JP2003014449A - Calibration method for surface property measuring apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To acquire a precise measurement result by allowing the acquirement of calibration information for a measurement result with a simple method in the connection of measured data for each partial measurement range, and to avoid the improper connection of a partial measurement range. SOLUTION: A calibration work 5 having a known shape is measured divisionally in two or more partial measurement ranges by a surface property measuring apparatus 100. An evaluation function Φ is defined from measured data S of every measurement range, and the rotating quantity R and parallel moving quantity T of each measured data S for minimizing the evaluation function Φis determined by nonlinear least square method. Constraint conditions related to R and T are integrated to the evaluation function Φ.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention
Regarding the calibration method of the surface texture measuring device that measures the surface texture such as two-dimensional shape, three-dimensional shape, surface roughness, waviness, and more specifically, it measures a wide measuring range that exceeds the measuring range that can be measured by a series of measuring operations. The present invention relates to a calibration method for a surface texture measuring device.

[0002]

2. Description of the Related Art When performing a highly accurate measurement over a wide area that cannot be covered by a series of measurement operations using a three-dimensional measuring machine or the like, the entire measurement range is divided into a plurality of partial measurement ranges. After measurement is performed for each partial measurement range, measurement data for the entire measurement range is obtained by connecting measurement data for the partial measurement ranges. As a method of dividing into partial measurement ranges, a method is known in which the entire measurement range is divided into a plurality of partial measurement ranges so as to partially overlap.

Several methods have been proposed as a method for connecting the measurement data in the partial measurement range. For example, by fitting the position and angle of each part measurement range so that the overlapping parts are connected most smoothly, the entire measurement range
A “fitting synthesis method” for obtaining the shape of A is known. Another method is to move each partial measurement range only in the normal direction and obtain the shape of the entire measurement range to which each partial measurement range is connected (luminous aspheric surface by aperture synthetic interferometry using hybrid fitting). Shape measurement: Shimizu et al., 1998 Precision Engineering Society Fall Conference Academic Lecture Proceedings p179) is known.

[0004]

By the way, the cause of the deviation of the measurement data between the partial measurement ranges is caused by positioning the measurement sensor for each partial measurement range or moving the mounting table. The main errors are instrumental errors such as positioning errors, mounting table straightness errors, and sensor non-linear errors. If these instrumental errors can be known, an appropriate connection should be made quickly. Also, due to reasons such as inappropriate operation methods or abnormalities in the machine itself,
Differences in magnitude, such as instrument errors, between the partial measurement ranges may become larger than expected. In such a case, it is not appropriate to continue the connection forcibly. However, in the past, partial measurement data was connected without considering what caused the deviation of measurement data between partial measurement ranges.
Not only does the connection take time, but there is an inconvenience that data in an inappropriate measurement range can be output.

The present invention has been made in view of the above-mentioned problems. When connecting measurement data of each partial measurement range, calibration information of measurement results can be obtained by a simple method, and the time is short. An object of the present invention is to provide a method for calibrating a surface texture measuring apparatus capable of acquiring a highly accurate measurement result with the above method. Another object of the present invention is to provide a method for calibrating a surface texture measuring apparatus that can avoid inappropriate connection of partial measurement ranges and thereby obtain accurate data of the entire measurement range.

[0006]

To this end, the calibration method for a surface texture measuring device according to the present invention is a method for measuring an object to be measured that is larger than the size of a measuring range that can be measured by a series of measuring operations. The measurement range is divided into partial measurement ranges that partially overlap each other, and after obtaining the measurement results of the measurement object in each partial measurement range, the measurement of the measurement object in each partial measurement range by a predetermined method In the calibration method of the surface texture measuring apparatus configured to obtain the surface texture of the entire measurement range by connecting the results, in order to measure the surface texture of the calibration workpiece having the known surface texture, it partially overlaps each other A first step of setting a partial measurement range; a second step of measuring partial surface properties of the calibration workpiece for each partial measurement range to obtain partial measurement data; and Based on the minute measurement data, a third step for identifying the correspondence in the overlapping portion of the adjacent partial measurement ranges, a fourth step for defining the evaluation function Φ for the correspondence, and minimizing the evaluation function Φ A fifth step of determining a conversion amount of the partial measurement data in the partial measurement range by a nonlinear least square method, and measuring the object to be measured based on the conversion amount determined by the fifth step. And a sixth step of calculating a correction value for correcting the result. In this calibration method, the measurement result of the calibration work is converted so as to approximate the known surface property of the calibration work. This conversion amount is considered to correspond to instrument error such as sensor positioning error and non-linear error of sensor.
The measurement result of the object to be measured can be corrected by this conversion amount. The conversion amount can be the rotation amount R and the translation amount T of the surface specified by the partial measurement data for each partial measurement range.

The calibration method for the surface texture measuring apparatus further includes the step of setting a predetermined constraint condition for the conversion amount and determining whether the conversion amount is within the range of the constraint condition. Is preferred. Thereby, an inappropriate connection of the partial measurement ranges can be avoided, and accurate data of the entire measurement range can be acquired. Furthermore, when it is determined that the conversion amount does not fall within the constraint conditions, a step of notifying the outside is preferably performed.

The correspondence relationship can be expressed by a distance between the corresponding points. Furthermore, it is preferable that the evaluation function Φ incorporates a function representing the constraint condition.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the surface texture measuring method according to the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a conceptual diagram showing an outline of a surface shape measuring apparatus 100 according to this embodiment. The surface shape measuring device 100 includes a sensor 2 that measures the displacement of the surface of the object 1 to be measured, a computing device 3 that computes the output of the sensor 2 to calculate shape measurement data, and a computation result of the computing device 3. And a display device 4 for displaying. Here, it is assumed that the object 1 to be measured has a continuous surface that is free from at least a step, a crack or the like.

The entire measurement range A of the object 1 to be measured is a plurality of partial measurement ranges B that can be measured by a single measurement.
And is measured for each partial measurement range Bi. Here, for the sake of simplicity, three partial measurement ranges B0, B1,
It shall be divided into B2. Each partial measurement range B0, B
1 and B2 are partially overlapped, and overlapping portions L ^(0,1) , L ^(1,
Set to have ²⁾ .

In this case, due to the above-described mechanical error, the measurement data in each of the partial measurement ranges B0, B1, and B2 is discontinuous as shown in FIG. 2 even though the measurement target 1 has a continuous surface. Data d (x, y) meaning surfaces S0, S1, S2
Usually it becomes. Therefore, the measurement data S0, S
In order to correct 1 and S2, the magnitude of the mechanical error is estimated by the following method, and the shape measuring apparatus 100 is calibrated.

Hereinafter, a calibration method for the shape measuring apparatus according to the present embodiment will be described with reference to conceptual diagrams shown in FIGS. 3 and 4 and a flowchart shown in FIG.

First, as shown in FIG. 3, a calibration work 5 having a known shape is set on a mounting table (not shown) of the surface shape measuring apparatus 100 (step 1). Here, it is assumed that the calibration workpiece 5 is a planar workpiece having a flatness sufficient to determine the mechanical error of the surface shape measuring apparatus 100. Moreover, it is preferable that the size of the calibration work 5 is at least approximately the same as the entire measurement range of the object to be measured.

Next, with respect to the calibration work 5, the object to be measured 1
As in the case of, partial measurement ranges B0 ', B1', B2 '
Is identified (step 2). This partial measurement range B0 ′,
B1 ′ and B2 ′ are the partial measurement ranges B0, B1, and B2 when measuring the measurement object 1 and the shape measuring device 1, respectively.
The positions are substantially the same as viewed from 00. Overlapping portions L ^(0,1) ′ and L ^(1,2) ′ exist between B0 ′ and B1 ′ and between B1 ′ and B2 ′, respectively.

In this situation, the calibration work 5 is measured by being divided into partial measurement ranges B0 ', B1', B2 '(step 3). If there is no mechanical error such as sensor positioning error and no error due to human error, etc.
The measurement results of each partial measurement range B0 ′, B1 ′, B2 ′ are as follows:
It coincides with one plane as shown in FIG. However, when there is a mechanical error such as a positioning error of the sensor, the measurement data d (x,
The surface specified by y) becomes data S _C0 , S _C1 , S _{C 2 in} which shift and rotation occur between the partial measurement ranges, as shown in FIG. 4B.

Next, the measurement results S0, S of the object 1 to be measured
In order to calculate correction values such as 1, S2, etc., these data S
The best fit calculation of _C0 , S _C1 and S _C2 is executed (step 4). The best-fit calculation means that the data S _C0 , S _C1 , and S _C2 that are shifted and rotated for each partial measurement range as shown in FIG. The correction means that the shape data is substantially the same as the shape data (in this case, a plane).

As will be described later in detail, the best fit calculation is performed on points on the surfaces S and S ′ indicating the measurement data S _Ci-1 and S _Ci of the adjacent partial measurement ranges B _n-1 ′ and B _n ′. Among these, the points existing on the overlapping portion L ′ on both sides are identified as corresponding points r _i ^(S) and r _i ^(S ′ ⁾ , and after defining the evaluation function Φ regarding the relationship between the corresponding points, this Φ is minimized. The rotation amount R and the parallel movement amount T of the data S _Ci are obtained by executing a convergence calculation by the nonlinear least square method.

Further, constraint conditions are set for the rotation amount R and the parallel movement amount T, and it is determined whether or not the rotation amount R and the parallel movement amount T are within the range of the constraint conditions (step 5). The constraint is determined from the maximum mechanical error that can result from normal use of the shape measuring device 100. If the constraint condition is exceeded, the display device 4 or other device (not shown) issues a warning to the operator that the shape measuring device 100 is abnormal or that the device itself is abnormal (step 6). Instead of issuing a warning, or in addition thereto, the measurement execution program may be forcibly terminated.

When it is determined that the value is within the constraint conditions, a correction value is calculated based on the obtained R and T, and the measurement result S0, S1 and S2 are corrected by this correction value (step 7).

Next, an example of the best-fit calculation method in step 4 and an example of the constraint condition determination method in step 5 will be described in detail with reference to FIG. In the following, it is assumed that there are Ns partial measurement ranges, and there are Ns sets of measurement data S to be best fit. As shown in FIG.
When dividing into three partial measurement ranges, Ns = 3 may be set.

Prior to the description of the best fit calculation, the meaning of various parameters used in the calculation will be defined.
First, the corresponding points in the overlapping portion of the surface S and the surface S ′ are N ^(S ,
^{S ′)} , and one set of corresponding points is denoted by r _i ^(S) , R _i ^(S
´ ⁾ (I = 1, 2,..., N ^(S , ^{S ′ )} ). In addition, when the surface S and the surface S ′ are best fit, the rotation of the surface S and the surface S ′ from the initial position to the best fit position is respectively R ^(S) , R ^{(S ′)} , surface S, The parallel movement amounts of the surface S ′ are T ^(S) and T ^{(S ′)} , respectively. R ^(S) ,
R ^{(S ′)} is, for example, φ ^{(S )} , θ ^(S) , ψ ^(S) with the X, Y, and Z axes of the orthogonal three-dimensional coordinate system as rotation axes as elements, and R ^{( S} Similarly, ^{S ′)} has φ ^{(S ′)} , θ ^{(S ′)} , and ψ ^{( S ′)} as elements, respectively.

[0022]

[Expression 1]

It can be expressed as T ^(S)
Are the translational components tx ^(S) and t in the X, Y and Z axis directions.
It is assumed that y ^(S) and tz ^(S) are expressed, and T ^{(S ′)} is
Similarly, translational components tx ^{(S ')} and ty in the X, Y and Z axis directions
^{(S ′)} and tz ^{(S ′)} are expressed as elements.

In the present embodiment, this φ^(S), Θ
^(S), Ψ^(S), Tx^(S), Ty^(S), Tz ^(S), Φ^(S´⁾, Θ
^(S´⁾, Ψ^(S´⁾, Tx^(S´⁾, Ty^(S´⁾, Tz^(S´⁾In
The following constraints are set.

[0025]

[Number 2] ^{-tx (sys) ≦ tx (s} ) ≦ tx (sys) -ty (sys) ≦ ty (s) ≦ ty (sys) -tz (sys) ≦ tz (s) ≦ tz (sys) - φ ^(sys) ≦ φ ^(s) ≦ φ ^(sys) ―θ ^(sys) ≦ θ ^(s) ≦ θ ^(sys) ―ψ ^(sys) ≦ ψ ^(s) ≦ ψ ^(sys) ―tx ^(sys ′ ⁾ ≦ tx ^(s ′ ⁾ ≦ tx ^(sys ′ ⁾ −ty ^(sys ′ ⁾ ≦ ty ^(s ′ ⁾ ≦ ty ^(sys ′ ⁾ −tz ^(sys ′ ⁾ ≦ tz ^(s ′ ⁾ ≦ tz ^(sys ′ ⁾ −φ ^(sys ′ ⁾ ≦ φ ^(s ′ ⁾ ≦ φ ^(sys ′ ⁾ ―θ ^(sys ′ ⁾ ≦ θ ^(s ′ ⁾ ≦ θ ^(sys ′ ⁾ ―ψ ^(sys ′ ⁾ ≦ ψ ^(s ′ ⁾ ≦ ψ ^(sys ´ ⁾

In this embodiment, this constraint is defined by a penalty function p as shown in [Equation 3], and a parameter X indicating the amount of rotation and translation of each measurement data Sci is obtained as will be described later. It is incorporated in the evaluation function. Details will be described later.

[0027]

[Equation 3]

However, γ _tx , γ _ty , γ _tz , γΦ , Γθ
, Γψ Is the weight of each penalty, and is a positive constant determined in advance as the reciprocal of the tolerance of the constraint condition.

Under the above definition, a method for calculating the best fitting of the surface S as the measurement result of each partial measurement range B will be described. The best fit calculation of the present embodiment uses the corresponding points r _i ^(S) , R _i ^(S ′ ⁾ Is performed based on the distance (distance between corresponding points) f _i ^(S , ^S ′ ⁾ . Corresponding point r _i ^(S) , R _i ^(S
′ ⁾ Is determined as follows. Overlapping part L ^(S , ^S ' ⁾ '
The point on the inner surface S ′ side is determined as one point r _i ^(S ′ ⁾ of the corresponding points. Then, to determine the corresponding points r _i of the point r _i ^{(S ')} point a point on the surface S that gives the shortest distance from the ^{_{r i (S') (S}} ). Similarly, the point on the surface S side in the overlapping portion L ^(S , ^S ′ ⁾ ′ is
It is determined as _one point r _{i + 1} ^(S) of a set of corresponding points. Then, from this point r _{i + 1} ^(S) , the point on the surface S ′ giving the shortest distance is determined as the corresponding point r _{i + 1} ^{(S`)</sup> of the point r <sub>i + 1</sub> <sup>(S)</sup> . Instead of the point giving the shortest distance, an intersection of lines along the coordinate axis may be used as the corresponding point. After the corresponding points are obtained in this way, the distances f <sub>i</sub> <sup>(S</sup> , <sup>S</sup> ′ <sup>)</sup> between the corresponding points are calculated. f <sub>i</sub>
<sup>(S</sup> , <sup>S</sup> ′ <sup>)</sup> takes into account their weights w <sub>i</sub> <sup>(S, S`)}

[0030]

[Expression 4]

Then,

An evaluation function vector F incorporating this f _i ^(S , ^S ′ ⁾ and the penalty function p described above is expressed by the following [Equation 5].
Defined by

[0033]

[Equation 5]

Also, the evaluation function Φ is

[Formula 6]

Is defined as follows. The unknown parameter X that minimizes Φ is obtained by repeatedly performing convergence calculation by the nonlinear least square method. The unknown parameter X is given by the following [Equation 7] and includes elements of the rotation amount R and the parallel movement amount T.

[0036]

[Expression 7]

A method for obtaining X by the nonlinear least square method will be described below. First, the evaluation function vector F
The Jacobian matrix J of is derived. The i th element of f constituting the F f _i, the i th element of p p _i, the parameter type of x ^(S) constituting the unknown parameter X (tx, ty,
If the elements of tz, Φ, θ, ψ) are x _K ^(S) , the Jacobian matrix J is

[0038]

[Equation 8]

Then, Each item of Jacobian J is

[0040]

[Equation 9]

[0041]

[Expression 10]

It can be calculated by replacing with numerical differentiation. Here, δ _K indicates the increment of each parameter type k, and I
_k ^{(S` ')} represents a column vector corresponding to the k-th column of the 6 × 6 small unit matrix I ^{( S)} constituting the following unit matrix I.

[0043]

## EQU11 ##

Note that f _i (X) = f _i ^{(s, s ′)} (x ^(s) ,
x ^{(s ')} ), If _i / ∂x _k ^(S'') is a value only if I _k ^(S'') δk changes x ^(S) , x ^(S'). And 0 otherwise.

Similarly, in consideration of p _i (X) = p _i (x _{K ′} ^{(S ′ ″)} ), I _k ^{(S ″)} δ _k changes x ^{(S ′ ″).} ∂p _i / ∂x _k ^{(S ″)} has a value, otherwise it is 0. The equation shown in the following [Equation 12] using the Jacobian J thus derived is

[0046]

[Expression 12] J · ΔX = −F

To find the increment ΔX of the unknown parameter X. Initially, a value that is considered appropriate as a value of X is set in advance. And Φ (X) by the set value X,
Comparison with Φ (X + ΔX) based on the new parameter X + ΔX is made to determine convergence. X + if not converged
ΔX is newly set to X, and the above procedure is repeated until convergence.

By the way, among the elements of the unknown parameter X, tx, ty, and tz are elements related to the parallel movement of the surface, while Φ, θ, and ψ are elements related to the rotation of the surface. It is shown. Therefore, in order to take into account the metric problem, a vector whose element is the increment δ _K of each parameter type k

[Formula 13]

Thus, it is preferable to scale Jacobian J. Find the solution ΔX ′ of the equation J ′ · ΔX ′ = − F using the Jacobian J ′ scaled by the increment vector δ. Using the obtained ΔX ′, each element of ΔX is

[0050]

Δx _k ^(S) = Δx ′ _k ^(S) · δ _k

Is obtained as follows. However,

[Expression 15]

Suppose that Thereafter, the convergence calculation is performed as described above to obtain the unknown parameter X. Based on the obtained unknown parameter X, the measured value S0,
A correction value for correcting S1, S2... Is calculated.

If the unknown parameter X includes an element that does not satisfy the constraint conditions, a warning is given to the display device 4 or measures such as forcibly terminating the measurement execution program are taken. Actually, since each element of the unknown parameter X is limited by the penalty function described above, each element is close to the limit boundary shown in Equation 2,
When the convergence calculation cannot be continued any more, it is detected that the unknown parameter X includes an element that does not satisfy the constraint condition.

Although the embodiments have been described above, the present invention is not limited to them. For example, in the above embodiment, the absolute values of the upper and lower limits are the same as shown in [Equation 2] for the constraint condition, but may be different values. Moreover, it is good also as only any one of the restrictions of an upper limit or a minimum. In the above embodiment, the constraint condition is incorporated as a penalty function in the evaluation function Φ. However, even if the penalty function is incorporated in another function and it is determined whether the constraint condition is satisfied in this other function. Good.

Further, in the above embodiment, the calibration work 5 is a flat surface, but if it has a known shape,
You can use other shapes such as a spherical surface,
Or it is good also as a calibration workpiece | work provided with the shape similar to a to-be-measured object. The calibration method shown above is the measurement target 1
Although it is appropriate to carry out each time the object is changed to another object, it may be performed periodically (for example, once a month) when the shape of the object 1 is limited to a similar shape.

[0056]

As described above, according to the present invention,
When connecting the measurement data of each partial measurement range, calibration information of the measurement result can be acquired by a simple method, and a highly accurate measurement result can be acquired. In addition, the limit of the correction amount can be detected, and inappropriate connection of the partial measurement ranges can be avoided, thereby making it possible to acquire accurate data for the entire measurement range.

[Brief description of the drawings]

FIG. 1 shows a configuration of a shape measuring apparatus 100 according to the present invention and a method for measuring by dividing into partial measurement ranges.
It is a figure for demonstrating the method implemented using 00. FIG.

FIG. 2 conceptually shows the relationship of data for each partial measurement range when the measurement method is carried out.

FIG. 3 is a conceptual diagram for explaining a calibration method of a measuring apparatus according to the present invention using a calibration workpiece 5;

FIG. 4 is a conceptual diagram for explaining a calibration method by a calibration method according to the present invention.

FIG. 5 is a flowchart of a calibration method according to the present invention.

FIG. 6 is a flowchart of a calibration method according to the present invention.

FIG. 7 is a conceptual diagram for explaining best-fit calculation.

[Explanation of symbols]

1 ... object to be measured, 2 ... sensor, 3 ... arithmetic device, 4 ...
Display device, 5 ... Calibration work

   ──────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Tomonori Goto             1-2 1-2 Kitajojo Nishi 1-chome, Kita-ku, Hokkaido               System Technology Institute Inc.             In the tute F-term (reference) 2F069 AA03 AA04 AA51 AA61 DD20                       FF00 GG12 GG73 HH30 MM23                       NN05 NN15 NN17

Claims (6)

[Claims] 1. When measuring an object to be measured that is larger than the size of a measurement range that can be measured by a series of measurement operations, the entire measurement range is divided into partial measurement ranges that partially overlap each other. After obtaining the measurement result of the object to be measured, the surface property measurement is configured to obtain the surface texture of the entire measurement range by connecting the measurement result of the object to be measured in each partial measurement range by a predetermined method. In the apparatus calibration method, in order to measure the surface properties of a calibration workpiece having a known surface property, a first step of setting partial measurement ranges that partially overlap each other, and the calibration workpiece for each partial measurement range A second step of performing measurement of partial surface properties and acquiring partial measurement data, and a correspondence relationship between overlapping portions of the adjacent partial measurement ranges based on the partial measurement data. A fourth step of defining an evaluation function Φ relating to the correspondence, and a nonlinear conversion amount of the partial measurement data in the partial measurement range that minimizes the evaluation function Φ A fifth step of calculating by a least square method, and a sixth step of calculating a correction value for correcting the measurement result of the device under test based on the conversion amount obtained by the fifth step. Calibration method for surface texture measuring device. 2. The method for calibrating a surface texture measuring apparatus according to claim 1, wherein the conversion amount is a rotation amount R and a translation amount T of a surface specified by partial measurement data for each partial measurement range. 3. A predetermined constraint condition is set for the conversion amount,
The method for calibrating a surface texture measuring apparatus according to claim 1, further comprising a step of determining whether or not the conversion amount is within the range of the constraint condition. 4. The method for configuring a surface texture measuring device according to claim 3, further comprising a step of notifying the outside when the amount of conversion is determined not to fall within the constraint conditions. . 5. The method for calibrating a surface texture measuring apparatus according to claim 3, wherein the evaluation function Φ incorporates a function representing the constraint condition. 6. The method for calibrating a surface texture measuring apparatus according to claim 1, wherein the correspondence relationship is expressed by a distance between the corresponding points.