JPH06201344A - Measurement of surface to be inspected - Google Patents

Abstract

(57) [Summary] [Object] The present invention is directed to an apparatus for measuring the entire surface 7a to be measured by connecting interference fringes 11 formed on one measurement section 11 ', and is caused by a setting deviation of the surface 7a to be measured. It is an object of the present invention to provide a method for performing highly accurate measurement by subtracting the error amount of [Arrangement] An aberration function is previously input to the arithmetic unit 15, and measurement data W (x,
y) is input to the calculation device 15, the coefficient Cn of the aberration function is calculated from a predetermined formula, the measurement data W (x, y) is corrected, and the true surface accuracy W (x, y) real is obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for measuring the surface shape and surface accuracy of a surface to be inspected by using the interference effect of light, and in particular,
The present invention relates to a method for correcting a setting deviation of a surface to be inspected.

[0002]

2. Description of the Related Art Coherent light from the same light source is applied to a test surface and a reference surface to form interference fringes on one measurement section of the test surface, and the test surface is scanned in a direction intersecting the measurement section. As a method of measuring the surface to be inspected, the applicant proposes a toroidal surface measuring device shown in FIGS. 11A and 11B in Japanese Patent Application No. 3-50104.

In FIG. 11 (a), 1 is a light source,
A gas laser or a semiconductor laser having high coherence is used. The coherent light from the light source 1 passes through the beam expander 2a, the stray light and the reflected light are cut by the spatial filter 3, passes through the optical isolator 4 and another beam expander 2b, and passes through the objective lens 6 to be received. The toroidal surface as the inspection surface 7a is reached. This toroidal surface is formed by rotating a G main radial line AB orthogonal to each other at the apex along the R main radial line CD, and the center of curvature of the R main radial line is on the rotary shaft 12.

The final surface of the objective lens 6 is a reference spherical surface 6a as a semi-transparent mirror, and it is arranged so that the center of curvature of the reference surface 6a is on the rotation axis 12. A part of the coherent light reaching the reference surface 6a from the light source 1 is reflected to become reference light, and the rest is transmitted. The transmitted coherent light is refracted by the objective lens 6, travels so as to converge on the rotation axis 12, and is vertically incident on the surface 7a to be inspected.

The test light reflected by the test surface 7a reverses the incident optical path, passes through the reference surface 6a, and is superimposed on the reference light.
The reference light and the test light that have been superimposed are λ of the optical isolator 4.
The image sensor 1 is reflected by the reflecting surface 4c by the action of the / 4 plate 4b and the beam splitter 4a, and passes through the converging lens 9.
Reaches 0.

By the way, the reference surface 6a is a spherical surface, and the test surface 7
Since a is a toroidal surface, the reference light and the test light produce interference fringes on one measurement cross section parallel to the R main diameter line, which can be regarded as substantially parallel to the reference surface, and the slit shape on the image sensor 10. Interference fringe image is formed. The shape and accuracy of the measurement cross section can be measured by this interference fringe image.
FIG. 11 (b) shows an interference fringe image 1 for one measurement section 11 '.
1 shows a state in which an image is formed on the image sensor 10.

The translation table 13 moves the subject 7 in a direction parallel to the rotation axis 12 (y direction). When one interference fringe image is formed as described above, the subject 7 is rotated. The entire toroidal surface can be measured by scanning in the same direction and similarly forming interference fringes one after another.

By using this apparatus, not only the toroidal surface but also the cylinder surface and the flat surface can be measured with high accuracy of wavelength or less.

However, in the above apparatus, if the surface 7a to be inspected is displaced from the ideal position, a large error will occur in the surface accuracy. This setting deviation is x,
Shifts in the y and z directions, tilts around the x axis (hereinafter referred to as “α tilt”), tilts around the y axis (hereinafter referred to as “β tilt”)
It can be divided into six types of tilts about the z axis (hereinafter referred to as “γ tilt”), and the actual setting deviation is a complex combination of these six deviations.

FIGS. 12 (a) to 12 (f) independently show the above six setting deviations, and show what the setting deviations are in the wavefront shape of the measured value when the test surface is a barrel-shaped toroidal surface. It shows whether or not it has an influence. However, the test surface 7a is assumed to have an ideal shape.
If the surface to be inspected is set to the ideal position,
The wavefront of the measurement data is flat.

(A) shows the case where the surface 7a to be inspected is shifted in the x direction, and the wavefront of the measurement data is tilted in the x direction. (b) shows the case where the surface 7a to be measured is shifted in the y direction, and the wavefront of the measurement data is tilted in the y direction.

(C) shows the case where the surface 7a to be tested is shifted (defocused) in the z direction, and the wavefront of the measurement data has a curvature in the x direction and the y direction, and becomes a toroidal wavefront. (d)
Indicates that the surface 7a to be inspected is tilted by α, and the wavefront of the measurement data is tilted in the y direction and has a curvature in the x direction.

(E) shows the case where the surface 7a to be inspected is β-tilted, and since the surface to be inspected has a surface having a rotation axis 12 parallel to the y-axis, the wavefront of the measurement data does not change and becomes flat. .
(f) is the case where the surface 7a to be inspected is tilted by γ, and the measurement data shows 45 ° astigmatism.

Although (g) is different from the setting deviation,
It is a figure which shows the wavefront shape at the time of performing shape measurement about the longitudinal direction (y direction) of the to-be-tested surface 7a. The wavefront of the measurement data is a cylinder wavefront that is flat in the x direction and has a curvature in the y direction. Of course, the surface to be inspected is in the ideal position.

FIGS. 13 (a) to 13 (f) illustrate the wavefront error shape associated with the setting deviation when the surface 7a to be detected is a cylinder surface. If the surface 7a to be inspected is set at the ideal position, the wavefront of the measurement data will be flat.

(A) shows the case where the surface 7a to be tested is shifted in the x direction, and the wavefront of the measurement data is tilted in the x direction. (b) is the case where the surface 7a to be inspected is shifted in the y direction, and no error occurs in the observation data.

(C) shows the case where the surface 7a to be measured is shifted (defocused) in the z direction, and the wavefront of the measurement data has an error component of the cylinder wavefront having a curvature only in the x direction.
(d) is the case where the surface 7a to be inspected is α-tilted, and the wavefront of the measurement data is a wavefront shape error that is tilted in the y direction and has a curvature in the x direction.

(E) is the case where the surface 7a to be inspected is tilted by β, and no error occurs in the measurement data for the same reason as in the case of the toroidal surface. (f) is the case where the surface 7a to be inspected is tilted by γ, and 45 ° astigmatism occurs in the wavefront of the measurement data.

FIGS. 14 (a) to 14 (f) explain the influence of the setting deviation when the surface 7a to be tested is a flat surface. Then, if the surface to be inspected 7a is set to an ideal position and is a perfect plane, the wavefront of the measurement data will be flat.

(A) is the case where the surface 7a to be measured is shifted in the x direction, (b) is the case where it is shifted in the y direction, and (c) is the z direction.
In case of shifting in the direction, (f) is in case of γ tilt, and in all of these cases, no error occurs in the measurement data,
It becomes a flat wavefront.

(D) shows the case where the surface 7a to be inspected is tilted by α. The wavefront of the measurement data has a wavefront shape error tilted in the y direction. (e) is the case where the test surface 7a is β-tilted, and a wavefront shape error tilted in the x direction occurs in the wavefront of the measurement data.

As described above, if a setting deviation occurs on the surface to be inspected, a large error will occur in the measurement data. In particular, when measuring the surface accuracy with an accuracy of less than or equal to the wavelength, the error component due to the setting deviation cannot be ignored. Also, barrel-shaped toroidal surface, long cylinder surface,
When measuring a long plane or the like, the influence of the setting deviation is large, and it was difficult to measure these with a conventional device.

[0023]

DISCLOSURE OF THE INVENTION The present invention is a device for measuring the entire surface by connecting interference fringes formed on one measurement cross section and subtracting the error due to the above-mentioned setting deviation to achieve high accuracy. It is an object of the present invention to provide a method and apparatus capable of measuring surface accuracy and surface shape and capable of measuring a barrel-shaped toroidal surface, a long cylinder surface, a long flat surface, and the like.

[0024]

To achieve the above object, the present invention irradiates a coherent light beam from the same light source on a test surface and a reference surface, and causes interference fringes on one measurement cross section of the test surface. And measuring the entire surface by scanning the surface to be measured in a direction intersecting with the measurement cross section and obtaining measurement data W (x, y) for the entire surface to be linearly independent. The following equation W (x, y) real = W (x, y) −ΣCnFn (x,
y) S = ∬ {W (x, y) −ΣCnFn (x, y)} ² dx
dy ∂S / ∂C ₁ = 0, ∂S / ∂C ₂ = 0, …… ∂S / ∂C
From n = 0, the coefficient Cn of the aberration function Fn is obtained by least-squares approximation, the measurement data W (x, y) is corrected, and the true surface accuracy W is obtained.
It is characterized by a configuration for obtaining (x, y) real.

When the surface to be inspected is a barrel-shaped toroidal surface, the aberration functions Fn are F ₁ : 1, F ₂ : x, F ₃ : y, F ₄ :
x ² , F ₅ : y ² , F ₆ : xy, and F ₇ : y−x ² y, the least square approximation is performed using these aberration functions, and the coefficient Cn
Is calculated.

When the surface to be inspected is a cylinder surface, the aberration relation
Number Fn, F₁: 1, F₂: x, F₃: x ², F_Four: xy, F_Five:
y-x²y, and if the surface to be inspected is a flat surface,
Number Fn, F₁: 1, F₂: x, F₃: y
In addition, the measurement data W (x, y) for the entire surface to be inspected
Then, a linearly independent aberration function Fn is determined, and the following equation S = ∬ {W (x, y) −ΣCnFn (x, y)}²dx
dy ∂S / ∂C₁= 0, ∂S / ∂C₂= 0, …… ∂S / ∂C
The coefficient Cn of the aberration function Fn is obtained by the least square approximation from n = 0.
Therefore, the setting deviation of the surface to be inspected is calculated from the coefficient and
6-axis fine adjustment for setting deviation correction in each direction according to the amount
If the drive device is used, there will be
If it is too large, it is possible to correct the deviation.

[0027]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the measuring device of the present invention. Since it is almost the same as that described in the conventional example, the difference will be described. Reference numeral 14 denotes a 6-axis drive device, which is a translation table 13 and a subject 7
It is located between and. Although not shown, inside the 6-axis drive device 14, x, y, z on the surface 7a to be inspected is detected.
It incorporates a mechanism that uses a stepping motor or the like to give direction shifts and α, β, and γ tilts. 1
Reference numeral 5 is a computing means, which uses a computer.

As described in the conventional example, the interference fringe image 1
When 1 is imaged on the image sensor 10, the output of each element of the image sensor 10 is input to the arithmetic unit 15, and surface data or wavefront data W (x,
y) is obtained. However, as described above, the measurement data W (x, y) includes an error due to the setting deviation.

If the distortion of the wavefront due to the setting deviation as described with reference to FIGS. 12, 13 and 14 can be expressed by the linearly independent aberration function Fn, this aberration function is input to the arithmetic unit 15 in advance. Then, the calculation device 15 can calculate an appropriate coefficient Cn for each aberration function Fn to subtract the error due to the setting deviation from the measurement data W (x, y). That is, the true value W (x, y) real can be obtained from the following expression W (x, y) real = W (x, y) -ΣCnFn (x, y) (1). As a method for obtaining the coefficient Cn, the least square method is used.
That is, if both sides of the above equation are squared and the sum of squares of W (x, y) real is E, S = ∬ {W (x, y) -ΣCnFn (x, y)} ² dxdy (2 ) Further, each coefficient C _{1 to} Cn can be obtained as ∂S / ∂C ₁ = 0, ∂S / ∂C ₂ = 0, ... ∂S / ∂Cn = 0 (3).

If the surface 7a to be tested is a barrel-shaped toroidal surface,
The setting deviation can be expressed by the following seven linearly independent aberration functions.

[Table 1] When these are shown in the figure, the wavefront shapes shown in Fig. 2 (a) to (g) are obtained.

By the way, as described above, the wavefront error due to the setting deviation of the barrel-shaped toroidal surface is shown in FIG. 12 (a).
Although it has a shape like (g), it can be approximated by the following function when the x and y coordinates are shown on the sin θ scale.

[Table 2]

The sum E _{1 of} aberration functions can be expressed as follows.

[Equation 1]

On the other hand, the setting error amount E ₂ can be expressed as follows based on Table 2. _{E 2 ≒ a 1 + a 2} (x) + a 3 (y) + a 4 (y 2) + a 5 (x 2 + y 2) + a 6 (xy) + a 7 (y-x 2 y) = a 1 + a 2 (x ) ＋ a ₃ (y) ＋ a ₅ (x ² ) ＋ (a ₄ ＋ a ₅ ) (y ² ) ＋ a ₆ (xy) ＋ a ₇ (y−x ² y)… (5)

That is, E ₁ and E ₂ can be expressed by the same equations, and the setting deviation can be corrected by the seven aberration functions from the equation (1). The results are shown in FIG. FIG. 3 (a) shows before setting correction and (b) shows after setting correction.

When the surface 7a to be detected is a cylinder surface, the setting error can be subtracted by the same procedure as in the case of the toroidal surface. For a cylinder surface, the aberration function is

[0036]

[Table 3] When these are shown in the figure, the wavefront shapes shown in Fig. 4 (a) to (e) are obtained.

By the way, the wavefront error due to the setting deviation of the cylinder surface has a shape as shown in FIGS. 13 (a) to 13 (f). When the x and y coordinates are shown on the sin θ scale, the following Table 4 It can be approximated by the function shown in.

[0038]

[Table 4]

Sum of aberration functions in Table 3 E ₁ (second side of right side of equation (1))
Item) can be expressed as follows.

[Equation 2]

On the other hand, the setting error amount E ₂ can be expressed as follows based on Table 4. E ₂ ≈a ₁ + a ₂ (x) + a ₃ (x ² ) + a ₄ (xy) + a ₅ (y−x ² y) (7) E ₁ and E ₂ are expressed in exactly the same form. Therefore, the error due to each setting deviation can be corrected by the five functions in Table 3 regarding the equation (1). Figure 5
(a) shows the results before the correction and (b) shows the results after the correction.

Next, when the surface 7a to be tested is a flat surface, the setting error can be subtracted by the same procedure as above.
The aberration function in the case of a plane is as follows.

[0042]

[Table 5] When these are represented in the figure, the wavefront shapes as shown in FIGS. 6 (a) to 6 (c) are obtained.

By the way, the wavefront error due to the setting deviation of the plane has a shape as shown in FIGS. 14 (a) to (f), but when the x and y coordinates are shown on the sin θ scale, it is approximated by the following function. it can.

[0044]

[Table 6]

Sum of aberration functions in Table 5 E ₁ (second side of right side of equation (1))
Item) can be expressed as follows.

[Equation 3]

On the other hand, the setting error amount E ₂ can be expressed as follows based on Table 6. E ₂ ≈a ₁ + a ₂ (x) + a ₃ (y) E ₁ and E ₂ are expressed in exactly the same form. Therefore, regarding the formula (1), the error due to each setting deviation is calculated by the function of Table 5. Can be corrected. FIG. 7A shows the results before correction, and FIG. 7B shows the results after correction.

As explained above, according to the present invention,
It is not necessary to correct the setting deviation of the surface 7a to be inspected, but if the setting error is too large, the correction accuracy becomes insufficient. That is, the wavefront shape for each setting deviation deviates from the approximation function.

8 to 10 show an embodiment for solving such a problem. FIG. 8 shows a setting deviation correcting device for the surface 7a to be tested, which is applied when the surface to be tested is a toroidal surface. The one-dot chain line indicates the part of the arithmetic unit 15 that calculates the aberration coefficient Cn in particular. Reference numeral 16 is a D / A converter, and 17-1 to 17-6 are amplifiers. 14-
1 to 14-6 are drive devices provided in the 6-axis drive device 14, 14-1 is an x-axis drive, 14-2
Indicates y-axis drive, 14-3 indicates z-axis drive, 14-5 indicates γ-axis drive, and 14-6 indicates α-axis drive.

The value of C ₂ calculated by the arithmetic unit 15 is D
A / A converter 16 converts into an analog value, and amplifier 17-
After being amplified by 1, it is input to the x-axis drive 14-1,
The x-axis drive feeds back the surface to be inspected 7a in the x-axis direction by feeding back it according to an input signal from the amplifier 17-1.

The same is done for C ₃ to C ₇ below. The C _5, but it should be inputted to the β-axis drive, as shown in FIG. 12 (e), since the data is not subject to change, it is not necessary to fix, the β-axis drive connected Not not.

FIG. 9 shows a setting deviation correcting device when the surface 7a to be measured is a cylinder surface. Aberration coefficients required for correction are C ₂ , C ₃ , C ₄ and C ₅ , and the amplifier 1
The signals are input to the x-axis drive 14-1, the z-axis drive 14-3, the γ-axis drive 14-5, and the α-axis drive 14-6 via 7-1 to 17-4.

FIG. 10 shows a correction device when the surface 7a to be tested is a flat surface. In this case, the aberration coefficients required for correction are C ₂ and C ₃ , and the α-axis drive 14-6 and the β-axis drive 14-
4 is input.

[0053]

As described above, according to the present invention, an interference fringe is formed on one measurement cross section of the surface to be inspected, and the interference fringe is scanned in a direction intersecting the measurement cross section to scan the entire surface of the inspection surface. When measuring surface accuracy and surface shape, even if there is a setting deviation on the surface to be inspected, the measurement error can be corrected and highly accurate measurement can be performed. Therefore, it has become possible to measure long flat mirrors, long cylinder surfaces, and barrel-shaped toroidal surfaces, which were difficult to measure in the past. Further, if the constitution is such that the aberration coefficient is calculated and the setting deviation of the surface to be inspected is corrected by the 6-axis drive device, it is possible to perform measurement even when the setting deviation is large, and it becomes easy to correct the setting of the surface to be inspected.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of an apparatus for carrying out the measuring method of the present invention, (a) is a yz plane view, and (b) is an xz plane view.

FIGS. 2A to 2G are diagrams showing aberration functions when the surface to be measured is a barrel-shaped toroidal surface.

FIG. 3 is a diagram showing a state of correction by an aberration function when the surface to be inspected is a barrel-shaped toroidal surface, where (a) is before correction and (b) is after correction.

FIGS. 4A to 4E are diagrams showing aberration functions when the surface to be measured is a cylinder surface.

5A and 5B are diagrams showing a state of correction by an aberration function when the surface to be inspected is a cylinder surface, in which FIG. 5A is before correction and FIG.

6A to 6C are diagrams showing aberration functions when the surface to be inspected is a flat surface.

FIG. 7 is a diagram showing a state of correction by an aberration function when the surface to be inspected is a flat surface, in which (a) is before correction and (b) is after correction.

FIG. 8 is a diagram showing a configuration of an apparatus for correcting a setting deviation when the surface to be inspected is a barrel-shaped toroidal surface.

FIG. 9 is a diagram showing a configuration of an apparatus for correcting a setting deviation when the surface to be inspected is a cylinder surface.

FIG. 10 is a diagram showing a configuration of an apparatus for correcting a setting deviation when the surface to be inspected is a flat surface.

11A and 11B are diagrams showing a configuration of a conventional barrel-type toroidal surface measuring device, in which FIG. 11A is a yz plane view, and FIG. 11B is a diagram showing a state in which an interference fringe image is formed on an image sensor.

FIGS. 12 (a) to 12 (f) are diagrams showing an error that occurs in a measurement wavefront due to a setting deviation when the surface to be measured is a toroidal surface, and FIG. 12 (g) shows no setting deviation and a shape in the y direction. It is a figure which shows the measured wavefront at the time of measuring.

13 (a) to 13 (f) are diagrams showing an error caused in a measurement wavefront due to a setting deviation when the surface to be inspected is a cylinder surface.

14A to 14F are diagrams showing an error caused in a measurement wavefront due to a setting deviation when the surface to be inspected is a flat surface.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 light source 6a reference surface 7a test surface 11 interference fringe image 11 'measurement cross section 14 6-axis drive device

Claims (5)

[Claims] 1. A coherent light beam from the same light source is applied to a test surface and a reference surface, interference fringes are formed on one measurement cross section of the test surface, and the test surface is scanned in a direction intersecting with the measurement cross section. Then, in the method of measuring the entire surface to be measured, the measurement data W (x, y) for the entire surface to be measured is obtained, the linearly independent aberration function Fn is determined, and the following equation W (x, y) real = W (x, y) -ΣCnFn (x,
y) S = ∬ {W (x, y) −ΣCnFn (x, y)} ² dx
dy ∂S / ∂C ₁ = 0, ∂S / ∂C ₂ = 0, …… ∂S / ∂C
From n = 0, the coefficient Cn of the aberration function Fn is obtained by least-squares approximation, the measurement data W (x, y) is corrected, and the true surface accuracy W is obtained.
A method for measuring a surface to be inspected, characterized by obtaining (x, y) real. 2. The test surface is a barrel-shaped toroidal surface,
The aberration function Fn is F ₁: 1, F₂: x, F₃: y, F_Four: x²,
F_Five: y², F₆: xy, F₇: y-x²y and these
The coefficient Cn is obtained by performing the least squares approximation with an aberration function.
The method for measuring an inspected surface according to claim 1, wherein
Law. 3. The surface to be measured is a cylinder surface, and the aberration functions Fn are F ₁ : 1, F ₂ : x, F ₃ : x ² , F ₄ : xy, F ₅ :
a y-x ² y, the measuring method of the test surface according to claim 1, wherein the determining the coefficients Cn performs the least square approximation in these aberration function. 4. The test surface is a flat surface, and the aberration function Fn
Is F ₁ : 1, F ₂ : x, F ₃ : y, and the least-squares approximation is performed by using these aberration functions.
The method for measuring the surface to be inspected. 5. A coherent light beam from the same light source is applied to a test surface and a reference surface, an interference fringe is formed on one measurement cross section of the test surface, and the test surface is scanned in a direction intersecting with the measurement cross section. Then, in the method of measuring the entire surface to be measured, the measurement data W (x, y) for the entire surface to be measured is obtained, the linearly independent aberration function Fn is determined, and the following equation S = ∬ {W (x , Y) -ΣCnFn (x, y)} ² dx
dy ∂S / ∂C ₁ = 0, ∂S / ∂C ₂ = 0, …… ∂S / ∂C
A characteristic is that the coefficient Cn of the aberration function Fn is obtained from n = 0 by least square approximation, the setting deviation of the surface to be inspected is calculated from the coefficient, and the setting deviation in each direction is corrected by the 6-axis fine movement drive device according to the deviation amount. And the measuring method of the surface to be inspected.