JP3169189B2 - Method and apparatus for measuring surface shape of surface to be measured - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field 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 method for measuring the surface shape of a surface to be measured and a device for measuring the surface shape of the surface to be measured for measuring the flatness of the surface to be measured.

[0002]

2. Description of the Related Art Conventionally, as a surface shape measuring method for measuring an optical surface shape of a surface to be measured, a three-plane matching method (for example, D. Malacara, Optical Shop Testing (John Wi
ley & Sons, 1978) see pages 41-42).

[0003] This three-plane alignment method uses three measurement surfaces A,
B and C are prepared, and two of the surfaces A, B and C to be measured are prepared.
Individuals are selected and made to interfere with each other as shown in FIG.

Now, the surface to be measured is represented using a rectangular coordinate system (X, Y) as shown in FIG.
The surface to be measured in Y) A, B, W the amount of deviation from the ideal plane of _{C A (X, Y),} W B (X, Y), representing W _C (X, Y) and.

Further, the measured value of the optical path difference between two surfaces obtained by facing the measured surface A and the measured surface B to each other is represented by W
₁ (X, Y), 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 is W
₂ (X, Y), the measured value of the optical path difference between the two surfaces obtained by facing the measured surface B and the measured surface C to each other is W ₃ (X, Y).
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) here, the first term and the second term of the right side of each equation The reason why the sign of X is inverted is that when the measurement is performed with the Y axis being inverted, the point on the right measured surface corresponding to the point (X, Y) on the left measured surface is (−). X, Y). In each of 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.

[0007] In the above formulas, variables X of the surface shape W _A, the surface shape W _B of the variable X, -X, the surface shape W _C variables -
X does not always have the same coordinate origin. This is because the absolute position cannot be determined by the rotation of the measured surface around the optical axis O and the replacement of each measured surface during measurement.
However, each time measurement is performed, the origin of each of the surfaces A, B, and C to be measured is determined on the optical axis O, and the origin is set as X = 0, and the above equation is solved.

[0008] at the X = 0, the above items (1) to equation using equation _{(3), W A (0, Y)} , W B (0, Y), W
_{When C} (0, Y) is obtained, the following equation is obtained.

[0009] _{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 amount of deviation (relative displacement of each surface) of each of the measured surfaces A, B, and C from the ideal plane along the Y-axis direction is calculated. You can ask.

However, in order to obtain the entire surface shape of the measured surface, at least one of the measured surfaces A, B, and C facing each other needs to be slightly rotated about the optical axis. This rotation operation is performed on the surface A to be measured.
And the surface to be measured B, the combination of the surface to be measured A and the surface to be measured C, and the combination of the surface to be measured B and the surface to be measured C, respectively. Accuracy may be reduced.

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

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.

For example, as shown in FIG. 5A, the measured surface D and the measured surface E face each other, and the deviation amount of the measured surface D from the ideal plane is represented by W _R (X, Y), The deviation amount (relative displacement of each surface) of the measured surface E from the ideal plane is represented by W _T1 (X,
Y) If the measured value representing the optical path difference between the two surfaces is W ₁ (X, Y), then W ₁ = W _R (X, Y) + W _T1 (X, Y) (7)

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

At this time, it is assumed that the coordinates of the surface D to be measured and the surface E to be measured coincide with each other.

Next, as shown in FIGS. 5B and 5C, the reference surface E is moved in a direction perpendicular 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 is changed. To W _T2 (X,
Y), assuming that the measured value is W ₂ (X, Y), W ₂ = W _R (X, Y) + W _T2 (X, Y) (8) By moving the reference plane E in the direction orthogonal to the optical axis O, rotating the reference plane E around the optical axis O, or exchanging the reference plane E, the n measured values W
_i (X, Y) (i = 1, 2,..., n) is obtained.

The n measurement values W _i (X, Y) (i =
, N), the following equation (9) is obtained.

(Equation 1) By the following equation (10) obtained by modifying the above equation (9), W _R (X,
Y) can be obtained.

(Equation 2) In the above equation (10), the second term on the right-hand side means an average of various shapes of the reference surface E. Therefore, when the number of measurements n is theoretically increased, the second term approaches zero. Therefore,
When n is sufficiently large, the following equation (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, as the number of measurements n increases, the measurement accuracy improves. Further, as the surface shape of the surface D to be measured is more random, the measurement accuracy is improved.

However, when the reference surface E has a curvature, the reference surface D is not averaged even if the reference surface D is moved in a direction orthogonal to the optical axis O or rotated about 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 plane E is biased toward a concave surface or a convex surface, and the accuracy of averaging may be deteriorated. When the surface D to be measured is a spherical surface, the surface shape and the curvature can be measured as different amounts.
When measuring the deviation amount from the ideal plane, the curvature itself also causes an error. Therefore, the wavefront averaging method is not suitable for measuring a deviation amount of the measured surface D from an ideal plane.

[0019]

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

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and a method and a method for measuring the surface shape of a surface to be measured, which can determine the surface shape of the surface to be measured with high accuracy in two dimensions. It is an object of the present invention to provide a surface shape measuring device.

[0021]

In order to solve the above-mentioned problems, a method for measuring the surface shape of a surface to be measured according to the present invention comprises the steps of:
Arbitrarily select one of the two surfaces to be measured, face the two surfaces to be measured, measure the optical path difference between the two surfaces two-dimensionally,
Fixing a first measurement step of performing a whole as 3 times by a combination of the measurement surface mutually different this measurement, one measurement surface randomly selected from among the three measurement surface used in the first measurement step to the one Then, the reference surface arbitrarily selected is faced to the other, and either the rotation operation of the reference surface around the optical axis, the movement operation in the direction orthogonal to the optical axis of the reference surface, or the reference surface exchange operation is performed. By performing the second measurement step of measuring the optical path difference between each of the two surfaces a plurality of times, only the curvature component is calculated from the surface shape of the measured surface obtained in the first measurement step, and the curvature component is obtained in the second measurement step. Calculating only the surface shape component excluding the curvature component from the surface shape of the measured surface to be measured, and synthesizing the curvature component obtained in the first measurement step and the surface shape component excluding the curvature of the measured surface. By the whole table of the measured surface It is characterized by determining the shape.

[0022]

Further, the surface shape measuring apparatus for a surface to be measured according to the present invention comprises: a measuring unit for two-dimensionally determining a surface interval between two facing surfaces to be measured; face to face two of the surface to be measured arbitrarily selected to measure the optical path difference between the two surfaces from among obtained by the first measurement operation performed overall three combinations of the measurement surface mutually different this measurement object Only the curvature component is calculated from the surface shape of the measurement surface, and one measurement surface arbitrarily selected from the three measurement surfaces used in the first measurement operation is fixed to one, and a reference surface facing the measurement surface. of each secondary do one of the of the exchange operation of the moving operation and the reference surface in a direction perpendicular to the optical axis of the rotation operation and the reference plane of the optical axis
Calculate a surface shape component excluding a curvature component from a surface shape of the measured surface obtained by a second measurement operation of measuring the optical path difference between surfaces a plurality of times, and calculate the curvature component and the surface shape component excluding the curvature component And an arithmetic control unit for calculating the entire surface shape of the measured surface by combining The measuring unit measures the distance between the facing surfaces to be measured.
To use a Fizeau-type interferometer
It is possible.

[0024]

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

FIG. 1 is a block diagram of the apparatus for measuring the surface shape of a surface to be measured according to the present invention. In this embodiment, a Fizeau-type interferometer is used to measure the surface interval between two facing surfaces to be measured. In FIG. 1, reference numeral 1 denotes a light source constituting a part of a 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 is collected by a condenser lens 2 and a collimator lens 4.
As a result, the beam diameter is enlarged, and the reference flat plate 5 and the DUT 6
It is led to. Reference numeral 51 denotes a reference surface, and reference numeral 61 denotes a measured surface.

The two light beams reflected by the reference plane 51 and the measured surface 61 cause interference, travel in opposite directions, and are reflected by the beam splitter 3 which forms a part of the measuring section. The interference light beam reflected by the beam splitter 3 is guided to the imaging device 8 via the imaging lens 7, and interference fringes are formed on the imaging device 8.

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

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

Assuming that the surface 61 to be measured is the surface A to be measured, its surface shape can be expressed as W _A (X, Y). this house,
The component of curvature is k (X ² + Y ² ), and the component other than curvature is W
_{Assuming that A-PO} (X, Y), the surface shape of the surface 61 to be measured 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 surface 61 to be measured has a curvature component k (X
² + Y ² ) and a component W _A-PO (X, Y) other than the curvature can be obtained.

Hereinafter, how to determine the two components will be described.

[Method of Determining Curvature Component k (X ² + Y ² )] First, in the first measurement step, the measured surface 61, the measured surfaces B and C
Is used to determine the curvature component k (X ² + Y ² ) from the measurement result by the three-plane matching method shown in FIG. The one-dimensional surface shape W _A (0, Y) of the surface 61 to be measured can be obtained from Expression (4), which can be separated into a component of curvature and other components by calculation. _A (0, Y) = k · Y ² + W _A-PO (0, Y) (13) In this equation (13), since X = 0, X is omitted, but k · Y ² is represented by k (X ² + Y
² ). To separate components by this operation,
For example, a 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 obtained.
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 ). Assuming that 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 Expression (11). Here, “′” (dash) is added 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 a measurement error accompanies this case. This surface shape W _A ′ (X, Y) can be similarly separated into a curvature component and other components by calculation, and the following equation is obtained.

[0034] _{W A '(X, Y)} = k'(X 2 + Y 2) + W A-PO (X, Y) ... (14) Thus, in the second measuring step of the surface shape of the measurement surface 61 The component W _A-PO (X, Y) other than the curvature is calculated.

The method for 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, When added to indicate Y) to (12), and finally two-dimensional surface shape W _a (X of the measurement surface 61, Y) is determined. FIG. 2 is a view for explaining the procedure for measuring the surface shape of the surface to be measured.
FIG. 2A shows the one-dimensional curvature component k (X ² + Y ² ) of the surface 61 to be measured. FIG. 2B shows a 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 components 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]

The method for measuring the surface shape of a surface to be measured and the apparatus for measuring the surface shape of a surface to be measured according to the present invention are configured as described above. Can be done.

[Brief description of the 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-plane alignment method.

FIG. 4 is an explanatory diagram of coordinates of 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 ... Object to be measured 61 ... Surface to be measured 7 ... Imaging lens 8 ... Image sensor 9 ... Operation control part

Claims (3)

(57) [Claims] 1. A three measured optical path difference in two dimensions between the face to face the two of the surface to be measured is arbitrarily selected respective two surfaces among the measured surface, the surface to be measured between different this measurement A first measurement step to be performed three times as a whole in combination with one measurement surface selected arbitrarily selected from the three measurement surfaces used in the first measurement process, and a reference arbitrarily selected to the other; facing surfaces, each by performing one operation and the exchange operation of the moving operation and the reference surface in the direction orthogonal rotational operation about the optical axis and the reference plane and the optical axis of the reference surface two
A second measuring step of measuring the optical path difference between the surfaces a plurality of times, and calculating only the curvature component from the surface shape of the measured surface obtained in the first measuring step, and calculating the curvature component of the measured surface obtained in the second measuring step. Only the surface shape component obtained by removing the curvature component from the surface shape is calculated, and the curvature component obtained in the first measurement step and the surface shape component obtained by removing the curvature of the surface to be measured are combined to obtain the surface shape of the measured surface. A method for measuring the surface shape of a surface to be measured, which comprises determining an entire surface shape. 2. A measurement section for two-dimensionally obtaining a surface interval between two facing surfaces to be measured, and a memory for storing measurement data and facing two surfaces to be arbitrarily selected from three surfaces to be measured. Together between each two sides
In the optical path difference is measured, as well as calculating a curvature only components from the surface shape of the whole surface to be measured obtained by the first measuring operation performed three times for a combination of the measurement surface mutually different this measurement, the first measurement operation A surface to be measured arbitrarily selected from the three surfaces to be measured is fixed to one side, and a rotation operation about the optical axis of the reference surface facing the surface to be measured and a direction perpendicular to the optical axis of the reference surface are performed. The curvature component is removed from the surface shape of the measured surface obtained by the second measurement operation in which the optical path difference between the two surfaces is measured a plurality of times by performing one of the movement operation and the reference surface exchange operation. An arithmetic control unit that calculates the surface shape component obtained, and combines the curvature component and the surface shape component excluding the curvature component to obtain the entire surface shape of the surface to be measured. measuring device. 3. The surface shape measuring device for a surface to be measured according to claim 2, wherein the measuring section has a Fizeau type interferometer.