

100 shape measuring apparatus (first embodiment)
DESCRIPTION OF SYMBOLS 10 Light source part 20 Collimating lens 30 Rotation mechanism 32 Angular position adjustment mechanism (Rotation symmetry axis holding means)
33 Rotating table (rotating means, first rotating means)
34 Second drive motor (second rotating means)
40 Objective lens 50 Imaging unit (imaging means)
60 Image processing unit 61 CPU (first information acquisition unit, second information acquisition unit, position calculation unit, shape measurement unit)
63a First information acquisition program (first information acquisition means)
63b Second information acquisition program (second information acquisition means)
63c Position calculation program (position calculation means)
63d Shape measurement program (shape measurement means)
200 Sphere (object to be measured)
201 stem (axis of rotational symmetry)
300 Shape measuring device (second embodiment)
330 Rotating mechanism (second embodiment)
363b Second information acquisition program (second information acquisition means (second embodiment))

Claims (9)

In the shape measuring method for measuring the cross-sectional shape of the measured object that is a rotationally symmetric body and measuring the shape of the measured object,
The object to be measured is a sphere,
Obtaining first information relating to a cross-sectional shape of the object to be measured parallel to the rotational symmetry axis of the object to be measured, each time the object to be measured is rotated by a predetermined angle around the rotational symmetry axis;
Obtaining second information relating to a cross-sectional shape of the measured object at an angle different from the rotational symmetry axis of the measured object;
By using a predetermined constraint condition between the cross-sectional shape of the measured object parallel to the rotational symmetry axis and the cross-sectional shape of the measured object at an angle different from the rotational symmetry axis, the first information and Calculating a relative position between the cross-sectional shapes in each of the cross-sectional shapes of the measured object parallel to the rotational symmetry axis acquired in the step of acquiring the first information based on the second information;
Calculating the shape of the object to be measured based on the calculated relative position;
With
A Y axis parallel to the rotational symmetry axis, a Z axis parallel to the optical axis at the time of measurement, and an X axis orthogonal to the Y axis and the Z axis,
The predetermined constraint condition is such that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and the cross-sectional shape of the object to be measured at an angle different from the rotational symmetry axis coincide with the center of each measured cross-sectional shape. In the coordinate system at the time of measurement passing through the center of the measured object perpendicular to the optical axis at the time of measurement, performing only parallel movement in the direction connecting the intersection of the ideal rotational symmetry body and the straight line including the two cross-sectional shapes, Shape measurement characterized in that translation is performed only in a plane where z = 0, and the translation component of the entire object to be measured is constrained so that the center of the object to be measured comes to the origin on coordinates. Method. The step of acquiring the first information includes the step of acquiring one-section shape information of the object to be measured parallel to the rotational symmetry axis, and the step of rotating the object to be measured around the rotational symmetry axis at a predetermined angle; By alternately repeating, the first information relating to the cross-sectional shape of the object to be measured is obtained,
The step of acquiring the second information includes the step of acquiring the cross-sectional shape information of the measured object after tilting the rotational symmetry axis to a predetermined angle and the measured object about the rotational symmetry axis before tilting. The shape measuring method according to claim 1, wherein the second information relating to the cross-sectional shape of the object to be measured is acquired by alternately repeating the step of rotating at a predetermined angle. The step of acquiring the first information includes the step of acquiring one-section shape information of the object to be measured parallel to the rotational symmetry axis, and the step of rotating the object to be measured around the rotational symmetry axis at a predetermined angle; By alternately repeating, the first information relating to the cross-sectional shape of the object to be measured is obtained,
The step of acquiring the second information includes the step of acquiring the cross-sectional shape information of the measured object after tilting the rotational symmetry axis to a predetermined angle and the measurement target around the rotational symmetry axis after tilting. The shape measuring method according to claim 1, wherein the second information related to the cross-sectional shape of the object to be measured is acquired by alternately repeating the step of rotating the object at a predetermined angle. A step of attaching a stem to the object to be measured;
4. The shape measuring method according to claim 2, wherein the step of rotating the object to be measured at a predetermined angle includes rotating the object to be measured at a predetermined angle together with the stem. Shape measuring method according to any one of claim 1 to 4, characterized in that to obtain said measured by non-contact measuring the first information and the second information relating to the cross-sectional shape of the object to be measured. In a shape measuring apparatus that measures the cross-sectional shape of a measurement object that is a rotationally symmetric body and measures the shape of the measurement object,
The object to be measured is a sphere,
Rotating means for rotating the object to be measured at a predetermined angle around the rotational symmetry axis;
Each time the object to be measured is rotated by a predetermined angle by the rotating means, a cross-sectional shape of the object to be measured parallel to the rotational symmetry axis of the object to be measured is calculated, and a first shape related to the cross-sectional shape of the object to be measured is calculated. First information acquisition means for acquiring one information;
Rotational symmetry axis holding means for holding the rotational symmetry axis at a predetermined angle;
Second information acquisition means for acquiring second information relating to a cross-sectional shape of the object to be measured, after the rotation symmetry axis is inclined at a predetermined angle by the rotation symmetry axis holding means;
The first information acquisition is performed by using a predetermined constraint condition between a cross-sectional shape of the measured object parallel to the rotational symmetry axis and a cross-sectional shape of the measured object at an angle different from the rotational symmetry axis. Based on the first information acquired by the means and the second information acquired by the second information acquisition means, the cross-sectional shape of the measured object parallel to the rotational symmetry axis acquired by the first information acquisition means Position calculating means for calculating a relative position between the cross-sectional shapes in each of them,
Shape measuring means for calculating the shape of the object to be measured based on the calculated relative position;
With
A Y axis parallel to the rotational symmetry axis, a Z axis parallel to the optical axis at the time of measurement, and an X axis orthogonal to the Y axis and the Z axis,
The predetermined constraint condition is such that the cross-sectional shape of the object to be measured parallel to the rotational symmetry axis and the cross-sectional shape of the object to be measured at an angle different from the rotational symmetry axis coincide with the center of each measured cross-sectional shape. In the coordinate system at the time of measurement passing through the center of the measured object perpendicular to the optical axis at the time of measurement, performing only parallel movement in the direction connecting the intersection of the ideal rotational symmetry body and the straight line including the two cross-sectional shapes, Shape measurement characterized in that translation is performed only in a plane where z = 0, and the translation component of the entire object to be measured is constrained so that the center of the object to be measured comes to the origin on coordinates. apparatus. The second information acquisition means includes
After the rotationally symmetric axis is tilted to a predetermined angle by the rotationally symmetric axis holding unit, the measured object is rotated by the rotating unit around the rotationally symmetric axis before the tilting by a predetermined angle. The shape measuring device according to claim 6 , wherein a second cross-sectional shape of the object to be measured is acquired by calculating a cross-sectional shape of the measured object. Second rotating means for rotating the object to be measured held by tilting the rotational symmetry axis at a predetermined angle by the rotational symmetry axis holding means at a predetermined angle around the rotational symmetry axis;
The second information acquisition means includes
Each time the rotationally symmetric axis is tilted to a predetermined angle by the rotationally symmetric axis holding means, the measured object is rotated at a predetermined angle by the second rotating means around the rotationally symmetric axis after tilting. The shape measuring apparatus according to claim 6 , wherein one shape of the cross section of the object to be measured is calculated, and second information related to the cross section of the object to be measured is acquired. A light source unit for irradiating the object to be measured with light;
Imaging means for imaging a map formed by irradiating the object to be measured with light output from the light source unit;
With
The first information acquisition unit and the second information acquisition unit are:
The shape measuring apparatus according to claim 6, wherein a cross-sectional shape of the object to be measured is calculated based on a map imaged by the imaging unit.

Images