JP3509005B2 - Shape measurement method - Google Patents

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 the shape of an object to be measured, and more particularly to a shape measuring method for measuring a wide measuring range that exceeds a single measuring range.

[0002]

2. Description of the Related Art When using a contact type or non-contact type three-dimensional measuring machine or the like to perform high-precision measurement over a wide range that cannot be covered by a single measurement, the entire measurement range is divided into a plurality of parts. After dividing into measurement ranges and performing measurement 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 measurement stage and the measurement target are positioned relative to each of the partial measurement ranges, the partial measurement ranges may be connected based on the values at the time of positioning. However, even if each partial measurement range is simply moved based on the positioning value, there are errors during positioning and changes in measurement conditions for each partial measurement range, so the partial measurement range is actually smooth. Can not be connected to, and sufficient measurement accuracy cannot be obtained.

Therefore, as shown in FIG.
Divide the entire measurement range A shown in Fig. 2 into multiple partial measurement ranges B so that some overlap, and correct each partial measurement range B sequentially so that the overlapping parts overlap. Finally, a method for obtaining the shape of the entire measurement range A in which overlapping parts are smoothly combined as shown in Fig. 6C (Measur
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 by moving each partial measurement range B only in the direction of its normal direction, the method of obtaining the shape of the total measurement range A to which each partial measurement range B is connected (hybrid fitting Measurement of photometric aspherical shape by aperture synthesis interferometry using SHIMIZU: Shimizu et al., Proc.

[0004]

However, in the case of the former of the above-mentioned conventional shape measuring methods, even if the overlapping portion is widened, an error is accumulated each time each partial measurement range B is overlapped, The wider the measurement range, the more error accumulation cannot be ignored, and the more accurate measurement becomes impossible. In the latter method, the work must be such that the correction direction can be specified to some extent, and there is a problem of lacking versatility.

The present invention has been made in view of the above problems, and an object of the present invention is to provide a highly versatile shape measuring method which enables accurate measurement without error accumulation.

[0006]

A first shape measuring apparatus according to the present invention divides an entire measuring range into a plurality of partial measuring ranges, performs a collective measurement for each partial measuring range, and then measures each partial measuring range. In the shape measuring 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 measurement data, and this step All measurements to obtain a representative measurement data of all measurement range in the extracted
A predetermined energy function represented by the spatial distance to the shape of the range is defined , and the whole measurement in which this energy function is the minimum
The method is characterized by including a step of obtaining a shape in a constant range and a step of moving the measurement data of each of the partial measurement ranges with respect to the shape obtained in this step.

According to the first shape measuring method of the present invention, the representative measurement data is extracted from each partial measurement range, and the shape in which the predetermined energy function is minimized with respect to the representative measurement data of the measurement range is obtained. 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 error accumulation 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 a highly versatile shape measuring method can be provided.

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

In a preferred aspect of the first shape measuring method according to the present invention, the step of moving the measurement data in each of the partial measurement ranges is to generate an average surface from the representative measurement data, and to measure each of the partial measurements. Measurement data of the range
A step of defining the spatial distance from the average surface, a step of correcting the representative measurement data based on a shape that minimizes the energy function, and a new average surface generated from the representative measurement data corrected by this step to a step, by the measurement data of the previous SL each partial measurement range defined by the spatial distance from the new average surface, corrects the measurement data of the respective partial measurement range.

In the second shape measuring method according to the present invention, the entire measuring range is divided into a plurality of partial measuring ranges so that the overlapping portions partially overlap each other, and the measurement is carried out collectively 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 partial measurement ranges from the measurement data group obtained for each partial measurement range The step of determining the corresponding points of and the evaluation function that shows the degree of coincidence of the corresponding points when both the corresponding partial measurement ranges where the overlapping part is common is moved, and the evaluation amount obtained from this evaluation function is the total measurement A step of obtaining a correction amount for moving each partial measurement range which becomes the minimum over the range, and a step of moving the measurement data of each partial measurement range 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 amount obtained from the evaluation function indicating the degree of coincidence of corresponding points when both of the partial measurement ranges in which each overlapping portion is common is moved. 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 made in the entire measurement range, and the problem of error accumulation does not occur.

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

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

In the evaluation function, it is also possible to define an average position between corresponding points of the corresponding partial measurement range as a target point.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION 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 diagram for explaining a shape measuring method by a surface shape measuring apparatus according to an embodiment of the present invention.
The surface shape measuring apparatus displays a sensor 2 for measuring the displacement of the surface of the object 1 to be measured, an arithmetic unit 3 for arithmetically processing the output of the sensor 2 to calculate shape measurement data, and an arithmetic result of the arithmetic unit 3. And a display device 4 that operates.

The total measuring range A of the object 2 to be measured is a plurality of partial measuring ranges B which can be measured by one collective measurement.
And is measured 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 showing the surface shape measuring method according to this 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 from each partial measurement range B as the representative data, 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 measurement data group (S).
2). As the energy function, for example, Membrane or Th
A function called “in plate” can be used alone or by combining. Each of these can be expressed as follows.

[0019]

[Equation 1]

[0020]

[Equation 2]

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

Next, as shown in FIG. 4, a surface 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 in the entire measurement region, unlike the conventional method of determining the surface for each partial measurement range B, there is no error accumulation.

Then, each partial measurement range B is moved with respect to the obtained surface f (x, y) (S4). Various methods are conceivable as a moving method. For example, FIG.
As shown in, for each partial measurement range, the average plane C is created from the measurement data d (x, y) extracted first, and for other measurement data, the spatial distance g from this average plane C is
Express it as (u, v). Then, as shown in FIG. 5B, an average surface C ′ is created from the extracted data corrected so that the energy function Em (f) is minimized, and the other data is created by this newly created average surface C. Spatial distance g
Correction is performed assuming that it is expressed by (u, v). The advantage of this method is that one partial measurement range B is considered as a rigid body,
All the data in this is assumed to be measured by the same sensor positioning error, and by correcting with the spatial distance g (u, v), both errors of rotation and translation are taken into consideration. is there. The average plane C,
C ′ may be any surface such as a flat surface, a spherical surface, and a free-form surface, but when the measurement area is small, it may be an average flat surface as an approximate shape, and in this case, the calculation efficiency is improved.

FIG. 6 is a diagram showing the result of shape measurement using the first shape measuring 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 the figure (a), a cylindrical surface with a radius of 2.5 mm and a height of 5.0 mm is divided into 100 (10 x 10) partial measurement ranges, and 100 (10 x 10) in each partial measurement range.
The measurement data was acquired for each measurement point. Each partial measurement range was randomly rotated within ± 0.5 ° around each axis of XYZ, and Gaussian noise of 3σ = 0.06 mm was added to the Z value. For the calculation of Membrane, representative measurement data of 4 points was extracted from each partial measurement range. As a result, as shown in (b) and (c) of the figure, in the method not applying this method, the boundary between the partial measurement ranges is conspicuous, whereas in the case of applying this method, ) And (e), the boundaries of the partial measurement ranges are smoothly combined.

Similarly, in the example shown in FIG. 7, as shown in FIG. 7A, 100 (10 × 10) surfaces each having a width of 10 × 10 mm and a step of 0.2 mm were measured. The measurement data of each partial measurement range is 100 (10 × 10) points. Each partial measurement range is randomly rotated within ± 0.5 ° around each axis of XYZ, and Z value is 3σ =
Gaussian noise of 0.06 mm was added. For the calculation of Membrane, representative measurement data of 4 points was extracted from each partial measurement range. As a result, as shown in (b) and (c) of the figure, in the method not applying this method, the boundary between the partial measurement ranges is conspicuous, whereas in the case of applying this method, ) And (e), the boundaries of the partial measurement ranges are smoothly combined.

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 has the same configuration as that shown in FIG.

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

First, the corresponding points of the overlapping portions between the partial measurement ranges B are determined from the measurement data d of each partial measurement range B (S).
11). That is, when performing the shape measurement according to the present invention using the measurement data obtained by the measurement, the given information is the measurement data point group. In order to determine the correspondence between these point group data, first, as shown in FIG. 9 (a), one (i-th) measurement data group [i] in the corresponding partial measurement range B having a common overlapping part A curved surface is generated from d ⁱ ₁ , d ⁱ ₂ , ..., D ⁱ _n ] by the method of least squares or the like. Next, the same figure (b)
, The other (i + 1) th measurement data d ^{i + 1} _j
From the point d ⁱ _j on the surface giving the shortest distance from
^{i + 1} _j corresponding points. Similarly, the other measurement data group
A surface is estimated from [d ^{i + 1} ₁ , d ^{i + 1} ₂ , ..., D ^{i + 1} _m ], and a point d ⁱ on the surface giving the shortest distance from one measurement data d ⁱ _k to this surface. 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 curved surface, a quadric 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 in each partial measurement range multiple times, it is considered that the same positioning error is included in the measurement data of the same partial measurement range. It is no problem to consider the range as one rigid body and replace it with one curved surface. In addition, although all the measurement data areas are represented by one curved surface in (a) of the figure, the data included in the overlapping section as shown in (c) of the figure is necessary because only the overlapping section needs to be calculated. You may make it estimate a curved surface from only. This method can also shorten the calculation time.

Next, an evaluation function φ indicating the degree of coincidence between corresponding points d ⁱ _j and d ^{i + 1} _k when both corresponding partial measurement ranges B are moved is defined (S12). Here, the contents proposed in the present embodiment are 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 is moved based on this. For example, in 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 so that only B _{i + 1} is moved. If the rotation of B _{i + 1} is R and the translation is T, then this evaluation function is

[0030]

[Equation 3]

Is given by Here, d ⁱ _j is a point on B _i corresponding to a point d ^{i + 1} _j on B _{i + 1} . However, if this method is applied to a many-body problem, errors accumulate as described above, and a highly accurate result cannot be obtained. Therefore, in this embodiment, the evaluation function φ _i used to obtain the optimum correction amount is determined so that both partial measurement ranges B _i and B _{i + 1} are moved. 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 parallel movement 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}That is the point above. like this
To B _{i + 1}→ B_i, B_i→ B_{i + 1}Evaluation function φ from both directions of
By creating one, you can create a base
This is different from the conventional method in which the evaluation function φ is fixed as
, There is no fixed criterion, and the conventional evaluation function φ
It was difficult to deal with the creation method due to the problem of error accumulation.
Even for multibody problems, evaluation is performed over the entire measurement range as follows.
This enables highly accurate calibration.
It

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, here, since the evaluation value is applied to the many-body problem, the number 4 obtained for each overlap region is calculated.
Is added over the entire area. If the evaluation amount in the i-th overlapping region is φ _i , the evaluation amount Φ is

[0035]

[Equation 5]

It becomes Here, w _i is a weighting function for the i-th partial measurement range B _i . And this evaluation amount Φ
From

[0037]

[Equation 6] minΦ

R ⁱ and T ⁱ that give are obtained.

The equation (6) can be obtained by calculating it by the nonlinear least squares method. Generally, the measurement data measured by using a certain shape measuring system shows the measurement accuracy of the system and the positioning of the sensor. Since there are errors, it is not preferable to make unnecessary corrections. Therefore, it is desirable that the correction amounts R and T are limited by the system, and the evaluation amount Φ is minimized under this constraint condition. Each partial measurement range B is moved based on the correction amounts R and T thus obtained (S14). As the 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 this embodiment, since the evaluation is performed on the entire measurement area, unlike the conventional method of determining the surface for each partial measurement range B, error accumulation is performed. There is no. Further, the conventional method can be applied only to a closed system as shown in FIG. 11 (a) (Zipp
ered Polygon Meshes from Range Images, Greg Turkand
Marc Levoy, In Proceedings of SIGGRAPH '94, p311-31
8, ACM Press, July 1994), the present invention can be applied to an open system as shown in FIG.

FIG. 12 is a diagram showing the result of shape measurement using the second shape measuring method according to the present invention. In this example, the conventional method and the present method are applied to the two-dimensional many-body problem, and the measurement data of each partial measurement range as shown in FIG. As a result, as shown in (b) of the same figure, in the conventional method of fixing one partial measurement range B, an error is accumulated, whereas when the present method is applied, (c) of the same figure is applied.
As shown in, high-precision calibration is completed.

In the above-described embodiment, both of the partial measurement ranges are moved without particularly setting the target point, but as a simple method, the target point of the evaluation function φ is fixed to obtain the solution. Can also be considered. For example, the evaluation function is as follows when the target point of the evaluation function φ is taken as the average position between the corresponding points.

[0043]

[Equation 7]

[0044]

As described above, according to the first shape measuring method of the present invention, representative measurement data is extracted from each partial measurement range, and a predetermined measurement data is extracted from the representative measurement data of the measurement range. Since the shape that minimizes the energy function is found and the measurement data of each partial measurement range is moved with respect to this shape, the most appropriate shape in the entire measurement range is specified, and error accumulation That problem does not occur.

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 corresponding points when both of the partial measurement ranges having the common overlapping part are moved. Since the correction amount that minimizes is calculated and the measurement data of each partial measurement range is moved based on this correction amount, the most appropriate shape in the entire measurement range is specified, and error accumulation That problem does not occur.

[Brief description of drawings]

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

FIG. 2 is a flowchart of the measuring method.

FIG. 3 is a diagram for explaining the same measuring method.

FIG. 4 is a diagram for explaining the same measuring method.

FIG. 5 is a diagram for explaining the same measuring method.

FIG. 6 is a diagram showing a measurement result in which the first shape measuring method according to the present invention is applied.

FIG. 7 is a diagram showing another example of a measurement result in which the first shape measuring method according to the present invention is applied.

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

FIG. 9 is a diagram for explaining the same measuring method.

FIG. 10 is a diagram for explaining the same measuring method.

FIG. 11 is a diagram for explaining the same measuring method.

FIG. 12 is a diagram showing a measurement result in which the second shape measuring method according to the present invention is applied.

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

[Explanation of symbols]

1 ... Measurement target 2 ... Sensor 3 ... Computing device 4 ... Display device A: Whole measuring range B: Partial measurement range

─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Shinichi Sadahiro 1-2-1, Kita-ku, Kita-ku, Sapporo-shi, Hokkaido System Technology Institute Ltd. (72) Inventor Kozo Umeda 7 Kita-ku, Kita-ku, Sapporo, Hokkaido 1-1-2 Jyosai System Technology Institute Co., Ltd. (56) Reference JP-A-4-290907 (JP, A) JP-A-10-206145 (JP, A) JP-A-9-106392 (JP , A) JP 9-218034 (JP, A) JP 9-33244 (JP, A) JP 7-174535 (JP, A) JP 10-160428 (JP, A) JP 5-10751 (JP, A) (58) Fields investigated (Int.Cl. ⁷ , DB name) G01B 21/20

Claims (7)

(57) [Claims] 1. The whole measurement range is divided into a plurality of partial measurement ranges, and the measurement is performed for each partial measurement range. Then, the shape of the entire measurement range is obtained from the measurement data obtained for each partial measurement range. In the shape measuring method for obtaining, a step of extracting at least a part of the measurement data obtained in each of the partial measurement ranges as representative measurement data,
And a step of defining a predetermined energy function represented by the spatial distance to the shape of the entire measurement range to be obtained, and obtaining the shape of the entire measurement range where this energy function is the minimum, and for the shape obtained in this step And a step of moving the measurement data of each of the partial measurement ranges. 2. The shape measuring method according to claim 1, wherein the partial measurement ranges are set such that adjacent partial measurement ranges partially overlap with each other. 3. The step of moving the measurement data of each partial measurement range generates an average plane from the representative measurement data, and the measurement data of each partial measurement range is defined by a spatial distance from the average plane. A step of correcting the representative measurement data based on a shape in which the energy function is the minimum, and a step of generating a new average surface from the representative measurement data corrected by this step, each of the partial measurements 3. The shape measuring method according to claim 1, wherein the measurement data of each partial measurement range is corrected by defining the measurement data of the range by the spatial distance from the new average plane. 4. The total measurement range is divided into a plurality of partial measurement ranges so that each of them partially overlaps, and a measurement is performed for each partial measurement range, and then the measurement is performed for each partial measurement range. In the shape measuring method for obtaining the shape of the entire measurement range from the obtained measurement data, the step of determining the corresponding point of the overlapping portion between the partial measurement ranges from the measurement data group obtained in the partial measurement ranges, Obtain an evaluation function that indicates the degree of coincidence of corresponding points when both corresponding partial measurement ranges that share a common part are moved,
A step of obtaining a correction amount for moving each partial measurement range in which the evaluation amount obtained from this evaluation function is the minimum over the entire measurement range, and a step of calculating the correction amount for each partial measurement range based on the correction amount obtained in this step And a step of moving the measurement data. 5. The step of determining the corresponding points of the overlapping portion includes the step of generating an estimated curved surface of the partial measurement range from the measurement data of one partial measurement range, and the data of each measurement point of the other partial measurement range. To a point on the estimated curved surface that gives the shortest distance from the to the estimated curved surface as a corresponding point of one partial measuring range with respect to a measuring point of the other partial measuring range. Shape measurement method described. 6. The shape according to claim 5, wherein the step of generating the estimated curved surface is a step of obtaining the estimated curved 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 of corresponding partial measurement ranges. Measuring method.