JPS6281518A - Method for removing set error in measurement of shape - Google Patents

Abstract

PURPOSE:To make it possible to measure a shape with high accuracy, by calculating the axial shift of a measuring system and a component of symmetry of rotation unrelated to the azimuth of the mount error of a work and further calculating a component of asymmetry of rotation relating to the azimuth. CONSTITUTION:In measuring the shape of a work 2 having a surface 3 to be inspected, the measuring points on four arbitrary azimuths crossing at right angles to each other from a measuring part, that is, black round spot rows at the intersecting points of the straight lines with curves in a drawing are selected and the arithmetic mean of the measured values in four azimuths on each annulus 4 is calculated. From the mean value, the shift of the rotary axis of a measuring system and the component of symmetry of rotation unrelated to an azimuth in the mount error of the work are calculated by a method of least squares to perform the correction of the measured value and, next, the component of asymmetry of rotation relating to the azimuth in the mount error of the work is calculated using the corrected measured value to perform the correction of the measured value.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for eliminating setting errors in shape measurement.

[Conventional technology]

In shape measurement, errors in mounting the workpiece and poor alignment of the measurement system can cause systematic errors in measured values and give incorrect information about the shape, but this is especially true when measuring the surface shape of aspherical lenses, molds, etc. This is an important issue because highly accurate measurements are required.

Simple examples of these, such as those seen when fixing a workpiece and measuring its shape with a three-dimensional measuring device, or when measuring only the cross section of a workpiece, are shown in Figure 7.
The measured value shown is obtained. In Fig. 7, the X and Y axes are the coordinate axes of the measurement system, and the measurement result shows that the workpiece is installed at an angle.
l, Y/ can be determined. Alternatively, in the case of a roundness measuring device, it is possible to perform Fourier analysis on the measured value to determine the amount of eccentricity and remove the influence of eccentricity from the measured value. In such a simple example, a method for eliminating workpiece mounting errors is known, but a general case in which the entire surface to be inspected is scanned has not been clarified.

[Problem that the invention seeks to solve]

In measurements that scan the entire surface to be tested and obtain information on the entire surface,
For example, if a scanning method is adopted that combines two types of rotation, the axis misalignment between the two types of rotation axes and workpiece installation errors that inevitably occur during measurement are automatically detected from the measured values, and the installation errors are automatically detected. Conventionally, there is no known means for correcting the influence of For this reason, a great deal of effort was required to attach the workpiece and adjust the machine.

Therefore, the present invention is achieved by obtaining the above means.

The object of the present invention is to facilitate the work of mounting a workpiece, reduce the burden on the worker, and enable highly accurate shape measurement.

[Means and actions for solving the problem] Methods for scanning the entire surface to be inspected can be roughly divided into two methods: a combination of linear scanning in two orthogonal directions, and a combination of two types of rotation. The invention is summarized in the latter case.

A conceptual diagram for explaining the present invention in detail is shown in FIG.
). Consider the case where the shape of the convex surface of the plano-convex workpiece 2 shown in FIG.

Figure (b) shows the annular locus 4 of the measurement points when the figure (,) is viewed from the direction of the arrow. The outermost one of these trajectories reaches the vicinity of the workpiece outline 5, indicating that it is possible to measure up to the effective diameter of the workpiece. From these measurement points, select measurement points in four orthogonal directions, in other words, select the black circle points at the intersections of the straight lines and curves in Figure 1 6), and measure the four directions on each of these annular zones. Find the arithmetic mean of the values. From these average values, the deviation between the rotation axes of the measurement system and the installation error of the workpiece are determined by the least squares method to find rotationally symmetrical components that are independent of orientation, and the measured values are corrected.
Next, using the corrected measured values, a rotationally asymmetrical component related to the orientation of the workpiece mounting error is determined, and the measured values are corrected. In this way, by combining the misalignment between the axes of the measurement system and the rotationally symmetrical component of the workpiece installation error, which is independent of orientation, it can be solved that the unknowns are orthogonal to each other when calculating the least squares method. This is because it is necessary for convergence.

As described above, the present invention selects measurement points in four arbitrary orthogonal directions from the measurement point sequence on the test surface 3, calculates the arithmetic average of the measured values in each of these four annular directions, From this average value, the deviation between the rotating axes of the measurement system and the installation error of the workpiece,
The first component of the measured value is
The present invention is characterized in that a second correction is performed, and then a corrected measured value is obtained, and a rotationally asymmetric component related to the orientation of the workpiece mounting error is obtained, and the second measured value is corrected.

〔Example〕

FIG. 2 is a diagram showing a measurement system according to an embodiment of the present invention. When scanning the test surface 3 by combining rotations, there are cases in which the interferometer is fixed and the test surface is rotated around its axis of symmetry as the rotation axis, and then further rotated around its approximate center of curvature, and when the interferometer is rotated. In some cases, the interferometer is rotated about the approximate center of curvature with respect to the surface to be inspected. FIG. 2 shows an example of the latter.

The workpiece 2 is attached to a rotation bearing 8 and can be rotated DK around a workpiece rotation shaft 9. The interferometer 6 has, for example, a non-contact optical probe 2, and is held on a rotary table 11 via a -axis slide table 10. The rotary table 11 is fixed to an N'C table 13. The rotary table rotation axis 12 is the surface to be inspected 3
is preset so that it passes very close to the approximate center of curvature. - The axis slide table 10 is connected to the test surface 3 and the optical probe 7.
It plays the role of adjusting the positional relationship with the The rotation bearing 8 is fixed to a main column of a measuring machine (not shown).

FIG. 3 is a diagram showing the concept of measurement using the measurement system shown in FIG. 2 above. FIG. 3 is a diagram corresponding to the top view of FIG. 2. The surface to be inspected 3 can be rotated around the work rotation axis 9 ◇The rotation axis 12 of the rotary table is at 0 in the figure.
One point is perpendicular to the plane of the paper. Point 0 is the approximate center of curvature of the surface to be inspected 3 and generally does not lie on the workpiece rotation axis 9 due to workpiece installation errors. Further, O' is also not on the work rotation axis 9 due to axis misalignment. An interferometer (not shown) has an optical probe 1 and is rotatable about a rotary table rotation axis 12. For example, the optical probe 7 rotates by θ from the position indicated by the solid line in the figure to the position indicated by the dotted line as indicated by the arrow. When the rotary tapes are stopped at this position and the surface to be tested 3 is rotated, a ring-like locus 4 of measurement points as shown in FIG. 1(b) is obtained. This operation is repeated until the effective diameter is reached, and the measurement is generally completed. Although the figures are exaggerated for convenience of explanation, in reality, points 0 and 0' are located very close to the rotary table rotation axis 12, usually within a few microns.

Figure 4 shows the measurement error that occurs when axis misalignment exists. For convenience of explanation, it is assumed that the approximate center of curvature O of the surface to be inspected 3 is on the work rotation axis. The rotary table rotation axis 12 passes through O' and is perpendicular to the plane of the paper, but generally does not lie on the workpiece rotation axis 9. The amount of deviation between 0 and O' is divided into two orthogonal directions, and they are defined as EP and δ as shown in the figure. If one point on the surface 3 to be inspected is P, 0'P is not equal to OP because EP and δ. This causes procedural errors in the measured values, giving incorrect information to shape recognition.

Figure 5 shows the measurement error when there is a rotationally asymmetric installation error. For the sake of simplicity, the case where KO' is on the work rotation axis 9, or in other words, the case where EP; 0, is shown. Approximate curvature center 0 of test surface 3 is constant ticY from work rotation axis 9
45th] Consider a case where shoulder 5i- is laterally displaced. When the test surface 3 is rotated by half a rotation, O moves to OI', and the test surface 3 moves from the position of the solid line to the position of the dotted line. Let P be a point on the surface to be inspected, and after half a rotation, P moves to P'.

Therefore, the measured value changes by a maximum of pp' as the surface to be inspected rotates 30 times, causing a systematic error in the measured value.

Next, specific means of the setting error removal method of the present invention will be described. Let the measured value be A(J, I), J: direction, l: ring number (function of θ). When the axis deviation EP, δ is small, the following equation approximately holds true.

However, the first term on the right side represents taking the arithmetic average of the four directions, and AS(I) corresponds to the aspheric amount in the OP force direction determined from the design value of the test surface 3 when 0' and 0 match. . The left side shows the case where the counter value is reset to O at the start of measurement (θ=0). Since the ring number is a function of θ, equation (1) holds true for various 0s, and since there are two unknowns, EP and δ, these can be found by the method of least squares. At this time, since EP and δ are two orthogonal right components of axis deviation, the convergence of the solution is good. The basis for equation (1) is that when an average of about 40,000 points is taken for each ring zone, the part of the workpiece installation error related to the orientation is canceled out.

Once the axis deviation EP, δ is determined, all measured values can be corrected using equation (1). The corrected measurement value is A
'(J, I), then using these, the mounting error related to the orientation can be determined. The following method is known as the method of least squares in general cases where the measured quantity is not a linear function of an unknown quantity in error theory. related to direction.

For lenses with clearly defined apexes, such as aspherical lenses, the mounting error is determined by determining the positional deviation of the apex.
l / r The former one can be omitted because the concept overlaps with δ, and the latter one can be omitted because the test surface 3 is rotated around the workpiece rotation axis for measurement.

Therefore, it can be seen that it is sufficient to have two each of EX and EY for the former, and two each of α and γ for the latter.

Here, EX and EY are the X and Y components of the amount of lateral deviation of the apex of the workpiece in the XY plane perpendicular to the two axes of rotational symmetry of the workpiece, and α and γ are the rotation of the test surface 3. It represents the inclination of the axis of symmetry, where 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 design value of the test surface 3 and the mounting error of the workpiece are known, then (2) L(JtItδ', EX, EY, α, γ)−
A' (J, I).

δ/: The residue of δ is generally a complex function of the installation error, but if the approximate value of the installation error is known, it can be found by Taylor expansion around it. However, El is an abbreviation of each installation error. Eio represents each approximate value, ΔEl represents the amount of deviation from the approximate value, and represents the value of the approximate value of the coefficient (2) t With a simple modification from equation (3), a (J, I) = A' ( J,I)-LO(J,I)L
o(JeI): The first term on the right side of equation (3) In equation (4), other quantities other than ΔEi can be calculated by calculation if the design value of the test surface is known. It can be determined using the least squares method using the measured values at each J and I. The number I of rings should be greater than the unknown installation error, but usually about 10 rings are selected. In fact, the least squares method is divided into a set of δ'EX, i and a set of a', EY, α. The reason for this is that, as shown in Figure 6, when the coordinate axes of the measurement system are x, y, and z, γ
is the rotation of two axes, so for convenience, if we define the vector of r as shown in the figure, then δ', EX.

The r values are orthogonal to each other, and convergence is good when using the least squares method. The same applies to δ', EY, and α. Further, since the approximate value of the mounting error is generally not known, O is selected as the initial value of each approximate value, and the values are determined by successive approximations.

As described above, the present invention selects measurement points in four arbitrary orthogonal directions from a series of measurement points on the surface to be inspected, and calculates the arithmetic average value of the measured values in the four directions on each of these annular zones. From these, the axis deviation EP of the measurement system and the rotationally symmetrical component δ of the workpiece mounting error, which is independent of orientation, are first determined, and the first correction of the measured value is performed, and using this corrected measured value, The method is characterized in that a rotational asymmetric component due to the orientation is determined in the workpiece mounting error, and a second correction of the measured value is performed. The feature of this method is that when calculating the least squares method, each unknown parameter is divided into orthogonal components, so convergence is fast and highly accurate solutions can be obtained.

The causes of the axis deviation component EP are not only poor initial settings of the measurement system, but also mechanical deformation due to temperature fluctuations, and movement of the rotating axis of the rotary table using an NC table when measuring workpieces with various radii of curvature. However, there are changes in EP at this time. For this reason, a method of calculating and correcting axis deviation components and workpiece mounting errors from measured values has become an indispensable means for shape measurement.

For convenience of explanation, we have given an example of a method in which the surface to be inspected is scanned by combining two types of rotation, but there are various variations that can be considered, for example, in which one rotation is approximated by a combination of two-dimensional linear motion. It goes without saying that the present invention is also summarized.

[R whole 8f3] By summarizing the present invention, when performing high-precision shape measurement such as measuring aspherical surfaces and molds, workpiece installation work is significantly facilitated, and the measurement system is improved. It facilitates adjustment, eases the specifications of the measurement system, and eases the environmental conditions of the measuring machine, making it possible to perform highly accurate measurements.

[Brief explanation of drawings]

Figures 1 (a) and (b) are conceptual diagrams of the method of the present invention, Figure 2 is a front view showing the configuration of a measurement system according to an embodiment of the present invention, and Figure 3 is a conceptual diagram of the measurement using the above measurement system. FIG. 4 and FIG. 5 are diagrams for explaining the operation of the same embodiment, and are diagrams showing the state of measurement errors, and FIG. 6 is a diagram for explaining the operation as well. FIG. 7 is an explanatory diagram of the prior art. 2... Workpiece, 3... Test surface, 4... Annular trajectory, 5... Workpiece outline, 6... Interferometer, 7... Optical probe, 8... Rotating bearing, 9...Work rotation axis, 1
0...Axis slide table, 11...Rotary table, 12...Rotary table rotation axis, 1B-...
・NC table. (a) (b) Fig. 1 Fig. 2 Fig. 4 Fig. 5 Fig. 6 Fig. 11 Director-General of the Agency Uγ1 Katsubu Tono 1, Display of Kushii 41 121 Application 1986-221442 Wing 2, Name shape of the invention Removal of 3ff constant errors in measurement, method 3, relationship with the person responsible for determining Nyama Tadashi 15th edition Applicant (037)] Rimbus Optical Industry Co., Ltd. 4, Agent Totaku 1-26 Toranomon, Minato-ku, Tokyo May 17th Mori Building 1
05 Telephone 03 (502) 3181 (main representative) 6.
Full text for details subject to amendment 7.7 Contents of Yamasho

Claims (1)

[Claims] When measuring the shape of a nearly rotationally symmetrical test surface, select measurement points in four arbitrary orthogonal directions from a series of measurement points on the test surface, and create a measurement system from the measured values in the four directions on each of these annular zones. axis deviation EP
Then, the rotationally symmetrical component δ of the workpiece mounting error is determined, and the first correction of the measured value is performed. From this corrected measurement value, the rotationally asymmetrical component of the workpiece mounting error is determined, and the rotationally asymmetrical component δ of the workpiece mounting error is determined. A method for removing setting errors in shape measurement, characterized by performing secondary correction.