JP4564632B2 - Shape evaluation method and component manufacturing method - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method and an apparatus for measuring and evaluating a curved surface shape such as a lens, a mirror, and a prism precisely, for example, with an error of 1 micrometer or less, and a method for correcting the result based on the result. In particular, the present invention can be satisfactorily applied to shape evaluation and correction processing of parts having a plurality of curved surfaces.
[0002]
[Prior art]
Generally, when measuring the shape of an object to be measured with a three-dimensional shape measuring device or the like, it is not possible to know exactly where the object to be measured is attached to the coordinate system of the measuring device. Therefore, conventionally, measurement has been performed in the form disclosed in Japanese Patent Publication No. 2520202. This will be described below.
[0003]
The point cloud measured with a 3D coordinate measuring device is moved to best fit the design shape. At this time, the amount by which the point cloud is moved is called a setting error, and the best fit by moving the point cloud is called setting error correction. In general, there are six degrees of freedom for setting errors in terms of X, Y, and Z translation and rotation around that axis.
Referring to FIG. 21, first, in (a), S is a measured free-form surface and is expressed in the coordinate system G1, and Q is expressed in a coordinate form G2 as a design point. Change the Q coordinate system G2 (b) to match S and Q as shown in the figure. At this time, the difference between G2 and G1 is a setting error. As described above, this setting error consists of six parameters.
[0004]
FIG. 22 is a flowchart showing this conventional calculation operation.
First, a point group {p} as a shape measurement result is measured and prepared by a three-dimensional shape measuring device or the like (1101). A design shape d is prepared (1102). Next, an initial value is substituted for the parameter α of the setting error (1103). Using the coordinate transformation function F including this parameter α, the measurement point group {p} is transformed into {q} (1104).
[0005]
Next, the evaluation value f (q, d) is calculated (1105). When this evaluation value does not change in the repeated loop, it is determined that the evaluation value has converged (1106). If the convergence is determined in 1106, the design shape is subtracted (1108), an error shape is obtained (1109), and the parameter α at the time of convergence becomes the setting error (1110). On the other hand, in the convergence determination of 1106, if it does not converge, the parameter correction amount dα is obtained so as to improve the evaluation value (1107), and the process is repeated from the step 1104 again with the corrected parameter (1111).
[0006]
Here, the evaluation function of 1106 is the sum of squares of the difference between the measurement point {p} and the design shape d, and the parameter correction amount of 1107 is calculated under the condition that the evaluation value stays with respect to the parameter correction amount. The method is least squares and is widely applied (references: Mahito Negishi, Manabu Ando, Masahumi Takimoto, Akinobu Deguchi, Hiroji Narumi, Nobuo Nakamura and Hironori Yamamoto: An On-Machine Coordinate Measuring System for the Canon Super Smooth Polisher SICE '94 Tokyo (1994), 941).
[0007]
FIG. 3 shows an example of a lens whose upper surface is a free-form surface and whose lower surface is a plane. (A) The figure shows the design shape. In the figure, h is the thickness of the lens, and this value usually allows some variation. That is, an allowable error is taken into consideration at the lens design stage. (B) The figure shows the measurement points. For the sake of simplicity of explanation, it is assumed that the shape error is zero, and there is only a tilt error as shown in the figure. Consider modifying the measured lens shape. First, the setting error and the shape error are calculated according to the procedure described so far.
[0008]
Based on this calculation result, FIG. 4 illustrates the calculation of the correction machining amount. First, when processing the upper surface (FIG. (A)), the measurement point on the lower surface and the design shape are fitted to obtain the difference between the measurement point on the upper surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed. When processing the lower surface (FIG. (B)), the measurement point on the upper surface and the design shape are fitted to obtain the difference between the measurement point on the lower surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed.
[0009]
FIG. 6 shows an example of a lens whose upper surface is a free-form surface and whose lower surface is a spherical surface. (A) The figure shows the design shape. In the figure, h is the thickness of the lens, and as before, this value allows some changes. (B) The figure shows the measurement points. For the sake of simplicity of explanation, it is assumed that the shape error is zero, and there is only a tilt error as shown in the figure. Consider modifying the measured lens shape. First, the setting error and the shape error are calculated according to the procedure described so far.
Based on this calculation result, FIG. 7 illustrates the calculation of the correction machining amount.
[0010]
First, when processing the upper surface (FIG. (A)), the measurement point on the lower surface and the design shape are fitted to obtain the difference between the measurement point on the upper surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed. When processing the lower surface (FIG. (B)), the measurement point on the upper surface and the design shape are fitted to obtain the difference between the measurement point on the lower surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed.
[0011]
FIG. 9 shows an example of a lens whose upper surface is a free curved surface and whose lower surface is also a free curved surface. (A) The figure shows the design shape. In the figure, h is the thickness of the lens, and this value usually allows some variation. (B) The figure shows the measurement points. For the sake of simplicity of explanation, it is assumed that the shape error is zero, and there is only a tilt error as shown in the figure. Consider modifying the measured lens shape. First, the setting error and the shape error are calculated according to the procedure described so far. Based on this calculation result, FIG. 10 illustrates the calculation of the correction machining amount.
[0012]
First, when processing the upper surface (FIG. (A)), the measurement point on the lower surface and the design shape are fitted to obtain the difference between the measurement point on the upper surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed. When processing the lower surface (FIG. (B)), the measurement point on the upper surface and the design shape are fitted to obtain the difference between the measurement point on the lower surface and the design shape. Since the lens thickness of the design shape may be changed, the correction processing amount can be obtained by adjusting the thickness as shown in the figure. If the black portion in the figure is removed and processed, a lens of the desired shape is completed.
[0013]
[Problems to be solved by the invention]
However, the above conventional example has the following problems.
[0014]
(1) When measuring parts consisting of multiple curved surfaces, the correct setting error cannot be calculated. In addition, the position of the remaining surface should be calculated based on the position of two or more parts of a part consisting of multiple free-form curved surfaces. I can't.
[0015]
Consider the case of measuring the shape of a part consisting of multiple curved surfaces. The conventional method calculates the setting error for each surface and calculates the position of each surface. Since this setting error has 6 degrees of freedom as described above, it has 6n degrees of freedom in the case of a part having n surfaces. However, as described above, since there is only one setting error or mounting error for each part, it should be only 6 degrees of freedom (translation of X, Y, Z and rotation around its axis). That is, the setting error calculated by the conventional method does not mean the mounting error when the part is mounted on the measuring apparatus. If the correct setting error cannot be calculated, the error shape cannot be calculated correctly, so that the shape measurement accuracy deteriorates.
[0016]
For the above reasons, if there are two or more surfaces, the correct setting error cannot be calculated from the beginning, so the position reference cannot be calculated.
[0017]
(2) Setting error may not be calculated.
[0018]
For example, when a part having a plane portion is measured, the position in the direction horizontal to the plane is not determined originally. In other words, it is not possible to calculate even if the component is mounted with being shifted in that direction. This is shown in the flowchart of FIG. 22 earlier, which corresponds to the fact that in step 107, the parameter correction amount α for improving the evaluation value cannot be calculated. Similarly, when measuring a part with a spherical portion, the rotation about any axis including the center of rotation of the spherical surface is not determined. In other words, a setting error of 6 degrees of freedom cannot be calculated.
[0019]
(3) If abnormal data is included in the measurement points, the impact is significant.
[0020]
In a three-dimensional measuring apparatus, there are occasionally cases where abnormal values appear in measurement points due to the influence of minute dust trapped between the probe and the object to be measured. In such cases, the parameter estimates are affected and change due to the data.
[0021]
(4) The amount of correction is large when correcting a lens composed of a free curved surface and a plane, a lens composed of a free curved surface and a spherical surface, a lens composed of two free curved surfaces, a part composed of a polyhedral free curved surface, and the like.
[0022]
As shown in FIGS. 4 (a), 4 (b), 7 (a), 7 (b), 10 (a), and 10 (b), the amount of correction is large. That is, when the example of the above-described lens is generalized and described as a case where correction processing is performed on a part composed of a polyhedral free-form surface, the amount of correction increases when a design value is fitted to any one surface and the remaining difference is corrected. This is because there is no idea in the calculation method to reduce the correction amount. If the amount of correction is large, processing time is required, the lens cost increases, and a large number of processing devices are required. Further, if the correction amount is large, the correction amount error must be controlled to be small. For example, when considering a polishing process with 10% removal unevenness, a removal error of 0.1 μm occurs for a corrected removal amount of 1 μm. If the correction removal amount is 0.1 μm from the beginning, an error of 0.01 μm is sufficient. That is, since the correction amount is large, the machining accuracy is deteriorated.
[0023]
In view of the above-mentioned problems, the object of the present invention is to correctly calculate the setting error of a multi-part of various shapes and reduce the influence on abnormal values included in the measurement data, thereby reducing the shape error measurement accuracy. It is to make it possible to realize an appropriate process using this.
[0024]
[Means for Solving the Problems]
In order to achieve the above object, the shape evaluation method of the present invention comprises: a member having a plurality of surfaces; a three-dimensional shape measurement result for each of the plurality of surfaces; and a design shape for each of the plurality of surfaces. Obtaining error information between the shape measurement result and the design shape when coordinate conversion of the shape measurement result or the design shape is performed so that an evaluation value indicating a difference between the two is minimized. To do.
[0025]
The three-dimensional shape measurement result is preferably obtained as point cloud data.
[0026]
The coordinate transformation is preferably performed using a coordinate transformation matrix.
[0027]
The evaluation value is preferably a sum of square sums of shape differences between the shape measurement result and the design shape for each surface when coordinate conversion of the shape measurement result or the design shape is performed.
[0028]
A series of loops for correcting the coordinate conversion parameter or the parameter included in the design shape to a value in a direction in which the evaluation value does not change and obtaining the evaluation value when coordinate conversion is performed again after the correction is performed. The coordinate transformation that minimizes the evaluation value is preferably obtained by executing until the evaluation value converges.
[0029]
The plurality of surfaces are a plane and a free-form surface, and the coordinate transformation parameters are an out-of-plane direction position and a 2-direction surface inclination for the plane, and a 3-direction position and other-direction inclination for the free-form surface. preferable.
[0030]
Preferably, the plurality of surfaces are a spherical surface and a free-form surface, and the coordinate transformation parameters are a three-direction position for the spherical surface and a one-direction position and a three-direction inclination for the free-form surface.
[0031]
Preferably, one of the plurality of surfaces is an axisymmetric aspheric surface, and the coordinate transformation parameter relating to the axisymmetric aspheric surface is a position inclination of 5 degrees of freedom excluding rotation about the axis of the axisymmetric aspheric surface. .
[0032]
It is preferable that the thickness of the member is further used as the coordinate conversion parameter for each surface.
[0033]
Furthermore, the expansion / contraction rate of the member is preferably used as the coordinate conversion parameter.
[0034]
The plurality of surfaces are a plurality of curved surfaces, and a first evaluation value indicating a difference between the shape measurement result and the design shape with respect to a part of the curved surfaces, and the plurality of curved surfaces For the remaining curved surfaces, the sum of the shape measurement result obtained by performing the same first coordinate transformation as the partial curved surface and the second evaluation value indicating the difference between the design shapes is minimized. The shape measurement result for the partial curved surface or the first coordinate transformation of the design shape and the shape measurement result or the second of the design shape for which the first coordinate transformation for the remaining curved surface is executed. It is preferable to obtain a coordinate transformation.
[0035]
The component manufacturing method of the present invention for achieving the above object is characterized in that the member is processed so as to correct the error obtained by using any one of the above-described shape evaluation methods.
[0036]
In order to achieve the above object, a shape evaluation apparatus of the present invention is characterized in that the shape error of the member is evaluated using any one of the shape evaluation methods described above.
[0037]
DETAILED DESCRIPTION OF THE INVENTION
An outline of an embodiment of the present invention will be shown using the flowchart of FIG. Hereinafter, the steps shown in the flowchart are executed in a computer (not shown).
[0038]
First, a shape measurement data point group on each surface of a component composed of a plurality of surfaces is measured by a three-dimensional shape measuring device or the like and prepared. In FIG. 1, a part consisting of two surfaces is assumed, and respective measurement data point groups {p1} and {p2} are prepared ((101a) and (101b)). Meanwhile, two design shapes d 1 and d 2 are prepared ((102a) and (102b)).
[0039]
An initial value is substituted for a parameter α representing a setting error (103). Using the coordinate transformation function F including the parameter α, the measurement point group {p1} is transformed into {q1} (104a). Similarly, the coordinate transformation function F including the parameter α is used to coordinate the measurement point group {p2} to {q2} (104b).
[0040]
Next, a sum f (q1, d1) + f (q2, d2) of evaluation values for each measurement surface is calculated (105). Next, convergence determination is performed (106). The determination method of convergence is determined by the fact that the evaluation value is not changed in the iteration loop. It is determined that only the first time does not converge unconditionally. If the convergence is determined in the convergence determination of 106, the design shape is subtracted from the first surface (108a), and the error shape of the first surface is obtained (109a). For the second surface, the design shape is subtracted (108b) to obtain the error shape of the second surface (109b). Also, the parameter α when converged is the setting error, (110).
[0041]
On the other hand, in the convergence determination of 106, if the convergence does not occur, the parameter correction amount δ is improved so that the evaluation value improves._α(107) and repeat the process from step 104 again with the corrected parameter (111). Where F is δ_αIt can be seen as a function with. The condition for stopping F (maximum or minimum) is δ_αThe partial derivative with respect to 0 becomes 0, that is, ∂F (α) / ∂δ_α= 0. (T.R. McCarra Original Science Library Information Computer = 8 Introduction to Numerical Computation for Computers, published by Science Co., Ltd., page 227 (see 8.3.8)) Here, 105 evaluation functions are measured points It is defined as the square of the difference between {p1} and {p2} and the design shapes d1 and d2, and in the parameter correction amount calculation of 107, the method of calculating under the condition that the evaluation function is stationary with respect to the parameter correction amount is the minimum This is a square method (see the first embodiment described later).
[0042]
When calculated in this way, unlike the conventional example, the parameter α representing a setting error of 6 degrees of freedom can be calculated using a plurality of surfaces, and thus the above-described problem does not occur. In addition, even if the shape of the first surface is a plane and the shape cannot be defined with 6 degrees of freedom, the evaluation function is defined using the data of the second surface. Is possible. Since the setting error, that is, the position where the part is attached can be accurately known, the shape measurement accuracy is improved. In addition, since multi-surface data is used, calculation can be performed using more measurement points than data on only one surface. Therefore, even if abnormal data is included in the measurement point, the influence can be reduced by averaging.
[0043]
In addition to the configuration described above, by including the parameter included in the design shape in the parameter for convergence calculation, a parameter having a large tolerance, for example, the lens thickness and the radius of curvature can be adjusted according to the measurement result. The difference between the measurement shape and the design shape can also be reduced. Details will be described in the second embodiment.
[0044]
Furthermore, for a part consisting of a plane and a free-form surface, the position parameter in the out-of-plane direction in the coordinate transformation matrix using the plane measurement point group, the surface tilt parameter in two directions, and the thickness parameter of the part, By using the measurement points of the free-form surface and fitting the other degrees of freedom in the coordinate transformation matrix and the thickness parameter of the part, the following effects are produced. That is, since there are three degrees of freedom for parameters regarding the position and orientation of the plane, there is sufficient freedom to determine the position and orientation error of the plane. Therefore, the error shape is minimized for the plane. On the other hand, with respect to the free-form surface, it is possible to perform calculation that minimizes the error shape among the remaining degrees of freedom. Therefore, the error shape is the minimum correction amount for correcting the relative position and orientation error of the two surfaces and correcting the surface error of the free-form surface.
[0045]
Especially when the free-form surface is an axisymmetric aspheric surface, the setting error parameter generally has 6 degrees of freedom, but in this case the axis is symmetrical, so 5 degrees of freedom excluding the rotation error around the symmetry axis is set. .
[0046]
In addition, for a part consisting of a spherical surface and a free-form surface, using the spherical measurement point group, the three position parameters in the coordinate transformation matrix and the thickness parameter of the part are transformed using the free-form measurement point group. By fitting other degrees of freedom in the matrix and the thickness parameter of the part, the following effects occur.
[0047]
That is, since there are three degrees of freedom of parameters for the spherical position and orientation, there is sufficient freedom to determine the spherical position and orientation error. Therefore, the error shape is minimized for the spherical surface. On the other hand, for a free-form surface, it is possible to perform a calculation that minimizes the error shape among the remaining degrees of freedom. Therefore, the error shape is the minimum correction amount for correcting the relative position and orientation error of the two surfaces and correcting the surface error of the free-form surface.
[0048]
In particular, when the free-form surface is an axisymmetric aspheric surface, the setting error parameter generally has 6 degrees of freedom, but in this case, since it is axially symmetric, 5 degrees of freedom excluding the rotation error around the symmetry axis is set.
[0049]
Here, if the fitting is performed without omitting the thickness parameter, the thickness as designed is used for the calculation, and thus the shape correction amount that brings the thickness closer to the designed value is calculated. For example, when the allowable range of the lens thickness is very strict, it is possible to correct the shape in consideration of the lens thickness more strictly.
[0050]
On the other hand, if the curvature radius of the surface is added to the fitting parameter, the curvature error is fitted according to the measurement result, so that the shape error can be reduced.
For example, in the case of a lens having a loose tolerance for the radius of curvature, the radius of curvature can be adjusted according to the measurement result, so that a small shape error, that is, a small shape correction amount can be calculated.
[0051]
It is also possible to use a part of the curved surface among the parts having a plurality of curved surfaces as a position reference, and calculate the position of another surface with respect to the position reference. First, setting errors are calculated for a plurality of curved surfaces used for position marks by the method described in claim 1. This setting error is a reference for the position. If the measurement result of the remaining surface is transformed with respect to the reference of this position, the measurement result based on the position mark is calculated, and the setting error is calculated once again, the setting error obtained is , The position of the surface with the position mark as a reference.
[0052]
The following method is also possible as a method for calculating a position of another surface with respect to the reference of the position by using a part of the curved surface among parts having a plurality of curved surfaces.
[0053]
The first coordinate transformation matrix representing the component setting error is converged using a plurality of curved surfaces used for the position mark, and the second coordinate transformation matrix representing the positional deviation of the surface is converged using the remaining curved surface. Since the converged first coordinate transformation matrix uses only the position mark data, it represents the coordinates based on the position mark. Since the same coordinate transformation is applied to the remaining curved surface, the coordinate transformation is performed to an expression based on the position mark. Therefore, the second coordinate conversion representing the positional deviation represents the positional deviation based on the position mark. This will be described in Embodiment 5.
[0054]
Further, when a part is manufactured by molding, the shrinkage rate in the molding can be calculated by using the measurement data of a plurality of surfaces by including the shrinkage rate in the parameters included in the design shape. This will be described in Embodiment 4.
[0055]
(First embodiment)
FIG. 1 shows a flowchart of the shape correction method in the first embodiment. FIG. 2 shows an example of a lens having two optical surfaces. FIG. 9 shows an example of a lens composed of two free-form surfaces. FIG. 11 shows the amount of correction processing.
[0056]
In FIG. 2, {p1} is a measurement data point group on the first surface, and is expressed using the coordinate system [Cp]. {P2} is a measurement data point group on the second surface, and is expressed using the coordinate system [Cp]. {D1} is the design shape of the first surface, and is expressed using the coordinate system [Cd]. {D2} is the design shape of the second surface and is expressed using the coordinate system [Cd].
[0057]
[Cp1] is a coordinate system representing the position of the first surface. (measurement data)
[Cp2] is a coordinate system representing the position of the second surface. (measurement data)
[Cd1] is a coordinate system representing the position of the first surface. (Design shape)
[Cd2] is a coordinate system representing the position of the second surface. (Design shape)
[0058]
The difference in position between the coordinate system [Cd] and the coordinate system [Cp] represents how much the actual part deviates from the designed position. That is, it represents a setting error. This is represented by coordinate transformation [T]. This coordinate transformation has six parameters (three parallel shifts and three rotational movements). These six parameters are collectively expressed as α.
That is, since the matrix [T] includes these parameters, it is expressed as [T (α)]. A calculation process is performed on the measurement data according to the calculation flow shown in FIG.
[0059]
Since the general operation of the flow chart has already been described, the partial operation will be described in detail here.
[0060]
The coordinate transformation in step 104 can be described in the form of matrix-vector multiplication using the matrix [T (α)] as follows.
[0061]
{Q1} = [T (α)] {p1}
{Q2} = [T (α)] {p2} (Formula 1)
[0062]
Considering the calculation by the method of least squares, the evaluation function in step 105 is the sum of squares of shape errors in the normal direction. That is,
f (q1, d1) + f (q2, d2) = Σ (({q1} − {d1}) · {n1}))²+ Σ (({q2} − {d2}) ・ {n2})²(Formula 2)
Here, {n1} and {n2} are normal vectors of the surface to be measured (refer to the reference above for the least square method, Mahito Negishi, Manabu Ando, Masahumi Takimoto, Akinobu Deguchi, Hiroji Narumi, Nobuo Nakamura and Hironori Yamamoto: An On-Machine Coordinate Measuring System for the Canon Super Smooth Polisher, SICE '94 Tokyo (1994), 941).
[0063]
The convergence determination in step 106 is determined to have converged when the evaluation value represented by Equation 1 no longer changes. When converged, all parameters α are obtained, and the coordinate transformation matrix [T] is determined. Then, at this time, the evaluation function defined by Equation 2 is the minimum, that is, the sum of the squares of the first surface shape error of the first term and the square sum of the second surface shape error of the second term. It has become.
[0064]
FIG. 9 shows an example of a lens whose upper surface is a free curved surface and whose lower surface is also a free curved surface. (A) The figure shows the design shape. In the figure, h is the thickness of the lens, and this value usually allows some variation. (B) The figure shows the measurement points. For simplicity of explanation, it is assumed that the shape error is zero and there is only a tilt error. Consider modifying the measured lens shape. First, the setting error and the shape error are calculated according to the procedure described so far. The conventional correction machining amount calculation has already been described with reference to FIG. FIG. 11 shows the amount of correction processing, that is, the shape error (109a and 109b in FIG. 1) obtained by the method according to the present invention. As described above, the evaluation value using the data of both the first surface and the second surface, that is, the sum of squares of the error represented by Equation 2 (step 105) is minimized, as shown in FIG. The amount of correction processing is much smaller than the conventional method.
[0065]
This embodiment has the following effects.
1) Since the setting error (6 degrees of freedom per part) can be calculated correctly, the shape measurement accuracy can be improved.
2) When the degree of freedom of the shape of one surface is small, for example, in the case of a plane, the position in the plane is not fixed, but it can be calculated because it is calculated using data of other surfaces. (However, if the first surface and the second surface are parallel planes, it is impossible.)
3) When the first and second surfaces are free-form surfaces, a much smaller correction amount can be calculated compared to the conventional method.
4) Since multi-surface data is used, calculation can be performed using more measurement points than data on only one surface. Therefore, even if abnormal data is included in the measurement point, the influence can be reduced by averaging.
[0066]
In this embodiment, since the evaluation function is defined as Equation 2, the shape errors of the first surface and the second surface are treated equally (the first term is the shape error of the first surface, the second term Is the second surface shape error). However, in order to preferentially fit one surface to the design shape, it is possible to apply a predetermined weight coefficient to each term. This is not described because the basic calculation procedure is the same.
[0067]
In this embodiment, after calculating the parameter correction amount (107), the parameter correction amount δ_αIt is also possible to perform convergence determination (106) based on whether or not is sufficiently small.
[0068]
Further, as described above, the setting error has a maximum of 6 degrees of freedom in parallel movement in the XYZ directions and rotation around the axis. In this embodiment, a lens composed of two free-form surfaces has been discussed. However, for example, in the case of an axisymmetric aspherical lens, the rotational attitude around the axis is not determined (because it is axially symmetric), so the rotation around the axis is excluded. It is desirable to think with 5 degrees of freedom. Even in that case, it is the same argument.
[0069]
Furthermore, in the present embodiment, the measurement point group is coordinate-transformed to fit the design shape, but conversely, the design shape may be coordinate-transformed to fit the measurement point group.
[0070]
Furthermore, in the present embodiment, the case of a component having two surfaces has been described, but the same applies to a component having three or more surfaces.
[0071]
(Second embodiment)
FIG. 12 shows a flowchart of the shape correcting method in the second embodiment. In FIG. 12, as an example of a lens having two optical surfaces, a lens having two free-form surfaces is shown in FIG. The correction processing amount will be described using the one shown in FIG.
[0072]
This embodiment is different from the first embodiment in that parameters are increased. That is, in the first embodiment, α (maximum 6 degrees of freedom) is assumed as a setting error parameter. However, there are other parameters in the design shape, and it may be desired to adjust according to the measured value. is there. For example, when it is desired to measure the radius of curvature of an aspheric lens, it is convenient if the parameter of the radius of curvature in the design value can be changed according to the measured value of the actual object. The parameter included in the first design shape d 1 is described as α1, the parameter included in the second design shape d 2 as α2, and the parameter of the setting error as α0. All these parameters are collectively described as α.
[0073]
In the flow chart of FIG. 12, first, a shape measurement data point group of each surface of a part composed of a plurality of surfaces is measured and prepared by a three-dimensional shape measuring device or the like. In the figure, a part consisting of two surfaces is assumed, and respective measurement data point groups {p1} and {p2} are prepared ((101a) and (101b)). Further, an initial value is substituted into a parameter α (parameters α0, α1, and α2) representing a setting error (103).
[0074]
A first design shape d1 is prepared (102a), and a parameter α1 included in the design shape is set (112a). A second design shape d2 is prepared (102b), and a parameter α2 included in the design shape is set (112b).
[0075]
The coordinate transformation function F including the setting error parameter α0 is used to transform the measurement point group {p1} into {q1} (104a). Similarly, the coordinate transformation function F including the parameter α0 is used to transform the measurement point group {p2} into {q2} (104b). Next, the sum f (q1, d1) + f (q2, d2) of the evaluation values for each measurement surface is calculated (105).
[0076]
Next, convergence determination is performed (106). The determination method of convergence is determined by the fact that the evaluation value is not changed in the iteration loop. If the convergence is determined in the convergence determination of 106, the design shape is subtracted from the first surface (108a), and the error shape of the first surface is obtained (109a). For the second surface, the design shape is subtracted (108b) to obtain the error shape of the second surface (109b). Further, the parameter α at the time of convergence is output (110). The parameter α includes a setting error α0, a parameter α1 included in the first design shape, and a parameter α2 included in the second design shape.
[0077]
On the other hand, in the convergence determination of 106, if the convergence does not occur, the parameter correction amount δ is improved so that the evaluation value improves._α(107), and the process is repeated again from the step (104) and the step (112) with the corrected parameter (111). Here, the evaluation function 105 is the square of the difference between the measurement points {pl} and {p2} and the design shapes d1 and d2, and the parameter correction amount is 107. The evaluation value is stopped with respect to the parameter correction amount. Calculate with conditions. The evaluation function is given by the same expression 2 as in the first embodiment.
[0078]
By calculating in this way, a parameter α representing a setting error of 6 degrees of freedom can be calculated using a plurality of surfaces, so that a correct setting error can also be calculated in the case of measuring a part made up of a plurality of curved surfaces. In addition, even if the shape of the first surface is a plane and the shape cannot be defined with 6 degrees of freedom, the evaluation function is defined using the data of the second surface. Is possible. Since the setting error, that is, the position where the part is attached can be accurately known, the shape measurement accuracy is improved. In addition, since multi-surface data is used, calculation can be performed using more measurement points than data on only one surface. Therefore, even if abnormal data is included in the measurement point, the influence can be reduced by averaging.
[0079]
As examples of parameters included in the design shape, the radius of curvature of the lens and the thickness h of the lens (see FIG. 9) can be considered. However, the parameters α do not converge unless they are independent of each other. For example, the vertical positions Z1 and Z2 in the first and second design shapes cannot be calculated. This is because the vertical position of the entire part is already included in the setting error parameter α0 and originally represents the same thing.
[0080]
FIG. 9 is an example of a lens whose upper surface is a free curved surface and whose lower surface is also a free curved surface as described above. FIG. 9A shows a design shape, and FIG. 9B shows a measurement point. For simplicity of explanation, it is assumed that the shape error is zero and there is only a tilt error. Consider modifying the measured lens shape. First, the setting error and the shape error are calculated according to the procedure described so far. The conventional correction machining amount calculation has already been described with reference to FIG. The amount of correction processing, that is, the error shape (109a and 109b in FIG. 12) obtained by the method according to the present embodiment is an evaluation value using both the data on the first surface and the second surface, that is, the error represented by Equation 2. Since the sum of squares (step 105) is determined so as to be minimized (since the least square method is used), the amount of correction processing can be reduced in the form as shown in FIG.
[0081]
The present embodiment has the following effects in addition to the case of the first embodiment.
1) Since the parameters included in the design shape can be changed so as to reduce the shape error, the shape error can be further reduced. Accordingly, the amount of correction processing is also reduced. If the amount of correction processing is small, the processing accuracy is improved as described above, and the processing time is shortened, so that the processing cost can be reduced.
2) Even if the object to be measured has an unknown shape, the parameters included in the assumed design shape can be determined according to the shape. Design parameters for an unknown shape can be determined (eg, the radius of curvature of a spherical lens).
[0082]
Also in the present embodiment, after calculating the parameter correction amount (107), the parameter correction amount δ_αIt is also conceivable to perform the convergence determination (106) depending on whether or not is sufficiently small.
[0083]
In the present embodiment, the measurement point group is coordinate-transformed to fit the design shape, but conversely, the design shape is coordinate-transformed and fitted to the measurement point group.
[0084]
Further, in the present embodiment, the case of a component having two surfaces has been described, but the same applies to a component having three or more surfaces.
[0085]
(Third embodiment)
FIG. 13 shows a flowchart of the third embodiment. This embodiment will be described using an example of a lens composed of a free curved surface and a plane shown in FIG. 3 and an example of a lens composed of a free curved surface and a spherical surface shown in FIG. 4 and 7 show calculation results with a large amount of correction calculated by the conventional method for each lens. Figures 5 and 8 show the results of calculation with a small amount of correction. FIG. 23 shows a list of parameters used for fitting calculation.
[0086]
The present embodiment is different from the second embodiment in the portion of coordinate transformation in 104 steps.
As described in the first embodiment, this coordinate transformation can be defined by multiplication with a matrix including a setting error as a parameter (Formula 1). The present embodiment is characterized in that the types of parameters used are different between the first surface and the second surface.
[0087]
Next, how to select this parameter for several types of cases will be described.
[0088]
First, consider a lens having a free-form surface and a flat surface as shown in FIG. As shown in the figure, the vertical direction is the Z axis. As shown in Fig. 4, with the conventional setting error correction for each surface, even if the upper surface is machined (Fig. 4 (a)) or when the lower surface is machined (Fig. 4 (b)), the amount of correction is large. Become. Therefore, a parameter is selected as follows to obtain a small correction amount. The lens thickness h is taken as the parameters on the free-form surface side of the upper surface as parameters included in the X, Y, and Z direction translations of the setting error, the rotation θz around the Z axis, and the design shape. The lens thickness h is taken as the parameter of the lower plane and the Z axis translation of the setting error, the rotation θx around the X axis and the rotation θy around the Y axis, and the parameters included in the design shape. When calculated in this way, the lower plane has two upper and lower Z and two degrees of freedom of rotation, so that the measurement point group can coincide with the plane that is the design shape. This is because it is possible to define the position of the plane with the Z position and two tilt angles. For the upper surface, the remaining parameters are adjusted so as to reduce the shape error. As a result, as shown in FIG. 5, the design shape and the measurement result are completely coincident with each other on the lower surface, and the fitting with which the shape error is minimized while the lower surface is fitted to the upper surface is realized. Thereby, a correction amount that is much smaller than the correction amount of FIG. 4, that is, an error shape can be calculated.
[0089]
Also, taking the movement in the Z direction, rotation θx, θy, and lens thickness h as the lower surface parameters, and taking the lens thickness h as the upper surface parameters, the upper and lower Z and two degrees of freedom of rotation are obtained for the lower surface plane. Therefore, it is possible to make the measurement point group coincide with the plane that is the design shape. On the other hand, for the free-form surface on the upper surface, only the lens thickness h is obtained, so the same calculation result as the conventional one shown in FIG. 4 (a) can be obtained.
[0090]
Similarly, it is possible to select a parameter that gives the result of FIG.
[0091]
Next, consider a lens having a free-form surface and a spherical surface shown in FIG. As shown in the figure, the vertical direction is the Z axis. As described above, with the conventional setting error correction for each surface, the amount of correction is large even when the upper surface is processed (FIG. 7A) or when the lower surface is processed (FIG. 7B). Therefore, parameters are selected as follows and a small correction amount is obtained.
[0092]
The parameters on the free curved surface side of the upper surface are set errors Z, θx, θy, θz and the lens thickness h, and the spherical parameters on the lower surface are set error XYZ and the lens thickness h. When calculated in this way, the spherical surface on the lower surface has XYZ degrees of freedom, so that the measurement point group can be matched with the spherical surface that is the design shape. This is because it is possible to define the position of the sphere with three degrees of freedom of XYZ at the center of the sphere.
For the upper surface, the remaining parameters are adjusted so as to reduce the shape error. As a result, as shown in FIG. 8, the design shape and the measurement result are completely coincident with each other on the lower surface, and the fitting with which the shape error is minimized under the condition of fitting the lower surface with respect to the upper surface is realized. Thereby, a much smaller correction amount than the correction amount in FIG. 7 can be calculated.
[0093]
Also in this case, taking the movement in the X, Y, and Z directions and the lens thickness h as the lower surface parameters and the lens thickness h as the upper surface parameters, the lower spherical surface has three degrees of freedom of X, Y, and Z. Therefore, it is possible to make the measurement point group coincide with the spherical surface as the design shape. On the other hand, for the free-form surface on the upper surface, only the lens thickness h is obtained, so that the same calculation result as that shown in FIG.
[0094]
Similarly, it is possible to select a parameter that gives the result of FIG.
[0095]
In the case of a lens composed of two free-form surfaces, the method is the same as that described in the first embodiment.
[0096]
The method of selecting the parameters described above is summarized as shown in the following table of FIG. This is the same even if the lens thickness parameter h is removed from the table. In this case, the correction amount when the lens thickness is set to the design value can be calculated. The same applies if a parameter for the radius of curvature is added. In this case, the radius of curvature can be calculated according to the measurement result.
[0097]
When the upper surface is a free-form surface and the lower surface is a cylindrical surface parallel to the Y axis, the upper surface parameters are Z, θy, h, and the lower surface parameters are X, Y, Z, θx, θz, h. Then, in order to define the cylindrical surface, there are parameters of a total of five degrees of freedom of θx and θz that determine the position LXYZ of the central axis of the cylinder and the direction of the axis, so that the measurement data and the design shape can be completely matched. On the other hand, with respect to the free-form surface, the measurement data and the design shape are fitted so that the shape error is minimized with the remaining degrees of freedom while maintaining the conditions.
[0098]
In the present embodiment, in addition to the effects of the second embodiment, the following effects are obtained.
1) A small correction amount can be obtained for a lens composed of a free-form surface and a flat surface.
2) A small correction amount can be obtained for a lens composed of a free-form surface and a spherical surface.
3) A small correction amount can be obtained for a lens composed of a free-form surface and a cylindrical surface.
[0099]
In the present embodiment, a component composed of a free curved surface and a plane or a spherical surface has been described. However, a free curved surface may be an axisymmetric aspherical surface. However, in this case, since the rotation around the axis of the axisymmetric aspherical shape is not originally determined, it must be excluded from the fitting parameters.
[0100]
In the present embodiment, a free-form surface and a plane component have been described, but the same applies to a plane having a very large curvature radius. For example, of course, the deviation from the plane is at the same level as the resolution of the measuring device.
[0101]
In the present embodiment, the free-form surface and the spherical part have been described, but the spherical surface is the same for a curved surface shape having a very small amount of aspheric surface. For example, it goes without saying that the deviation from the spherical surface is at the same level as the resolution of the measuring device.
[0102]
Also in the present embodiment, after calculating the parameter correction amount (107), the parameter correction amount δ_αIt is also conceivable to perform the convergence determination (106) depending on whether or not is sufficiently small.
[0103]
In the present embodiment, a two-part component including only one free-form surface has been described, but the same is true if the number of free-form surfaces is further increased. In this case, all parameters of the free-form surface are the same as those of the upper surface in FIG. Since the operation and the effect are the same, the description is omitted.
[0104]
Also, in this embodiment as in the previous embodiment, the measurement point group is coordinate-transformed to fit the design shape, but conversely, the design shape is coordinate-transformed to fit the measurement point group. is there.
[0105]
(Fourth embodiment)
The fourth embodiment is a case where a plastic free-form surface prism having three surfaces is manufactured, and will be described with reference to FIGS. 14, 15, 16, and 17. FIG. FIG. 14 shows a trihedral free-form prism. Fig. 14 (a) shows the design shape of the three free-form surfaces and the three coordinate systems representing their positions. FIG. 14 (b) shows a measurement point group of a plastic molded product measured with a three-dimensional shape measuring apparatus or the like. In the case of a plastic molded product, shrinkage immediately after molding or expansion due to humidity can be considered. Therefore, as shown in FIG. This enlargement factor can be included in the design shape parameters. This is calculated as follows, for example.
[0106]
First, the design shape shown in FIG. 14 (a) is calculated. Next, multiply the XYZ coordinate value of the calculated point by m. Now, a shape enlarged or reduced by m times around the origin can be calculated. Using this design shape and measurement point group, the correction amount calculation according to the present invention is performed. The calculation procedure is the same as that already described in the second embodiment with reference to FIG. However, in the case of the second embodiment, the fitting is made on only two surfaces, while the three surfaces are fitted. In addition to the six degrees of freedom of setting error (X, Y, Z, θx, θy, θz), the parameter uses an enlargement factor m included in the design shape.
[0107]
FIG. 16 shows the shape error thus calculated, that is, the correction amount. Since the parameters are adjusted so that the square sum of the shape errors of all three surfaces is minimized, a small correction amount can be calculated.
[0108]
FIG. 17 shows how to use the obtained correction amount. In this embodiment, since plastic molding is considered, it is necessary to correct the shape of the mold. The procedure of FIG. 17 will be described. First, a mold is manufactured (201) and molded using the mold (202). The shape of the molded product is measured (203), and the correction amount is calculated (204). This correction amount is obtained by the method described in the second embodiment. Next, it is determined whether the correction amount, that is, the error shape has reached the desired accuracy (205). If the accuracy is still insufficient in step 205, the error shape is subtracted from the die shape to obtain the next die shape (206 ), The process returns to step 201.
If the accuracy is sufficient in step 205, the correction amount obtained in step 204 is subtracted from the mold shape, and this is repeated from step 201 as a new mold shape.
[0109]
This embodiment has the following effects in addition to the case shown in the second embodiment.
1) The shrinkage rate can be calculated. Since the properties of the material can be checked with this, the mold can be manufactured in anticipation of the shrinkage rate checked in advance when molding with the same material next time.
2) Since the parameters are adjusted so that the square sum of the shape errors of all three surfaces is minimized, a small correction amount can be calculated.
[0110]
In the present embodiment, the plastic molded product has been described, but the same applies to a glass molded product.
[0111]
In the present embodiment, a three-part component has been described, but the same applies to four or more parts. Although it has been described in the present embodiment that the shrinkage rate can be included in the fitting parameter, other parameters included in the design shape can be included in the fitting parameter as well. For example, a radius of curvature can be considered.
[0112]
(Fifth embodiment)
The fifth embodiment is a case where a part having four free-form surfaces is used as a position reference, and three of the four parts are used as position references, and the positional deviation error of the remaining one free-form surface is calculated. FIG. 18 explains the shape of the component, FIG. 19 explains the coordinate system used in the design shape, and FIG. 20 explains the flowchart.
[0113]
FIG. 18 shows a mirror component 5 having first, second, and third free-form surfaces 1, 2, and 3, and a fourth free-form surface 4. The objective is to use the first, second, and third free-form surfaces as positioning marks (position marks) for this part, and to measure the position error of the fourth surface with reference to the positioning marks. Such an optical component can be positioned with higher accuracy than the three position marks. FIG. 19 shows the coordinate diameter [Cd] representing the design position and the coordinate systems [Cd1], [Cd2], [Cd3], and [Cd4] representing the design position of each surface. Although there are four surfaces, the flowchart is the same as that of the third embodiment (FIG. 13).
[0114]
However, the fitting parameters used on the first, second, and third surfaces are X, Y, Z, θx, θy, and θz with 6 degrees of freedom. This is α0. The fourth surface uses a coordinate transformation matrix from the coordinate system [Cd] representing the design position to the coordinate system [Cd4] representing the position of the fourth surface (generally having six degrees of freedom). This is α1. This parameter and the coordinate transformation matrix represent the positional deviation error of the fourth surface. That is, the parameters used for fitting are 12 in total including α0 and α1. Together, this is written as α.
[0115]
FIG. 20 shows a flowchart of the fifth embodiment. First, a shape measurement data point group on each surface of a component composed of a plurality of surfaces is measured by a three-dimensional shape measuring device or the like and prepared. In the figure, since the component consists of four surfaces, respective measurement data points {p1}, {p2}, {p3}, {p4} are prepared ((101a), (101b), (101c), (101d)). An initial value is substituted into a parameter α (parameters α0 and α1) representing a setting error (103). The first design shape d 1 is prepared (102a), the second design shape d 2 is prepared (102b), the third design shape d 3 is prepared (102c), and the fourth design shape d 4 is prepared. Preparation (102d), using the coordinate transformation function Fl including the parameter α0 of the setting error, the coordinate transformation of the measurement point group {P1} to {q1} (104a), and the measurement point group {p2} to {q2} The coordinates are transformed (104b), and the measurement point group {p3} is transformed into {q3} (104c). On the other hand, the measurement point group {p4} is also transformed into {q4 '} (104d).
[0116]
As shown in the first embodiment, the coordinate transformation function F1 can be described in the form of multiplication of the following matrix and vector.
[0117]
{Q1} = [T (α0)] {pl}
{Q2} = [T (α0)] {p2}
{Q3} = [T (α0)] {p3}
{Q4 '} = [T (α0)] {p4} (Formula 3)
[0118]
Further, the coordinate conversion function F2 including the positional error error parameter α1 is used to coordinate-transform the measurement point group {q4 ′} into {q4} (113).
[0119]
{Q4} = [T (α1)] {q4} (Formula 4)
This coordinate transformation is the same as in Equation 3, except that the parameter is α1.
[0120]
Next, the sum f (q1, d1) + f (q2, d2) + f (q3, d3) + f (q4, d4) of the evaluation values for each measurement surface is calculated (105).
[0121]
Next, convergence determination is performed (106). The determination method of convergence is determined by the fact that the evaluation value is not changed in the iteration loop. If the convergence is determined in the convergence determination of 106, the design shape is subtracted from the first surface (108a), and the error shape of the first surface is obtained (109a). Similarly, the design shape of the second surface is subtracted (108b), the error shape of the second surface is obtained (109b), the design shape of the third surface is subtracted (108c), and the error shape of the third surface is obtained. (109c), the design shape is subtracted from the fourth surface (108d), and the error shape of the fourth surface is obtained (109d). Further, the parameter α at the time of convergence is output (110). The parameter α includes a setting error α0 and a fourth surface misalignment error α1. On the other hand, in the convergence determination of 106, if the convergence does not occur, the parameter correction amount δ is improved so that the evaluation value improves._α(107) and repeat from step (104) again with the modified parameter (111).
[0122]
Here, the evaluation function of 105 is set to the square of the difference between the measurement points {pl} to {p4} and the design shapes d1 to d4, and the parameter correction amount of 107 is the evaluation value is stopped with respect to the parameter correction amount. Calculate with conditions. The evaluation function is given by the following equation as in the first embodiment.
[0123]
f (q1, d1) + f (q2, d2) + f (q3, d3) + f (q4, d4)
= Σ (({q1} − {d1}) ・ {n1}))²+ Σ (({q2} − {d2}) ・ {n2})²
+ Σ (({q3} − {d3}) ・ {n3}))²+ Σ (({q4} − {d4}) ・ {n4})²        (Formula 5)
[0124]
As described above, in the present embodiment, the setting error can be determined as the parameter α0 calculated based on the positions of the three surfaces 1, 2, and 3. Further, the positional deviation error of the fourth surface can be determined as the parameter α1. Also, the shape error of the first to fourth surfaces can be calculated.
[0125]
In the present embodiment, the case of a component having four surfaces has been described, but the same applies to a case where there are more surfaces.
[0126]
In the present embodiment, the same applies even if a parameter included in the design shape, for example, a radius of curvature is added to the fitting parameter. In the present embodiment, the three free-form surfaces used as position marks can be handled in the same way even if they are spherical surfaces.
[0127]
As in the previous embodiments, in this embodiment, the measurement point group is coordinate-transformed to fit the design shape, but conversely, the design shape is coordinate-transformed and fitted to the measurement point group.
[0128]
【The invention's effect】
As explained above, according to the present invention,
1) Setting errors can be calculated accurately even for parts consisting of multiple curved surfaces.
2) Since setting errors can be calculated accurately, measurement accuracy can be improved.
3) Since multi-sided data is used, calculation is performed using more data than single-sided data. Therefore, even if abnormal data is included in the measurement points, the influence can be reduced by averaging.
4) Even if the surface has few degrees of freedom, such as a plane or sphere, the data for other surfaces are also used, so the setting error can be calculated correctly.
5) Since the calculation is performed so that the shape error of multiple curved surfaces is small, a small shape error and therefore a small amount of shape correction can be calculated.
6) Since a small amount of shape correction can be calculated, the cost required for correction can be reduced. In particular, when the shape is corrected by polishing or the like, since the removal amount is small, the influence of the removal error is reduced, and high-precision machining is possible.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a first embodiment of the present invention.
FIG. 2 is a diagram showing a lens having a free-form surface according to the first embodiment of the present invention.
FIG. 3 is a diagram illustrating an example of a lens including a free-form surface and a flat surface.
FIG. 4 is a diagram showing a calculation result with a large amount of correction calculated by a conventional method.
FIG. 5 is a diagram illustrating a calculation result with a small correction amount.
FIG. 6 is a diagram illustrating an example of a lens including a free-form surface and a spherical surface.
FIG. 7 is a diagram showing a calculation result with a large amount of correction calculated by a conventional method.
FIG. 8 is a diagram showing a calculation result with a small correction amount.
FIG. 9 is a diagram illustrating an example of a lens including two free-form surfaces.
FIG. 10 is a diagram showing a calculation result with a large amount of correction calculated by a conventional method.
FIG. 11 is a diagram illustrating a calculation result with a small correction amount.
FIG. 12 is a flowchart showing a second embodiment of the present invention.
FIG. 13 is a flowchart showing a third embodiment of the present invention.
FIG. 14 is a diagram showing a three-surface free-form surface prism for explaining a fourth embodiment of the present invention.
FIG. 15 is a diagram for explaining a shrinkage rate.
FIG. 16 is a diagram showing a calculation result with a small correction amount for explaining a fourth embodiment of the present invention.
FIG. 17 is a flowchart for explaining a fourth embodiment of the present invention.
FIG. 18 is a diagram showing an optical component composed of four free-form surfaces for explaining the fifth embodiment of the present invention.
FIG. 19 is a diagram showing four coordinate systems for explaining a fifth embodiment of the present invention.
FIG. 20 is a flowchart for explaining a fifth embodiment of the present invention.
FIG. 21 is a diagram for explaining the operation of a conventional shape measuring apparatus.
FIG. 22 is a flowchart illustrating a conventional calculation operation.
FIG. 23 is a table of parameters according to a third embodiment of the present invention.
[Explanation of symbols]
{P1} Measurement data point group on the first surface
{P2} Measurement data point group on the second surface
{Dl} Design shape of the first surface
{D2} Design shape of second surface
[Cp] Coordinate system used to represent measurement data point cloud
[Cd] Coordinate system used to represent design shape
[Cp1] A coordinate system representing the position of the first surface is used. (measurement data)
[Cp2] A coordinate system representing the position of the second surface is used. (measurement data)
[Cdl] A coordinate system representing the position of the first surface is used. (Design shape)
[Cd2] A coordinate system representing the position of the first surface is used. (Design shape)
1 First free-form surface
2 Second free-form surface
3 Third free-form surface
4 Fourth free-form surface
5 Parts with 4 free-form surfaces

Claims (13)

For a member having a plurality of surfaces, the shape is such that the evaluation value indicating the difference between the three-dimensional shape measurement result of each of the plurality of surfaces and the design shape of each of the plurality of surfaces is minimized. A shape evaluation method for obtaining error information between the shape measurement result and the design shape when coordinate conversion of the measurement result or the design shape is performed. The shape evaluation method according to claim 1, wherein the three-dimensional shape measurement result is obtained as point cloud data. The shape evaluation method according to claim 1, wherein the coordinate transformation is performed using a coordinate transformation matrix. 2. The evaluation value is a sum of square sums of shape differences between the shape measurement result and the design shape for each surface when coordinate conversion of the shape measurement result or the design shape is performed. Shape evaluation method. A series of loops for correcting the coordinate conversion parameter or the parameter included in the design shape to a value in a direction in which the evaluation value does not change and obtaining the evaluation value when coordinate conversion is performed again after the correction is performed. The shape evaluation method according to claim 1, wherein coordinate transformation that minimizes the evaluation value is obtained by executing until the evaluation value converges. The plurality of surfaces are a plane and a free-form surface, and the coordinate transformation parameters are an out-of-plane direction position and a 2-direction surface inclination for the plane, and a 3-direction position and other-direction inclination for the free-form surface. 5. The shape evaluation method according to 5. The shape evaluation method according to claim 5, wherein the plurality of surfaces are a spherical surface and a free-form surface, and the coordinate conversion parameters are a three-direction position for the spherical surface and a one-direction position and a three-direction inclination for the free-form surface. 6. One of the plurality of surfaces is an axisymmetric aspheric surface, and the coordinate transformation parameter relating to the axisymmetric aspheric surface is a position inclination of 5 degrees of freedom excluding rotation about the axis of the axisymmetric aspheric surface. The shape evaluation method described. The shape evaluation method according to claim 6, wherein the thickness of the member is further used as the coordinate conversion parameter for each of the surfaces. Furthermore, the shape evaluation method of Claim 5 which uses the expansion-contraction rate of the said member as the said coordinate conversion parameter. The plurality of surfaces are a plurality of curved surfaces, and a first evaluation value indicating a difference between the shape measurement result and the design shape with respect to a part of the curved surfaces, and the plurality of curved surfaces For the remaining curved surfaces, the sum of the shape measurement result obtained by performing the same first coordinate transformation as the partial curved surface and the second evaluation value indicating the difference between the design shapes is minimized. The shape measurement result for the partial curved surface or the first coordinate transformation of the design shape and the shape measurement result or the second of the design shape for which the first coordinate transformation for the remaining curved surface is executed. The shape evaluation method according to claim 1, wherein coordinate transformation is obtained. 12. A component manufacturing method, wherein the member is processed so as to correct the error obtained by using the shape evaluation method according to claim 1. A shape evaluation apparatus that evaluates a shape error of the member using the shape evaluation method according to claim 1.

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