JP2001227940A - Shape measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a shape measuring method of high versatility capable of taking accurate measurements without accumulation of errors. SOLUTION: Representative measurement data d(x, y) are extracted from each partial measuring range B. Next, a predetermined energy function Em (f) is defined (S2) from the group of representative measurement data extracted, and a plane f (x, y) on which the energy function Em defined is minimized is determined (S3). Finally, each partial measuring range B is moved relative to the plane f (x, y) determined.

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 for measuring a shape of an object to be measured, and more particularly to a shape measuring method for measuring a wide measuring range exceeding a single measurement range.

[0002]

2. Description of the Related Art When performing high-precision measurement over a wide range that cannot be covered by a single measurement using a contact type or non-contact type three-dimensional measuring device, the entire measurement range is divided into a plurality of parts. After the measurement is divided into measurement ranges and measurement is performed for each partial measurement range, these partial measurement ranges are connected to obtain measurement data of the entire measurement range. in this case,
Since the relative position between the measurement stage and the measurement target is determined for each partial measurement range, the respective partial measurement ranges may be connected based on the value at the time of this positioning. However, even if each partial measurement range is simply moved based on the value at the time of positioning, there is an error in positioning and a change in measurement conditions for each partial measurement range. Cannot be connected, and sufficient measurement accuracy cannot be obtained.

[0003] Therefore, as shown in FIG.
Is divided into a plurality of partial measurement ranges B so as to partially overlap each other as shown in FIG. 3B, and the respective partial measurement ranges B are sequentially corrected so that the overlapping portions overlap. Finally, a method (Measur) for determining the shape of the entire measurement range A in which overlapping portions are smoothly combined as shown in FIG.
ement of large plane surface shape by connecting s
mall-aperture interferograms, M.Otsubo et al., Opt.Eng., V
ol.33, No.2, 1994) or a method to determine the shape of the entire measurement range A to which each partial measurement range B is connected by moving each partial measurement range B only in the normal direction (hybrid fitting Measurement of luminous aspheric shape by aperture synthetic interferometry using SHIMIZU: Shimizu et al., Proc.

[0004]

However, in the former of the above-mentioned conventional shape measuring methods, errors accumulate each time the partial measuring ranges B are superimposed, even if the overlapping portion is widened. As the measurement range becomes wider, the accumulation of errors cannot be ignored and accurate measurement cannot be performed. Further, in the latter method, the work must be such that the correction direction can be specified to some extent, and there is a problem that versatility is lacking.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and has as its object to provide a highly versatile shape measurement method capable of accurate measurement without accumulation of errors.

[0006]

According to a first shape measuring method of the present invention, the whole measuring range is divided into a plurality of partial measuring ranges, and after performing a collective measurement for each of the partial measuring ranges, each shape is measured. In the shape measurement method for obtaining the shape of the entire measurement range from the measurement data obtained for each measurement range, a step of extracting at least a part of the measurement data obtained in each of the partial measurement ranges as representative data; and A step of applying a predetermined energy function to the extracted representative measurement data of the entire measurement range to obtain a shape in which the energy function is minimized, and a step of obtaining the shape obtained in this step with respect to the shape obtained in this step. Moving the measurement data.

According to the first shape measuring method according to the present invention, representative measurement data is extracted from each partial measurement range, and a shape having a predetermined energy function minimum with respect to the representative measurement data in the measurement range is determined. Since the measured data of each partial measurement range is moved with respect to this shape, the most appropriate shape is specified in the entire measurement range, and the problem of accumulation of errors does not occur. Further, according to the present invention, since the measurement data of each partial measurement range is moved with respect to the obtained shape,
It can be applied to any shape, and can provide a highly versatile shape measuring method.

The partial measurement ranges are set so that, for example, adjacent partial measurement ranges partially overlap.

In a preferred embodiment of the first shape measuring method according to the present invention, the step of moving the measurement data of each of the partial measurement ranges includes generating an average plane from the representative measurement data, Range of measured data,
Defining by a spatial distance from the average plane, correcting the representative measurement data based on a shape having the minimum energy function, and generating a new average plane from the representative measurement data corrected by this step. And correcting the measurement data of each of the partial measurement ranges by defining the measurement data of each of the partial measurement ranges by the spatial distance from the new average plane.

In a second shape measuring method according to the present invention, the entire measuring range is divided into a plurality of partial measuring ranges so that each partially overlaps with an overlapping portion, and measurement is performed for each partial measuring range. After that, in the shape measuring method for obtaining the shape of the entire measurement range from the measurement data obtained for each partial measurement range, the overlapping portion between the respective partial measurement ranges is obtained from the measurement data group obtained for each of the partial measurement ranges. Determining an evaluation function indicating the degree of coincidence of the corresponding points when moving both of the corresponding partial measurement ranges where the overlapping portion is common, and the evaluation amount obtained from this evaluation function is the total measurement amount A step of obtaining a correction amount for moving each of the partial measurement ranges that is minimized over the range; and a step of moving the measurement data of each of the partial measurement ranges based on the correction amount obtained in this step. Characterized by comprising and.

According to the second shape measuring method of the present invention, the evaluation quantity obtained from the evaluation function indicating the degree of coincidence of the corresponding point when both of the partial measurement ranges sharing the respective overlapping portions are moved is obtained. Find the minimum correction amount over the entire measurement range,
Since the measurement data of each partial measurement range is corrected from both sides based on this correction amount, the most appropriate correction is performed over the entire measurement range, and the problem of accumulation of errors does not occur.

Further, the step of determining the corresponding point of the overlapping portion includes, for example, a step of generating an estimated curved surface of the partial measurement range from the measurement data of one partial measurement range and a step of generating an estimated curved surface of the other partial measurement range. Setting a point on the estimated curved surface that gives the shortest distance from the data to the estimated curved surface as a corresponding point of one partial measurement range with respect to the measurement point of the other partial measurement range.

In a preferred embodiment of the present invention,
In the step of generating the estimated surface, the estimated surface is obtained using only the measurement data of the overlapping portion of the corresponding partial measurement range.

The evaluation function may define an average position between corresponding points in a corresponding partial measurement range as a target point.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the shape measuring method according to the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a view for explaining a shape measuring method using a surface shape measuring apparatus according to one embodiment of the present invention.
The surface profile measuring device includes a sensor 2 for measuring the displacement of the surface of the object 1 to be measured, a computing device 3 for computing the output of the sensor 2 to calculate the profile measurement data, and displaying the computation result of the computing device 3. And a display device 4 to be provided.

The entire measurement range A of the measured object 2 includes a plurality of partial measurement ranges B which can be measured by one measurement.
And the measurement is performed for each partial measurement range B. Each partial measurement range B is preferably set so that a part thereof overlaps.

Next, the shape measuring method of this embodiment will be described in detail. FIG. 2 is a flowchart illustrating the surface shape measuring method according to the present embodiment. First, representative measurement data d (x, y) is extracted from each partial measurement range B (S1). As shown in FIG. 3, at least a part of the measurement data is extracted as the representative data from each of the partial measurement ranges B, but all the measurement data may be used as the representative measurement data.

Next, a predetermined energy function Em (f) is defined from the extracted representative measured data group (S
2). As the energy function, for example, Membrane or Th
A function called in Plate can be used alone or in combination. These can be respectively expressed as follows.

[0019]

(Equation 1)

[0020]

(Equation 2)

Here, as shown in FIG. 4, f (x, y) is an expression indicating the shape data to be obtained, and λ is a parameter. Various cases can be dealt with by changing the energy function Em (f).

Next, as shown in FIG. 4, a plane f (x, y) that minimizes the defined energy function Em (f) is obtained (S3). At this time, since one energy function Em (f) is defined for the entire measurement area, there is no accumulation of error unlike the conventional method of determining a plane for each partial measurement range B.

Subsequently, the respective partial measurement ranges B are moved with respect to the determined plane f (x, y) (S4). Various methods can be considered as a moving method. For example, FIG.
As shown in FIG. 7, for each partial measurement range, an average plane C is created from the measurement data d (x, y) extracted first, and for the other measurement data, the spatial distance g from this average plane C is calculated.
(U, v). Then, as shown in FIG. 5B, an average plane C ′ is created from the extracted data corrected so that the energy function Em (f) is minimized. 'To the spatial distance g
Correction is made as if expressed by (u, v). The advantage of this method is that considering one partial measurement range B as a rigid body,
The data in this is assumed to be all measured by the same sensor positioning error, and that both rotation and translation errors are taken into account by correcting with the spatial distance g (u, v). is there. Note that the average surface C,
C ′ may be any surface such as a plane, a sphere, or a free-form surface, but if the measurement area is small, it may be an average plane as an approximate shape, in which case the calculation efficiency is improved.

FIG. 6 is a diagram showing the results of shape measurement using the first shape measurement method according to the present invention. In this example, the energy function is based on Membrane, and a modified function is used. As shown in FIG. 3A, a cylindrical surface having a radius of 2.5 mm and a height of 5.0 mm is divided into 100 (10 × 10) partial measurement ranges, and 100 (10 × 10)
Measurement data was obtained for each of the measurement points. Each partial measurement range was randomly rotated around each axis of XYZ within a range of ± 0.5 °, and Gaussian noise of 3σ = 0.06 mm was added to the Z value. For the calculation of Membrane, representative measurement data of four points was extracted from each partial measurement range. As a result, as shown in FIGS. 3B and 3C, the boundary of each partial measurement range is largely conspicuous in the method without applying this method, whereas in the case of applying this method, as shown in FIG. ) And (e), the boundaries of the respective partial measurement ranges are smoothly connected.

Similarly, in the example shown in FIG. 7, 100 (10 × 10) planes having a width of 10 × 10 mm and a step of 0.2 mm were measured as shown in FIG. The measurement data of each partial measurement range is 100 (10 × 10) points. Each partial measurement range is randomly rotated around each axis of XYZ within the range of ± 0.5 °, and 3σ = 3σ =
Gaussian noise of 0.06 mm was added. For the calculation of Membrane, representative measurement data of four points was extracted from each partial measurement range. As a result, as shown in FIGS. 3B and 3C, the boundary of each partial measurement range is largely conspicuous in the method without applying this method, whereas in the case of applying this method, as shown in FIG. ) And (e), the boundaries of the respective partial measurement ranges are smoothly connected.

Next, a preferred embodiment of the second shape measuring method according to the present invention will be described with reference to the accompanying drawings. FIG. 8 is a flowchart showing a shape measuring method by the surface shape measuring apparatus according to this embodiment. The surface shape measuring device used here is the same as the configuration in FIG.

Also in this embodiment, the entire measurement range A of the measurement object 2 is divided into a plurality of partial measurement ranges B that can be measured by one measurement, and the measurement is performed for each of the partial measurement ranges B. You. Each partial measurement range B is set so that a part thereof overlaps.

First, a corresponding point of an overlapping portion between the partial measurement ranges B is determined from the measurement data d of each partial measurement range B (S
11). That is, when the shape measurement according to the present invention is performed using the measurement data obtained by the measurement, the provided information is a group of measurement data points. To determine the correspondence between these point cloud data, first, as shown in FIG. 9A, one (i-th) measurement data group [i] of the corresponding partial measurement range B having a common overlapping portion. ^{_{d i 1, d i 2,}} ..., for generating a curved surface by a least square method from d ⁱ _n]. Next, FIG.
, The other (i + 1) -th measurement data d ^{i + 1} _j
The point d ⁱ _j on the curved surface which gives the shortest distance to the curved surface from d
_{Let it be} the corresponding point of ^{i + 1} _j . Similarly, the other measurement data group
_{^{[d i + 1 1, d}} i + 1 2, ..., d i + 1 m] from the estimated curved, points d ⁱ on the curved surface which gives the shortest distance to the curved surface from one of the measurement data d ⁱ _k Let ⁺¹ _{k be} the corresponding point of d ⁱ _k . Here, the form of the curved surface shape may be appropriately selected depending on the situation, such as a free-form surface, a quadratic surface, a plane, or a triangular mesh. In addition, in the method of obtaining the shape of the entire measurement range by performing the measurement within each partial measurement range a plurality of times, it is considered that the measurement data of the same partial measurement range includes the same positioning error. There is no problem if the range is regarded as one rigid body and replaced with one surface. Also, in FIG. 5A, all the measurement data areas are represented by one curved surface. However, since only the information of the overlapping part is necessary for the calculation, the data included in the overlapping part as shown in FIG. The curved surface may be estimated only from the surface. This method can also reduce the calculation time.

Next, corresponding point d ⁱ _j when moving both the corresponding portions measurement range B, and defining an evaluation function φ indicating the matching degree of _{^{d i + 1 k (S12)}} . Here, the content proposed in the present embodiment is different from the conventional one in the method of creating the evaluation function φ. According to the conventional method, one of the two bodies is not moved, and the evaluation function is determined so that the other body is moved based on this. For example, FIG.
As shown in (a), in the alignment processing between the i-th and (i + 1) -th partial measurement ranges B _i and B _{i + 1} , first, B _i
Is fixed, and an evaluation function φ _i is given to move only B _{i + 1} . Assuming that the rotation of B _{i + 1} is R and the translation is T, this evaluation function is

[0030]

(Equation 3)

Is given by Here, d ⁱ _j is a point on the corresponding B _i to the point d ^{i + 1} _j on B i _{+ 1.} However, when this method is applied to the many-body problem, errors accumulate as described above, and a highly accurate result cannot be obtained. Therefore, in the present embodiment, the evaluation function φ _i used for obtaining the optimum correction amount is determined so as to move both the partial measurement ranges B _i and B _{i + 1} . For example, in the above problem, the rotation of B _i is R ⁱ , the translation is T ⁱ , and the rotation of B _{i + 1} is R _i.
^{If i + 1} and the translation are T ^{i + 1} ,

[0032]

(Equation 4)

Here, the evaluation function φ_iD inⁱ _jIs B_{i + 1}
Upper point d^{i + 1} _jB corresponding to_iThe upper point, d^{i + 1} _kIs B_i
Upper point dⁱ _kB corresponding to_{i + 1}This is the point above. like this
And B _{i + 1}→ B_i, B_i→ B_{i + 1}Evaluation function φ from both directions
By creating, based on one of the target surfaces
Fixed as the standard and different from the conventional method of giving the evaluation function φ.
Therefore, there is no fixed criterion, and the conventional evaluation function φ
In the creation method, accumulation of errors became a problem and it was difficult to respond
In the case of many-body problems, evaluation is performed over the entire measurement range as follows.
High accuracy calibration is possible
You.

Next, the surface correction amounts R and T that minimize the evaluation amount Φ obtained from the defined evaluation function φ over the entire measurement range are obtained (S13). That is, in order to apply the evaluation value to the many-body problem here, the number 4 obtained for each overlapping region
Is added over the entire area. Assuming that the evaluation amount in the i-th overlapping region is φ _i , the evaluation amount Φ is

[0035]

(Equation 5)

## EQU1 ## Here, w _i is a weight function for the i-th partial measurement range B _i . And this evaluation amount Φ
From

[0037]

[Formula 6] minΦ

R ⁱ and T ⁱ giving the following are obtained.

Equation 6 can be obtained by calculating by the nonlinear least-squares method. In general, measurement data measured using a certain shape measuring system is based on the measurement accuracy of the system and the positioning of the sensor. Due to errors and the like, it is not preferable to perform correction more than necessary. Therefore, it is desirable to add a restriction determined by the system to the correction amounts R and T, and solve the evaluation amount Φ as a so-called non-linear least-squares method with equality inequality constraints that minimizes the evaluation amount Φ under these constraints. The respective partial measurement ranges B are moved based on the correction amounts R and T obtained in this way (S14). As a method of this movement, the method of the above-described embodiment or the like can be used.

As described above, according to the method of the present embodiment, since the evaluation is performed over the entire measurement area, unlike the conventional method of determining a plane for each partial measurement range B, accumulation of errors There is no. Further, the conventional method can be applied only to a closed system as shown in FIG.
ered Polygon Meshes from Range Images, Greg Turkand
Marc Levoy, In Proceedings of SIGGRAPH '94, p311-31
8, ACM Press, July 1994), and the present invention can be applied to an open system as shown in FIG.

FIG. 12 is a view showing the result of shape measurement using the second shape measurement method according to the present invention. In this example, the conventional method and the present method are applied to a two-dimensional many-body problem, and measurement data of each partial measurement range as shown in FIG. As a result, in the conventional method of fixing one partial measurement range B as shown in FIG. 2B, accumulation of errors is observed, whereas when this method is applied, FIG.
As shown in the figure, high-precision calibration has been performed.

In the above-described embodiment, both the partial measurement ranges are moved without particularly setting the target point. However, as a simple method, the solution is obtained by fixing the target point of the evaluation function φ. Is also conceivable. For example, when a method is used in which a target point of the evaluation function φ is determined as an average position between the corresponding points, the evaluation function is as follows.

[0043]

(Equation 7)

[0044]

As described above, according to the first shape measuring method according to the present invention, the representative measurement data is extracted from each partial measurement range, and the predetermined measurement data is determined with respect to the representative measurement data in the measurement range. Since the shape that minimizes the energy function is determined and the measurement data in each partial measurement range is moved to this shape, the most appropriate shape is specified for the entire measurement range, and errors are accumulated. The problem does not arise.

Further, according to the second shape measuring method of the present invention, the evaluation amount obtained from the evaluation function indicating the degree of coincidence of the corresponding point when both of the partial measurement ranges sharing the overlapping portion are moved. Is determined and the measurement data of each partial measurement range is moved based on this correction amount, so that the most appropriate shape is specified in the entire measurement range, and the accumulation of errors The problem does not arise.

[Brief description of the drawings]

FIG. 1 is a view for explaining a first shape measuring apparatus and a measuring method using the same according to the present invention.

FIG. 2 is a flowchart of the measurement method.

FIG. 3 is a diagram for explaining the measurement method.

FIG. 4 is a diagram for explaining the measurement method.

FIG. 5 is a diagram for explaining the measurement method.

FIG. 6 is a diagram showing a measurement result obtained by applying the first shape measurement method according to the present invention.

FIG. 7 is a diagram showing another example of a measurement result obtained by applying the first shape measuring method according to the present invention.

FIG. 8 is a flowchart of a second shape measuring method according to the present invention.

FIG. 9 is a diagram for explaining the measurement method.

FIG. 10 is a diagram for explaining the measurement method.

FIG. 11 is a diagram for explaining the measurement method.

FIG. 12 is a diagram showing a measurement result obtained by applying the second shape measuring method according to the present invention.

FIG. 13 is a view for explaining a conventional shape measuring method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Measurement object 2 ... Sensor 3 ... Calculation device 4 ... Display device A ... Full measurement range B ... Partial measurement range

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Shinichi Sadahiro 1-1-2-1, Kita 7-jo Nishi, Kita-ku, Sapporo-city, Hokkaido Inside System Technology Institute (72) Inventor Kozo Umeda Kita-ku, Sapporo, Hokkaido Article 1-2 Nishi 1-chome 1-2 term F term in System Technology Institute Co., Ltd. (reference) 2F069 AA51 DD30 GG01 GG06 GG39 GG49 GG52 GG56 GG62 HH01 JJ08 JJ26 LL03 NN05 NN06 QQ05

Claims (7)

[Claims] 1. The method according to claim 1, further comprising: dividing the entire measurement range into a plurality of partial measurement ranges; performing a collective measurement for each of the partial measurement ranges; and determining a shape of the total measurement range from measurement data obtained for each of the partial measurement ranges. Extracting at least a part of the measurement data obtained in each of the partial measurement ranges as representative measurement data, and performing a predetermined measurement on the representative measurement data of the entire measurement range extracted in this step. Applying an energy function to obtain a shape that minimizes the energy function; and moving measurement data of each of the partial measurement ranges with respect to the shape obtained in this step. Shape measurement method. 2. The shape measuring method according to claim 1, wherein the partial measurement range is set so that adjacent partial measurement ranges partially overlap with each other. 3. The step of moving the measurement data of each of the partial measurement ranges includes generating an average plane from the representative measurement data, and defining the measurement data of each of the partial measurement ranges by a spatial distance from the average plane. Correcting the representative measurement data based on a shape in which the energy function is minimized; and generating a new average plane from the representative measurement data corrected by the step. 3. The shape measurement method according to claim 1, wherein the measurement data of each of the partial measurement ranges is corrected by defining measurement data of the range by the spatial distance from the new average plane. 4. The whole measurement range is divided into a plurality of partial measurement ranges so that each of them partially overlaps with an overlapping portion, and measurement is performed for each of the partial measurement ranges. Determining a corresponding point of the overlapping portion between the partial measurement ranges from a measurement data group determined in each of the partial measurement ranges; Obtain an evaluation function indicating the degree of coincidence of the corresponding point when moving both of the corresponding partial measurement ranges that share the part,
Obtaining a correction amount for moving each of the partial measurement ranges in which the evaluation amount obtained from the evaluation function is minimized over the entire measurement range; and, based on the correction amounts obtained in this step, Moving the measurement data. 5. The step of determining the corresponding point of the overlapping portion includes the steps of: generating an estimated curved surface of the partial measurement range from measurement data of one partial measurement range; and data of each measurement point of the other partial measurement range. Setting a point on the estimated surface that gives the shortest distance from the to the estimated surface to a corresponding point in one partial measurement range with respect to the measurement point in the other partial measurement range. The shape measurement method described. 6. The shape according to claim 5, wherein the step of generating the estimated surface is a step of obtaining the estimated surface using only the measurement data of the overlapping portion of the corresponding partial measurement range. Measuring method. 7. The shape according to claim 4, wherein the evaluation function is defined as an average position between corresponding points in a corresponding partial measurement range as a target point. Measuring method.