JP2011237196A - Wavefront generating optical system and interferometer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an aspheric wave generating optical system that generates target aspheric waves more accurately.SOLUTION: The aspheric wave generating system for generating aspheric waves comprises: a first Alvarez lens having a first aspheric surface; a second Alvarez lens having a second aspheric surface; and a relay optical system disposed between the first Alvarez lens and the second Alvarez lens, in which the first aspheric surface and the second aspheric surface are disposed at conjugate positions to each other with respect to the relay optical system. In an xyz coordinate system having the optical axis of the aspheric wave generating optical system as the z-axis, the first aspheric surface and the second aspheric surface have shapes satisfying f2(x,y)=f1(βx,βy)+C, where the shape of the first aspheric surface is expressed by z=f1(x,y) and the shape of the second aspheric surface is expressed by z=f2(x,y), β represents a magnification of the relay optical system, and C represents a constant.

Description

  The present invention relates to a wavefront generating optical system and an interferometer, and more particularly to a wavefront generating optical system having an Alvarez lens and an interferometer including the same.

  Patent Document 1 discloses an interferometer for measuring the aspherical shape of a test surface having an aspherical shape. The interferometer has an Alvarez lens to generate a wavefront for measurement. The Alvarez lens described in Patent Document 1 is configured by arranging two lenses having the same shape in proximity to each other along the optical axis. When the shape of the two lenses is f (x, y) and the two lenses are shifted by Δ and −Δ along the y direction perpendicular to the optical axis, the transmitted wavefront W (x, y) of the Alvarez lens is obtained. ) Is expressed by the following approximate expression, where n is the refractive index of the glass material of the two lenses. When the relative shift between the two lenses is 0, that is, when Δ is 0, the transmitted wavefront W (x, y) is a plane wave. When Δ is other than 0, the transmitted wavefront W (x, y) is an aspheric wave other than a plane wave.

      W (x, y) ≈2Δ (n−1) (∂f (x, y) / ∂y)

JP 2002-310624 A

  The above equation is accurate when the distance between the two lenses is zero. However, in order to allow relative shifting of the two lenses, it is necessary to provide a suitable distance between the two lenses. On the other hand, when such an interval is provided, an error occurs between the generated wavefront and the wavefront represented by the above formula, thereby causing a measurement error. In order to reduce this measurement error, optical calculation such as ray tracing is required, which complicates the calculation.

  The present invention has been made with the above problem recognition as an opportunity, and an object thereof is to more accurately generate a target aspheric wave.

One aspect of the present invention relates to an aspheric wave generating optical system for generating an aspheric wave, the spherical wave generating optical system including a first Alvarez lens having a first aspheric surface and a second aspheric surface. And a relay optical system disposed between the first and second Alvarez lenses, wherein the first aspherical surface and the second aspherical surface are the relays. In an xyz coordinate system that is arranged at a conjugate position with respect to the optical system and has an optical axis of the aspherical wave generating optical system as a z-axis, the shape of the first aspherical surface is z = f1 (x, y), and the first 2 When the aspheric shape is z = f2 (x, y), the magnification of the relay optical system is β, and the constant is C,
The first aspheric surface and the second aspheric surface are:
f2 (x, y) = f1 (βx, βy) + C
It has a shape that can satisfy.

  According to the present invention, a target aspheric wave can be generated more accurately.

It is a figure which shows the interferometer of embodiment of this invention. It is a figure which shows the structure of the aspherical wave generation optical system of 1st, 3rd embodiment of this invention. It is a figure which shows the structure of the aspherical wave generation optical system of 2nd Embodiment of this invention. It is a figure which shows the structure of the aspherical wave generation optical system of 4th Embodiment of this invention. It is a figure which shows the structure of the aspherical wave generation optical system of 5th Embodiment of this invention.

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

  An embodiment of the present invention will be described with reference to FIG. FIG. 1 shows an example in which the present invention is applied to a Twiman Green interferometer in order to provide a more specific example. However, the present invention is not limited to other examples such as a Fizeau interferometer and a shearing interferometer. This method can also be applied to an interferometer of the type. In the interferometer 100 illustrated in FIG. 1, a parallel light beam 1 that is a plane wave is provided from a light source (not shown), and the light beam 1 is partially reflected by the half mirror 2 and travels toward the reference surface 6. A light beam vertically reflected by the reference surface 6 is referred to as reference light. The reference light passes through the half mirror 2 and enters the imaging surface of an imaging sensor 8 such as a CCD via the imaging optical system 7. On the other hand, another part of the light beam 1 provided from the light source passes through the half mirror 2 and enters the aspherical wave generating optical system 3. The aspherical wave generating optical system 3 is a wavefront conversion optical system that converts a plane wave into an aspherical wave (aspherical wave close to a spherical wave). The light beam emitted from the aspherical wave generating optical system 3 enters the collimator lens 4. The collimator lens 4 is a lens configured to emit a spherical wave when a plane wave is incident. The collimator lens 4 and the aspherical wave generating optical system 3 form a wavefront that is incident on the test surface 5a of the test object 5. The test surface 5a can generally be an aspherical surface having a shape close to a spherical surface.

  The light beam reflected by the test surface 5a is called test light. The test light returns along the optical path substantially the same as the forward path, is reflected by the half mirror 2 and enters the imaging optical system 7. The imaging optical system 7 is an optical system in which the test surface 5a and the image sensor 8 have an object image relationship (conjugate relationship), and the test light from the test surface 5a is connected to the image pickup surface of the image sensor 8. Let me image.

  Interference fringes due to the reference light and the test light are formed on the imaging surface of the image sensor 8, and the interference fringes are imaged by the image sensor 8. A phase shift method can be used to derive the relative shape of the test surface 5a (observed through the aspherical wave generating optical system 3 and the collimator lens 4) with respect to the reference surface 6 based on the interference fringe image. The phase shift method is based on imaging a plurality of interference fringes while driving the reference surface 6 or the test object 5 in the optical axis direction by a driving element such as a piezo element, and based on temporal changes in the intensity of the plurality of interference fringes. This is a method for obtaining phase information. Alternatively, instead of driving the reference surface 6 or the test object 5, the phase shift can be realized by temporally changing the wavelength of the light beam 1 from the light source. In addition, instead of the phase shift method, an interference fringe including a spatial carrier fringe is imaged by giving a relative inclination or shift between the reference surface 6 and the test surface 5a, and the phase is determined based on the interference fringe. A method for obtaining information, for example, a Fourier transform method or an electronic moire method may be used.

  Hereinafter, some embodiments of the aspherical wave generating optical system 3 will be described. First, a first embodiment of the aspheric wave generating optical system 3 will be described with reference to FIG. The aspherical wave generating optical system 3 of the first embodiment includes an Alvarez lens pair composed of a first Alvarez lens 10 and a second Alvarez lens 11, and a relay optical system 12. The first Alvarez lens 10 includes a first aspheric surface 10a and a first plane 10b. The second Alvarez lens 11 includes a second aspherical surface 11a and a second flat surface 11b. The relay optical system 12 is disposed between the Alvarez lens 10 and the second Alvarez lens 11 so as to face the first aspherical surface 10a and the second aspherical surface 11a. A point on the first aspherical surface 10 a of the first Alvarez lens 10 forms an image on a point on the second aspherical surface 11 a of the second Alvarez lens 11 via the relay optical system 12. In the example illustrated in FIG. 2, the relay optical system 12 is a lens configured to form an inverted image of an object. Here, in the xyz coordinate system in which the optical axis AX of the aspherical wave generating optical system 3 is the z axis, the shape of the first aspherical surface 10a of the first Alvarez lens 10 is z = f1 (x, y), the second The shape of the second aspherical surface 11a of the Alvarez lens 11 is z = f2 (x, y). When the first Alvarez lens 10 and the second Alvarez lens 11 are arranged without being decentered with respect to the optical axis AX of the aspherical wave generating optical system 3, the expression (1) is satisfied. That is, the first aspherical surface 10a and the second aspherical surface 11a have shapes that can satisfy Expression (1). Here, x, y, and z are the x, y, and z coordinates in the xyz coordinate system, respectively, and C is a constant. In the example shown in FIG. 2, C = 4f. β is the magnification (imaging magnification) of the relay optical system 12, and β = −1 in the example shown in FIG.

f2 (x, y) = f1 (βx, βy) + C (1)
When the first Alvarez lens 10 and the second Alvarez lens 11 are not decentered with respect to the optical axis AX of the aspherical wave generating optical system 3, the light beam emitted from the aspherical wave generating optical system 3 is a plane wave. It remains. This is because the pair of the first Alvarez lens 10 and the second Alvarez lens 11 can be regarded as a parallel plate.

  If both the first Alvarez lens 10 and the second Alvarez lens 11 are shifted by δ in the same direction along the x-axis perpendicular to the optical axis AX, the light emitted from the aspherical wave generating optical system 3 The wavefront W is expressed by equation (2).

W (X, Y) = 2 · δ · (n−1) · (∂f (X, Y) / ∂x) (2)
Here, the shape of the first aspherical surface 10a of the first Alvarez lens 10 and the shape of the second aspherical surface 11a of the second Alvarez lens 11 is f (X, Y) (= f2 (x, y) = f1 (βx, βy) + C). X and Y are coordinates that are standardized so that the outer radius of the region through which the light beam passes is 1 in the first and second Alvarez lenses 10 and 11. n is the refractive index of the glass material constituting the first and second Alvarez lenses 10 and 11.

  The shift direction may be either the x-axis direction or the y-axis direction, but the value obtained by differentiating the shape of the aspherical surface of the Alvarez lens with respect to the shift direction needs to be proportional to the wavefront of the aspherical wave to be generated. When the shift amount δ is zero, the right side of Equation (2) becomes zero and becomes a plane wave.

  When the relay optical system 12 is an equal magnification system, the wavefront can be changed by moving the relay optical system 12 in a direction perpendicular to the optical axis AX instead of the first and second Alvarez lenses 10 and 11. It is. In this case, the wavefront W (X, Y) generated when the shift amount is δ is equal to the right side of Equation (2) with a minus sign.

  The shift of the first and second Alvarez lenses 10 and 11 can be realized by a driving mechanism attached to the first and second Alvarez lenses 10 and 11. Alternatively, only one of the first and second Alvarez lenses 10 and 11 may be shifted by providing a drive mechanism. In this case, W (X, Y) is ½ of the right side of Equation (2). In the first embodiment, the relay optical system 12 is disposed between the first Alvarez lens 10 and the second Alvarez lens 11. For this reason, it is not necessary to bring the first Alvarez lens 10 and the second Alvarez lens 11 close to each other, and a spatial margin can be provided in the first Alvarez lens 10 and the second Alvarez lens 11. The distance between the first Alvarez lens 10 and the second Alvarez lens 11 can be arbitrarily determined by the design of the relay optical system 12. Therefore, the degree of freedom of arrangement of the drive mechanism of the first Alvarez lens 10 and / or the second Alvarez lens 11 is large, and the arrangement is easy. Further, the above-described measurement error problem is solved.

  The relay optical system 12 is preferably a double-sided telecentric optical system. For example, as illustrated in FIG. 2, this can be realized by disposing the lenses 13 and 14 having a focal length f at an interval of 2 · f. The distance between the first Alvarez lens 10 and the lens 13 and the distance between the second Alvarez lens 11 and the lens 14 are set to f.

  In the bilateral telecentric optical system, the principal ray is parallel to the optical axis AX. Therefore, even if the distance between the first and second Alvarez lenses 10 and 11 in the direction of the optical axis AX deviates from the target distance, the first aspherical surface 10a of the first Alvarez lens 10 and the second Alvarez lens 11 The deviation of the correspondence relationship of coordinates with the 2 aspherical surface 11a is reduced. For this reason, the influence of the displacement error on the emitted aspherical wave is reduced, and the arrangement and driving of the first and second Alvarez lenses 10 and 11 are facilitated. The relay optical system 12 may be composed of three or more lenses for the purpose of correcting aberrations, for example.

  In the example shown in FIG. 2, the relay optical system 12 is an equal magnification system, but may be an enlargement system or a reduction system. In this case, the focal length of the lens 14 of the relay optical system 12 is f ′ different from the focal length f of the lens 13, and the distance between the lens 13 and the lens 14 is f + f ′. The magnification β at this time is β = −f ′ / f. When it is desired to reduce, f ′ <f, and when it is desired to enlarge, f ′> f.

  The shape f (X, Y) and the shift amount δ of the aspheric surfaces 10a and 11a of the Alvarez lenses 10 and 11 are determined so that the wavefront W (X, Y) substantially matches the aspheric shape of the test surface 5a. Is done. As an example, let us consider a case where the shape of the test surface 5a is given by PA (X, Y) in Expression (3). Here, PA (X, Y) is the amount of deviation from the spherical shape and is a shape that generates astigmatism. CA is an amplitude in the shape.

PA (X, Y) = CA · (X ² −Y ² ) (3)
In this case, the shape f (X, Y) of the aspherical surfaces 10a and 11a of the Alvarez lenses 10 and 11 is given by Expression (4).

f (X, Y) = DA · (X ³ / 3-X · Y ² ) (4)
Here, DA represents the size of the aspherical shape. By substituting Equation (4) into Equation (2), it is possible to determine the wavefront W of the illumination light that illuminates the test surface 5a having the shape indicated by PA (X, Y). Further, by adjusting the shift amount δ, light having a wavefront having the same amplitude as that of the shape PA (X, Y) of the surface 5a to be measured is emitted from the aspherical wave generating optical system 3. . As a result, the illumination light is reflected substantially perpendicularly on the surface 5a to be measured, and the image sensor 8 can obtain substantially one-color null interference fringes.

  A second embodiment of the aspherical wave generating optical system 3 will be described with reference to FIG. The aspherical wave generating optical system 3 of the second embodiment includes an Alvarez lens pair composed of a first Alvarez lens 26 and a second Alvarez lens 27, and a relay optical system 24. The first Alvarez lens 26 includes a first aspheric surface 26a and a first plane 26b. The second Alvarez lens 27 includes a second aspheric surface 27a and a second plane 27b. The relay optical system 24 is arranged between the first Alvarez lens 26 and the second Alvarez lens 27 so as to relay an erect image. In the example illustrated in FIG. 3, the relay optical system 24 includes four lenses 20, 21, 22, and 23 having a focal length f. The relay optical system 24 can also be considered to have a configuration in which two relay optical systems 12 in the first embodiment are arranged. The inverted image of the first aspheric surface 26 a of the first Alvarez lens 26 is relayed to the aspheric surface 25 by the lens 20 and the lens 21. Further, the inverted image is further inverted by the lens 22 and the lens 23 and relayed to the second aspheric surface 27 a of the second Alvarez lens 27 and relayed to the second aspheric surface 27 a of the second Alvarez lens 27. As a result, the relay optical system 24 as a whole forms an erect image of the first aspheric surface 26 a of the first Alvarez lens 26 on the second aspheric surface 27 a of the second Alvarez lens 27.

  Also in the second embodiment, the shape of the first aspheric surface 26a of the first Alvarez lens 26 is f1 (x, y), and the shape of the second aspheric surface 27a of the second Alvarez lens 27 is f2 (x, y). Then, the relationship of Formula (1) is realized between both. In the example shown in FIG. 3, β = + 1.

  In order to generate an aspherical wave, the first Alvarez lens 26 and the second Alvarez lens 27 are shifted by | δ | along the x axis and in opposite directions. In this case, the wavefront W emitted from the aspherical wave generating optical system 3 is expressed by Expression (2) on the assumption that the sign of δ follows the shift direction of the second Alvarez lens 27.

  Also in the second embodiment, the relay optical system 24 is preferably a double-sided telecentric optical system. This can be realized by setting the interval between the four lenses 20, 21, 22, 23 to 2f. The distance between the first Alvarez lens 26 and the lens 20 and the distance between the second Alvarez lens 27 and the lens 23 are set to f.

  In the example shown in FIG. 3, the focal lengths of the lenses 21 and 22 are the same as the focal lengths of the lenses 20 and 23, but the focal lengths of the lenses 21 and 22 may be fa different from f. In this case, the interval between the lenses 20 and 21 and the interval between the lenses 22 and 23 are set to f + fa, and the interval between the lenses 21 and 22 is set to 2fa. If fa <f, the total length of the relay optical system 24 is shortened, which is advantageous for downsizing the interferometer. As in the first embodiment, a reduction system or an enlargement system may be used instead of the equal-magnification relay optical system.

  A third embodiment of the aspherical wave generating optical system 3 will be described with reference to FIG. When the relay optical system 12 is an optical system that generates an inverted image of the first aspherical surface 10a on the second aspherical surface 11a, instead of shifting the Alvarez lenses 10 and 11, the relay optical system 12 is perpendicular to the optical axis AX. May be shifted in any direction. Due to the shift of the relay optical system 12, the image of the first aspheric surface 10 a of the first Alvarez lens 10 is also shifted on the aspheric surface 11 a of the second Alvarez lens 11. Therefore, the Alvarez lenses 10 and 11 are optically shifted relative to each other. In this case, a driving mechanism that fixes the first Albarez lens 10 and the second Alvarez lens 11 and drives the relay optical system 12 is provided. Consider a case where the relay optical system 12 is an equal magnification system and the relay optical system 12 is driven by δ in the x-axis direction. In this case, the image of the first aspherical surface 10 a of the first Alvarez lens 10 is formed at a position shifted relative to the second aspherical surface 11 a of the second Alvarez lens 11 by δ. Therefore, the wavefront emitted from the aspherical wave generating optical system 3 is ½ of the value on the right side of Expression (2). According to the third embodiment, since the aspherical wavefront can be formed by driving the relay optical system 12, the configuration of the interferometer is simplified. However, at least one of the relay optical system 12 and the two Alvarez lenses 10 and 11 can be provided with a drive mechanism.

A fourth embodiment of the aspherical wave generating optical system 3 will be described with reference to FIG. When the test surface 5a has a component that generates coma and / or a component that generates spherical aberration in addition to the component that generates astigmatism, generation of an aspheric wave corresponding to each component What is necessary is just to arrange | position an optical system in series. FIG. 4 shows an example of an aspherical wave generating optical system 3 that combines two or more different types of wavefronts. Here, an example in which a wavefront having astigmatism and a wavefront having coma aberration are combined will be described. The aspherical wave generating optical system 3 has a unit 3a and a unit 3b arranged in series. The unit 3a is a unit that generates a wavefront having astigmatism, and may have the same configuration as that shown in FIG. The unit 3b is a unit that generates a wavefront having coma aberration. The unit 3b for generating a wavefront having coma aberration also includes a pair of Alvarez lenses 15 and 16 and a relay optical system 17 as in FIG. The shape fc (X, Y) of the aspheric surfaces 15a, 16a of the first Alvarez lens 15 and the second Alvarez lens 16 of the unit 3b is the coma aberration component PC (X, Y) of the shape of the test surface 5a.
PC (X, Y) = CC · (X ³ + X · Y ² ),
Then,
^{f2 (x, y) = DC} · (X 4/4 + X 2 · Y 2/2),
It can be. Here, CC represents the amplitude of the frame shape, and DC represents the size of the aspherical shape. The first Alvarez lens 15 and the second Alvarez lens 16 are arranged such that the aspheric surfaces 15 a and 16 b are in an imaging relationship with the relay optical system 17. When changing the magnitude of the wavefront having coma aberration, the first and second Alvarez lenses 15 and 16 of the unit 3b are shifted by a drive mechanism (not shown), and the relative shift amount is changed. be able to. Alternatively, the relay optical system 17 may be shifted. Further, when other aspheric waves such as spherical aberration are generated, units for generating the respective aspheric waves may be arranged in series.

  A fifth embodiment of the aspherical wave generating optical system 3 will be described with reference to FIG. The fifth embodiment provides another example of combining two or more different types of wavefronts. In FIG. 5, the same members as those in FIG. 4 are denoted by the same reference numerals. In the fifth embodiment, a plurality of pairs of Alvarez lenses share the relay optical system 12. The Alvarez lenses 10 and 11 constitute one Alvarez lens pair and generate astigmatism components. The Alvarez lenses 15 and 16 generate one Alvarez lens pair and generate a coma aberration component. The Alvarez lenses 10 and 11 for generating astigmatism components are arranged at conjugate positions with respect to the relay optical system 12. In the example of FIG. 5, the Alvarez lenses 10 and 11 are arranged at positions shifted from the focal position of the relay optical system 12 by t1. Further, the Alvarez lenses 15 and 16 for generating the coma aberration component are also arranged at conjugate positions with respect to the relay optical system 12. In the example of FIG. 5, the third Alvarez lens 15 and the fourth Alvarez lens 16 are arranged at positions shifted in the same direction by t2 from the focal position. Here, the relay optical system 12 may be an equal magnification system. The relay optical system 12 may be an enlargement or reduction system. In this case, the position of the Alvarez lens is changed according to the magnification. Furthermore, when increasing the number of combined aspheric wavefronts, the Alvarez lenses are arranged so that two pairs of Alvarez lenses are conjugated with each other via the relay optical system 12. A driving mechanism for relative shifting of the Alvarez lens may be provided in each Alvarez lens, or may be provided in both the relay optical system and the Alvarez lens.

Claims (6)

An aspheric wave generating optical system for generating an aspheric wave,
A first Alvarez lens having a first aspheric surface;
A second Alvarez lens having a second aspheric surface;
A relay optical system disposed between the first Alvarez lens and the second Alvarez lens;
The first aspherical surface and the second aspherical surface are arranged at positions conjugate to each other with respect to the relay optical system;
In an xyz coordinate system in which the optical axis of the aspheric wave generating optical system is the z axis, the shape of the first aspheric surface is z = f1 (x, y), and the shape of the second aspheric surface is z = f2 (x Y), the magnification of the relay optical system is β, and the constant is C,
The first aspheric surface and the second aspheric surface are:
f2 (x, y) = f1 (βx, βy) + C
Having a shape that can satisfy
An aspherical wave generating optical system. The relay optical system is a telecentric optical system,
The aspherical wave generating optical system according to claim 1.   The drive mechanism for driving at least one of the first Alvarez lens, the second Alvarez lens, and the relay optical system in a direction perpendicular to the optical axis is further provided. Aspherical wave generation optical system. A plurality of units are arranged in series along the optical axis,
Each of the plurality of units includes the first Alvarez lens, the second Alvarez lens, and the relay optical system.
The aspherical wave generating optical system according to any one of claims 1 to 3, wherein A third and fourth Alvarez lens constituting an Alvarez lens pair;
The aspherical surface of the third Alvarez lens and the aspherical surface of the fourth Alvarez lens are arranged at conjugate positions with respect to the relay optical system;
The aspherical wave generating optical system according to any one of claims 1 to 3, wherein An aspherical wave generating optical system according to any one of claims 1 to 5,
A collimator lens on which light emitted from the aspherical wave generating optical system is incident;
An imaging sensor that images interference fringes formed by reference light and test light that is light emitted from the collimator lens and reflected by the test surface;
An interferometer comprising:

Images