JPH08219758A - Shape measuring method - Google Patents

Shape measuring method

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Publication number
JPH08219758A
JPH08219758A JP2440695A JP2440695A JPH08219758A JP H08219758 A JPH08219758 A JP H08219758A JP 2440695 A JP2440695 A JP 2440695A JP 2440695 A JP2440695 A JP 2440695A JP H08219758 A JPH08219758 A JP H08219758A
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JP
Japan
Prior art keywords
measured
shape
dimensional
χ
δz
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP2440695A
Other languages
Japanese (ja)
Inventor
Takashi Shimizu
Hidenori Yamada
秀則 山田
敬司 清水
Original Assignee
Fuji Xerox Co Ltd
富士ゼロックス株式会社
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Application filed by Fuji Xerox Co Ltd, 富士ゼロックス株式会社 filed Critical Fuji Xerox Co Ltd
Priority to JP2440695A priority Critical patent/JPH08219758A/en
Publication of JPH08219758A publication Critical patent/JPH08219758A/en
Pending legal-status Critical Current

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Abstract

(57) [Summary] (Correction) [Purpose] The overlapping parts of partial areas can be connected with high accuracy without using a high-precision stage, and complex three-dimensional shapes such as aspherical surfaces can also be measured with high accuracy. [Structure] FIG. 1 shows a shape measuring apparatus for measuring a surface shape based on a shape measuring method of the present invention, and a rough shape measuring instrument 1 for measuring a rough shape of an object to be measured 2 and a rough shape measuring instrument 1
A precision measuring device 3 equipped with a probe 3A capable of more highly accurate measurement, a relative position / posture conversion stage 4 for converting the relative position and posture of the object 2 to be measured, and a surface to be measured of the object 2 to be measured are predetermined. Of the divided measurement results by the general shape measuring instrument 1 and the precise measuring instrument 3 as well as the division condition for dividing into the partial regions of 3 and the precision measuring instrument 3 and the relative position / orientation conversion stage 4 are controlled. It is composed of a calculator 6 for connection and a display 7 for displaying a calculation result of the calculator 6.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a shape measuring method, and more particularly to measuring a three-dimensional shape of a surface to be measured having a complicated curved surface shape such as an aspherical lens or its cross-sectional shape with a highly accurate measuring device. In this case, the present invention relates to a measuring method in the case where the surface to be measured has a size, depth, and inclination that exceed the measurable range of the measuring instrument.

[0002]

2. Description of the Related Art Conventionally, in a three-dimensional space coordinate system (x, y, z), a displacement probe for measuring displacement in the z direction is provided, and x
A three-dimensional shape (x, y,
There is a shape measuring method for measuring z).

FIG. 7 shows the structure of a precision measuring instrument used in a conventional shape measuring method. The displacement probe 10 for measuring the displacement of the object to be measured in the z direction and the displacement probe 10 are movable in the x and y directions. It has a supporting stage 11.

FIG. 8 shows a three-dimensional shape (x, y, z) of the object to be measured 12 which can be expressed by a function z = f (x, y) in an x, y, z orthogonal coordinate system. The precision measuring device measures the displacement of the object to be measured 12 by scanning the displacement probe 10 in the x and y directions according to the three-dimensional shape (x, y, z) of the object to be measured 12 to measure the displacement in the z direction. The shape of the surface 12A is measured.

When measuring such a three-dimensional shape of the object 12 to be measured, the surface 12A to be measured has a size exceeding the moving range of the stage 11 of the precision measuring instrument, or the displacement probe 10 can be measured in the z direction. However, there is the inconvenience that the measurement cannot be performed when the length and the inclination are exceeded.

As a method for solving such inconvenience, FIG.
As shown in, after measuring the three-dimensional shape of the measured surface 12A with a rough measuring device that measures the rough shape of the measured surface 12A or the designed shape, the three-dimensional shape of the measured surface 12A is measured with higher accuracy than the rough measuring device. When a precision measuring instrument 13 such as an interferometer capable of shape measurement is used and the relative position and orientation of the precision measuring instrument 13 with respect to the object to be measured are appropriately set as shown in FIG. 9A, An area (partial area) of the measured surface 12A of interest in the measurement range 13A of the precision measuring device 13
, The division condition is determined so that the division is performed with a portion (overlap portion) a that partially overlaps with another adjacent region, and the relative position and orientation of the precision measuring instrument 13 are appropriately set based on the division condition. By repeating the setting operation, as shown in FIG.
As shown in (b), the three-dimensional shape information of the partial areas 14A, 14B, and 14C corresponding to the entire area of the surface 12A to be measured is collected, and the three-dimensional shape information of these partial areas is used as the overlapping portion a.
There is a shape measuring method for obtaining three-dimensional shape information of the entire measured surface 12A shown in FIG.

In the above-described shape measuring method, a partial region n1 and a partial region n2 which are adjacent to each other and have an overlapping portion with an arbitrary partial region n1 and a partial region n1 on the surface to be measured are connected to each other. Will be described below.

First, the partial area n measured by the precision measuring device
The function z = B (x, y) that best fits the three-dimensional shape of 2 is obtained, and the set value of the relative position between the surface to be measured and the precision measuring instrument determined by the division condition in this function z = B (x, y). The coordinate conversion is performed using the set value x0 of the translational movement amount in the x direction and the set value y0 of the translational movement amount in the y direction based on

Next, the partial region n1 obtained by the precision measuring instrument
K1 three-dimensional coordinate data (xi, yi, zi) (i = 1, 2, ...
The function z = B (xx) in which the coordinate conversion is performed on k1).
0, y−y0), an approximation function z = C ′ obtained by performing coordinate conversion represented by a rotation amount δθx around the x axis, a rotation amount δθy around the y axis, and a translational movement amount δz in the z axis direction. (X, y) = B (x−x0, y−y0) + x · δθy + y · δθx + δz −−− (4) is χ0 2 = Σ {zi−C ′ (xi, yi)} 2 −−− (5 ) Is obtained to obtain δθx, δθy, and δz.

Then, δθx, δθy, δz obtained by the equations (4) and (5) and the set value x of the translational movement amount.
By using 0 and y0, a plurality of k2 pieces of three-dimensional coordinate data (xi, yi, zi) (i =
1, 2 ,. . . The partial regions n1 and n2 are connected by performing coordinate conversion of rotation and translation for all of k2). By connecting the partial areas in this manner, it is possible to obtain three-dimensional shape information of the entire surface to be measured.

[0011]

However, according to the conventional shape measuring method, the parameter x is a parameter other than the rotation amount δθx about the x-axis, the rotation amount δθy about the y-axis, and the translational movement amount δz in the z-axis direction. For the translational movement amount δx in the axial direction, the translational movement amount δy in the y-axis direction, and the rotation amount δθz about the z-axis, the relative position set value of the precision measuring device determined by the division condition is used, and therefore the aspherical shape is used. When measuring a surface to be measured that has a large amount of deformation as described above, a plurality of k1 three-dimensional coordinate data (x
There is an inconvenience that the error in the value of z of i, yi, zi) (i = 1, 2, ..., K1) becomes large and the connection accuracy of the partial region is lowered. In order to eliminate this error, it is necessary to position the stage of the precision measuring instrument with high accuracy,
It is difficult to position the x, y, and z axes simultaneously with high accuracy. Therefore, an object of the present invention is to provide a shape measuring method capable of connecting overlapping portions of partial regions with high accuracy without using a highly accurate stage.

Another object of the present invention is to provide a shape measuring method capable of measuring with high accuracy even a surface to be measured having a complicated three-dimensional shape such as an aspherical surface.

[0013]

According to the present invention, overlapping parts of partial areas can be connected with high accuracy without using a high-accuracy stage, and even a surface to be measured having a complicated three-dimensional shape such as an aspherical surface is high. In order to be able to measure with accuracy, a function z = B (x, y) that fits the shape information of the connected partial region connected by the arbitrary partial region and the overlapping portion is obtained, and the function z = B (x, y) of the arbitrary partial region in the overlapping portion is calculated. A plurality of k1 pieces of three-dimensional coordinate data (xi, yi, zi) that is shape information (i = 1,
2 ,. . . For k1), the function z = C (x, y) resulting from the coordinate transformation of rotation and three-dimensional translation in a three-dimensional space described by four or more variables is χ0 2 = Σ {zi -C (xi, yi)} 2 --- (6) The coordinate transformation of rotation and three-dimensional translation is found so as to give the minimum value, and a plurality of k2 three-dimensional coordinates which are the shape information of the connected partial region. Data (xi, yi, zi) (i = 1,
2 ,. . . k2) To provide a shape measuring method for connecting an arbitrary partial area and a connected partial area by performing coordinate transformation for all.

[0014]

In order to simplify the explanation, the explanation will be given here based on the measurement of the surface to be measured having a two-dimensional shape. In the two-dimensional Cartesian coordinate system (x, z), the function z = B that best fits the shape information of the measured partial area in the overlapping portion by the precision measuring device.
Find (x). By subjecting this function z = B (x) to coordinate transformation of the rotational movement δθ and the two-dimensional translational movements δx, δz in the two-dimensional space, an arbitrary point (x, z) can be transformed into the following coordinates (x · cosδθ + z · sinδθ + δx). , −x ・ sin δθ
+ Z · cos δθ + δz). From this fact, z = B (x) is expressed as in equation (7). −x · sin δθ + z · cos δθ + δz = B (x · cos δθ + z · sin δθ + δ x) −−− (7) Here, when δθ is a small amount, sin δθ =
Since δθ and cos δθ = 1, the equation (7) becomes (8)
It is expressed as an expression. −x · δθ + z + δz = B (x + z · δθ + δx) −−− (8) In the formula (8), when δx, δz, z · δθ is a small amount, B (x + z · δθ + δx) = B (x )
+ (DB / dx) · (z · δθ + δx) (9)
Expression, expressed as Expression (10). −x · δθ + z + δz = B (x) + (dB / dx) · (z · δθ + δx) −− (9) z = [1 / {1-δθ · (dB / dx)}] · [B (x) + (DB / dx) .delta.x-.delta.z + x.delta..theta.] --- (10) In equation (10), when .delta..theta .. (dB / dx) is a minute amount, approximately 1 / {1-.delta..theta. dB / dx)}
= 1 + δθ · (dB / dx), and the equation (10) becomes (1
It is expressed as in equation (1). z = [1 + δθ ・ (dB / dx)] ・ [B (x) + (dB / dx) ・ δx-δ z + x ・ δθ] --- (11) Eliminates high-order minute amounts from the equation (11). Then, (12)
It is expressed as an expression. z = B (x) + (dB / dx) .delta.x-.delta.z + {x + B (x). (dB / dx)}. delta.theta.≡D (x) --- (12) From the above, the variables .delta..theta., .delta.x, .delta.z. , Z ・ δθ, δθ ・
When (dB / dx) is a minute amount, D (x) becomes almost equal to C (x). Therefore, δθ, δx, in the case of δz is small amount can be used χ0 2 = Σ {zi-C (xi)} 2 instead the χ 2 = Σ {zi-D (xi)} 2. Further, when the weight due to the measurement error is taken into consideration at each point of the two-dimensional coordinate data (xi, zi), χ 2 is expressed by the equation (13). χ 2 = Σ [{zi-D (xi)} / σi] 2- (13) where σ is the standard deviation of the measurement value error of the precision measuring instrument.
As described above, the function z = C (x) after the coordinate conversion is shown, and by performing the coordinate conversion of the rotation and the translation so as to give the minimum value of the expression (13), it is possible to perform arbitrary calculation through the overlapping portion. The connection accuracy between the partial area and the connected partial area is improved.
In the three-dimensional space coordinates (x, y, z), the above process
This holds even when the surface to be measured has a three-dimensional shape (x, y, z).

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The shape measuring method of the present invention will be described below in detail with reference to the drawings.

FIG. 1 shows a shape measuring apparatus for measuring a surface shape (three-dimensional shape) based on the shape measuring method of the present invention.
A schematic shape measuring device 1 for measuring a schematic shape of the DUT 2,
A probe 3 capable of measuring with higher accuracy than the general shape measuring instrument 1.
Precision measuring device 3 including A, relative position / orientation conversion stage 4 for converting the relative position and orientation of object 2 to be measured, and division for dividing the surface to be measured of object 2 into predetermined partial areas A division control unit 5 that calculates the conditions and controls the precision measuring device 3 and the relative position / orientation conversion stage 4, and a calculation unit 6 that connects the divided measurement results by the rough shape measuring device 1 and the precision measuring device 3. The display 7 is configured to display the calculation result of the unit 6. The precision measuring device 3 may be a probe scanning type or may be one that measures a three-dimensional shape such as an interferometer.

FIG. 2 shows a flow chart of surface measurement by the shape measuring method of the present invention. Hereinafter, the shape measuring method of the present invention will be described for each step of the flowchart.

In step 1, the outline shape information obtained by scanning the object 2 to be measured by the outline shape measuring device 1 is output to the division controller 5, and the division controller 5 receives the outline information from the outline shape measuring device 1. Surface to be measured 2A based on shape information
Understand the general shape of. At this time, the general shape may be grasped by inputting a three-dimensional shape design formula or the like to the division control unit 5.

In step 2, when the general shape of the object to be measured 2 is grasped, the measurable length and depth of the probe 3A of the precision measuring device 3 are taken into consideration, and a region overlapping with an adjacent partial region (overlapping part) ), And the division conditions are set so that each partial region fits within the measurable length, depth, and inclination of the probe 3A.

In step 3, after the division conditions are set, the relative position / orientation conversion stage 4 is moved to set the relative position / orientation conversion of the DUT 2. Here, the relative position / orientation conversion stage 4 may be manually moved.

In step 4, the precision measuring device 3 and the relative position / orientation conversion stage 4 measure the respective partial regions divided based on the division conditions, and the partial region data 1 to n (n is the partial region data) is measured. The number of divided measurement results and the relative position / orientation set value at the time of divided measurement are output to the calculation unit 6.

The calculation unit 6 performs coordinate conversion of the partial area 2D and the partial area 2D connected via the overlapping portion based on the divided measurement result and the set value of the relative position and orientation at the time of the divided measurement (step 5A). , A function z = B that best fits the shape information of the partial area 2D in the overlapping portion by the precision measuring device 3.
(X) is calculated (step 5B), and the two-dimensional coordinate data (x
i, zi) considering the weight due to the measurement error at each point (step 5C), a plurality of k1 three-dimensional coordinate data (xi, yi, zi) which is the shape information of the partial region 2B in the overlapping portion by the precision measuring device 3 is taken into consideration. ) (I = 1, 2, ... K1), a variable that gives the minimum value of χ 2 = Σ [{zi-D (xi, yi)} / σi] 2- (16), δx, δy, δz, δθ
x, δθy, δθz are obtained (step 5D), δx is a translational movement amount in the x direction in the coordinate conversion, δy is a translational movement amount in the y direction in the coordinate conversion, and δz is z in the coordinate conversion.
In the shape information of the partial region 2D, the translation amount in the direction, δθx is the rotation amount around the x axis in the coordinate conversion, δθy is the rotation amount around the y axis in the coordinate conversion, and δθz is the rotation amount around the z axis in the coordinate conversion. A plurality of k2 pieces of three-dimensional coordinate data (xi, yi, zi) (i = 1, 2, ...).
k2) The partial region 2B and the partial region 2D are connected by repeating the coordinate transformation of rotation and translation for all (step 5E) until Δχ 2 <1 is obtained.

In step 6, the connection result of the partial areas 2B and 2D measured for all the partial areas is displayed on the display 7.

FIG. 3 shows a shape measuring device for measuring a cross-sectional shape (two-dimensional shape) based on the shape measuring method of the present invention, and a schematic cross-sectional shape measuring device 8 for measuring a schematic cross section of the DUT 2. Precision cross-section measuring instrument 9 equipped with probe 9A capable of measuring with higher accuracy than general cross-section shape measuring instrument 1, relative position / posture conversion stage 4 for converting relative position and posture of DUT 2, and DUT The division control unit 5 that calculates the division condition for dividing the surface to be measured 2 into the predetermined partial areas and controls the precision cross-section measuring device 9 and the relative position-posture conversion stage 4, the rough cross-section shape measuring device 8, Precision cross-section measuring device 9
And a calculation unit 6 for connecting the divided measurement results by
It is composed of a display 7 for displaying the calculation result in. The precision cross-section measuring device 9 may be a probe scanning type or may be one that measures a three-dimensional shape such as an interferometer.

FIG. 4 shows a flowchart of cross-section measurement by the shape measuring method of the present invention. Hereinafter, the shape measuring method of the present invention will be described for each step of the flowchart.

In step 1, the schematic sectional shape information obtained by scanning the DUT 2 by the schematic sectional shape measuring instrument 8 is output to the division control section 5, and the division control section 5 receives the schematic sectional shape measurement instrument 8. Based on the rough cross-sectional shape information from, the rough shape of the cross-sectional position of the measured surface 2A to be measured is grasped. At this time, the division control unit 5 has a cross-sectional shape design formula.
You may input and make it grasp a rough shape.

In step 2, when the general shape of the object to be measured 2 is grasped, the measurable length and depth of the probe 9A of the precision cross-section measuring device 9 are taken into consideration, and a region overlapping with an adjacent partial region (overlap). Part), and each partial region is a probe 9A
Set the division condition so that it fits within the measurable length and depth of.

In step 3, after the division conditions are set, the relative position / orientation conversion stage 4 is moved to set the relative position / orientation of the object to be measured 2. Here, the relative position / orientation conversion stage 4 may be manually moved.

In step 4, the precision cross-section measuring device 9 and the relative position / orientation conversion stage 4 measure the respective partial regions divided based on the dividing conditions, and the partial region data 1 to n (n is a partial region) is measured. The number of divided measurement results and the relative position and orientation set values at the time of divided measurement are output to the calculation unit 6.

In step 5, the calculation unit 6 calculates, based on the divided measurement result and the set value of the relative position and orientation at the time of divided measurement,
Partial region 2 connected to the partial region 2B via an overlapping portion
The coordinate transformation of D is performed (step 5A), and the function z = B (x) that best fits the shape information of the partial region 2D in the overlapping portion by the precision cross-section measuring device 9 is obtained (step 5B).
Considering the weight due to the measurement error of each point of the two-dimensional coordinate data (xi, zi) (step 5C), a plurality of k1 two-dimensional coordinate data which is the shape information of the partial region 2B in the overlapping portion by the precision section measuring device 9 (Xi, zi) (i = 1,
2 ,. . . For k1), variables δθ, δx, δz that give the minimum value of χ 2 = Σ [{zi-D (xi)} / σi] 2- (14) are obtained (step 5D), and δx is The translation amount in the x direction in the coordinate conversion, δz is the translation amount in the z direction in the coordinate conversion, and δθ is the rotation amount around the origin in the coordinate conversion.
Coordinate conversion of rotation and translation for all of a plurality of k2 pieces of two-dimensional coordinate data (xi, zi) (i = 1, 2, ... k2) which is the shape information of the partial region 2D (step 5E).
Is repeatedly performed until Δχ 2 <1 is obtained, thereby connecting the partial regions 2B and 2D.

In step 6, the connection result of the partial areas 2B and 2D measured for all the partial areas is displayed on the display 7.

FIG. 5 shows the results of divisional measurement of the partial area 2B and the partial area 2D displayed on the display 7, and the sectional shape of the surface 2A to be measured has the following series z = −3.26 × 10 −. 4 x 2 -3.36 x 10 -8 x 4 +7.95 x 10 -13 x 6 -1.05 x 10 -17 x 8 -5.47 x 10 -22 x 10 --- When expressed by (15), the partial area 2B and the partial area 2D are x =-
It is connected through the overlapping part 2C from 20 to x = 20.

FIG. 6 shows the residual error of the translational movement amount in the x direction in the coordinate conversion at the time of the convergence calculation for repeatedly obtaining the minimum value of χ 2 in order to obtain the minimum value of χ 2 in the equation (14). Even when the initial error of the translational movement amount in the x direction, which is the error of the relative position / orientation conversion stage 4, is 5 mm as shown by the solid line A, the residual error x is converged to 0.015 mm by the five iterations. . Also, as shown by the solid line B, it is confirmed that the residual error similarly converges even when the initial error is 1 mm by 5 times of iterative calculation, and also converges in the z direction and the θ direction not shown. Has been done.

As described above, the coordinate data measured for each partial area of the surface to be measured is rotated and translated, and the partial areas are connected through the overlapping portion, whereby the connection accuracy of the partial areas is increased. Therefore, it becomes possible to use an inexpensive relative position / posture conversion stage on which the object to be measured is mounted.

[0035]

As described above, according to the shape measuring method of the present invention, the function z = B adapted to the shape information of the connected partial area connected by the arbitrary partial area and the overlapping portion.
(X, y) is obtained, and the function z = C (x, y) obtained as a result of performing coordinate transformation of rotation and three-dimensional translation on the shape information of an arbitrary partial region in the overlapping portion is χ0 2 = Σ {zi- C (xi, yi)} 2 --- (16) The coordinate transformation of rotation and three-dimensional translation is found so as to give the minimum value, and the coordinate transformation is applied to all the shape information of the connected partial region to determine an arbitrary value. Since the partial area and the connected partial area are connected, the overlapping portion of the partial areas can be connected with high accuracy without using a high-precision stage,
Even a surface to be measured having a complicated three-dimensional shape such as an aspherical surface can be measured with high accuracy.

[Brief description of drawings]

FIG. 1 is an explanatory view showing a shape measuring device for measuring a surface shape (three-dimensional shape) in a shape measuring method of the present invention.

FIG. 2 shows a flowchart of the shape measuring method of the present invention.

FIG. 3 is an explanatory view showing a shape measuring device for measuring a cross-sectional shape (two-dimensional shape) in the shape measuring method of the present invention.

FIG. 4 shows a flowchart of the shape measuring method of the present invention.

FIG. 5 is an explanatory diagram showing a division measurement result displayed on the display 7.

FIG. 6 is an explanatory diagram showing a residual error of a translational movement amount in the x direction in the shape measuring method of the present invention.

FIG. 7 is an explanatory diagram showing a configuration of a precision measuring device in a conventional shape measuring method.

FIG. 8 is an explanatory diagram showing a three-dimensional shape (x, y, z) of the measured object represented by a function z = f (x, y).

FIG. 9 is an explanatory diagram showing a method of connecting the measured surface 12 in the conventional shape measuring method.

[Description of sign]

 1, rough shape measuring device 2, measured object 2A, measured surface 2B, partial area 2C, overlapping portion 2D, partial area 3, precision measuring device 3A, probe 4, relative position / orientation conversion stage 5, division control unit 6, Calculation unit 7, display 8, schematic cross-section shape measuring instrument 9, precision cross-section measuring instrument 9A, probe 10, displacement probe 11, stage 12, measured object 12A, measured surface 13, precision measuring instrument 13A, measuring range 14A, 14B , 14C, partial area

Claims (5)

[Claims]
1. An object to be measured based on rough shape information obtained by measuring a target object arranged in a three-dimensional space represented by coordinates (x, y, z) with a rough measuring device. By measuring the surface to be measured with a precision measuring device capable of measuring with higher accuracy than the rough measuring device, dividing into a plurality of partial regions having overlapping portions, and connecting the plurality of partial regions through the overlapping portions. In a shape measuring method for obtaining a three-dimensional shape (x, y, z) of the entire surface to be measured, a function z = B (x) adapted to shape information of an arbitrary partial area and a connected partial area connected by the overlapping portion. , Y)
A plurality of k1 pieces of three-dimensional coordinate data (xi, yi, z), which is shape information of the arbitrary partial area in the overlapping portion.
i) (i = 1, 2, ... K1)
Function z = C resulting from coordinate transformation of rotation and three-dimensional translation in three-dimensional space described by one or more variables
The coordinate transformation of the rotation and the three-dimensional translation is obtained so that (x, y) gives the minimum value of χ0 2 = Σ {zi-C (xi, yi)} 2- (1). A plurality of k2 pieces of three-dimensional coordinate data (xi, yi, zi) (i = 1,
2 ,. . . k2) A shape measuring method, characterized in that the arbitrary partial area and the connected partial area are connected by performing the coordinate transformation for all of them.
2. The plural k1 three-dimensional coordinate data (x
i, yi, zi) (i = 1, 2, ..., K1), the following function χ 2 = Σ [{zi-D (xi, yi)} / σi] 2- (2 ) However, D (x, y) = B (x, y) + δx (∂B / ∂x) + δy (∂B / ∂y) −δz + (y + B (x, y) (∂B / ∂y)) δθx + ( x + B (x, y) (∂B / ∂x)) δθy + (x (∂B / ∂y) + y (∂B / ∂x)) δθz --- (3) σ is the measurement value error of the precision measuring instrument , Δx is a translation amount in the x direction in the coordinate conversion, δy is a translation amount in the y direction in the coordinate conversion, δz is a translation amount in the z direction in the coordinate conversion, and δθx is x in the coordinate conversion. The amount of rotation about the axis, δθy is the amount of rotation about the y axis in the coordinate conversion, and δθz is the minimum value of the amount of rotation about the z axis in the coordinate conversion. To δx, δy,
The shape measuring method according to claim 1, wherein δz, δθx, δθy, and δθz are set.
3. The plurality of k2 three-dimensional coordinate data (x
i, yi, zi) (i = 1, 2, ... K2) all
In contrast, δx, δy, δz, δθx, δθy, and
By performing the coordinate transformation based on δθz,
Function z = B 'adapted to the shape information of the connected partial area
(X, y) is obtained, and the function z = B '(x, y) is replaced with the function z = B (x, y).
Substituting, and with respect to the function z = B (x, y) after the substitution, (2),
Χ based on equation (3) 2Δx, to give a local minimum of
Excessive setting of δy, δz, δθx, δθy, and δθz
Χ2By repeating until the values of converge,
χ2Δx, δy, δz, δθ to give the minimum value of
A contract characterized by setting x, δθy, and δθz
The shape measuring method according to claim 2.
4. The plurality of k2 three-dimensional coordinate data (x
i, yi, zi) (i = 1, 2, ..., K2) based on the set values of the relative position and orientation of the precision measuring device when the surface to be measured is divided, The coordinate transformation is performed so that the regions are connected via the overlapping portion, and a function z = B (x, y) that is suitable for the shape information of the connected partial region in the overlapping portion after the coordinate transformation is used.
For the function z = B (x, y), the above (2),
Δx, so as to give a minimum value of χ 2 based on the equation (3),
The shape measuring method according to claim 3, wherein the process of setting δy, δz, δθx, δθy, and δθz is repeated until the value of χ 2 converges.
5. The process of setting the quantities δx, δy, δz, δθx, δθy, and δθz that give the minimum value of χ 2 based on the equations (2) and (3) until the value of χ 2 converges. When iterating, the plurality of k1 three-dimensional coordinate data (xi, yi, zi) in the first calculation process for obtaining the minimum value of χ 2
From (i = 1, 2, ..., K1), the distance in the x direction and the y direction used for calculation is defined as the relative position and orientation of the surface to be measured and the precision measuring device when the surface to be measured is divided. Is set to the same magnitude as the setting error between the set value and the actual measured value, and thereafter, the interval is narrowed every time the minimum value of χ 2 is repeatedly calculated based on the equations (2) and (3). The shape measuring method according to claim 3 or 4, characterized in that.
JP2440695A 1995-02-13 1995-02-13 Shape measuring method Pending JPH08219758A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007536539A (en) * 2004-05-04 2007-12-13 カール マール ホールディング ゲーエムベーハー Apparatus and method for detection based on a combination of geometric interference and imaging, especially in microsystem technology

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007536539A (en) * 2004-05-04 2007-12-13 カール マール ホールディング ゲーエムベーハー Apparatus and method for detection based on a combination of geometric interference and imaging, especially in microsystem technology
JP4644707B2 (en) * 2004-05-04 2011-03-02 カール マール ホールディング ゲーエムベーハー An apparatus for detection based on a combination of geometric interference and imaging, especially in microsystem technology

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