A measurement system and a diffraction grating therefor

Abstract

A measurement system (shearing interferometer) is for determining an aberration map for a projection system (for example within a lithographic apparatus). The measurement system comprises: a first patterning device positionable in an object plane of the projection system; a second patterning device positionable in an image plane of the projection system; and a radiation detector arranged to receive radiation from the second patterning device. The second patterning device has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device is non-uniform. The pitch of the second patterning device may have an extremum value at a first position on the second patterning device and the pitch of the second patterning device may either increases or decreases as a function of distance from the first position.

Description

A MEASUREMENT SYSTEM AND A DIFFRACTION GRATING THEREFORCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23199378.3 which was filed on September 25, 2023 and which is incorporated herein in its entirety by reference.FIELD

[0002] The present invention relates to a measurement system for determining an aberration map for a projection system. In particular, the measurement system may be a phase-stepping measurement system. The projection system may form part of a lithographic apparatus. The present invention also relates to a lithographic apparatus comprising such a measurement system for determining an aberration map for a projection system. The present invention also relates to diffraction gratings for such a measurement system for determining an aberration map for a projection system. In particular, the present invention relates to a two-dimensional diffraction grating for a shearing phase-stepping interferometric measurement system, the diffraction grating being formed by an array of circular apertures, or pinholes, in a substrate.BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern at a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate.

[0004] To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which can be formed on the substrate. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[0005] Radiation that has been patterned by the patterning device is focussed onto the substrate using a projection system. The projection system may introduce optical aberrations, which cause the image formed on the substrate to deviate from a desired image (for example a diffraction limited image of the patterning device).

[0006] It may be desirable to provide methods and apparatus for accurately determining such aberrations caused by a projection system such that these aberrations can be better controlled.SUMMARY

[0007] According to a first aspect of the present disclosure there is provided a measurement system for determining an aberration map for a projection system, the measurement system comprising: a first patterning device positionable in an object plane of the projection system; a second patterning device positionable in an image plane of the projection system; a radiation detector arranged to receive radiation from the second patterning device; and a positioning apparatus operable to move at least one of the first and second patterning devices in a shearing direction; wherein the second patterning device has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device that originate from the same order diffraction beam of the first patterning device is non-uniform; and wherein the pitches of the first and second patterning devices are matched such that an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the first patterning device is generally matched to an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the second patterning device that originate from the same order diffraction beam of the first patterning device, taking into account any reduction or magnification factor applied by the projection system; and wherein the variable pitch of the second patterning device is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device are not matched to an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the first patterning device, taking into account any reduction or magnification factor applied by the projection system.

[0008] The measurement system according to the first aspect of the present disclosure is advantageous, as now discussed.

[0009] The measurement system may be used to measure aberrations caused by the projection system. Such a measurement system may be used within a lithographic apparatus and may comprise a shearing interferometer. The measurement system typically uses a patterning device at reticle level (i.e., disposed in an object plane of the lithographic apparatus) and a sensor at wafer level (i.e., disposed in an image plane of the lithographic apparatus). The reticle-level patterning device may, for example, comprise a diffraction grating. The wafer level sensor comprises a second patterning device (for example a two-dimensional diffraction grating) and a radiation detector (for example an array of sensing elements). The reticle-level patterning device is illuminated with radiation to form a plurality of first diffraction beams, the first diffraction beams being separated in a shearing direction. The projection system at least partially captures the plurality of first diffraction beams and images these onto the patterning device of the wafer level sensor. The second patterning device receives the first diffraction beams from the projection system and forms a plurality of second diffraction beams from each of the first diffraction beams, which are incident on the radiation detector.

[0010] In use, at least one of the reticle level patterning device and the wafer level sensor apparatus is scanned or stepped in the shearing direction such that an intensity of radiation received by each part of the radiation detector varies as a function of this movement in the shearing direction so as to form an oscillating signal. A phase of a harmonic (for example the first harmonic) of the oscillating signal at aplurality of positions on the radiation detector (for example at each sensing element) is determined. From these, a set of Zernike coefficients that characterize the aberration map of the projection system are determined.

[0011] In some known arrangements, the pitches of the first and second patterning devices are matched in a shearing direction, taking into account any reduction factor applied by the projection system, such that the pitch of the second patterned region in said shearing direction is an integer multiple of the pitch of the first patterned region in said shearing direction or, alternatively, the pitch of the first patterned region in said shearing direction is an integer multiple of the pitch of the second patterned region in said shearing direction.

[0012] With such known arrangements, in general, there will be a plurality of different contributions to the harmonic of the oscillating signal at the radiation detector, each having a different overlay with the detector (i.e., coinciding with a different set of sensing elements) and, in general, having a different intensity. In a transmissive deep ultraviolet (DUV) lithographic apparatus, one known arrangement uses a one-dimensional diffraction grating for the patterning device at reticle level with a duty cycle of 50% and a checkerboard grating for the patterning device at wafer level. With such an arrangement, across most of the radiation detector the first harmonic of the oscillating (phasestepping) signal at the radiation detector receives only two contributions which have the same the same intensity. This simplifies the reconstruction of the aberration map significantly.

[0013] However, a true checkerboard grating requires a transmissive support layer, which is unsuitable for use in extreme ultraviolet (EUV) lithographic systems since (a) EUV radiation is strongly absorbed by most materials and (b) such a transmissive carrier will rapidly become contaminated in a wafer production environment of an EUV lithographic system, which would render the transmissive carrier non-transmissive for EUV. For the above-mentioned reasons a checkerboard grating arrangement is difficult to implement for lithographic systems that use EUV radiation and existing arrangements typically use a pinhole array at wafer level in place of a checkerboard grating.

[0014] The use of a pinhole array geometry for the wafer level patterning device generates unwanted interference beams that contribute to the first harmonic of the phase stepping signal. In particular, in addition to the two contributions that are present with a checkerboard grating, there are a large number of additional interference beams with small, but non-zero, intensities at the radiation detector. Furthermore, each of these contributions has a different overlap with the radiation detector, for example with a circular portion of the radiation detector that corresponds to the numerical aperture of the projection system.

[0015] The intensities of the additional interference beams that contribute to the first harmonic of the oscillating (phase- stepping) signal are small (in comparison to the intensities of the two contributions present when a checkerboard is used). Therefore, a first type of known aberration measurement system for EUV radiation neglects these terms (i.e., assumes that they are zero) in the reconstruction of the wavefront to find the set of Zernike coefficients. This assumption impacts theaccuracy of the wavefront measurement. In turn, this has a negative impact on system imaging, overlay and focus performance of the lithographic apparatus. Embodiments of the present disclosure have been devised to at least partially address the above-described problems for aberration measurement systems for EUV radiation.

[0016] With the measurement system according to the first aspect, the pitches of the first and second patterning devices are matched such that an angular separation between the zeroth and first order diffraction beams of the first patterning device is generally matched to an angular separation between the zeroth and first order diffraction beams of the second patterning device, taking into account any reduction or magnification factor applied by the projection system. As a result, the same two contributions to the first harmonic of the oscillating (phase-stepping) signal at the radiation detector are present as when a one-dimensional diffraction grating for the patterning device at reticle level with a duty cycle of 50% and a checkerboard grating for the patterning device at wafer level are used.

[0017] Furthermore, the second patterning device has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device is non- uniform. In addition, a variation of the variable pitch of the second patterning device is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device are not matched to an angular separation between the zeroth and first order diffraction beams of the first patterning device, taking into account any reduction or magnification factor applied by the projection system. Advantageously, as a result, additional contributions to the first harmonic of the oscillating (phase-stepping) signal at the radiation detector are eliminated, or at least reduced. In particular, the overlap between unwanted diffraction beams that have a coherence relationship (and therefore could contribute to an interference pattern at the radiation detector) is disturbed.

[0018] In use, the first patterning device may be configured to receive a radiation beam and to form a plurality of first diffraction beams. In use, the projection system may be configured to project first diffraction beams formed by the first patterning device onto the second patterning device. In use, the second patterning device may be configured to receive the first diffraction beams from the projection system and to form a plurality of second diffraction beams from each of the first diffraction beams.

[0019] The pitch of the second patterning device may have an extremum value at a first position on the second patterning device and the pitch of the second patterning device may either increase or decrease as a function of distance from the first position.

[0020] For example, the extremum may be a minimum and the pitch of the second patterning device may increase as a function of distance from the first position. Alternatively, the extremum may be a maximum and the pitch of the second patterning device may decrease as a function of distance from the first position.

[0021] The first position may be, but is not necessarily, in the centre of the second patterning device.

[0022] The pitch of the second patterning device may vary linearly with distance from the first position.

[0023] Alternatively, the pitch of the second patterning device may vary non-linearly with distance from the first position. In general, the pitch of the second patterning device may be a monotonic function of distance from the first position.

[0024] The pitch of the second patterning device may vary by at least 2% over the second patterning device.

[0025] In some embodiments, the pitch of the second patterning device may vary by at least 3% over the second patterning device. In some embodiments, the pitch of the second patterning device may vary by of the order of 4% or more.

[0026] The second patterning device may be a two-dimensional diffraction grating.

[0027] The second patterning device may be a transmissive grating. The second patterning device may be a pinhole grating.

[0028] The second patterning device may comprise a substrate provided with a two-dimensional array of circular through-apertures.

[0029] A distance between the centres of adjacent through- apertures may be referred to as the local pitch of the second patterning device.

[0030] A duty cycle of the second patterning device may also be variable. That is, for a pinhole grating, a ratio of the radius of the circular apertures to the distance between the centres of adjacent apertures may vary over the second patterning device. For example, the plurality of apertures may all be of a fixed dimension and the variation in pitch (and duty cycle) may be achieved by varying a distance between the centres of adjacent apertures across the second patterning device.

[0031] Typically, a diffraction grating used as the wafer-level grating for a measurement system for determining an aberration map for a projection system of a lithographic apparatus comprises a plurality of apertures that are distributed such that a distance between the centres of adjacent apertures is uniform across the diffraction grating. This is achieved by arranging the apertures such that a centre of each of the circular through-apertures coincides with one of a square array of positions. In contrast, the second patterning device according to the first aspect may be formed by arranging the apertures such that a distance between the centres of adjacent apertures varies across the second patterning device.

[0032] The second patterning device may comprise at least 10-unit cells across the or each dimension of a pattern of the second patterning device.

[0033] In some embodiments, the second patterning device may comprise between around 3- and 100-unit cells across each dimension. For example, the second patterning device may comprise of the order of 30-unit cells across each dimension.

[0034] The second patterning device and the radiation detector may together form a sensor apparatus. The measurement system may further comprise: a controller configured to: control the positioning apparatus so as to move at least one of the first patterning device and the sensor apparatusin the shearing direction such that an intensity of radiation received by each part of the radiation detector varies as a function of the movement in the shearing direction so as to form an oscillating signal; determine from the radiation detector a phase of a harmonic of the oscillating signal at a plurality of positions on the radiation detector; and determine a set of coefficients that characterize the aberration map of the projection system from the phase of a harmonic of the oscillating signal at the plurality of positions on the radiation detector.

[0035] According to a second aspect of the present disclosure, there is provided a lithographic apparatus comprising the measurement system of any preceding claim.

[0036] According to a third aspect of the present disclosure, there is provided a diffraction grating for a phase-stepping measurement system for determining an aberration map for a projection system, wherein a pitch of the diffraction grating has an extremum value at a first position on the diffraction grating and wherein the pitch of the diffraction grating either increases or decreases as a function of distance from the first position.

[0037] For example, the extremum may be a minimum and the pitch of the diffraction grating may increase as a function of distance from the first position. Alternatively, the extremum may be a maximum and the pitch of the diffraction grating may decrease as a function of distance from the first position.

[0038] The first position may be, but is not necessarily, in the centre of the diffraction grating.

[0039] Advantageously, with such a diffraction grating, the variation in pitch is such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device is non-uniform. In particular, the variation in pitch is such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device either increases or decreases for higher-order diffraction beams. Such a diffraction grating can be used as the second patterning device of the measurement system according to the first aspect of the present disclosure.

[0040] That is, the pitch of such a diffraction grating may be matched to that of a first patterning device (taking into account any reduction or magnification factor applied by the projection system) such that an angular separation between the zeroth and first order diffraction beams of the first patterning device is generally matched to an angular separation between the zeroth and first order diffraction beams of the diffraction grating according to the third aspect. For example, this may be achieved by matching the extremum value of the pitch of the diffraction grating to the pitch of the first patterning device (taking into account any reduction or magnification factor applied by the projection system). That is, the extremum value of the pitch of the diffraction grating in a shearing direction may be is an integer multiple of the pitch of the first patterned region in that shearing direction or, alternatively, the pitch of the first patterned region in the shearing direction may be an integer multiple of the extremum value of the pitch of the diffraction grating in a shearing direction.

[0041] Furthermore, the variation of the pitch of the diffraction grating may be such that an angular separation between other pairs of adjacent pairs of diffraction beams of the diffraction grating are notmatched to an angular separation between the zeroth and first order diffraction beams of the first patterning device (taking into account any reduction or magnification factor applied by the projection system).

[0042] The diffraction grating may, in use, form the measurement system according to the first aspect of the present disclosure. The diffraction grating according to the third aspect of the present disclosure is therefore further advantageous for the reasons discussed above with reference to the measurement system according to the first aspect of the present disclosure.

[0043] The pitch of the diffraction grating may vary linearly with distance from the first position.

[0044] Alternatively, the pitch of the diffraction grating device may vary non-linearly with distance from the first position. In general, the pitch of the diffraction grating may be a monotonic function of distance from the first position.

[0045] The pitch of the diffraction grating may vary by at least 2% over the diffraction grating.

[0046] In some embodiments, the pitch of the diffraction grating may vary by at least 3% over the diffraction grating. In some embodiments, the pitch of the diffraction grating may vary by of the order of 4% or more.

[0047] The diffraction grating may be a two-dimensional diffraction grating.

[0048] The diffraction grating may be a transmissive grating. The diffraction grating may be a pinhole grating.

[0049] The diffraction grating may comprise at least 10-unit cells across the or each dimension of a pattern of the diffraction grating.

[0050] In some embodiments, the diffraction grating may comprise between around 3- and 100- unit cells across each dimension. For example, the diffraction grating may comprise of the order of 30- unit cells across each dimension.

[0051] The diffraction grating may be self-supporting.

[0052] Since the diffraction grating is self-supporting it does not need, for example a transmissive supporting layer. Such an arrangement is particularly beneficial for use in a phase-stepping measurement system for determining an aberration map for a projection system that uses EUV radiation since the use of such a transmissive supporting layer would significantly reduce the amount of EUV radiation that is transmitted by the two-dimensional diffraction grating.

[0053] The diffraction grating may comprise a substrate provided with a two-dimensional array of circular through-apertures.

[0054] A distance between the centres of adjacent through- apertures may be referred to as the local pitch of the diffraction grating.

[0055] A duty cycle of the diffraction grating may also be variable. That is, for a pinhole grating, a ratio of the radius of the circular apertures to the distance between the centres of adjacent apertures may vary over the second patterning device. For example, the plurality of apertures may all be of afixed dimension and the variation in pitch (and duty cycle) may be achieved by varying a distance between the centres of adjacent apertures across the diffraction grating.

[0056] Typically, a diffraction grating used as the wafer-level grating for a measurement system for determining an aberration map for a projection system of a lithographic apparatus comprises a plurality of apertures that are distributed such that a distance between the centres of adjacent apertures is uniform across the diffraction grating. This is achieved by arranging the apertures such that a centre of each of the circular through-apertures coincides with one of a square array of positions. In contrast, the diffraction grating according to the third aspect may be formed by arranging the apertures such that a distance between the centres of adjacent apertures varies across the diffraction grating.

[0057] The substrate may comprise a radiation absorbing layer and the through-apertures may extend through the radiation absorbing layer.

[0058] The radiation absorbing layer may, for example, be formed from aluminium nitride (AIN). Alternatively, the radiation absorbing layer may, for example, be formed from a metal such as, for example, chromium (Cr), nickel (Ni) or cobalt (Co).

[0059] In some embodiments, the substrate may further comprise: a support layer adjacent to the radiation absorbing layer and the through-apertures may extend through both the support layer and the radiation absorbing layer.

[0060] The support layer may, for example, be formed from SiN. The radiation absorbing layer may, for example, be formed from a metal such as, for example, chromium (Cr), nickel (Ni) or cobalt (Co).BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:Figure 1 depicts a lithographic system comprising a lithographic apparatus and a radiation source;Figure 2 is a schematic illustration of a measurement system according to an embodiment of the invention;Figures 3A and 3B are schematic illustrations of a patterning device and a sensor apparatus which may form part of the measurement system of Figure 2;Figure 4 is a schematic illustration of a measurement system according to an embodiment of the invention, the measurement system comprising a first patterned region and a second patterned region, the first patterned region arranged to receive radiation and to form a plurality of first diffraction beams;Figures 5A to 5C each shows a different set of second diffraction beams formed by the second patterned region of the measurement system shown in Figure 4, that set of second diffraction beams having been produced by a different first diffraction beam formed by the first patterned region;Figure 6A shows the scattering efficiency for one dimensional diffraction grating with a 50% duty cycle and which may represent the first patterned region of the measurement system shown in Figure 4;Figure 6B shows the scattering efficiency for two-dimensional diffraction grating of the form of a checkerboard with a 50% duty cycle and which may represent the second patterned region of the measurement system shown in Figure 4;Figure 6C shows an interference strength map for the measurement system shown in Figure 4 when employing the first patterned region shown in Figure 6A and the second patterned region shown in Figure 6B, each of the interference strengths shown representing the second interference beams which contribute to the first harmonic of the oscillating phase-stepping signal and which have a different overlap, at the radiation detector, with a circle that represents the numerical aperture of the projection system PS;Figures 7 A, 7B and 7C show the portion of the numerical aperture of the projection system of the measurement system shown in Figure 4 that is filled by the three different first diffraction beams shown in Figure 4;Figures 8A-8C show a portion of the radiation detector of the measurement system shown in Figure 4 which corresponds to the numerical aperture of the projection system of the measurement system, and which is filled by three second diffraction beams which originate from the first diffraction beam represented by Figure 7B;Figures 9A-9C show a portion of the radiation detector of the measurement system shown in Figure 4 which corresponds to the numerical aperture of the projection system of the measurement system, and which is filled by three second diffraction beams which originate from the first diffraction beam represented by Figure 7A;Figures 10A-10C show a portion of the radiation detector of the measurement system shown in Figure 4 which corresponds to the numerical aperture of the projection system of the measurement system, and which is filled by three second diffraction beams which originate from the first diffraction beam represented by Figure 7C;Figure 11 A show a portion of the radiation detector of the measurement system shown in Figure 4 which corresponds to the numerical aperture of the projection system of the measurement system, and which represents the overlap between the second diffraction beams shown in Figures 8B and 9A and the overlap between the second diffraction beams shown in Figures 8A and 10B;Figure 1 IB show a portion of the radiation detector of the measurement system shown in Figure 4 which corresponds to the numerical aperture of the projection system of the measurement system, and which represents the overlap between the second diffraction beams shown in Figures 8B and 10C and the overlap between the second diffraction beams shown in Figures 8C and 9B;Figure 12 shows a unit cell of a grating comprising an array of circular pinholes and having a 50% (by area) duty cycle;Figure 13A shows the scattering efficiency for one dimensional diffraction grating with a 50% duty cycle and which may represent the first patterned region of the measurement system shown in Figure 4;Figure 13B shows the scattering efficiency for two-dimensional diffraction comprising the unit cell of Figure 12 and which may represent the second patterned region of the measurement system shown in Figure 4;Figure 13C shows an interference strength map for the measurement system shown in Figure 4 when employing the first patterned region shown in Figure 13A and the second patterned region shown in Figure 13B, each of the interference strengths shown representing the second interference beams which contribute to the first harmonic of the oscillating phase-stepping signal and which have a different overlap, at the radiation detector, with a circle that represents the numerical aperture of the projection system;Figure 14A is a representation of 21 second diffraction beams generated by a second patterned region having a unit cell as shown in Figure 12, the second diffraction beams corresponding to diffraction efficiencies contained within the white dotted line in Figure 13B;Figure 14B is a representation of 16 interference beams, each generated by the interference of pairs of the second diffraction beams shown in Figure 14 A, each of the interference beam corresponding to an interference strength contained within the white dotted line in Figure 13C;Figure 15A is a schematic representation of a set of second diffraction beams produced by a second patterning device that has a uniform pitch from each of the first diffraction beams (shown in Figure 4); Figure 15A is equivalent to a combination of Figures 5A to 5C;Figure 15B is a schematic representation of a set of second diffraction beams produced by a second patterning device according to an embodiment of the present disclosure that has a non-uniform pitch from each of the first diffraction beams (shown in Figure 4);Figure 16A is a schematic representation of a first example diffraction grating having a non- uniform pitch that could be used as the second (wafer-level) patterning device of a measurement system for determining aberrations according to an embodiment of the present disclosure, the first diffraction grating being a two-dimensional pinhole array grating;Figure 16B is a schematic representation of a second example diffraction grating having a non- uniform pitch, the second diffraction grating being a linear (one-dimensional), transmissive diffraction grating;Figure 17 shows a diffraction spectrum for a linear grating of the type shown in Figure 16B but having a uniform pitch, the diffraction spectrum shows the intensity of the diffraction pattern as a function of diffraction order, nx. where the diffraction order, nx. represents a scattering angle of 0, where sin(9) = nx. / 2P, where P is the uniform pitch and A is the wavelength of the radiation; the diffraction spectrum 90 is shown for three cases: (a) a grating comprising a single unit cell; (b) a grating comprising N=30 unit cells; and (c) a grating comprising an infinite number of unit cells;Figure 18A shows a diffraction spectrum for a linear diffraction grating of the type shown in Figure 16B and having a pitch that increases from a centre of the diffraction grating, having a variation of pitch of 4% across the diffraction grating; the diffraction spectrum shows the intensity of the diffraction pattern as a function of diffraction order, nx, where diffraction order, nx, represents a scattering angle of 9,is the minimum pitch of the diffraction grating; the diffraction spectrum 92 is again shown for three cases: (a) a grating comprising a single unit cell; (b) a grating comprising N=30 unit cells; and (c) a grating comprising an infinite number of unit cells; andFigure 18B shows an enlarged portion of the diffraction spectrum shown in Figure 18 A.DETAILED DESCRIPTION

[0062] Figure 1 shows a lithographic system comprising a radiation source SO and a lithographic apparatus LA. The radiation source SO is configured to generate an EUV radiation beam B and to supply the EUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT configured to support a patterning device MA (e.g., a mask), a projection system PS and a substrate table WT configured to support a substrate W.

[0063] The illumination system IL is configured to condition the EUV radiation beam B before the EUV radiation beam B is incident upon the patterning device MA. Thereto, the illumination system IL may include a facetted field mirror device 10 and a facetted pupil mirror device 11. The faceted field mirror device 10 and faceted pupil mirror device 11 together provide the EUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to, or instead of, the faceted field mirror device 10 and faceted pupil mirror device 11.

[0064] After being thus conditioned, the EUV radiation beam B interacts with the patterning device MA. As a result of this interaction a patterned EUV radiation beam B’ is generated. The projection system PS is configured to project the patterned EUV radiation beam B’ onto the substrate W. For that purpose, the projection system PS may comprise a plurality of mirrors 13, 14 which are configured to project the patterned EUV radiation beam B’ onto the substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV radiation beam B’ thus forming an image with features that are smaller than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated as having only two mirrors 13, 14 in Figure 1, the projection system PS may include a different number of mirrors (e.g., six or eight mirrors).

[0065] The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus LA aligns the image, formed by the patterned EUV radiation beam B’ , with a pattern previously formed on the substrate W.

[0066] A relative vacuum, i.e., a small amount of gas (e.g., hydrogen) at a pressure well below atmospheric pressure, may be provided in the radiation source SO, in the illumination system IL, and / or in the projection system PS.

[0067] The radiation source SO may be a laser produced plasma (LPP) source, a discharge produced plasma (DPP) source, a free electron laser (FEL) or any other radiation source that is capable of generating EUV radiation.

[0068] In general, the projection system PS has an optical transfer function which may be non- uniform, which can affect the pattern which is imaged on the substrate W. For unpolarized radiation such effects can be fairly well described by two scalar maps, which describe the transmission (apodization) and relative phase (aberration) of radiation exiting the projection system PS as a function of position in a pupil plane thereof. These scalar maps, which may be referred to as the transmission map and the relative phase map, may be expressed as a linear combination of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on a unit circle. A determination of each scalar map may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be obtained from a measured scalar map by calculating the inner product of the measured scalar map with each Zernike polynomial in turn and dividing this by the square of the norm of that Zernike polynomial. In the following, unless stated otherwise, any reference to Zernike coefficients will be understood to mean the Zernike coefficients of a relative phase map (also referred to herein as an aberration map). It will be appreciated that in alternative embodiments other sets of basis functions may be used. For example, some embodiments may use Tatian Zernike polynomials, for example for obscured aperture systems.

[0069] The wavefront aberration map represents the distortions of the wavefront of light approaching a point in an image plane of the projection system PS from a spherical wavefront (as a function of position in the pupil plane or, alternatively, the angle at which radiation approaches the image plane of the projection system PS). As discussed, this wavefront aberration map W(x, y) may be expressed as a linear combination of Zernike polynomials:where x and y are coordinates in the pupil plane, Zn(x, y) is the nth Zernike polynomial and cnis a coefficient. It will be appreciated that in the following, Zernike polynomials and coefficients are labelled with an index, which is commonly referred to as a Noll index. Therefore, Zn(x, y) is the Zernike polynomial having a Noll index of n and cnis a coefficient having a Noll index of n. The wavefront aberration map may then be characterized by the set of coefficients cnin such an expansion, which may be referred to as Zernike coefficients.

[0070] It will be appreciated that only a finite number of Zernike orders are taken into account. Different Zernike coefficients of the phase map may provide information about different forms of aberration which are caused by the projection system PS. The Zernike coefficient having a Noll index of 1 may be referred to as the first Zernike coefficient, the Zernike coefficient having a Noll index of 2 may be referred to as the second Zernike coefficient and so on.

[0071] The first Zernike coefficient relates to a mean value (which may be referred to as a piston) of a measured wavefront. The first Zernike coefficient may be irrelevant to the performance of the projection system PS and as such may not be determined using the methods described herein. The second Zernike coefficient relates to the tilt of a measured wavefront in the x-direction. The tilt of a wavefront in the x-direction is equivalent to a placement in the x-direction. The third Zernike coefficient relates to the tilt of a measured wavefront in the y-direction. The tilt of a wavefront in the y-direction is equivalent to a placement in the y-direction. The fourth Zernike coefficient relates to a defocus of a measured wavefront. The fourth Zernike coefficient is equivalent to a placement in the z- direction. Higher order Zernike coefficients relate to other forms of aberration which are caused by the projection system (e.g., astigmatism, coma, spherical aberrations and other effects).

[0072] Throughout this description the term “aberrations” should be intended to include all forms of deviation of a wavefront from a perfect spherical wavefront. That is, the term “aberrations” may relate to the placement of an image (e.g., the second, third and fourth Zernike coefficients) and / or to higher order aberrations such as those which relate to Zernike coefficients having a Noll index of 5 or more. Furthermore, any reference to an aberration map for a projection system may include all forms of deviation of a wavefront from a perfect spherical wavefront, including those due to image placement.

[0073] The transmission map and the relative phase map are field and system dependent. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e., for each spatial location in its image plane).

[0074] As will be described in further detail below, the relative phase of the projection system PS in its pupil plane may be determined by projecting radiation from an object plane of the projection system PS (i.e., the plane of the patterning device MA), through the projection system PS and using a shearing interferometer to measure a wavefront (i.e., a locus of points with the same phase). The shearing interferometer may comprise a diffraction grating, for example a two-dimensional diffraction grating, in an image plane of the projection system (i.e., the substrate table WT) and a detector arranged to detect an interference pattern in a plane that is conjugate to a pupil plane of the projection system PS.

[0075] The projection system PS comprises a plurality of optical elements (including mirrors 13, 14). As already explained, although the projection system PS is illustrated as having only two mirrors 13, 14 in Figure 1, the projection system PS may include a different number of mirrors (e.g., six or eight mirrors). The lithographic apparatus LA further comprises adjusting means PA for adjusting these optical elements so as to correct for aberrations (any type of phase variation across the pupil plane throughout the field). To achieve this, the adjusting means PA may be operable to manipulate opticalelements within the projection system PS in one or more different ways. The projection system may have a co-ordinate system wherein its optical axis extends in the z direction (it will be appreciated that the direction of this z axis changes along the optical path through the projection system, for example at each mirror or optical element). The adjusting means PA may be operable to do any combination of the following: displace one or more optical elements; tilt one or more optical elements; and / or deform one or more optical elements. Displacement of optical elements may be in any direction (x, y, z or a combination thereof). Tilting of optical elements is typically out of a plane perpendicular to the optical axis, by rotating about axes in the x or y directions although a rotation about the z axis may be used for non-rotationally symmetric optical elements. Deformation of an optical element may be performed for example by using actuators to exert force on sides of the optical element and / or by using heating elements to heat selected regions of the optical element. In general, it may not be possible to adjust the projection system PS to correct for apodizations (transmission variation across the pupil plane). The transmission map of a projection system PS may be used when designing masks MAs for the lithographic apparatus LA.

[0076] In some embodiments, the adjusting means PA may be operable to move the support structure MT and / or the substrate table WT. The adjusting means PA may be operable to displace (in any of the x, y, z directions or a combination thereof) and / or tilt (by rotating about axes in the x or y directions) the support structure MT and / or the substrate table WT.

[0077] A projection system PS which forms part of a lithographic apparatus may periodically undergo a calibration process. For example, when a lithographic apparatus is manufactured in a factory the optical elements (e.g., mirrors) which form the projection system PS may be set up by performing an initial calibration process. After installation of a lithographic apparatus at a site at which the lithographic apparatus is to be used, the projection system PS may once again be calibrated. Further calibrations of the projection system PS may be performed at regular intervals. For example, under normal use the projections system PS may be calibrated every few months (e.g., every three months).

[0078] Calibrating a projection system PS may comprise passing radiation through the projection system PS and measuring the resultant projected radiation. Measurements of the projected radiation may be used to determine aberrations in the projected radiation which are caused by the projection system PS. Aberrations which are caused by the projection system PS may be determined using a measurement system. In response to the determined aberrations, the optical elements which form the projection system PS may be adjusted so as to correct for the aberrations which are caused by the projection system PS.

[0079] Figure 2 is a schematic illustration of a measurement system 12 which may be used to determine aberrations which are caused by a projection system PS. The measurement system 12 comprises an illumination system IL, a measurement patterning device MA’, a sensor apparatus 21 and a controller CN. The measurement system 12 may form part of a lithographic apparatus. For example, the illumination system IL and the projection system PS which are shown in Figure 2 may be theillumination system IL and projection system PS of the lithographic apparatus which is shown in Figure 1. For ease of illustration additional components of a lithographic apparatus are not shown in Figure 2.

[0080] The measurement patterning device MA’ is arranged to receive radiation from the illumination system IL. The sensor apparatus 21 is arranged to receive radiation from the projection system PS. During normal use of a lithographic apparatus, the measurement patterning device MA’ and the sensor apparatus 21 which are shown in Figure 2 may be located in positions that are different to the positions in which they are shown in Figure 2. For example, during normal use of a lithographic apparatus a patterning device MA which is configured to form a pattern to be transferred to a substrate W may be positioned to receive radiation from the illumination system IL and a substrate W may be positioned to receive radiation from the projection system PS (as is shown, for example, in Figure 1). The measurement patterning device MA’ and the sensor apparatus 21 may be moved into the positions in which they are shown in Figure 2 in order to determine aberrations which are caused by the projection system PS. The measurement patterning device MA’ may be supported by a support structure MT, such as the support structure which is shown in Figure 1. The sensor apparatus 21 may be supported by a substrate table, such as the substrate table WT which is shown in Figure 1. Alternatively, the sensor apparatus 21 may be supported by a measurement table (not shown) which may be separate to the sensor table WT.

[0081] The measurement patterning device MA’ and the sensor apparatus 21 are shown in more detail in Figures 3 A and 3B. Cartesian co-ordinates are used consistently in Figures 2, 3A and 3B. Figure 3A is a schematic illustration of the measurement patterning device MA’ in an x-y plane and Figure 3B is a schematic illustration of the sensor apparatus 21 in an x-y plane.

[0082] The measurement patterning device MA’ comprises a plurality of patterned regions 15 a- 15c. In the embodiment which is shown in Figures 2 and 3A the measurement patterning device MA’ is a reflective patterning device MA’. The patterned regions 15a-15c each comprises a reflective diffraction grating. Radiation which is incident on the patterned regions 15a-15c of the measurement patterning device MA’ is at least partially scattered by thereby and received by the projection system PS. In contrast, radiation which is incident on the remainder of the measurement patterning device MA’ is not reflected or scattered towards the projection system PS (for example, it may be absorbed by the measurement patterning device MA’).

[0083] The illumination system IL illuminates the measurement patterning device MA’ with radiation. Whilst not shown in Figure 2, the illumination system IL may receive radiation from a radiation source SO and condition the radiation so as to illuminate the measurement patterning device MA’ . For example, the illumination system IL may condition the radiation so as to provide radiation having a desired spatial and angular distribution. In the embodiment, which is shown in Figure 2, the illumination system IL is configured to form separate measurement beams 17a- 17c. Each measurement beam 17a-17c illuminates a respective patterned region 15a-15c of the measurement patterning device MA’ .

[0084] In order to perform a determination of aberrations which are caused by the projection system PL, a mode of the illumination system IL may be changed in order to illuminate the measurement patterning device MA’ with separate measurement beams 17a-17c. For example, during normal operation of a lithographic apparatus, the illumination system IL may be configured to illuminate a patterning device MA with a slit of radiation. However, the mode of the illumination system IL may be changed such that the illumination system IL is configured to form separate measurement beams 17a- 17c in order to perform a determination of aberrations caused by the projection system PL. In some embodiments different patterned regions 15 a- 15c may be illuminated at different times. For example, a first subset of the patterned regions 15a-15c may be illuminated at a first time so as to form a first subset of measurement beams 17a-17c and a second subset of patterned regions 15a-15c may be illuminated at a second time so as to form a second subset of measurement beams 17a-17c.

[0085] In other embodiments the mode of the illumination system IL may be unchanged in order to perform a determination of aberrations caused by the projection system PS. For example, the illumination system IL may be configured to illuminate the measurement patterning device MA’ with a slit of radiation (e.g., which substantially corresponds with an illumination area used during exposure of substrates). Separate measurement beams 17a-17c may then be formed by the measurement patterning device MA’ since only the patterned regions 15a-15c reflect or scatter radiation towards the projection system PS.

[0086] In the Figures the Cartesian co-ordinate system is shown as being conserved through the projection system PS. However, in some embodiments the properties of the projection system PS may lead to a transformation of the co-ordinate system. For example, the projection system PS may form an image of the measurement patterning device MA’ which is magnified, rotated and / or mirrored relative to the measurement patterning device MA’ . In some embodiments the projection system PS may rotate an image of the measurement patterning device MA’ by approximately 180° around the z- axis. In such an embodiment the relative positions of a first measurement beam 17a and a third measurement beam 17c which are shown in Figure 2, may be swapped. In other embodiments the image may be mirrored about an axis which may lie in an x-y plane. For example, the image may be mirrored about the x-axis or about the y-axis.

[0087] In embodiments in which the projection system PS rotates an image of the measurement patterning device MA’ and / or the image is mirrored by the projection system PS, the projection system is considered to transform the co-ordinate system. That is, the co-ordinate system which is referred to herein is defined relative to an image which is projected by the projection system PS and any rotation and / or mirroring of the image causes a corresponding rotation and / or mirroring of the co-ordinate system. For ease of illustration, the co-ordinate system is shown in the Figures as being conserved by the projection system PS. However, in some embodiments the co-ordinate system may be transformed by the projection system PS.

[0088] The patterned regions 15a-15c modify the measurement beams 17a-17c. In particular, the patterned regions 15a-15c cause a spatial modulation of the measurement beams 17a-17c and cause diffraction in the measurement beams 17a-17c. In the embodiment which is shown in Figure 3B the patterned regions 15a-15c each comprise two distinct portions. For example, a first patterned region 15a comprises a first portion 15a’ and a second portion 15a”. The first portion 15a’ comprises a diffraction grating which is aligned parallel to a u-direction and the second portion 15a” comprises a diffraction grating which is aligned parallel to a v-direction. The u and v-directions are depicted in Figure 3A. The u and v-directions are both aligned at approximately 45° relative to both the x and y- directions and are aligned perpendicular to each other. Second 15b and third 15c patterned regions which are shown in Figure 3A are identical to the first patterned region 15a and each comprise first and second portions whose diffraction gratings are aligned perpendicular to each other.

[0089] The first and second portions of the patterned regions 15a-15c may be illuminated with the measurement beams 17a-17c at different times. For example, the first portions of each of the patterned regions 15a-15c may be illuminated by the measurement beams 17a-17c at a first time. At a second time the second portions of each of the patterned regions 15a-15c may be illuminated by the measurement beams 17a-17c. As was mentioned above in some embodiments different patterned regions 15a- 15c may be illuminated at different times. For example, the first portions of a first subset of patterned regions 15a-15c may be illuminated at a first time and the first portions of a second subset of patterned regions 15a-15c may be illuminated at a second time. Second portions of the first and second subsets of patterned regions may be illuminated at the same or different times. In general, any schedule of illuminating different portions of patterned regions 15a-15c may be used.

[0090] The modified measurement beams 17a-17c are received by the projection system PS. The projection system PS forms an image of the patterned regions 15a-15c on the sensor apparatus 21. The sensor apparatus 21 comprises a plurality of diffraction gratings 19a-19c and a radiation detector 23. The diffraction gratings 19a-19c are arranged such that each diffraction grating 19a-19c receives a respective modified measurement beam 17a-17c which is output from the projection system PL. The modified measurement beams 17a-17c which are incident on the diffraction gratings 19a-19c are further modified by the diffraction gratings 19a- 19c. The modified measurement beams which are transmitted at the diffraction gratings 19a-19c are incident on the radiation detector 23.

[0091] The radiation detector 23 is configured to detect the spatial intensity profile of radiation which is incident on the radiation detector 23. The radiation detector 23 may, for example, comprise an array of individual detector elements or sensing elements. For example, the radiation detector 23 may comprise an active pixel sensor such as, for example, a CMOS (complementary metal-oxide- semiconductor) sensor array. Alternatively, the radiation detector 23 may comprise a CCD (charge- coupled device) sensor array. The diffraction gratings 19a-19c and portions of the radiation sensor 23 at which the modified measurement beams 17a- 17c are received form detector regions 25a-25c. For example, a first diffraction grating 19a and a first portion of the radiation sensor 23 at which a firstmeasurement beam 17a is received together form a first detector region 25 a. A measurement of a given measurement beam 17a-17c may be made at a respective detector region 25a-25c (as depicted). As was described above, in some embodiments the relative positioning of the modified measurement beams 17a-17c and the co-ordinate system may be transformed by the projection system PS.

[0092] The modification of the measurement beams 17a- 17c which occurs at the patterned regions 15a-15c and the diffraction gratings 19a- 19c of the detector regions 25a-25c results in interference patterns being formed on the radiation detector 23. The interference patterns are related to the derivative of the phase of the measurement beams and depend on aberrations caused by the projection system PS. The interference patterns may therefore be used to determine aberrations which are caused by the projection system PS.

[0093] In general, the diffraction gratings 19a-19c of each of the detector regions 25a-25c comprises a two-dimensional transmissive diffraction grating. In the embodiment which is shown in Figure 3B the detector regions 25a-25c each comprise a diffraction grating 19a-19c which is configured in the form of a checkerboard. As described further below, embodiments of the present disclosure have particular application to arrangements where the detector regions 25a-25c each comprises a two- dimensional transmissive diffraction grating 19a-19c that is not configured in the form of a checkerboard.

[0094] Illumination of the first portions of the patterned regions 15a-15c may provide information related to aberrations in a first direction and illumination of the second portions of the patterned regions 15a-15c may provide information related to aberrations in a second direction.

[0095] In some embodiments, the measurement patterning device MA’ and / or the sensor apparatus 21 is sequentially scanned and / or stepped in two perpendicular directions. For example, the measurement patterning device MA’ and / or the sensor apparatus 21 may be stepped relative to each other in the u and v-directions. The measurement patterning device MA’ and / or the sensor apparatus 21 may be stepped in the u-direction whilst the second portions 15a”-15c” of the patterned regions 15a- 15c are illuminated and the measurement patterning device MA’ and / or the sensor apparatus 21 may be stepped in the v-direction whilst the first portions 15a’-15c’ of the patterned regions 15a-15c are illuminated. That is, the measurement patterning device MA’ and / or the sensor apparatus 21 may be stepped in a direction which is perpendicular to the alignment of a diffraction grating which is being illuminated.

[0096] The measurement patterning device MA’ and / or the sensor apparatus 21 may be stepped by distances which correspond with a fraction of the grating period of the diffraction gratings. Measurements which are made at different stepping positions may be analysed in order to derive information about a wavefront in the stepping direction. For example, the phase of the first harmonic of the measured signal (which may be referred to as a phase stepping signal) may contain information about the derivative of a wavefront in the stepping direction. Stepping the measurement patterning device MA’ and / or the sensor apparatus 21 in both the u and v-directions (which are perpendicular toeach other) therefore allows information about a wavefront to be derived in two perpendicular directions (in particular, it provides information about a derivative of the wavefront in each of the two perpendicular directions), thereby allowing the full wavefront to be reconstructed.

[0097] In addition to stepping of the measurement patterning device MA’ and / or the sensor apparatus 21 in a direction which is perpendicular to the alignment of a diffraction grating which is being illuminated (as was described above), the measurement patterning device MA’ and / or the sensor apparatus 21 may also be scanned relative to each other. Scanning of the measurement patterning device MA’ and / or the sensor apparatus 21 may be performed in a direction which is parallel to the alignment of a diffraction grating which is being illuminated. For example, the measurement patterning device MA’ and / or the sensor apparatus 21 may be scanned in the u-direction whilst the first portions 15a’- 15c’ of the patterned regions 15a-15c are illuminated and the measurement patterning device MA’ and / or the sensor apparatus 21 may be scanned in the v-direction whilst the second portions 15a”- 15c” of the patterned regions 15a-15c are illuminated. Scanning of the measurement patterning device MA’ and / or the sensor apparatus 21 in a direction which is parallel to the alignment of a diffraction grating which is being illuminated allows measurements to be averaged out across the diffraction grating, thereby accounting for any variations in the diffraction grating in the scanning direction. Scanning of the measurement patterning device MA’ and / or the sensor apparatus 21 may be performed at a different time to the stepping of the measurement patterning device MA’ and / or the sensor apparatus 21 which was described above.

[0098] It will be appreciated that a variety of different arrangements of the patterned regions 15 a- 15c and the detector regions 25a-25c may be used in order to determine aberrations caused by the projection system PS. The patterned regions 15a-15c and / or the detector regions 25a-25c may comprise diffraction gratings. In some embodiments the patterned regions 15a-15c and / or the detector regions 25a-25c may comprise components other than a diffraction grating. For example, in some embodiments the patterned regions 15a- 15c and / or the detector regions may comprise a single slit or a pinhole opening through which at least a portion of a measurement beam 17a-17c may propagate. In general, the patterned regions and / or the detector regions may comprise any arrangement which serves to modify the measurement beams.

[0099] The controller CN receives measurements made at the sensor apparatus 21 and determines, from the measurements, aberrations which are caused by the projection system PS. The controller may be configured to control one or more components of the measurement system 12. For example, the controller CN may control a positioning apparatus PW which is operable to move the sensor apparatus 21 and / or the measurement patterning device MA’ relative to each other. The controller may control an adjusting means PA for adjusting components of the projection system PS. For example, the adjusting means PA may adjust optical elements of the projection system PS so as to correct for aberrations which are caused by the projection system PS, and which are determined by the controller CN.[000100] In some embodiments, the controller CN may be operable to control the adjusting means PA for adjusting the support structure MT and / or the substrate table WT. For example, the adjusting means PA may adjust support structure MT and / or substrate table WT so as to correct for aberrations which are caused by placement errors of patterning device MA and / or substrate W (and which are determined by the controller CN).[000101] Determining aberrations (which may be caused by the projection system PS or by placement errors of the patterning device MA or the substrate W) may comprise fitting the measurements which are made by the sensor apparatus 21 to Zernike polynomials in order to obtain Zernike coefficients. Different Zernike coefficients may provide information about different forms of aberration which are caused by the projection system PS. Zernike coefficients may be determined independently at different positions in the x and / or the y-directions. For example, in the embodiment which is shown in Figure 2, 3A and 3B, Zernike coefficients may be determined for each measurement beam 17a-17c.[000102] In some embodiments the measurement patterning device MA’ may comprise more than three patterned regions, the sensor apparatus 21 may comprise more than three detector regions and more than three measurement beams may be formed. This may allow the Zernike coefficients to be determined at more positions. In some embodiments the patterned regions and the detector regions may be distributed at different positions in both the x and y-directions. This may allow the Zernike coefficients to be determined at positions which are separated in both the x and the y-directions.[000103] Whilst, in the embodiment which is shown in Figures 2, 3A and 3B the measurement patterning device MA’ comprises three patterned regions 15a-15c and the sensor apparatus 21 comprises three detector regions 25a-25c, in other embodiments the measurement patterning device MA’ may comprise more or less than three patterned regions 15a-15c and / or the sensor apparatus 21 may comprise more or less than three detector regions 25a-25c.[000104] Methods for determining aberrations caused by a projection system PS are now described with reference to Figure 4.[000105] In general, measurement patterning device MA’ comprises at least one first patterned region 15a-15c and the sensor apparatus 21 comprises at least one second patterned region 19a-19c.[000106] Figure 4 is a schematic illustration of a measurement system 30 which may be used to determine aberrations which are caused by a projection system PS. Measurement system 30 may be the same as the measurement system 12 shown in Figure 2, however, it may have a different number of first patterned regions (on measurement patterning device MA’) and second patterned regions (in the sensor apparatus 21). Therefore, the measurement system 30 shown in Figure 4 may include any features of the measurement system 12 shown in Figure 2 described above and these features will not be further described below.[000107] In Figure 4, only a single first patterned region 31 is provided on the measurement patterning device MA’ and a single second patterned region 32 is provided in the sensor apparatus 21.[000108] The measurement patterning device MA’ is irradiated with radiation 33 from the illumination system IL. For ease of understanding only a single line (which may, for example, represent a single ray, for example the chief ray, of an incident radiation beam) is shown in Figure 4. However, it will be appreciated that the radiation 33 will comprise a range of angles incident on the first patterned region 31 of the measurement patterning device MA’. That is, each point on the first patterned region 31 of the measurement patterning device MA’ may be illuminated by a cone of light. In general, each point is illuminated by substantially the same range of angles, this being characterized by the intensity of radiation in a pupil plane of the illumination system IL (not shown).[000109] The first patterned region 31 is arranged to receive the radiation 33 and to form a plurality of first diffraction beams 34, 35, 36. A central first diffraction beam 35 corresponds to a 0thorder diffraction beam of first patterned region 31 and the other two first diffraction beams 34, 36 correspond to the ±lstorder diffraction beams of first patterned region 31. It will be appreciated that more, higher order diffraction beams will, in general, also be present. Again, for ease of understanding, only three first diffraction beams 34, 35, 36 are shown in Figure 4.[000110] It will also be appreciated that, as the incoming radiation 33 comprises a cone of radiation converging on a point on the first patterned region 31, each of the first diffraction beams 34, 35, 36 also comprises a cone of radiation diverging from that point on the first patterned region 31.[000111] To achieve the generation of the first diffraction beams 34, 35, 36, the first patterned region 31 may be of the form of a diffraction grating. For example, the first patterned region 31 may be generally of the form of the patterned region 15a shown in Figure 3A. In particular, at least a portion of the first patterned region 31 may be of the form of the first portion 15a’ of the patterned region 15a shown in Figure 3A, i.e., a diffraction grating which is aligned parallel to a u-direction (note that Figure 4 is shown in the z-v plane). Therefore, the first diffraction beams 34-36 are separated in a shearing direction, which is the v-direction.[000112] The first diffraction beams 34-36 are at least partially captured by the projection system PS, as now described. How much of the first diffraction beams 34-36 is captured by the projection system PS will be dependent on: the pupil fill of the incident radiation 33 from the illumination system IL; the angular separation of the first diffraction beams 34-36 (which in turn is dependent on the pitch of the first patterned region 31 and the wavelength of the radiation 33); and the numerical aperture of the projection system PS.[000113] The measurement system 30 may be arranged such that first diffraction beam 35 that corresponds to the 0thorder diffraction beam substantially fills the numerical aperture of the projection system PS, which may be represented by a circular region of a pupil plane 37 of the projection system PS, and the first diffraction beams 34, 36 that correspond to the ±lstorder diffraction beams overlap significantly with the first diffraction beam 35 that corresponds to the 0thorder diffraction beam. With such an arrangement, substantially all of the first diffraction beam 35 that corresponds to the 0thorder diffraction beam and most of the first diffraction beams 34, 36 that correspond to the ±lstorder1 diffraction beams are captured by the projection system PS and projected onto the sensor apparatus 21. (Furthermore, with such an arrangement a large number of diffraction beams generated by the first patterned region 31 are at least partially projected onto the sensor apparatus 21).[000114] The role of the first patterned region 31 is to introduce spatial coherence, as now discussed. [000115] In general, two rays of radiation 33 from the illumination system IL that are incident on the same point of the measurement patterning device MA’ at different angles of incidence are not coherent. By receiving the radiation 33 and forming a plurality of first diffraction beams 34, 35, 36, the first patterned region 31 may be considered to form a plurality of copies of the incident radiation cone 33 (the copies having, in general different phases and intensities). Within any one of these copies, or first diffraction beams 34, 35, 36, two rays of radiation which originate from the same point on the measurement patterning device MA’ but at different scattering angles, are not coherent (due to the properties of the illumination system IL). However, for a given ray of radiation within any one of the first diffraction beams 34, 35, 36 there is a corresponding ray of radiation in each of the other first diffraction beams 34, 35, 36 that is spatially coherent with that given ray. For example, the chief rays of each of the first diffraction beams 34, 35, 36 (which correspond to the chief ray of the incident radiation 33) are coherent and could, if combined, interfere at the amplitude level.[000116] This coherence is exploited by the measurement system 30 to determine an aberration map of the projection system PS.[000117] The projection system PS projects part of the first diffraction beams 34, 35, 36 (which is captured by the numerical aperture of the projection system) onto the sensor apparatus 21.[000118] In Figure 4, the sensor apparatus 21 comprises the single second patterning region 32. As described further below (with reference to Figures 5A-5C), the second patterned region 32 is arranged to receive these first diffraction beams 34-36 from the projection system PS and to form a plurality of second diffraction beams from each of the first diffraction beams. In order to achieve this, the second patterning region 32 comprises a two-dimensional transmissive diffraction grating. In Figure 4, all radiation that is transmitted by the second patterning region 32 is represented as a single arrow 38. This radiation 38 is received by a detector region 39 of the radiation detector 23 and is used to determine the aberration map.[000119] Each of the first diffraction beams 34-36 that is incident on the patterning region 32 will diffract to from a plurality of second diffraction beams. Since the second patterning region 32 comprises a two-dimensional diffraction grating, from each incident first diffraction beam, a two-dimensional array of secondary diffraction beams is produced (the chief rays of these secondary diffraction beams being separated in both the shearing direction (v-direction) and the direction perpendicular thereto (the u-direction). In the following, a diffraction order that is nthorder in the shearing direction (the v- direction) and mthorder in the non-shearing direction (the u-direction) will be referred to as the (n, m)thdiffraction order of the second patterned region 32. In the following, where it is not important what order a second diffraction beam is in the non-shearing direction (the u-direction), the (n, m)thdiffractionorder of the second patterned region 32 may be referred to simply as the nthorder second diffraction beam.[000120] Figures 5A to 5C show a set of second diffraction beams produced by each of the first diffraction beams 34-36. Figure 5A shows a set of second diffraction beams 35a-35e produced by the first diffraction beam 35 that corresponds to the 0thorder diffraction beam of first patterned region 31. Figure 5B shows a set of second diffraction beams 36a-36e produced by the first diffraction beam 36 that corresponds to the -1storder diffraction beam of first patterned region 31. Figure 5C shows a set of second diffraction beams 34a-34e produced by the first diffraction beam 34 that corresponds to the +lstorder diffraction beam of first patterned region 31.[000121] In Figure 5A, second diffraction beam 35a corresponds to the 0thorder diffraction beam (of second patterned region 32, and in the shearing direction), whereas second diffraction beams 35b, 35c correspond to the ±lstorder diffraction beams and second diffraction beams 35d, 35e correspond to the ±2ndorder diffraction beams. It will be appreciated that Figures 5A-5C are shown in the v-z plane and the shown second diffraction beams may, for example, correspond to 0thorder diffraction beam of second patterned region 32 in the non-shearing direction (i.e., the u-direction). It will be further appreciated that there will be a plurality of copies of these second diffraction beams, representing higher order diffraction beams in the non-shearing direction that are into or out of the page of Figures 5A-5C. [000122] In Figure 5B, second diffraction beam 36a corresponds to the 0thorder diffraction beam (of second patterned region 32, and in the shearing direction), whereas second diffraction beams 36b, 36c correspond to the ±lstorder diffraction beams and second diffraction beams 36d, 36e correspond to the ±2"dorder diffraction beams.[000123] In Figure 5C, second diffraction beam 34a corresponds to the 0thorder diffraction beam (of second patterned region 32, and in the shearing direction), whereas second diffraction beams 34b, 34c correspond to the ±lstorder diffraction beams and second diffraction beams 34d, 34e correspond to the ±2ndorder diffraction beams.[000124] It can be seen from Figures 5A-5C that several of the second diffraction beams spatially overlap with each other. For example, the second diffraction beam 35b that corresponds to the -1storder diffraction beam of second patterned region 32, which originates from the 0thorder diffraction beam 35 of first patterned region 31 overlaps with the second diffraction beam 36a that corresponds to the 0thorder diffraction beam of second patterned region 32, which originates from the -1storder diffraction beam 36 of first patterned region 31. All of the lines in Figures 4 and 5A-5C may be considered to represent a single ray of radiation that originates from a single input ray 33 from the illumination system IL. Therefore, as explained above, these lines represent spatially coherent rays that, if spatially overlapping at radiation detector 23 will produce an interference pattern. Furthermore, the interference is between rays which have passed though different parts of the pupil plane 37 of the projection system PS (which are separated in the shearing direction). Therefore, the interference of radiation thatoriginates from a single input ray 33 is dependent on phase differences between two different parts of the pupil plane.[000125] In known arrangements, this spatial overlapping and spatial coherence of the second diffraction beams at radiation detector 23 is achieved by matching the first and second patterned regions 31, 32 such that the angular separation (in the shearing direction) between different second diffraction beams that originate from a given first diffraction beam is the same as the angular separation (in the shearing direction) between different first diffraction beams as they converge on the second patterned region 32. Typically, this spatial overlapping and spatial coherence of the second diffraction beams at radiation detector 23 is achieved by matching the pitches of the first and second patterned regions 31, 32 in the shearing direction. It will be appreciated that this matching of the pitches of the first and second patterned regions 31, 32 in the shearing direction takes into account any reduction factor applied by the projection system PS. As used herein, the pitch of a two-dimensional diffraction grating in a particular direction is defined as follows.[000126] It will be appreciated that a one-dimensional diffraction grating comprises a series of lines that are formed from a repeating pattern (of reflectivity or transmissivity) in a direction perpendicular to these lines. In the direction perpendicular to the lines, the smallest non-repeating section from which the repeating pattern is formed is referred to as the unit cell and the length of this unit cell is referred to as the pitch of the one-dimensional diffraction grating. In general, such a one -dimensional diffraction grating will have a diffraction pattern such that an incident radiation beam will be diffracted so as to form a one-dimensional array of angularly spaced (but potentially spatially overlapping) diffraction beams. The first patterned region 31 forms such a one-dimensional array of angularly spaced first diffraction beams 34-36, which are offset (angularly spaced) in the shearing direction.[000127] It will be appreciated that a two-dimensional diffraction grating comprises a two- dimensional repeating pattern of reflectivity or transmissivity. The smallest non-repeating section from which this repeating pattern is formed may be referred to as the unit cell. The unit cell may be square and a fundamental pitch of such a two-dimensional diffraction grating may be defined as a length of the square unit cell. In general, such a two-dimensional diffraction grating will have a diffraction pattern such that an incident radiation beam will be diffracted so as to form a two-dimensional array of, angularly spaced (but potentially spatially overlapping) diffraction beams. The axes of this two- dimensional (square) array of diffraction beams are parallel to the sides of the unit cell. The angular separation between adjacent diffraction beams in these two directions may be given by the ratio of the wavelength of the radiation to the pitch of the grating. Therefore, the smaller the pitch, the larger the angular separation between the adjacent diffraction beams.[000128] In some embodiments, the axes of the unit cell of the two-dimensional second patterned region 32 may be arranged at a non-zero angle to the shearing and non-shearing directions as defined by the first patterned region 31. For example, the axes of the unit cell of the two-dimensional second patterned region 32 may be arranged at 45° to the shearing and non-shearing directions as defined bythe first patterned region 31. As previously explained, spatial overlapping and spatial coherence of the second diffraction beams at radiation detector 23 which allows the wavefront to be measured is achieved by ensuring that that the angular separation (in the shearing direction) between different second diffraction beams that originate from a given first diffraction beam is the same as the angular separation (in the shearing direction) between different first diffraction beams as they converge on the second patterned region 32. For an arrangement wherein the axes of the unit cell of the two-dimensional second patterned region 32 are arranged at a non-zero angle (for example 45°) to the shearing and non-shearing directions, it can be useful to define a pseudo-unit cell and a pseudo-pitch as follows. The pseudo-unit cell is defined as the smallest non-repeating square from which the repeating pattern of the diffraction grating is formed, which is orientated such that its sides are parallel to the shearing and non-shearing directions (as defined by the first patterned region 31. The pseudo-pitch may be defined as a length of the square pseudo-unit cell. This may be referred to as the pitch of a two-dimensional diffraction grating in the shearing direction. It is this pseudo-pitch which should be matched to (an integer multiple or fraction of) the pitch of the first patterned region 31.[000129] The diffraction pattern of the diffraction grating may be considered to form a two- dimensional array of angularly spaced (but potentially spatially overlapping) pseudo-diffraction beams, the axes of this two-dimensional (square) array of pseudo-diffraction beams being parallel to the sides of the pseudo-unit cell. Since this square is not the unit cell (defined as to the smallest square of any orientation from which the repeating pattern of the diffraction grating is formed), the pseudo-pitch will be larger than the pitch (or fundamental pitch). Therefore, there will a smaller separation between adjacent pseudo-diffraction beams in the diffraction pattern (in a direction parallel to the sides of the pseudo-unit cell) than there is between adjacent diffraction beams in the diffraction pattern (in a direction parallel to the sides of the unit cell). This can be understood as follows. Some of the pseudodiffraction beams correspond to diffraction beams in the diffraction pattern and the other pseudodiffraction beams are unphysical and do not represent a diffraction beam generated by the diffraction grating (and only arise due to the use of a pseudo-unit cell that is larger than the true unit cell).[000130] Taking any reduction (or enlargement) factor applied by the projection system PS into account, either the pitch of the second patterned region 32 in the shearing direction should be an integer multiple of the pitch of the first patterned region 31 in the shearing direction or the pitch of the first patterned region 31 in the shearing direction should be an integer multiple of the pitch of the second patterned region 32 in the shearing direction. In the example shown in Figures 5A-5C, the pitches of the first and second patterned regions 31, 32 in the shearing direction are substantially equal (taking into account any reduction factor).[000131] As can be seen from Figures 5A-5C, each point on the detector region 39 of the radiation detector 23 will, in general, receive several contributions that are summed coherently. For example, the point on the detector region 39 which receives the second diffraction beam 35b that corresponds to the -1storder diffraction beam of second patterned region 32, which originates from the 0thorderdiffraction beam 35 of first patterned region 31 overlaps with both: (a) the second diffraction beam 36a that corresponds to the 0thorder diffraction beam of second patterned region 32, which originates from the -1storder diffraction beam 36 of first patterned region 31; and (b) the second diffraction beam 34d that corresponds to the -2ndorder diffraction beam of second patterned region 32, which originates from the +lstorder diffraction beam 34 of first patterned region 31. It will be appreciated that when higher order diffraction beams of the first patterned region 31 are taken into account there will be more beams that should be summed coherently at each point on the detector region 39 in order to determine the intensity of radiation as measured by that part of the detector region 39 (for example a corresponding pixel in a two-dimensional array of sensing elements).[000132] In general, a plurality of different second diffraction beams contribute to the radiation received by each part of the detector region 39. The intensity of radiation from such a coherent sum is given by:I = DC + Spairs {i] Yi cosCAc ), (2) where DC is a constant term (which is equivalent to the incoherent sum of the different diffraction beams), the sum is over all pairs of different second diffraction beams, y,- is an interference strength for that pair of second diffraction beams and Acfy is a phase difference between that pair of second diffraction beams.[000133] The phase difference A<[>;between a pair of second diffraction beams is dependent on two contributions: (a) a first contribution relates to the different part of the pupil plane 37 of the projection system PS from which they originate; and (b) a second contribution relates to the position within the unit cells of each of the first and second patterned regions 31, 32 from which they originate.[000134] The first of these contributions can be understood to arise from the fact that the different coherent radiation beams have passed through different parts of the projection system PS and are therefore related to the aberrations that it is desired to determine (in fact they are related to a difference between two points in the aberration map that are separated in the shearing direction).[000135] The second of these contributions can be understood to arise from the fact that the relative phases of multiple rays of radiation that arise from a single ray incident on a diffraction grating will depend on which part of the unit cell of that grating the ray was incident. This therefore does not contain information relating to the aberrations. As explained above, in some embodiments, the measurement patterning device MA’ and / or the sensor apparatus 21 are sequentially scanned and / or stepped in the shearing direction. This causes the phase differences between all of pairs of interfering radiation beams received by the radiation detector 23 to change. As the measurement patterning device MA’ and / or the sensor apparatus 21 are sequentially stepped in the shearing direction by an amount that is equivalent to a fraction of the pitches (in the shearing direction) of the first and second patterned regions 31, 32,in general, the phase differences between pairs of second diffraction beams will all change. If the measurement patterning device MA’ and / or the sensor apparatus 21 are stepped in the shearing direction by an amount that is equivalent to an integer multiple of the pitches (in the shearing direction) of the first and second patterned regions 31, 32 the phase differences between pairs of second diffraction beams will remain the same. Therefore, as the measurement patterning device MA’ and / or the sensor apparatus 21 are by sequentially scanned and / or stepped in the shearing direction, the intensity received by each part of the radiation detector 23 will oscillate. The first harmonic of this oscillating signal (which may be referred to as a phase-stepping signal), as measured by the radiation detector 23, is dependent on the contributions to equation (1) that arise from adjacent first diffraction beams 34-36, i.e., first diffraction beams that differ in order by ±1. Contributions that arise from first diffraction beams that differ in order by a different amount will contribute to higher order harmonics of the signal determined by the radiation detector 23 due to such phase stepping techniques.[000136] For example, of the three overlapping second diffraction beams discussed above (35b, 36a and 34d) only two of the three possible pairs of these diffraction beams will contribute to the first harmonic of the phase stepping signal: (a) second diffraction beams 35b and 36a (which originate from the 0thorder diffraction beam 35 and the -1storder diffraction beam 36 of first patterned region 31 respectively); and (b) second diffraction beams 35a and 34d (which originate from the 0thorder diffraction beam 35 and the + 1storder diffraction beam 34 of first patterned region 31 respectively).[000137] Each pair of second diffraction beams will result in an interference term of the form shown in equation (2), which contributes to the first harmonic of the phase stepping signal, i.e., an interference term of the form:2TT y cos( - v + AW) (3) where y is an amplitude of the interference term, p is the pitch of the first and second patterned regions 31 , 32 (in the shearing direction), v parameterizes the relative positions of the first and second patterned regions 31, 32 in the shearing direction and AW is a difference between the value of the aberration map at two positions in the pupil plane of the projection system PS, the two positions corresponding to the positions from which the two second diffraction beams originate. The amplitude y of the interference term is proportional to the product of the compound scattering efficiencies of the two second diffraction beams, as discussed further below. The frequency of the first harmonic of the phase stepping signal is given by the inverse of the pitch p of the first and second patterned regions 31, 32 in the shearing direction. The phase of the phase stepping signal is given by AW (the difference between the values of the aberration map at two positions in the pupil plane of the projection system PS, the two positions corresponding to the positions from which the two second diffraction beams originate).[000138] The interference strength for a pair of second diffraction beams is proportional to the product of the compound scattering efficiencies of the two second diffraction beams, as now discussed. [000139] In general, the scattering efficiency of the diffraction beams produced by a diffraction grating will depend on the geometry of the grating. These diffraction efficiencies, which may be normalised to the efficiency of a 0thorder diffraction beam, describe the relative intensities of the diffraction beams. As used herein, the compound scattering efficiency of a second diffraction beam is given by the product of the scattering efficiency of the first diffraction beam from which it originates and the scattering efficiency for the diffraction order of the second patterned region 32 to which it corresponds.[000140] In the above description of the embodiments shown in Figures 3A to 5C, where the first portion 15a’ of the patterned region 15a shown in Figure 3 A is illuminated, the shearing direction corresponds to the v-direction and the non-shearing direction corresponds to the u-direction. It will be appreciated that when the second portion 15a” of the patterned region 15a shown in Figure 3A is illuminated, the shearing direction corresponds to the u-direction and the non-shearing direction corresponds to the v-direction. Although in these above-described embodiments, the u and v-directions (which define the two shearing directions) are both aligned at approximately 45° relative to both the x and y-directions of the lithographic apparatus LA, it will be appreciated that in alternative embodiments the two shearing directions may be arranged at any angle to the x and y-directions of the lithographic apparatus LA (which may correspond to non-scanning and scanning directions of the lithographic apparatus LA). In general, the two shearing directions will be perpendicular to each other. In the following, the two shearing directions will be referred to as the x-direction and the y-direction. However, it will be appreciated that these shearing directions may be arranged at any angle relative to both the x and y-directions of the lithographic apparatus LA.[000141] Figure 6A shows the scattering efficiency for a first patterned region 31 that is of the form of the first portion 15a’ of the patterned region 15a shown in Figure 3A, having a 50% duty cycle. The horizontal axis represents the diffraction order in the shearing direction. The diffraction efficiencies shown in Figure 6A are normalised to the efficiency of a 0thorder diffraction beam, such that the efficiency of the 0thorder diffraction beam is 100%. With this geometry (a 50% duty cycle), the efficiencies of the even diffraction orders (except the 0thdiffraction order) are zero. The efficiencies of the ±lstorder diffraction beams are 63.7%.[000142] Figure 6B shows the scattering efficiency for a second patterned region 32 that is of the form of the diffraction grating 19a shown in Figure 3B, i.e., in the form of a checkerboard with a 50% duty cycle. The horizontal axis represents the diffraction order in the shearing direction. The vertical axis represents the diffraction order in the non-shearing direction. The diffraction efficiencies shown in Figure 6B are normalised to the efficiency of the (0, 0)thorder diffraction beam, such that the efficiency of the (0, 0)thorder diffraction beam is 100%.[000143] As explained above, the first harmonic of the oscillating phase-stepping signal only depends on the contributions to equation (1) from first diffraction beams that differ in order by ±1. As can be seen from Figure 6A, with a 50% duty cycle grating on the measurement patterning device MA’ , the only two pairs of first diffraction beams that differ in order by +1 are the 0thorder beam with either of the ±lstorder beams. Furthermore, with this geometry for the first patterned region 31, the scattering efficiencies are symmetric such that the efficiencies of the +lstorder diffraction beams are both the same (63.7%). Therefore, the interference strengths yLfor all pairs of second diffraction beams that contribute to the first harmonic of the oscillating phase-stepping signal can be determined as follows. A second copy of the scattering efficiency plot for the second patterned region 32 shown in Figure 6B is weighted by the scattering efficiency for the +ls1order diffraction beams of the first patterned region 31 and then overlaid with the scattering efficiency plot for the second patterned region 32 shown in Figure 6B but shifted in the shearing direction by the separation of 1 pair of diffraction orders (of the first patterned region 31). Here, the pitches of the first and second patterned regions 31, 32 in the shearing direction are equal (taking into account any reduction factor applied by the projection system PS) and therefore, in this example, the second copy of the scattering efficiency plot for the second patterned region 32 is shifted in the shearing direction by 1 diffraction order of the second patterned region 31. The product of the scattering efficiencies of these two overlaid scattering efficiencies plots is then determined. Such a plot of the interference strengths ytfor all pairs of second diffraction beams that contribute to the first harmonic of the oscillating phase-stepping signal is shown in Figure 6C.[000144] Note that each of the interference strengths shown in Figure 6C actually represents two different pairs of second diffraction beams. For example, the left-hand pixel shown in Figure 6C represents both: (a) interference between second diffraction beams 35a and 34b and (b) second diffraction beam 35b and 36a. Similarly, the right-hand pixel shown in Figure 6C represents both: (a) interference between second diffraction beam 35a and 36c and (b) second diffraction beam 35c and 34a. In general, each pixel of such a map represents two pairs of second diffraction beams: (a) a first pair of second diffraction beams that include one second diffraction beam that originated from the first diffraction beam 35 corresponding to the 0thdiffraction order of first patterning device 31 and another second diffraction beam that originated from the first diffraction beam 34 corresponding to the +lstorder diffraction order of first patterned region 31; and (b) a second pair of second diffraction beams that include one second diffraction beam that originated from the first diffraction beam 35 corresponding to the 0thdiffraction order of first patterning device 31 and another second diffraction beam that originated from the first diffraction beam 36 corresponding to the -1storder diffraction order of first patterned region 31.[000145] In general, each of the interference strengths ytshown in Figure 6C represents two different pairs of second diffraction beams: (a) one pair comprising an n,horder second diffraction beam produced by the first diffraction beam 35 (that corresponds to the 0thorder diffraction beam of first patterned region 31); and (b) another pair comprising an (n+l)thorder second diffraction beam produced by thefirst diffraction beam 35. Therefore, each interference strength Yt may be characterized by the two diffraction orders of the first diffraction beam 35 ((n, m)thand (n+1, m)th) that contribute, and may be denoted as yn ra+i;m. In the following, where it is clear that m=0, or the value of m is unimportant, this interference strength may be denoted as yn,n+i-[000146] Although each of the interference strengths yt(or ynin+i;m shown in Figure 6C represents two different pairs of second diffraction beams, each of the interference strengths ytshown in Figure 6C represents the second diffraction beams which contribute to the first harmonic of the oscillating phase- stepping signal and which have a different overlap, at the radiation detector 23, with a circle that represents the numerical aperture of the projection system PS, as now described.[000147] Figures 7A, 7B and 7C show the portion of the pupil plane 37 of the projection system PS which corresponds to the numerical aperture of the projection system PS that is filled by first diffraction beams 34, 35, 36 respectively. In each of Figures 7A, 7B and 7C the numerical aperture of the projection system PS is represented by a circle 40 and the portion of the pupil plane 37 of the projection system PS that is filled by first diffraction beams 34, 35, 36 is shown by a shaded region of this circle 40 in Figures 7A, 7B and 7C respectively. As can be seen from Figure 7B, in the example shown, the central first diffraction beam 35 which corresponds to a 0thorder diffraction beam substantially fills the numerical aperture of the projection system PS. As can be seen from Figure 7A and 7C, each of the two first diffraction beams 34, 36 which correspond to the ±lstorder diffraction beams of first patterned region 31 have been shifted such that they only partially fill the numerical aperture. It will be appreciated that this shift of the first order first diffraction beams 34, 36 relative to the numerical aperture is in practice very small and has been exaggerated here for ease of understanding.[000148] Figures 8 A- 10C show the portion of the radiation detector 23 that is filled by various second diffraction beams. In each of Figures 8A-10C the numerical aperture of the projection system PS is represented by a circle 40 and the portion of this circle that is filled by the second diffraction beams is shown by a shaded region of this circle 40. Figures 8A-8C show the portion of the circle 40 that is filled by (-1, 0)*, (0, 0)thand (1, 0)thorder diffraction beams 35b, 35a, 35c which originate from the first diffraction beam 35 which corresponds to a 0thorder diffraction beam of the first patterned region 31. Figures 9A-9C show the portion of the circle 40 that is filled by (-1, 0)th, (0, 0)thand (1, 0)thorder diffraction beams 34b, 34a, 34c which originate from the first diffraction beam 34 which corresponds to the 1storder diffraction beam of the first patterned region 31. Figures 10A-10C show the portion of the circle 40 that is filled by (-1, 0)th, (0, 0)thand (1, 0)thorder diffraction beams 36b, 36a, 36c which originate from the first diffraction beam 36 which corresponds to the -1storder diffraction beam of the first patterned region 31.[000149] It can be seen from Figures 8B, 9A, 8A and 10B that the region of the radiation detector which receives a contribution from both: (a) interference between second diffraction beams 35a and 34b and (b) second diffraction beam 35b and 36a is the region 41 shown in Figure 11 A. Similarly, itcan be seen from Figures 8B, IOC, 8C and 9B that the region of the radiation detector which receives a contribution from both: (a) interference between second diffraction beam 35a and 36c and (b) second diffraction beam 35c and 34a is the region 42 shown in Figure 11B.[000150] In general, each of the interference strengths Yt shown in Figure 6C may be considered to represent a beam of radiation formed by a plurality of interfering second interference beams, each such beam of radiation formed by a plurality of interfering second interference beams propagating in a different direction, such that the overlap of each such beam of radiation at the radiation detector 23, with a circle that represents the numerical aperture of the projection system PS is different.[000151] In general, the second diffraction beams can be considered to form a plurality of beams of radiation, each such beam of radiation being formed by a set of interfering second diffraction beams. Each such beam of radiation may be referred to herein as an interference beam. Each such interference beam formed by a plurality of interfering second interference beams may be considered to propagate in a different direction, such that the overlap of each interference beam at the radiation detector 23 with a circle that represents the numerical aperture of the projection system PS is different. Although they may be considered to propagate in different directions and have a different overlap with a circle that represents the numerical aperture of the projection system PS, there is significant overlap between the different interference beams at the radiation detector 23. Each of the interference strengths shown in Figure 6C may be considered to represent a different interference beam (formed by a plurality of interfering second interference beams).[000152] As previously described, each of the interference strengths (or yn,n+i;m) shown in Figure 6C represents two different pairs of second diffraction beams. However, for a given position on the radiation detector, both of these pairs of contributing second diffraction beams comprise two interfering rays that originate from the same two points in the pupil plane 37 of the projection system PS. In particular, for a position (x, y) on the radiation detector (these co-ordinates corresponding to coordinates of the pupil plane 37 of the projection system PS and the x direction corresponding to the shearing direction), the two pairs of interfering second diffraction beams that contribute and have an interference strengths yra n+1;meach comprise a ray of a second diffraction beam that originated from a position (x-ns, y-ms) in the pupil plane 37 and a ray of a second diffraction beam that originated from a position (x-(n+l)s, y-ms) in the pupil plane 37, where s is a shearing distance. The shearing distance s corresponds to the distance in the pupil plane 37 between two coherent rays of adjacent first diffraction beams 34-36. Therefore, both pairs of contributing second diffraction beams give rise to an interference term of the form of expression (3), where AW is a difference between the value of the aberration map at these two positions in the pupil plane 37.[000153] It can be seen from Figure 6C that with a second patterned region 32 which is of the form of a 50% duty cycle checkerboard there are only two sets of second diffraction beams that contribute to the first harmonic of the phase stepping signal, both with an interference strength W-i o, y0,+i ) °f25.8%. This is due to the checkerboard geometry, which, as can be seen in from Figure 6A, results in a diffraction efficiency plot where, with the exception of the (-1, 0)th, (0, 0)thand (1, 0)thorder diffraction beams, moving in the shearing direction, every other diffraction beam has a diffraction efficiency of 0%. That is, the grating efficiencies of the (n, m)thdiffraction orders wherein n+m is an even number are all zero, except the (0, 0)thdiffraction order. As a result of these grating efficiencies being zero, all of the interference strengths which contribute to the first harmonic of the phase stepping signal are zero except for interference strengths y_1 0and y0>+1.[000154] The portion of the radiation detector 23 that corresponds to the numerical aperture of the projection system PS (represented by circle 40 in Figures 7A to 1 IB) may be considered to comprise three sections, each distinguished by the interference beams that contribute to the first harmonic of the oscillating phase- stepping signal in these sections. These three sections may be considered to be: a first crescent moon-shaped section to which only the interference beam with interference strength y_1 0contributes; a second crescent moon-shaped section to which only the interference beam with interference strength yg,+i contributes; and central portion to which both of these interference beams contribute. The first crescent moon-shaped section is the white portion shown in Figure 1 IB; the second crescent moon-shaped section is the white portion shown in Figure 11 A; and the central portion is the overlap between the two regions 41, 42. The central portion, which is the overlap between the two regions 41, 42, may be referred to as the three-beam region of the radiation detector 23.[000155] For the overlap between the two regions 41, 42 shown in Figures 11 A and 1 IB (this overlap region will form the majority of circle 40 for small shearing angles) the first harmonic of the oscillating phase- stepping signal will be proportional to the sum of two cosines (cf. equation (2) and expression (3)): = DC + y_1;0cos(PV_1- ) + y0,+1cos(lT(1-+1) (4) where the first cosine is of a difference in the aberration map between a first two points in the pupil plane and the second cosine is of a difference in the aberration map between a second two points in the pupil plane (here the phase stepping terms have been omitted for clarity of understanding). In particular, for a given position (x, y) on the radiation detector (x referring to the shearing direction), the first two points include a corresponding point in the pupil plane (x, y) (represented as Woin equation (4)) and another point which is shifted in a first direction along the shearing direction by the shearing distance (x-s, y) (represented as IV_1in equation (4)). Similarly, the second two points include a corresponding point in the pupil plane (x, y) (represented as 1VOin equation (4)) and another point which is shifted in a second direction along the shearing direction by the shearing distance (x+s, y) (represented as W+1in equation (4)).[000156] Existing wavefront reconstruction techniques exploit the fact that the two interference strengths in equation (4) are equal such that this sum of two cosines can be re-written using trigonometric identities as a cosine of half the difference in the aberration map between two positions that are separated in the shearing direction by twice the shearing distance, i.e. cosf-^ CU j — W+1)), multiplied by a factor that is approximately 1 for small shearing distances. Therefore, such known techniques involve the determination of a set of Zernike coefficients by equating the phase of the first harmonic of a phase stepping signal (within the overlap between the two regions 41 , 42) to half of the difference in the aberration map between positions in the pupil plane that are separated in the shearing direction by twice the shearing distance. Optionally, in the first and second crescent moon-shaped sections the phase of the first harmonic of a phase stepping signal may be equated to the difference in the aberration map between positions in the pupil plane that are separated in the shearing direction by the shearing distance. However, as noted above, since the overlap between the two regions 41, 42 shown in Figures 11A and 11B forms the majority of circle 40 for small shearing angles, some existing reconstruction algorithms only use the overlap between the two regions 41, 42 (and does not use the first and second crescent moon-shaped sections of the radiation detector 23). Recall that the aberration map depends on the Zernike coefficients (see equation (1)). This is done for a plurality of positions on the radiation sensor (for example at a plurality of pixels or individual sensing elements in an array) first for a first shearing direction and then subsequently for a second, orthogonal direction. These constraints for the two shearing orthogonal directions are simultaneously solved to find the set of Zernike coefficients.[000157] As discussed above, the combination of a first patterned region 31 comprising a linear grating and a second patterned region 32 comprising a two-dimensional checkerboard is advantageous (since only two interference beams contribute to the first harmonic of the phase stepping signal). Due to the geometry of the checkerboard, checkerboard gratings typically comprise an optical transmissive carrier or support layer. However, EUV radiation is strongly absorbed by most materials and therefore no good transmissive materials exist for EUV radiation. Furthermore, such a transmissive carrier is not favourable in a wafer production environment of an EUV lithographic system, since the transmissive carrier will rapidly become contaminated in such an environment. This would render the transmissive carrier non-transmissive for EUV. Such contamination problems which could only be addressed by regular cleaning actions that would impact system availability and therefore the throughput of the lithographic system. For the above-mentioned reasons a checkerboard grating arrangement is difficult to implement for lithographic systems that use EUV radiation.[000158] For this reason, existing aberration measurement systems for EUV radiation use, as a second patterned device 32, a geometry which uses an array of circular pinholes. Figure 12 shows the unit cell 50 of such a grating, having a 50% (by area) duty cycle. The unit cell 50 comprises a circular aperture 51 provided in an EUV absorbing membrane 52. The circular aperture 51 is a through aperturewhich represents a void in the EUV absorbing membrane 52 through which EUV radiation is transmitted. In order to achieve a 50% (by area) duty cycle, the ratio of the radius r of the aperture 51 to the pitch p of the grating (i.e., the distance between the centres of adjacent apertures) is given by:which is approximately 0.4. However, such a pinhole array geometry (as shown in Figure 12) generates unwanted interference beams that contribute to the first harmonic of the phase stepping signal, as now discussed with reference to Figures 13A-13B.[000159] Figure 13A shows the scattering efficiency for a first patterned region 31 that is of the form of the first portion 15a’ of the patterned region 15a shown in Figure 3A, having a 50% duty cycle (of the same geometry as that shown in Figure 6A). Again, the diffraction efficiencies are normalised to the efficiency of a 0thorder diffraction beam, such that the efficiency of the 0thorder diffraction beam is 100%. Figure 13B shows the scattering efficiency for a second patterned region 32 that is of the form of a pinhole array having the unit cell 50 shown in Figure 12. The diffraction efficiencies shown in Figure 13B are normalised to the efficiency of the (0, 0)thorder diffraction beam, such that the efficiency of the (0, 0)thorder diffraction beam is 100%.[000160] Figure 13C is a plot of the interference strengths yn n+1for interference beams that contribute to the first harmonic of the oscillating phase- stepping signal (this is constructed from the scattering efficiencies of Figures 13A and 13B in an analogous manner to the construction of Figure 6C from the scattering efficiencies of Figures 6A and 6B).[000161] It can be seen from Figure 13C that with a second patterned region 32 which has the unit cell 50 shown in Figure 12, in addition to the two main interference beams (with interference strengths y_1 0, Fo,+i °f 25.2%), there are a number of additional interference beams with small, but non-zero, interference strengths yn n+1. Furthermore, each of the interference beams has a different overlap at the radiation detector 23 with the circular portion of the radiation detector 23 that corresponds to the numerical aperture of the projection system PS, as now discussed with reference to Figures 14A and 14B.[000162] Figure 14A is a representation of 21 second diffraction beams generated by a second patterned region 32 having a unit cell 50 as shown in Figure 12. In particular, these may be considered to be the second diffraction beams generated by such a second patterned region 32 and originating from the 0thorder first diffraction beam 35. Figure 14A shows the diffraction efficiencies of these second diffraction beams and these correspond to the diffraction efficiencies contained within the dotted line in Figure 13B. Actually, the dotted line in Figure 13B corresponds to 25 second diffraction beams, however, the diffraction efficiencies for 4 of these are negligible and therefore they have not beenincluded on Figure 14A. In addition, in Figure 14A a dashed circular line indicates a region on the radiation detector 23 which corresponds to the numerical aperture of the projection system PS.[000163] Figure 14B is a representation of 16 interference beams, each generated by the interference of pairs of the second diffraction beams shown in Figure 14A with second diffraction beams generated by this second patterned region 32 and originating from the ±lstorder first diffraction beams 34, 36. Figure 14B shows the interference strengths of these interference beams and these correspond to the interference strengths contained within the dotted line in Figure 13C. Again, the dotted line in Figure 13C actually corresponds to 20 different second diffraction beams, however, the interference strengths for 4 of these are negligible and therefore they have not been included on Figure 14B. In addition, in Figure 14B a dashed circular line indicates a region on the radiation detector 23 which corresponds to the numerical aperture of the projection system PS.[000164] It can be seen from Figures 13C and 14B that with a second patterned region 32 which has the unit cell 50 shown in Figure 12, in addition to the two main interference beams (with interference strengths y_lj0, Ko,+i °f 25.2%), there are a number of additional interference beams with small, but non-zero, interference strengths Yn / n+1- Since the interference strengths for these additional interference beams are not the same, for regions of the radiation detector 23 where multiple interference beams overlap, the first harmonic of the oscillating phase-stepping signal will be proportional to a weighted sum of a plurality of cosines (cf. equation (4)), the cosines having different weights. As a result, they cannot be combined easily using trigonometric identities. However, since the interference strengths yn / Tl+1for the additional interference beams are small (in comparison to the interference strengths0, Ko,+i),someknown existing aberration measurement systems for EUV radiation neglect these terms (i.e., assume they are zero) in the reconstruction of the wavefront to find the set of Zernike coefficients.[000165] This assumption impacts the accuracy of the wavefront measurement. In turn, this has a negative impact on system imaging, overlay and focus performance. Embodiments of the present invention have been devised to at least partially address the above-described problems for aberration measurement systems for EUV radiation.[000166] Embodiments of the present invention relate to new solutions that are proposed to address the problems caused by the presence of additional interference beams (in addition to the two main interference beams that have interference strengths y_li0, Ko,+i)- Inparticular, some embodiments of the present invention relate to new and alternative two-dimensional diffraction gratings for use as the second patterned region 32. Some embodiments of the present disclosure relate to a new measurement system for determining an aberration map for a projection system PS that is generally of the form of the measurement system 12 shown in Figure 2 or the measurement system 30 shown in Figure 4 and described above.[000167] That is, the new measurement system comprises: a first patterning device 15a, 15b, 15c, 31; a second patterning device 19a, 19b, 19c, 32; a radiation detector 23; and a positioning apparatus. The first patterning device 15a, 15b, 15c, 31 is positionable in an object plane of the projection system PS. The second patterning device 19a, 19b, 19c, 32 is positionable in an image plane of the projection system PS. The radiation detector 23 is arranged to receive radiation 17 , 17b, 17c, 38 from the second patterning device 19a, 19b, 19c, 32. The positioning apparatus is operable to move at least one of the first and second patterning devices 15a, 15b, 15c, 31, 19a, 19b, 19c, 32 in a shearing direction.[000168] In contrast to the arrangements described above, the second patterning device 19a, 19b, 19c, 32 of the new measurement system has a variable pitch. In particular, the second patterning device 19a, 19b, 19c, 32 is such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device is non-uniform. This is explained further below with reference to Figures 15A and 15B.[000169] The pitches of the first and second patterning devices 15a, 15b, 15c, 31, 19a, 19b, 19c, 32 are matched such that an angular separation between the zeroth order diffraction beam 35 and the first order diffraction beams 34, 36 of the first patterning device 15a, 15b, 15c, 31 is generally matched to an angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 19a, 19b, 19c, 32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 15a, 15b, 15c, 31 , taking into account any reduction or magnification factor applied by the projection system PS. That is, an angular separation between the zeroth order diffraction beam 35 and the first order diffraction beams 34, 36 of the first patterning device 15a, 15b, 15c, 31 is generally matched to: (a) an angular separation between the zeroth order diffraction beam 35a and the first order diffraction beams 35b, 35c of the second patterning device 19a, 19b, 19c, 32 that originate from the zeroth order diffraction beam 35 of the first patterning device 15a, 15b, 15c, 31; (b) an angular separation between the zeroth order diffraction beam 34a and the first order diffraction beams 34b, 34c of the second patterning device 19a, 19b, 19c, 32 that originate from the +lstorder diffraction beam 34 of the first patterning device 15a, 15b, 15c, 31; (c) and an angular separation between the zeroth order diffraction beam 36a and the first order diffraction beams 36b, 36c of the second patterning device 19a, 19b, 19c, 32 that originate from the -1storder diffraction beam 36 of the first patterning device 15a, 15b, 15c, 31.[000170] How the pitches of the first and second patterning devices 15a, 15b, 15c, 31, 19a, 19b, 19c, 32 are matched will be discussed further below with reference to Figures 18A and 18B.[000171] Furthermore, the variable pitch of the second patterning device 19a, 19b, 19c, 32 is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device 19a, 19b, 19c, 32 are not matched to an angular separation between the zeroth order diffraction beam 35 and the first order diffraction beams 34, 36 of the first patterning device 15a, 15b, 15c, 31, taking into account any reduction or magnification factor applied by the projection system PS. Another consequence of the variable pitch of the second patterning device 19a, 19b, 19c, 32 is that anintensity of higher order diffraction beams is reduced, as will be discussed further below with reference to Figures 18A and 18B.[000172] Figure 15A is a schematic representation of a set of second diffraction beams produced by a second patterning device 32 that has a uniform pitch from each of the first diffraction beams 34-36 (shown in Figure 4 and described above). Figure 15A is equivalent to a combination of Figures 5A to 5C shown above.[000173] Figure 15A shows: a set of second diffraction beams 35a-35e produced by the first diffraction beam 35 that corresponds to the 0thorder diffraction beam of first patterned region 31 (cf. Figure 5A); a set of second diffraction beams 36a-36e produced by the first diffraction beam 36 that corresponds to the -1storder diffraction beam of first patterned region 31 (cf. Figure 5B); and a set of second diffraction beams 34a-34e produced by the first diffraction beam 34 that corresponds to the + 1aorder diffraction beam of first patterned region 31 (cf. Figure 5C). Figure 15A shows a spatial distribution of (for example a chief ray of) the second diffraction beams 34a-34e, 35a-35e, 36a-36e displayed as follows. The second diffraction beams from the same diffraction beam of first patterned region 31 are shown in a line, separated from each other in a shearing direction. Second diffraction beams from the different diffraction beams of first patterned region 31 are offset in a direction perpendicular to the shearing direction such that they are shown in different lines. It will be appreciated that this offset is merely for ease of understanding since, otherwise, several of the second diffraction beams would overlap each other. In reality, all of these second diffraction beams 34a-34e, 35a-35e, 36a-36e should be at the same position in the non-scanning direction.[000174] Since Figure 15A corresponds to an arrangement with a second patterning device 32 having a uniform pitch, the angular separation between adjacent pairs of diffraction beams formed by the second patterning device 32 is uniform. As a result, in the spatial distribution of the second diffraction beams 34a-34e, 35a-35e, 36a-36e there is a uniform distance 60 between adjacent pairs of diffraction beams.[000175] Figure 15B is a schematic representation of a set of second diffraction beams produced by a second patterning device 32 that has a non-uniform pitch from each of the first diffraction beams 34- 36 (shown in Figure 4 and described above). Since Figure 15B corresponds to an arrangement with a second patterning device 32 having a non-uniform pitch, the angular separation between adjacent pairs of diffraction beams formed by the second patterning device 32 that originate from the same first diffraction beam 34-36 is non-uniform. As a result, in the spatial distribution of the second diffraction beams 34a-34e, 35a-35e, 36a-36e there is a non-uniform distance between adjacent pairs of diffraction beams.[000176] There is a distance 62 between a second diffraction beam 35a that corresponds to the 0thorder diffraction beam which originates from the 0thorder diffraction beam 35 and a second diffraction beam 35b, 35c that corresponds to the ±lstorder diffraction beams which originate from the 0thorder diffraction beam 35. Similarly, there is a distance 64 between a second diffraction beam 35b, 35c thatcorresponds to the +lstorder diffraction beam which originate from the 0thorder diffraction beam 35, and a second diffraction beam 35d, 35e that corresponds to the ±2“* order diffraction beams which originate from the 0thorder diffraction beam 35. Similarly, there is a distance 66 between a second diffraction beam 35d, 35e that corresponds to the ±2ndorder diffraction beam which originate from the 0thorder diffraction beam 35, and a second diffraction beam that corresponds to the ±3rdorder diffraction beams which originate from the 0thorder diffraction beam 35.[000177] The distances 62, 64 and 66 are different, due to the non-uniform pitch of the second patterning device 32. In this embodiment, the spatial separation 62, 64, 66 between adjacent diffraction orders increases with increasing diffraction order.[000178] There is a distance 62 between a second diffraction beam 34a that corresponds to the 0thorder diffraction beam which originates from the +lstorder diffraction beam 34 and a second diffraction beam 34b, 34c that corresponds to the ±lstorder diffraction beams which originate from the +lstorder diffraction beam 34. Similarly, there is a distance 64 between a second diffraction beam 34b, 34c that corresponds to the ±lstorder diffraction beam which originate from the +lstorder diffraction beam 34, and a second diffraction beam 34d, 34e that corresponds to the +2ndorder diffraction beams which originate from the +lstorder diffraction beam 34. Similarly, there is a distance 66 between a second diffraction beam 34d, 34e that corresponds to the ±2ndorder diffraction beam which originate from the +lstorder diffraction beam 34, and a second diffraction beam that corresponds to the ±3rdorder diffraction beams which originate from the +lstorder diffraction beam 34.[000179] There is a distance 62 between a second diffraction beam 36a that corresponds to the 0thorder diffraction beam which originates from the -1storder diffraction beam 36 and a second diffraction beam 36b, 36c that corresponds to the ±lstorder diffraction beams which originate from the -1storder diffraction beam 36. Similarly, there is a distance 64 between a second diffraction beam 36b, 36c that corresponds to the ±lstorder diffraction beam which originate from the -1storder diffraction beam 36, and a second diffraction beam 36d, 36e that corresponds to the ±2ndorder diffraction beams which originate from the -1storder diffraction beam 36. Similarly, there is a distance 66 between a second diffraction beam 36d, 36e that corresponds to the ±2ndorder diffraction beam which originate from the -1storder diffraction beam 36, and a second diffraction beam that corresponds to the ±3rdorder diffraction beams which originate from the -1storder diffraction beam 36.[000180] It can be seen from Figures 15A and 15B that, due to the non-uniform pitch of the second patterning device 32, in Figure 15B several of the second diffraction beams no longer spatially overlap with each other.[000181] It can be seen from Figure 15B that even with the second patterning device 32 having a non-uniform pitch, the pairs of second diffraction beams that contribute to the first interference beam (second diffraction beams 35a and 34b and second diffraction beam 35b and 36a) still spatially overlap. It can also be seen from Figure 15B that even with the second patterning device 32 having a non-uniform pitch, the pairs of second diffraction beams that contribute to the second interference beam (seconddiffraction beam 35a and 36c and second diffraction beam 35c and 34a) still spatially overlap. However, the spatial overlap between pairs of second diffraction beams that correspond to the other (unwanted) interference beams has been at least partially destroyed by the non-uniform pitch.[000182] The new measurement system having a second patterning device 19a, 19b, 19c, 32 with a variable pitch is advantageous, as now discussed.[000183] The new measurement system allows for the use of a pinhole array geometry for the wafer level patterning device 19a, 19b, 19c, 32 without generating unwanted interference beams that contribute to the first harmonic of the phase stepping signal. In particular, the large number of additional interference beams with small, but non-zero, intensities that are present when using a pinhole array with a uniform pitch are no longer present or, at least, have significantly reduced intensities. Note that this is due to both: (a) less spatial overlap between the second diffraction beams that contribute to the unwanted interference beams; and (b) a reduction in the intensity of the second diffraction beams that contribute to the unwanted interference beams.[000184] With the new measurement system, the pitches of the first and second patterning devices 31, 32 are matched such that an angular separation between the zeroth order diffraction beam 35 and first order diffraction beams 34, 36 of the first patterning device 31 is generally matched to an angular separation between the zeroth order diffraction beam 34a, 35a, 36a and first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device that originate from the same order diffraction beam of the first patterning device 31, taking into account any reduction or magnification factor applied by the projection system PS. As a result, the same two contributions to the first harmonic of the oscillating (phase-stepping) signal at the radiation detector are present as when a one-dimensional diffraction grating for the patterning device at reticle level with a duty cycle of 50% and a checkerboard grating for the patterning device at wafer level are used.[000185] Furthermore, the second patterning device 32 has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second device 31 is non-uniform. In addition, a variation of the variable pitch of the second patterning device 32 is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device that originate from a given diffraction order of the first patterning device 31 are not matched to an angular separation between the zeroth order diffraction beam 35 and the first order diffraction beams 34, 36 of the first patterning device 31 , taking into account any reduction or magnification factor applied by the projection system PS. Advantageously, as a result, additional contributions to the first harmonic of the oscillating (phase-stepping) signal at the radiation detector 23 are eliminated, or at least reduced. In particular, the overlap between unwanted diffraction beams that have a coherence relationship (and therefore could contribute to an interference pattern at the radiation detector) is disturbed.[000186] As explained above with reference to Figure 4, in use, the first patterning device 31 may be configured to receive a radiation beam 33 and to form a plurality of first diffraction beams 34, 35, 36. In use, the projection system PS may be configured to project first diffraction beams 34, 35, 36formed by the first patterning device 31 onto the second patterning device 32. In use, the second patterning device 32 may be configured to receive the first diffraction beams 34, 35, 36 from the projection system PS and to form a plurality of second diffraction beams from each of the first diffraction beams 34, 35, 36.[000187] Contributions of different diffraction orders of the first diffraction beams 34, 35, 36 will, in general, gain a different phase contribution from the projection system PS. As a result, each pixel of the radiation detector 23 does not receive a clean phase signal of a single path through the projection optics PS but rather a combination of paths surrounding the 0thorder first diffraction beam 35. This may be referred to as phase blurring.[000188] The accuracy of wavefront fitting in a measurement system 12, 30 is expected to strongly improve due to the variable pitch second patterning device 32 because the number of convolution orders, or interference beams, that contribute to the first harmonic of the phase stepping signal is strongly reduced. This will reduce the phase blurring at sensor level (i.e. at the radiation detector 23) and will ensure a better match with a wavefront fitting algorithm than is currently implemented. In turn, this will reduce the Zernike gain and / or crosstalk errors and may also reduce bias errors for such a measurement system 12, 30. It is possible to input a pure Zernike wavefront aberration map (for example Zn) into a reconstruction algorithm and to assess how the reconstruction algorithm reconstructs this as a linear combination of Zernike polynomials. Ideally, the reconstruction algorithm should output a set of Zernike coefficients cmsuch that cm= 1 for m = n and cm= 0 for m = n. Any variation of cnfrom 1 may be referred to as a gain error. Any variation of cmfrom 0 where mn may be referred to as a crosstalk error.[000189] In addition, the higher diffraction orders also show a reduction in diffraction intensity (see, for example Figures 17, 18A and 18B below). This is very useful because this will also limit the magnitude of contributions of the unwanted convolution orders, or interference beams, that contribute to the first harmonic of the phase stepping signal.[000190] The measured intensity signal at the radiation detector 23 is a convolution of the grating function of both the first patterning device 15a, 15b, 15c, 31 (at reticle level) and the second patterning device 19a, 19b, 19c, 32 (at wafer level). For example, if both reticle level and wafer level gratings are binary lines, the phase stepping signal would be generally pyramid-shaped. Similarly, a binary grating at the reticle level and a checkerboard grating at the wafer level would result in a more cosine-shaped phase stepping signal. In both of these two examples, with constant pitch reticle level and wafer level gratings, the measured phase stepping signals are repeated periodically with the same amplitude. However, for a variable pitch grating at wafer level (i.e., the second patterning device 19a, 19b, 19c, 32 having a variable pitch), the phase stepping signal is not repeated periodically. In addition, the amplitude of the phase stepping signal will decay as the local pitches of the reticle level and wafer level gratings becomes less well matched. In short, with a periodic grating at wafer level the measurement method cannot resolve alignments that are larger than the grating pitch due to the periodic phasestepping signal, since the amplitude of the phase stepping signal is the same for every period. In contrast, with a variable pitch grating at wafer level (i.e., the second patterning device 19a, 19b, 19c, 32 having a variable pitch), the amplitude of the phase stepping signal will have a bell-shaped envelope. From the max value of this bell-shaped envelope, one can determine the best alignment position of the reticle level marker (i.e., the first patterning device 15a, 15b, 15c, 31), even when a misalignment is larger the pitch of the reticle level marker. Therefore, it is expected that this type of grating / design concept (having a second patterning device 19a, 19b, 19c, 32 having a variable pitch) will solve unwanted period jumps that sometimes occur in such measurement systems 12, 30 (for example due to relative misalignment of the reticle level and wafer level gratings).[000191] The pitch of the second patterning device 32 may have an extremum value at a first position on the second patterning device 32 and the pitch of the second patterning device 32 may either increase or decrease as a function of distance from the first position.[000192] For example, the extremum may be a minimum and the pitch of the second patterning device 32 may increase as a function of distance from the first position. Alternatively, the extremum may be a maximum and the pitch of the second patterning device 32 may decrease as a function of distance from the first position.[000193] The first position may be, but is not necessarily, in the centre of the second patterning device.[000194] The pitch of the second patterning device 32 may vary linearly with distance from the first position. Alternatively, the pitch of the second patterning device 32 may vary non-linearly with distance from the first position. In general, the pitch of the second patterning device may be a monotonic function of distance from the first position.[000195] The pitch of the second patterning device 32 may vary by at least 2% over the second patterning device 32. In some embodiments, the pitch of the second patterning device 32 may vary by at least 3% over the second patterning device 32. In some embodiments, the pitch of the second patterning device 32 may vary by of the order of 4% or more.[000196] The second patterning device 32 may be a two-dimensional diffraction grating. The second patterning device 32 may be a transmissive grating. The second patterning device 32 may be a pinhole grating.[000197] The second patterning device 32 may comprise a substrate provided with a two- dimensional array of circular through-apertures.[000198] A distance between the centres of adjacent through- apertures may be referred to as the local pitch of the second patterning device 32.[000199] A duty cycle of the second patterning device 32 may also be variable. That is, for a pinhole grating, a ratio of the radius of the circular apertures to the distance between the centres of adjacent apertures may vary over the second patterning device 32. For example, the plurality of apertures mayall be of a fixed dimension and the variation in pitch (and duty cycle) may be achieved by varying a distance between the centres of adjacent apertures across the second patterning device.[000200] Typically, a diffraction grating 32 used as the wafer-level grating for a measurement system 12, 30 for determining an aberration map for a projection system PS of a lithographic apparatus LA comprises a plurality of apertures that are distributed such that a distance between the centres of adj acent apertures is uniform across the diffraction grating. This is achieved by arranging the apertures such that a centre of each of the circular through-apertures coincides with one of a square array of positions. In contrast, the second patterning device 32 according to embodiments of the present disclosure may be formed by arranging the apertures such that a distance between the centres of adjacent apertures varies across the second patterning device 32.[000201] The second patterning device 32 may comprise at least 10 unit cells across the or each dimension of a pattern of the second patterning device.[000202] The second patterning device 32 may comprise between around 3 and 100 unit cells across each dimension. For example, the second patterning device 32 may comprise of the order of 30 unit cells across each dimension.[000203] Some aspects of the present disclosure relate to a lithographic apparatus comprising the new measurement system described above.[000204] Some aspects of the present disclosure relate to a diffraction grating for use in a phasestepping measurement system 12, 30 for determining an aberration map for a projection system PS.[000205] Figure 16A is a schematic representation of a first example diffraction grating 70 having a non-uniform pitch that could be used as the second patterning device 32. The diffraction grating 70 is a two-dimensional diffraction grating 70. The diffraction grating 70 is a transmissive grating. The diffraction grating 70 is a pinhole grating.[000206] The first example diffraction grating 70 comprises a substrate provided with a two- dimensional array of circular through-apertures 72. A distance between the centres of adjacent through- apertures 72 may be referred to as the local pitch of the diffraction grating.[000207] The plurality of apertures 72 are all of a fixed dimension and the variation in pitch is achieved by varying a distance between the centres of adjacent apertures across the diffraction grating 70. Therefore, in this example, a duty cycle of the diffraction grating 70 is also variable. That is a ratio of the radius of the circular apertures 72 to the distance between the centres of adjacent apertures 72 varies over the diffraction grating 70.[000208] Typically, a diffraction grating used as the wafer-level grating for a measurement system 12, 30 for determining an aberration map for a projection system PS of a lithographic apparatus LA comprises a plurality of apertures that are distributed such that a distance between the centres of adj acent apertures is uniform across the diffraction grating. This is achieved by arranging the apertures such that a centre of each of the circular through-apertures coincides with one of a square array of positions. In contrast, the diffraction grating 70 shown in Figure 16A may be formed by arranging the apertures 72such that a distance between the centres of adjacent apertures 72 varies across the diffraction grating 70.[000209] In the example shown in Figure 16A, a pitch of the diffraction grating 70 has a minimum value at a first position on the diffraction grating 70, in this example the centre of the diffraction grating. The pitch of the diffraction grating 70 increases in all directions from the first position as a function of distance from the first position (the centre of the grating 70), as can be seen by the local pitches pi, p2 and ps labelled in Figure 16A ( pi<p2).[000210] In alternative embodiments, there may be a maximum pitch at a first position and the pitch of the diffraction grating may decrease as a function of distance from the first position. In other embodiments, the first position need not be in the centre of the diffraction grating.[000211] Advantageously, with such a diffraction grating 70, the variation in pitch is such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device 32 is non-uniform. In particular, the variation in pitch is such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device 32 increases for higher- order diffraction beams. Such a diffraction grating can be used as the second patterning device 32 of the new measurement system 12, 30 described above.[000212] The pitch pi, pz and p * of the diffraction grating 70 may vary linearly with distance from the first position (the centre of the diffraction grating 70). Alternatively, the pitch pi, pz and ps of the diffraction grating device 70 may vary non-linearly with distance from the first position (for example as a parabolic function). In general, the pitch of the diffraction grating 70 may be a monotonic function of distance from the first position.[000213] The pitch pi, pz and p ? of the diffraction grating 70 may vary by at least 2% over the diffraction grating 70. In some embodiments, the pitch pi, pz and pa of the diffraction grating 70 may vary by at least 3% over the diffraction grating 70. In some embodiments, the pitch pi, pz and p ? of the diffraction grating 70 may vary by of the order of 4% or more.[000214] Figure 16B is a schematic representation of a second example diffraction grating 80 having a non-uniform pitch. The diffraction grating 80 is a linear (one-dimensional) diffraction grating 80. The diffraction grating 80 is a transmissive grating.[000215] As with the first example grating 70 shown in Figure 16A, the second example grating 80 shown in Figure 16B has a pitch pi, pz, ps and a duty-cycle that both vary over the grating 80, with the pitch increasing from a centre of the grating 80. For simplicity, the diffraction pattern of such a onedimensional diffraction grating 80 is discussed in order to provide a qualitative teaching of how such a variable pitch alters the diffraction pattern of a diffraction grating.[000216] Figure 17 shows a diffraction spectrum 90 for a linear grating of the type shown in Figure 16B but having a uniform pitch, P. The diffraction spectrum 90 shows the intensity of the diffraction pattern as a function of diffraction order, nx. Here the diffraction order, nx, represents a scattering angle of 9, where sin(3') = nx. A / 2P. where P is the uniform pitch and 2 is the wavelength of theradiation. The diffraction spectrum 90 is shown for three cases: (a) a grating comprising a single unit cell; (b) a grating comprising N=30 unit cells; and (c) a grating comprising an infinite number of unit cells. The diffraction spectra for N=30 and N=«> are almost indistinguishable.[000217] Figure 18A shows a diffraction spectrum 92 for a linear diffraction grating 80 of the type shown in Figure 16B and having a pitch that increases from a centre of the diffraction grating 80, having a variation of pitch of 4% across the diffraction grating 80. The diffraction spectrum 92 shows the intensity of the diffraction pattern as a function of diffraction order, nx. Here the diffraction order, nx, represents a scattering angle of 9, where sin(0) = nx. / 2p,L,is the minimum pitch of the diffraction grating 80. The diffraction spectrum 92 is again shown for three cases: (a) a grating comprising a single unit cell; (b) a grating comprising N=30 unit cells; and (c) a grating comprising an infinite number of unit cells. Figure 18B shows an enlarged portion of the diffraction spectrum 92 shown in Figure 18 A.[000218] The following general features of the diffraction spectrum 92 can be identified from Figures 18A and 18B. First, for N =<», the variable pitch linear grating 80 generates a diffraction spectrum 92 where the higher diffraction orders have an increasing angular separation (which is equivalent to a decreasing pitch). Recall that for a fixed pitch diffraction grating, the larger the pitch, the smaller the angular separation between adjacent pairs of diffraction beams. This can be most easily seen in Figure 18B where the lines of the 3rd and 5th diffraction orders that represent N=oo are shifted out to values that are higher than would be expected if the grating had a uniform pitch of p1.[000219] Second, for diffraction grating 80 comprising a finite number of unit cells (see, for example, the case of N=30), the amplitudes of the higher diffraction orders are more strongly reduced in intensity compared to the lower diffraction orders. For example, the 1st order peak is reduced by -50% while the 3rd and 5th order peaks are reduced by -20% and -5% respectively.[000220] Third, the position of the peaks of the diffraction beam is dependent not only on the pitch and the variation of pitch but also on the number of unit cells used for the grating 80. Note that this is in contrast to the diffraction spectrum 90 for a uniform pitch grating, wherein the position of the peaks of the diffraction beam is not dependent on the number of unit cells (although a width of the peaks is). This is important as this has a bearing on an angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 31. Therefore the number of unit cells also has an influence over how the pitches of the first and second patterning devices 31, 32 are matched (so as to ensure that an angular separation between the zeroth order diffraction beam 35 and the first order diffraction beams 34, 36 of the first patterning device31 is generally matched to an angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 31, taking into account any reduction or magnification factor applied by the projection system PS).[000221] For example, for infinite N it may be that the minimum pitch should be matched to the pitch of the reticle-level grating 31. However, this is not the case for N=30. The angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 31 may be defined as the angular separation between the peak values of these diffraction orders. With this definition, it can be seen from Figure 19B that the angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 31 is larger than would be expected for a uniform pitch grating having a pitch equal to the minimum pitch pt. Therefore, for such situations having a finite number of unit cells, the pitch of the first patterning device 31 should be matched to a value that is larger than the minimum pitch pr. Exactly how much larger can be determined given the diffraction spectrum of the variable pitch grating 32.[000222] For example, how this matching should be done can be determined, for example, by: (a) determining the diffraction spectrum for the variable pitch second patterning device 32; (b) determining the angular positions of the peaks the zeroth order diffraction beams 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 32 (for example by fitting a curve to the peaks, for example a least squares fit); (c) determining the angular separation between the zeroth order diffraction beam 34a, 35a, 36a and the first order diffraction beams 34b, 34c, 35b, 35c, 36b, 36c of the second patterning device 32 that originate from the same order diffraction beam 34, 35, 36 of the first patterning device 31; and (d) determining an effective pitch of the second patterning device 32 as a pitch that would achieve the same angular separation for adjacent diffraction orders for a uniform pitch diffraction gratings.[000223] The diffraction gratings 70, 80 shown in Figures 16A, 16B may be is self-supporting. Since the diffraction gratings 70, 80 are self-supporting they do not need, for example a transmissive supporting layer. Such an arrangement is particularly beneficial for use in a phase-stepping measurement system 12, 30 for determining an aberration map for a projection system PS that uses EUV radiation since the use of such a transmissive supporting layer would significantly reduce the amount of EUV radiation that is transmitted by the two-dimensional diffraction grating.[000224] In some embodiments, the diffraction gratings 70, 80 discussed above may be self- supporting. In use, the diffraction gratings 70, 80 may be provided with a support for the absorbing layer. The support may only contact a peripheral portion of the absorbing layer. That is, the support may be of the form of a frame, and which is not adjacent to a central portion of the absorbing layer. With such an arrangement, in a central portion of the absorbing layer, the absorbing layer may be considered to be self-supporting. To achieve this, the absorbing layer may be tensioned on the support (for example such that it remains generally planar).[000225] Advantageously, for embodiments wherein the central portion of the absorbing layer is self- supporting, the grating does not need, for example, a transmissive supporting layer. Such an arrangement is particularly beneficial for use in a phase-stepping measurement system for determining an aberration map for a projection system that uses EUV radiation since the use of such a transmissive supporting layer would significantly reduce the amount of EUV radiation that is transmitted by the diffraction grating.[000226] In some embodiments, in the diffraction gratings discussed above, the substrate (in which the apertures are formed) comprises a radiation absorbing layer. The radiation absorbing layer may, for example, be formed from a metal such as, for example, chromium (Cr), nickel (Ni), cobalt (Co) or aluminium (Al).[000227] In some embodiments, the absorbing layer may comprise a ceramic. The ceramic may comprise a metal or metalloid component having a relatively high extinction coefficient for EUV radiation and a non-metal component. Both components may have a refractive index for EUV which is relatively close to 1. The ceramic may comprise aluminium nitride (AIN). In some embodiments, the absorbing layer may comprise aluminium nitride (AIN).[000228] In some embodiments, in the diffraction gratings discussed above, the substrate (in which the apertures are formed) may further comprise a support layer. The through-apertures may extend through both the support layer and the radiation absorbing layer. The support layer may, for example, be formed from SiN.[000229] Although the above described embodiments use the first harmonic of a phase stepping signal it will be appreciated that in alternative embodiments higher harmonics of the phase stepping signal may alternatively be used.[000230] Although the above described embodiments use a first patterned region 31 comprising a one-dimensional diffraction grating 31 with a 50% duty cycle it will be appreciated that in alternative embodiments other the first patterned region 31 may use different geometries. For example, in some embodiments, the first patterned region 31 may comprise a two-dimensional checkerboard diffraction grating with a 50% duty cycle.[000231] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquidcrystal displays (LCDs), thin-film magnetic heads, etc.[000232] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (orother patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non- vacuum) conditions.[000233] Where the context allows, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world.[000234] The present invention can also be formulated by the following clauses:1. A measurement system for determining an aberration map for a projection system, the measurement system comprising: a first patterning device positionable in an object plane of the projection system; a second patterning device positionable in an image plane of the projection system; a radiation detector arranged to receive radiation from the second patterning device; and a positioning apparatus operable to move at least one of the first and second patterning devices in a shearing direction; wherein the second patterning device has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device that originate from the same order diffraction beam of the first patterning device is non-uniform; and wherein the pitches of the first and second patterning devices are matched such that an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the first patterning device is generally matched to an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the second patterning device that originate from the same order diffraction beam of the first patterning device, taking into account any reduction or magnification factor applied by the projection system; and wherein the variable pitch of the second patterning device is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device are not matched to an angular separation between the zeroth order diffraction beam and the firstorder diffraction beams of the first patterning device, taking into account any reduction or magnification factor applied by the projection system.2. The measurement system of clause 1 wherein the pitch of the second patterning device has an extremum value at a first position on the second patterning device and wherein the pitch of the second patterning device either increases or decreases as a function of distance from the first position.3. The measurement system of clause 2 wherein the pitch of the second patterning device varies linearly with distance from the first position.4. The measurement system of any preceding clause wherein the pitch of the second patterning device varies by at least 2% over the second patterning device.5. The measurement system of any preceding clause wherein the second patterning device is a two-dimensional diffraction grating.6. The measurement system of any preceding clause wherein the second patterning device comprises a substrate provided with a two-dimensional array of circular through- apertures.7. The measurement system of any preceding clause wherein the second patterning device comprises at least 10 unit cells across the or each dimension of a pattern of the second patterning device.8. The measurement system of any preceding clause, wherein the second patterning device and the radiation detector together form a sensor apparatus, the measurement system further comprising: a controller configured to: control the positioning apparatus so as to move at least one of the first patterning device and the sensor apparatus in the shearing direction such that an intensity of radiation received by each part of the radiation detector varies as a function of the movement in the shearing direction so as to form an oscillating signal; determine from the radiation detector a phase of a harmonic of the oscillating signal at a plurality of positions on the radiation detector; and determine a set of coefficients that characterize the aberration map of the projection system from the phase of a harmonic of the oscillating signal at the plurality of positions on the radiation detector.9. A lithographic apparatus comprising the measurement system of any preceding clause.10. A diffraction grating for a phase-stepping measurement system for determining an aberration map for a projection system, wherein a pitch of the diffraction grating has an extremum value at a first position on the diffraction grating and wherein the pitch of the diffraction grating either increases or decreases as a function of distance from the first position.11. The diffraction grating of clause 10 wherein the pitch of the diffraction grating varies linearly with distance from the first position.12. The diffraction grating of clause 10 or clause 11 wherein the pitch of the diffraction grating varies by at least 2% over the diffraction grating.13. The diffraction grating of any one of clauses 10 to 12 wherein the diffraction grating is a two- dimensional diffraction grating.14. The diffraction grating of any one of clauses 10 to 13 wherein the diffraction grating comprises at least 10 unit cells across the or each dimension of a pattern of the diffraction grating.15. The diffraction grating of any one of clauses 10 to 14 wherein the diffraction grating is self- supporting.16. The diffraction grating of any one of clauses 10 to 15 wherein the diffraction grating comprises a substrate provided with a two-dimensional array of circular through-apertures.17. The diffraction grating of clause 16 wherein the substrate comprises: a radiation absorbing layer, and wherein the through- apertures extend through the radiation absorbing layer.18. The diffraction grating of clause 17 wherein the substrate further comprises: a support layer adjacent to the radiation absorbing layer, and wherein the through-apertures extend through both the support layer and the radiation absorbing layer.[000235] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

Claims

CLAIMS1. A measurement system for determining an aberration map for a projection system, the measurement system comprising: a first patterning device positionable in an object plane of the projection system; a second patterning device positionable in an image plane of the projection system; a radiation detector arranged to receive radiation from the second patterning device; and a positioning apparatus operable to move at least one of the first and second patterning devices in a shearing direction; wherein the second patterning device has a variable pitch such that an angular separation between adjacent pairs of diffraction beams formed by the second patterning device that originate from the same order diffraction beam of the first patterning device is non-uniform; and wherein the pitches of the first and second patterning devices are matched such that an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the first patterning device is generally matched to an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the second patterning device that originate from the same order diffraction beam of the first patterning device, taking into account any reduction or magnification factor applied by the projection system; and wherein the variable pitch of the second patterning device is such that an angular separation between other pairs of adjacent pairs of diffraction beams of the second patterning device are not matched to an angular separation between the zeroth order diffraction beam and the first order diffraction beams of the first patterning device, taking into account any reduction or magnification factor applied by the projection system.

2. The measurement system of claim 1 wherein the pitch of the second patterning device has an extremum value at a first position on the second patterning device and wherein the pitch of the second patterning device either increases or decreases as a function of distance from the first position.

3. The measurement system of claim 2 wherein the pitch of the second patterning device varies linearly with distance from the first position.

4. The measurement system of any preceding claim wherein the pitch of the second patterning device varies by at least 2% over the second patterning device.

5. The measurement system of any preceding claim wherein the second patterning device is a two- dimensional diffraction grating.

6. The measurement system of any preceding claim wherein the second patterning device comprises a substrate provided with a two-dimensional array of circular through- apertures.

7. The measurement system of any preceding claim wherein the second patterning device comprises at least 10 unit cells across the or each dimension of a pattern of the second patterning device.

8. The measurement system of any preceding claim, wherein the second patterning device and the radiation detector together form a sensor apparatus, the measurement system further comprising: a controller configured to: control the positioning apparatus so as to move at least one of the first patterning device and the sensor apparatus in the shearing direction such that an intensity of radiation received by each part of the radiation detector varies as a function of the movement in the shearing direction so as to form an oscillating signal; determine from the radiation detector a phase of a harmonic of the oscillating signal at a plurality of positions on the radiation detector; and determine a set of coefficients that characterize the aberration map of the projection system from the phase of a harmonic of the oscillating signal at the plurality of positions on the radiation detector.

9. A lithographic apparatus comprising the measurement system of any preceding claim.

10. A diffraction grating for a phase-stepping measurement system for determining an aberration map for a projection system, wherein a pitch of the diffraction grating has an extremum value at a first position on the diffraction grating and wherein the pitch of the diffraction grating either increases or decreases as a function of distance from the first position.

11. The diffraction grating of claim 10 wherein the pitch of the diffraction grating varies linearly with distance from the first position.

12. The diffraction grating of claim 10 or claim 11 wherein the pitch of the diffraction grating varies by at least 2% over the diffraction grating.

13. The diffraction grating of any one of claims 10 to 12 wherein the diffraction grating is a two- dimensional diffraction grating.

14. The diffraction grating of any one of claims 10 to 13 wherein the diffraction grating is self- supporting.

15. The diffraction grating of any one of claims 10 to 14 wherein the diffraction grating comprises a substrate provided with a two-dimensional array of circular through-apertures.

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