JPH0797027B2 - Method for eliminating setting error in shape measurement - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method for eliminating a setting error in shape measurement.

[Conventional technology]

In shape measurement, work mounting errors and measurement system axis misalignment cause systematic errors in measured values, giving false information about the shape, but especially when measuring surface shapes such as aspherical lenses and molds. This is an important issue because accuracy measurement is required.

Of these, the simple ones, such as the case where the work is fixed and the shape is measured by a three-dimensional measuring instrument, or the case where only the cross section of the work is measured, are shown in FIG.
The measured value shown by is obtained. In FIG. 7, the X and Y axes are the coordinate axes of the measuring system, and the measurement result shows that the workpiece is mounted at an inclination, and new coordinate systems X'and Y'can be determined by simple calculation. Alternatively, in an example found in a roundness measuring instrument or the like, it is possible to perform Fourier analysis on the measured value to obtain the amount of eccentricity and remove the influence of eccentricity from the measured value. In such a simple example, a method for removing a work mounting error is known, but a general case of scanning the entire surface to be inspected has not been clarified.

[Problems to be solved by the invention]

In the measurement to obtain information on the entire surface by scanning the entire surface to be inspected,
For example, when a method of scanning by combining two types of rotations is adopted, the axial deviation between the two types of rotating shafts and the work mounting error that inevitably occur during measurement are automatically detected from the measured values, and the mounting error is detected. Conventionally, a means for correcting the influence of is not known. For this reason, a great deal of labor was required for work mounting work and machine adjustment.

Therefore, an object of the present invention is to make it possible to facilitate the work of attaching a work, reduce the burden on the operator, and enable highly accurate shape measurement by obtaining the above means.

[Means and Actions for Solving Problems]

The method of scanning the entire surface to be inspected is roughly classified into a combination of linear scanning in two directions orthogonal to each other and a combination of two types of rotation, but the present invention is summarized in the latter case. First, a conceptual diagram for explaining the method of the present invention.
It shows in figure (a) (b). Consider a case where the shape of the convex surface of the plano-convex work 2 shown in FIG. The figure (b) shows the annular locus 4 of the measurement point when the figure (a) is seen from the direction of the arrow. The outermost ones of these loci reach the vicinity of the workpiece outer shape 5, indicating that measurement up to the workpiece effective diameter is possible. From these measurement points, the measurement points in any four orthogonal directions, in other words, the series of black circles at the intersections of the straight line and the curved line in FIG. 1 (b), are selected, and the measurement in the four directions on each of these zones is performed. Calculate the arithmetic mean of the values. From these average values, the least squares method is used to correct the measured values by finding the rotationally symmetric component that does not depend on the bearing among the deviations between the rotational axes of the measuring system and the work mounting error, and then correct the measured values. Using the value, the rotationally asymmetric component related to the bearing is calculated from the work mounting error, and the measured value is corrected. In this way, combining the misalignment between the axes of the measurement system and the rotationally symmetric component that does not depend on the orientation of the mounting error of the workpiece is that the unknowns are in a relationship of being orthogonal to each other when applying the method of least squares. The present invention, as described above, selects measurement points on arbitrary four orthogonal directions from the measurement point sequence on the surface to be inspected 3 as described above. Obtaining the arithmetic mean of the measurement values of the azimuth, from the average value of the axis deviation between the rotation axes of the measurement system and the work mounting error,
The first of the measured values is obtained by obtaining the rotationally symmetric component that does not depend on the azimuth.
The second correction is performed, and then the corrected measured value is obtained to obtain the rotationally asymmetric component related to the azimuth in the work mounting error and the second measured value is corrected.

〔Example〕

FIG. 2 is a diagram showing a measuring system according to an embodiment of the present invention. When scanning the surface to be inspected 3 in combination with rotation, the interferometer is fixed and the surface to be inspected is rotated about its axis of symmetry as a rotation axis, and further rotated about its approximate curvature center. The interferometer may be rotated around the approximate curvature center with respect to the surface to be inspected. FIG. 2 shows the latter example.
The work 2 is attached to a rotary bearing 8 so that it can rotate around a work rotation shaft 9. The interferometer 6 has, for example, a non-contact optical probe 7, and has a uniaxial slide table.
It is held on the rotary table 11 via 10. The rotary table 11 is fixed to the NC table 13. The rotary table rotation shaft 12 is preset so as to pass in the vicinity of the approximate curvature center of the surface 3 to be inspected. The uniaxial slide table 10 serves to adjust the positional relationship between the surface 3 to be inspected and the optical probe 7. The rotary bearing 8 is fixed to a main pillar of a measuring machine (not shown).

FIG. 3 is a diagram showing the concept of measurement by the measurement system of FIG. FIG. 3 is a view corresponding to FIG. 2 seen from above. The surface 3 to be inspected is rotatable about a workpiece rotation shaft 9. The rotary shaft 12 of the rotary table is O'in the figure.
It passes through the dots and is perpendicular to the paper surface. The point O is the approximate center of curvature of the surface 3 to be inspected, and is generally not on the work rotation axis 9 because of a work mounting error. Also, O'is not on the work rotating shaft 9 because of the axis deviation. The interferometer (not shown) is an optical probe 7.
And is configured to be rotatable about the rotary table rotation shaft 12. For example, the optical probe 7 rotates from the position indicated by the solid line to the position indicated by the dotted line by θ as shown by the arrow. When the rotary table is stopped at this position and the surface 3 to be inspected is rotated, the orbital locus 4 of the measuring point shown in FIG. 1B is obtained. This operation is repeated until the full effective diameter is reached, and the measurement is generally completed. Although the drawing is exaggerated for convenience of explanation, the points O and O'are actually located very close to the rotary table rotation shaft 12 and are usually within several microns.

FIG. 4 shows the state of measurement error that occurs when there is an axis deviation. For convenience of explanation, the approximate center of curvature O of the surface 3 to be inspected is on the workpiece rotation axis. In other words, consider the case where there is a rotationally symmetric setting error that is invariant to the rotation of the work. The rotary table rotary shaft 12 passes through O ′ and is perpendicular to the paper surface, but generally not on the work rotary shaft 9. The amounts of deviation between O and O'are directed in two orthogonal directions, and EP and δ are set as shown in the figure. If one point on the surface 3 to be inspected is P, then ′ ′ is not equal to ▲ ▼ because of EP and δ. As a result, systematic errors occur in the measured values, giving incorrect information for shape recognition. Let Q be the intersection of the workpiece rotation axis 9 and the surface 3 to be inspected. A perpendicular line is drawn from the point O ′ at which the rotary table rotary shaft 12 cuts the plane of the paper to the work rotary shaft 9, and its foot is C
And A parallel line is drawn through O through C, and the intersection with the surface 3 to be inspected is A. A parallel line is drawn through O through O'P, and the intersection with the surface 3 to be inspected is E. OE corresponds to the true shape measured when setting error δ and EP is zero. The foot of the perpendicular drawn from C to O'P is a line segment from B and O.
CA is the amount measured when EP = 0, where D is the foot lowered to CA. CA = BP, ignoring the second minute amount of EP
And when compared with the amount O′P actually measured, B
O'difference occurs. This can be written as EPsinθ. OE is the amount observed when δ = 0, and the difference from CA is CD, ignoring the second-order small amount of δ, and is represented by δcosθ.

FIG. 5 shows the measurement error when there is a rotationally asymmetric mounting error with respect to the rotation of the work. For the sake of simplicity, if O'is on the workpiece rotation axis 9, in other words EP =
The case of O is shown. The approximate center of curvature O of the surface 3 to be inspected is a fixed amount from the work rotation axis 9. Consider only the case of lateral displacement. When the surface 3 to be inspected is rotated a half turn, O moves to O ″, and the surface 3 to be inspected moves from the position indicated by the solid line to the position indicated by the dotted line. As a result, the measured value changes by a maximum of {circle around (1)} with the rotation of the surface 3 to be measured, which causes a systematic error in the measured value.

Next, specific means of the setting error removing method of the present invention will be described. Let the measured values be A (J, I), J: azimuth, I: ring zone number (function of θ). The azimuth J corresponds to the rotation angle φ of the work, and the ring zone number I corresponds to the rotation angle θ of the rotary table. When the axis deviation EP, δ is small, the equation (1) approximately holds.

More specifically, when EP = 0, in other words, when the rotary table rotary shaft 12 passes through the point C, the measured value when θ = 0 is CQ.
However, the radius of the approximate spherical surface at the vertex Q of the surface 3 to be inspected is
If R ₀ , then R ₀ = OQ and CQ = R ₀ + δ. In the interferometric measurement, the measured value when θ = 0 is normally reset to 0. Under this condition, CA (written as CA _r here, the subscript r represents the time of reset) is CA _r = R ₀ + δcos θ-AS (I)-(R ₀ + δ) = δ (cos θ-1)- AS (I) Here, −AS (I) is measured when the rotary table is rotated to reach the first ring zone (for example, θ = θ _i ),
It represents the amount of aspherical surface (the amount of deviation from the spherical surface) when there is no setting error. The sign (-) differs depending on whether the amount of deviation from the spherical surface is (+) or (-) when the surface 3 to be inspected comes outside the approximate spherical surface, and is arbitrary. Here, it is set to -AS (I). In the measurement of the case likewise BP is not _{0, O'P r = (BP-} EPsinθ) r = (CA-EPsinθ) r = δ (cosθ-1) -AS (I) -EPsinθ = -AS m (I) Here, −AS _m (I) is such that the approximate center of curvature of the surface to be inspected 3 is correctly set on the rotation axis of the work shown in FIG.
It represents the amount of aspheric surface measured when there is a setting error of δ and EP. Rewriting the, δ (1-cosθ) + EPsinθ = AS m (I) -AS (I) further approximation center of curvature of the object surface 3 on the rotation axis of the workpiece shown in Figure 5 is not set correctly, polarized When set with care, the workpiece rotates (the rotation angle is φ) and the PP 'in Fig. 5 changes sinusoidally as the PV value (Peak to Value) (specifically PP' / 2sinφ ) Is obtained. The average value is AS _m (I). Specifically AS _m
Instead of (I), A (J, I) = AS _m (I) + (PP '/ 2) sinφ is measured. Where J is the azimuth (workpiece rotation angle φ = φ
_j ), I is an annular zone (rotational angle θ of the rotary table =
θ _i ), and A (J, I) represents the measured value at the azimuth φ _j and the annular zone θ _i . Measured values at four points in two orthogonal directions on the same first annular zone shown in FIG. 1 (b) {φ, φ + (π / 2),
If the arithmetic mean of φ + π, φ + (3π / 2)} is calculated, sin φ + sin {φ + (π / 2)} + sin (φ + π) + sin {φ + (3π / 2)} = 0 and the average value is AS _m (I) Matches If written in a formula, AS _m (I) = ΣA (J, I) / 4 From the above, the formula (1) is established.

However, the first term on the right side represents taking the arithmetic mean of four directions, and AS (I) corresponds to the aspheric amount of ▲ ▼ determined from the design value of the surface 3 to be inspected when O ′ and O match. . The left side shows the case where the counter value is reset to 0 at the start of measurement (θ = 0). Since the ring zone number I is a function of θ, the equation (1) holds for various θ, and the unknowns can be obtained by the least square method from EP and δ. At this time, since EP and δ are two orthogonal components of axis deviation, the convergence of the solution is good. The basis of the equation (1) is that when the average of the four bearings for each ring zone is taken, the case relating to the mounting error of the work is almost canceled.

When the axis deviation EP, δ is obtained, all measured values can be corrected using the equation (1) (first-order correction). Assuming that the corrected measured value is A '(J, I), A' (J, I) = A (J, I)-{[delta] (1-cos _[ theta _{] i} ) + EPsin [theta] _i } is obtained. These can then be used to determine the orientation-related mounting error. The following method is a known method as a least square method in the general case where the quantity measured in error theory is not a linear function of unknown quantity. The mounting error related to the azimuth is such that the vertex is clearly defined like an aspherical lens, and if there are three coordinates that determine the positional deviation at the vertex and three angles that determine the direction of the axis of symmetry of the surface to be tested. All determined. One of the former can be omitted because the concept overlaps with δ, and one of the latter can be omitted because the surface to be inspected 3 is rotated around the workpiece rotation axis for measurement. Therefore, it can be seen that EX and EY are required for the former and α and γ are required for the latter. Where EX and EY are the rotational symmetry axes of the workpiece, the X and Y components of the lateral displacement of the workpiece apex in the XY plane perpendicular to the Z axis, and α and γ are the rotational symmetry axes of the test surface 3. Represents the inclination of, and α corresponds to the rotation around the X axis and γ corresponds to the rotation around the Y axis.

If L is the expected value of the measured value obtained by calculation when the set value of the surface 3 to be inspected and the work mounting error are known, (2) L (J, I, δ ′, EX, EY, α, γ) = A '(J, I),
δ ′: Residue of δ Here, the specific form of L will be described in detail.
The coordinates are determined as shown in FIG. The center of rotation of the rotary table is C (0,0, R). When the rotary table is rotated by θ _i and the workpiece is rotated by φ _j , the difference in length between the moving radius CP _ij and the spherical surface becomes the measured value L (J, I).

L (J, I) = L _ij = − (R−Z _ij ) (1 + sin ² θ _i sec ² φ _j ) ^1/2 + (R−Z ₀ ) where R = R ₀ + δ (δ << R ₀ ) L (J, I) = − R ₀ + δ−Z _ij ) (1 + sin ² θ _i sec ² φ _j ) ^1/2 + (R ₀ + δ−Z ₀ ) Z _ij is the aspherical equation Z = ^{cS 2 / [1+ {1- (} k + 1) c 2 S 2} 1/2] + a 1 S 2 + a 2 S 4 + a 3 S 6 + a 4 S 8 + a 5 S 10 + ... c-1 / R 0 here ^{, S 2 = x 2 + y} 2, k, A 1, A 2, A 3, A 4, A 5, ... has now constant, varying by a small amount setting error.

L is generally a complicated function of the mounting error, but if the approximate value of the mounting error is known, Taylor's expansion can be performed around it. However, E _i is an abbreviation for each mounting error, E _i0 represents each approximate value, ΔE _i is the deviation from the approximate value, Indicates a value at an approximate value of the partial differential coefficient due to each mounting error of L.

With simple modifications from equations (2) and (3) However, a (J, I) = A ′ (J, I) −L ₀ (J, I) L ₀ (J, I): The first term on the right-hand side of equation (3) other than ΔE _{i in} equation (4) Other quantities can be obtained by calculation when the design value of the surface to be inspected is known, and thus can be obtained by the method of least squares using the measured values at J and I. As the number I of ring zones, it is sufficient that the number is equal to or greater than the unknown mounting error, but usually about 10 is selected. In practice, the least squares method is required separately for the set of δ ', EX, γ and the set of δ', EY, α. The reason for this is that when the coordinate axes of the measurement system are X, Y, and Z as shown in FIG. 6, γ is rotation around the Z axis, so if the vector of γ is defined as shown in the figure for convenience, then δ ′, EX and γ are orthogonal to each other and have good convergence when the least squares method is required. The same applies to δ ′, EY and α. Further, since the approximate value of the mounting error is generally unknown, 0 is selected as the initial value of each approximate value,
Sequentially approximate.

The present invention, as described above, selects the measurement points on any four orthogonal directions from the measurement point sequence on the surface to be inspected, and obtains the arithmetic mean value of the measurement values in the four directions on each of these zones. From these, the rotational deviation EP of the measurement system and the rotationally symmetric component δ of the mounting error of the work that does not depend on the direction are first obtained, and the first-order correction of the measured values is performed. Using the corrected measured values, Among the work attachment errors, the rotationally asymmetric component depending on the direction is obtained, and the measurement value is secondarily corrected. The feature of this method is that when the least squares method is required, unknown parameters are divided into orthogonal components, so that the solution can be converged quickly and highly accurate.

The cause of the axis deviation component EP is not only the poor initial setting of the measurement system, but also the mechanical deformation due to temperature fluctuations and the movement of the rotary shaft of the rotary table by the NC table when measuring workpieces with various radii of curvature. At this time, there are variations in EP. Therefore, the method of calculating and correcting the axis deviation component and the work mounting error from the measured values is an indispensable means for shape measurement.

For convenience of explanation, the method of scanning the surface to be inspected by combining two types of rotation has been illustrated, but various modifications are conceivable, for example, one rotation is approximated by a combination of two-dimensional linear motions. Needless to say, the present invention is also applied.

〔The invention's effect〕

By applying the present invention, when performing highly accurate shape measurement such as measurement of an aspherical surface or a mold, the work of attaching the work is markedly facilitated, the measurement system is easily adjusted, and the specifications of the measurement system are set. It has the effect of alleviating and mitigating the environmental conditions of the measuring instrument, which enables highly accurate measurement.

[Brief description of drawings]

1 (a) and 1 (b) are conceptual views of the method of the present invention, FIG. 2 is a front view showing the configuration of a measurement system according to an embodiment of the present invention, and FIG. 3 is a concept of measurement by the above measurement system. FIG. 4, FIG. 5 and FIG. 5 are views for explaining the operation in the same embodiment, showing the state of the measurement error, and FIG. 6 is a view for explaining the same operation. FIG. 7 is an explanatory diagram of a conventional technique. FIG. 8 is a diagram showing coordinates for explaining the operation according to the embodiment of the present invention. 2 ... Work, 3 ... Surface to be inspected, 4 ... Ring-shaped locus, 5 ...
… Work outline, 6 …… Interferometer, 7 …… Optical probe, 8 ・ ・ ・
… Rotary bearings, 9 …… Workpiece rotation axis, 10 …… Axis slide table, 11 …… Rotary table, 12 …… Rotary table rotation axis, 13 …… NC table.

Claims (1)

[Claims] 1. In measuring the shape of a substantially rotationally symmetrical surface to be inspected, a measurement point on the surface to be inspected is selected from arbitrary measurement points in four orthogonal directions, and four measurement points in each of these ring zones are selected. Of the axial deviation EP of the measuring system and the work mounting error from the measured values, the rotational symmetry component δ is found and the first-order correction of the measured value is performed. From this corrected measured value, the work mounting error is rotationally asymmetric. A method for eliminating a setting error in shape measurement, which comprises performing a second-order correction of a measured value by obtaining a different component.