JPH05240626A - Method and instrument for measuring shape of surface to be measured - Google Patents

Abstract

PURPOSE:To two-dimensionally find the shape of a surface to be measured with high accuracy by finding the whole shape of the surface to be measured by composing surface forming components except the curvature component obtained in a first measuring process and the curvature of the surface to be measured. CONSTITUTION:Two luminous fluxes reflected by a reference plane 51 and surface 61 to be measured advance in the opposite direction while the luminous fluxes interfere with each other and are reflected by a beam splitter 3. After reflection, the luminous fluxes are led to an image pickup element 8 through an image forming lens 7. Image signals based on interference fringes obtained by means of the element 8 are inputted to an arithmetic and control section 9 and the section 9 calculates the interval between the plane 51 and surface 61 based on the distribution of the interference fringes. In a first measuring process, the curvature component K(X<2>+Y<2>) of the shape of the surface 61 is calculated. In a second measuring process, the component WA-PO(X, Y) of the surface shape of the surface 61 other than the curvature is calculated. Then when WA(X, Y)=K(X<2>+Y<2>)+WA-PO(X, Y) is calculated, the two-dimensional shape WA(X, Y) of the surface 61 is finally found.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a surface shape of a surface to be measured,
In particular, the present invention relates to a surface shape measuring method for measuring a surface to be measured and a surface shape measuring apparatus for measuring the surface to be measured.

[0002]

2. Description of the Related Art Conventionally, as a surface shape measuring method for optically measuring the surface shape of a surface to be measured, a three-face matching method (for example, D. Malacara, Optical Shop Testing (John Wi
ley & Sons, 1978) p41-42) are known.

This three-sided alignment method uses three measured surfaces A,
Prepare B and C, and select 2 from the measured surfaces A, B and C.
Individual pieces are selected, and light waves are caused to interfere with each other as shown in FIG.

Now, the surface to be measured is represented by using an orthogonal coordinate system (X, Y) as shown in FIG.
The deviation amounts of the measured surfaces A, B, and C in Y) from the ideal plane are expressed as W _A (X, Y), W _B (X, Y), and W _C (X, Y).

Further, the measured value of the optical path difference between the two surfaces obtained by making the surface A and the surface B to be measured face each other is W.
₁ (X, Y), W is the measured value of the optical path difference between the two surfaces obtained by facing the measured surface A and the measured surface C to each other.
₂ (X, Y), and the measured value of the optical path difference between the two surfaces obtained by making the measured surface B and the measured surface C face each other is W ₃ (X,
Y), the following relational expression is obtained.

W ₁ (X, Y) = W _A (X, Y) + W _B (−X, Y) (1) W ₂ (X, Y) = W _A (X, Y) + W _C (−X) , Y) (2) W ₃ (X, Y) = W _B (X, Y) + W _C (-X, Y) (3) where the first and second terms on the right side of each equation The sign of X inverts because the point on the right measured surface corresponding to the point (X, Y) on the left measured surface is (- This is because X, Y). In the above equations, the plane component related to the distance between the two surfaces is
It is omitted because it does not affect the result of the operation.

In the above equations, the variable X of the surface shape W _A , the variable X of the surface shape W _B , -X, the variable of the surface shape W _C-
The origin of the coordinates of X is not necessarily the same. This is because the absolute position cannot be determined by the rotation of the surface to be measured about the optical axis O and the replacement of each surface to be measured during measurement.
However, the origin of each of the measured surfaces A, B, and C is set on the optical axis O at each measurement, and the origin is set as X = 0 to solve the above equation.

When X = 0, using the above formulas (1) to (3), W _A (0, Y), W _B (0, Y), W
_{When C} (0, Y) is obtained, the following formula is obtained.

W _A (0, Y) = {W ₁ (0, Y) + W ₂ (0, Y) −W ₃ (0, Y)} / 2 (4) W _B (0, Y) = { _{W 1 (0, Y) -W} 2 (0, Y) + W 3 (0, Y)} / 2 ... (5) W C (0, Y) = {- W 1 (0, Y) + W 2 (0 , Y) + W ₃ (0, Y)} / 2 (6) Therefore, the deviation amount (relative displacement of each surface) of each measured surface A, B, C from the ideal plane along the Y-axis direction can be calculated. You can ask.

However, in order to obtain the overall surface shape of the measured surface, at least one of the measured surfaces A, B and C facing each other needs to be rotated little by little around the optical axis. There is a rotation of the measured surface A
And measurement surface B, measurement surface A and measurement surface C, and measurement surface B and measurement surface C must be repeated. The accuracy may decrease.

A wavefront averaging method (Japanese Patent Application No. 1-328066) is used as a method for measuring the surface shape other than the three-face matching method.
No.) is known. In this wavefront averaging method, as shown in FIG. 5, one side is set as a measured surface D and the other side is set as a reference surface E, which are opposed to each other. Then, any one of a rotating operation of the reference plane E around the optical axis O, a moving operation of the reference plane E in a direction orthogonal to the optical axis O, and an exchange operation of the reference plane E is performed, and the measurement is repeated many times. .. 5 (a), 5 (b) and 5 (c) show a state in which the reference plane E is moved in a direction orthogonal to the optical axis O and measurement is performed.

Then, the shape error is reduced by averaging the measured values obtained by the multiple measurements, and as a result, the surface shape of the surface D to be measured is obtained.

[0013] For example, as shown in FIG. 5 (a), face-to-face and the measurement surface D and the measured surface E, the amount of deviation from an ideal plane of the surface to be measured _{D W R (X, Y)} , The amount of deviation of the measured surface E from the ideal plane (relative displacement of each surface) is calculated as W _T1 (X,
Y), expressed a measurement value representing the optical path difference between the two surfaces when the _{W 1 (X, Y),} W 1 = W R (X, Y) + W T1 (X, Y) ... and (7).

In the above equation, the plane component related to the distance between the surfaces is omitted because it does not affect the calculation result.

At this time, the coordinates of the surface to be measured D and the surface to be measured E are made to coincide with each other.

Next, as shown in FIGS. 5B and 5C, the reference surface E is moved in a direction orthogonal to the optical axis O while the surface D to be measured is fixed, and the shape of the reference surface E at this time. W _T2 (X,
Y) and the measured value is W ₂ (X, Y), W ₂ = W _R (X, Y) + W _T2 (X, Y) (8) As described above, the reference surface E is moved in the direction orthogonal to the optical axis O, the reference surface E is rotated around the optical axis O, or the reference surface E is exchanged.
_i (X, Y) (i = 1, 2, ..., N) is calculated.

The n measured values W _i (X, Y) (i =
1, 2, ..., N) are all added, the following expression (9) is obtained.

[Equation 1] By the following equation (10) which is a modification of the above equation (9), W _R (X,
Y) can be obtained.

[Equation 2] In the above equation (10), the second term on the right side means an average of various shapes of the reference surface E, and therefore theoretically approaches zero when the number of measurements n is increased. Therefore,
If n is made sufficiently large, the following formula (11) can be obtained.

[Equation 3] That is, the surface shape W _R (X, Y) of the measured surface D can be obtained. In this wavefront averaging method, the larger the number of times of measurement n, the higher the measurement accuracy. Further, the more random the surface shape of the surface D to be measured, the higher the measurement accuracy.

However, if the reference surface E has a curvature, it will not be averaged even if the reference surface D is moved in a direction orthogonal to the optical axis O or rotated around the optical axis O of the reference surface E. ,
Even if a plurality of reference planes E are used, there is a possibility that the reference planes E are concave or convex, and the accuracy of averaging may deteriorate. When the measured surface D is a spherical surface, the surface shape and the curvature can be measured as different quantities.
When measuring the amount of deviation from the ideal plane of, the curvature itself also causes an error. Therefore, the wavefront averaging method is not suitable for measuring the amount of deviation of the measured surface D from the ideal plane.

[0019]

That is, in the three-face matching method, it is difficult to obtain the surface shape of the entire surface to be measured, and in the wavefront averaging method, the curvature of the shape error of the measured surface is obtained. There was a problem that it was difficult. Therefore, the appearance of a method for measuring the surface shape of a surface to be measured and a surface shape measuring device for the surface to be measured that accurately measures the shape error over the entire surface of the surface to be measured has been strongly desired.

The present invention has been made to solve the above-mentioned problems, and is a method for measuring the surface shape of a surface to be measured and a surface to be measured which can accurately obtain the surface shape of the surface to be measured two-dimensionally. An object of the present invention is to provide a surface profile measuring device.

[0021]

In order to solve the above problems, the method for measuring the surface shape of a surface to be measured according to the present invention is 3
One of the two surfaces to be measured is arbitrarily selected, the two surfaces to be measured are faced to each other, and the relative displacement of each surface is two-dimensionally measured. This measurement is performed three times as a whole by combining different surfaces to be measured. One measurement surface and one measurement surface arbitrarily selected from the three measurement surfaces used in the first measurement step are fixed to one side, and the other surface facing this is a reference surface arbitrarily selected. The second measurement step in which the relative displacement of each surface is measured a plurality of times by rotating or moving, or by exchanging the reference surfaces, and the curvature from the surface shape of the measured surface obtained in the first measurement step. Only the component is obtained by calculation, only the surface shape component obtained by removing the curvature component from the surface shape of the surface to be measured obtained by the second measurement step is obtained by calculation, and the curvature component obtained by the first measurement step and the surface to be measured are obtained. Table excluding the curvature of It is characterized by determining the entire surface shape of the surface to be measured by combining the shape component.

The method for measuring the surface shape of the surface to be measured according to the present invention is characterized by measuring the surface distance between the surfaces to be measured facing each other.
It is possible to adopt a Fizeau type interferometer.

Further, the surface shape measuring apparatus for measuring the surface to be measured according to the present invention has a measuring unit for two-dimensionally determining the surface distance between two opposed surfaces to be measured, and stores the measurement data and three surface to be measured. Measure the relative displacement of each of the two faces to be measured arbitrarily selected from the above, and perform this measurement three times as a whole for a combination of different faces to be measured. Only the curvature component is calculated from the surface shape of the surface, and one measured surface arbitrarily selected from the three measured surfaces used in the first measurement operation is fixed to one side, and the reference surface opposite to this is fixed. A second operation in which the relative displacement of each surface is measured a plurality of times by performing any one of an operation of rotating around the optical axis, an operation of moving the reference surface in a direction orthogonal to the optical axis, and an operation of exchanging the reference surface. Is it the surface shape of the measured surface obtained by the measurement operation? An arithmetic control unit for calculating a surface shape component excluding a curvature component and synthesizing the curvature component and the surface shape component excluding the curvature component to obtain an overall surface shape of the surface to be measured. Characterize.

[0024]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram of a surface shape measuring apparatus for a surface to be measured according to the present invention. In this embodiment, a Fizeau-type interferometer is used to measure the surface distance between two measurement surfaces facing each other. In FIG. 1, reference numeral 1 is a light source that constitutes a part of the measuring unit. As the light source 1, for example, a helium / neon laser or the like is used. The laser light emitted from the light source 1 has a condenser lens 2 and a collimator lens 4
The beam diameter is expanded by the reference flat plate 5 and the DUT 6.
Be led to. Reference numeral 51 is a reference surface, and 61 is a surface to be measured.

The two light beams reflected by the reference plane 51 and the surface 61 to be measured interfere with each other, travel in opposite directions, and are reflected by the beam splitter 3 which constitutes a part of the measuring section. The interference light flux reflected by the beam splitter 3 is guided to the image sensor 8 via the imaging lens 7, and interference fringes are formed on the image sensor 8.

A video signal based on the interference fringes obtained by the image pickup device 8 is input to the arithmetic control unit 9. The arithmetic control unit 9 calculates the surface distance between the reference plane 51 and the measured surface 61 based on the distribution of the interference fringes. The arithmetic control unit 9 is composed of, for example, a microcomputer, a memory, an operation unit, and a display unit.

Next, the measuring principle of the surface shape measuring method of the surface to be measured according to the present invention will be described.

If the measured surface 61 is the measured surface A, its surface shape can be expressed as W _A (X, Y). this house,
The curvature component is k (X ² + Y ² ), and the components other than curvature are W
_{Assuming A-PO} (X, Y), the surface shape of the measured surface 61 can be expressed by the following equation (12).

W _A (X, Y) = k (X ² + Y ² ) + W _A-PO (X, Y) (12) That is, the surface shape of the measured surface 61 has a curvature component k (X
² + Y ² ) and a component other than the curvature W _A-PO (X, Y) can be obtained.

The methods for obtaining the two components will be described below.

[Determination of Curvature Component k (X ² + Y ² )] First, in the first measuring step, the measured surface 61, the measured surfaces B and C are measured.
Is used to calculate the curvature component k (X ² + Y ² ) from the measurement result by the three-face matching method shown in FIG. The one-dimensional surface shape W _A (0, Y) of the measured surface 61 can be obtained from the equation (4), which can be separated into a curvature component and other components by calculation. _A (0, Y) = k · Y ² + W _A-PO (0, Y) (13) In this formula (13), since X = 0 is represented, X is omitted, but k · Y ² is replaced by k (X ² + Y
^It may be expressed as ² ). To separate the components by this operation,
For example, the least squares method can be used. Thus, in the first measurement step, the curvature component k of the surface shape of the measured surface 61 is
Calculate (X ² + Y ² ).

[0033] "Determination of components other than the curvature _{W A-PO (X, Y} ) " Next, in the second measuring step, components other than the curvature from the measured result by the wavefront averaging method W _A-PO (X, Y ). If the measured surface 61 is the measured surface D, the surface shape W _A ′ (X, Y) of the measured surface D can be obtained from the equation (11). Here, “′” (dash) is attached to W _A (X, Y) because the average shape of the measured surface E represented by the second term on the right side of the equation (10) has a curvature component. This is because it is assumed that there is a measurement error, assuming the case. This surface shape W _A ′ (X, Y) can also be similarly separated into a curvature component and other components, and the following equation is obtained.

W _A ′ (X, Y) = k ′ (X ² + Y ² ) + W _A-PO (X, Y) (14) As described above, in the second measurement step, among the surface shapes of the measured surface 61, _A component W _A-PO (X, Y) other than the curvature is calculated.

The method of obtaining the two components has been described above. The curvature component k (X ² + Y ² ) obtained in the first measurement step and the component W _A-PO (X, other than the curvature obtained in the second measurement step) Y) is added as shown in the equation (12) to finally obtain the two-dimensional surface shape W _A (X, Y) of the measured surface 61. FIG. 2 is for explaining the measurement procedure of the surface shape of the measured surface,
FIG. 2A shows the curvature component k (X ² + Y ² ) of the measured surface 61 one-dimensionally. FIG. 2B shows the component W other than the curvature.
_A-PO (X, Y) is shown one-dimensionally. FIG. 2C shows the entire surface shape W _A (X, Y) of the measured surface 61 obtained by adding the curvature component of FIG. 2A and the component other than the curvature of FIG. 2B. Is shown.

In this embodiment, the curvature component is k (X ² +
Are displayed in Y ^2), but another display method may be, it is also possible to display on, for example, as ^{k {2 (X 2 + Y} 2) -1}.

[0037]

[Effect] Since the method for measuring the surface shape of the surface to be measured and the apparatus for measuring the surface shape of the surface to be measured according to the present invention are configured as described above, the surface shape of the surface to be measured can be accurately obtained two-dimensionally. Can be done.

[Brief description of drawings]

FIG. 1 shows a configuration of an embodiment of the present invention.

FIG. 2 is a diagram for explaining a measurement order.

FIG. 3 is a diagram for explaining a conventional three-sided alignment method.

FIG. 4 is an explanatory diagram of coordinates on a measurement surface.

FIG. 5 is a diagram for explaining a conventional wavefront averaging method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Light source 2 ... Condensing lens 3 ... Beam splitter 4 ... Collimator lens 5 ... Reference plane plate 51 ... Reference plane 6 ... Measured object 61 ... Measured surface 7 ... Imaging lens 8 ... Imaging element 9 ... Computation control part

Claims (3)

[Claims] 1. A relative displacement of each surface is two-dimensionally measured by arbitrarily selecting two surfaces to be measured from three surfaces to be measured, and this measurement is performed by combining different surfaces to be measured. The first measurement step, which is performed three times as a whole, and one measurement surface arbitrarily selected from the three measurement surfaces used in the first measurement step are fixed to one side, and the reference surface arbitrarily selected to the other side. Relative displacement of each surface can be measured by facing, rotating the reference surface around the optical axis, moving the reference surface in a direction orthogonal to the optical axis, or replacing the reference surface. Only the curvature component was calculated from the surface shape of the measured surface obtained by the second measuring step and the first measuring step, and the curvature component was removed from the surface shape of the measured surface obtained by the second measuring step. First measurement by calculating only the surface shape component Surface shape measuring method of the surface to be measured, wherein the determination of the overall surface shape of the surface to be measured by combining the surface shape components except the curvature of the resulting curvature component the surface to be measured by the degree. 2. The surface distance between two measured surfaces facing each other is 2
The measurement unit that obtains dimensionally and the measurement data are stored, and the relative displacement of each surface is measured by facing two measured surfaces selected arbitrarily from the three measured surfaces, and this measurement is performed on different measured surfaces. The curvature component alone is calculated from the surface shape of the measured surface obtained by the first measurement operation performed three times as a whole for the combination of the surfaces, and any one of the three measured surfaces used in the first measurement operation is arbitrarily selected. Any one of the operation of fixing one surface to be measured to one side and rotating the reference surface facing the optical axis around the optical axis, the operation of moving the reference surface in a direction orthogonal to the optical axis, and the operation of exchanging the reference surface. By performing the above operation to measure the relative displacement of each surface a plurality of times, a surface shape component is calculated by removing the curvature component from the surface shape of the measured surface obtained by the second measurement operation, and the curvature component and the curvature component are calculated. And the surface shape component A surface shape measuring device for the surface to be measured, which comprises: an arithmetic control unit for obtaining the overall surface shape of the surface to be measured. 3. The method for measuring the surface shape of a surface to be measured according to claim 2, wherein the measuring unit has a Fizeau interferometer.