GB2427267A - Method of manufacturing an optical element using interferometric measurements. - Google Patents
Method of manufacturing an optical element using interferometric measurements. Download PDFInfo
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- GB2427267A GB2427267A GB0610629A GB0610629A GB2427267A GB 2427267 A GB2427267 A GB 2427267A GB 0610629 A GB0610629 A GB 0610629A GB 0610629 A GB0610629 A GB 0610629A GB 2427267 A GB2427267 A GB 2427267A
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- 230000003287 optical effect Effects 0.000 title claims abstract description 174
- 238000005259 measurement Methods 0.000 title claims abstract description 53
- 238000004519 manufacturing process Methods 0.000 title claims abstract description 13
- 238000000034 method Methods 0.000 claims abstract description 33
- 238000009826 distribution Methods 0.000 claims abstract description 9
- 239000011248 coating agent Substances 0.000 claims description 12
- 238000000576 coating method Methods 0.000 claims description 12
- 238000003384 imaging method Methods 0.000 claims description 7
- 238000007519 figuring Methods 0.000 claims description 6
- 238000000227 grinding Methods 0.000 claims description 6
- 239000006117 anti-reflective coating Substances 0.000 claims description 5
- 238000010884 ion-beam technique Methods 0.000 claims description 5
- 238000012545 processing Methods 0.000 claims description 5
- 238000005498 polishing Methods 0.000 claims description 4
- 238000003801 milling Methods 0.000 claims description 3
- 239000011253 protective coating Substances 0.000 claims description 3
- 238000005530 etching Methods 0.000 claims description 2
- 230000002093 peripheral effect Effects 0.000 abstract description 19
- 238000012360 testing method Methods 0.000 description 29
- 239000000758 substrate Substances 0.000 description 9
- 238000003754 machining Methods 0.000 description 6
- 239000000463 material Substances 0.000 description 4
- 230000005855 radiation Effects 0.000 description 4
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 3
- 230000035945 sensitivity Effects 0.000 description 3
- 230000001427 coherent effect Effects 0.000 description 2
- 238000000205 computational method Methods 0.000 description 2
- 238000007796 conventional method Methods 0.000 description 2
- 238000000151 deposition Methods 0.000 description 2
- MRELNEQAGSRDBK-UHFFFAOYSA-N lanthanum(3+);oxygen(2-) Chemical compound [O-2].[O-2].[O-2].[La+3].[La+3] MRELNEQAGSRDBK-UHFFFAOYSA-N 0.000 description 2
- 238000012067 mathematical method Methods 0.000 description 2
- 230000001681 protective effect Effects 0.000 description 2
- 238000010998 test method Methods 0.000 description 2
- KJTLSVCANCCWHF-UHFFFAOYSA-N Ruthenium Chemical compound [Ru] KJTLSVCANCCWHF-UHFFFAOYSA-N 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 239000003989 dielectric material Substances 0.000 description 1
- 238000010894 electron beam technology Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 230000005484 gravity Effects 0.000 description 1
- CPBQJMYROZQQJC-UHFFFAOYSA-N helium neon Chemical compound [He].[Ne] CPBQJMYROZQQJC-UHFFFAOYSA-N 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 238000005305 interferometry Methods 0.000 description 1
- ORUIBWPALBXDOA-UHFFFAOYSA-L magnesium fluoride Chemical compound [F-].[F-].[Mg+2] ORUIBWPALBXDOA-UHFFFAOYSA-L 0.000 description 1
- 229910001635 magnesium fluoride Inorganic materials 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 229910000476 molybdenum oxide Inorganic materials 0.000 description 1
- PQQKPALAQIIWST-UHFFFAOYSA-N oxomolybdenum Chemical compound [Mo]=O PQQKPALAQIIWST-UHFFFAOYSA-N 0.000 description 1
- 229910052707 ruthenium Inorganic materials 0.000 description 1
- 229910052814 silicon oxide Inorganic materials 0.000 description 1
- 238000004544 sputter deposition Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/255—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring radius of curvature
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- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Instruments For Measurement Of Length By Optical Means (AREA)
Abstract
A method of manufacturing an optical element such as a lens or mirror having an optical surface of an aspherical target shape. The method comprises a first interferometric measurement comprising a first interferometric optics (Fig.3) to image a first central portion of the optical surface to a detector and a second interferometric measurement comprising a second interferometric optics (Fig.4) to image a second peripheral portion of the optical surface. Deviations of the optical surface from the target shape are determined based on the two corresponding distributions of light intensities. The second portion overlaps with the first portion. A reference light may be reflected from a Fizeau surface (Fig. 3, 19a; Fig.4 19a'). The second portion may have a ring shape and the first and second interferometer optics may comprise a hologram.
Description
Method of Manufacturing an Optical Element
Background of the Invention
Field of the Invention
The present invention relates to a method of manufacturing an optical element. In particular, the invention relates to a method of manufacturing an optical element having an aspherical optical surface.
Brief Description of Related Art
An optical element having an optical surface is, for example, an optical component such as an optical lens or an optical mirror used in optical systems, such as telescopes used in astronomy, and systems used for imaging structures, such as structures formed on a mask or reticle, onto a radiation sensitive substrate, such as a resist, in a lithographic method. The success of such an optical system is substantially determined by the accuracy with which the optical surface can be machined or manufactured to have a target shape determined by a designer of the optical system. In such manufacture it is necessary to compare the shape of the machined optical surface with its target shape, and to determine differences between the machined and target surfaces. The optical surface may then be further machined at those portions where differences between the machined and target surfaces exceed e.g. predefined thresholds.
Interferometric apparatuses are commonly used for high precision measurements of optical surfaces. Examples of such apparatus are disclosed in US 4,732,483, US 4,340,306, US 5,473,434, US 5,777,741, US 5, 488,477. The entire contents of these documents are incorporated herein by reference.
The conventional interferometer apparatus for measuring a spherical optical surface typically includes a source of sufficiently coherent light and an interferometer optics for generating a beam of measuring light incident on the surface to be tested, such that wavefronts of the measuring light have, at a position of the surface to be tested, a same shape as the target shape of the surface under test.
In such a situation, the beam of measuring light is orthogonally incident on the surface under test, and is reflected therefrom to travel back towards the interferometer optics. Thereafter, the light of the measuring beam reflected from the surface under test is superimposed with light reflected from a reference surface and deviations of the shape of the surface under test and its target shape are determined from a resulting interference pattern.
While spherical wavefronts for testing spherical optical surfaces may be generated with a relatively high precision by conventional interferometer optics, more advanced optics, which are also referred to as compensators, null lens arrangements, or K-systems, are necessary to generate beams of measuring light having aspherical wavefronts such that the light is orthogonally incident at each location of the aspherical surface under test. Background information relating to null lens arrangements or compensators is available e.g. from the text book of Daniel Malacara "Optical Shop Testing", 2'' Edition, John Wiley & Sons, Inc. 1992, Chapter 12.
The compensator for generating the aspherical wavefronts may comprise one or more refractive optical elements, such -3..
as lenses. It is also known to use a diffractive element, such as a hologram, in a compensator for generating the aspherical wavefronts. Background information and examples of using holograms in interferometric measurements are illustrated in Chapters 15.1, 15.2, and 15.3 of the text book of Daniel Malacara mentioned above. The hologram may be a real hologram generated by exposing a suitable material, such as a photographic plate, with interfering light beams, or a synthetic hologram, such as a computer generated hologram (CGH) generated by simulating the interferometer set up by a suitable computational method, such as ray tracing, and producing the hologram by manufacturing steps using a pen plotter and optical reduction, lithographic steps, laser beam recorders, electron beam recorders and others.
The article of Taehee Kim et al. "Null test for a highly paraboloidal mirror", APPLIED OPTICS, Vol. 43, No. 18, 18/20 June 1994, pages 3614 to 3618, discloses two alternative methods of a similar accuracy for testing a mirror of a paraboloidal shape. The first method uses a CGH for generating aspherical wavefronts of the paraboloidal shape from spherical wavefronts such that the measuring light is orthogonally incident on the mirror at each location thereof. The second method, which is referred to as autocollimation test, uses an additional flat mirror in the beam path of the measuring light. Measuring light having spherical wavefronts is incident on the paraboloidal mirror and reflected therefrom to be orthogonally incident on the flat mirror.
It has been found that the conventional methods of testing an aspherical optical surface have an insufficient accuracy in some applications.
Suitnnary of the Invention The present invention has been accomplished taking the above problems into consideration.
Embodiments of the present invention provide a method of testing and manufacturing an optical element having an optical surface of a high accuracy.
Further embodiments of the present invention provide a method of testing and manufacturing an optical element having an aspherical surface of a relatively high accuracy.
According to an embodiment of the present invention, a method comprises testing an optical surface using different interferometer optics for testing at least two different overlapping portions of the optical surface. A first interferometer optics generates measuring light which is substantially orthogonally incident on the optical surface within a first portion thereof, and a first interferometric measurement is performed using the measuring light which is substantially orthogonally reflected from the first portion of the optical surface. A second interferometer optics generates measuring light which is not orthogonally incident on a second portion of the optical surface and reflected therefrom to be substantially orthogonally incident on an additional mirror. A second interferometric measurement is performed using the measuring light substantially orthogonally reflected from the additional mirror and again reflected from the second portion of the optical surface.
According to an exemplary embodiment of the invention, the first portion of the optical surface includes a point of intersection of the optical surface with an axis of rotational symmetry of a target shape of the optical surface, and an area of the second portion has, as an average, a greater distance from the axis of rotational symmetry than the first portion.
The inventor has found that a limited accuracy in positioning the aspherical surface relative to the interferometer optics is one limitation for the overall accuracy of testing aspherical surfaces using the conventional method. This is in particular the case for aspherical surfaces having a high numerical aperture which are well-approximated by a sphere in a central region about an axis of rotational symmetry of the target shape of the aspheric surface, and which deviate from such sphere more and more with increasing distance from the axis of rotational symmetry. Therefore, the method according to the present invention may use the first interferometer optics for testing a central first portion of the optical surface about the axis of rotational symmetry, and the second interferometer optics for testing a peripheral second portion of the optical surface of measuring light which is substantially orthogonally reflected from the additional mirror.
According to an exemplary embodiment of the invention, the method comprises: disposing the optical element relative to a first interferometer optics and performing a first interferometric measurement by: directing a first beam of measuring light onto the optical surface using the first interferometer optics such that the measuring light is substantially orthogonally incident on the optical surface; imaging a first portion of the optical surface onto a light receiving surface using measuring light of the first beam reflected from the first portion of the optical surface, the first portion including a point of intersection of the optical surface with an axis of rotational symmetry of the target shape; directing reference light onto the light receiving surface; and detecting at least one first distribution across the light receiving surface of light intensities of the superimposed reference light and measuring light; disposing the optical element relative to a second interferometer optics and relative to a mirror, and performing a second interferometric measurement by: directing a second beam of measuring light onto the optical surface using the second interferorneter optics such that measuring light is reflected from the optical surface to be orthogonally incident on a mirror surface of the mirror; imaging at least a portion of the mirror onto a light receiving surface using measuring light of the second beam reflected from a second portion of the optical surface after reflection from the mirror, wherein the second portion overlaps with the first portion and wherein an average distance of all locations of the second portion from the axis of rotational symmetry is greater than an average distance of all locations of the first portion from the axis of rotational symmetry; directing a reference light onto the light receiving surface; and detecting at least one second distribution across the light receiving surface of light intensities of the superimposed reference light and measuring light; determining deviations of the optical surface from the target shape based on the least one first distribution of light intensities and on the at least one second distribution of light intensities; and processing the optical surface of the optical element based on the determined deviations.
According to an exemplary embodiment of the invention, the second portion has a ring shape and is disposed about a periphery of the first portion.
According to a further exemplary embodiment, at least one of the first interferometer optics and the second interferonieter optics comprises a compensator for generating wavefronts of aspherical shapes. According to an exemplary embodiment herein, the compensator comprises a hologram, such as a computer generated hologram.
According to an exemplary embodiment, the target shape is a convex shape, and the mirror may have an aperture traversed by the second beam of measuring light. According to an embodiment herein, the mirror has a surface of a concave shape.
According to a further embodiment of the invention, the target shape is a concave shape, wherein the mirror may have a surface of a convex shape.
According to an exemplary embodiment, at least one of the first and second interferometer optics is of a Fizeau type having a Fizeau surface disposed in a beam path of the first and second beam of measuring light, respectively.
Within the context of the present application, an optical surface may be referred to as an aspherical surface if the aspherical surface differs from its best approximating sphere by more than a predetermined criterion. One such criterion is based on a gradient of the difference between the aspherical surface and its best approximating sphere, and the optical surface is referred to as an aspherical surface if such gradient exceeds a value of 6 jim divided by an effective diameter of the optical surface.
The machining of the optical surface may comprise a machining such as milling, grinding, loose abrasive grinding, polishing, ion beam figuring, magneto-rheological figuring, reactive ion beam etching and finishing of the optical surface of the optical element.
According to an embodiment, the finishing comprises applying a coating to the optical surface. The coating may comprise a coating such as a reflective coating, an anti- reflective coating and a protective coating.
Brief Description of the Drawings
The forgoing as well as other advantageous features of the invention will be more apparent from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. It is noted that not all possible embodiments of the present invention necessarily exhibit each and every, or any, of the advantages identified herein.
Figure 1 illustrates a first interferometer system for testing a central portion of an optical element according to a first embodiment of the invention; Figure 2 illustrates a second interferometer system for testing a peripheral portion of the optical element shown in Figure 1 according to a first embodiment of the invention; Figure 3 illustrates a first interferometer system for testing a central portion of an optical element according to a second embodiment of the invention; Figure 4 illustrates a second interferometer system for testing a peripheral portion of the optical element shown in Figure 3 according to a second embodiment of the invention; Figure 5 illustrates a second interferometer system for testing a peripheral portion of an optical element according to a third embodiment of the invention; and Figure 6 is a flowchart for illustrating the method of manufacturing the optical element according to the embodiments of the present invention.
Detailed Description of Exemplary Embodiments
In the exemplary embodiments described below, components that are alike in function and structure are designated as far as possible by alike reference numerals. Therefore, to understand the features of the individual components of a specific embodiment, the descriptions of other embodiments and of the summary of the invention should be referred to.
An interferometer system 1 according to an embodiment of the present invention is illustrated in Figure 1. The interferometer system 1 is used for testing a central portion 7 of an aspherical mirror surface 3 of a mirror 5.
The mirror 5 is mounted relative to a first interferometer optics 15 on a test piece holder (not shown in Figure 1).
The interferometer system 1 comprises a light source 11 for generating a beam 13 of measuring light. The light source 11 may comprise a helium neon laser 15 emitting a laser beam 17. Beam 17 is focused by a focusing lens 19 onto a pin hole aperture of a spatial filter 20 such that a diverging beam 18 of coherent light emerges from the pin hole. Wavefronts in diverging beam 18 are substantially spherical wavefronts.
The diverging beam 18 emitted from the light source 11 is collimated by one or more lenses 21 to form the parallel beam 13 of measuring light having substantially flat wavefronts. Beam 13 is supplied to and traverses the interferometer optics 15 which transforms and shapes a beam 14 of measuring light such that the beam 14 supplied by the interferometer optics 15 and incident on the optical surface 3 has wavefronts of a shape which corresponds to a target shape of optical surface 3 at each location within the central portion 7 thereof. Thus, if the optical surface 3 is machined such that its surface shape corresponds to the target shape, the light of beam 14 is orthogonally incident on the optical surface 3 at each location within the central portion 7 thereof. The light reflected from the optical surface 3 will then travel back substantially the same way as it was incident on the optical surface 3, traverse the interferometer optics 15, and a portion thereof will be reflected from a beam splitter 31 disposed in diverging beam 18 of measuring light.
A beam 29 reflected from the beam splitter 31 traverses a spatial filter 38 having an aperture and is imaged onto a photo sensitive surface 37 of a camera chip 39 through an objective lens system 35 of a camera 34, such that the central portion 7 of the optical surface 3 is imaged onto the camera 39.
The interferometer optics 15 comprises a wedge shaped substrate 17 having a flat surface 19 which is oriented orthogonally to the parallel beam 13 of measuring light having traversed substrate 17. Surface 19 forms a Fizeau surface of interferometer system 1 in that it reflects a portion of the beam 13 of measuring light. The reflected portion of the beam 13 of measuring light forms reference light for the interferometric method. The reference light reflected back from Fizeau surface 19 travels back a same path as it was incident on surface 19, and is thus superimposed with the measuring light reflected from optical surface 3. It is also possible to orient the Fizeau surface under a small predetermined angle relative to a plane orthogonal to the beam 13 for intentionally generating interference patterns having a predetermined number of fringes. The reference light is also deflected by beam splitter 31 and imaged onto the photo sensitive surface 37 of camera 34, such that an interference pattern generated by superimposing the wavefronts reflected from the optical surface 3 and the wavefronts reflected back from Fizeau surface 19 may be detected by camera 34.
As mentioned above, the interferometer optics 15 iS designed such that it transforms the entering beam 13 of measuring light having the parallel wavefronts into the beam 14 of measuring light having the aspherical wavefronts at the position of the optical surface 3. For this purpose, the interferometer optics 15 comprises a substrate 23 having two parallel flat surfaces 24, 25 wherein one surface 25 disposed opposite to the optical surface 3 carries a hologram. The hologram is a computer generated hologram (CGH) configured such that it diffracts the beam 13 having the flat wavefronts such that the wavefronts in the beam 14 at the position of the optical surface 3 will have a shape which substantially corresponds to the target shape of the optical surface 3. The hologram may be generated by exposing a photographic plate to reference light and light reflected from an optical surface having a surface corresponding to the target shape to a high accuracy, or, the hologram may be generated by calculating a corresponding grating using a computer involving methods such as ray tracing and plotting the calculated grating on surface 25 of the substrate. The grating may be formed by a lithographic method, for example. Background information with respect to holograms used in interferometry may be obtained from Chapter 15 of the above mentioned text book of Daniel Malacara.
The spatial filter 38 of the detector 34 has a function of preventing undesired measuring light from being incident on the detection surface 37 of the detector 34. Undesired measuring light may comprise measuring light reflected from surfaces other than the Fizeau surface 19 and the surface 3 to be manufactured. Further, the undesired measuring light may comprise light diffracted by the computer generated hologram 25 into a diffraction order other than a desired diffraction order.
In the following, details of the interferometer optics 15 and the optical surface 3 are illustrated. The aspherical optical surface 3 may be represented by the following Formula: Rr +Ar4+Br6+Cr8+Dr' +Er'2+Fr'4+Gr'6 + 1+,j1_(1+k)R2r2 (Formula 1) where z is the sag of the surface parallel to the z- axis, R is the curvature at the pole of the surface, k is the conic coefficient (K) and A,B,C,D,E,F,G are the 4th 6th 8th 10th 12th, 14th, 16th order deformation coefficients respectively; A=B=C=D=E=F=G=O for a pure conic 2 2 2 surface r =x +y In the illustrated example of Figure 1, the parameters of optical surface 3 in this Formula are: - 13R=185.306 k=-O.55 A=1.42267*10 9 B= -1.53486*10' C =6.21144*10' D= 4. 79448.1024 E=7.189427*1028 F= 3.29456*1O G = 1.23O28.1036 The optical data of the optical elements in the beam path of the measuring light of interferometer system 1 are given
in Table 1.
________ __________ __________ __________ _____________ Table_1 Radius Thickness Diameter Surface Glass Conic _____ [mmj [mmj ______ Immi _______ 19 __________ 200.00 __________ 88.7594 0 24 __________ 6.35 SUPRASIL 88.7594 0 __________ 90.55 __________ 88.7594 0 7 -185.306 0.00 __________ 152.20 -0.55 3 -185.306 __________ __________ 304.40 -0.55 The phase function of the hologram on surface 25 may be represented by the polynomial 1=MA r', (Formula 2) where N is the number of polynomial coefficients in the series, A* is the coefficient of the power of r, which is the normalized radial aperture coordinate.
The coefficients have units of radians. The coefficients of this polynomial are: A1 = 52.3 93349 A2 = -0.00323371 A3 = 5.713483*10 A4 = 1.3914832*10' A5 3.4372903*10' A6 = 6.4172407.1O18 A7 = 6.020553.1022 The central portion 7 of optical surface 3 is tested with the first interferometer system 1 shown in Figure 1 as illustrated above.
Figure 2 schematically illustrates a second interferometer system 1' for testing a peripheral portion 41 of the optical surface 3. The peripheral portion 41 is ring shaped and symmetrically disposed about axis 9 of rotational symmetry of the target shape of the optical surface 3, wherein an inner portion of the peripheral portion. 41 overlaps with an outer portion of the central portion 7.
The second interferometer system 1' may be of any suitable type. In the example shown in Figure 2, the interferometer system 1' has components which are similar to those shown in Figure 1, and these components are indicated by the same reference numerals as those of Figure 1, wherein the reference numerals are supplemented by an apostrophe.
In particular, the interferometer system 1' comprises a light source 11' for generating a beam 13' of measuring light, a camera 34', a beam splitter 31' and an interferometer optics 15' for generating a beam 14' of measuring light which is incident on a peripheral portion 41 of the optical surface 3 to be tested. The interferometer system 1' further comprises a half sphere 43 having a spherical mirror surface 45 disposed between the optical surface 3 and the interferometer optics 15'. A substrate 23' of the interferometer optics 15' carries on a surface 25' a hologram for diffracting beam 13' of measuring light having substantially flat wavefronts such that the beam 14' of measuring light diffracted by the hologram has aspherical wavefronts such that the beam 14' is reflected from the optical surface 3 and is substantially orthogonally incident on mirror surface 45.
The measuring light reflected from mirror surface 45 travels back substantially the same beam path as is it was incident thereon, such that the measuring light reflected from the mirror surface 45 will be again reflected from the optical surface, traverse the hologram 25' and Fizeau surface 19' to be incident on a photosensitive surface 37' of camera 34'. With such arrangement, a peripheral portion of mirror surface 45 is imaged onto the photosensitive surface 37'. Also reference light reflected from Fizeau surface 19' will be incident on the photosensitive surface 37' to generate a interference pattern with the incident measuring light.
The optical data of the optical elements of the beam path of the measuring light of interferometer system 1' are
given in Table 2.
_______ ___________ ______________ __________ _____________ Table 2 Radius Thickness Diameter Surface Glass Conic _____ [mmj Emmi ______ [mmj _______ 19' co 200.00 _________ 114.2159 0 24' __________ 6.35 SUPRASIL 114.2159 0 25' cc 500.00 _________ 114.2159 0 41 -185.306 -76.39865 __________ 304.40 -0.55 -30.00 ______________ __________ 58.12187 0 Coefficients of the phase function according to Formula 2 of the hologram on surface 25' are: Al = 22.851928 A2=-0.003377605 A3 = 2.5652085.1006 A4 = 1.874096.1009 A5 = 1. 0712329.1012 A6 = 4.3382935.1016 A7= 1.1419132*10' The interference patterns detected in the first and second interferometric measurements may be evaluated to determine deviations of the optical surface 3 from its target shape.
Background information on interferogram evaluation and wavefront fitting may be taken from chapters 13.1 and 13.2 of the above mentioned textbook of Daniel Malacara. Shape - 16 - errors of the central portion 7 of surface 3 may be determined from the first interferometric measurement, and shape errors of the outer portion 41 of surface 3 may be determined from the second interferometric measurement.
Herein, the overlapping portion 7/41 where the outer portion 41 overlaps with the inner portion 7, is measured by both the first and second interferometric measurements.
In practice, the shape errors of the overlapping portion 7/41 determined from the second interferometric measurement will not be the same as those determined from the first interferometrjc measurement. Such difference results, for example, from an inaccurate positioning of the surface 3 to be measured relative to the interferometer optics 15 and 15', wherein the second interferometric measurement is more sensitive to positioning errors than the first interferometrjc measurement. Wavefront errors generated by displacing a surface 3 conforming exactly with its target shape by 1 jm relative to the interferometer optics 15 in the first interferometric measurement in the direction of optical axis are illustrated in Table 3 below: _________________ ________________________ Table 3 Zernike Coefficient Optical Path difference Optical Path difference _______________ _____________________ (nmj Ci 0.064080 40.550097 Ci 0. 062873 39.78593 1 Ci -0.001166 -0.737668 Ci 0.000040 0.025356 Ci -0. 000002 -0.001090 Column 1 of Table 3 indicates the respective Zernike coefficient (in the notation used in section 13.2.2 of the textbook of Daniel Malacara) of the corresponding wavefront error, wherein the letter "i" in Ci1, stands for "inner" surface portion 7; column 2 indicates the resulting optical path difference in units of the wavelength ? of measuring light (632.8 nm in the present example using the He-Ne- laser); and column 3 indicates the corresponding optical path difference in nm. Table 3 can be understood as illustrating a sensitivity of the Zernike coefficients with respect to variations of the distance between the measured surface and the interferometer in the first interferometric measurement.
Table 4 below illustrates the corresponding wavefront error generated in a situation where the surface 3 having exactly the target shape is displaced by 1 jim relative to the interferometer optics 15' in the direction of the optical axis in the second interferometric measurement.
_______________ Table4 Zernike Coefficient Optical Path difference Optical Path difference _______________ [XJ Inmi Co 0.654657 414.266909 Co 0.588229 372.23 1252 Co -0.060174 -38.078326 Co 0.005773 3.653096 Co -0.000438 -0.277456 Co 0. 000042 0.026833 Co -0.000004 -0.002829 Similarly, Table 4 illustrates a sensitivity of the Zernike coefficients with respect to variations of the distance between the measured surface and the interferometer in the second interferometrjc measurement (The letter "0" in Cor, stands for "outer" surface portion 41) From a comparison between Tables 3 and 4 it appears that the second interferometric measurement is more sensitive to positioning errors than the first interferometric measurement, or, in other words, some rotational symmetric parameters of the surface shape can be determined in the first interferometric measurement with a higher accuracy than in the second interferometric measurement.
Further, if the surface has been measured in the first interferornetric measurement of the central portion 7 of the surface 3, it is possible to use the thus determined surface profile when evaluating the outer portion 41 measured in the second interferometric measurement. For this purpose, a compensating wavefront is determined from the measurement data obtained from the overlapping portion 7/41, and the compensating wavefront is applied to the measurement data of the outer portion 41 of surface 3 in the second interferometric measurement. This may be achieved by minimizing the following expression: [hr _{hr' -A*x1 -B*y1 -k.Co20.Z20(xYJ)}] =min (Formula 3) wherein ij represents a number of a pixel location on the measured surface in x- and y-direction, respectively, X,))J represents acoordinate on the surface 3 corresponding to pixel location i,j, h represents a height of surface 3 at location (xj,yj) determined from the first interferometric measurement, hot represents a height of surface 3 at location (xj,yj) determined from the second interferometric measurement, 19- z, represents the Zernike polynomial in the notation used in section 13.2. 2 of the textbook of Daniel Malacara, are the Zernike coefficients (distance sensitivities) of the second interferometrjc measurement taken from
Table 3,
k is a free parameter of the minimization and may be understood as representing a distance error, and A,B are free parameters which are necessary for allowing to perform the minimization and which may be understood as representing a tilt about the x-axis and y-axis, respectively.
By using a suitable computational method, the parameters k, A and B are determined such that the minimum of Formula 3 above is obtained. The expression k.>Co20 *Z 1, represents the compensating wavefront which is subtracted from the measurement result of the second interferometric measurement to determine the surface shape of surface 3 in the outer portion 41 using the following Formula 4: h = - co2 z (, , (Formula 4) wherein, /" represents the surface shape of the outer portion directly obtained from the second interferometric measurement, and represents the corrected surface shape in the outer portion.
- 20 - In this Formula, the terms proportional to A and B which were present in Formula 1, have been omitted since they represent a tilt which has no physical meaning to the surface shape and were only necessary as a degree of freedom in the minimization according to Formula 3.
The surface shape of the whole surface 3 is then determined by h obtained from the first interferometric measurement and the corrected values obtained from the second interferometric measurement.
Thus, an actual surface shape of the whole optical surface 3 is obtained by stitching together the determined surface shapes of the central portion 7 and the peripheral portion 41. With the present method, a high accuracy may be achieved in determining the overall surface shape of the optical surface 3.
In the example illustrated with reference to Figures 1 and 2 above, the optical surface 3 to be tested is a concave nearly elliptical surface. Figures 3 and 4 schematically illustrate portions of interferometer systems for testing a convex nearly hyperbolic optical surface 3a.
Figure 3 illustrates a portion of an interferometer system la for testing a central portion 7a of optical surface 3a.
An interferometer optics 15a comprises a Fizeau surface 19a and a substrate 23a carrying a hologram on a surface 25a thereof. The hologram is configured such that a beam 14a of measuring light is substantially orthogonally incident on optical surface 3a in the central portion 7a thereof.
Figure 4 illustrates a portion of an interferometer system la' for testing a peripheral portion 4la of optical surface 3a, wherein an interferometer optics l5a' comprises a Fizeau surface l9a', a focusing lens 51 and a substrate 23a' carrying on a surface 25a' thereof a hologram which is configured such that a beam 14a1 Of measuring light is incident on the optical surface 3a under an angle different from 900 to be reflected towards a mirror 43a. The mirror 43a is disposed between the interferometer optics 15a' and the optical surface 3a and has a central aperture 44 for allowing the beam 14a' to pass therethrough. A mirror surface 45a of mirror 43a is of a concave spherical shape, and the measuring light reflected from the peripheral portion 41a of optical surface 3a is substantially orthogonally incident on the mirror surface 45a at each location thereof. Thus, the measuring light reflected from the optical surface 3a is retro-reflected from mirror surface 45, reflected again from the optical surface 3a, traverses the interferometer optics l5a' and is incident on a photosensitive surface of a camera not shown in Figure 4. With such arrangement, the mirror surface 45a is imaged onto the photosensitive surface.
The measuring results of the central portion 7a obtained with the interferometer system la and of the peripheral portion 41a obtained with the interferometer system la' are stitched together to obtain the overall surface shape of optical surface 3a to a high accuracy.
Figure 5 illustrates a configuration of an interferometer system ib' for testing a peripheral portion 41b of a concave nearly hyperbolic surface 3b. The interferometer system lb' is of a similar configuration as that shown in Figure 2 having a spherical mirror surface 45b disposed between optical surface 3b and an interferometer optics l5b'. The interferometer optics 15b' comprises a hologram on a surface 25b' of a substrate 23b' to generate a beam of measuring light l4b' which is reflected from the peripheral portion 41b of optical surface 3b to be substantially orthogonally incident on mirror surface 45b. -22 -
A central portion 7b of mirror surface 3b may be tested with an interferometer system similar to that shown in Figure 1. Again, the measuring results of the peripheral portion 4lb and the central portion 7b may be stitched together to obtain an actual surface shape of the optical surface 3b to a high accuracy.
A method of manufacturing the aspherical surface 3 to a high accuracy is illustrated with reference to the flowchart shown in Figure 6. After starting the procedure, the optical surface is positioned relative to the interferometer optics of the first interferometer system 1 (shown in Figures 1 and 3) in a step 101. A first interferometric measurement of optical surface 3 is performed in a step 103.
Thereafter, the optical surface is positioned relative to the interferometer optics and mirror surface 45 of the second interferometer system 1 (shown in Figures 1, 3 and 5) in a step 105. A second interferometric measurement of a peripheral portion 41 of the optical surface 3 is performed in a step 107.
In a step 109, a surface map of the optical surface 3 is determined by stitching together measuring results of the first and second interferometrjc measurements obtained in steps 103 and 107.
Differences between the measured shape of the aspherical surface 3 and its target shape are calculated in a step 111, based on the surface map determined in step 109. In a step 123, a decision is made as to whether the tested aspherical surface corresponds to the specification for the finished optical surface 3. If the differences are below suitably chosen thresholds, a finishing step 125 is -23 - performed on the aspherical surface 3. The finishing may include a final polishing of the surface 3 or depositing a suitable coating, such as a reflective coating, an antireflective coating, and a protective coating applied to the optical surface 3 by suitable methods, such as sputtering.
The reflective coating may comprise, for example, a plurality of layers, such as ten layers of alternating dielectric materials, such as molybdenum oxide and silicon oxide. Thicknesses of such layers may be about 5 nm and will be adapted to a wavelength to be reflected from. the optical surface, such that a reflection coefficient is substantially high. Finally, the reflective coating may be covered by a protective cap layer for passivating the reflective coating. The cap layer may include a layer formed by depositing materials such as ruthenium. The anti- reflective coating which is intended to reduce reflections of radiation from the optical surface of the optical element, such as a lens element, may include materials, such as magnesium fluoride, lanthanum oxide and other suitable materials. Also the anti-reflective coating may be passivated by a protective cap layer.
If the determined differences are below the thresholds in step 123, processing is continued at a step 129 of machining the optical surface. For this purpose, the optical element 5 is removed from the beam path of the second interferometer optics and mounted on a suitable machine tool to remove those surface portions of the optical surface 3 at which differences between the determined surface shape and the target shape exceed the threshold. Thereafter, processing is continued at step 101 and the optical element is again mounted in the beam 14 of measuring light in the first interferometer system 1, and the measurement of the surface shape of optical surface 3, determining differences from the target shape and machining is repeated until the differences are below the thresholds.
- 24 - The machining may include operations such as milling, grinding, loose abrasive grinding, polishing, ion beam figuring and magneto-rheological figuring.
After the optical surface 3 is finished in step 125, the optical element is delivered and incorporated in an optical system in a step 127. Thereafter a next optical element 5e to be manufactured is mounted in the interferometer beam path in a step 101 and repeated measuring and machining of such next surface is performed until this surface fulfils
the specifications.
The above threshold values will depend on the application of the optical surface in the optical system for which it is designed. For example, if the optical surface is a lens surface in an objective for imaging a reticle structure onto a resist with radiation of a wavelength X = 193 nm, such threshold value may be in a range of about 1 nm to 10 nm, and if the optical surface will be used as a mirror surface in an imaging objective using EUV (extreme ultraviolet) radiation with a wavelength of X = 13.5 nm, the threshold value will be in a region of about 0.1 nm to 1.0 nm. It is to be noted that it is not necessary that the above mentioned threshold is a constant threshold over the whole area of the optical surface. It is possible that the threshold is dependent on e.g. a distance from a center of the optical surface or some other parameters. In particular, plural thresholds may be defined each for different ranges of spatial frequencies of differences between the measured surface and its target shape.
In the above illustrated embodiments, the interferometer systems are of a Fizeau type. It is to be noted, however, that the invention is not limited to such type of interferometer. Any other type of interferorneter, such as a Twyman-Green-type of interferometer, examples of which are illustrated in chapter 2.1 of the text book edited by Daniel Malacara, Optical Shop Testing, 2nd edition, Wiley interscjence Publication (1992), a Michelson-type interferometer, examples of which are illustrated in chapter 2.1 of the text book edited by Daniel Malacara, a Mach-Zehndertype of interferonieter, examples of which are illustrated in chapter 2.6 of the text book edited by Daniel Malacara, a point-diffraction type interferometer, examples of which are illustrated in US 5,548,403 and, in the article "Extreme-ultraviolet phase-shifting point- diffraction interferometer: a wavefront metrology tool with subangstrom reference-wave accuracy" by Patrick P. Naulleau et al., Applied Optics-IP, Volume 38, Issue 35, pages 7252 to 7263, December 1999, and any other suitable type of interferometer may be used.
It is further possible to perform absolute calibrations of the interferometer optics used in the methods illustrated above. Interferometer errors determined in such calibrations may be taken into account when evaluating the detected interference patterns in the interferometric measurements.
It is further to be noted that the optical components involved in the above interferornetrjc methods are subject to gravity during measurement. This may result in deformations of the surfaces of those components which are fixed in suitable mounts for arranging the components within the beam path of the interferometer. Even though the optical axis is oriented horizontally in Figures 1 to 5, it is also possible to perform the same measurements with an optical axis oriented vertically or in any other direction in the gravitational field. In any event, it is possible to use mathematical methods to simulate deformations of the optical components in the gravitational field. One such - 26 - method is known as FEM (finite element method). All determinations of optical properties and deviations illustrated above may involve taking into account results of such mathematical methods for correcting and/or improving the determined results.
Summarized, a method of manufacturing an optical element comprises at least one first interferometric measurement and at least one second interferometric measurement. The first interferometric measurement uses a first interferometer optics to image a first portion of the optical surface onto a detector, and the second interferometric measurement uses a second interferometer optics to image a mirror surface onto a detector using measuring light reflected from a peripheral portion of the optical surface.
The present invention has been described by way of exemplary embodiments to which it is not limited.
Variations and modifications will occur to those skilled in the art without departing from the scope of the present invention as recited in the appended claims and equivalents thereof.
Claims (15)
- - 27 - What is claimed is: 1. A method of manufacturing an optical elementhaving an optical surface of an aspherical target shape, the method comprising: disposing the optical element relative to a first interferometer optics and performing a first interferometric measurement by: directing a first beam of measuring light emitted from the first interferometer optics onto the optical surface such that the measuring light is substantially orthogonally incident on the optical surface; imaging a first portion of the optical surface onto a light receiving surface using measuring light of the first beam reflected from the first portion of the optical surface; directing reference light onto the light receiving surface; and detecting at least one first distribution across the light receiving surface of light intensities of the superimposed reference light and measuring light; disposing the optical element relative to a second interferometer optics and relative to a mirror, and performing a second interferometric measurement by: directing a second beam of measuring light emitted from the second interferometer optics onto the optical surface such that measuring light is reflected from the optical surface to be orthogonally incident on a mirror surface of the mirror; imaging at least a portion of the mirror onto a light receiving surface using measuring light of the second beam reflected from a second portion of the optical surface after reflection from the mirror, wherein the second portion overlaps with the first portion and wherein an average distance of all locations of the second portion from an axis of rotational symmetry of the target shape is greater than an average distance of all locations of the first portion from the axis of rotational symmetry; directing reference light onto the light receiving surface; and detecting at least one second distribution across the light receiving surface of light intensities of the superimposed reference light and measuring light; and determining deviations of the optical surface from the target shape based on the least one first distribution of light intensities and on the at least one second distribution of light intensities.
- 2. The method according to claim 1, wherein the second portion has a ring shape.
- 3. The method according to claim 1, wherein at least one of the first interferometer optics and the second interferometer optics comprises a hologram.
- 4. The method according to claim 1, wherein the target shape is a convex shape.- 29 -
- 5. The method according to claim 4, wherein the mirror has an aperture traversed by the second beam of measuring light.
- 6. The method according to claim 4, wherein the mirror surface is of a concave shape.
- 7. The method according to claim 1, wherein the target shape is a concave shape.
- 8. The method according to claim 7, wherein the mirror surface is of a convex shape.
- 9. The method according to claim 1, wherein the mirror surface has a substantially spherical shape.
- 10. The method according to claim 1, wherein the first beam traverses a Fizeau surface, and wherein the reference light directed onto the light receiving surface in the first interferometric measurement is reflected from the Fizeau surface.
- 11. The method according to claim 1, wherein the second beam traverses a Fizeau surface, and wherein the reference light directed onto the light receiving surface in the second interferometric measurement is reflected from the Fizeau surface.
- 12. The method according to claim 1, further comprising: processing the optical surface of the optical element based on the determined deviations.- 30 -
- 13. The method according to claim 1, wherein the processing of the optical surface of the optical element comprises at least one of milling, grinding, loose abrasive grinding, polishing, ion beam figuring, magnetorheological figuring, reactive ion beam etching, and finishing the optical surface of the optical element.
- 14. The method according to claim 13, wherein the finishing comprises applying a coating to the optical surface.
- 15. The method according to claim 14, wherein the coating comprises at least one of a reflective coating, an anti-reflective coating and a protective coating.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2594896A1 (en) * | 2010-07-15 | 2013-05-22 | Canon Kabushiki Kaisha | Method and apparatus for measuring shape of surface to be inspected, and method for manufacturing optical element |
| DE102022206650A1 (en) | 2022-06-30 | 2024-01-04 | Carl Zeiss Smt Gmbh | Method and measuring arrangement for the interferometric determination of the surface shape of a test specimen |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030011783A1 (en) * | 2001-03-06 | 2003-01-16 | Akiyoshi Suzuki | Interferometer and interferance measurement method |
| WO2005114101A1 (en) * | 2004-05-14 | 2005-12-01 | Carl Zeiss Smt Ag | Method of manufacturing an optical element |
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- 2006-05-30 GB GB0610629A patent/GB2427267A/en not_active Withdrawn
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030011783A1 (en) * | 2001-03-06 | 2003-01-16 | Akiyoshi Suzuki | Interferometer and interferance measurement method |
| WO2005114101A1 (en) * | 2004-05-14 | 2005-12-01 | Carl Zeiss Smt Ag | Method of manufacturing an optical element |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2594896A1 (en) * | 2010-07-15 | 2013-05-22 | Canon Kabushiki Kaisha | Method and apparatus for measuring shape of surface to be inspected, and method for manufacturing optical element |
| EP2594896A4 (en) * | 2010-07-15 | 2014-12-31 | Canon Kk | Method and apparatus for measuring shape of surface to be inspected, and method for manufacturing optical element |
| DE102022206650A1 (en) | 2022-06-30 | 2024-01-04 | Carl Zeiss Smt Gmbh | Method and measuring arrangement for the interferometric determination of the surface shape of a test specimen |
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| GB0610629D0 (en) | 2006-07-05 |
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