JP2008209244A - Method of constructing three-dimensional shape from surface data by three-dimensional surface shape measuring instrument, and method of measuring thickness of plate-like object - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of constructing a three-dimensional shape of high-accuracy measured surface data by a three-dimensional surface shape measuring instrument, and to provide a method of measuring thickness of a plate-like object. <P>SOLUTION: A sphere is used as a tool for positioning. A center coordinate of the sphere to serve as a reference point is identified from a plurality of measured surface position coordinates. Center coordinates of three or more identified spheres having different diameters are used as different reference points. Respective data are combined by numerical computation, from a condition where the reference points are common in the respective surface data to construct the three-dimensional shape. In addition, position data of a front surface and a rear surface expressed by common coordinates for the platelike object are used and the thickness is evaluated. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

The present invention relates to a method for constructing a three-dimensional shape from surface data by a three-dimensional surface shape measuring instrument and a method for measuring the thickness of a plate-like object.

In recent years, the accuracy of non-contact type measuring instruments such as laser displacement sensors has improved, so measuring devices combined with biaxial moving devices are often used for measuring the three-dimensional shape of surfaces. In particular, a commercially available high-precision surface shape measuring instrument (Fig. 1) that combines an electric two-axis stage and a laser displacement sensor is often used to measure the surface shape of small objects.
In general, these devices place an object to be measured on a horizontally set stage, move the stage at a preset measurement pitch in a horizontal plane, and an encoder with the horizontal plane (xy) coordinates attached to the stage. In the structure, the coordinates of the vertical plane (z) are measured by a laser displacement sensor fixed independently on the upper part of the stage. Therefore, the range that can be measured at one time is limited to the surface facing the laser displacement sensor on the stage, and the measurement data is discrete for each measurement pitch. Because of these restrictions, it is not easy to construct a 3D shape by combining two or more individual surface shape measurement data such as the front and back surfaces.
In order to solve such problems, a reference point for combining multiple individual data is required. Three or more reference points are required for one object to be measured, and it must be collimated at each measurement separately. In addition, since the measurement accuracy of the reference point greatly affects the final combined data, it is required to show an accurate point (point) from any location.
Taking these conditions into consideration, the conventional methods are (a) a method using the corner of the object to be measured as a reference point (Non-Patent Document 1), and (b) two or more references arranged regularly on a rotating stage. A method using a sphere (Non-Patent Document 2), (c) For a plate-like object, the target (target) is set on the front and back of the point where the thickness of the object to be measured is known, and individual measurement data on the front and back sides are combined. (d) There is a method that uses the intersection of four baselines with different colors drawn on the reference plane plate on which the object to be measured is placed as the reference point and integrates them by image measurement (Non-patent Document 3). In addition, as a method of dividing and measuring objects to be measured that exceed the range that can be measured at once, (e) a method using a sphere as a reference point and using its center coordinates is considered. (Patent Document 1)
In the method (a), it is difficult to collimate the corner as a reference point from any direction, and it is difficult to accurately measure the corner point in a system that measures at a constant pitch. In addition, it is not possible to easily identify the corner points that are three or more reference points when measuring each surface. In method (b), the shape of the stage is limited, and an image of the bottom surface of the measurement object placed on the stage cannot be obtained. In the method (c), the accuracy decreases when the plate is warped. There is also an error in measuring the plate thickness. In the method (d), a certain amount of thickness is unavoidable in the base line, and the reference point obtained as the intersection has a certain size. The method of identifying the reference point by changing the baseline color can only be used for image measurement. The method (e) proposes an integration method for one aspect of the object to be measured, and cannot be said to be a method for integrating coordinates in a three-dimensional space. In addition, there is no specific method for obtaining the center coordinates or automatic identification of three or more reference points with different diameters, and using this to construct a solid shape from individual surface data.
Kurashiki Spinning Electronics Co., Ltd .: 3D photo measurement system Kraves-k product description, http://www.kurabo.co.jp/el/3d/kuraves_01.html Pulstec Industrial Co., Ltd .: 3D SCANNER TDS SERIES catalog Keio University Sato Laboratory: 3D measurement multi-view distance image integration explanation, http://www.ozawa.ics.keio.ac.jp/sato/research/3D_measurement/system.htm Patent Gazette Patent No. 3307060

(1) Challenges in ensuring the measurement accuracy of the reference point Ideally, the reference point is the point. However, the above-mentioned surface shape measuring instrument mechanism measures the surface shape (vertical coordinates) of non-measurement objects in a grid pattern in the horizontal plane at a set fixed pitch, so the measurement data is discrete. Therefore, when the target is set small, it does not match the measurement point and the measurement value cannot be obtained (Fig. 2), or there are multiple measurement values for the target and the target value cannot be identified ( Figure 3) occurs both theoretically and practically. Therefore, in order to measure the target that is definitely the reference point during measurement, it is necessary to consider setting the measurement pitch as small as possible and increasing the target within an allowable range. Setting the measurement pitch to a small value will increase the number of data for the measurement time, and increasing the reference point will reduce the accuracy when constructing the solid shape. It is often difficult to set a small target that can be collimated in any case of individual surface measurement.
As described above, the problem to be solved by the present invention is that the reference point in the conventional method must be large, and high-precision surface shape measuring instrument measurement data is secured at the time of construction of the three-dimensional shape. This is not possible.
(2) Problems in measuring three-dimensional shapes with surface shape measuring instruments Although surface shape measuring instruments can easily measure surface shapes, on the other hand, only planar shapes can be measured. For example, as shown in (Fig. 4) For example, when there is a shadowed surface as seen from the laser displacement sensor, only the surface shown thick in Fig. 4 can be measured.
(3) Problems in measuring plate thickness of plate-like objects In measuring plate-like objects, calipers, micrometers, ultrasonic plate thickness gauges, etc. are used. In calipers and micrometers, the structure of the measuring instrument is as shown in FIG. In addition, the plate thickness cannot be measured even at positions beyond the offset distance from the plate end face. Further, as shown in FIG. 6, the ultrasonic thickness gauge cannot accurately measure unevenness on the surface of the plate that is equal to or smaller than the probe width.
(4) Reference point identification work required Not only the coordinate integration for creating the 3D shape proposed here, but also 3 or more points common to each measurement in order to integrate multiple 3D coordinate measurement data The reference point is required. In other words, multiple coordinate data can be integrated by matching these three reference points. Therefore, the three reference points must be identified at every measurement time.
In general, an identification number (or symbol) is used as a reference point as a means of identification. However, the target 3D surface measuring instrument deals only with position coordinate data and recognizes the identification number. Cannot. In addition, as shown in Non-Patent Document 3, although identification by color is simple, it cannot be identified by a three-dimensional surface measuring instrument for the same reason.
The present invention has been made in view of the above-described conventional situation, and an object thereof is to provide a method for constructing a three-dimensional shape from individually measured surface shape measurement data.

The method of constructing a three-dimensional shape from surface data by the three-dimensional surface shape measuring instrument of the present invention uses a sphere as a positioning jig, and the center of the sphere serving as a reference point from the position coordinates of a plurality of measured surfaces Identify the coordinates, use the center coordinates of the three or more identified spheres with different diameters as different reference points, and combine each individual data by numerical calculation from the condition that the reference point is shared in individual surface data However, it is characterized by constructing a solid shape.
In addition, an approximately true sphere was used as the sphere, and the diameter of the sphere was sufficiently large with respect to the measurement pitch (preferably the diameter of the sphere was set to about 5 times the measurement pitch or more). The center coordinate of a sphere serving as a reference point is identified by a least square method from a plurality of surface data.
By using a sphere as a target, the target can be set large, and as a target, a highly accurate sphere close to a true sphere is used, and the size of the sphere is sufficiently larger than the measurement pitch (the diameter of the sphere is about 5 times the measurement pitch). By doing so, the surface of the sphere can be collimated from any angle, and it can be measured without missing the position coordinates of multiple sphere surfaces using a surface shape measuring instrument. Furthermore, the center point of the sphere, which is the reference point, is obtained from the measured surface data with the least squares method. In order to calculate the center coordinates of the sphere, three or more measurements of the sphere surface coordinates are required. In practice, 10 to several hundred points are preferred to ensure accuracy. Each reference point can be clearly distinguished by using spheres of different radii.
The accuracy of the reference point can be ensured by using the center coordinates of the sphere as the reference point. Using the center coordinates of multiple spheres (three or more) as a reference point, each individual data can be combined by numerical calculation based on the condition that this reference point is shared in individual surface data, and a solid (three-dimensional) shape can be constructed. In addition, by identifying each reference point from the diameter of the sphere, it is possible to improve the efficiency of data combination work.
By using spheres with different diameters, it is possible to recognize each sphere by obtaining the diameter of the sphere from the measurement data, and it is possible to automate the identification of the reference point.

In the conventional method, it is necessary to consider setting the measurement pitch as small as possible and increasing the target within an allowable range. Setting the measurement pitch to a small value increases the measurement time and the number of data, and increasing the target as the reference point decreases the accuracy when constructing the solid shape. It is often difficult to set a small target that can be collimated in any case of individual surface measurement.
By using a sphere as the target as in the present invention, the target can be set large and collimation can be performed from any direction. Furthermore, by using the center coordinates of the sphere as the reference point, the accuracy of the reference point can be ensured and the reference point can be easily identified by changing the diameter of the sphere. According to the present invention, it is possible to construct a high-precision measurement data of a surface shape measuring instrument without reducing the measurement pitch as in the conventional method and without reducing the accuracy by increasing the target as a reference point. This can be ensured at the time of measuring the thickness of a plate-like object.

Embodiments of the present invention will be described below with reference to the drawings.

(A) Spherical jig as a target A substantially spherical sphere is used as a target, and the center point is used as a reference point for integrating each surface data. Each reference point can be clearly distinguished by using spheres of different radii. The sphere to be used is bonded and fixed to the object to be measured. However, if the object to be measured can be bonded with a magnet, the jig shown in FIG. In this method, a sphere is fixed to a magnet and adhered to the object to be measured by the magnet. In FIG. 7, two spheres are fixed to one bonding jig. However, the spheres may be fixed one by one.
b) Measurement procedure and 3D method As an example of use, a disk with a square relief on the front side and a square relief on the back side as shown in Fig. 8 is integrated into 3D by integrating the data of each surface measured by the surface shape measuring instrument. An example of measuring plate thickness will be explained.
In this example, assuming that the side surface is flat, a pseudo three-dimensional shape is created by forming a surface connecting the outer edges of the measurement data on the two front and back surfaces. This method can be applied even when integrating measurement data of planes or more.
First, three spheres (1, 2, 3) with different target diameters are bonded to the side of the object to be measured, and the surface shape of the front surface including the spheres is measured. The position of the sphere can be any position. The center coordinates of each sphere serving as the reference point are obtained from the corresponding surface position data using the minimum two-modulus method. Using the center coordinates and radius r _i of sphere i shown in Equation 1 as unknown quantities, the unknown is such that the binary error associated with the position measurement data (shown in Equation 2) of the sphere surface expressed by Equation 4 is minimized. The center coordinates (shown in Equation 3) and the radius r _i are obtained by optimizing the quantity.

Here, n means the number of surface data of the sphere i, and I means various quantities when measuring the front surface.
Next, the object to be measured is reversed with the three spheres (1, 2, 3) adhered (FIG. 10), and the back surface II is measured in the same manner as the front surface, and the center coordinates of the three spheres ( (Shown in equation 5).

Next, the three-dimensional shape is reproduced by integrating the measurement data of Ototora from the condition that three reference points are shared (FIG. 11). The formulation for integration is shown below.
The basis vectors of the space-fixed right-handed orthogonal linear coordinates (shown in Equation 6) used when measuring the front surface (α = I) and the back surface (α = II) are shown in Equation 7, The position data of the obtained surface is expressed by Equation 8, and the position coordinates of three common reference points (i = 1, 2, 3) obtained by measurement of each surface are expressed by Equation 9. Do it.

Here, since the position of the object to be measured or the measuring instrument changes during each surface measurement, the position coordinates (α = I, II) fixed in space are different.
As a coordinate system for integrating the position data of the two surfaces α = I and II, based on the position coordinates of the common reference point fixed to the object to be measured, the origin is the reference point 1 and the basis vector (Equation 10 Defines a right-handed orthogonal linear coordinate system (shown in Equation 11) defined by the following equation (shown in Equation 12).

here

When the surface position data (shown in Equation 14) at the time of each surface measurement is converted into a value (shown in Equation 15) in the measured object fixed coordinate system (shown in Equation 16), , The surface position data of the two back surfaces (α = I, II) can be integrated.

Specifically, a method of converting space-fixed position data (shown in Equation 17) measured by a measuring instrument into values (shown in Equation 19) of moving coordinates (shown in Equation 18) fixed to the object to be measured is shown. In this conversion, since the origin of the moving coordinates (indicated by Expression 18) fixed to the object to be measured is the reference point 1, the position vector (indicated by Expression 20) of the surface position data point relating to the reference point 1 (indicated by Expression 17). ) Is as shown in Equation 21.
Further, when the relationship between the basis vectors of Equations 22 and 23 shown in Equation 12 is substituted into Equation 21, Equation 17 is converted into Equation 19 as shown in Equation 24.
As a result, the position data number 19 of each surface (α = I, II) converted from Expression 24 is integrated with respect to the object fixed coordinate system, Expression 18.

  Next, the case where the data of the back surface (α = II) is integrated into the space fixed coordinate system (shown by Equation 25) defined when measuring the front surface (α = I) will be described. That is, the position coordinate of the point m shown by the equation 27 on the surface of α = II expressed by the space fixed coordinate system (shown by the equation 26) is converted into the space fixed coordinate system, the equation 25. When the position coordinates (indicated by Expression 28) converted in this way are represented by Expression 29, the position vector regarding the space fixed coordinates (indicated by Expression 25) of the point m on the α = II plane is represented by Expression 30. II) is used to express as shown in Equation 31.

Substituting the right side of Equation 24 into the rightmost side of Equation 31, the basis vector (indicated by Equation 32) of the object fixed coordinate system is represented by Equation 12 and the basis vector (indicated by Equation 34) of the space fixed coordinate system In the end, equation 35 is finally converted into equation 37 as equation 36.
Thus, the surface data of α = II is integrated into the surface data of α = I.

c) Plate Thickness Calculation Method for Plate Object In plate thickness calculation of a plate object, if the front and back surfaces of the plate object are respectively α = I and II, α = I surface represented by Equation 38 The plate thickness at the upper position can be obtained by searching for the point at which the distance represented by Equation 40 is minimum from the position data of the α = II plane shown by Equation 39.

In the case where three or more reference points are provided, the accuracy can be improved by calculating the position coordinates shown in the above formula 37 and obtaining the average value for all possible combinations of the three points.

INDUSTRIAL APPLICABILITY The present invention can be used as a method for constructing a three-dimensional shape from surface data by a three-dimensional surface shape measuring instrument and a plate thickness measurement of a plate-like object.

It is the figure which showed the surface shape measuring device of the commercially available high precision small object which combined the electric biaxial stage and the laser displacement sensor. Since the conventional surface shape measuring instrument mechanism measures the surface shape (vertical coordinates) of non-measurement objects in a grid pattern in a horizontal plane at a set fixed pitch, the measurement data is discrete. It is explanatory drawing which shows the case where a target is small and a measurement value does not correspond and a measurement value cannot be obtained. Since the conventional surface shape measuring instrument mechanism measures the surface shape (vertical coordinates) of non-measurement objects in a grid pattern in a horizontal plane at a set fixed pitch, the measurement data is discrete. It is explanatory drawing which shows the case where there are a plurality of measured values with respect to the target and the accurate reference point is unknown. It is explanatory drawing which shows the subject in the measurement of the three-dimensional shape by a surface shape measuring device, ie, the case where there exists a surface which becomes a shadow seeing from a laser displacement sensor, since only a plane shape can be measured. In case of calipers and micrometers, there is an offset amount that depends on the shape of the device, so it is impossible to measure the thickness at the part other than the edge of the plate-like object (the position within the offset distance from the edge of the plate) It is explanatory drawing. It is explanatory drawing which shows that an ultrasonic plate thickness meter cannot measure a plate | board thickness correctly according to the unevenness | corrugation state of a plate | board surface, and a probe does not contact | ground well. It is explanatory drawing which shows the structure of the spherical jig | tool of this invention Example. It is explanatory drawing which shows the example of a to-be-measured object of this invention Example. FIG. 3 is an explanatory diagram showing that three spheres (1, 2, 3) having different diameters are bonded to the side surface of an object to be measured and the surface shape of the front surface including the sphere is measured. It is explanatory drawing which shows measuring a back surface like a front surface by reversing a to-be-measured object, bonding three spherical bodies (1,2,3). It is explanatory drawing which shows that data are integrated and the three-dimensional shape is reproduced from the condition that three reference points are shared with Otomeura measurement data.

Claims (4)

  Using a sphere as an alignment jig, identify the center coordinates of the sphere that is the reference point from the position coordinates of the measured surfaces, and determine the center coordinates of the three or more identified spheres with different diameters. Surface data from a three-dimensional surface shape measuring instrument characterized in that it is used as different reference points, and each individual data is combined by numerical calculation from the condition that the reference points are shared in the individual surface data, and a three-dimensional shape is constructed. To build a solid shape from   Using a sphere as a positioning jig, the center coordinates of the sphere serving as the reference point are identified from the position coordinates of the front and back surfaces of the plate-like object to be measured, and the three identified A method of measuring the plate thickness of a plate-like object by numerical calculation using the above-mentioned center coordinates of spheres having different diameters as different reference points and using the condition that the reference points are shared in each measurement data.   A substantially true sphere is used as the sphere according to claim 1, and the diameter of the sphere is sufficiently large with respect to the measurement pitch (preferably, the diameter of the sphere is set to about 5 times the measurement pitch or more). The method for constructing a three-dimensional shape according to claim 1, wherein center coordinates of a sphere serving as a reference point are identified from a plurality of surface data obtained by a least square method.   A substantially true sphere is used as the sphere according to claim 2, and the diameter of the sphere is sufficiently large with respect to the measurement pitch (preferably, the diameter of the sphere is set to about 5 times the measurement pitch or more). 3. The plate thickness measurement method according to claim 2, wherein center coordinates of a sphere serving as a reference point are identified from the surface data of the front and back surfaces by a least square method.