JP3041063B2 - Method and apparatus for measuring toroidal surface - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for positioning a reference surface and a surface to be measured when measuring the state of a toroidal surface using the interference of light.

[0002]

2. Description of the Related Art An optical scanning optical system used for a laser beam printer, a laser facsimile, or the like is generally constituted by an anamorphic optical system using a cylindrical lens, a toroidal lens, or the like, in order to correct a tilt of a polygon mirror. . Note that the cylindrical surface can be considered to be a case where one of the radii of curvature is infinite on the toroidal surface. Therefore, in this specification, the toroidal surface includes the cylindrical surface unless otherwise specified.

[0003] These lenses are required to have a surface precision of about 0.1 µm in order to increase the density and uniformity of dots formed on the photosensitive member. From such a background, it is necessary to measure the toroidal surface with a high accuracy of the wavelength λ or less.

In general, a laser interferometer is widely known as a device for measuring a surface with high precision. This interferometer can measure a flat surface or a spherical surface, but can measure an in-plane surface such as a toroidal surface. Cannot be measured for curved surfaces having different centers of curvature of orthogonal main diameter lines.

[0005] Therefore, conventionally, methods for measuring such toroidal surfaces with high accuracy include (a) a "contact needle method" in which a contact needle such as diamond or ruby is brought into contact with a surface to be measured and scanned, or (b) ) There is an "optical probe method" or the like in which light is irradiated on a surface to be measured as a minute spot and the spot is scanned over the entire surface to be measured.

However, in the "contact needle method" of (a), since a hard needle is brought into contact with the surface to be measured, there is a problem that the surface to be measured is damaged or stained. In the optical probe method (b), there is no problem that the surface to be measured is damaged or stained, but it takes a long time to measure because the surface to be measured is scanned at points. there were.

In order to solve this problem, the applicant has proposed a toroidal surface measuring apparatus as shown in FIGS. 7 (a) and 7 (b) in Japanese Patent Application No. 2-126649.

In FIGS. 7A and 7B, reference numeral 1 denotes a light source, and a gas laser or a semiconductor laser having high coherence is used. Reference numerals 2a and 2b denote beam expanders for expanding a narrow light beam from the light source 1 or the like to an appropriate size. Reference numeral 3 denotes a spatial filter that cuts off unnecessary light such as stray light and reflected light. Reference numeral 4 denotes an optical isolator, which includes a beam splitter 4a and a λ / 4 plate 4b. The luminous flux expanded by the beam expanders 2a and 2b is
Through the toroidal surface 7a as the measured surface of the subject 7
Reach The toroidal surface 7a has main diameter lines AB and CD orthogonal to each other at the apex.
Is formed by rotating along the other main diameter line AB, and the main diameter line CD is hereinafter referred to as the G main diameter line, AB
Is referred to as an R main diameter wire.

The final surface of the objective lens 6 is a reference surface 6a as a semi-transparent mirror, and is formed as a spherical surface having a predetermined radius of curvature. That is, the center of curvature of the reference surface 6a is disposed at a position substantially coincident with the finished center of curvature of the G main diameter line (CD) of the toroidal surface 7a. Further, the reference surface 6a or the toroidal surface 7a is arranged so as to be able to slightly shift and / or tilt in the XZ section. Then, a part of the light incident on the objective lens 6 is reflected by the reference surface 6a,
The rest transmits and irradiates the toroidal surface 7a.

Reference numeral 8 denotes a turntable for fixing the object 7 to be measured, which has a rotation axis coinciding with the center of curvature of the R main diameter line (AB) of the toroidal surface 7a, and is driven by a DC servo motor, a stepping motor or the like (not shown). The coherent light that has passed through the reference surface 6a can scan the toroidal surface 7a, which is the surface to be measured, along the R main diameter line. In addition, the turntable 8
It is possible to shift in the optical axis direction so that the center of rotation of the turntable 8 and the center of curvature of the reference surface 6a can be matched. The shift in the optical axis direction may be performed on the reference surface 6a or the objective lens 6.

The reference light reflected by the reference surface 6a and the test light reflected by the toroidal surface 7a return along the optical path that came together and are superimposed. Then, when returning to the optical isolator 4, all of the light is reflected by the reflection surface 4c of the beam splitter 4a by the action of the λ / 4 plate 4b and the beam splitter 4a, and reaches the image sensor 10 via the focusing lens 9.

Incidentally, since the reference surface 6a is usually a spherical surface and the surface to be measured is the toroidal surface 7a, interference occurs in an elongated rectangular measurement portion parallel to the G main diameter line whose both surfaces can be regarded as substantially parallel.

Therefore, by moving the objective lens 6 and the focusing lens 9 in the optical axis direction, an image 11 of the interference fringe of the measurement portion 11 'can be formed on the image sensor 10 as shown in FIG. .

Further, by rotating the turntable 8 along the R main diameter line, it is possible to observe the surface shape of the entire toroidal surface 7a and surface accuracy such as surface roughness and surface undulation. Measurement data relating to surface accuracy can be obtained from the output.

Although the above example is a Fizeau interferometer, other interferometers such as a Michelson interferometer can be similarly applied.

When observed with the above-mentioned interference system, if the ideal toroidal surface without any deviation in surface accuracy and surface shape is located at an ideal position with respect to the reference surface, the wavefront of the reference light is used as a reference. The wavefront of the test light is flat.

[0017]

However, in the above-described measurement method and the measurement by the optical probe method described above,
If the setting of the toroidal surface 7a as the surface to be measured deviates from the ideal position, a large error occurs in the surface accuracy measurement.

When the toroidal surface 7a is shifted from the ideal position, the shift is determined by shifting in the x direction, shifting in the y direction,
A shift in the z direction, rotation around the x axis (hereinafter referred to as “α tilt”), rotation around the y axis (hereinafter referred to as “β tilt”), and rotation around the z axis (hereinafter referred to as “γ tilt”) are considered separately.

Then, the shape of the wavefront of the test light with respect to the ideal toroidal surface changes as shown in FIG. 9 due to the above-described shifts and tilts.

FIG. 9A shows a case where a shift has occurred in the x direction, and the wavefront is tilted (β tilt) in the x direction.

FIG. 9B shows a case where a shift in the y direction or α tilt occurs. The wavefront tilts in the y direction (α tilt) and has a curvature in the x direction.

FIG. 9C shows a case where a shift in the z direction (shift in the optical axis direction) occurs, and the wavefront is defocused in the x direction and the y direction, and becomes a toroidal wavefront.

FIG. 9D shows a case where β tilt occurs. The wavefront has β tilt and has a curvature in the y direction.

FIG. 9E shows a case where a γ tilt has occurred, and the wavefront has astigmatism in the 45 ° direction.

FIG. 9F shows a case where the entire turntable 8 has a z-shift (shift in the optical axis direction). The wavefront in this case is a cylinder wavefront having a curvature in the x direction.

That is, when the surface to be measured is shifted or tilted from the ideal position, the measurement data obtained from the entire surface includes the above setting error.

The present invention has been made in order to solve the above-mentioned problem, and has as its object to provide a method for measuring a toroidal surface that reduces a setting error.

[0028]

In order to achieve the above object, the present invention irradiates coherent light from the same light source to a surface to be measured and a reference surface serving as a reference, and reflects reflected light from both surfaces. In the method of measuring the surface accuracy by making interference fringes by superimposing,
An interference fringe is created for a measurement portion parallel to one of the orthogonal main diameter lines on the toroidal surface to be measured, and the measurement portion is scanned in parallel with the other main diameter line to measure data on the entire surface. W (x, y) is obtained, and an aberration function Sn is obtained,

(Equation 7) (1)

(Equation 8) (2)

(Equation 9) (3) A coefficient Cn of the aberration function is obtained from the above, and the measurement data W (x, y) is corrected to obtain a true surface accuracy W (x, y) real.
Is adopted.

Alternatively, the surfaces to be measured are defined as x,
It is desirable to adopt a configuration in which a position in which the Cn is minimized is obtained by shifting in the y and z axis directions and / or tilting around the x, y and z axes.

[0030]

The reference light reflected by the reference surface and the test light reflected by the measurement surface interfere with each other on a measurement portion along one main diameter line of the toroidal surface to form interference fringes. By scanning this interference fringe along the other major diameter line of the toroidal surface, surface data of the entire toroidal surface can be obtained.

As described above, the data W of the entire surface to be measured is obtained.
(X, y)

[Table 1] Define each aberration function Sn as

(Equation 10) (1)

[Equation 11] (2)

(Equation 12) The coefficient Cn of the aberration function is calculated according to (3), the correction is subtracted from each measurement data W (x, y), and the true surface accuracy W (x, y) real is obtained. Shape and surface accuracy can be known.

The driving means shifts the surface to be measured in x, y, and z axis directions orthogonal to each other,
By tilting around the y and z axes, a position where the Cn is minimized is determined, and setting is performed so that the measured surface approaches the ideal position.

[0033]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a toroidal surface measuring apparatus according to the present invention, which is substantially the same as that shown in the conventional example shown in FIG. 7, so that the subject 7 can be shifted in the x, y, and z axis directions. The difference is that a six-axis fine drive unit 12 capable of α, β, and γ tilting with respect to the x, y, and z axes is provided. or,
A turntable z-axis drive 12 ′ for moving the turntable 8 in the optical axis direction is provided below the turntable 8 as a part of the fine movement drive device 12. And the center of curvature of the reference surface 6a, and is the same as that described in the above-mentioned prior application.
These drive units are designed to be able to move
For example, it is composed of an electrostrictive element or the like.

FIG. 2 is a flowchart for explaining the operation of the present invention. As described in the conventional example, an interference fringe is formed for each measurement portion 11 'by the toroidal surface accuracy measuring device of FIG. 1, and the interference fringe is scanned along the main diameter line AB to measure the entire toroidal surface. .

The measurement result is taken out as the output of the image sensor 10, and a large number of measurement data W (x, y) for the entire toroidal surface is obtained (S1).

The measurement data W thus obtained
(X, y) is input to the next arithmetic unit 12 as wavefront data.

As described above, actually, the measured surface 7a
Is not an ideal surface, and the position of the surface 7a to be measured is displaced from the ideal position, so that the wavefront is distorted.
The surface shape must be measured accurately. Arithmetic unit 13
First, it is determined whether or not the setting error is to be corrected (S2). If the correction is not necessary, it is output as it is as the surface accuracy data (S6). If the correction is necessary, the following procedure is performed.

The present invention employs the concept of a linearly independent aberration function Sn in order to express the wavefront distortion due to the setting deviation, and is defined by the equations shown in the following table.

[Table 2]

FIGS. 3A to 3G show the above aberration function Sn
Shows the wavefront shape represented by. In addition, the setting deviation that can be expressed by each aberration function Sn is described in the above table.

By introducing such an aberration function,
The wavefront distortion caused by setting the deviation of the following (a) (f), ( a) in x shift S _2, (b) y shift and α shift in S ₃ and S _8, (c) z Shift in S ₄ and S ₅ is,
(d) β tilt is S ₂ and S ₇ , (e) γ tilt is S
In _6, (f) z shift of the turntable in S _4, the can be respectively represented.

Generally, when the above-mentioned aberration function Sn is used,
The true surface accuracy W (x, y) real can be expressed as the following equation.

(Equation 13) (1) Here, W (x, y): measurement data of the wavefront Sn: aberration function of the wavefront due to setting deviation Cn: coefficient of the aberration function The coefficient Cn of the above-mentioned aberration function is unknown, but a method of obtaining this value , A least squares approximation is applied. First, square both sides of equation (1) to obtain {W (x, y) real} ²
= E is obtained as E = S (S3),

[Equation 14] (2)

(Equation 15) The condition (3), determine the Cn from the coefficients C ₁ of the aberration function (S4), the true surface accuracy W (x, y) from Equation (1) determine the real (S5).

The correction value is obtained from the value of the coefficient Cn of the aberration function thus obtained, the measurement data W (x, y) is corrected, and the wavefront generated by the setting error is subtracted to obtain the true surface accuracy W (x, y) Calculate and output real (S
6).

FIG. 4 shows an example of the above procedure.
(a) is the measurement data W obtained from the output of the image sensor 10.
The state of the toroidal surface 7a represented by (x, y) is shown. Since this includes setting errors,
As shown in (b), the error is calculated from the above equations (1) and (3). Then, as shown in (c), the true surface accuracy W
Find (x, y) real.

FIG. 5 is a block diagram for controlling the fine-movement drive device 12 based on the output of the arithmetic unit 13. The fine-movement drive device 12 includes the rotary table z-axis drive 1 described above.
2 'is also merged. Since the rotary table z-axis drive matches the center of rotation of the rotary table 8 with the center of curvature of the reference surface 6a, it may be provided on the objective lens 6 as described above. FIG. 6 shows a fine movement drive device 1.
6 is a flowchart showing a method for automatically correcting a setting error by controlling the setting of the second setting.

That is, as described above, the aberration function Sn,
And the coefficient Cn of the aberration function is obtained, and if the influence of Cn is not negligible with respect to the required true surface accuracy W (x, y) real, the surface to be inspected is moved by the fine movement drive device 12, and Repeat until the value is sufficiently small and the effect on surface accuracy is negligible.

In this case, as shown in FIG. 5, the calculated value of Cn is converted into an electric analog signal by a D / A converter, and is amplified to an appropriate gain.
By controlling the input to 2, the setting deviation can be suppressed to a smaller extent.

Outputs corresponding to C _{2 to} C ₈ output by the arithmetic unit 13 are input to the fine movement drive unit 12 and are used for shifting in the x, y, and z directions and α, β, and γ tilts in the unit. The drive of each axis corresponding to the axis is driven.

Thereafter, the measurement of the toroidal surface 7a is performed again, and the obtained measurement data W (x, y) is input to the arithmetic unit 13, and Cn is calculated. If Cn is small enough to be ignored, , The true surface accuracy W (x, y) real is output, and the measurement is terminated.

For example, C ₄ is output from the aberration function x ² , which is multiplied by a and input to the z-axis drive of the turntable. The z-axis drive of the turntable moves the turntable 8 in the z-axis direction by an amount corresponding to the input.

Similarly, the output of C ₅ is multiplied by b, and the z
Enter the shaft drive, receives the output of the C ₂ to c times the x-axis drive. Moreover, inputting the output of the C ₇ to d times to β axis drives. Further, the output of C ₃ is multiplied by e, and
The output of ₈ is multiplied by f and combined by an adder circuit and input to the y-axis drive or α-axis drive. Finally, the output of C ₆ is multiplied by g and input to the γ-axis drive.

The above method can be performed automatically,
Setting deviation can be minimized.

[0052]

As described above, according to the present invention, the surface shape and surface accuracy of the toroidal surface as the surface to be measured are
The measurement can be performed in a state where an error due to a deviation from the reference plane is eliminated. Further, since the setting error can be known by calculating the coefficient of the aberration function, it is possible to correct the error by minimizing the error by controlling the fine movement drive device, and it becomes possible to measure the surface shape and the surface accuracy with higher precision. .

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a toroidal surface measuring device of the present invention.

FIG. 2 is a flowchart showing an embodiment of a toroidal surface measuring method according to the present invention.

FIGS. 3A to 3G are diagrams showing a wavefront shape represented by an aberration function. FIGS.

4A is a diagram showing a state of a surface to be measured indicated by measurement data, FIG. 4B is a diagram showing a setting error, and FIG.
It is a figure showing the state of the true measurement side.

FIG. 5 is a block diagram of a device for correcting a setting error by a fine movement drive device from an aberration function.

FIG. 6 is a flowchart illustrating a method of automatically correcting a setting error by a fine movement drive device from an aberration function.

7A and 7B are diagrams showing a toroidal surface measuring apparatus described in the prior application, wherein FIG. 7A is a yz plane view, FIG. 7B is an xz plane view,

FIG. 8 is a diagram of interference fringes for a measurement portion imaged on an image sensor.

FIGS. 9A to 9F are diagrams showing the relationship between various setting errors and the wavefront of the test light.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Light source 6a Reference surface 7 Subject 7a Test surface 8 Turntable 10 Image sensor 11 Interference fringe 11 'Measuring part 12 Fine movement drive device 13 Computing device CD One main diameter line (G main diameter line) orthogonal to the toroidal surface AB The other main diameter line (R main diameter line) Sn aberration function Cn coefficient of aberration function

──────────────────────────────────────────────────続 き Continued on the front page (58) Fields surveyed (Int. Cl. ⁷ , DB name) G01B 9/00-11/30 102 G01M 11/00-11/08

Claims (4)

(57) [Claims] 1. A method of irradiating coherent light from the same light source to a surface to be measured and a reference surface serving as a reference, superimposing reflected light from both surfaces to form interference fringes, and measuring surface accuracy,
An interference fringe is created for a measurement portion parallel to one of the orthogonal main diameter lines on the toroidal surface to be measured, and the measurement portion is scanned in parallel with the other main diameter line to measure data on the entire surface. W (x, y) is obtained, and the aberration function Sn and (1) [Equation 2] (2) [Equation 3] (3) calculating the coefficient Cn of the aberration function from the measurement data, and correcting the measurement data W (x, y) to obtain a true surface accuracy W (x, y) real. Measurement method. 2. A toroidal surface is defined by x,
The method for measuring a toroidal surface according to claim 1, wherein a position where the Cn is minimized is obtained by shifting in the y and z axis directions and / or tilting around the x, y and z axes. 3. An apparatus for irradiating coherent light from the same light source to a surface to be measured and a reference surface serving as a reference, superimposing reflected light from both surfaces to form interference fringes, and measuring surface accuracy,
A reference surface having a predetermined curvature with respect to one of the orthogonal main diameter lines on the toroidal surface of the subject having the toroidal surface, and a turntable for rotating along the other main diameter line, The subject is shifted to x, y, z axes and x, y
a fine movement drive device that tilts around the y and z axes, an image sensor that forms an image of interference fringes, measurement data W (x, y) output from the image sensor, and an aberration function Sn
And (1) [Equation 5] (2) [Equation 6] A torsion surface measuring device, comprising: an arithmetic device for obtaining a coefficient Cn of the aberration function according to (3), and obtaining a true surface accuracy W (x, y) real from the above result. 4. The toroidal surface measuring device according to claim 3, wherein the fine drive device is controlled by an output of the arithmetic unit.