JPH09101137A - Shape measuring device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To evaluate the wear distribution state of uniform grinding by a high elastic body polisher and its reproducibility by measuring having a reference surface provided on an object as a reference, and decomposing a shape change into a DC component, a power component, and a waviness component to display it. SOLUTION: The measuring device 1 is equipped with a main body 10, a moving stage part 11, a probe part 12, and a sample base 13, and a work 3 is fitted on the sample base 13 with good reproducibility. A probe 12a fitted to the probe part 12 is moved along the object surface 3a of the work 3 by the stage part 11, and obtained shape data is output to a processing device 2 so as to be processed. The probe 12a picks up the standard reference surface 3b of a high precision plane provide on the outer peripheral part of the work 3 before and after the measurement so that the zero standard of a Z coordinate of the work 3 is taken. A shape change obtained from shape data measure before and after the object surface 3a receives the shape change, is decomposed into a DC component, a power component, and a waviness component to be displayed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for evaluating surface shape changes during lens polishing.

[0002]

2. Description of the Related Art Usually, an optical lens formed of a spherical surface (hereinafter, an object to be polished is referred to as "workpiece") is polished by using a polisher having a relatively larger area than the workpiece.
In this case, first, the work-affected layer of the work roughly ground into the designed shape is removed by grain removal polishing to obtain a polished surface.
Next, the shape (curvature radius and sphericity) error is optically measured using a Newton gauge or the like, and the polishing conditions of the polishing machine are set again so that the shape error becomes smaller, and the correction polishing is performed. Get the surface shape of.

Since the purpose of this correction polishing step is to control the shape of the surface to be polished after grain removal, controllability is more important than the removal amount of polishing. Note that the relative displacement of the surface to be polished that occurs before and after polishing is due to the non-polishing surface (for example,
A surface other than the surface to be polished, such as a back surface opposite to the surface to be polished) is used as a reference for an absolute position and is represented by a deviation shape of the surface to be polished. The deviation shape will be described in detail later, but it is considered that the deviation component further includes a DC component and does not include a DC component. In the present specification, the former is referred to as "removal distribution shape" and the latter is referred to as "wear distribution shape" to distinguish them.

On the other hand, even in the case of an aspherical lens having at least one aspherical surface, a polisher having a relatively larger area than the work is applied to the grain removal polishing. For this grain removal polishing, a high-elasticity polisher is used to create a work-affected layer evenly on the entire surface of the workpiece without destroying the aspherical surface (hereinafter referred to as "pre-machined surface") created in the previous process as much as possible. A so-called "uniform polishing" is known in which polishing and removal are performed.

The reproducibility of the removal distribution shape in this uniform polishing is a very important requirement for efficiently removing the work-affected layer. It is for the following reasons. First, in order to improve the shape accuracy of the surface to be processed, at least reproducibility of the wear distribution shape is required for the following reason. That is, when the pre-processed surface is finished in the desired shape,
As long as the uniformity (including reproducibility) of the uniform polishing which is a post-process can be secured, the surface shape after the uniform polishing can also achieve a desired surface shape. In addition, even if this uniformity cannot be ensured and the wear distribution shape contains a power component and a swell component, as long as the reproducibility of the wear distribution shape by uniform polishing is ensured at least, the wear This is because it is possible to finish the surface shape after uniform polishing into a desired surface shape by superimposing a reverse shape of the distribution shape on the pre-processed surface.

However, in the former case (uniformity can be ensured), the work surface shape does not change even if the polishing time increases, whereas in the latter case (uniformity cannot be ensured), the polishing time Since the uniformity becomes worse as the number of times increases (the power component and the waviness component also increase), it is necessary to make the polishing time constant and evaluate when considering the wear distribution shape of the uniform polishing.

Next, in order to improve the machining efficiency, not only the reproducibility of the wear distribution shape but also the reproducibility of the removal distribution shape is required for the following reasons. That is, assuming that the depth of the work-affected layer generated in the pre-processing is constant, and further assuming that the energy spent for uniform polishing is constant, the minimum removal amount of uniform polishing is It requires more than the depth of the altered layer. At this time, in order to surely remove the work-affected layer, it is necessary to set a long polishing time in consideration of safety against variations in the removal distribution shape, and if the removal distribution shape has good reproducibility, this extra polishing This is because it is possible to reduce the time.

If the above two assumptions are assumed,
Uniformity (including reproducibility) is also required as a necessary condition for removing the work-affected layer by uniform polishing in the shortest time (minimum polishing removal amount).

[0009]

However, in the conventional measurement, the wear distribution shape itself, which is the basis for evaluating the reproducibility of the removal distribution shape, and the DC component of the removal distribution shape are accurately measured. There was a problem that it lacked. For example, regarding the former, the surface shape measurement data is apt to include power errors due to surface characteristics (surface roughness, etc.) of the surface to be inspected and temperature fluctuations in the measurement environment, resulting in a wear distribution shape. However, there was a problem that mixing of power errors was unavoidable.

Also in the latter case, when the back surface of the work is adopted as the measurement reference surface, for example, there is a problem that a DC component error is likely to occur due to variations in the support state of the work before and after polishing. The present invention has been made in view of the above-mentioned drawbacks of the prior art, and an object of the present invention is to provide a shape measuring apparatus capable of accurately evaluating the wear distribution shape of uniform polishing by a highly elastic polisher and its reproducibility.

[0011]

In order to solve the above problems, the present invention provides a "measuring device for measuring the shape of a surface to be inspected and a shape data obtained by the measuring device. A shape measuring device for determining the shape change from the shape data measured before and after the shape change of the surface to be inspected, wherein a reference surface provided on the object to be inspected is used as a reference. The shape measuring device is characterized in that the shape change is decomposed into a DC component, a power component, and an undulation component and displayed by performing the measurement.

[0012]

BEST MODE FOR CARRYING OUT THE INVENTION First, the wear distribution shape is evaluated based on the following actions. FIG. 1A is based on the shape measurement data of the surface to be polished before polishing when the uniform polishing is performed only once (replaced flat), and the shape measurement data of the surface to be polished after polishing is XZ. It is plotted as a deviation shape on Cartesian coordinates. That is, n measurement points at equal intervals are sampled in the X-axis direction, and the deviation shape of the surface to be polished before and after polishing is taken as b _j (j = 1 to n), and the positive direction of the Z-axis (downward in the figure). Is plotted. It is assumed that the variation in the shape measurement data of the surface to be polished before and after polishing at each measurement point is equal to σ _S (represented by a double arrow in the figure).

Both the wear distribution shape and the removal distribution shape are
Since it is defined as the relative displacement (deviation shape) of the surface to be polished that occurs before and after polishing, it essentially has a relative property. Therefore, when the removal distribution shape obtained once is evaluated, even if the surface shape before polishing is replaced flat as shown in FIG. 1A, the generality is not lost (however, the actual removal distribution shape is It should be noted that it changes depending on the shape of the pre-processed surface to which uniform polishing is applied). At this time, the deviation shape b _j gives the removal distribution shape, and the variation Δb _{j of} b _j obtained by removing the DC component from the removal distribution shape gives the wear distribution shape.

FIG. 1B shows the removal distribution shape of m pieces obtained by performing uniform polishing m times, with the shape of the pre-machined surface as zero standard (flat) as in FIG. 1A. ,
It is superimposed on the XZ orthogonal coordinates, and the X coordinate values of n sampling points are 2 on the device before and after polishing.
Do not change during xm measurements. Further, as shown in FIG. 1 (c), the deviation data of m removal distribution shapes are
ij (i = 1 to m, j = 1 to n). a _1j (j = 1 to 1
n) is equal to b _j (j = 1 to n) in FIG. In addition, the wear distribution shapes of the m pieces are set to MBK _i (i = 1 to m)
Expressed by

Now, when obtaining the average shape of the wear distribution shape, MBK _i is d _i for each m × n data so that the sum of squares S from the average value is minimized.
The offset is (i = 1 to m). Here, S is defined by the following equation. [Equation 1] S≡ΣΣ (a _ij −d _i −h _j ) ² However, the summation is performed at i = 1 to m and j = 1 to n. Further, h _j (j = 1 to n) in the equation is an average value of m deviations at each measurement point and is defined by the following equation. [Equation 2] h _j ≡Σ (a _ij −d _i ) / m However, the total sum is i = 1 to m. By solving the condition [Equation 3] ∂S / ∂d _i = 0 (i = 1 to m) that minimizes S as a simultaneous equation, d _i can be obtained as a function of d _{1 by} the following procedure. First, the average value v _i of the measured data in the line direction for each MBK _i is defined by the following equation. [Equation 4] v _i ≡Σa _ij / n However, the summation is performed with j = 1 to n. At this time, the simultaneous equations of [Equation 3] can be solved as [Equation 5] d _i −d _i−1 = v _i −v _i−1 . Even if "d ₁ = 0" is set as the standard with the first "measurement data in the line direction (line-shaped data in the moving direction of the sampling point)" as standard, the generality is not lost. At this time, [Formula 6] can be transformed into d _i = v _i −v ₁ . This is "Z = v _i" a straight line of MBK _i
Of each MBK _i on the basis of v _i (ie,
It is shown that, by superimposing it on the reference line “Z = v ₁ ” of the measurement data in the first line direction (offset by d _i ), it is possible to superimpose the wear distribution shape on a root-mean-square basis. ing.

Further, since the reference line of each MBK _i can be obtained without knowing the absolute coordinate values in the Z direction before and after polishing, when evaluating only the reproducibility of the wear distribution shape, the Z before and after polishing can be evaluated. It can be seen that the coordinate value correlation is not always necessary. In addition, the reference line of the measurement data in the first line direction may be set as “v _i = 0”. In this way, the wear distribution shape obtained by offsetting the reference line of MBK _i up to the line of "Z = 0" is represented by MBK _i .

For the above reasons, the wear distribution shape defined as the deviation shape of the two shape data before and after polishing is overlapped by offsetting the average line of the measurement data as a reference and superimposing it. It becomes possible to evaluate reproducibility excluding. Next, consider the wear distribution shape by decomposing it into a power component and a swell component. The power component can be defined in various ways, but in the present invention, it is defined as follows.

First, the rotationally symmetrical work surface shape to be uniformly polished is expressed by the following equation. [Equation 7] Z = X ² / R / {1 + √ (1-κX ² /
R ² )} + C ₂ X ² + C ₄ X ⁴ + C ₆ X ⁶ + C ₈ X ⁸ +
C ₁₀ X ¹⁰ The first half of this equation is the second-order aspherical component, and the coefficient κ in the equation,
And R are the aspherical coefficient and the central radius of curvature, respectively. To simplify the formula, “1 + κ” is replaced with “κ” in the general notation. The latter half of the equation is a high-order aspherical component.

This basic equation will be expressed in the functional form of the following equation. However, i is an even number up to the tenth order. [Equation 8] Z = Z (κ, R, C _i ) Further, the state after polishing is represented by an upper subscript a and the state before polishing is represented by an upper subscript b. At this time, the wear distribution shape is generally expressed by the following equation. [Expression ^{9] MBK = Z (κ a} , R a, C i a) -Z
(Κ ^b , R ^b , C _i ^b ) In the present invention, “κ is an index representing an aspherical shape, and even if the power of the work surface shape changes before and after polishing due to temperature change and the like, κ before and after polishing is common. The power change is limited to the change of R “ΔR”. At this time, Expression 9 is [Expression 10] MBK = Z (κ ^b , R ^b + ΔR, C _i ^a ) −Z
It will be expressed as (κ ^b , R ^b , C _i ^b ). By defining the power component in this way, the swell component can be defined by a residual shape obtained by removing the power component from the wear distribution shape.

Next, consider MBK _i (i = 1 to m) of a cross section having no waviness component but only power component, and FIG.
It should be overlapped as shown in (d). In this case, there are two regions where the variation is substantially zero, as indicated by the solid circles in the figure. However, with respect to the variation of the wear distribution shape, it is inevitable that the area has peculiarity. This indicates that the reproducibility evaluation of the wear distribution shape including the power component is not appropriate. Therefore, the variation of the uniform polishing is evaluated by the residual obtained by removing the power component p _i (i = 1 to m) from each MBK _i , that is, the waviness component q _ij .

Incidentally, the removal of the power component must be the removal of the power component of the cross section when the shape of the cross section is evaluated. Because, if "the obtained cross-sectional shape is rotated about the lens center axis, 3
When the three-dimensional power removal is performed on the “dimensional shape data”, it is expected that the power component remains in the cross-sectional shape of the three-dimensional waviness component passing through the center axis of the lens (because of this. , Power removal was applied to a certain cross-sectional shape,
Regarding the "waviness component of the cross section", the areas above and below the reference line are equal, but for the three-dimensional waviness data obtained by rotating the "waviness component of the cross section" about the lens center axis, the volume above and below the reference line Is not equal to each other), and at that time, the singularity in the vicinity of ● in FIG. 1 (d) cannot be excluded.

In addition, there are two peculiar neighborhoods in the case of a waviness component formed by a cos wave of "period = WD" equivalent to the power component. For example, "period = 2"
In the case of the waviness component formed by the cos wave of “× WD”, there may be four in the vicinity. Here, WD represents the diameter of the test surface. As described above, ● The vicinity may be generated by a swell component other than the power component, but the reason for removing only the power component from the wear distribution shape is as described in [Problems to be Solved by the Invention]. In the shape data of the surface to be inspected, a power error due to the surface property of the surface to be inspected or temperature fluctuation of the measurement environment is likely to occur, and as a result it is expected that the wear distribution shape will also be affected by the power error. This is for the purpose of evaluating the variation caused by the uniform polishing itself.

[0023] Now, when attention is paid to the undulation component q _ij cross-section, just like the above-described process, it is possible to average the waviness component q _ij. Let L be the averaged measurement data in the line direction, and let σ _uj (j = 1 to n) be the variation in the waviness component q _ij at each of the n measurement sampling points (FIG. 2).
(A)). The average value of the power components p _i (i = 1 to m) is p _h , and its variation is σ _p . p _h , σ _p
Both may be considered as the amount of sag in the Z-axis direction.

At this time, the flatness of the wear distribution shape is "L +
it is possible to represent by _{p h} ± 3 × σ p ". FIG.
An average value σ of n σ _uj (j = 1 to n) as shown in (b)
_{The ave} and the variation σ _sgm are respectively expressed by the following equations. [Equation 11] σ _ave ≡ Σσ _uj / n However, the total sum is j = 1 to n. [Equation 12] σ _sgm ² ≡Σ (σ _uj −σ _ave ) ² / (n−
1) However, the total sum is j = 1 to n.

At this time, the variation of the waviness component L can be expressed as follows using the σ _ave and σ _sgm . For example, the approximate variation width of the swell component L is
Using “ΔL = σ _ave + k × σ _sgm ”, “± 3 × Δ
It becomes possible to calculate by "L". The value of k depends on the percentage of the confidence interval, but may be approximately 2-3.

The above discussion assumes that the variations are random and follow a substantially normal distribution.

[0027]

EXAMPLE The operation example described in the operation is the first embodiment of the present invention, which is an example of operation using a shape measuring device capable of evaluating reproducibility of wear distribution shape, and FIG. It is an outline of a device configuration. The measuring instrument 1 is composed of a main body 10, a moving stage unit 11, a probe unit 12, a sample table 13 and the like. The work 3 can be attached to the sample table 13 with good reproducibility. The probe 12a attached to the professional section 12
The movement stage unit 11 moves along the surface 3a to be inspected of the work, sends the obtained shape data to the arithmetic unit 2,
Perform arithmetic processing. The probe 12a has a high precision plane reference reference surface 3b provided on the outer peripheral portion of the work before and after the measurement.
The zero reference of the Z coordinate of the work is taken by picking up.

The reference surface may be provided on the back surface side of the work. For example, when the work is used as a mirror and the back surface shape is free, the back surface of the work itself may be finished into a highly accurate flat surface. Further, even when the work is used as a lens, it is sufficient to finish the back surface of the work piece with high accuracy in a state where the work piece is attached to the work piece. In either case, the probe of the profilometer cannot pick up the reference surface, but there is no problem unless the relative relationship between the reference surface and the surface to be inspected is destroyed.

A pre-processed surface (aspherical surface) on which uniform polishing is performed
Is generally rotationally symmetric, though it depends on how it is created. Therefore, it can be expected that the wear distribution shape (cross-sectional shape) whose reproducibility should be evaluated also has axial symmetry. If this axial symmetry is broken at the level of waviness as a result of uniform polishing, for example, the pre-processed surface used when evaluating reproducibility is the first cause other than the reason due to uniform polishing itself. It is thought that this is due to the axial symmetry and no waviness. Because, for elastic body polishing,
In addition to the ability to remove the work-affected layer generated in the pre-processing without breaking the shape of the pre-processed surface (however, the undulation component of low frequency) (especially when using a high elastic body polisher) This is because it also has a high swell component removal ability (particularly when a low elastic body polisher is used). Therefore, when the pre-machined surface does not have axial symmetry and undulations of high frequency are superimposed, the obtained wear distribution shape loses axial symmetry. On the contrary, if the axial symmetry of the wear distribution shape collapses when such waviness does not overlap, it can be determined that the uniform polishing itself causes asymmetry.

When waviness (level of surface roughness) having an extremely high frequency is superimposed on the entire surface of the pre-processed surface, the variation σ _{s in} measuring the shape of the pre-processed surface becomes large (polishing after uniform polishing. It is expected that it will be much larger than the variation in surface shape measurement), and the value of σ _uj will inevitably become large. Therefore, in the case of uniform polishing that is used for the purpose of removing a normal work-affected layer,
In (a), the actual measurement accuracy of each measurement is evaluated in advance with respect to the measurement error σ _s , which is assumed to be the same in the measurement of 2 × n times, and, for example, a low pass for cutting the surface roughness is used. It is also necessary to use a filter together when evaluating the wear distribution shape.

FIG. 4 shows a first modification of the first embodiment of the present invention, in which the obtained wear distribution shape is processed by a low-pass filter. As described above, this is to prevent the asymmetrical waviness component of the pre-machined surface and the variation caused by the surface texture of the pre-machined surface from being superimposed on the wear distribution shape. This low-pass filter may be used when measuring the shape of the work surface before processing, or may be used as the swell component after removing the power component.

As a second modification of the first embodiment of the present invention, a calculation example for comparative evaluation of removal distribution shapes of uniform polishing by different polishing modes will be given. As aforementioned,
Even if uniform polishing is performed on a workpiece of the same glass type by applying constant energy for a certain period of time, depending on the polishing mode,
The removal distribution shape (wear distribution shape + polishing removal amount) is different. At this time, the criteria for judging the superiority or inferiority of these polishing forms are the flatness (including reproducibility) of the wear distribution shape per unit processing removal amount and the polishing removal amount per unit processing time,
It is necessary to distinguish them. The reason is that removing the work-affected layer may require "processing takes time, but the uniformity of the uniform polishing itself is good," and removal of the same work-affected layer may require "working time is short. This is because the shape may be greatly destroyed. ”

The latter "polishing removal amount per unit processing time" can be easily calculated from the removal distribution shape. However, when the removal distribution shape is a cross-sectional shape, the volume of the shape obtained by rotating the workpiece about the rotational symmetry axis,
It goes without saying that it is necessary to calculate the removal amount. When the former "flatness of wear distribution shape per unit machining removal amount" is calculated, it is possible to specify the machining removal amount serving as a denominator from the removal distribution shape.

[0034]

As described above, by adopting the shape measuring apparatus according to the present invention, it becomes possible to accurately evaluate the wear distribution shape of uniform polishing by the high elastic body polisher and its reproducibility.

[Brief description of the drawings]

FIG. 1 is a principle diagram according to the present invention.

FIG. 2 is a principle diagram according to the present invention.

FIG. 3 is a first embodiment according to the present invention.

FIG. 4 is a first modification of the first embodiment according to the present invention.

[Explanation of symbols]

 1 ... Measuring machine 2 ... Arithmetic device 3 ... Work (object to be measured) 3a ... Surface to be inspected 3b ... Reference reference surface 10 ... Measuring machine main body 11 ・ ・ ・ Movement stage part 12 ・ ・ ・ Probe part 12a ・ ・ ・ ・ Probe 13 ・ ・ ・ Sample stand

Claims (1)

[Claims] 1. A measuring device for measuring the shape of a surface to be inspected,
A shape measuring device for calculating the shape change from the shape data measured before and after the surface to be inspected undergoes a shape change, which comprises an arithmetic device for arithmetically processing the shape data obtained by the measuring device. A shape measuring device characterized in that the shape change is decomposed into a DC component, a power component, and a waviness component and displayed by performing measurement with reference to a reference surface provided on the test object.