WO2008110239A1 - Diffractive component, interferometer arrangement, method for qualifying a dual diffraction grating, method of manufacturing an optical element, and interferometric method - Google Patents

Diffractive component, interferometer arrangement, method for qualifying a dual diffraction grating, method of manufacturing an optical element, and interferometric method Download PDF

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WO2008110239A1
WO2008110239A1 PCT/EP2008/001022 EP2008001022W WO2008110239A1 WO 2008110239 A1 WO2008110239 A1 WO 2008110239A1 EP 2008001022 W EP2008001022 W EP 2008001022W WO 2008110239 A1 WO2008110239 A1 WO 2008110239A1
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grating
regions
type
according
light
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PCT/EP2008/001022
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French (fr)
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Stefan Schulte
Jochen Hetzler
Rolf Freimann
Matthias Dreher
Bernd DÖRBAND
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Carl Zeiss Smt Ag
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B27/00Other optical systems; Other optical apparatus
    • G02B27/42Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4233Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive element [DOE] contributing to a non-imaging application
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using infra-red, visible or ultra-violet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47Scattering, i.e. diffuse reflection
    • G01N21/4788Diffraction
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B27/00Other optical systems; Other optical apparatus
    • G02B27/42Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4261Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive element with major polarization dependent properties
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B5/00Optical elements other than lenses
    • G02B5/18Diffraction gratings
    • G02B5/1814Diffraction gratings structurally combined with one or more further optical elements, e.g. lenses, mirrors, prisms or other diffraction gratings
    • G02B5/1819Plural gratings positioned on the same surface, e.g. array of gratings
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B5/00Optical elements other than lenses
    • G02B5/18Diffraction gratings
    • G02B5/1814Diffraction gratings structurally combined with one or more further optical elements, e.g. lenses, mirrors, prisms or other diffraction gratings
    • G02B5/1819Plural gratings positioned on the same surface, e.g. array of gratings
    • G02B5/1823Plural gratings positioned on the same surface, e.g. array of gratings in an overlapping or superposed manner
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using infra-red, visible or ultra-violet light
    • G01N21/17Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47Scattering, i.e. diffuse reflection
    • G01N2021/4792Polarisation of scatter light

Abstract

A diffractive component comprises a grating (25) including plural regions (A, A', B) of different types, wherein the gratings in the different regions differ with respect to lattice period and orientation. The different regions can be arranged according to an irregular pattern. Further, the gratings of the different types can be inverse to each other, or parameters of grating forming structures can vary between regions of the different types. A structural parameter of a dual grating is determined using a first phase function of the dual grating. A deviation of a surface of an optical element from a target surface is determined in an interferometric measurement using a second phase function of the dual grating taking into account the determined structural parameter of the grating. In an interferometric method using a diffraction grating harbouring different phase functions in different types of regions arranged in a superlattice for measuring a surface of an object perturbing superlattice diffraction orders are destructively interfered by adapting the diffraction grating having a periodicity of the superlattice that varies across the grating.

Description

Diffractive Component, Interferometer Arrangement, Method for Qualifying a Dual Diffraction Grating, Method of Manufacturing an Optical Element, and lnterferometric Method

Background of the invention

Field of the invention

The present invention relates to a diffractive component, an interferometer arrangement having such diffractive component and a method of manufacturing an optical element using such interferometer arrangement. Further, the present invention relates to a method for qualifying a dual diffraction grating. Furthermore, the present invention relates to a method for manufacturing an optical element using the qualified dual diffraction grating.

Furthermore, the present invention relates to an interferometric method using a diffraction grating having a varying local lattice period, in particular to an interferometric method using a dual diffraction grating comprising a superlattice with a varying local lattice period.

Brief Description of Related Art

The optical element having the 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 processed or manufactured to have a target shape determined by a designer of the optical system. In such a manufacture it is necessary to compare the shape of the processed optical surface with its target shape, and to determine differences between the processed and target surfaces. The optical surface may then be further processed at those portions where differences between the processed 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 an optical surface typically includes a source of 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.

The interferometer optics for generating the beam of measuring light incident on the surface to be tested may comprise one of more refractive optical elements, such as lenses. It is also known to use a diffractive component such as a hologram in an interferometer optics. 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, Optical Shop Testing", 2nd Edition, John Wiley & Sons, Inc. 1992, New York. 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.

It has been found that the conventional methods of testing and manufacturing optical surfaces using diffractive components have an insufficient accuracy in some applications.

It has also been recognized that an actual structure of a diffractive component used within an interferometer for testing optical elements deviates from an original design structure. Thereby, an actual wavefront generated from this diffractive component can deviate from a target wavefront designed to match a shape of a surface of an optical element to be tested. Thus, deviations of an actual shape of the surface of the optical element from a target shape of the surface of the optical element cannot be determined accurately. Therefore, there is a need for determining structural parameters of the diffractive component in order to take these structural parameters into account when determining deviations of an actual shape of the surface of the optical element from a target shape of the surface of the optical element. It has been recognized in a number of cases that conventional methods for measuring a surface of an object using an interferometric arrangement comprising a dual diffraction grating has an insufficient accuracy. Thus, a further object of the present invention is to provide an interferometric method for measuring a surface of an object using a dual diffraction grating.

Summary of the Invention

The present invention has been accomplished taking the above problems into consideration.

Embodiments of the present invention provide a diffractive component comprising a substrate and a grating provided thereon, wherein the grating comprises plural regions of at least a first type and a second type. Such diffractive component can be advantageously used in an interferometer arrangement to generate two or more types of wavefronts serving different functions. For example, wavefronts of a first type may be generated such that they are orthogonally incident on a surface of an optical element to be tested, wherein the wavefronts of a second type may be used for generating reference wavefronts which coincide on a detector of the interferometer arrangement with wavefronts having interacted with the optical surface to be tested for generating interference patterns which can be analyzed for determining deviations of the optical surface from its target shape. Further, in other embodiments the wavefronts of the second type can be generated such that they are orthogonally incident on a surface of a reference object used for calibrating the interferometer arrangement. Examples of interferometer arrangements including diffractive gratings having regions of different types are known from DE 102 23 581 B4 or DE 198 20 785 A1.

A grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating. The local lattice period may be also defined as the inverse of a line density of the lattice. The grating-forming structures are each composed of at least two features of differing optical properties. The different features differ in view of optical properties, such phase-shift, extinction, or other properties to light interacting with the grating-forming structures. In particular, the grating-forming structures can be each composed of plural different elongated optical elements which are arranged adjacent to each other in the direction transverse to the direction of elongation of the grating-forming structures. For example, the different elongated optical elements of one grating-forming structure may comprise a transparent elongated optical element and a non-transparent elongated optical element such that a binary amplitude grating is formed. According to another example, one grating-forming structure of a grating may comprise groove portions formed between adjacent plateau portions and plateau portions formed between adjacent groove portions, such that a binary phase grating is formed.

In a grating having plural regions of different types, regions of different types are adjacent to each other such that properties of the grating change significantly when crossing a boundary line between two adjacent regions of different types. In particular, the grating on one side of the boundary line can be different from the grating on the other side of the boundary line with respect to local lattice period and/or with respect to the orientation of the lines along which the grating-forming structures are arranged. This can be expressed by the following relation:

-1 wherein

Figure imgf000006_0001

pA is the local lattice period at a first location close to the boundary line and within the region of the first type;

pB is the local lattice period at a second location close to the first location and within the region of the second type;

VA is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surroundings of the first location; and

VB is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the second location, wherein VA ■ VB > 0 .

According to other embodiments of the invention, the grating forming structures can be arranged such that

-/

Figure imgf000006_0002

According to an embodiment of the present invention, the regions of the first type and the regions of the second type are arranged according to an irregular pattern. If such diffractive component is used in an interferometer arrangement, the grating formed by the regions of the first type and the grating formed by the regions of the second type have different phase functions such that wavefronts of light diffracted at the different gratings can provide different functions. In particular, the grating provided by the regions of a same type may be defined by a same smoothly varying phase function.

If the regions of the different types were arranged according to a regular pattern, such regular pattern would form a "super-lattice" which provokes additional diffraction of light traversing the diffractive component. According to the illustrated embodiment, the regions of the first type are arranged according to an irregular pattern such that a precisely regular arrangement of the regions of the first and second types is avoided, resulting in suppression of light intensities diffracted at such super-lattice.

According to embodiments of the present invention, extensions of at least one of the regions of the first type and the regions of the second type have varying lateral dimensions, wherein the lateral dimensions are each greater than 3 times the local lattice period of the respective region.

According to other embodiments of the invention, the lateral dimensions can be greater than 5 times or also greater than 10 times the local lattice period of the respective region.

According to particular embodiments herein, the regions have a minimum lateral extension and a maximum lateral extension and wherein a distribution of all lateral extensions has a standard deviation greater than 5 % of the average lateral extensions of the regions. In particular, the lateral extensions can be randomly distributed about an average lateral extension of the regions.

A relative difference between the minimum lateral extension and the maximum lateral extension can be more than ten percent as defined by the following relation:

d - d .

2 -=≡ '≡- ≥ O.J , wherein d ma ,x + d m_m.

dmin is the minimum lateral extension of the at least one of the regions of the first type and the regions of the second type, and

dmax is the maximum lateral extension of the at least one of the regions of the first type and the regions of the second type. Generally, the lateral extension of a region can be defined as being the greatest lateral dimension of the respective region.

However, if the region has a shape of an elongated band or stripe, the lateral extension is advantageously defined as a width in a direction transverse to a direction of elongation of the band or stripe defining the shape of the region.

According to further embodiments of the invention, a number of the regions of the first type and a number of the regions of the second type are each greater than 100, or 1000 and may also exceed a number of several thousand.

According to a further embodiment of the present invention, a lowest value of minimum lateral extension of the regions of the first and second types is at least 3 times, 5 times or even more than 10 times a lattice period of the lattice within the respective regions. An upper limit for the maximum lateral extension of the regions may depend on the application in which the grating is used. According to an embodiment of the present invention, an interferometer arrangement including a diffractive component as described above also includes a detector arrangement for detecting measuring light, and the highest width of the regions is selected such that it is smaller than two times a diameter of the grating divided by a square root of a number of pixels of the detector. Pixels of the detector are then supplied with light originating from different types of gratings.

According to a further embodiment of the present invention, a grating of a diffractive component comprises regions of at least first, second and third types wherein the gratings provided by the regions of the first and second types are substantially inverse to each other which means that differences between lattice periods and lattice orientations of the regions of the first and second types disposed next to each other are relatively small, and wherein the gratings provided by the regions of the first and second types differ in their relative phases of periodic arrangement of the grating-forming structures by an amount close to π.

In other words, when the grating-forming structures are each composed of at least two features of differing optical properties, wherein an arrangement pattern of the at least two features on a first side of a boundary line between two regions is obtainable by translating an arrangement pattern of the at least two features on a second side of the boundary line in a direction parallel to the lines along which the grating-forming structures are distributed and in a direction orthogonal thereto by an amount of less than 0.7 and greater than 0.3 times the local lattice period. If such diffractive component is incorporated in an interferometer arrangement, the gratings provided by the regions of the first and second types may provide a substantially same function, whereas the grating provided by the regions of the third type provides a function different therefrom. However, a super-lattice which might be formed by a regular arrangement of the regions of the first, second and third types will then have a diffraction property which is non-symmetric with respect to a suitably chosen diffraction orders of diffraction at the grating and the super-lattice. This may then prevent undesired light diffracted by the super-lattice from reaching the detector of the interferometer arrangement.

According to a further embodiment of the present invention, a grating comprises plural regions of at least a first type and a second type, wherein the following relations are fulfilled at locations about boundary lines between regions of the first type and regions of the second type: the direction of extensions of the lines along which the grating- forming structures are distributed in the first region is substantially equal to the direction of extensions of the lines along which the grating-forming structures are distributed in the second region; and

(N - 0.l) - pA ≤ pB ≤ (N + (U) - J^ , wherein

pA is the local lattice period at a first location close to the boundary and within the region of the first type;

pB is the local lattice period at a second location close to the first location and within the region of the second type; and

N is an integer number greater than 1.

Using such diffractive component in an interferometer arrangement allows for avoiding deviations of light diffraction occurring at the grating from light diffraction as calculated by scalar diffraction theory based on a geometry of the grating. This is based on the following considerations: the effect of a diffraction grating having lower line densities or greater lattice vectors, respectively, can be typically precisely predicted with relatively high precision by using scalar diffraction theory. At certain higher line densities, particular physical effects, such as surface plasmons generated by the incident light, cause a phase deviation of diffracted light which can not be explained by scalar diffraction theory. In such situations, more rigorous diffraction theories will be necessary for determining the effects of diffraction gratings. However, these effects depend on further properties of the diffraction grating, such as shapes and material properties of the grating-forming structures. With the above diffractive component it is possible to avoid such problems in that line densities at which these problems might occur can be avoided at all. If a region of the grating shall generate a certain diffraction angle which is achievable by first order diffraction at a grating having a critical lattice period pA , the same diffraction angle can be obtained by using second order diffraction at a grating having a lattice period pB of half of the lattice period pλ .

According to a further embodiment of the present invention, deviations from scalar diffraction theory are avoided by using a grating in which a first local lattice period at a first location differs from a second local lattice period at a second location by more than

10% and wherein another parameter of the grating at the first and second locations differs also by more than 10%. Such grating can be advantageous in a situation where deviations from scalar diffraction theory do not occur at the first location with a given lattice period and a given other parameter of the grating. However, at the second location, having the different lattice period, deviations from scalar diffraction theory would occur if the other parameter of the grating at the second location were the same as at the first location. However, in the illustrated embodiment, the other parameter of the grating is modified at the second location as compared to the first location such that such deviations from scalar diffraction theory will not occur.

According to an embodiment, the other parameter of the grating is a relative width of different features having different optical properties and providing the grating-forming structures. According to a further embodiment, the other parameter of the grating is a relative height of the features forming the grating-forming structures.

According to a still further embodiment of the present invention, a grating comprises plural regions of at least a first type and a second type, wherein the regions of the first and second types are distributed across the grating according to a regular pattern such that a super-lattice is provided which also diffracts light interacting with the grating. The regions of the first and second types differ from each other by at least one other parameter of the grating influencing deviations of light diffraction at the grating from scalar diffraction theory.

Thus, if a certain area of the grating has a line density or lattice period in a range such that deviations from scalar diffraction theory occur in regions of the first type, such deviations will not occur in the regions of the second type. This results in that the regions of the first and second types have different optical properties which generate diffraction at the super-lattice formed by the regular arrangement of the regions of the first and second types. Such additional diffraction can be identified by analyzing the measuring results obtained from the interferometer arrangement. It is then possible to eliminate these identified effects from the measuring result.

According to a further embodiment of the present invention, a method of manufacturing an optical element comprises: generating a beam of measuring light, directing the beam of measuring light onto an optical surface of the optical element such that the measuring light is substantially orthogonally incident thereon, wherein a diffractive component according to one of the embodiments illustrated above is disposed in the beam path of the measuring light, performing at least one interferometric measurement by superimposing reference light with measuring light having interacted with the optical surface and which has been diffracted by the grating of the diffractive component, determining deviations of the optical surface from its target shape based on the at least one interferometric measurement and processing of the optical surface of the optical element based on the determined deviations.

According to an embodiment of the present invention a method for qualifying a dual diffraction grating formed by a plurality of grating forming structures according to a first phase function and a second phase function comprises: illuminating at least a portion of the grating with light; detecting an intensity of the light diffracted at the grating forming structures according to the first phase function; determining at least one structural parameter of the grating forming structures based on the detected intensity, wherein the at least one structural parameter is at least one of a profile depth, a duty cycle and a edge steepness.

The dual diffraction grating is characterized such that its grating forming structures are formed according to a first phase function and a second phase function which is different from the first phase function. Except for a multiplication factor the phase function used within this application corresponds to the ikonal function as defined in chapter III, section 3.1.1 , pages 111 to 113 of the book "Principles of Optics" by Born and Wolf, third (revised) edition, Pergamon Press, 1965, Oxford. The phase function is also described in chapter III, section 14 on page 426 of the book "Optik", Volume 3 of "Lehrbuch der Experimentalphysik", seventh edition, by Bergmann and Schaefer, DeGruyter, 1978, Berlin. In general a phase function is a scalar valued function depending on three spatial coordinates. Disregarding the time dependence of an electromagnetic wave the phase function describes the phase of the electromagnetic wave. Surfaces of constant phase and therefore constant phase function correspond to wave fronts of the electromagnetic wave. To mathematically describe the electromagnetic wave, the phase function appears in the argument of a trigonometric function, such as a cosine or sine function. A phase function implemented in a diffraction grating depends only on two spatial coordinates in a plane of an extension of the grating. When grating forming structures according to a first phase function and a second phase function are formed on a dual diffraction grating, the dual diffraction grating is thus capable of generating two wavefronts corresponding to the two phase functions, when the grating is illuminated with appropriate light. According to an inventive method, light diffracted at the grating forming structure according to only one phase function is used, to determine a structural parameter of the grating.

According to an embodiment of the present invention the illuminating comprises illuminating the portion of the grating with polarized light. Polarized light in the context of the present application means that the electric field vector or the magnetic field vector of the light wave oscillates in a certain direction at a given point in time. Polarized light comprises linearly polarized light, circularly polarized light, elliptically polarized light, and the like.

According to an embodiment of the present invention the light diffracted at the grating forming structures is reflected light. When qualifying the dual diffraction grating the light may traverse the grating, when it is adapted to be a transmission grating. However, the light illuminating the grating may also be reflected from the grating and the reflected light may be detected, in order to determine a structural parameter of the grating.

According to an embodiment of the present invention the method for qualifying a diffraction grating comprises polarizing the light diffracted at the grating forming structures, wherein the detecting comprises detecting of the polarized light diffracted at the grating forming structures. Before detecting the intensity of light diffracted at the grating, the light may be polarized, wherein the kind of polarization (linearly, circularly, elliptically) may depend on the polarization state of the light illuminating the grating.

According to an embodiment of the present invention the light diffracted at the grating forming structures is light diffracted at a diffraction order different from a Oth diffraction order. The diffraction order may be a (+1 ) diffraction order or a (-1 ) diffraction order, or may be a (+2) or a (-2) diffraction order or may be a higher diffraction order. These diffraction orders can be used to employ a so called Littrow condition. Littrow condition means that the diffracted light propagates in a direction opposite to the incident light.

According to an embodiment of the present invention an average of a profile depth of a majority of grating forming structures of the grating satisfies: {N+ 0.4) λ ≤ (n- ή- h ≤ (N+ 0.6) λ , wherein

h is the average of the profile depth of the majority of grating forming structures;

λ is a wavelength of the light illuminating the grating;

n is a refractive index of the grating forming structures taken at the wavelength λ\ and

N is an integer number.

The grating forming structures may be formed by protrusions and recesses or grooves in a substrate of the grating. The protrusions may protrude orthogonally to a plane of an extension of the grating. The profile depth may then be a difference of a height of the protrusions and a height of the recesses of the grating. Besides others the difference between a phase of light traversing a groove and a phase of light traversing a protrusion depends on the profile depth of the grating forming structures at this location and on the refractive index of the substrate. When this phase difference is substantially half of the wavelength of the light used to illuminate the grating, the portions of light traversing the groove and the protrusion, respectively, will interfere destructively and thus there will be substantially no intensity of light in a Oth transmitted diffraction order. This kind of grating will therefore only generate substantial light intensities for diffraction orders greater than a 0th diffraction order.

According to an embodiment of the present invention an average value of a profile depth of the grating forming structures is between 660 nm and 700 nm.

According to an embodiment of the present invention the light comprises wavelengths between 620 nm and 650 nm.

According to an embodiment of the present invention a refractive index of the grating forming structures at a wavelength of the light illuminating the grating is between 1.4 and 1.5.

Illuminating a grating having a profile depth of substantially 680 nm and a refractive index of substantially 1.45 with light having a wavelength of substantially 635 nm will result in substantially no intensity of light diffracted in the 0th transmitted diffraction order, when furthermore a duty cycle of the grating is substantially 0.5. According to an embodiment of the present invention an average of a duty cycle of the grating is between 0.4 and 0.6. A duty cycle is understood to be a ratio of a width of a protrusion to a sum of widths of the protrusion and a neighbouring recess.

According to an embodiment of the present invention the plurality of grating-forming structures are distributed across the grating along first lines and second lines and repeatedly arranged adjacent to each other in a first direction and a second direction transverse to a direction of extension of the first lines and second lines, respectively, wherein a first local lattice period and a second local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating relating to the first phase function and the second phase function, respectively, wherein the following relation is fulfilled at a majority of locations of the grating: -V. > 1.0 mm-' ; and VA VB > 0

Figure imgf000014_0001

wherein

pA is the first local lattice period at a location;

pB is the second local lattice period at the location;

VA is a unit vector having an orientation orthogonal to a direction of extension of the first lines in a surrounding of the location; and

VB is a unit vector having an orientation orthogonal to a direction of extension of the second lines in a surrounding of the location.

The grating forming structures are arranged such that a first local lattice period and a second local lattice period can be assigned at each location of the grating. To assign the first local lattice period and the second local lattice period, it may be necessary to consider a region surrounding the location, which region is large enough to recognize two periodicities in the grating forming structures. Although the grating forming structures are distributed along first lines and second lines, there may be portions of the first lines or the second lines, which do not comprise grating forming structures. The region to be considered may have an extension such as two or more first local lattice periods or two or more second local lattice periods. The first local lattice period and the second local lattice period relates to the first phase function and the second phase function respectively. A change of the phase function between two locations of the grating spaced apart by an amount of the first local lattice period pA in a direction of the first unit vector VA is 2π or 0. An analogous statement holds for pB and VB . The grating forming structures are designed to generate two electromagnetic light waves having two phase distributions across the grating corresponding to the first and second phase function, respectively, when the grating is illuminated with an appropriate light wave. The two unit vectors VΛ and VB are defined such that an angle between the two vectors is equal or smaller than 90 °. The provision of this embodiment ensures that the first phase function is actually different from the second phase function. This difference is reflected by a deviation of the first lines and the second lines regarding their direction of extension and/or their periodicity traverse to their direction of extension. It is possible to qualify a dual grating, wherein the two phase functions are either implemented by "complex coding" or by "separate coding". In the case of "complex coding" the two phase functions are concurrently present at every location of the grating. In the case of "separate coding" there are distinct regions of a first type and a second type, wherein in the regions of the first type only the first phase function is implemented and in the regions of the second type only the second phase function is implemented. In the latter case, it may be necessary to consider a region to assign a first local lattice period and a second local lattice period at a location of the grating, which is large enough to comprise regions of both types of regions, as mentioned above.

According to an embodiment of the present invention the plurality of grating-forming structures are distributed across the grating along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating; wherein the grating comprises plural regions of at least a first type (A) and a second type (B), implementing the first phase function and the second phase function, respectively, wherein the following relations are fulfilled at boundary lines between regions of the first type and regions of the second type:

— 1— . ΛV 1 .-,

V A — - V V B > 1.0 mm ; and V VR > 0

Figure imgf000015_0001

wherein

PA is the local lattice period at a first location close to the boundary line and within the region of the first type;

pB is the local lattice period at a second location close to the first location and within the region of the second type; VA is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the first location; and

VB is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the second location.

According to this embodiment, the two phase functions of the grating are implemented by "separate coding" as defined above. Adjacent or neighbouring regions of the first type and the second type differ either in their local lattice periods or the direction of their unit vectors. This ensures that the two phase functions separately implemented in the grating by the grating forming structures are actually different from each other.

According to an embodiment of the present invention pA and VA are constant within an area of 0.8 times or more of a total area of the grating across an extension of the grating. By this provision the dual grating comprises a linear grating having grating forming structures extending in a direction that is constant across a considerable portion of the grating and which are arranged according to a constant periodicity. This linear grating can be used as a Littrow grating for an incident plane wave.

According to an embodiment of the present invention the illuminating comprises directing the light onto the grating along an incident direction and the detecting of the intensity comprises detecting light diffracted at the grating forming structures into a direction which is substantially opposite to the incident direction. Light is illuminated onto the grating in an incident direction and is reflected in a substantially opposite direction. This is the so-called Littrow condition.

According to an embodiment of the present invention the illuminating comprises illuminating the portion of the grating with polarized light, which is polarized in a polarization direction, and an angle between the polarization direction and the vectors Vx is between 40° and 50°, in particular between 44° and 46°, or which is circularly polarized with a phase difference between the two orthogonal linear modes between 80° and 100° and an amplitude ratio between 1.1 and 0.9.

According to an embodiment of the present invention the illuminating comprises illuminating at plural different wavelengths, the detecting comprises detecting plural intensities of light at the plural wavelengths and the determining is based on the plural detected intensities. The illuminating at plural different wavelengths allows still higher accuracy in determining the structural parameter of the grating. According to an embodiment of the present invention the method is performed on a plurality of portions of the grating to cover the entire grating, wherein the plurality of different portions are subsequently illuminated. Portions of the grating are scanned with an illuminating beam subsequently, wherein the at least one structural parameter is determined based on detected intensities for each portion of the grating.

According to an embodiment of the present invention the detecting comprises detecting intensities of the light diffracted at the grating forming structures from a spatially resolving detector. Without scanning portions of the grating intensities of light are detected that has been diffracted from substantially a total area of the grating.

According to an embodiment of the present invention a method for manufacturing an optical element is provided, comprising: determining at least one structural parameter of a dual diffraction grating according to an embodiment of a method for qualifying a dual diffraction grating according to the invention; directing measuring light onto the dual diffraction grating for generating shaped measuring light by diffracting measuring light at the grating forming structures according to the second phase function of the grating; detecting light formed by superimposing reference light with the shaped measuring light having interacted with a surface of the optical element; processing the optical element based on the determined at least one structural parameter and on the detected light.

At least one structural parameter of the dual diffraction grating is determined using diffraction provided by the first phase function of the grating. The at least one structural parameter is then used in the manufacturing method to analyze measuring data obtained in an interferometric method measuring a surface shape of an optical element by diffracting measuring light at the grating forming structures of the dual grating according to the second phase function. Thus, the first phase function can optimally be adapted to allow convenient and accurate determination of at least one structural parameter of the grating. The second phase function, in turn, can optimally be adapted to generate a wavefront corresponding to a target shape of a surface of the optical element to be tested. The at least one structural parameter of the grating determined using the first phase function of the dual grating is then inferred to portions of the grating forming structures providing diffraction of the grating according to the second phase function. This is applicable in either case, whether the grating forming structures are formed by complex coding such that they provide diffraction according to both the first phase function and the second phase function concurrently at every location of the grating, or they are formed by separate coding on a common grating such that at any location of the grating there is only one type of grating forming structure present corresponding to one of the two phase functions. In both cases they have been concurrently manufactured including processes such as electron lithography, etching, and performing chemical reactions causing their structural parameters, such as profile depth, edges steepness and duty cycle and others to be equal or at least very similar.

According to an embodiment of the present invention the detecting of light comprises detecting an interference pattern formed by superimposing reference light with the shaped measuring light having interacted with the surface of the optical element.

According to an embodiment of the present invention the processing of the optical element is based on determining a deviation of a shape of the surface of the optical element from a target shape of the surface based on the detected light and on the determined at least one structural parameter of the grating.

The determined at least one structural parameter allows to compute by numerical computation a deviation of an actual shape of a wavefront generated by diffraction at the grating according to the second phase function from a target shape of the wavefront. This deviation can then be accounted for when determining a deviation of an actual shape of the surface of the optical element to be tested from a target shape of the surface. According to an embodiment of the present invention, light diffracted at the grating forming structures of the grating according to the first phase function serves as reference light to form an interference pattern when superimposed with shaped measuring light having interacted with the surface of the optical element. Thus, the first phase function serves here two tasks, the first one to qualify the grating forming structures by determining at least one structural parameter, and the second one by providing reference light in the interferometric measuring method for measuring a surface of an optical element.

According to an embodiment of the present invention the determining of the deviation of the shape of the surface of the optical element from the target shape of the surface of the optical element comprises determining a deviation of a shape of a wave front of the generated shaped measuring light from a target shape thereof based on the determined at least one structural parameter qualifying the grating.

According to an embodiment of the present invention the processing of the optical element comprises at least one of milling, grinding, loose abrasive grinding, polishing, ion beam figuring, magneto-rheological figuring, reactive ion beam etching, and finishing the optical surface of the optical element. According to an embodiment of the present invention the finishing comprises applying a coating to the surface of the optical element.

According to an embodiment of the present invention the coating comprises at least one of a reflective coating, an anti-reflective coating and a protective coating.

According to an embodiment of the present invention, an interferometric method comprises forming a first light beam by diffracting a measuring light beam according to a predetermined first diffraction order at a diffraction grating and forming a second light beam by diffracting the measuring light beam according to a predetermined second diffraction order at the diffraction grating. Herein, the diffraction grating is illuminated by the measuring light beam substantially across an entire extension of the grating such that by diffracting the measuring light beam according to the first, respectively second, diffraction order two wavefronts are generated emanating the diffraction grating across the entire extension of the grating. The interferometric method further comprises reflecting the first light beam and the second light beam at a surface of an object, diffracting the reflected first light beam and the reflected second light beam at the diffraction grating such that at least portions of the diffracted reflected first and second light beams interferometrically superimpose.

In general the diffraction order is indicated by the value of the integer number N in Bragg's diffraction equation

Nλ = 2ps\n S ,

wherein

λ is the wavelength of the measuring light, p is the local lattice period, and

9 is the angle between the propagation direction of the wave incident on the diffraction grating and the propagation direction of the light wave emanating from the diffraction grating.

The predetermined first diffraction order and the predetermined second diffraction order are different from each other and may be any diffraction order, in particular not necessarily the +1 or +2 diffraction order. The predetermined first and second diffraction order may be any of for example the ..., -3, -2, -1 , +1 , +2, +3, ... diffraction order.

The reflecting of the first light beam and second light beam and the diffracting the reflected first light beam and the reflected second light beam may comprise for a plurality of pairs of a first location and a second location of the surface of the object: Reflecting a portion of the first light beam at the first location; reflecting a portion of the second light beam at the second location, wherein the first location is disposed apart from the second location by a distance; and diffracting the reflected portions of the first and second light beams such that the diffracted reflected portions of the first and second light beams interferometrically superimpose.

lnterferometrically superimposing the first light beam reflected at the surface of the object and the second light beam reflected at the surface of the object requires that the two light beams have substantially the same polarisation, substantially the same wavelengths, substantially a fixed phase relation relative to each other requiring that the measuring light beam has a sufficiently large coherence length, and that the two light beams substantially traversed in the same direction along substantially common paths. Depending on an optical path difference traversed by the first light beam and the second light beam an amplitude of an electromagnetic wave formed by a superposition of the first and second light beams diffracted, reflected and diffracted again, may be larger or smaller than amplitudes of the individual electromagnetic waves forming the first, respectively second, light beam.

For the diffraction grating used in the interferometric method a local lattice period is assignable at each location of the diffraction grating and a variation of the local lattice period across the diffraction grating is greater than 1 %, in particular greater than 2%, further in particular greater than 5%, and even further greater than 10%.

The diffraction grating typically comprises grating forming structures formed on a substrate. The grating forming structures are provided to influence a phase and/or an amplitude of an electromagnetic wave interacting with the diffraction grating. The local lattice period is obtainable by determining a periodicity of the grating forming structures at a particular location of the diffraction grating. The substrate of the grating may extend in a base level plane and at least portions of the grating forming structures may protrude substantially perpendicular to this plane. The periodicity of the grating forming structures varies across an extension of the grating and thus the local lattice period is in particular not constant across the grating. A measure of a variation of the local lattice period may be determined by considering a deviation of a mean of the local lattice period across the diffraction grating. In particular, an absolute value of this deviation may be averaged across the diffraction grating to obtain a measure of the variation of the local lattice period. According to an embodiment of the present invention, the grating comprises plural regions of at least a first type and a second type, wherein the regions of the first type are formed by a plurality of the first grating forming structures according to a first phase function and the regions of the second type are formed by a plurality of second grating forming structures according to a second phase function different from the first phase function. Thereby, an arrangement of the regions of the first type and the regions of the second type across the grating forms a superlattice. The grating forming structures of the two types of regions of the diffraction grating are devised to implement two different phase functions, the first phase function and the second phase function. Each such phase function mathematically describes the influence of the corresponding grating forming structures on a phase or/and an amplitude of an electromagnetic wave interacting with the respective grating forming structures and thus with the grating. A difference between the two phase functions can be confirmed by determining for each of the first type and the second type of regions a local lattice period and a local lattice vector for a number of locations of the grating. The two phase functions are considered to be different, if a deviation of these or similar parameters characterizing the respective grating forming structures in the regions of the first type, respectively the second type, exceed predetermined thresholds.

According to an embodiment of the present invention, the diffraction grating is arranged and adapted such that the diffracted reflected first and second light beams substantially destructively interfere. Thus, the diffracted reflected first and second light beams substantially exhibit an optical phase difference of an arbitrary odd multiple of half of the wavelength of the measuring light. In particular, the majority of first and second light beams reflected from first, respectively second, locations of the surface of the object and diffracted by the grating destructively interfere. In particular, the grating is arranged and adapted in dependence of at least a shape of the surface of the object.

According to an embodiment of the present invention, the interferometric method further comprises: forming a probing light beam by diffracting the measuring light beam according to a predetermined probing diffraction order at the plurality of first grating forming structures and according to a predetermined probing superlattice diffraction order at the superlattice; reflecting the probing light beam from the surface of the object; diffracting the reflected probing light beam according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the predetermined probing superlattice diffraction order at the superlattice; interferometrically superimposing the reflected and diffracted probing light beam with a reference light beam; and detecting the superimposed light beams. Also the reflected and diffracted probing light beam is interferometrically superimposed with the reference light beam in order to detect phase differences of optical paths traversed by the reflected and diffracted probing light beam and the reference light beam. The optical path traversed by the reflected and diffracted probing light beam thereby depends on a shape of the surface of the object. Thus, by detecting the superimposed light beams information representing the shape or the characteristics of the surface of the object can be obtained.

The grating comprises two types of regions harbouring first grating forming structures, respectively second grating forming structures, wherein these two different types of regions are arranged in a superlattice. The grating forming structures in one of these regions are substantially designed to provide a wavefront having a shape substantially matching a target shape. Grating forming structures formed in the other type of region of the grating may advantageously be used to fulfil another function during the measuring process. For example, a function may be for providing a wavefront for calibrating the measurement set up, for providing a reference wavefront, for providing a wavefront having a shape of a further target surface, and the like. Generally this flexibility is considered to provide a significant advantage of using a diffraction grating implementing at least two different phase functions over the usage of a diffraction grating implementing only one phase function. However, when these at least two phase functions are implemented by first, respectively second, grating forming structures formed in a first type, respectively second type of regions forming a superlattice, diffraction at the superlattice occurs during the measurement process that may lead to disturbing light hampering an accuracy of the measurement process.

The interferometric method according to the present invention advantageously reduces a disturbing influence of light diffracted at the first grating forming structures, additionally diffracted at the superlattice, reflected from different locations of the surface of the object, again diffracted at the first grating forming structures and additionally diffracted at the superlattice being incident on a light sensitive surface of a detector during the detecting in conventional methods and systems. Thus, an accuracy of a determination of the shape of the object can be improved.

According to an embodiment of the present invention, the first light beam is formed by diffracting the measuring light beam both according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the predetermined first diffraction order at the superlattice; the second light beam is formed by diffracting the measuring light beam both according to the predetermined probing diffraction order at the plurality of the first grating forming structures and according to the predetermined second diffraction order at the superlattice; and the reflected portions of the first and second light beams are diffracted both according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the second diffraction order, respectively first diffraction order, at the superlattice.

According to an embodiment of the present invention, the predetermined first diffraction order is different from the predetermined second diffraction order.

According to an embodiment of the present invention, at least one of an arrangement and shapes of the regions of the first type and the regions of the second type across an area of the grating are determined based on at least one of a gradient of the surface of the object and a distance of the surface of the object from the grating. An arrangement and shapes of the regions of the first type and the regions of the second type substantially characterises a diffraction of light at the superlattice. For example, a deflection angle of light diffracted at the superlattice is determined in dependence of a periodicity of the regions of the first type and the second type which in turn is based on an arrangement and shapes of the regions of the first type and the second type. The deflection angle of light diffracted at the superlattice varies in accordance to a variation of the local lattice period of the superlattice. The deflection angle changes across the grating primarily in dependence of a variation of a surface height of the object, in particular in dependence of a gradient of the surface of the object, and in dependence of a distance of the surface of the object from the grating. Thus, the deflection angle are devised such that light diffracted at the superlattice according to disturbing diffraction orders advantageously destructively interferes in order not to disturb the process of measuring the surface of the object.

According to an embodiment of the present invention, the regions of the first type and the regions of the second type are alternately arranged and substantially extend orthogonally to the gradient of the surface of the object projected to the area of the grating. In particular, the regions of the first type and the second type substantially extend parallel to lines of constant height of the surface of the object.

According to an embodiment of the present invention, the regions of the first type and the regions of the second type comprise elongated bands having varying thicknesses. In particular, the regions of the first type and the regions of the second type may be formed by rings or portions of rings which are alternately arranged. In particular, the rings may be oval or concentric rings.

According to an embodiment of the present invention, the thicknesses are at least ten times a first local lattice period assignable to the first grating forming structures and the thicknesses vary by less than 50 % across the grating. Thus, the thicknesses of the regions of the first type and the second type are typically much greater than the periodicity of the first grating forming structures defining the first local lattice period. The thicknesses may be measured in a direction parallel to the gradient of the surface of the object projected to the area of the grating.

According to an embodiment of the present invention, the total area of the regions of the first type is substantially equal to one of one and two times a total area of the regions of the second type.

According to an embodiment of the present invention, one of the first diffraction order and the second diffraction order is one of a + 1 and a - 1 diffraction order of the superlattice. In this particular case, the predetermined probing superlattice diffraction order may be a 0th diffraction order of the superlattice.

According to an embodiment of the present invention, the grating further comprises plural regions of a third type, wherein the regions of the third type are formed by a plurality of third grating forming structures according to a third phase function. The third phase function is substantially given by the first phase function by adding a phase shift of an arbitrary odd multiple of an absolute value of π, wherein an arrangement of the regions of the first type, the regions of the second type, and the regions of the third type across the grating forms the superlattice. According to this embodiment, the third phase function substantially represents an inverse of the first phase function. Thereby, a 0th diffraction order of the superlattice is substantially extinguished. The predetermined probing superlattice diffraction order may in this case be chosen as for example the - 1 , + 1 diffraction order.

According to an embodiment of this configuration, total areas of the regions of the first type, of the second type, and of the third type are substantially equal.

According to an embodiment the first diffraction order and the second diffraction order is one of a + 4 and a - 2 diffraction order of the superlattice. In this particular case, the predetermined probing superlattice diffraction order is a + 1 or a - 1 diffraction order.

According to an embodiment of the present invention, the measuring light beam is diffracted in transmission according to the predetermined probing diffraction order at the plurality of the first grating forming structures and according to the predetermined probing superlattice diffraction order at the superlattice to form the probing light beam being substantially orthogonally incident on the surface of the object. According to an embodiment of the present invention, the measuring light beam diffracted at the second grating forming structures forms the reference light beam. Alternatively, the measuring light beam diffracted at the second grating forming structures may serve a different function, such as providing a wavefront for calibrating the measurement set up or the like.

According to an embodiment of the present invention, the method further comprises forming a calibrating beam by diffracting the measuring light beam at the second grating forming structures in transmission and reflecting it at a calibrating surface.

According to an embodiment of the present invention, a method for measuring a surface of an object is provided, wherein the method comprises: directing a measuring light beam to a dual diffraction grating exhibiting a first phase function and a second phase function different from the first phase function implemented by complex coding; forming a probing light beam by diffracting the measuring light beam at the dual diffraction grating according to the first phase function; reflecting the probing light beam from the surface of the object; diffracting the reflected probing light beam at the dual diffraction grating according to the first phase function; generating a reference light beam by diffracting the measuring light beam at the dual diffraction grating according to the second phase function; interferometrically superimposing the reflected and diffracted probing light beam with the reference light beam; and detecting the superimposed light beams to determine a shape of the surface of the object, wherein a maximal deviation of the determined shape of the surface of the object from the actual shape of the surface of the object in the medium to high spatial frequency range is at most 1 nm across the surface of the object. Using a conventional diffraction grating harbouring two different phase functions coded in a superlattice having constant lattice constant does not allow such an accuracy.

According to an embodiment of the present invention, a method for manufacturing an optical element is provided, wherein superimposed light beams are detected according to embodiments of the present invention; a shape of the optical element is determined based on the detected superimposed light beams and the optical element is processed based on the determined shape of the optical element.

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 an interferometer arrangement for testing an optical element according to an embodiment of the present invention;

Figure 2 illustrates an interferometer arrangement for testing an optical element according to another embodiment of the present invention;

Figures 3a and 3b are schematic elevational views of a diffractive component according to embodiments of the invention and which can be used in an interferometer arrangement as shown in Figures 1 and 2;

Figure 4 is an illustration of geometric properties of gratings used in embodiments according to the present invention;

Figure 5 is a schematic illustration of an unfolded beam path in a conventional interferometer arrangement;

Figures 6a and 6b are schematic illustrations of further diffractive components according to further embodiments of the present invention and which can be used in the interferometer arrangement shown in Figures 1 and 2;

Figure 7 shows intensities of light diffracted at the grating shown in Figure 6b;

Figure 8, Figure 9, Figure 10 are schematic illustrations of diffractive components according to further embodiments similar to that shown in Figure 6; Figure 11 is an elevational view of a diffractive grating, where critical regions are identified;

Figure 12 is a sectional view of a diffractive component according to a further embodiment of the present invention;

Figure 13 is a graph representing a lattice vector of the grating shown in Figure 12;

Figure 14 is a graph representing a lattice vector of a diffractive component according to a further embodiment of the present invention;

Figure 15 is a graph representing a further geometric property of the grating illustrated in Figure 14;

Figure 16 is a graph showing a still further geometric property of the grating illustrated in Figure 14;

Figure 17 is an elevational view of a portion of a diffractive component according to a further embodiment of the invention;

Figure 18 is a graph representing intensities of light diffracted at the grating illustrated in Figure 17;

Figure 19 schematically illustrates a system for performing a method for qualifying a dual diffraction grating according to the present invention;

Figure 20 schematically illustrates another system for performing a method for qualifying a dual diffraction grating according to an embodiment of the present invention;

Figure 21 schematically illustrates a still further system for performing a method for qualifying a dual diffraction grating according to another embodiment of the present invention; Figure 22 schematically illustrates a still further system for performing a method for qualifying a dual diffraction grating according to another embodiment of the present invention;

Figure 23 illustrates a flow diagram of an embodiment of a method for qualifying a dual diffraction grating according to the present invention;

Figure 24a, Figure 24b illustrate processing steps in an embodiment of a method for qualifying a dual diffraction grating according to the present invention;

Figure 25 schematically illustrates an embodiment of a dual diffraction grating used in systems and methods of the present invention;

Figure 26 schematically illustrates an elevational view of a dual diffraction grating according to embodiments of the present invention;

Figure 27 schematically illustrates an elevational view of a dual diffraction grating according to embodiments of the present invention;

Figure 28 schematically illustrates an embodiment of a system for manufacturing an optical element according to the present invention;

Figure 29 schematically illustrates another embodiment of a system for manufacturing an optical element according to the present invention;

Figure 30 illustrates a flow diagram of an embodiment of a method for manufacturing an optical element according to the present invention;

Figure 31 is an illustration of a conventional dual diffraction grating; Figure 32a, Figure 32b illustrate beam paths of light diffracted according to disturbing diffraction orders;

Figure 33 illustrates in an enlarged view beam paths of light diffracted according to disturbing diffraction orders which are addressed by a method provided by the present invention;

Figure 34 illustrates an intensity distribution of different diffraction orders of light diffracted at a superlattice of a dual diffraction grating;

Figure 35 illustrates an interferogram generated by light diffracted according to disturbing diffraction orders at the conventional diffraction grating illustrated in Figure 31 ;

Figure 36a, Figure 36b, Figure 36c, Figure 36d illustrate characteristics of a dual diffraction grating according to the present invention;

Figure 37 illustrates an intensity distribution of different diffraction orders of light diffracted at a superlattice of a dual diffraction grating according to the present invention;

Figure 38 illustrates an intensity distribution of different diffraction orders of light diffracted at a superlattice of a dual diffraction grating according to the present invention;

Figure 39a, Figure 39b illustrate characteristics of a dual diffraction grating according to the present invention; and

Figure 40a, Figure 40b illustrate beam paths according to a method 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.

Figure 1 is a schematic illustration of an interferometer arrangement according to an embodiment of the present invention.

The interferometer arrangement 1 comprises a light source 11 for generating a beam 14 of measuring light. The light source 11 comprises a helium neon laser 4 emitting a laser beam 6. Beam 6 is focused by a focusing lens 8 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 is collimated by a lens or group of lenses 21 to form the parallel beam 13 of measuring light having substantially flat wavefronts. Beam 13 traverses an interferometer optics 15 which transforms and shapes the beam 13 of measuring light such that a beam 14 supplied by the interferometer optics 15 and incident on an optical surface 3 has wavefronts of a shape which corresponds to a target shape of optical surface 3 at each position 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 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 the portion of the beam 13 of measuring light where beam 13 is the parallel beam having the flat wavefronts. A beam 29 reflected from the beam splitter 31 is imaged onto a photo sensitive surface 37 of a camera chip 39 through a pinhole aperture 38 by an objective lens system 35 of a camera 34, such that the optical surface 3 is imaged onto the camera 39.

The interferometer optics 15 comprises a wedge shape 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. The reference light is also deflected by beam splitter 31 and imaged onto the photo sensitive surface 37 of camera 39, 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 39.

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 wavefronts conforming with the surface 3 of the optical element 5 at the position of the optical surface 3. For this purpose, the interferometer optics 15 comprises a substrate 23 having two parallel flat surfaces wherein one surface 25 disposed opposite to the optical surface 3 carries a grating. The grating is a computer generated hologram (CGH) designed such that it diffracts the beam 13 having the flat wavefronts exactly 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 grating 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 grating 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 gratings used in interferometry may be obtained from Chapter 15 of the above mentioned text book of Daniel Malacara.

Details of the grating 25 will be illustrated below.

Figure 2 is a schematic illustration of an interferometer arrangement 1 according to a further embodiment of the present invention. The interferometer arrangement 1 shown in Figure 2 differs from that shown in Figure 1 in that an interferometer optics 15 does not comprise a wedge-shaped glass substrate for providing a Fizeau surface. However, a grating 25 provided on a substrate 23 of the interferometer optics 15 shown in Figure 2 provides two functions: one function is to generate a beam 14 which is orthogonally incident on an optical surface 3 to be tested at each location thereof, and a second function of the grating 25 is to generate a reflected wavefront which is a reference wavefront and travels back towards lens 21 to be imaged onto the detector 39. Thus, the hologram 25 provides the function of the Fizeau surface of the interferometer arrangement 1 in Figure 1. The interferometer arrangement 1 shown in Figure 2 differs from that shown in Figure 1 further in that the hologram 25 deflects the incident beam 13 by an average angle α to form the beam 14 of measuring light incident on surface 3 to be tested. Thus, also an axis of symmetry 9' of the surface 3 to be tested is arranged under an angle α with respect to main axis 9 of the incident beam 13. For this purpose, the hologram 25 is embodied as a carrier-frequency hologram having a certain line density to achieve the deflection, wherein the line density is modulated to achieve the function of shaping the wavefronts of beam 14 such that they substantially coincide with the surface 3 to be tested at each location thereof.

Embodiments of such grating providing two different functions will be illustrated below.

Figure 3 is an elevational view of a portion of a diffractive component 23 having a grating formed on a surface thereof. The grating is formed by a plurality of elongated grating-forming structures, such as grooves, which are repeatedly arranged adjacent to each other. The grating-forming structures are not illustrated in Figure 3a. Figure 3a illustrates that the grating comprises a plurality of elongated regions 41 which are, in the illustrated example, formed as bands or stripes distributed adjacent to each other across the grating 25 surface. Each region 41 provides a grating, wherein two different types of gratings are provided by the set of regions 41. A first type of grating is provided by regions 41 labelled A and a second type of grating is provided by regions 41 labelled B. The regions A and B are alternatingly arranged next to each other on the surface of the grating 25.

The stripes 41 have irregular widths WA, WB which are randomly distributed within minimum and maximum width defined for each of WA and wβ.

Figure 3b illustrates a further possible arrangement of different regions A1 B and C, providing different types of gratings. The regions have shapes of triangles and quadrangles arranged as an irregular pattern, wherein the regions 41 have randomly distributed lateral extensions. Herein, the lateral extension of a region is defined as its maximum width, i.e. the length of a side or diagonal of the region which is maximum.

Figure 4 schematically illustrates geometric properties of gratings formed by alternating regions A and B. The gratings 25-| and 252 formed in the regions A and B, respectively are each formed by grating-forming structures 41 which are repeatedly arranged adjacent to each other, and wherein each of the grating-forming structures is composed of two different elongated optical elements 42 and 43 which are arranged adjacent to each other and which have different optical properties with respect to a phase-shift and/or an extinction of light interacting with the grating 25-| ,2- In the illustrated example, the substrate of the diffractive component 23 is made of a glass material which is transparent for light, and the optical elements 42 are formed by a layer of a metal, such as chrome, provided on the substrate surface. The optical elements 43 are free of a metal surface layer such that light may traverse the grating through elements 43, whereas light may not traverse the grating through elements 42. Optical elements 42 and 43 form a binary amplitude grating, accordingly.

The grating-forming structures 41 are repeatedly or periodically arranged adjacent to each other such that a local lattice period p can be assigned to each location of the grating. A unit vector V can be defined to be oriented orthogonal to a direction of elongation of the grating-forming structures 41. A vector V- p defined as the product of the local lattice period and the unit vector V has a length which corresponds to a distance between adjacent grating-forming structures. The distance between adjacent grating-forming structures can be determined by measuring a distance between corresponding features of the optical elements of adjacent grating-forming structures 41. For example, the distance between the left edges of optical elements 43 located next to each other can be measured to determine the length and orientation of V- p .

Figure 4 illustrates a grating 25 having two different regions A and B alternatingly arranged adjacent to each other, wherein gratings 25-| formed in regions A have substantially similar vectors pA - VA , wherein the gratings 252 formed in regions B have substantially similar vectors pB ■ VB and wherein the vectors pΛ VA and pB VB differ substantially from each other.

The lowest width of the regions A, B is about 5 times a wavelength of the measuring light of the interferometer arrangement 1 in which the grating 25 is incorporated. In other embodiments, the lowest width of the regions A, B can be, for example, 3 times or 10 times or more of the wavelength of the measuring light.

Further, the maximum width wmax can be lower than a diameter of the grating divided by a square root of the number of pixels of the detector 39. In the present example, the diameter of the grating 25 is 50 mm, and the detector has 1000x1000 pixels, such that the maximum wmax is lower than 0.1 mm.

The non-constant widths w^ and Wβ of the regions A and B have an advantageous effect when the grating 25 is used in an interferometer arrangement as shown in Figures 1 and 2. The repeatedly arranged pattern of regions A and B having different optical properties due to the difference of the gratings 25-| , 252 formed by the regions A and B, respectively, provides a "super-lattice" composed of gratings 25-| and 252- Measuring light 13 of the interferometer arrangement shown in Figures 1 and 2 is thus diffracted not only at the gratings 25^ and 252 formed by regions A and B, respectively, but also at the super-lattice formed of the arrangement of regions A and B. The diffraction at the super-lattice is basically not intended and generates additional interference patterns on the detector which can make it more difficult to analyze the interference patterns formed by the referenca light and the measuring light having interacted with the optical surface 3 to be tested. Due to the non-constant widths w^ and Wβ of regions A and B, a regularity of such super-lattice is reduced, which also reduces an intensity of light diffracted at the thus formed super-lattice. Thus, compared to a completely regular super-lattice, light diffracted by the super-lattice will contribute to disturbing interference patterns by a lesser amount and increases only an average light distribution on the detector.

Figure 5 is a schematic illustration of a beam path in an interferometer such as shown in Figure 2 for illustrating a disturbing effect of diffraction at a super-lattice formed by a grating having alternating regions A and B. The beam path illustrated in Figure 5 is an unfolded beam path in that the beam path is not depicted as being reflected at the optical surface 3 to be tested but traversing that surface. An exemplary light ray 51 of beam 13 is incident on the grating 25 and diffracted at the grating 25-| or 252 provided by the region A or B on which the ray 51 is incident. Further, a diffraction occurs at the super-lattice formed by the alternating regions A and B. Ray 52 in Figure 5 represents light of ray 51 diffracted with a desired diffraction order, which is, in the present example, the plus first (+1 ) diffraction order at the grating 25 and which experienced no diffraction (0-order) at the super-lattice. Ray 53 represents an undesired ray which was diffracted with the desired diffraction order at grating 25 but with plus first (+1 ) diffraction order at the super-lattice. Similarly ray 54 represents an undesired ray which was diffracted with the minus first (-1 ) diffraction order at the super-lattice. Arrow 55 represents the desired light after reflection from the optical surface 3 to be tested and arrow 56 represents the undesired light diffracted with diffraction order (-1 ) at the super- lattice.

Arrow 57 represents light having traversed the grating 25 a second time wherein it was diffracted at the grating 5 with the desired diffraction order, which is in this example the minus first (-1 ) diffraction order, and with 0th order at the super-lattice. Such desired light represented by arrow 57 is oriented such that it may traverse the aperture 38, as illustrated by arrow 58. Arrow 59 represents a portion of the light represented by arrow 56 which has been diffracted at the grating 25 with the desired diffraction order (-1 ) and at the super-lattice with 0th diffraction order. This portion of the undesired light is oriented such that it will not traverse the aperture 38. However, arrow 60 represents a portion of the undesired light represented by arrow 56 which has been diffracted at the grating 25 with the desired diffraction order (-1 ) and at the super-lattice with plus first (+1 ) diffraction order. This undesired light represented by arrow 60 propagates substantially parallel to the desired light represented by arrow 57 and will also traverse the aperture 38 as represented by arrow 61. Thus, the undesired light which was diffracted at the super-lattice with diffraction order (-1 ) upon traversing the grating for the first time and subsequently with diffraction order (+1 ) upon traversing the grating for the second time will contribute to forming an interference pattern on the detector 37. Similarly, undesired light which was first diffracted at the super-lattice with (-1 ) diffraction order and subsequently with (+1 ) diffraction order will also contribute to the interference pattern formed on the detector.

In the embodiment illustrated with reference to Figures 3 and 4, the intensity of light diffracted at the super-lattice and contributing to the interference pattern is reduced by making the super-lattice irregular due to the varying widths w^ and Wβ of the different regions A and B.

Figure 6a illustrates a further arrangement of a diffraction grating 25 providing two different functions and suppressing diffraction at a super-lattice formed by the regions of gratings provided by the different functions.

Figure 6a shows that grating 25 comprises three different regions A, A' and B, wherein the grating formed in region B is substantially different from the grating formed in region A and the grating formed in region B is also substantially different from the grating formed in region A1.

It is apparent that the lattices formed in regions A and B differ with respect to their lattice period and with respect to their orientation. Also the lattices formed in regions A1 and B differ with respect to lattice period and orientation.

However, the gratings formed in regions A and A1 have a substantially same period of arrangement and orientation of their optical elements. However, the gratings formed in regions A and A1 differ from each other in that the gratings are inverse to each other. The arrangement pattern in regions A' can be obtained by translating the arrangement pattern of the grating in region A in a direction parallel to the lines along which the grating forming structures are distributed and by further translating the pattern of the region A in a direction orthogonal to that line by an amount of about 0.5 times the lattice period. Figure 6b shows a further embodiment of a grating 25 comprising three different regions A1 A1 and B, wherein regions A and A1 are inverse to each other. Further, the grating forming structures formed in regions A, A' and B are all oriented in a same direction. Such grating 25 has an advantageous effect when it is incorporated in an interferometer optics of an interferometer apparatus as shown in Figure 2 as will be illustrated below.

Figure 7 shows intensities of light diffracted at the super lattice formed by regions A, A' and B in dependence of a wavevector difference Δk between diffracted light and incident light. Diffraction orders ms of light diffracted at the super lattice are indicated in Figure 7 by -4, -2, -1 , +1 , +2 and +4. It is apparent that intensities of light corresponding to the diffraction orders -3, 0 and +3 are nearly completely suppressed due to the arrangement of regions A, A1 and B having a substantially same width. With such hologram 25 it is possible to select, for example, ms = -1 as the desired diffraction order at the super lattice, wherein with reference to Figure 5, the interferometer arrangement is then arranged such that light diffracted at the super lattice with diffraction order ms = -1 will traverse the aperture 28 to be incident on the detector 37. As illustrated above with reference to Figure 5, other combinations of diffraction orders at the super lattice may generate undesired light which also traverses aperture 38 to contribute to background intensity on the detector 37. However, due to the particular arrangement of the regions A, A1 and B according to Figure 6b, the diffracted light intensities as shown in Figure 7 have the advantageous effect that, for example, light diffracted with ms = -2 upon its first transition of the grating 25 and with ms = 0 upon its second transition of the grating 25 and which would be able to traverse the aperture 38 does substantially not contribute to background intensity on the detector because the diffraction order ms = 0 is strongly suppressed as shown in Figure 7. Similarly, light diffracted with ms = -3 upon its first transition of the grating 25 and ms = +1 upon its second transition of the grating 25 and which could traverse the aperture 38 does substantially not contribute to background intensity since ms = -3 is strongly suppressed in the spectrum shown in Figure 7. However, light with ms = -4 upon first transition and ms = +2 upon second transition can contribute to a small background intensity.

Figures 8, 9 and 10 show variations of an arrangement of regions providing gratings having different functions. Figure 8 shows a hexagonal arrangement of triangular regions A, A', B and C, wherein gratings formed in regions A and A" are inverse to each other and different from gratings formed in regions B and C.

Figure 9 shows a hexagonal arrangement of regions providing gratings A, A1 and B, wherein circular regions B are provided in the centers of the hexagons, whereas regions A and A1 are alternatingly distributed about the regions B and within the hexagons. Again, regions A and A' provide gratings which are inverse to each other and which substantially differ from the gratings formed in regions B.

Figure 10 shows a rectangular arrangement of regions A, A', B, B' and C within a grating 25. In this examples, the gratings provided by regions A and A' are inverse to each other and substantially differ from gratings provided in regions B, B' and C, the gratings provided in regions B, B1 are inverse to each other and are substantially different from the gratings provided in regions C.

In the embodiments shown in Figures 8, 9 and 10, the different regions forming the different types of gratings are arranged according to a regular pattern. However, since the regular pattern includes regions providing gratings which are inverse to each other, diffraction at the super-lattice formed by the regular arrangement is made non- symmetric with respect to the diffraction angle such that undesired light diffracted at the super-lattice can be prevented from reaching the detector of the interferometer arrangement since such light can be absorbed by aperture 38.

Figure 11 shows an evelational view of a grating 25 used in an interferometer arrangement as shown in Figures 1 and 2, wherein Figure 11 indicates regions 71 within the grating. These regions 71 are those regions of the grating 25 where lattice periods and orientations of incident light are such that diffraction at the grating 25 occurring in practice deviates from a diffraction calculated based on scalar diffraction theory by an amount exceeding accuracy limitations. Outside of regions 71 , the diffraction occurring at the grating 25 in practice can be well-described using scalar diffraction theory, such that wavefronts generated by the grating outside of regions 71 conform with desired wavefronts calculated based on scalar diffraction theory within the accuracy limitations of the given application.

It is desirable to avoid regions 71 of a grating 25 in which significant deviations between occurring diffraction and diffraction calculated based on scalar diffraction theory are generated.

Figure 12 illustrates an embodiment of a diffractive component 23 carrying a grating 25 which avoids effects as illustrated above.

Figure 13 shows a graph representing a lattice period p of the grating shown in Figure 12. The grating 25 has two regions A and B, wherein the lattice period p gradually increases with increasing values of coordinate x in the region A as represented by a line 73 in Figure 13. If the lattice period p would continue to increase in region B as indicated by broken line 73', significant deviations from scalar diffraction theory would occur in region B. Therefore, a structure of the grating 25 is modified upon transition from region A to region B in that the lattice period is doubled upon transition from region A to region B. This means that light diffracted with first diffraction order in region A is diffracted by substantially a same angle as light diffracted in region B with second diffraction order. The lattice period in region B is represented by a line 74 which avoids values according to broken line 73' which are subject to deviations of scalar diffraction theory.

Figures 14 and 15 illustrate a further embodiment of a grating 25 which avoids deviations from scalar diffraction theory. A line 77 in Figure 14 represents the lattice period of the grating along coordinate x, and a line 79 in Figure 15 represents a ratio of widths w-| and W2 of optical elements 42 and 43 providing the grating-forming structures of grating 25 (see Figure 12). In region A the ratio of w<| and W2 has a first value which increases upon transition from region A to region B to a higher second value. In this example, it is assumed that deviations from linear diffraction theory would occur in region B if the ratio of w-| and W2 would be maintained at the first value as represented by broken line 69' in Figure 15. However, in region B the value of w-|/w2 is selected such that in combination with the value of the lattice period p in region B, deviations from scalar diffraction theory are still negligible within the desired accuracy limits.

Similarly, Figures 14 and 16 together represent a further embodiment of a grating 25 in which deviations from scalar diffraction theory are avoided in region B by reducing a height difference h between optical elements 42, 43 providing the grating forming structures. In this example it is assumed that deviations from scalar diffraction theory would occur in region B if the height difference h was maintained at a same value (represented by broken line 81" as in region A) and can be avoided by reducing the height difference h in region B as represented by line 81.

Figures 12 to 16 show that it is possible to avoid deviations from scalar diffraction theory at certain line densities or lattice periods by modifying certain parameters of the structure of the diffraction grating. These parameters include multiplying the lattice period from one region to the other region by a factor of two, three, four ... and using higher diffraction orders for the measurement in the interferometer apparatus. These parameters also include widths of optical elements providing the grating forming structures, height differences of the optical elements providing the grating-forming structures, refractive indices of the optical elements and others. Figure 17 is an elevational view of a portion of a grating 25 in which regions A and B are arranged according to a regular pattern. Regions A and B differ from each other in at least one of the above-mentioned properties of the gratings such as doubled or tripled lattice periods, widths of optical elements, height differences of optical elements and refractive indices of optical elements providing the grating-forming structures. Regions 71 indicated in Figure 17 represent those regions were deviations from scalar diffraction theory occur in practice at certain line densities. Due to the differences of the gratings provided in regions A and B, the deviations from scalar diffraction theory are modulated according to the spatial pattern of arrangement of region A and B. This means also deviations of wavefronts generated by grating 25 from a desired shape of wavefronts based on scalar diffraction theory is modulated according to the spatial pattern of the arrangement of regions A and B. It is then possible to eliminate these deviations from a measuring result by suitably analyzing interference patterns as follows: Lines 91 in Figure 17 represent lines of equal line density within the grating 25. If a function of detected light intensity depending on a position along a line 91 is subjected to a Fourier transform, a resulting power spectrum will have a shape as schematically illustrated in Figure 18 for those lines 91 which traverse regions 71 in which deviations from scalar diffraction theory occur. Due to the modulation of such deviations with arrangement periods pmod' tπe power spectrum has peaks at values 1/pmod> 2^PmOd- ■■■ 'f these peaks are eliminated by a suitable filter at spatial frequencies above 1/D, wherein D represents a diameter of the grating. The remaining power spectrum in which the peaks are removed can then be subjected to a reversing Fourier transform which then represents wavefronts from which the effects of non-scalar diffraction theory have been removed. These wavefronts can form the basis for further analysis to determine deviations of the measured optical surface from its target shape.

Based on an interferometric measurement as illustrated above, determined deviations of the shape of the optical surface 3 from its target shape can be used for scheduling processing steps performed on the optical surface to reduce the deviations of the shape of the optical surface from its target shape. If the optical surface fulfils desired requirements with respect to its shape, the optical element may undergo further processing such as coating of the surface with dielectric layers to form a surface of high or low reflectance, and the optical element may then be included in an optical system, such as an objective lens arrangement used in exposure steps of lithographic methods for manufacturing miniaturized devices.

Figure 19 illustrates a system 100 for performing an embodiment of a method for qualifying a dual diffraction grating according to the present invention. A laser 101 generates a light beam 102 that traverses a beam shaping optics 103 comprising lenses to form a light beam 105. Light beam 105 impinges onto a mirror 107, and is reflected substantially at a right angle to traverse a polarizer 109. Light emanating from the polarizer 109 is linearly polarized light. The polarization direction (the direction of the electric field of the electromagnetic light wave) can be changed by rotating the polarizer 109. The polarized light 111 emanating from the polarizer 109 traverses a diffractive component comprised of a substrate 123 and a dual diffraction grating 125 and is diffracted at a portion 125-| of the grating 125 to form a diffracted beam 113. The diffracted beam 113 is detected by the detector 115. A signal representing an intensity of the detected light is transferred to a control and processing system 117. Control and processing system 117 is adapted to process the received signal in order to determine a profile depth of the portion 125-| of the dual grating 125. Control and processing system 117 uses for the processing also the polarization direction of light 111 received from the polarizer 109 and calibration data retrieved from the database 118. Control and processing system 117 then sends control signals (indicated by an arrow on the line connecting it with the polarizer 109) to the polarizer 109 in order to rotate it to a further direction, in which light 105 traversing the polarizer 109 is to be polarized to form the polarized light beam 111. Also, the polarizer 109 can manually be rotated and its rotational position can be transferred to the control and processing system 117, as indicated by the arrow on the line connecting the polarizer 109 with the control and processing system 117. In the exemplary embodiment described this second polarization direction is perpendicular to a polarization direction used in the first measurement. An intensity of light 111 polarized in the second polarization direction and diffracted by the portion 125-1 of the dual grating 125 is again detected by detector 115.

The signal corresponding to the detected intensity is again received by the control and processing unit 117. Using plural signals corresponding to different polarization directions of the polarizer 109 the control and processing unit 117 determines the profile depth of the portion 125-1 of the dual grating 125. The control and processing unit 117 then generates control signals to translate the mirror 107 in one of the directions indicated by arrow 108 in order to illuminate a further portion 1252 °f the dual grating 125. As for the portion 125-| of the dual grating 125 light 111 polarized in a particular direction diffracted at the portion 1252 's received by the detector 115 and transferred to the control and processing unit 117, in order to determine a profile depth of the portion 1252 °f tne dual grating 125. Finally, by scanning across the entire area of the dual grating 125, detecting intensities of light polarized in different directions and diffracted at portions of the grating 125 the profile depth for each portion of the dual grating 125 is obtained. The map of the profile depth corresponding to values of the profile depth at each portion of the dual grating 125 is then stored in the database 118. Figure 20 schematically illustrates a further system 100a for performing a method for qualifying a dual diffraction grating according to the present invention. Elements equal or similar to elements of the embodiment illustrated in Fig. 19 are referenced with equal or similar numerals but are followed by the letter "a". Laser 101a generates a light beam 102a that traverses a shaping optics 103a to form light 105a comprising substantially plane wavefronts. Light 105a traverses a polarizer 109a to form light 111a that is polarized in a direction that forms an angle of 45° with the drawing plane. Polarized light 111a then traverses a diffractive component comprising a substrate 123a and a dual grating 125a. The dual grating 125a comprises grating forming structures according to a first phase function and a second phase function. The two phase functions can be implemented into the dual grating 125a by either complex coding or separate coding, as defined above. Examples for the case of separate coding are illustrated in Figures 3a, 4, and 17. Further examples will be shown below in Figures 25, 26, and 27. Polarized light 111a diffracted at the grating forming structures according to the first phase function of the dual grating 125a at a first diffraction order traverses a second polarizer 114a which polarizes light in the same direction as the polarizer 109a polarizes light. Polarized light 113a1 emanating from the polarizer 114a traverses a lens 140, an aperture opening of a beam stop 141 , a lens 142 and is detected by the CCD 115a. The beam stop 142 is arranged to block light diffracted at undesired diffraction orders and as well as stray light. The CCD 115a comprises 1024x1024 light-sensitive pixels to detect light diffracted from substantially a total area of the dual grating 125a. An intensity of light detected by a particular pixel of the CCD 115a is representative of the profile depth of a region of the dual grating 125a which is imaged at this pixel of the CCD 115a. The detected pixel image is received by the processing system 117a. Processing system 117a comprises a computer equipped with image processing software in order to determine a map of a profile depth across the dual grating 125a. Thereby calibration data stored in the database 118a are utilized. The determined map of profile depths is stored in database 118a.

Figure 21 illustrates another system 100b for performing a method for qualifying a dual diffraction grating according to an embodiment of the present invention. Components or elements similar to elements shown in Figure 20 are designated with the same or similar numerals but followed by the letter "b". Laser 101 b generates a laser beam 102b with a spectrum of wavelengths centered at a wavelength of 633 nm. Laser beam 102b traverses a beam shaping optics 103b to form light 105b comprising substantially plane wavefronts. Light 105b traverses a beam splitter 116b and subsequently traverses a polarizer 109b. Light 111 b emanating from the polarizer 109b is light linearly polarized in a polarization direction that includes an angle of 45° with the drawing plane. The polarized light 111 b is then incident onto a diffractive component comprising a substrate 123b and a dual grating 125b. The dual grating 125b comprises grating forming structures according to a first phase function and a second phase function. The first phase function is implemented by grating forming structures which are distributed along straight first lines which are oriented substantially perpendicular to the plane of the drawing. A first local lattice period relating to the first phase function and therefore representing a periodicity of the first lines is constant across a total area of the dual grating 125b. Thus, the first phase function corresponds to a linear Littrow lattice. The dual grating 125b is designed to have a profile depth of 703 nm. Further, a refractive index of the grating forming structures of the dual grating 125b is n = 1.45. Furthermore, the first local lattice period of the dual grating 125b, which is constant in this case, is such that there are 515 first lines per millimetre when proceeding across the grating in a direction traverse to a direction of extension of the lines. Linearly polarized light 111 b reflected and diffracted at the dual grating 125b traverses as light 113b the polarizer 109b, where it is polarized in a direction that is inclined 45° relative to the drawing plane, to form polarized light 113b1. A portion of polarized light 113b1 is reflected by the beam splitter 116b and traverses an imaging optics 119b comprising lenses and a beam stop 120b, to form light 113b". Light 113b" is detected by plural pixels comprised in the CCD 115b. Plural signals representing intensities detected by the pixels of the CCD 115b are received by the processing unit 117b. The signals from the pixels of the CCD 115b form an image representing values of a profile depth across the dual grating 125b. Processing unit 117b is equipped with a computer and image processing software to determine for each region of the dual grating 125b, which is imaged to a pixel of the CCD 115b, the profile depth of grating forming structures in this region. The values of the profile depths determined are stored within the database 118b.

Figure 22 shows still a further system 100c for performing a method for qualifying a dual diffraction grating according to an embodiment of the present invention. Components similar to components illustrated in Figure 21 are designated with same numerals but followed by the letter "c". There are a number of components that are arranged in the same manner as in Figure 21. A difference between the systems illustrated in Figure 21 and 22 is that in Figure 22 the polarizer 109c is disposed between the shaping optics and the beam splitter 116c, whereas in the system illustrated in Figure 21 the polarizer 109b corresponding to the polarizer 109c in Figure 22 is disposed between the beam splitter 116b corresponding to beam splitter 116c in Figure 22, and the dual grating 125b. Further, in Figure 22 there is an additional polarizer 114c disposed between the imaging optics 119c and the CCD 115c. The system illustrated in Figure 21 has the advantage that only one polarizer 109b is required to construct the measuring system, whereas the system illustrated in Figure 22 requires two polarizers 109c and 114c. These polarizers can also be disposed at other locations, as long as polarized light is incident on the grating 25 and is diffracted therefrom and the diffracted light is polarized before it is detected by the detector 115c.

According to embodiments of the invention, circularly or elliptically polarized light is prepared by an appropriate polarizer to direct light onto the dual grating, diffracted at the grating forming structures according to the first phase function, polarized again, and detected. Embodiments of the methods of qualifying a diffraction grating comprise also varying a polarization direction of linearly polarized light, directing the linearly polarized light onto the dual grating, diffracting the polarized light, polarizing the diffracted light in a direction different from the polarization direction of light directed onto the dual grating, and detecting the polarized diffracted light.

Figure 23 illustrates an embodiment of a method for qualifying a dual diffraction grating according to the present invention. The method starts by illuminating a dual diffraction grating with polarized light (step 201 ). An intensity of polarized light diffracted and reflected at the grating forming structures according to the first phase function of the grating is detected (step 203). Based on the detected intensity at least one of a profile depth, a duty cycle and an edge steepness of the grating is determined (step 205).

By complex elaboration the inventors surprisingly found that a linear Littrow lattice behaves under certain conditions like a λ/2-plate. A λ/2-plate transforms for example right circularly polarized light into left circularly polarized light. Also, the direction of polarization of light polarized in a direction that includes an angle of 45° with an optical axis of the λ/2-plate is rotated by 90° by the λ/2-plate upon traversal of the light through the λ/2-plate. By experimentation and computational simulations the inventors were able to devise a diffraction grating with analogous properties. They designed a Littrow lattice with 515 lines per millimeter which were engraved into a substrate having a refractive index of n = 1.45. The intensity of light and the phase of light reflected and diffracted at the first diffraction order at such a Littrow grating was calculated in dependence of a polarization direction of incident light and in dependence of the profile depth of the Littrow lattice. Results of these computations are shown in Figures 24a and 24b. The x-axes in Figures 24a and 24b represent a profile depth of the Littrow lattice. The y-axis of Figure 24a represents an intensity of light reflected and diffracted from the Littrow lattice at the first diffraction order, wherein the dashed line 210 in Figure 24a represents an intensity of diffracted light, when the incident light is polarized perpendicular to the straight lines of the Littrow lattice and the dashed and pointed line 211 represents an intensity of diffracted light, when the incident light is polarized parallel to the lines of the Littrow lattice. As can be seen, there are considerable differences of the intensities of reflected light between the two polarization directions. Also, there is a huge modulation of the intensities in both polarization directions of the profile depth of the Littrow lattice with varying profile depth.

The y-axis in Figure 24b represents an optical path (modulo an integer number of a wavelength λ of incident light) of light reflected and diffracted at a first diffraction order at the Littrow lattice divided by λ for two perpendicular polarization directions of incident light. Again, the dashed line 220 represents values when the incident light is polarized perpendicular to the lines of the Littrow lattice, whereas the dashed and pointed line 221 represents values when the incident light is polarized parallel to the lines of the Littrow lattice. A solid line 223 represents a difference between the optical path length experienced by light which is polarized perpendicular and light that is polarized parallel to the lines of the Littrow lattice. As can be seen from the solid curve 223 in Figure 24b this difference is very sensitive to the profile depth of the grating forming structures of the Littrow lattice. At a profile depth of 680 nm the value jumps from +λ/2 (reference number 224) to -λ/2 (reference number 225) because there is no unwrapping. At the maximum 224 (profile depth 680 nm) and minimum 225 the difference of the phase between light polarized perpendicular and light polarized parallel to the lines of the Littrow lattice is +λ/2 and -λ/2, respectively. The same effect occurs upon directing light polarized in a direction that includes an angle of 45° with an optical axis onto a λ/2- plate. This effect causes the direction of polarization to be rotated by 90° upon traversing such a λ/2-plate. Thus, a same polarization direction rotating effect is achieved using a Littrow lattice under the above mentioned conditions, when the profile depth is 680 nm. In contrast, when the profile depth of the grating is different from 680 nm the polarization direction of incident light will be rotated by an angle different from 90 ° by the Littrow lattice.

According to an embodiment of the present invention, the dual grating comprising a Littrow lattice designed as illustrated above is illuminated with light that is polarized in a direction including an angle of 45° with the lines of the Littrow lattice. If the actual profile depth of the grating would be equal to the designed profile depth of 680 nm, reflected and diffracted light would be polarized perpendicular to the polarization direction of incident light. Thus, substantially no intensity of light would be detected upon further polarizing the diffracted light in the same direction as the polarization direction of the incident light. Therefore, detection of substantially no intensity is indicative for the profile depth of the grating being 680 nm. Detecting non-zero intensities is therefore indicative for profile depths different from 680 nm which exact values can be obtained from the graph shown in Figure 24b. In order to determine the exact profile depths of the grating embodiments of the present invention acquire intensities detected upon illumination with different wavelengths or with different polarization directions or acquire intensities detected at different diffractions orders, such as second or higher diffraction orders.

Figure 25 schematically illustrates a dual diffraction grating 25a that can be qualified according to embodiments of methods for qualifying a dual diffraction grating according to the present invention. The grating 25a illustrated in Figure 25 is an example of implementing two different phase functions in a single grating by complex coding. The dual diffraction grating 25a comprises a substrate 23a that is made of glass with an refractive index n = 1.45. Thus, it is designed to influence a phase of light interacting with the grating, which is called a "phase grating", in particular a "binary phase grating". The grating 25a comprises plural grating forming structures 41a that are arranged adjacent to each other and are distributed along first lines 130-] and second lines 1302- The directions of the first lines 130-| vary across an extension of the grating 25a. Also the directions of the second lines 1302 vary across the extension of the grating 25a. A first local lattice period PA can be assigned at each location of the grating 25a as a repetition distance of grating forming structures 41a in a direction orthogonal to a direction of the first lines 130-| . The grating forming structures 41a comprise protrusions 42a and base level areas 43a-| and 43a2, wherein the base level areas 43a-| are disposed between neighbouring protrusions 42a which are spaced apart in a direction orthogonal to a direction of first lines 130γ Similarly, base level areas 43a2 are disposed between neighbouring protrusions 42a which are spaced apart in a direction orthogonal to a direction of second lines 1302- Base level areas 43a-| and 43a2 are situated substantially in a base level plane of an extension of the grating 25a. Protrusions 42a protrude from this base level plane of the grating 25a by an amount of h, which is also called the profile depth. Thus, the protrusions 42a comprise plateaus substantially parallel to the base level plane of the grating 25a that are elevated by an amount h relative to the base level plane of the grating 25a. Between the plateaus of the protrusions 42a and the base level areas 43a-| there are edges 131 -| . Between the plateaus of the protrusions 42a and the base level areas 43a2 there are edges 1312- Thus, the edges 131 -j and 1312 lead from the plateaus of the protrusions 42a, which are elevated by an amount h above a base level plane of the grating 25a to the level of the base level areas 43ai and 43a2- In the illustrated examples, the edges 1311 are not orthogonal to a base level plane of the grating 25a but are tilted from the normal of this base level plane by an angle of α. A value of the first local lattice period PA can be obtained by virtually shifting a protrusion 42a and a neighbouring base level area 43a-| in a direction orthogonal to a direction of first lines until the virtually shifted structure of the protrusion 42a and base level area 43a-| substantially matches a structure of a neighbouring protrusion 42a and base level area 43a-] . In this way, in each location of the grating 25a a first local lattice period p^ can be assigned. Further, the shift direction mentioned above, that is orthogonal to a direction of first lines 130^ defines a unit vector F1. In a way analogous to the procedure described above, a second local lattice period PB and a unit vector VB can be assigned at each location of the grating 25a. According to embodiments of the present invention, portions of the grating forming structures which implement a first phase function of the grating are used in a qualifying measurement of the grating to determine a structural parameter of the grating such as the profile depth h, the duty cycle w^/PA or tne edge steepness α. As can be seen from Figure 25 at least the edge steepness α and the profile depth h characterize structural features of the grating 25a which apply to both implementing phase function of the grating. Thus, a first phase function of the grating 25a can be used to determine these structural parameters of the grating and infer them to the implemented second phase function.

Figure 26 schematically illustrates an elevational view of a dual diffraction grating 25b that can be qualified according to embodiments of a method of qualifying a dual diffraction grating according to the present invention. As the diffraction grating 25a illustrated in Figure 25 the dual diffraction grating 25b illustrated in Figure 26 is a dual grating, wherein two different phase functions are implemented by complex coding. The grating 25b can be a phase and/or an amplitude grating. Grating forming structures 41 b are arranged along first lines 130b-| and second lines 130b2 periodically in two dimensions. Shaded areas 42b in Figure 26 illustrate protrusions and the areas 43b-| and 43b2 illustrate base level areas between the protrusions 42b. Two avoid obstruction edges leading from the protrusions 42b to the base level areas 43b-) and 43b2 are omitted in this drawing but they are present in the grating 25b. The Figure 26 illustrates how to assign a first local lattice period p^ and a second local lattice period PB at a location P of the grating 25b. In order to recognize a periodic arrangement of protrusions 42b and base level areas 43b-| and 43b2 a region 135 confined by a circle 136, which region surrounds the location P of the grating 25b, can be considered. The radius of the circle 136 must be at least as large as the largest lattice period of the first local lattice period and the second local lattice period. By virtually shifting the grating forming structures 41 b in a direction VA by an amount p^ a structural match is obtained with a neighbouring grating forming structure 41 b. In this way, the first local lattice period p^ and the unit vector VA is obtained at the location P of the grating 25b. By virtually shifting the grating forming structure 41 b in a different second direction and matching it with a neighbouring grating forming structure the second local lattice period PB and the unit vector VB may be obtained at the location P of the grating 25b.

Figure 27 schematically illustrates an elevational view of a dual diffraction grating 25c which can be qualified according to embodiments of a method for qualifying a dual diffraction grating according to the present invention. In contrast to the diffraction grating 25b illustrated in Figure 26 the dual diffraction grating 25c implements two different phase functions by separate coding. In the illustrated example protrusions 42c2 and base level areas 43c2 are manufactured in regions 25c2 of the grating 25c. In regions 25c-i of the grating 25c protrusions 42c-| and base level areas 43c-| are manufactured. Thereby, regions 25c-| and regions 25c2 of the grating 25c are distinct from each other without overlap and are arranged according to a regular rectangular two-dimensional lattice.

Figure 27 illustrates how a first local lattice period p^, a unit vector VA , a second local lattice period PB and a unit vector VB can be obtained at a location P of the grating. The selected location P is situated in a region 25c-| of the grating 25c where there are only protrusions 42c-| and base level areas 43c-| present. Thus, at first sight it may seem that a second local lattice period PB and a corresponding unit vector VB cannot be obtained at the location P, when only the region 25c-| in which the location P is located is considered. However, if a larger area of the grating 25c is considered which is for example confined by a circle 138, the two local lattice periods p^ and PB and the corresponding unit vectors can be obtained by virtually shifting grating forming structures in two different directions and matching them with neighbouring grating forming structures. However, for this purpose an area of sufficient extension such as an area defined by the circle 138 has to be considered. Thus, although at each mathematical point P of the grating 25c there is only one type of grating forming structures present, that means either the one that is implemented by protrusions 42c-| and base level areas 43c-| , or the one that is implemented by protrusions 42c2 and base level areas 43C2, it is possible to assign the first and the second local lattice period and the corresponding unit vectors at each location of the grating 25c by extrapolating periodicities of the two types of grating forming structures found in a sufficiently large surrounding of the considered point P into the point P. In the exemplary embodiment illustrated in Fig. 27, there are very few grating forming structures in either regions 25c-| or 25c2- In other embodiments these regions may comprise a larger number of grating forming structures, such as 5, 10, or 100, depending on the application.

Figure 28 illustrates a system 1a for manufacturing an optical element according to an embodiment of the present invention. The system 1 a is similar to the system 1 illustrated in Figure 1 and elements designated with same numerals but followed by the letter "a" serve similar function as the function served in system 1 illustrated in Figure 1. Therefore, repetition of a detailed description of these similar elements and their function is suppressed. A difference between the system 1a to the system 1 is that system 1a comprises a dual diffraction grating 25a that has been qualified according to embodiments of the present invention such as these illustrated in Figures 19, 20, 21 , 22 and 23. In this particular case the profile depth h of the grating 25a has been determined. A profile depth map representing values of the profile depths across the dual diffraction grating 25a are stored in database 118a. When measuring an optical element 5a having an optical surface 3a using the system 1a, the map of profile depths is taken into account to determine a deviation of the shape of the surface 3a of the optical element 5a from a target shape of the surface of the optical element from detecting light formed by superimposing reference light with light having interacted with the surface 3a of the optical element 5a. For this purpose the analysis system 130a reads detected intensity values from the detector 39a as well as the map of profile depths of the grating 25a and processes these data.

Figure 29 illustrates a system 1 b for manufacturing an optical element that is similar to system 1 illustrated in Figure 2. Again, components in the two Figures 2 and 29 designated by a same numeral serve a similar function and a detailed repeating description of these components will be suppressed. A difference between the systems 1 b illustrated in Figure 29 and system 1 illustrated in Figure 2 is that system 1 b, as system 1a illustrated in Fig. 28, is equipped with a dual diffraction grating 25c that has been qualified according to embodiments of the method for qualifying a dual diffraction grating described above. However, in this case the grating forming structures according to the first phase function comprised in dual diffraction grating 25c not only serve for conveniently qualifying and determining a structural parameter of the grating 25c but also to provide a reference wavefront to be superimposed with measuring light having interacted with the surface 3b of the optical element 5b and to be detected by the camera 39b. In this embodiment the first phase function implemented into the grating 25c thus serves a double function. As in system 1a illustrated in Figure 28 the map of profile depths of grating 25c determined by a method of qualifying a dual diffraction grating according to embodiments of the present invention is stored in database 118b and is taken into account by the analysis system 130b when processing received intensity data from camera 39b, to determine deviations of the shape of the surface 3b of the optical element 5b from a target shape of the surface of the optical element 5b.

Figure 30 illustrates a flow diagram of a method for manufacturing an optical element according to an embodiment of the present invention. In step 301 at least one of a profile depth, a duty cycle and an edge steepness of a dual diffraction grating using a first phase function of the grating is determined. In step 303 shaped measuring light is generated by diffracting measuring light at the grating according to the second phase function of the grating. Subsequently in step 305 light is detected, which is formed by superimposing reference light with shaped measuring light having interacted with the surface of the optical element to be manufactured. In step 307 the optical element is processed based on the determined at least one of the profile depth, the duty cycle and the edge steepness and on the detected light comprising milling, grinding, loose abrasive grinding, polishing, ion beam figuring, magneto-rheological figuring, reactive ion beam etching and finishing the optical surface of the optical element. The optical element may then be integrated into an objective used to project a mask onto a wafer in lithography applications of the semiconductor industry.

Figure 31 illustrates a dual diffraction grating 25d according to the prior art. The diffraction grating 25d comprises plural regions 25d-| and 25d2 shaped in vertical stripes having a constant thickness across the grating 25d. The regions 25d-| and 25d2 comprise grating forming structure providing a first and a second phase function, respectively, not resolved in Figure 31. In Figure 31 the two types of different regions 25d-| and 25d2 are depicted schematically by black, respectively white, stripes. Due to the constant thickness of the stripes of the two different regions 25d^ and 25d2 a lattice period measuring a periodicity of the alternating regions has a value ps which is constant across the grating 25d. The periodic arrangement of the two different regions of the grating 25d forms a superlattice that leads to diffraction, when light is incident on the diffraction grating 25d.

Figures 32a and 32b illustrate portions of the interferometric systems illustrated in Figures 1 , 2, 28 and 29 with particular emphasis on light beam paths generated by diffraction at a superlattice of a dual diffraction grating 25, such as dual diffraction grating 25d illustrated in Figure 31. A measuring light beam 13 is diffracted at the grating 25 formed on the substrate 23 according to a predetermined first diffraction order to form a first light beam 161 , as illustrated in Figure 32b. The first light beam 161 is illustrated in Figure 32b as comprised of plural portions 161 -| , 1613, 1615, ..., I6I2N+1 which are incident on plural locations 3-| , 33, 35, ..., 32N+1 of the surface 3 of the object 5. The first light beam 161 reflected at the plural locations of the surface 3 of the object 5 is illustrated as comprised of plural portions 161 'i , 161*3, 161*5. ..., 161'2N+1 travelling back to the grating 25, where they are diffracted to form a light beam 17. As is apparent from Figure 32b, the portion 161 -| of the first light beam 161 is not orthogonally incident at the location 3<| of the surface 3 of the object 5 such that the reflected portion 161'i does not travel back the same path as the portion 161 -| travelled towards the location 3-| of the surface 3 of the object 5. Instead, the directions of the beam portions 1611 and 161'i include an angle unequal to zero. In particular the portions of the first light beam 161 are generated by diffracting the measuring light beam 13 about a deflecting angle that is larger than a deflecting angle of a diffracted beam which is orthogonally incident on the surface 3 of the object 5. Such a deflection is caused by a diffraction according to a - 1 diffraction order of the superlattice on the way towards the object and by a diffraction according to a + 1 diffraction order of the superlattice on the way emanating from the surface 3 of the object 5.

In contrast, Figure 32a illustrates the case, where by diffraction at the superlattice order + 1 on the way towards the surface 3 of the object 5 the measuring beam 13 is deflected by an angle less than an angle which would result in a diffracted beam being orthogonally incident on the surface 3 of the object 5. On the way emanating from the object 3 at the location 32 the reflected beam 162'2 is diffracted according to a - 1 diffraction order of the superlattice to assume a direction parallel to the travelling direction of the measuring light beam 13 but vertically offset by a distance. The occurrence of opposing vertical offsets results in the occurrence of interferences of the beams diffracted at different diffraction orders of the superlattice. This is illustrated in more detail in Figure 33.

Figure 33 illustrates in an enlarged view a combination of portions of Figures 32a and 32b. The substrate 23 carries a dual diffraction grating 25 in which two different phase functions are implemented in spatially distinct regions which form a superlattice. In this particular example, the first phase function and the superlattice are devised to generate a probing light beam 14 that is substantially orthogonally incident on the surface 3 of the object 5 by diffracting the measuring light beam 13 at the superlattice according to the 0th diffraction order and at the grating forming structures implementing the first phase function according to a predetermined probing diffraction order. As an example, the portion 14-| 2 °f tne probing beam 14 generated by such a combined diffraction is illustrated in Figure 33 which portion is orthogonally incident at the location 3-| 2 of the surface 3 of the object 5. The reflected portion 14"i 2 travels the path travelled by the portion 14-| 2 back, is diffracted at the grating 25 according to the 0th diffraction order of the superlattice and according to the predetermined probing diffraction order at the grating forming structures implementing the first phase function in order to contribute to the light beam 17-] 2 leaving the dual diffraction grating 25 in a direction opposite to a travelling direction of the measuring beam 13.

Using a conventional dual diffraction grating 25, light beam 17^ 2 however also includes light beams caused by perturbing diffractions at the superlattice different from a 0th diffraction order of the superlattice. Namely, measuring beam 13 is also diffracted according to the predetermined probing diffraction order at the grating forming structures implementing the first phase function and according to the - 1 diffraction order of the superlattice forming a first light beam 161 -| . The first light beam 161 -] is, due to the diffraction at the superlattice in the - 1 diffraction order, more strongly deflected, that means deflected by a larger angle, than a probing light beam 14 that is orthogonally incident on the surface 3 of the object 5. Thus, the first light beam 1611 is reflected at a location 3-| of the surface 3 of the object 5 and travels back as a reflected first light beam 161 '-| towards the dual diffraction grating 25. Light beam 161 '^ is diffracted by the diffraction grating 25 according to the predetermined probing diffraction order at the plurality of grating forming structures implementing the first phase functions and additionally according to the + 1 diffraction order of the superlattice. Thereby, it is deflected to travel in a direction opposite to the travelling direction of the measuring light beam 13. Thus, the diffracted reflected first light beam 161 -j contributes to the light beam 17-| 2-

Furthermore, measuring light beam 13 is diffracted at the grating forming structures implementing the first phase function according to the predetermined probing diffraction order and additionally according to the + 1 diffraction order of the superlattice, in order to form to portion 1622 °f tne second light beam 162. The portion 1622 °f tne second light beam is reflected at the surface 3 of the object 5 at a location 32 to form the portion 162'2 of the reflected second light beam. The portion 162'2 of the reflected portion 1622 of the second light beam 162 is diffracted at the grating 25 according to the predetermined probing diffraction order of the grating forming structures implementing the first phase function and additionally according to the - 1 diffraction order of the superlattice. Thereby, the beam 162'2 is deflected such that it travels back in a direction opposite to the travelling direction of measuring light beam 13. Thus, also this disturbing light beam contributes to light beam 17-j 2-

One aspect of the present invention has been achieved by establishing, carefully analyzing and appropriately manipulating characteristics of the beam paths illustrated in Figures 32a, 32b and 33. Further, appropriate ways have been found to advantageously manipulate the characteristics of the beam paths.

Figure 34 illustrates the spectrum of light that has been diffracted at a dual diffraction grating exhibiting two different types of regions having a same total area. In particular, the two different regions occupy a same total area on the grating. The x-axis represents a momentum transfer of a light wave experienced due to diffraction at the grating. A dual diffraction grating, wherein two different types of regions are arranged in a superlattice, provides discrete momentum transfers that are commonly labelled by diffraction order numbers of the grating. The discrete momentum transfers are multiples of the reciprocal lattice vector 2π/ps. The y-axis in Figure 34 represents an intensity of light diffracted at the grating according to a number of different diffraction orders. The peak labelled by "0" represents the intensity of the 0th diffraction order of the superlattice. At the same time, this peak carries the reference numeral 1(14) being the intensity of the probing light beam 14 in Figure 33. To the left and to the right of the peak 1(14) the "- 1" and "+ 1 " diffraction orders of the superlattice occur. These two peaks also carry the reference numerals 1(161), respectively 1(162), being the intensities of the first light beam 161 , respectively the second light beam 162, in Figure 33. It is apparent that the intensities of these first and second light beams are substantially equal. Thus, depending on an optical phase difference between the beam paths traversed by the combination of beam 161 -| and 161 '-j and the combination of beams 1622 and 162'2 a constructive, destructive, or some interference in between may occur upon superimposing the two beams contributing to the beam 17-| 2-

Figure 35 illustrates an interferogram 150 generated by superimposing a perturbation beam, such as diffracted beam 161 '-j or 161*2, w'tn a reference beam occurring in a conventional dual diffraction grating, such as dual diffraction grating 25d illustrated in Figure 31. In the measurement setup an object having a surface of a target shape was measured and the dual diffraction grating 25d was arranged such that grating forming structures implementing the first phase function generated a light wave having a shape corresponding to the target shape. The interferogram was measured in the interferometric system illustrated in Figure 1. Although there are no deviations between the shape of the surface of the object and the target shape, concentric rings of high and low intensity values are imaged to the detector. Based on this detected interferogram a user would be let to conclude that the surface of the object exhibits substantial deviations from a target shape of the object. This judgement however would be erroneous, since the shape of the surface of the object exactly corresponds to the target shape. The interferogram 150 showing varying intensities across its area simply results from interfering of perturbation light beams being incident on the camera of the interferometric system.

The inventor found a way to eliminate or at least substantially reduce these perturbing interferences which reduce an accuracy of a shape measurement method. By an interferometric method provided by the present invention, the first beam 161 and the second beam 162 substantially destructively interfere after being reflected at the surface

3 of the object 5 and being diffracted at the dual diffraction grating 25. Thus, the two beams do not contribute to the beam 17-| 2 such that beam 17-j 2 "s substantially only comprised of the reflected probing light beam 14 and a reference beam. Thereby, an accuracy of the shape measuring method is improved.

In order to achieve destructive interference of light beams generated by unwanted diffraction at the superlattice, a particular arrangement of the regions of the first type and the second type forming the superlattice has been invented. An example of a grating having such a superlattice is illustrated in Figures 36a and 36b as grating 25e. In this illustrated example, the grating 25e has been adapted for measuring an object having an aspheric surface, wherein a deviation from a best fitted sphere is 283 μm, wherein the radius is 254,8 mm, wherein the free diameter of the object is 121 mm and wherein a distance between the object surface and the dual diffraction grating 25e is 20 mm. Furthermore, the dual diffraction grating 25e has been designed such that a mean width of the regions of the first type and the second type is 30 μm, that a ratio of areas of the regions of the first type and the regions of the second type is 1 :1 and such that the perturbation orders of the superlattice (+ 1 , - 1 ) and (- 1 , + 1 ) are substantially destructively interfered in order not to perturb the measuring process. In particular, an optical phase difference between the different perturbation light beams has been designed to amount to λ/2. As in Figure 31 illustrating the conventional dual diffraction grating 25d, also in Figure 36a illustrating the dual diffraction grating 25e according to the present invention, the regions of the first type 25e-| are depicted as black areas and the regions of the second type 25β2 are depicted as white areas. The arrangement of regions of the first type and regions of the second type in diffraction grating 25e illustrated in Figure 36a is very different from the arrangement of regions of the first type and regions of the second type in the conventional dual diffraction grating 25d illustrated in Figure 31. In the dual diffraction grating 25e the regions of the first type and regions of the second type have a shape of concentric rings having widths varying from the center of the grating 25e at a relative radius r = 0 towards the boundary of the dual diffraction grating 25e at a relative radius r = 1. From the rotationally symmetric aspheric surface of the object to be measured and from other parameters of the measurement setup the particular shape of the regions of the first type and the regions of the second type formed by concentric rings result. When measuring other objects having non- rotationally symmetric surfaces other shapes of the regions of the first type and the regions of the second type would be provided according to the invention.

Figure 36b depicts a graph showing a superlattice period ps in dependence of a location at the grating 25e measured as a relative radius r. This dependency is illustrated as a curve 26e in Figure 36b. It is apparent that at the center of the grating 25e (r = 0) the superlattice period ps = 18 μm. When moving radially outwards, the superlattice period decreases to be less than 15 μm at around a relative radius r = 0.3. Moving further radially outwards leads to an increase of the superlattice period to above 20 μm at the boundary of the grating 25e (r = 1.0). Thus, it is apparent that the superlattice period which is the sum of adjacent widths of a region of the first type and of a region of the second type varies by more than 25 % across the grating. This variation of the superlattice period ps across the grating leads at a particular superlattice diffraction order to varying deflection angles of diffracted light. The variation of the deflection angle is such that light beams diffracted at perturbation diffraction orders of the superlattice substantially destructively interfere.

The particular design of the grating 25e including the design of the arrangement and shapes of the regions of the first type and the regions of the second type has been constructed using an optic design program known in the art, such as the optical design program "Code V" by OEC AG, Munich, Germany or the optical design program "ZEMAX" by Optima Research, Stansted, United Kingdom. The optic design program typically comprises ray tracing techniques.

Dual diffraction gratings exhibiting a superlattice can be devised for a large number of geometries of surfaces of an object to be measured. A common property of such devised dual diffraction gratings is that local lattice vectors of the superlattice are generally oriented parallel to the maximal gradient of the surface of the object to be measured. The gradient 33 of the surface 3 of the object 5 is indicated in Figure 33. The gradient 33 at a particular point of the surface 3 of the object 5 lies in a tangential plane of the surface at this point and is directed in a direction of largest ascend of the surface of the object. In Figure 33 also a projection 34 of the gradient 33 is indicated, wherein the projection 34 of the gradient 33 is obtained by projecting the gradient 33 to a plane of extension of the grating 25.

As is explained in more detail for other embodiments of the present invention, a lattice vector generally indicates a direction in which structures of the grating are periodically arranged. As the local lattice period the local lattice vector may vary across the grating such that it points into different directions at different locations across the grating. For the grating 25e illustrated in Figure 36a, the local superlattice vector points in a radial direction at any location of the grating 25e. Due to the aforementioned property of the superlattice, the superlattice may assume a same symmetry as the symmetry of the surface of the object to be measured. As mentioned above, the dual diffraction grating 25e illustrated in Figure 36a and 36b is primarily adapted to suppress perturbation diffraction orders + 1 and - 1 of the superlattice. Higher order diffraction peaks (- 3, + 3, - 5, + 5, ...) are not necessarily suppressed in a measuring method using dual diffraction grating 25e. However, as can be observed from Figure 34, the intensities of such higher diffraction orders of the superlattice are much lower than the intensities of the - 1 and + 1 diffraction orders. Furthermore, wavefronts generated by diffraction according to these higher superlattice diffraction orders exhibit a significantly higher gradient than the gradient of the wavefront generated by the + 1 or - 1 superlattice diffraction order. This is illustrated in Figures 36c and 36d illustrating wavefronts generated by diffraction according to the + 1 superlattice diffraction order (Figure 36c) and diffraction according to the + 3 superlattice diffraction order (Figure 36d). The x-axis in both Figures represents a relative radius of the grating and the y-axis represents a location of the wavefront generated by diffraction according to the corresponding diffraction order in multiples of the wavelength λ. In Figure 36c the maximum at the y-axis amounts to 75λ, whereas in Figure 36d the maximum amounts to 600λ. Thus, it is apparent that the wavefront represented by the curve 273 illustrated in Figure 36d generated by diffraction according to superlattice diffraction order + 3 or - 3 exhibits a much larger gradient than the wavefront represented by curve 27-| illustrated in Figure 36c generated by diffraction according to the superlattice diffraction order + 1 or - 1. Wavefront 27-j is substantially destructively interfered due to the particular design of the dual diffraction grating 25e illustrated in Figures 36a and 36b and thus does not contribute to the detected intensities for determining a shape of the surface 3 of the object 5. However, although disturbing light beams generated by diffraction according to superlattice diffraction order + 3 or - 3 are not automatically destructively interfered and thereby suppressed, these disturbing wavefronts exhibit such a steep gradient that they are blocked by an aperture of the interferometer optics. Thus, these wavefronts are not incident on the detector and thereby do not contribute to the measured interferogram representing a shape of the surface 3 of the object 5 to be measured.

Figure 37 illustrates a spectrum of light diffracted at another dual diffraction grating according to the present invention. The geometry of the object and the measuring parameters are the same as those described in connection with the dual diffraction grating 25e which characteristics are illustrated in Figures 36a, 36b, 36c and 36d. As in the example of dual diffraction grating 25e, the regions of the first type comprise grating forming structures for generating a probing light beam that is substantially orthogonally incident on the surface 3 of the object 5. However, in contrast to the property of dual diffraction grating 25e, a ratio between areas of regions of the first type and regions of the second type is in this example 2:1. For this ratio of total areas of regions of the first type and regions of the second type, the intensities of light diffracted according to the - 1 or + 1 superlattice diffraction order is reduced compared to the example illustrated in Figure 34 (compare the height of 1(161 ) and 1(162) in both Figures). In order to suppress perturbation superlattice diffraction orders - 1 and + 1 this further dual diffraction grating exhibits the same design as dual diffraction grating 25e illustrated in Figures 36a, 36b, 36c and 36d.

The present invention also provides diffraction gratings that comprise regions of three different types. As a particular example, a diffraction grating 25f is described carrying a first type of regions providing a first phase function (A), a second type of regions providing an inverse of the first phase function (A1), and a third type of regions providing a third phase function (B). A ratio of the sum of total areas of the regions of the first type, the sum of total areas of the regions of the second type, and the total areas of the regions of the third type is 1 :1 :1. The phase function A1 corresponds to the phase function A shifted in phase by 180 c (shifted in space by λ/2). A spectrum obtained by diffracting light at such a grating 25f is illustrated in Figure 38. Due to the aforementioned inverse relationship between phase functions A and A1 and due to the ratio of areas as defined above, the superlattice does not lead to a diffraction peak according to a 0th superlattice diffraction order. Thus, a central peak labelled 11O" is missing in Figure 38. In this case, the probing light beam 14 may be generated by diffracting the measuring light beam according to a predetermined probing diffraction order at the grating forming structures implementing the first phase function A and additionally at the superlattice according to the + 1 or - 1 superlattice diffraction order. Thus, the + 1 superlattice diffraction order is in this case not a perturbation diffraction order. However, in this case, other combinations of perturbing superlattice diffraction orders result which are the - 2 and + 4, respectively + 2 and -4 superlattice diffraction orders, the latter if the -1 diffraction order of the superlattice is the carrier of the surface information of the object to be measured. The surface of the object may in particular be an asphere. In the conventional diffraction grating, light diffracted according to these diffraction orders would be incident on the detector and add an intensity signal varying across the detector thereby decreasing an accuracy of the measuring method. Also for this kind of diffraction grating the invention provides a design for suppressing these disturbances.

Figures 39a and 39b schematically illustrate characteristics of a diffraction grating 25f providing phase functions A, A1 and B in three different types of regions. For simplicity two adjacent white and black areas in Figure 39a represent adjacent regions of the three types. Thus, a superlattice period ps is again the sum of the widths of adjacent black and white concentric rings. In order to suppress perturbation superlattice diffraction orders - 2 and + 4, respectively + 2 and - 4, the superlattice period ps varies across the grating, as illustrated as curve 26f in the graph of Figure 39b. In dependence of the relative radius of the grating 25f (x-axis) the curve 26f represents a superlattice period ps. At the center of the grating (r = 0), the superlattice period is almost 54 μm and decreases when moving in a radial direction to r = 0.3, where the superlattice period ps is below 44 μm. Moving further in a radial direction of the grating an increase of the superlattice period is observed reaching a value above 60 μm at the boundary of the grating (r = 1.0). Thus, the superlattice period ps varies by about 25 % across the grating. An advantage of a superlattice having three types of regions is that the periodicity is larger than if the grating comprises only two types of regions. Thereby a difference to a periodicity of grating forming structures provided to generate a light wave to be substantially orthogonally incident onto the surface of the object to be measured is increased decreasing a coupling between the lattices having the two different periodicities.

The diffraction grating exhibiting two or three different types of regions for providing two or three different phase functions, such as diffraction grating 25e, 25f can be used in the interferometric systems illustrated in Figures 1 , 2, 28 and 29. Furthermore, the diffraction gratings designed by methods according to the present invention may comprise more than three different types of regions, such as four or five. Also in the case of three different regions the second type of regions may provide a phase function completely unrelated to phase functions provided by either the first or the third type of regions. The different types of phase functions provided by different regions of diffraction gratings may serve different functions in a method for measuring a shape of a surface of an object. In particular, in the case of a dual diffraction grating having two different types of regions arranged in a superlattice, the first type of region may provide a phase function for generating a probing light beam that is being substantially orthogonally incident on the surface 5 of the object 3. The second type of region may provide a phase function for generating a reference beam, in particular in reflection.

Figure 40a and Figure 40b illustrate a further combination of functions provided by the first and second type of regions of a dual diffraction grating designed according to the present invention. The first type of regions is designed to provide a probing light beam 14 that is being substantially orthogonally incident on the surface 5 of the object 3 by diffracting a measuring light beam 13 at grating forming structures formed in the first type of regions of diffraction grating 25. Diffraction of the incident measuring light beam 13 at the second type of regions comprised in the grating 25 causes the generation of light beam 16 that is being reflected at a calibrating surface 18 which is disposed laterally offset from the object 5 which is not shown in Figure 40b. The calibrating surface may be a calibrating sphere or a calibrating asphere. The light beam 16 reflected from the calibrating surface may be utilized as a calibrating light beam for calibrating the measurement set up.

Several aspects of the present invention may be combined to even further improve an accuracy of a measurement method and a measurement system for measuring a surface of an object. For example, structural or optical parameters of grating forming structures may be varied across the grating for the inventive diffraction grating harbouring two or more different types of regions arranged in a superlattice which grating is adapted to suppress unwanted disturbing deflection at the superlattice. Furthermore, these types of gratings may be qualified according to methods of the present invention. By this kind of combination of advantageous methods and systems provided by the present invention, an accuracy of a measuring method and measuring system can be significantly improved.

While the invention has been described with respect to certain exemplary embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, the exemplary embodiments of the invention set forth herein are intended to be illustrative and not limiting in any way. Various changes may be made without departing from the spirit and scope of the present invention as defined in the following claims.

Claims

What is claimed is:
1. A diffractive component, comprising a substrate and a grating provided thereon;
wherein the grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating;
wherein the grating comprises plural regions of at least a first type (A) and a second type (B),
wherein the following relations are fulfilled at boundary lines between regions of the first type and regions of the second type:
— •VA - —-VB > 1.0 mm'1 ; and VA ■ V8 > 0
Figure imgf000059_0001
wherein
pA is the local lattice period at a first location close to the boundary line and within the region of the first type;
pB is the local lattice period at a second location close to the first location and within the region of the second type;
VA is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the first location; and
VB is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the second location;
wherein the regions of the first type and the regions of the second type are arranged according to an irregular pattern.
2. The diffractive component according to claim 1 , wherein extensions of at least one of the regions of the first type and the regions of the second type have varying lateral dimensions.
3. The diffractive component according to claim 2, wherein the regions of the first type and the second type have lateral extensions greater than 3 times of the local lattice period of the respective region.
4. The diffractive component according to claim 2 or 3, wherein at least one of the regions of the first type and the regions of the second type have a minimum lateral extension and a maximum lateral extension and wherein a distribution of all widths of the at least one of the regions of the first type and the regions of the second type has a standard deviation greater than 5 % of the average extension of the respective regions.
5. The diffractive component according to claim 4, wherein the following relation is fulfilled:
2 "1^ ~ """ ≥ O.l max min
wherein
dmjn is the minimum lateral extension of the at least one of the regions of the first type and the regions of the second type, and
dmax is the maximum lateral extension of the at least one of the regions of the first type and the regions of the second type.
6. The diffractive component according to one of claims 2 to 5, wherein the lateral extensions of the regions are determined as being the greatest lateral extension of the respective regions.
7. The diffractive component according to one of claims 2 to 6, wherein the regions of the first type and the regions of the second type have shapes of elongated bands and wherein the lateral extensions of the regions are determined in directions transverse to directions of elongation of the bands of the respective regions.
8. The diffractive component according to one of claims 1 to 7, wherein a number of the regions of the first type and a number of the regions of the second type are each greater than 100.
9. An interferometer arrangement, comprising:
a source of measuring light; interferometer optics for generating a beam of measuring light, wherein an object to be measured can be disposed in the beam of measuring light; a detector arrangement for receiving measuring light having interacted with the object; wherein the interferometer optics comprises a diffractive component as defined in one of claims 1 to 8.
10. The interferometer arrangement according to claim 9, wherein the highest lateral extension of each region is smaller than two times a diameter of the grating divided by a resolution of the detector of the detector arrangement.
11. The interferometer arrangement according to claim 9, wherein a highest lateral extension of each region is smaller than two times a diameter of the grating divided by a square root of a number of pixels of a detector of the detector arrangement.
12. A diffractive component, comprising a substrate and a grating provided thereon;
wherein the grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating;
wherein the grating comprises plural regions of at least a first type (A), a second type (A') and a third type;
wherein the following relations are fulfilled at locations about boundary lines between regions of the first type and regions of the second type:
the local lattice period of the region of the first type is substantially equal to the local lattice period of the region of the second type;
the direction of extensions of the lines along which the grating-forming structures are distributed in the first region is substantially equal to the direction of extensions of the lines along which the grating-forming structures are distributed in the second region;
wherein the grating-forming structures are each composed of at least two features of differing optical properties, wherein an arrangement pattern of the at least two features on a first side of the boundary line is obtainable by translating an arrangement pattern of the at least two features on a second side of the boundary line in a direction parallel to the lines along which the grating-forming structures are distributed and in a direction orthogonal thereto by an amount of less than 0.6 and greater than 0.4 times the local lattice period.
13. An interferometer arrangement, comprising: a source of measuring light; interferometer optics for generating a beam of measuring light, wherein an object to be measured can be disposed in the beam of measuring light; a detector arrangement for receiving measuring light having interacted with the object; wherein the interferometer optics comprises a diffractive component as defined in claim 12.
14. The interferometer arrangement according to claim 13, wherein the grating further comprises regions of a third type, wherein the regions of the first, second and third types are disposed in a regular pattern forming a superlattice.
15. The interferometer arrangement according to claim 14, wherein relative surface amounts of the regions of the first, second and third types amount to about 1 :1 :1.
16. The interferometer arrangement according to claim 14, wherein relative widths of the regions of the first, second and third types amount 1 :1 :1.
17. The interferometer arrangement according to one of claims 14 to 16, wherein the interferometer arrangement is arranged such that measuring light diffracted at the diffractive component by the gratings provided in the third regions and is received by the detector and such that measuring light diffracted at the diffractive component by both the superlattice and the gratings provided in the first and second regions and having interacted with a second object is received by the detector.
18. A diffractive component, comprising a substrate and a grating provided thereon; wherein the grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating;
wherein the grating comprises plural regions of at least a first type (A) and a second type (B),
wherein the following relations are fulfilled at locations about boundary lines between regions of the first type and regions of the second type:
the direction of extensions of the lines along which the grating-forming structures are distributed in the first region is substantially equal to the direction of extensions of the lines along which the grating-forming structures are distributed in the second region; and
(N - 0.l) - pA ≤ pB ≤ (N + OJ) - pA ,
wherein
pA is the local lattice period at a first location close to the boundary and within the region of the first type;
pB is the local lattice period at a second location close to the first location and within the region of the second type; and
N represents an integer number greater than 1.
19. A diffractive component, comprising a substrate and a grating provided thereon,
wherein the grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating; wherein the grating comprises plural regions of at least a first type (A) and a second type (B),
wherein the following relations are fulfilled at locations about boundary lines between regions of the first type and regions of the second type:
the local lattice period of the region of the first type is substantially equal to the local lattice period of the region of the second type;
the direction of extensions of the lines along which the grating-forming structures are distributed in the first region is substantially equal to the direction of extensions of the lines along which the grating-forming structures are distributed in the second region; and
wherein the grating-forming structures are each composed of at least two features of differing optical properties;
wherein at least one of the following relations is fulfilled at the first and second locations:
a ratio of a width of first features and a width of second features in a region about the first location differs from a ratio of the width of the first features and the width of the second features in a region about the second location by more than 10 %; and a height difference between the first features and the second features in a region about the first location differs from a height difference between the first features and the second features in a region about the second location by more than 10 %.
20. A diffractive component, comprising a substrate and a grating provided thereon,
wherein the grating is formed by a plurality of grating-forming structures which are distributed along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating, wherein the grating-forming structures are each composed of at least two features of differing optical properties; wherein the grating comprises plural regions of at least a first type (A) and a second type (B), wherein the regions of the first and second type are distributed across the grating according to a substantially regular pattern; and
wherein at least one of the following relations is fulfilled at locations about boundary lines between regions of the first type and regions of the second type:
(a) the direction of extensions of the lines along which the grating-forming structures are distributed in the region of the first type is substantially equal to the direction of extensions of the lines along which the grating- forming structures are distributed in the region of the second type; and
{N - 0.l) - pA < pB < {N + 0.l) - pA wherein
pA is the local lattice period at a first location close to the boundary and within the region of the first type; pB is the local lattice period at a second location close to the first location and within the region of the second type; and
N represents an integer number greater than 1.
(b) a ratio of a width of first features and a width of second features in a region about the first location differs from a ratio of the width of the first features and the width of the second features in a region about the second location by more than 10 %; and
(c) a height difference between the first features and the second features in a region about the first location differs from a height difference between the first features and the second features in a region about the second location by more than 10 %.
21. A method of manufacturing an optical element having a reflecting surface of a target shape, the method comprising:
generating a beam of measuring light;
directing the beam of measuring light onto the reflecting surface such that the measuring light incident on the reflecting surface is substantially orthogonally incident thereon, wherein the diffractive component according to one of the preceding claims and the reflecting surface are disposed in the beam path of the measuring light; performing at least one interferometric measurement by superimposing reference light with measuring light which has been reflected from the reflecting surface and has been diffracted by the grating of the diffractive component;
determining deviations of the reflecting surface from its target shape based on the at least one interferometric measurement; and
processing the reflecting surface of the optical element based on the determined deviations.
22. A method for qualifying a dual diffraction grating formed by a plurality of grating forming structures according to a first phase function and a second phase function, the method comprising:
illuminating at least a portion of the grating with light;
detecting an intensity of the light diffracted at the grating forming structures according to the first phase function;
determining at least one structural parameter of the grating forming structures based on the detected intensity,
wherein the at least one structural parameter is at least one of a profile depth, a duty cycle and an edge steepness.
23. The method according to claim 22, wherein the illuminating comprises illuminating the portion of the grating with polarized light.
24. The method according to claim 22 or 23, wherein the light diffracted at the grating forming structures is reflected light.
25. The method according to one of claims 22 to 24, further comprising polarizing the light diffracted at the grating forming structures, wherein the detecting comprises detecting of the polarized light diffracted at the grating forming structures.
26. The method according to one of claims 22 to 25, wherein the light diffracted at the grating forming structures is light diffracted at a diffraction order different from a Oth diffraction order.
27. The method according to one of claims 22 to 26, wherein an average of a profile depth of a majority of grating forming structures of the grating satisfies:
(N + 0A)- λ ≤ (n - l)- h ≤ (N + 0.6)- λ ,
wherein h is the average of the profile depth of the majority of grating forming structures A is a wavelength of the light illuminating the grating; n is a refractive index of the grating forming structures taken at the wavelength λ\ and
N is an integer number.
28. The method according to one of claims 22 to 27, wherein an average of a profile depth of the grating forming structures is between 660 nm and 700 nm.
29. The method according to one of claims 22 to 28, wherein the light comprises wavelengths between 620 nm and 650 nm.
30. The method according to one of claims 22 to 29, wherein a refractive index of the grating forming structures at a wavelength of the light illuminating the grating is between 1.4 and 1.5.
31. The method according to one of claims 22 to 30, wherein an average of a duty cycle of the grating is between 0.4 and 0.6.
32. The method according to one of claims 22 to 31 , wherein the plurality of grating- forming structures are distributed across the grating along first lines and second lines and repeatedly arranged adjacent to each other in a first direction and a second direction transverse to a direction of extension of the first lines and second lines, respectively, wherein a first local lattice period and a second local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating relating to the first phase function and the second phase function, respectively,
wherein the following relation is fulfilled at a majority of locations of the grating:
1 1
vA > 1.0 mm'1 ; and V. VB ≥ 0
PA PB wherein
pΛ is the first local lattice period at a location;
pB is the second local lattice period at the location;
VA is a unit vector having an orientation orthogonal to a direction of extension of the first lines in a surrounding of the location; and
VB is a unit vector having an orientation orthogonal to a direction of extension of the second lines in a surrounding of the location.
33. The method according to one of claims 22 to 32, wherein the plurality of grating- forming structures are distributed across the grating along lines and repeatedly arranged adjacent to each other in a direction transverse to a direction of extension of the lines, wherein a local lattice period can be assigned to the arrangement of the grating forming structures at each location of the grating;
wherein the grating comprises plural regions of at least a first type (A) and a second type (B), implementing the first phase function and the second phase function, respectively,
wherein the following relations are fulfilled at boundary lines between regions of the first type and regions of the second type:
\ and V4 ■ VR ≥ 0
Figure imgf000068_0001
wherein
pA is the local lattice period at a first location close to the boundary line and within the region of the first type;
pB is the local lattice period at a second location close to the first location and within the region of the second type;
VA is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the first location; and VB is a unit vector having an orientation orthogonal to the direction of extension of the lines in a surrounding of the second location.
34. The method according to claim 32 or 33, wherein pA and VA are constant within an area of 0.8 times or more of a total area of the grating across an extension of the grating.
35. The method according to claim 34, wherein the illuminating comprises directing the light onto the grating along an incident direction and the detecting of the intensity comprises detecting light diffracted at the grating forming structures into a direction which is substantially opposite to the incident direction.
36. The method according to one of claims 32 to 35, wherein the illuminating comprises illuminating the portion of the grating with polarized light, which is polarized in a polarization direction, and an angle between the polarization direction and the vector VA is between 40° and 50°, in particular between 44° and 46°, or which is circularly polarized with a phase difference between the two orthogonal linear modes between 80° and 100° and an amplitude ratio between 1.1 and 0.9.
37. The method according to one of claims 22 to 36, wherein the illuminating comprises illuminating at plural different wavelengths, the detecting comprises detecting plural intensities of light at the plural wavelengths and the determining is based on the plural detected intensities.
38. The method according to one of claims 22 to 37 performed on a plurality of portions of the grating to cover the entire grating, wherein the plurality of different portions are subsequently illuminated.
39. The method according to one of claims 22 to 38, wherein the detecting comprises detecting intensities of the light diffracted at the grating forming structures from a spatially resolving detector.
40. A method for manufacturing an optical element comprising:
determining at least one structural parameter of a dual diffraction grating according to the method of one of the claims 22 to 39; directing measuring light to the dual diffraction grating for generating shaped measuring light by diffracting measuring light at the grating forming structures according to the second phase function of the grating;
detecting light formed by superimposing reference light with the shaped measuring light having interacted with a surface of the optical element;
processing the optical element based on the determined at least one structural parameter and on the detected light.
41. The method for manufacturing an optical element according to claim 40, wherein the detecting of light comprises detecting an interference pattern formed by superimposing reference light with the shaped measuring light having interacted with the surface of the optical element.
42. The method for manufacturing an optical element according to claim 40 or 41 , wherein the processing of the optical element is based on determining a deviation of a shape of the surface of the optical element from a target shape of the surface based on the detected light and on the determined at least one structural parameter of the grating.
43. The method for manufacturing an optical element according to claim 42, wherein the determining of the deviation of the shape of the surface of the optical element from the target shape of the surface of the optical element comprises determining a deviation of a shape of a wave front of the generated shaped measuring light from a target shape thereof based on the determined at least one structural parameter qualifying the grating.
44. The method for manufacturing an optical element according to one of claims 40 to 43, wherein the processing of the optical element comprises at least one of milling, grinding, loose abrasive grinding, polishing, ion beam figuring, magneto- rheological figuring, reactive ion beam etching, and finishing the optical surface of the optical element.
45. The method according to claim 44, wherein the finishing comprises applying a coating to the surface of the optical element.
46. The method according to claim 45, wherein the coating comprises at least one of a reflective coating, an anti-reflective coating, and a protective coating.
47. An interferometric method, comprising:
forming a first light beam (161 ) by diffracting a measuring light beam (13) according to a predetermined first diffraction order at a diffraction grating (25);
forming a second light beam (162) by diffracting the measuring light beam (13) according to a predetermined second diffraction order at the diffraction grating;
reflecting the first light beam (161) and the second light beam (162) at a surface
(3) of an object (5);
diffracting the reflected first light beam (161') and the reflected second light beam (162') at the diffraction grating (25) such that at least portions of the diffracted reflected first and second light beams interferometrically superimpose,
wherein a local lattice period (ps) is assignable at each location of the diffraction grating (25) and wherein a variation of the local lattice period (ps) across the diffraction grating is greater than 1 %.
48. The method according to claim 47, wherein the grating comprises plural regions of at least a first type (25i) and a second type (252), wherein the regions of the first type (25i) are formed by a plurality of first grating forming structures according to a first phase function (A) and the regions of the second type (252) are formed by a plurality of second grating forming structures according to a second phase function (B) different from the first phase function (A), wherein an arrangement of the regions of the first type and the regions of the second type across the grating forms a superlattice.
49. The method according to claim 48, wherein the grating is arranged and adapted such that the diffracted reflected first and second light beams substantially destructively interfer.
50. The method according to claim 49, further comprising:
forming a probing light beam (14) by diffracting the measuring light beam according to a predetermined probing diffraction order (183) at the plurality of first grating forming structures and according to a predetermined probing superlattice diffraction order (173) at the superlattice; reflecting the probing light beam (14) from the surface (3) of the object (5);
diffracting the reflected probing light beam (141) according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the predetermined probing superlattice diffraction order at the superlattice;
interferometrically superimposing the reflected and diffracted probing light beam with a reference light beam; and
detecting the superimposed light beams.
51. The method according to claim 50, wherein
the first light beam (161 ) is formed by diffracting the measuring light beam (13) both according to the predetermined probing diffraction order (183) at the plurality of first grating forming structures and according to the predetermined first diffraction order (171 ) at the superlattice;
the second light beam (162) is formed by diffracting the measuring light beam (13) both according to the predetermined probing diffraction order (183) at the plurality of first grating forming structures and according to the predetermined second diffraction order (172) at the superlattice; and
the reflected portions of the first and second light beams (161\ 162') are diffracted both according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the predetermined second diffraction order (172), respectively predetermined first diffraction order (171 ), at the superlattice.
52. The method according to one of claims 47 to 51 , wherein the predetermined first diffraction order (171 ) is different from the predetermined second diffraction order (172).
53. The method according to one of claims 48 to 52, wherein at least one of an arrangement and shapes of the regions of the first type (25^ and the regions of the second type (252) across an area of the grating (25) are determined based on at least one of a gradient (33) of the surface (3) of the object (5) and a distance (I) of the surface of the object from the grating (25).
54. The method according to claim 53, wherein the regions of the first type and the regions of the second type are alternately arranged and substantially extend orthogonally to the (34) gradient (33) of the surface of the object projected to the area of the grating (25).
55. The method according to claim 54, wherein the regions of the first type and the regions of the second type comprise elongated bands having varying thicknesses (ps/2).
56. The method according to one of claims 48 to 55, wherein the lattice period of the superlattice ps is at least 10 times a first local lattice period assignable to the first grating forming structures.
57. The method according to one of claims 48 to 56, wherein a total area of the regions of the first type is substantially equal to one of one and two times a total area of the regions of the second type.
58. The method according to one of claims 48 to 57, wherein one of the first diffraction order and the second diffraction order is one of a +1 and a -1 diffraction order of the superlattice.
59. The method according to one of claims 48 to 56, wherein the grating further comprises plural regions of a third type, wherein the regions of the third type are formed by a plurality of third grating forming structures according to a third phase function (A'), wherein the third phase function is substantially given by the first phase function (A) by adding a phase shift of an odd multiple of an absolute value of π, wherein an arrangement of the regions of the first type, the regions of the second type, and the regions of the third type across the grating forms the superlattice.
60. The method according to claim 59, wherein total areas of the regions of the first type, the second type, and the third type are substantially equal.
61. The method according to claim 59 or 60, wherein one of the first diffraction order and the second diffraction order is one of a +4, a -4, a +2, and a -2 diffraction order of the superlattice.
62. The method according to one of claims 50 to 61 , wherein the forming the probing light beam (14) comprises diffracting the measuring light beam in transmission according to the predetermined probing diffraction order at the plurality of first grating forming structures and according to the predetermined probing superlattice diffraction order at the superlattice, wherein the probing light beam is substantially orthogonally incident on the surface of the object.
63. The method according to one of claims 50 to 62, wherein the measuring light beam diffracted at the second grating forming structures comprised in the regions of the second type forms the reference light beam.
64. The method according to claim 63, further comprising forming a calibrating beam by diffracting the measuring light beam at the second grating forming structures in transmission and reflecting it at a calibrating surface.
65. A method for measuring a surface of an object, the method comprising:
directing a measuring light beam (13) to a dual diffraction grating (25) exhibiting a first phase function (A) and a second phase function (B) different from the first phase function implemented by complex coding;
forming a probing light beam (14) by diffracting the measuring light beam (13) at the dual diffraction grating according to the first phase function (A);
reflecting the probing light beam (14) from the surface (3) of the object (5);
diffracting the reflected probing light beam at the dual diffraction grating according to the first phase function (A);
generating a reference light beam by diffracting the measuring light beam (13) at the dual diffraction grating according to the second phase function (B);
interferometrically superimposing the reflected and diffracted probing light beam with the reference light beam; and
detecting the superimposed light beams to determine a shape of the surface of the object, wherein a maximal deviation of the determined shape of the surface of the object from the actual shape of the surface of the object in the medium to high spatial frequency range is at most 1 nm across the surface of the object.
66. A method for manufacturing an optical element comprising:
detecting superimposed light beams according to one of claims 50 to 65;
determining a shape of the optical element based on the detected superimposed light beams;
processing the optical element based the determined shape of the optical element.
PCT/EP2008/001022 2007-03-15 2008-02-11 Diffractive component, interferometer arrangement, method for qualifying a dual diffraction grating, method of manufacturing an optical element, and interferometric method WO2008110239A1 (en)

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