JP4950783B2 - Method and apparatus for measuring shape of test surface - Google Patents

Description

  The present invention relates to a method and apparatus for measuring the shape of a test surface such as an optical lens.

  A Fizeau interferometer is generally used as a method for measuring the shape of an optical surface with an interferometer. The Fizeau interferometer performs relative measurement with a reference surface serving as a reference, but in the case of high-accuracy measurement in which the measurement accuracy is required to be less than λ / 20, it is necessary to separate the test surface shape from the reference surface shape. is there.

  Japanese Patent Application Laid-Open No. 2004-133867 discloses a conventional technique for acquiring shape data while moving a test surface of a measurement object, and separating the test surface and a system error shape using the obtained shape data. 1 and 2 show two measurement positions where the position of the test surface 2 with respect to the reference surface 1 is different from each other.

  The first position shown in FIG. 1 is a position where the optical axis 11 of the optical system coincides with the center position of the test surface 2 and the center axis 10 of the test surface passing through the center of curvature. The second position shown in FIG. 2 indicates a state where the test surface 2 is tilted along an arc, that is, a state where the central axis 10 of the test surface is tilted by γ from the optical axis 11 of the optical system.

  FIG. 3 shows a flow for calculating the shape of the test surface. In step 101, at the first position, the test surface 2 is rotated with respect to the central axis 10 of the test surface using the θz stage of the stage, and n pieces of first data A1 to An are measured. In step 102, the n first data A1 to An measured in the 101st step are simply averaged to obtain first rotating average shape data A. The first rotation average shape data A is the sum of the reference surface shape data and the rotationally symmetric component of the test surface about the central axis 10 of the test surface at the first position. In step 103, at the second position, the test surface 2 is rotated with respect to the central axis of the test surface using the θz stage of the stage, and m pieces of second data B1 to Bm are measured. In step 104, the m second data B1 to Bm measured in the 103rd step are simply averaged to obtain second rotating average shape data B. The second rotation average shape data B is the sum of the reference surface shape data and the rotationally symmetric component of the test surface about the central axis 10 of the test surface at the second position.

In step 105, a rotationally symmetric component of the test surface is calculated. When the difference between the first rotation average shape data A and the second rotation average shape data B is taken, the reference surface shape data is canceled out and becomes a difference between rotationally symmetric components of the test surface at the first position and the second position. The rotationally symmetric component of the test surface shape is calculated using the properties of concentric contour lines that the rotationally symmetric component has. In step 106, the reference plane shape data and the rotationally symmetric component of the test surface shape are subtracted from one of the first data A1 measured at the first position to obtain the rotationally asymmetric component of the test surface shape. In step 107, the shape of the test surface is obtained by taking the sum of the rotationally symmetric component and the rotationally asymmetric component of the test surface shape.
Japanese Patent No. 3146590

  However, when measuring the surface to be measured, there may be irregular and unstable rotationally asymmetric noise caused by the image sensor, air, vibration, stage drive, and the like. In this case, shape data is obtained from the interference pattern affected by noise, and calculation is performed to separate the shape data of the test surface and the shape data of the reference surface from the shape data. Unstable noise cannot be separated from the shape of the test surface, and a problem has occurred in which part of the noise component remains in the shape data of the test surface. In addition, irregular and unstable noise has raised concerns about measurement reproducibility and stable measurement. Furthermore, when a shape different from the actual shape is calculated due to the influence of noise and surface shape correction processing is performed using the calculated shape, there is a problem in that a surface that is significantly deviated from the design shape is processed.

  It is an object of the present invention to provide a method and apparatus for measuring the shape of a test surface in which the influence of irregular and unstable rotationally asymmetric noise is reduced.

A first aspect of the present invention is a method for measuring the shape of a test surface based on an interference pattern between reflected light from the test surface and reflected light from the reference surface, using an optical system having a reference surface. is there. The method of measuring the shape of the test surface is that the test surface is rotated a plurality of times with respect to the center axis of the test surface at a first position where the optical axis of the optical system and the central axis of the test surface form a first angle. A first step of acquiring a plurality of first data measured at a position rotated by an angle, and a test surface at a second position where the optical axis of the optical system and the center axis of the test surface form a second angle. A second step of acquiring a plurality of second data measured at positions rotated by a plurality of rotation angles with respect to the central axis of the surface to be detected; and a first rotation of the surface to be detected by averaging the plurality of first data A third step of calculating average shape data and averaging a plurality of second data to calculate second rotation average shape data of the test surface; first data; first rotation average shape data; and second rotation average shape A fourth step of calculating reference surface shape data and test surface shape data from the data. The fourth step calculates a rotationally symmetric component of the test surface at the first position or the second position from the difference between the first rotation average shape data and the second rotation average shape data, and at the calculated first position The reference surface is obtained by subtracting the rotation target component of the test surface from the first rotation average shape data or subtracting the calculated rotation target component of the test surface at the second position from the second rotation average shape data . And calculating the shape data of the test surface at a plurality of rotation angle positions at the first position from the plurality of first data and the calculated shape data of the reference surface. The step of converting the shape data of the test surface at the plurality of rotation angle positions at the first position into the plurality of shape data of the test surface at the same rotation angle position, and the converted plurality of shape data of the test surface A step of calculating an average of And wherein the door.

According to a second aspect of the present invention, there is provided an optical system having a reference surface, a stage for driving the test surface, an image sensor for imaging an interference pattern between reflected light from the test surface and reflected light from the reference surface, and And an optical system, a stage, and an image sensor, and a control unit that calculates the shape of the test surface based on the captured interference pattern, and measures the shape of the test surface. The control unit is configured to rotate the test surface at a first position where the optical axis of the optical system and the central axis of the test surface form a first angle and to rotate the test surface by a plurality of rotation angles with respect to the central axis of the test surface. A first acquisition means for acquiring a plurality of measured first data; and a center axis of the test surface at a second position where the optical axis of the optical system and the center axis of the test surface form a second angle. Second acquisition means for acquiring a plurality of second data measured at positions rotated at a plurality of rotation angles with respect to the same, and calculating the first rotation average shape data of the test surface by averaging the plurality of first data and a first calculating means for calculating a second rotation average shape data of the test surface by averaging the plurality of second data, a plurality of first data from a first rotational average shape data and the second rotation averaged shape data Second calculating means for calculating shape data of the reference surface and shape data of the test surface. The second calculation means calculates a rotationally symmetric component of the test surface at the first position or the second position from the difference between the first rotation average shape data and the second rotation average shape data, and at the calculated first position, By subtracting the rotation target component of the test surface from the first rotation average shape data or by subtracting the calculated rotation target component of the test surface at the second position from the second rotation average shape data Means for calculating surface shape data; means for calculating shape data of the test surface at a plurality of rotation angle positions at the first position from the plurality of first data and the calculated reference surface shape data; Means for converting the shape data of the test surface at the plurality of rotation angle positions at the first position into the plurality of shape data of the test surface at the same rotation angle position, and the plurality of shapes of the converted test surface Means for calculating the average of the data, And wherein the Rukoto.

  ADVANTAGE OF THE INVENTION According to this invention, the method and apparatus which measure the shape of the to-be-tested surface where the influence of the irregular and unstable rotationally asymmetric noise was reduced can be provided.

  An example of a method and apparatus for measuring the shape of the test surface according to the present invention will be described with reference to FIGS. 1, 2, 4, 5, 6, and 7.

  FIG. 5 shows a Fizeau interferometer system used as an apparatus for measuring the shape of the test surface in this embodiment. The Fizeau interferometer system drives a light source 4, a semi-transparent mirror 5, a Fizeau lens 6 including a reference surface 1, an imaging lens 9, an image sensor 3, a control unit 7, and a test surface 2. Stage 8. The light source 4, the semi-transparent mirror 5, the Fizeau lens 6 and the imaging lens 9 constitute an optical system having the reference surface 1. The image sensor 3 captures an interference pattern between the reflected light from the test surface 2 and the reflected light from the reference surface 1. The stage 8 includes an x stage, a y stage, a z stage, a θz stage that rotates the specimen about an axis perpendicular to the x and y stages, and a tilt that tilts the specimen about the center of curvature of the specimen. Including stage. The control unit 7 controls the optical system, the stage 8, and the image sensor 3, and calculates the shape of the test surface 2 based on the captured interference pattern.

  FIG. 1 shows an arrangement state of the reference surface 1 and the test surface 2 at a first position where the optical axis 11 of the optical system and the central axis 10 of the test surface form a first angle. In the present embodiment, the first position is a position where the optical axis 11 of the optical system coincides with the central axis 10 of the test surface. FIG. 2 shows an arrangement state of the reference surface 1 and the test surface 2 at a second position where the optical axis 11 of the optical system and the central axis 10 of the test surface form a second angle. The second position is a state where the test surface 2 is tilted along an arc using the θx stage of the stage 8, that is, a state where the central axis 10 of the test surface is tilted by γ from the optical axis 11 of the optical system. .

  FIG. 4 shows a flowchart of a method for measuring the shape of the test surface.

  In step 1 as the first process, the control means 76 of the control unit 7 uses a θz stage of the stage 8 to set a plurality of test surfaces 2 with respect to the central axis 10 of the test surface (n pieces) at the first position. ). And the 1st acquisition means 71 of the control part 7 acquires the 1st data A1-An of several (n pieces) measured at the position which rotated the to-be-tested surface 2 several (n) rotation angle. At this time, the rotation angles α1 to αn are recorded in a storage means (not shown).

  The control means 76 uses the θz stage of the stage 8 to rotate the test surface 2 by a plurality (n) of rotation angles so that the rotation axis of the test surface 2 coincides with the central axis 10 of the test surface. In addition, it is preferable to control the driving of the stage 8. As for the driving amount of the stage 8, the center coordinate of the shape data is calculated using a mask function or the like, and the driving amount is calculated from the shift amount of the center position.

  In step 2, the calculation means 73 of the control unit 7 simply averages the n pieces of first data A <b> 1 to An acquired in step 1 to calculate the first rotation average shape data A of the test surface 2. The first rotation average shape data A is the sum of the shape data of the reference surface 1 and the rotationally symmetric component of the test surface 2 around the central axis 10 of the test surface at the first position.

  In step 3 as the second step, the control means 76 uses the θz stage of the stage 8 to rotate the test surface 2 to a plurality of (m) rotation angles with respect to the central axis 10 of the test surface at the second position. Just rotate. And the 2nd acquisition means 72 of the control part 7 acquires several (m pieces) 2nd data B1-Bm measured in the position which rotated the to-be-tested surface 2 several (m pieces) rotation angle. Similarly to step 1, the control means 76 uses the θz stage of the stage 8 to rotate the test surface 2 by a plurality (m) of rotation angles, so that the rotation axis of the test surface 2 is the same as that of the test surface. It is preferable to control the drive of the stage 8 so as to coincide with the central axis 10.

  In step 4, the calculating means 73 simply averages the m pieces of second data B <b> 1 to Bm acquired in step 3 to calculate the second rotating average shape data B of the test surface 2. The second rotation average shape data B is the sum of the shape data of the reference surface 1 and the rotationally symmetric component of the test surface 2 around the central axis 10 of the test surface at the second position. Step 2 and Step 4 constitute a third step of calculating the first rotating average shape data A and the second rotating average shape data B of the test surface 2 from the n first data and the m second data, respectively. To do.

In step 5, the distortion means 75 of the control unit 7 corrects the first data A1 to An, the first rotation average shape data A, and the second rotation average shape data B so as to reduce the distortion error of the optical system. As the distortion correction value, a value obtained by measurement in advance or a design value can be used. Separation means 74 (second calculation means) of the control unit 7 includes the shape data of the reference surface 1 and the surface 2 to be examined from the first data A1 to An, the first rotation average shape data A, and the second rotation average shape data B. In the fourth step of separately calculating the shape data, data in which the distortion error is corrected is used.

  In step 6, the separating unit 74 calculates a rotationally symmetric component of the test surface 2. When the difference between the first rotation average shape data A and the second rotation average shape data B is taken, the reference surface shape data is canceled out and becomes a difference between rotationally symmetric components of the test surface at the first position and the second position. The rotationally symmetric component of the test surface shape is calculated using the properties of concentric contour lines that the rotationally symmetric component has.

  A rotationally symmetric component calculation method using the properties of concentric contour lines will be described with reference to FIG. The solid line in FIG. 7 indicates the rotation average shape RI1 of the first rotation average shape data A, and the dotted line indicates the rotation average shape RI2 of the second rotation average shape data B. The positions of the same radius are concentric contour lines. A and B, and C and D are represented as RI1A and RI1B on the equivalent height line of the first rotating average shape, respectively. B and D, and A and C are represented as RI2A and RI2B on the equivalent high line of the second rotating average shape, respectively. In FIG. 7, since the difference between the first rotation average shape and the second rotation average shape, A, B, C, and D are RI1A-RI2B, RI1A-RI2A, RI1B-RI2B, and RI1B-RI2A, respectively. There are four unknowns, RI1A, RI1B, RI2A, and RI2B, and substantially three equations can be obtained. Therefore, RI1B, RI2A, and RI2B based on RI1A can be obtained. When this is performed on the entire surface, a rotationally symmetric component of the surface to be measured is obtained.

  In step 7, the test surface calculated by the separation means 74 in step 6 from the first rotation average shape data A that is the sum of the shape data of the reference surface 1 and the rotationally symmetric component of the test surface 2 at the first position. The shape data of the reference surface is calculated by subtracting the rotationally symmetric component of the shape.

  In step 8, the separation means 74 subtracts the reference surface shape data calculated in step 7 from the first data A1 to An acquired in step 1, and the shape of the test surface 2 at n rotation angle positions is obtained. Calculate the data.

  In step 9, the separation means 74 converts the shape data of the test surface 2 at the n rotation angle positions calculated in step 8 into a plurality of shape data of the test surface at the same rotation angle position. The same rotation angle position is, for example, a position where the rotation angle is 0 °. Each of the first data A1 to An obtained by rotating the test surface 2 by the rotation angles α1 to αn is converted into data obtained by reversely rotating the coordinate system by the rotation angles α1 to αn. In other words, the first data A1 acquired by rotating the test surface 2 by + α1 is converted into data of a coordinate system obtained by rotating the coordinate system of the first data A1 by −α1.

  When the rotation angles α1 to αn are other than π / 2, π, 3π / 2, one pixel before the rotation does not correspond to one pixel after the rotation 1: 1. In this case, one pixel after rotation is obtained by interpolating from the shape data before rotation. This is performed for all pixels.

  In step 10, the separation means 74 calculates an average of n shape data of the test surface at the same rotation angle position converted in step 9, for example, a rotation angle of 0 ° position, and the calculated average data is used as the test surface. Use shape data.

  In the present embodiment, the state in which the first angle is formed is described as the state in which the optical axis 11 of the optical system and the center axis 10 of the surface to be tested coincide with each other. However, even when the state forming the first angle is not the position where the optical axis 11 of the optical system and the center axis 10 of the test surface coincide with each other, the calculation may be performed by performing the same coordinate conversion.

  In the present embodiment, the test surface 2 is moved to the first position and the second position. However, instead of moving the test surface 2, a drive stage may be provided on the reference surface side to move the reference surface 1. it can.

  In the present embodiment, a plurality of second data is acquired at the second position, but the second data may be a single data.

  In the present embodiment, the calculation for obtaining the rotationally symmetric component of the test surface has been described. However, the present invention is not limited to this, and all the shape data obtained in the state forming the first angle and the state forming the second angle are used. Applicable in measurement.

  In this embodiment, the Fizeau interferometer is used. However, the present invention is not limited to this, and the present invention can be similarly applied to another interferometer called an amplitude division type.

  In the present embodiment, the case where the calculation is performed using the data acquired at the first position and the second position has been described. However, the present invention is not limited to this, and the case where the data obtained at three or more measurement positions is used. Can be applied similarly.

  In the present embodiment, the case where the test surface is a spherical surface has been described. However, the present invention is not limited to this, and the present invention is applicable even if the test surface is a flat surface.

  In this embodiment, shape data is obtained while rotating the test surface once, and information on the rotationally asymmetric component of the test surface is eliminated (only information on the rotationally symmetric component of the reference surface and the test surface is used). However, when the rotational asymmetry of the test surface is known in advance, the rotational asymmetry component of the test surface may be subtracted from each angle state.

  If the optical component measured using the method or apparatus for measuring the shape of the test surface of the present invention is used in the projection optical system or illumination optical system of the exposure apparatus, an exposure apparatus with better performance than before can be provided. .

The figure which shows the state which makes | forms the 1st angle in which the optical axis of an optical system and the central axis of a to-be-tested surface correspond. The figure which shows the state which makes the 2nd angle in which the test surface inclines along the circular arc, ie, makes the central axis of the test surface incline only (gamma) from the optical axis of an optical system. The flowchart of the method of measuring the shape of the to-be-tested surface in a prior art. The flowchart which shows an example of the method of measuring the shape of the to-be-tested surface which concerns on this invention. The figure which shows the Fizeau interferometer as an example of the apparatus which measures the shape of the test surface which concerns on this invention. The figure which shows the structure of the control part 7 in FIG. Explanatory drawing of the calculation using the property of a concentric contour line.

Explanation of symbols

1: reference surface, 2: test surface, 3: imaging device, 4: light source, 5: semi-transparent mirror, 6: Fizeau lens, 7: control unit, 71: first acquisition means, 72: second acquisition means, 73 : Calculation means, 74: separation means, 74: distortion correction means, 76: control means, 8: stage, 9: imaging lens, 10: central axis of test surface, 11: optical axis of optical system

Claims (6)

A method of measuring the shape of the test surface based on an interference pattern between reflected light from the test surface and reflected light from the reference surface, using an optical system having a reference surface,
Measured at a position where the optical axis of the optical system and the central axis of the test surface are at a first angle, and the test surface is rotated a plurality of rotation angles with respect to the central axis of the test surface. A first step of acquiring a plurality of first data items,
Measured at a position where the optical axis of the optical system and the central axis of the test surface are at a second angle, and the test surface is rotated a plurality of rotation angles with respect to the central axis of the test surface. A second step of acquiring a plurality of second data that has been performed;
A first rotation average shape data of the test surface is calculated by averaging the plurality of first data , and a second rotation average shape data of the test surface is calculated by averaging the plurality of second data. 3 steps,
A fourth step of calculating shape data of the reference surface and shape data of the test surface from the plurality of first data, the first rotation average shape data, and the second rotation average shape data;
Including
The fourth step includes
The rotationally symmetric component of the test surface at the first position or the second position is calculated from the difference between the first rotational average shape data and the second rotational average shape data, and the calculated first position The rotation target component of the test surface is subtracted from the first rotation average shape data, or the calculated rotation target component of the test surface at the second position is calculated from the second rotation average shape data. Calculating the shape data of the reference surface by subtracting ;
Calculating shape data of the test surface at the plurality of rotation angle positions at the first position from the plurality of first data and the calculated shape data of the reference surface;
A step of converting a plurality of shape data of the test surface at the same rotational angle position of the shape data of the test surface in the plurality of rotational angle positions in the first position the calculated,
Calculating an average of a plurality of shape data of the converted test surface;
A method comprising the steps of:   2. The method according to claim 1, wherein in the first step and the second step, the test surface is driven so that a rotation axis of the test surface coincides with a central axis of the test surface. . Correcting the plurality of first data, first rotating average shape data and second rotating average shape data so as to reduce distortion errors of the optical system;
2. The corrected plurality of first data, the corrected first rotating average shape data, and the corrected second rotating average shape data are used in the fourth step. 2. The method according to 2. An optical system having a reference surface, a stage for driving the test surface, an imaging device for imaging an interference pattern between reflected light from the test surface and reflected light from the reference surface, the optical system, and the stage And a device for controlling the image sensor and calculating the shape of the test surface based on the captured interference pattern, and measuring the shape of the test surface,
The controller is
Measured at a position where the optical axis of the optical system and the central axis of the test surface are at a first angle, and the test surface is rotated a plurality of rotation angles with respect to the central axis of the test surface. First acquisition means for acquiring a plurality of first data items,
Measured at a position where the optical axis of the optical system and the central axis of the test surface are at a second angle, and the test surface is rotated a plurality of rotation angles with respect to the central axis of the test surface. Second acquisition means for acquiring a plurality of second data,
A first rotation average shape data of the test surface is calculated by averaging the plurality of first data , and a second rotation average shape data of the test surface is calculated by averaging the plurality of second data . 1 calculating means;
Second calculation means for calculating shape data of the reference surface and shape data of the test surface from the plurality of first data, the first rotation average shape data, and the second rotation average shape data;
Including
The second calculation means includes
The rotationally symmetric component of the test surface at the first position or the second position is calculated from the difference between the first rotational average shape data and the second rotational average shape data, and the calculated first position The rotation target component of the test surface is subtracted from the first rotation average shape data, or the calculated rotation target component of the test surface at the second position is calculated from the second rotation average shape data. Means for calculating the shape data of the reference surface by subtracting ;
Means for calculating shape data of the test surface at the plurality of rotation angle positions at the first position from the plurality of first data and the calculated shape data of the reference surface;
It means for converting a plurality of shape data of the test surface at the same rotational angle position of the shape data of the test surface in the plurality of rotational angle positions with the calculated first position,
Means for calculating an average of a plurality of shape data of the converted test surface;
A device comprising:   The apparatus according to claim 4, wherein the control unit controls driving of the stage so that a rotation axis of the test surface coincides with a central axis of the test surface. Correction means for correcting the plurality of first data, first rotation average shape data, and second rotation average shape data so as to reduce a distortion error of the optical system;
The said 2nd calculation means uses the corrected 1st data, the 1st corrected rotation average shape data, and the 2nd corrected rotation average shape data, The Claim 4 or Claim characterized by the above-mentioned. 5. The apparatus according to 5.

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