JPH08285570A - Method and apparatus for measuring shape parameter - Google Patents

Abstract

PURPOSE: To determine a shape parameter of a free curved surface such as that of a non-spherical lens by a method wherein a theoretical shape is applied corresponding to a measuring data and an abnormal data is removed from the shape measuring data to determine a normal vector and a foot of a perpendicular in the shape measuring data with respect to the theoretical shape. CONSTITUTION: A theoretical shape specifying means 910 extracts a necessary theoretical shape data using an input means 903 from a data of work as subject in a memory means 908 or inputs a necessary data directly. A memory means 909 stores the data specified. A correction data generating means 913 generates a roundness correction data from a measuring data as obtained by measuring a spherical prototype stored in a memory means 912 to be stored into a memory means 914. An abnormal point removing means 916 removes an abnormal measuring data from the theoretical shape initialized and the measuring data and the results are passed to a shape evaluating means 917. The means 917 evaluates a shape conforming to an evaluation reference from the data and the results are stored into a memory means 918, and it is shown on a display means 904.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention is based on shape measurement data obtained from a contact type coordinate measuring machine, and based on shape measurement data, multi-dimensional shape parameters such as general geometric shapes and free-form surface shapes can be used for determining the sphericity of a contactor or more. And apparatus for measuring with the accuracy of.

[0002]

2. Description of the Related Art In recent years, coordinate measuring machines typified by coordinate measuring machines have been remarkably spread in the field of inspection and measurement. The reason for this is that using a coordinate measuring machine, compared to conventional measuring instruments such as calipers and micrometers, makes it possible to accurately measure the size and shape of a wide variety of complex and diverse objects to be measured. This is because it is possible to measure and evaluate, and it is also possible to realize flexible automation.

In the coordinate measuring machine, the shape of the object to be measured is sampled by a contact sensor using a touch trigger or a non-contact sensor using light as a medium.
Spatial coordinate value data is input to the electronic computer as shape measurement data. In a computer, the shape measurement data is substituted into a mathematical equation representing the corresponding multidimensional shape such as a straight line, circle, cylinder, plane, cone, sphere, and free-form surface, and the shape parameter ( For example, position, orientation, size, deviation, etc.) are generally calculated. For example, when a cylinder is considered as a multidimensional shape, the position is the coordinate on the central axis, the posture is the direction vector of the central axis, and the dimension is the radius. If these evaluation results are compared with the design shape described in the drawings or the like, it is extremely easy to determine whether or not the component is correctly manufactured according to the instructions in the drawings.

Further, in the measurement of optical components such as a spherical lens, it is possible to measure and evaluate the shape with an accuracy of 1 nm or less by an optical interferometry method. For things that are out of shape,
Since such an interferometric method cannot be used, it is measured by another method. The coordinate measuring machine is also effective for measuring the free-form surface shape represented by the aspherical lens and the mold for the aspherical lens, and the contactor is brought into contact with the target lens,
A well-known method is to perform a best fit to the designed free-form surface from the coordinate value data by the least square method or the like to evaluate the shape of the curved surface. These days, there is no doubt that such measurement methods will become the mainstream in the future because of the increasing speed, higher functionality and lower price of electronic computers.

The reason why the least squares method is adopted in the above-mentioned prior arts is that the algorithm is simple and the program is easy to construct, the calculation time is fast, the stability of the calculation is high, and it is insensitive to abnormal measurement points. This is because there are many advantages such as However, most of the reasons are from the standpoint of the manufacturer of the measuring machine, and the least squares method is not an appropriate shape evaluation method from the viewpoint of functional evaluation of the object to be measured. In fact, JIS specifies the measurement method by the minimum area method, the maximum inscribed method, and the minimum circumscribed method instead of the least square method (JIS B0021, B00.
22, B0621-1984), ISO, ANSI and the like. Generally, even with the same shape data, the shape parameters calculated by the least square method, the minimum area method, the maximum inscribed method, and the minimum circumscribed method are different from each other. However, in the past, adequate measurement methods and devices for shape parameters such as the minimum area method, maximum inscribed method, and minimum circumscribed method have not been fully established, so there is a problem in terms of calculation time, stability, usage conditions, etc. Many,
In practice, the only way to rely was on the least squares method.

In view of these problems, the present inventors have proposed a measuring method for stably and quickly obtaining shape parameters of a multidimensional shape by the minimum area method, maximum inscribed method, and minimum circumscribed method. He invented the device and filed a patent application earlier (Japanese Patent Application No. 5-66439). Hereinafter, this application will be referred to as a prior invention. The invention of the prior application, in measuring and inspecting using a coordinate measuring machine which has become mainstream in recent years, is a multidimensional dimension based on a practical minimum area method, maximum inscribed method, and minimum circumscribed method in order to truly achieve its effect. The invention was made with the recognition that the realization of a shape parameter measuring method and apparatus is the most important issue.

That is, in the first invention, firstly, "the shape parameter of the multi-dimensional shape is determined by aligning the mathematical theoretical shape with respect to the shape data obtained by actually measuring the multi-dimensional shape. In the measuring method to be obtained, a first step of giving the theoretical shape corresponding to the shape data, and at least an amount of translational movement or rotation of the theoretical shape so that an error between the theoretical shape and the shape data becomes small. A second step of calculating a movement amount, a third step of translating or rotating the theoretical shape with the calculated translational movement amount or rotational movement amount, and the translational movement amount and a preset translational movement amount. Or a fourth step of comparing and judging the set value of the rotational movement amount or the set value of the rotational movement amount set in advance, and the fourth step,
According to the result of comparison and judgment, the second, third, fourth
A fifth step of repeating the steps, and like the fifth step,
And a sixth step of obtaining a shape parameter at that time based on the result of the comparison and judgment in the fourth step.

A second aspect of the invention of the prior application is "Measurement for obtaining the shape parameter of the multidimensional shape by aligning the mathematical theoretical shape with respect to the shape data obtained by actually measuring the multidimensional shape. In the method, a first step of providing the theoretical shape corresponding to the shape data, and at least a translational movement amount or a rotational movement amount of the theoretical shape so that an error between the theoretical shape and the shape data becomes small. And a third step of comparing and judging the translational movement amount and a preset value of the translational movement amount, or a third step of comparing and judging the rotational movement amount and a preset value of the rotational movement amount. In the step, the theoretical shape is translated or rotated with the translational movement amount or the rotational movement amount according to the result of comparison and determination, and the second step, the third step A fourth step of repeating the floor, the fourth
Similarly to the step, in the third step, there is provided a fifth step of obtaining the shape parameter at that time based on the result of the comparison and judgment ".

A third aspect of the invention of the prior application is "a device for obtaining the shape parameter of the multidimensional shape by aligning the mathematical theoretical shape with respect to the shape data obtained by actually measuring the multidimensional shape. In input means for inputting the shape data, designating means for designating the theoretical shape, and at least an amount of translational movement or rotational movement of the theoretical shape so that an error between the theoretical shape and the shape data becomes small. An arithmetic means 1 for calculating an amount, an arithmetic means 2 for translating or rotating the theoretical shape with the calculated translational movement amount or rotational movement amount, and setting of the translational movement amount and a preset translational movement amount. A value, or a judgment means for comparing and judging a preset value of the rotational movement amount with the preset value of the rotational movement amount, and a result judged by the determination means. Based on the result of the judgment, the calculation means 1, the calculation means 2, and the judgment means are repeated, and the output means outputs the shape parameter of the multidimensional shape based on the judgment result. It is a measuring device characterized by that.

In the invention of the prior application, the method of linear approximation and iterative calculation is applied to the theory of calculation of the shape parameters, which should originally be a non-linear simultaneous equation, and systematized as a new methodology, so that only the least squares method is obtained. It was realized that the shape parameters could be measured stably and in a short time by methods such as minimum area / maximum inscribed / minimum circumscribed, which were impossible in the past. Furthermore, the direction of error evaluation of the shape parameter is always taken to be the surface normal vector direction of the target shape, and theoretical shape data required in the calculation process is calculated from drawing data or shape data designed by a CAD system or the like. Many functions were realized, such as the method of extracting and using, the method of direct input by the operator, or the method of inputting only the shape type.

[0011]

As described above, if a normal spherical lens is used, it is 1 nm by the optical interferometry method.
The shape evaluation is realized with the following accuracy. However, recently, as the performance required for optical products has become more sophisticated, lenses with aspherical shapes have to be used frequently. However, in this optical interferometry method, it is possible to measure a free-form surface such as an aspherical lens.
It cannot be evaluated. Therefore, measurement of these aspherical lenses
Currently, the evaluation is performed by various other methods.
Among them, the shape evaluation method using a contact type coordinate measuring machine is often used because it is flexible and reliable even for various shapes.

In such a conventional contact-type coordinate measuring technique, the shape measurement data obtained by measurement is the center coordinate value of a spherical contactor (stylus), and the contactor and the non-measuring object are actually measured. It does not mean that the coordinate value of the contact position of is obtained. Therefore, when obtaining the shape parameter from this shape measurement data, after calculating the shape parameter that passes through the center coordinate value of the contact once, the calculated shape parameter is offset by the radius value of the stylus that is obtained in advance. I am taking the method of seeking. However, this method is based on the assumption that the contactor is a true sphere and its radius value does not change at any position of the contactor. Further, although there is no problem in the general geometric shape, it is not an easy technique to generate a strict offset surface offset from the calculated evaluation shape by the radius of the contact in the evaluation of the free-form surface.

Conventionally, the measuring accuracy itself of the coordinate measuring machine is 0.1.
Since it was about μm to several μm, the contactor was sufficiently within the range that could be regarded as a true sphere. In general, even a very well-finished contactor has a sphericity of about several tens of nm. Therefore, there is no problem if the required measurement accuracy is such that the sphericity of the contact can be ignored, but if the required accuracy becomes about 1 nm or less like an optical component such as an aspherical lens, the conventional method is used. It becomes impossible to deal with at all.

Further, when the required accuracy is about this level, dust and the like adhering to the object to be measured becomes a serious problem. Usually, the dust has a size of several tens nm to several μm. Further, in the shape measurement of a free-form surface such as an aspherical lens, measurement data of tens of thousands to millions of points can be obtained. Therefore, unless these abnormal measurement data are removed in advance from this enormous amount of shape measurement data, the influence of the abnormal measurement data cannot be directly obtained, and the original correct shape parameter cannot be obtained. I will end up. However, it is impossible in reality for humans to remove these abnormal measurement data from the data obtained by measuring optical components with diameters of several tens of millimeters to several hundreds of millimeters. I don't get it.

Further, as a geometrical tolerance representing the shape accuracy for a shape deviating from a general geometrical shape such as a free-form surface,
According to JIS / ISO and the like, what is called "surface contour degree" is specified. When obtaining the contour degree, the evaluation by the minimum area method must be performed instead of the evaluation by the least square method as described above. However, at present, it is a very difficult technique not only to evaluate the minimum area of a free-form surface, but also to evaluate by the method of least squares, and there are many techniques that can be realized only under very limited conditions.

The present invention has been made in view of the above problems, and provides a measuring method and apparatus for accurately and stably obtaining a shape parameter of a free-form surface, which is represented by an aspherical lens, and is free. The purpose is to enable accurate measurement and evaluation of the contour of curved surfaces.

[0017]

According to the present invention, when a shape parameter representing a free-form surface shape such as an aspherical lens and a metal mold for optical parts finished with high accuracy is accurately obtained by a contact type coordinate measuring machine. In response to the requirements, the shape accuracy is as accurate as required by optical theory, and JIS / IS
It is possible to realize a method and device that can be calculated by evaluation criteria (minimum area method, maximum inscribed method, minimum circumscribed method, etc.) according to standards such as O, and that can evaluate the tolerance of the contour degree for a free-form surface We recognized that this is the most important issue for maintaining the required performance for the increasingly sophisticated optical products, and have achieved the results of our earnest research.

That is, according to claim 1 of the present invention, the mathematical theoretical shape of the shape measurement data consisting of the center coordinates of the contactor, which is obtained by bringing the contactor into contact with the object to be measured having a multidimensional shape, In the measuring method for determining the shape parameter of the multidimensional shape by performing the alignment of the first shape, the first step of giving the theoretical shape corresponding to the shape measurement data, and the abnormal shape measurement data from the shape measurement data. From the calculated result, a second step of removing, a third step of obtaining a normal vector and a foot of a perpendicular to the theoretical shape of the shape measurement data, and further calculating a normal direction error amount thereof, A fourth step of calculating a contact point between the contactor and the theoretical shape and a correction amount of the sphericity of the contactor, and correcting the error amount in the normal direction at that time, the shape measurement data and the theoretical shape. The fifth step of calculating the translational movement amount or the rotational movement amount of the theoretical shape and the translational movement amount or the rotational movement amount of the theoretical shape so as to reduce the error in the normal direction between the theoretical shape and the theoretical shape are translated or rotated. Based on the sixth step, the seventh step of comparing the translational movement amount or the rotational movement amount with these preset values, and the result of the comparison determination in the seventh step, the third and the third From the 8th step of repeating the 4th, 5th, 6th, and 7th steps and the 9th step of calculating the shape parameter at that time based on the result of comparison and judgment in the 7th step, the contactor is directly activated. It is characterized in that shape parameters are obtained by correcting the radius and the sphericity.

According to claim 2 of the present invention, in addition to claim 1, the second step of removing the abnormal measurement data is the third, fifth, sixth, seventh, eighth and ninth steps. A tenth step of calculating a threshold value of the normal direction error amount from the shape parameter calculated by the step and the normal direction error amount, and an eleventh step of sieving the target shape measurement data by the threshold value. And a twelfth step of comparing and determining the difference between the calculated shape parameter and the previously calculated shape parameter with a preset value, and the third and third values based on the result of the comparison and determination in the twelfth step. 5, 6th, 7th,
It is composed of eighth and ninth steps, a thirteenth step of repeating the tenth, eleventh and twelfth steps, and a fourteenth step of using the shape data screened by the twelfth step as new shape data. .

Further, according to claim 3 of the present invention, claim 1
In addition, the fourth step of calculating the correction amount of the sphericity of the contact from the previously obtained radius value and the normal vector and correcting the normal direction error at that time is the normal vector. And a fifteenth step of calculating a correction amount for correcting the sphericity of the contact corresponding to the normal vector from the correction data of the sphericity created in advance, and the calculated correction amount and the A 16th step in which a value obtained by subtracting the effective radius of a given contactor is set as a new normal direction error amount.

According to claim 4 of the present invention, in addition to claim 2, the sphericity of the contact corresponding to the normal vector is calculated from the normal vector and correction data of the sphericity created in advance. The fifteenth aspect for calculating a correction amount for correction
In the step, a spherical prototype having a known sphericity is measured in advance, and the obtained shape data and the shape parameters obtained in the third, fifth, sixth, seventh, and eighth steps are used. A seventeenth step of calculating a contact point between the contactor and the spherical prototype and a normal direction error at that point, and an eighteenth step of relating the normal direction error to the surface position of the contactor,
Using the associated normal direction error, it is possible to calculate the sphericity correction amount of the contact in the linear direction from the center coordinate value of the contact and the straight line in the direction of the normal vector passing through the center position. And the nineteenth step of changing to the mathematical form

A fifth aspect of the present invention is obtained by bringing a contactor into contact with an object to be measured having a multidimensional shape.
In the measuring device for obtaining the shape parameter of the multidimensional shape by aligning the mathematical theoretical shape with respect to the shape measuring data composed of the center coordinates of the contact, the theoretical shape corresponding to the shape measuring data. And a second means for removing abnormal shape measurement data from the shape measurement data, a normal vector of the shape measurement data to the theoretical shape, and a foot of a perpendicular line,
Further, the third means for calculating the normal direction error amount and the correction amount of the contact point between the contactor and the theoretical shape and the sphericity of the contactor are calculated from the calculation result, and the normal direction error amount at that time is calculated. And a fifth means for calculating a translational movement amount or a rotational movement amount of the theoretical shape so that an error in a normal direction between the shape measurement data and the theoretical shape becomes small. Sixth means for translating or rotating the theoretical shape with a moving amount or a rotational moving amount, and a seventh means for comparing and judging the translational moving amount or the rotational moving amount with these preset values, According to the result of comparison and judgment by the seventh means, the third,
Eighth means for repeating the fourth, fifth, sixth and seventh means, and ninth means for calculating the shape parameter at that time based on the result of comparison and judgment by the seventh means are provided, and the contactor is directly connected. It is characterized in that shape parameters are obtained by correcting the effective radius and the sphericity of.

[0023]

According to the present invention, even if the contactor is required to have a required accuracy such that it cannot be regarded as a true sphere, a method of correcting it and a method of removing abnormal measurement data, and a method of directly measuring the center coordinate value of the contactor By devising a method to calculate the shape parameter of the target shape, it is possible to calculate the accurate shape parameter not only for the general geometric shape but also for the free-form surface with a high degree of accuracy that cannot be achieved by the conventional method. It was made possible. Further, in the present invention, since the shape evaluation based on the minimum area method standard for the free-form surface shape is possible, it is also possible to evaluate the "surface contour degree" tolerance according to the standards such as JIS / ISO.

Of course, the present invention is similar to the prior invention,
Since the direction of error evaluation of the shape parameter is always performed in the direction of the surface normal vector of the target shape, very accurate evaluation is possible.

[0025]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a method and apparatus for measuring a highly accurate shape parameter of a multidimensional shape according to the present invention will be described in detail below with reference to the drawings. In the present invention, a free curved surface shape such as an aspherical lens will be mainly described as an example, but general geometric shapes such as a spherical surface and a flat surface can be evaluated by the same method.

FIG. 1 shows an example of a basic theory for obtaining the amount of movement and rotation of the measured object with respect to the theoretical shape, based on the measured data of the shape of the measured object. Although this theory is explained in the prior invention, it will be explained because it is used in the present invention as well. First, the position vector of the i-th measurement point of the shape measurement data composed of N measurement points is Mi, the corresponding position vector of the theoretical point on the theoretical shape before alignment is Mthi, and the theoretical shape at that position Let ni be the unit normal vector of M, and Mopt be the position vector of the theoretical point on the theoretical shape after alignment. The vector from Mthi to Mopt is DMthi.

Here, the amount (the amount of translation and the amount of rotation) relating to the alignment is very small, and the unit normal vector ni on the theoretical point Mthi before the alignment and the theoretical point M after the alignment.
It is assumed that the direction of the unit normal vector on opt does not change. Under this assumption, the error amount ei between the basic theoretical shape after alignment and the measurement point is expressed by the following equation.

[0028]

[Equation 1]

Here, the symbol “·” in the equation represents the inner product of two vectors. Further, it is possible to express the DMthi of Expression 1 by the following equation, where A is an arbitrary reference position (vector) of the theoretical shape on the assumption that the amount of alignment is minute.

[0030]

[Equation 2]

Here, VMA is a vector from the theoretical point Mthi to an arbitrary reference position A. DA is a vector representing the translation amount of A and R is a vector representing the rotation amount around A. The symbol "x" in the equation represents the cross product of two vectors. Also, DA
The two vectors R and R are collectively called the screw vector. In a three-dimensional space, these two vectors can also be expressed as the following equation.

[0032]

(Equation 3)

Here, dx, dy and dz are coordinate components of the translation vector in the three-dimensional space, and u, v and w are coordinate components of the rotation vector. Substituting the equation 2 into the equation 1, the following equation 4 is obtained. Here, VAM is a vector obtained by inverting the vector VMA.

[0034]

[Equation 4]

In other words, the expression 4 represents the error amount after the alignment between the measurement point and the basic theoretical shape. By applying this number 4 to all measurement points,
DA and R are unknown variables (total number of elements in 3D space is 6)
It will be an individual, the following will proceed with the assumption of a three-dimensional space)
Thus, N simultaneous linear equations are obtained. Therefore, according to this theoretical formula, if there are at least six measurement points, each element of the unknown variables DA and R can be determined.

When the number of measuring points is 6, DA and R are uniquely determined by directly solving the simultaneous linear equations. However, if the number of measurement points is more than 6,
By applying various evaluation functions when solving this system of linear equations, various solutions according to the evaluation functions can be obtained.Here, the number of evaluation functions is Consider minimizing the ei of 4. There are various ways to minimize it, but here J
An evaluation function in the case of evaluating a spherical surface is shown by taking the least square method and the minimum area method defined by standards such as IS and ANSI as examples.

(1) Least square method

[0038]

(Equation 5)

(2) In case of the minimum area method

[0040]

(Equation 6)

Here, r represents the radius of the sphere. Also max
() Means to find the variable in parentheses that maximizes W. Therefore, by applying the equation (4) to all the measurement data, creating N simultaneous linear equations and solving them according to the evaluation function of the equation (5) or (6), the amount of movement and rotation with respect to the theoretical shape can be obtained. . When obtaining a solution with the evaluation function of Equation 5, the coefficient matrix of simultaneous linear equations may be solved by a generally known matrix solution method. Further, when the solution is obtained by the evaluation function of the equation 6, simultaneous linear equations may be solved by the linear programming method. The above is the basic theory for aligning the measurement point and the theoretical shape.

However, when considering the actual shape measurement and its evaluation, the assumption that "the amount relating to the alignment (the amount of translation and the amount of rotation) is minute", which is a prerequisite of the above theory, does not generally hold. . Therefore, in the invention of the prior application, the above theory is used as a method for alignment,
By applying the iterative theory to this and developing it as a new theoretical system, the shape can be evaluated even when the above process is not established.

FIG. 2 is a flowchart showing the procedure of the shape parameter measuring method according to the present invention. In this method, the theoretical shape, shape measurement data, sphericity correction data, and evaluation type (least square method / minimum area method / maximum inscribed method / minimum circumscribed method) are input as the first step (201). still,
The sphericity correction data will be described later. Then the second
The rough alignment of the theoretical shape and the shape measurement data input as the step of is executed. Usually, the theoretical shape is defined on a virtual coordinate system created at the design stage, and therefore does not match the unique coordinate system of the actual coordinate measuring machine. Therefore, it is necessary to roughly align the shape measurement data and the theoretical shape before actually performing shape evaluation. At that time, if all of the input shape measurement data of several million points is used, a huge amount of time is required for calculation processing. At this point, alignment is sufficient so as not to cause any inconvenience in later evaluation calculation, so an appropriate number of data is extracted from the input shape data (202), and the data and the theoretical shape are roughly used. Perform proper alignment (2
03).

When extracting the shape measurement data, the minimum number of points representing the shape may be used. For example, four points are enough for a spherical surface. However, since such a minimum number of points cannot be determined in a free-form surface, it is said that the input shape data is several tenths to several hundredths, or several hundreds of all the data. As a matter of fact, the method of thinning out at an appropriate interval that is sufficient to represent the theoretical shape is the simplest.

After the rough alignment is completed, abnormal data such as dust is removed as the third step (204). FIG. 3 shows the principle of this removing method.
As described above, the deviation amount at the measurement point affected by the foreign matter such as dust is several tens to several hundred times larger than the deviation amount at the normal measurement point. If the number of abnormal points is relatively small compared to the normal measurement points, even if the shape evaluation by the least squares method is executed as it is, the deviation of the abnormal points will be larger than other points due to the error averaging effect. . Therefore, the abnormal point removing method is realized by performing shape evaluation by the method of least squares and separating and removing the deviation amount of each point obtained from the result by a predetermined threshold value. However, this process does not have to be performed once, and needs to be repeated several times until the evaluation shape by the least squares method does not change.

FIG. 4 shows a flowchart for performing this abnormal point processing. First, data is input and each initial setting is performed (401). Next, the shape evaluation is executed from the input shape measurement data and the theoretical shape by the least square method using the evaluation method of the present invention described below (without correcting the sphericity) (402). Next, the deviation amount (error amount in the normal direction) at all measurement points is calculated from the obtained evaluation shape and the input shape measurement data, and the threshold value is determined from this deviation amount. It is generally known that the random error has a normal distribution. Therefore, the value of the standard deviation σ is obtained from this deviation amount, and the amount (3σ) obtained by multiplying this value by 3 is obtained as the threshold value (403). Note that various methods other than the above method can be considered for obtaining this threshold value, but the above example is given as the simplest method. Next, compare the threshold value and the deviation amount of each point, and exclude the points deviating from the threshold value (mark,
Processing is performed to make it possible to distinguish from a normal point (404).
Using the shape measurement data thus discriminated, shape evaluation by the least squares method is repeatedly executed again. The shape evaluation result obtained in this way is compared with the previous shape evaluation result (405) and repeated until the difference becomes sufficiently small. This makes it possible to automatically remove abnormal data.

Ideally, it is best to repeat until there is no difference in the shape evaluation results, but if the object to be measured is a very well-finished object such as an aspherical lens, it will be practically repeated several times. Repeat is enough. With the above, selection of normal data and abnormal data is completed. Returning to FIG. 2 again, as the fourth step, the original shape evaluation is started. Note that this flowchart is drawn on the assumption that an evaluation shape by the minimum area method is obtained as an evaluation reference. Therefore, first, the shape evaluation is performed by the least square method (205). If the required evaluation criterion is the least squares method, the shape parameter is output from the evaluation result obtained at this stage, and the processing is ended (207).

Finally, as a fifth step, when the required evaluation criterion is the minimum area method (surface contour degree), the evaluation result obtained by the least squares method in the preceding stage is used as the initial theoretical shape.
The shape is evaluated according to the minimum area method standard (208).
Then, the final shape parameter based on the minimum area method standard is output from the obtained evaluation result (209). In the case of performing the minimum area method evaluation, a method of executing the evaluation by the minimum area method after once executing the evaluation by the least square method and obtaining a result, using this evaluation shape as an initial theoretical shape. In this way, the initial theoretical shape that is sufficiently close to the true value is obtained rather than performing the evaluation by the minimum area method from the beginning, so that the solution can be obtained more stably.
The above is the overall processing procedure of the shape evaluation method according to the present invention.

Next, a shape evaluation method to which the sphericity correction of the contact according to the present invention is added will be described. 5 and 6 are flowcharts showing the procedure of this method. The shape parameter measuring method according to the present invention uses the above-mentioned theory as one theory for alignment as in the prior invention. First, as the first step, the initial theoretical shape, shape data, sphericity correction data, and evaluation type are input (501). In the present invention, the theoretical shape input here is already aligned by the above-described initial alignment or least squares method evaluation to such an extent that it does not hinder subsequent processing. After that, initial setting of each set value is performed (502).

Next, as a second step, the foot of the normal line from the shape measurement data to the theoretical shape, the normal vector, and the normal direction distance (error amount) are calculated for each coordinate value of each point according to the above theory ( 503). Of course, since the shape measurement data is the center coordinate value of the contact, this error amount includes the average radius of the contact, the sphericity error, and the original shape error. Therefore, if the average radius and the sphericity error can be removed from the error amount obtained here, the shape can be evaluated directly with the original error amount.

Therefore, the sphericity error in the direction of the normal vector is calculated from the normal vector calculated as the third step and the sphericity correction data (504). The contactor is fixed with respect to the coordinate system of the coordinate measuring machine, and the normal vector is obtained as a vector on this coordinate measuring machine.
Therefore, the sphericity correction data may be of any format as long as it can determine the error amount in the normal direction of the contact in this direction from the straight line in the direction of the normal vector passing through the center coordinate value of the contact.

FIG. 7 shows an example of the sphericity correction data and the correction amount calculation method. Usually, as a method for realizing this, data of the error amount in the normal direction corresponding to the surface position of the contact (stylus) is prepared, and based on this, the free-form surface patch (702) on the surface of the contact. It may be stored and held as mathematical data, such as expressed as. The radius of the contactor and the sphericity correction amount are obtained as the distance from the intersection point (705) of the free-form surface patch and the normal line to the center coordinate value (703) of the contactor.
In this way, if the sphericity correction data is represented by the free-form surface patch, the radius and the correction amount can be directly calculated from the intersection coordinate and the center coordinate value.

Next, returning to FIG. 5, as the fourth step, the coordinate value of the contact point is calculated from the shape measurement data, the normal vector and the radius value / correction amount (505), and that point is given to the theoretical shape. It is determined whether or not it is within the specified area (506). The shape measurement data is the center coordinate value of the contact. Therefore, from this point, the point offset by the correction amount and the radius of the contact in the direction opposite to the normal vector is approximately (because there are errors in the spherical prototype and other errors in practice) to be measured. It can be regarded as a point of contact with an object. Therefore, if the coordinate value is outside the area, the data is not used for calculation and is not used for shape evaluation. This process is not necessary when simply evaluating the shape, but the contour area of the surface may specify the evaluation area for the design value shape. The inside / outside determination of this area is a process corresponding to the standard of this geometrical tolerance evaluation.

As a fifth step, using the obtained sphericity correction amount and contactor radius, a value obtained by subtracting these amounts from the normal direction distance obtained in the second step is used as a new normal line. As the direction error amount (507), the equation of the equation 4 is created (60
1). Then, a coefficient matrix is created from the coefficients of this equation, and the matrix is solved by a method according to the input evaluation standard (602). At this time, if there is no solution, the subsequent processing is interrupted and the processing ends (603).

In the sixth step, if a solution exists, the amount of movement and rotation of the theoretical shape is calculated from this result, and in the sixth step, the theoretical shape is moved / rotated (60).
5). After that, this movement and rotation amount is compared with a preset numerical value (606), and when it is smaller than the set value, it is considered that the solution has sufficiently converged, and the theoretical shape at that time is used to determine a predetermined shape parameter. Is calculated and the processing ends (607). If it is larger than the set value,
The number of repetitions is increased by 1 (608), and the processing of the second and subsequent steps is repeated again. At this time, the number of repetitions is compared with a preset number of times, and if the number of repetitions is larger than the set number of times, it is determined that the solution does not converge and the process is interrupted and terminated (610).

The above is the method for directly evaluating the shape from the shape measurement data while correcting the sphericity error of the contact and also correcting the radius value thereof. Next, a method of creating the above-mentioned sphericity correction data will be described. FIG. 8 shows a flowchart of this data creating method. At present, with a normal spherical lens, it is possible to evaluate the shape of the lens with an accuracy of about λ / 10000 (where λ is the wavelength of light) by an optical interferometry method using spherical waves. It is also possible to create a highly accurate spherical lens. Therefore, the sphericity correction data of the contactor can be obtained by actually measuring the spherical lens (spherical prototype) that is finished with high accuracy in this way and actually measuring it. Take the method of creating from data.

In this method, first, as a first step, the surface of the spherical prototype is measured in a pattern in which it is easy to create the required sphericity correction data, and the center coordinate value of the contact is obtained. (801). At this time, measure so that the shape measurement data is in a mesh shape with equal intervals, or
The method of measuring in two directions orthogonal to each other by the scan method of equal intervals is convenient for the subsequent calculation processing as a free-form surface patch by splines.

Next, the shape measurement data of the spherical prototype obtained as the second step is subjected to spherical evaluation based on the minimum area standard according to the above-mentioned evaluation procedure (802), and the normal line for each point. The vector and the normal direction distance (error amount) are calculated (803). However, at this time, calculation is performed without correcting the radius of the contactor and the sphericity. Further, the coordinate value of the contact point between the spherical prototype and the contact is calculated from this result (804). As a result, the error amount is obtained as an amount with respect to the ideal spherical surface that passes through the center coordinate value of the contact, but since the spherical prototype is a spherical surface finished with high accuracy, the ideal spherical surface of the contact is practically used. Can be considered equivalent to the amount of error from. If the radius of the spherical prototype is accurately obtained at this point, subtract the radius of the spherical prototype from the radius obtained when performing the above-mentioned evaluation of the spherical surface to obtain the radius of the contact at the same time. The value can also be calculated.

As a third step, a process for associating the obtained error amount with the surface of the contactor is performed (805). The most suitable method for this association is to create the sphericity correction data as a free-form surface patch using a spline curved surface. As described above, when the spherical surface evaluation is executed, the foot of the normal to the ideal spherical surface and the normal vector are obtained from the shape measurement data at that time. Since the shape measurement data is the center coordinate value of the contact, it is approximate that the point is offset from this point in the direction opposite to the normal vector by the radius of the contact and the error amount at that point is offset. , It can be regarded as the contact point between the spherical prototype and the contactor (80
4). Therefore, if this offset point is obtained for all measurement data and a spline curved surface passing through this point is created (8
06), which is the sphericity correction data directly associated with the spherical surface of the contactor. The method of creating the spline curved surface from the passing points is described in various books and papers, and therefore will not be described here. As described above, if the spherical prototype is measured so as to form a mesh shape with equal intervals on the spherical surface, the process of creating the interpolation curved surface by the spline becomes easy.

Originally, the sphericity correction data only needs to be able to calculate the correction value of the radius value from the center coordinate value of the contactor and the normal vector at the contact point with the object to be measured. The same effect can be obtained regardless of the computer format. As described above, by these methods, it is possible to evaluate the shape of an arbitrary free-form surface within the accuracy of the spherical prototype. Moreover, according to the present invention, since the shape can be evaluated by the minimum area method in addition to the least square method, it is possible to accurately evaluate the contour degree of the surface defined by JIS / ISO or the like.

FIG. 9 is a block diagram showing a preferred embodiment of the shape parameter measuring apparatus according to the present invention. The CAD (901) is a device for designing a work (object to be measured), and drawing data or shape data is input by the designer. The first storage means (902) is C
The drawing data or shape data of the work created by AD is stored. The (coordinate) measuring machine (905) is a device for measuring the actual shape element of the work. Second storage means (9
06) stores the measurement data of the actual shape obtained by the measuring machine as a coordinate value data group of measurement points for each actual shape element.

The display means (904) is composed of a display, a printer, a dedicated display device, an external output device such as a communication device, and displays or outputs various data such as characters and figures output from this device (919). It is a device. The input means (903) is a means such as a keyboard, a mouse, a communication device, etc. for inputting data from the operator or the outside to this device.

The shape data input means (907) inputs the data of the first storage means and stores it in the third storage means (908). The measurement data input means (911) inputs the measurement data stored in the second storage means, and the fifth storage means (91)
Store in 2). The theoretical shape designating means (910) allows the operator to interactively use the input means while displaying the figure or information on the display means if the data of the target work is stored in the third storage means. Extract the theoretical shape data required for or input the required data directly. The fourth storage means (909) stores the data designated by the theoretical shape designation means. The correction data creation means (913) creates the sphericity correction data by the above-mentioned method from the measurement data of the spherical prototype stored in the fifth storage means. Seventh storage means (914)
Stores the sphericity correction data created here. The initial positioning means (915) performs rough initial positioning based on the measurement data in the object to be measured stored in the fifth storage means and the theoretical shape stored in the fourth storage means, and the result is calculated as follows. Pass to processing. Abnormal point removal means (916)
In accordance with the method described above, removes abnormal measurement data from the initially positioned theoretical shape and measurement data, and passes the result to the next process. The shape evaluation means (917) performs shape evaluation according to a predetermined evaluation standard from the measurement data from which the abnormal points have been removed and the theoretical shape, calculates shape parameters at that time, and stores the shape parameters in the sixth storage means (918). . Then, the shape evaluation result stored in the sixth storage means is displayed on the display means in accordance with an instruction from the input means or the like.

The shape data input means (90 described above)
7), third storage means (908), fourth storage means (90)
9), theoretical shape designation means (910), measurement data input means (911), fifth storage means (912), correction data creation means (913), seventh storage means (914), initial positioning means (915), The abnormal point removal means (916), the shape evaluation means (917), the sixth storage means (918), the input means (903), and the display means (904) are the shape measuring device (9).
19). The measuring device (919) is preferably composed of an electronic computer.

[0065]

According to the present invention, in the shape evaluation of a multi-dimensional shape by a coordinate measuring machine, the required accuracy is such that the contact cannot be regarded as a true sphere, which is completely impossible by the conventional method. In addition, it is possible to stably calculate the shape parameters of not only the general geometric shape but also the free curved surface with the same accuracy as that of the spherical prototype.

Further, according to the present invention, the shape evaluation based on the minimum area method standard for the free-form surface shape is made possible.
It is also possible to evaluate the "face contour" tolerance according to standards such as S / ISO. Of course, in the present invention, as in the case of the prior invention, the direction of the error evaluation of the shape parameter is always performed in the direction of the surface normal vector of the target shape, and therefore a very accurate evaluation becomes possible.

[Brief description of drawings]

FIG. 1 is a diagram showing a basic theory for alignment in the present invention.

FIG. 2 is a flowchart showing the overall procedure of a shape evaluation method according to the present invention.

FIG. 3 is a diagram showing the principle of an abnormal point removing method.

FIG. 4 is a flowchart showing a procedure of an abnormal point removing method.

FIG. 5 is a flowchart showing a procedure of a shape evaluation method in which sphericity correction is added.

FIG. 6 is a flowchart showing a procedure of a shape evaluation method in which sphericity correction is added.

FIG. 7 is a diagram showing a method of calculating sphericity correction data and a correction amount.

FIG. 8 is a flowchart showing a method of creating sphericity correction data.

FIG. 9 is a diagram showing a configuration example of a shape evaluation apparatus according to the present invention.

Claims (5)

[Claims] 1. The position of the mathematical theoretical shape of the shape measurement data, which is obtained by bringing the contact into contact with an object to be measured having a multidimensional shape, and which is composed of the center coordinates of the contact, In the measuring method for obtaining the shape parameter of the multidimensional shape, a first step of giving the theoretical shape corresponding to the shape measurement data, a second step of removing abnormal shape measurement data from the shape measurement data, A third step of obtaining a normal vector and a foot of a perpendicular to the theoretical shape of the shape measurement data, and further calculating an error amount in the normal direction, and a contact between the contactor and the theoretical shape from the calculated result. The fourth step of calculating the correction amount of the sphericity of the point and the contact and correcting the error amount in the normal direction at that time, and reducing the error in the normal direction between the shape measurement data and the theoretical shape. Thus, a fifth step of calculating the translational movement amount or the rotational movement amount of the theoretical shape, a sixth step of translating or rotating the theoretical shape with the translational movement amount or the rotational movement amount, and the translational movement amount Alternatively, according to the seventh step of comparing and determining the rotational movement amount with these preset values, and the result of the comparison and determination in the seventh step, the third, fourth, fifth, sixth, 8th which repeats 7 steps
The shape parameter in which the effective radius and the sphericity of the contactor are directly corrected is obtained from the step and the ninth step of calculating the shape parameter at that time based on the result of comparison and judgment in the seventh step. Measuring method of shape parameter of multidimensional shape. 2. The second step of removing the abnormal measurement data includes the shape parameter calculated in the third, fifth, sixth, seventh, eighth and ninth steps and the normal direction error amount. From the above, a tenth step of calculating the threshold value of the normal direction error amount, an eleventh step of sieving the target shape measurement data by the threshold value, the calculated shape parameter and the shape calculated last time A twelfth step of comparing and judging a difference with a parameter with a preset value, and the third, fifth, sixth, seventh, eighth and ninth steps depending on the result of the comparison and judgment in the twelfth step. And the first
The thirteenth step of repeating 0th, the eleventh, and the twelfth step, and the fourteenth step of using the shape data screened by the twelfth step as new shape data. Shape parameter measurement method. 3. The fourth step of calculating the correction amount of the sphericity of the contactor from the previously obtained radius value and the normal vector and correcting the normal direction error at that time, A fifteenth step of calculating a correction amount for correcting the sphericity of the contact corresponding to the normal vector from the line vector and the correction data of the sphericity created in advance, and the calculated correction amount. The shape parameter measuring method according to claim 1, further comprising: a 16th step in which a value obtained by subtracting an effective radius of a contact given in advance is used as a new normal direction error amount. 4. The fifteenth step of calculating a correction amount for correcting the sphericity of a contact corresponding to the normal vector from the normal vector and correction data of the sphericity created in advance. In, the spherical prototype of which sphericity is known in advance is measured, and from the obtained shape data and the shape parameters obtained in the third, fifth, sixth, seventh, and eighth steps,
A seventeenth step of calculating a contact point between the contactor and the spherical prototype and a normal direction error at that point, and a first step of making the normal direction error correspond to the surface position of the contactor
8 steps, and using the associated normal direction error, from the center coordinate value of the contact and the straight line in the direction of the normal vector passing through the center position, correct the sphericity of the contact in the straight direction. The shape parameter measuring method according to claim 2, further comprising: a nineteenth step of changing the quantity into a mathematical form capable of being calculated. 5. The position of the mathematical theoretical shape is aligned with the shape measurement data consisting of the center coordinates of the contact, which is obtained by bringing the contact into contact with an object to be measured having a multidimensional shape, In the measuring device for obtaining the shape parameter of the multidimensional shape, first means for giving the theoretical shape corresponding to the shape measurement data, and second means for removing abnormal shape measurement data from the shape measurement data, Third means for obtaining a normal vector and a perpendicular foot to the theoretical shape of the shape measurement data, and further calculating an amount of error in the normal direction thereof, and a contact point between the contactor and the theoretical shape from the calculation result, and Fourth means for calculating the correction amount of the sphericity of the contact and correcting the error amount in the normal direction at that time, and reducing the error in the normal direction between the shape measurement data and the theoretical shape. Fifth means for calculating a translational movement amount or a rotational movement amount of the theoretical shape; a sixth means for translating or rotating the theoretical shape with the translational movement amount or a rotational movement amount; and a translational movement amount or the rotation amount. The seventh, fourth, fifth, sixth, and seventh means are again determined by the seventh means for comparing and determining the amount of movement and these preset values, and the result of the comparison and determination by the seventh means. Repeat 8th
And a ninth means for calculating the shape parameter at that time on the basis of the result of comparison and determination by the seventh means, and directly obtaining the shape parameter in which the effective radius and sphericity of the contactor are corrected. Characteristic multi-dimensional shape parameter measuring device.