WO2025228613A1

WO2025228613A1 - Method and measurement system for determining data relating to aberrations caused by a projection system

Info

Publication number: WO2025228613A1
Application number: PCT/EP2025/059154
Authority: WO
Inventors: Marcel Theodorus Maria VAN KESSEL
Original assignee: ASML Netherlands BV
Current assignee: ASML Netherlands BV
Priority date: 2024-04-30
Filing date: 2025-04-03
Publication date: 2025-11-06
Anticipated expiration: 2026-10-30

Abstract

A method is provided of determining data relating to aberrations, the method comprising: providing a patterning device and a sensor apparatus with a plurality of detector regions; illuminating the patterning device with radiation, wherein each patterned region patterns a measurement beam; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in a first configuration; moving the patterning device or the sensor apparatus to provide a second configuration; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region in the second configuration; and determining, from the radiation measurements, data relating to aberrations caused by the projection system.

Description

METHOD AND MEASUREMENT SYSTEM FOR DETERMINING DATA RELATING TO ABERRATIONS CAUSED BY A PROJECTION SYSTEM

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 24173224.7 which was filed on

April 30, 2024 and which is incorporated in its entirety by reference.

FIELD

[0002] The present invention relates to a method of determining data relating to aberrations caused by a projection system. The method may be used in connection with a lithographic apparatus. The present invention relates to a measurement system for determining data relating to aberrations caused by a projection system.

BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that circumstance, a mask or a reticle (which may be referred to as a patterning device), may be used to generate a circuit pattern corresponding to an individual layer of the IC, and this pattern can be imaged onto a target portion (e.g. comprising part of, one or several dies) on a substrate (e.g. a silicon wafer) that has a layer of radiation-sensitive material (resist). In general, a single substrate will contain a network of adjacent target portions that are successively exposed. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion in one go, and so-called scanners, in which each target portion is irradiated by scanning the pattern through the beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction.

[0004] Radiation that has been patterned by a 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 that which is imparted by the patterning device. It is desirable to determine data relating to such aberrations.

[0005] Although some mechanisms for determining data relating to aberrations are known, the known mechanisms leave room for improvement. In particular, as advances are made to pattern smaller features on the substrate, it is even more important to determine such data relating to aberrations with a high level of accuracy. This is of particular importance when checking a projection system on setup.

[0006] It is an object of the present invention to provide a method and/or measurement system which at least partially addresses one or more of the problems of the prior art, whether identified herein or elsewhere. SUMMARY

[0007] According to an aspect of the invention a method is provided method of determining data relating to aberrations caused by a projection system, the method comprising: providing a patterning device with a plurality of patterned regions and a sensor apparatus with a plurality of detector regions; illuminating the patterning device with radiation, wherein each patterned region patterns a measurement beam; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in a first configuration; moving at least one of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a second configuration; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the second configuration; and determining, from the radiation measurements, data relating to aberrations caused by the projection system.

[0008] According to an aspect of the invention a measurement system is provided for determining data relating to aberrations caused by a projection system, the measurement system comprising: a patterning device comprising a plurality of patterned regions, wherein each patterned region is configured to pattern a measurement beam when illuminated with radiation; an illumination system arranged to illuminate the patterning device with radiation; a sensor apparatus comprising a plurality of detector regions, wherein the sensor apparatus is configured to measure radiation at the detector regions; a projection system configured to project the patterned measurement beam onto the sensor apparatus, wherein the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region in a given configuration; a positioning apparatus configured to move at least one of the patterning device and the sensor apparatus so as to change the relative configuration of the patterning device and the sensor apparatus between a first configuration and a second configuration; and a controller configured to: receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the first configuration; receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the second configuration; and determine, from the radiation measurements, data relating to aberrations caused by the projection system.

[0009] According to an aspect of the invention a lithographic apparatus is provided comprising the measurement system.

BRIEF DESCRIPTION OF THE DRAWINGS [00010] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

[00011] Figure 1 is a schematic illustration of a lithographic apparatus;

[00012] Figure 2 is a schematic illustration of a measurement system according to an embodiment of the invention;

[00013] 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;

[00014] Figure 4is a schematic illustration of a measurement system according to an embodiment of the invention;

[00015] Figures 5A, 5B and 5C are schematic illustrations of relative configurations of a patterning device and a sensor apparatus;

[00016] Figures 6A and 6B are schematic illustrations of a patterning device and a sensor apparatus;

[00017] Figure 7 is an embodiment of the sensor apparatus;

[00018] Figures 8A-C are schematic illustrations of an embodiment of a patterning device and a sensor apparatus in a first configuration and Figures 8D-F are schematic illustrations of an embodiment of a patterning device and a sensor apparatus in a second configuration;

[00019] Figure 9 is a model of measurements taken for the stitching method;

[00020] Figures 10A, 10B and 10C are schematic representations of design matrices which may be used to determine data relating to aberrations caused by a projection system according to an embodiment of the invention.

DETAIEED DESCRIPTION

[00021] 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, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid-crystal displays (ECDs), thin film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist) or a metrology or inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers. [00022] The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of 365, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g. having a wavelength in the range of 4-20 nm), as well as particle beams, such as ion beams or electron beams.

[00023] The term “patterning device” used herein should be broadly interpreted as referring to a device that can be used to impart a radiation beam with a pattern in its cross-section. For example, a radiation beam may be imparted with a pattern in its cross-section in order to create a pattern in a target portion of a substrate. Additionally or alternatively a radiation beam may be imparted with a pattern in its cross-section in order to illuminate a sensor apparatus with a patterned radiation beam. It should be noted that when a pattern is created in a target portion of a substrate, the pattern imparted to a radiation beam may not exactly correspond to a desired pattern in the target portion of the substrate. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[00024] A patterning device may be transmissive or reflective. Examples of patterning device include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase- shift, and attenuated phaseshift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions; in this manner, the reflected beam is patterned.

[00025] The support structure holds the patterning device. It holds the patterning device in a way depending on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support can use mechanical clamping, vacuum, or other clamping techniques, for example electrostatic clamping under vacuum conditions. The support structure may be a frame or a table, for example, which may be fixed or movable as required and which may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device”.

[00026] The term “projection system” used herein should be broadly interpreted as encompassing various types of projection system, including refractive optical systems, reflective optical systems, and catadioptric optical systems, as appropriate for example for the exposure radiation being used, or for other factors such as the use of an immersion fluid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

[00027] The illumination system may also encompass various types of optical components, including refractive, reflective, and catadioptric optical components for directing, shaping, or controlling the beam of radiation, and such components may also be referred to below, collectively or singularly, as a “lens”.

[00028] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more support structures). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure.

[00029] The lithographic apparatus may also be of a type wherein the substrate is immersed in a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the final element of the projection system and the substrate. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems.

[00030] Figure 1 schematically depicts a lithographic apparatus. The apparatus comprises: an illumination system (illuminator) IL to condition a beam PB of radiation (e.g. UV radiation or DUV radiation). a support structure MT to support a patterning device (e.g. a mask) MA and connected to first positioning device PM to accurately position the patterning device with respect to item PL; a substrate table (e.g. a wafer table) WT for holding a substrate (e.g. a resist coated wafer) W and connected to second positioning device PW for accurately positioning the substrate with respect to item PL; and a projection system (e.g. a refractive projection lens) PL configured to image a pattern imparted to the radiation beam PB by patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[00031] Also shown in Figure 1 are Cartesian co-ordinates which are used consistently throughout the Figures.

[00032] As here depicted, the apparatus is of a transmissive type (e.g. employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (e.g. employing a programmable mirror array of a type as referred to above).

[00033] The illuminator IL receives a beam of radiation from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising for example suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[00034] The illuminator IL may alter the intensity distribution of the beam. The illuminator may be arranged to limit the radial extent of the radiation beam such that the intensity distribution is non-zero within an annular region in a pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL may also be operable to limit the distribution of the beam in the pupil plane such that the intensity distribution is non-zero in a plurality of equally spaced sectors in the pupil plane. The intensity distribution of the radiation beam in a pupil plane of the illuminator IL may be referred to as an illumination mode.

[00035] The illuminator IL may comprise adjusting means AM for adjusting the intensity distribution of the beam. Generally, at least the outer and/or inner radial extent (commonly referred to as o-outer and o-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. The illuminator IL may also be operable to vary the angular distribution of the beam. For example, the illuminator may be operable to alter the number, and angular extent, of sectors in the pupil plane wherein the intensity distribution is non-zero. By adjusting the intensity distribution of the beam in the pupil plane of the illuminator, different illumination modes may be achieved. For example, by limiting the radial and angular extent of the intensity distribution in the pupil plane of the illuminator IL, the intensity distribution may have a multi-pole distribution such as, for example, a dipole, quadrupole or hexapole distribution. A desired illumination mode may be obtained by inserting an optic which provides that illumination mode into the illuminator IL.

[00036] In addition, the illuminator IL generally comprises various other components, such as an integrator IN and a condenser CO. The illuminator provides a conditioned beam of radiation PB, having a desired uniformity and intensity distribution in its cross section.

[00037] The radiation beam PB is incident on the patterning device MA, which is held on the support structure MT. Having traversed the patterning device MA, the beam PB passes through the projection system PL, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioning device PW and position sensor IF (e.g. an interferometric device), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the beam PB. Similarly, the first positioning device PM and another position sensor (which is not explicitly depicted in Figure 1) can be used to accurately position the patterning device MA with respect to the path of the beam PB, e.g. after mechanical retrieval from a mask library, or during a scan. In general, movement of the object tables MT and WT will be realized with the aid of a long- stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the positioning device PM and PW. However, in the case of a stepper (as opposed to a scanner) the support structure MT may be connected to a short stroke actuator only, or may be fixed. Patterning device MA and substrate W may be aligned using patterning device alignment marks Ml, M2 and substrate alignment marks Pl, P2.

[00038] The depicted apparatus can be used in the following preferred modes:

1. In step mode, the support structure MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the beam PB is projected onto a target portion C in one go (i.e. a single static exposure). The substrate table WT is then shifted in the x and/or y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the beam PB is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure MT is determined by the (de-)magnification and image reversal characteristics of the projection system PL. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion.

3. In another mode, the support structure MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the beam PB is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[00039] Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed.

[00040] The projection system PL 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 PL 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 determined by calculating the inner product of a measured scalar map with each Zernike polynomial in turn and dividing this by the square of the norm of that Zernike polynomial.

[00041] The transmission map and the relative phase map are field and system dependent. That is, in general, each projection system PL will have a different Zernike expansion for each field point (i.e. for each spatial location in its image plane).

[00042] As will be described in further detail below, the relative phase of the projection system PL in its pupil plane may be determined by projecting radiation from an object plane of the projection system PL (i.e. the plane of the patterning device MA), through the projection system PL 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 grid, 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 PL. Any appropriate detector may be used.

[00043] The projection system PL may comprise a plurality of lens elements and may further comprise adjusting means PA for adjusting the lens 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 lens elements within the projection system PL in one or more different ways. The projection system may have a co-ordinate system wherein its optical axis extends in the z direction. The adjusting means PA may be operable to do any combination of the following: displace one or more lens elements; tilt one or more lens elements; and/or deform one or more lens elements. Displacement of lens elements may be in any direction (x, y, z or a combination thereof). Tilting of lens 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 aspherical lens elements. Deformation of lens elements may include both low frequency shapes (e.g. astigmatic) and high frequency shapes (e.g. free form aspheres). Deformation of a lens element may be performed for example by using actuators to exert force on sides of the lens element and/or by using heating elements to heat selected regions of the lens element. In general, it may not be possible to adjust the projection system PL to correct for apodizations (transmission variation across the pupil plane). The transmission map of a projection system PL may be used when designing masks MAs for the lithographic apparatus LA.

[00044] A projection system PL which forms part of a lithographic apparatus may need to be tested when installed to determine whether or not it is functioning as required. For example, when a lithographic apparatus is manufactured in a factory the optical elements (e.g. lenses) which form the projection system PL may be set up by performing an initial calibration process. Additionally, the projection system PL may periodically undergo a calibration process at later stages.

[00045] Testing and calibrating a projection system PL may comprise passing radiation through the projection system PL and measuring the resultant projected radiation. Measurements of the projected radiation may be used to determine data relating to aberrations in the projected radiation which are caused by the projection system PL. Data relating to aberrations which are caused by the projection system PL may be determined using a measurement system. A user may determine whether or not the projection system PL meets certain requirements based on the determined data relating to these aberrations. Additionally, in response to the determined data related to the aberrations, the optical elements which form the projection system PL may be adjusted so as to correct for the aberrations which are caused by the projection system PL.

[00046] 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.

[00047] Preferably, the projection system PL is measured regarding aberrations over the full field. This can be used to determine which optical components (e.g. mirrors) should be adjusted and the measurements can be used for qualification of the projection system PL. As related systems continue to advance and rely on radiation with smaller wavelengths (e.g. EUV), the level of accuracy preferred (or required) to qualify the projection system PL is higher. For example, it may be preferable to determine data relating to the aberrations with an accuracy of approximately 50 pm or preferably smaller. Known measurements systems do not measure the complete assembly (i.e. across the whole field) and the accuracy is approximately 200 pm.

[00048] Although measurements can be taken to qualify the projection system PL, errors are generally introduced from a number of different sources, i.e. not solely from the projection system PL. Thus, measurements will also be affected by other errors, some of which may be significantly larger than an acceptable error in the projection system PL. It is beneficial to provide a measurement system which is capable of determining data relating to the aberrations caused by the projection system. As is described in further detail below, stitching methods can be used to determine data relating to the aberrations caused by the projection system based on the radiation measurements, i.e. to disentangle the contribution of the projection system PL from other errors.

[00049] In order to determine data relating to the aberrations caused by the projection system PL, the measurements are taken when the projection system PL is set up. This means that measurements used for determining data relating to the aberrations are generally taken using a sensor in the scanner. Movements in the system can affect thermal equilibrium, i.e. lead to thermal variation in the system. Such thermal variation can lead to more errors as it can result in deformation of components in the system, such as the sensor. Therefore, it is beneficial to reduce such thermal variation, or at least, keep it to a minimum. Additionally, there are often constraints regarding the sensors available in the system due to physical limitations on space available. In general, it may be particularly beneficial to rely on sensors which may be used for other measurements after qualification of the projection system PL and/or provide sensors which do not get in the way of other sensors used in the lithographic apparatus at other times.

[00050] After installation of a lithographic apparatus, the projection system PL may once again be calibrated. Further calibrations of the projection system PL may be performed at regular intervals. For example, under normal use the projections system PL may be calibrated every few months (e.g. every three months).

[00051] Measurements of the projected radiation are used to determine data relating to aberrations in the projected radiation which are caused by the projection system PL. Data relating to aberrations which are caused by the projection system PL may be determined using a measurement system. In response to the determined data relating to aberrations, at least some of the optical elements of the projection system PL may be adjusted so as to correct for the aberrations which are caused by the projection system PL.

[00052] Figure 2 is a schematic illustration of a measurement system 10 which may be used to determine data relating to aberrations which are caused by a projection system PL. The measurement system 10 comprises an illumination system IL, a measurement patterning device MA’, a sensor apparatus 21, a projection system PL, a positioning apparatus PW and a controller CN. For ease of reference, the positioning apparatus PW referred to below may be the first positioning device PM and/or the second positioning device PW shown in figure 2 (even if only one or other of the first positioning device PM and the second positioning device PW is referred to or shown). The measurement system 10 may form part of a lithographic apparatus. For example, the illumination system IL and the projection system PL which are shown in Figure 2 may be the illumination system IL and projection system PL of the lithographic apparatus which is shown in Figure 1. For ease of illustration additional components of a lithographic apparatus (e.g. a radiation source SO) are not shown in Figure 2.

[00053] 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 PL. During normal use of a lithographic apparatus, the measurement patterning device MA’ and the sensor apparatus 21 which are shown in Figure 2 may not be located in 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 PL (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 data relating to aberrations which are caused by the projection system PL. 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.

[00054] Part of the measurement patterning device MA’ and part of the sensor apparatus 21 are shown in more detail in Figures 3 A and 3B. Cartesian co-ordinates are used consistently in Figures 2, 3 A and 3B. Figure 3 A is a schematic illustration of part of the measurement patterning device MA’ in an x-y plan and Figure 3B is a schematic illustration of part of the sensor apparatus 21 in an x-y plane.

[00055] The measurement patterning device MA’ comprises a plurality of patterned regions 15a-15c. Each patterned region 15a-15c is configured to pattern a measurement beam when illuminated with radiation. In the embodiment which is shown in Figures 2 and 3A the measurement patterning device MA’ is a transmissive patterning device MA’. The patterned regions 15a-15c each comprise an opening in the measurement patterning device MA’, in which a transmissive diffraction grating is disposed. Radiation which is incident on the patterned regions 15a-15c of the measurement patterning device MA’ is at least partially transmitted, and radiation which is incident on the remainder of the measurement patterning device MA’ is not transmitted.

[00056] It will be understood that other forms of measurement patterning device MA’ may be used, for example, a reflective measurement patterning device may be used instead of a transmissive patterning device. In this case, the radiation which is incident on a patterned region would be reflected based on the patterned region as described above for the transmissive patterning device.

[00057] 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 can be used to illuminate one of the patterned regions 15a-15c of the measurement patterning device MA’. As described in further detail below, the illumination system may only provide one of the measurement beams 17a- 17c at any one time.

[00058] In the Figures the Cartesian co-ordinate system is shown as being conserved through the projection system PL. However, in some embodiments the properties of the projection system PL may lead to a transformation of the co-ordinate system. For example, the projection system PL 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 PL 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.

[00059] In embodiments in which the projection system PL rotates an image of the measurement patterning device MA’ and/or the image is mirrored by the projection system PL, the projection system PL 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 PL 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 PL. However, in some embodiments the coordinate system may be transformed by the projection system PL. [00060] The modified measurement beams 17a-17c are input to the projection system PL. The projection system PL forms an image of the modified measurement beams 17a-17c which is projected on to the sensor apparatus 21. Thus, the projection system PL is configured to project the patterned measurement beams onto the sensor apparatus 21. Therefore, when one of the measurement beams 17a-17c has been patterned by one of the patterned regions 15a-15c, the projection system PL projects each respective patterned measurement beam 17a-17c to the sensor apparatus 21.

[00061] The sensor apparatus 21 comprises a plurality of detector regions. For example, the sensor apparatus 21 comprises a plurality of detector regions 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.

[00062] 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. Any appropriate detector element may be used. For example, the radiation detector 23 may comprise a CCD array. Alternatively, the radiation detector 23 may comprise a transmission image sensor (TIS) 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 first measurement beam 17a is received together form a first detector region 25 a.

[00063] The sensor apparatus 21 is configured to measure radiation at the detector regions. 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 PL.

[00064] 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 which are present in wavefronts which have propagated through the projection system PL. The interference patterns may therefore be used to determine data relating to aberrations which are caused by the projection system PL. As will be described in further detail below, the interference patterns may also depend on the configuration and relative positioning of the patterned regions 15a-15c and detector regions 17a-17c. [00065] The patterned regions 15a-15b modify the measurement beams 17a-17c. In particular, the patterned regions 15 a- 15b cause a spatial modulation of the measurement beams and cause diffraction in the measurement beams 17a-17b. As shown in figure 3A, the patterned regions 15a-c may 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 3 A are identical to the first patterned region 15a and each comprise first and second portions whose diffraction gratings are aligned perpendicular to each other. 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.

[00066] The patterned regions 15a-15c and/or the detector regions 25a-25c may be scanned and/or stepped relative to each other in one or more directions (e.g. two perpendicular directions) whilst measurements are made by a radiation sensor 23 which forms part of the sensor apparatus 21. The measurement patterning device MA’ and the sensor apparatus 21 may still be considered to be in the first relative configuration even during scanning and/or stepping of the patterned regions 15a-15c and/or the detector regions 25a-25c as long as the correspondence between patterned regions 15a-15g, measurement beams 17a-17c and detector regions 25a-25c remains as depicted in Figure 2.

[00067] A series of measurements which are performed during stepping and/or scanning of the patterned regions 15a-15c and/or the detector regions 25a-25c for each detector region may be considered to form a single measurement. For example, the patterned regions and/or the detector regions may be scanned relative to each other in one or more directions (e.g. two perpendicular directions) whilst measurements are made by a radiation sensor 23 which forms part of the sensor apparatus 21. The measurement patterning device MA’ and the sensor apparatus 21 may still be considered to be in the first relative configuration even during scanning of the patterned regions 15a- 15g and/or the detector regions 25a-25g as long as the correspondence between patterned regions 15a- 15g, measurement beams 17a-17g and detector regions 25a-25g remains, e.g. as depicted in Figure 5 A. A series of measurements which are performed during scanning of a patterned region, e.g. 15a and/or a corresponding detector region, e.g. 25a, whilst the measurement patterning device MA’ and the sensor apparatus 21 are in a given relative configuration may be considered to form a single measurement.

[00068] The arrangements of diffraction gratings which form the patterned regions 15a-15c and the detector regions 25a-25c in the embodiment which is shown in Figures 2, 3A and 3B are presented merely as an example embodiment. It will be appreciated that a variety of different arrangements of the patterned regions 15a-15c and the detector regions 25a-25c may be used in order to determine data relating to aberrations caused by the projection system PL. Thus, each single measurement may be made in a different way and may or may not involve movement in the u and/or v-directions as described above. The patterned regions 15a-15c and/or the detector regions 25a-25c may comprise diffraction gratings.

[00069] 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 pin-hole 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.

[00070] The sensor apparatus 21 and the measurement patterning device MA’ may be provided in a given configuration wherein the sensor apparatus 21 and measurement patterning device MA’ are in a specific position relative to each other. The positioning apparatus PW is operable to move the sensor apparatus 21 and/or the measurement patterning device MA’ relative to each other. Thus, the positioning apparatus PW is configured to move at least one of the sensor apparatus 21 and the measurement patterning device MA’ so as to change a relative configuration of the measurement patterning device MA’ and the sensor apparatus 21 between different configurations, e.g. from a first configuration to a second configuration.

[00071] In a given configuration, the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region 25a-c which aligns with a patterned region 15-c. This means that the measurement system projects radiation onto one detector region 25 at a time. Therefore, the measurement system projects the measurement beams 17a-c one at a time for each detector region which lines up with a patterned regions 15a-c in a given configuration. This is particularly beneficial because it means that the detector regions 25a-c can be close together than they would otherwise be. If the detector regions 25a-c are provided close together and multiple detector regions are illuminated at any one time, any given detector region 25a-c may detect radiation from an adjacent diffraction grating 19a-c. For example, detector region 25a may receive radiation via diffraction grating 19a and 19b. Providing measurement beams 17a-c one by one, i.e. sequentially, avoids this issue without having to spread out the detector regions 25a-c. It is preferable to keep the detector regions 25a-c closer together because this provides for more measurements in relation to the projection system PL which provides greater accuracy in the determination of data relating to aberrations.

[00072] Additionally, taking a measurement at each detector region which aligns with a patterned region 17a-c in a given configuration provides additional information for quantifying the projection system to ensure that the projection system provides desired level of accuracy. Larger number of measurements may not be preferred when using the method/apparatus for calibration as this increases the overall time taken to determine data relating to aberrations. However, when quantifying the projection system, it is particularly beneficial to include such additional measurements and as the quantification need only happen once, i.e. when checking the projection system after setup/delivery of an apparatus, the additional time taken for processing the additional measurement information is acceptable for the improved accuracy of the data determination.

[00073] Therefore, although taking the measurements in this way may be slower than in other known systems which use alternative methods, this is not such a concern as in other systems which are used for calibration. The present system is particularly useful for determining whether a projection system PL can be qualified (i.e. does not introduce larger aberrations than are acceptable) which would only need to be done upon installation/set up of the projection system. Thus, although this system might take longer than alternative known methods, the additional time is not an issue as it might be with other systems and the improved accuracy is particularly beneficial.

[00074] 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. In order to perform a determination of data relating to 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, although this is not a necessity.

[00075] The measurement system may be configured to sequentially project each measurement beam 17a-c in a number of different ways. 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 data relating to aberrations caused by the projection system PL. For example, the illumination system IL may be configured to illuminate a single patterned region of the patterning device at a time. In other words, only one of the measurement beams 17a-c may be formed by the illumination system IL at a time. The illumination system may provide a first measurement beam 17a to illuminate a first patterned region 15a, and then provide a second measurement beam 17b to illuminate a second patterned region 15b, and then provide a third measurement beam 17c to illuminate a second patterned region 15c, and so on. The illumination system may provide each measurement beam only long enough to take a measurement at the corresponding detector region. Additionally or alternatively, a masking device could be provided in addition to the measurement patterning device MA’ . The masking device may be configured to mask the patterned measurement beams to allow for one patterned measurement beam to reach the sensor apparatus 21 at a time. The masking device may only have a single aperture. Radiation which is incident on the aperture of the masking device is transmitted, and radiation which is incident on the remainder of the masking device is not transmitted. In this embodiment, the mode of the illumination system IL may be the same as during normal operation and the masking device may be used to control the projection of one measurement beam at a time. [00076] The controller CN receives measurements made at the sensor apparatus 21 and determines, from the measurements, data relating to aberrations which are caused by the projection system PL. The controller CN is configured to receive measurement of radiation from the detector regions when the measurement patterning device MA’ and the sensor apparatus 21 are positioned in the first configuration and the second configuration. The measurements from the first configuration and the second configuration are used by the controller CN to determine data relating to aberrations caused by the projection system PL.

[00077] The controller CN may be configured to control one or more components of the measurement system 10. For example, the controller CN may control the positioning apparatus. The controller CN may control the second positioning device PW. The controller CN may control the first positioning device PM. The controller may control a positioning device PM used to position the masking device MD (if provided). The controller CN may control an adjusting means PA for adjusting components of the projection system PL. For example, the adjusting means PA may adjust lens elements of the projection system PL so as to correct for aberrations which are caused by the projection system PL and which are determined by the controller CN. It will be understood that the controller CN may be a single controller or may be separate controllers which may or may not be in communication with each other, e.g. wirelessly or via a wired connection.

[00078] The positioning apparatus PW is configured to move at least one of the measurement patterning device MA’ and the sensor apparatus 21 in a first direction and/or a second direction. The second direction is substantially perpendicular to the first direction. The first direction may be the x- direction shown in the figures. The second direction may be the y-direction. Movement of the measurement patterning device MA’ and/or the sensor apparatus 21 in the first and/or second directions can provide the measurement patterning device MA’ and the sensor apparatus 21 in different configurations. This is beneficial in projecting measurement beams through different patterning regions 15a-c onto different detector regions 25a-c and sometimes, using different measurement beams 17a-c for the same combination of patterning region 15a-c and detector region 25a-c. All the measurements made in different configurations is beneficial in more accurately determining data relating to aberrations due to the projection system PL.

[00079] Figures 5A-5C are representations of stages of a method of determining data relating to aberrations caused by a projection system PL according to an embodiment of the invention. In the embodiment which is represented in Figures 5A-5C a measurement patterning device MA’ comprises seven patterned regions 15a-15g. Seven measurement beams 17a-17g are formed and a sensor apparatus 21 comprises seven detector regions 25a-25g.

[00080] Figure 5A is a schematic representation of the correspondence between the patterned regions 15a-15g, the measurement beams 17a-17g and the detector regions 25a-25g during a first stage of a method of determining data relating to aberrations caused by a projection system PL. Figure 5B is a schematic representation of the correspondence between the patterned regions 15a-15g, the measurement beams 17a-17g and the detector regions 25a-25g during a second stage of the method. Figure 5C is a schematic representation of the correspondence between the patterned regions 15a-15g, the measurement beams 17a-17g and the detector regions 25a-25g during a third stage of the method. [00081] In the illustrations which are shown in Figures 5A-5C the measurement patterning device MA’ and the senor apparatus 21 are displayed relative to the same co-ordinate system. As was described above, in some embodiments the co-ordinate system may be transformed by the projection system PL.

[00082] During the first, second and third measurement stages of the method which is represented in Figures 5A-5C, each measurement beam 17a-17g is modified at a corresponding patterned region 15a- 15g.

[00083] During the first measurement stage of the method (as shown in Figure 5A) the measurement patterning device MA’ and the sensor apparatus 21 are in a first relative configuration in which modified measurement beams 17a-17f are each received at a corresponding detector region 25b-25g respectively. Thus, the detector regions and the patterning regions are aligned in the first direction when the measurement patterning device MA’ and the sensor apparatus 21 are in the first configuration. As the measurement beams are projected sequentially, the measurement beams are only provided one at a time, but are shown together in figures 5A-5C to indicate how the measurement beam is projected from the respective patterning regions to the detector regions.

[00084] Whilst the measurement patterning device MA’ and the sensor apparatus 21 are in the first relative configuration, each of the measurement beams 17a-f are sequentially projected onto the respective detector region 25b-g. Measurements can be made for each detector region which aligns with a patterned region, which as shown in figure 5A is detector regions 25b-g. In the embodiment shown in figure 5A, all of the detector regions are aligned with a respective patterned region except for detector region 25a. Thus, a measurement would be made sequentially at the aligned detector regions 25b-g.

[00085] When a measurement has been made for each detector region which aligns with a patterned region in the first configuration, the method comprises moving at least one of the patterning device and the sensor apparatus. Between figures 5 A and 5B, the sensor apparatus is moved in the x- direction relative to the measurement patterning device MA’. Thus, in this embodiment, the sensor apparatus 21 is moved to provide the measurement patterning device MA’ and the sensor apparatus 21 in a second configuration.

[00086] During the second measurement stage of the method (as shown in Figure 5B) the measurement patterning device MA’ and the sensor apparatus 21 are in a second relative configuration. Thus, the detector regions and the patterning regions are aligned in the first direction when the measurement patterning device MA’ and the sensor apparatus 21 are in the second configuration. [00087] In the second relative configuration, the detector regions 25a-25g receive a different measurement beam 17a-17g to the measurement beam which was received at the respective detector region 25a-25g when the measurement patterning device MA’ and the sensor apparatus 21 were positioned in the first relative configuration. For example, in the first relative configuration (as shown in Figure 5 A) a second detector region 25b receives a first measurement beam 17a, whereas in the second relative configuration (as shown in Figure 5B) the second detector region 25b receives a second measurement beam 17b (which was received by a third detector region 25c in the first relative configuration).

[00088] Whilst the measurement patterning device MA’ and the sensor apparatus 21 are in the second relative configuration, each of the measurement beams 17a-g are sequentially projected onto the respective detector region 25a-g. Measurements can be made for each detector region which aligns with a patterned region, which as shown in figure 5B is all of detector regions 25a-g. In the embodiment shown in figure 5B, all of the detector regions are aligned with a respective patterned region. Thus, a measurement would be made sequentially at each of the detector regions 25a-g.

[00089] When a measurement has been made for each detector region which aligns with a patterned region in the second configuration, the method may comprise moving at least one of the patterning device and the sensor apparatus. Between figures 5B and 5BC the sensor apparatus is moved in the x-direction relative to the measurement patterning device MA’. Thus, in this embodiment, the sensor apparatus 21 is moved to provide the measurement patterning device MA’ and the sensor apparatus 21 in a third configuration.

[00090] During the third measurement stage of the method (as shown in Figure 5C) the measurement patterning device MA’ and the sensor apparatus 21 are in a third relative configuration. Thus, the detector regions and the patterning regions are aligned in the first direction when the measurement patterning device MA’ and the sensor apparatus 21 are in the third configuration.

[00091] In the third relative configuration, the detector regions 25a-25f receive a different measurement beam 17b-17g to the measurement beam which was received at the respective detector region 25a-25f when the measurement patterning device MA’ and the sensor apparatus 21 were positioned in the second relative configuration (or the first relative configuration). For example, in the second relative configuration (as shown in Figure 5B) a second detector region 25b receives a second measurement beam 17b, whereas in the third relative configuration (as shown in Figure 5C) the second detector region 25b receives a third measurement beam 17c (which was received by a third detector region 25c in the second relative configuration).

[00092] Whilst the measurement patterning device MA’ and the sensor apparatus 21 are in the third relative configuration, each of the measurement beams 17b-g are sequentially projected onto the respective detector region 25a-f. Measurements can be made for each detector region which aligns with a patterned region, which as shown in figure 5C is all of detector regions 25a-f. In the embodiment shown in figure 5C, all of the detector regions are aligned with a respective patterned region except for detector region 25g. Thus, a measurement would be made sequentially at the aligned detector regions 25a-f.

[00093] When a measurement has been made for each detector region which aligns with a patterned region in the third configuration, the method may comprises moving at least one of the patterning device and the sensor apparatus to at least one other configuration.

[00094] As shown in figures 5A-5C, at least some of the patterning regions 15a-g of the measurement patterning device MA’ are spaced apart from each other in the first direction (the x- direction). As shown in figures 5A-C, at least some of the detector regions of the sensor apparatus 21 are spaced apart from each other in the first direction (the x direction). The patterning regions 15a-g and the detector regions 25a-g may be spaced apart in the first direction by corresponding amounts. In other words, the patterning regions 15a-g and the detector regions 25a-g may be spaced apart in the first direction such that a plurality of the patterning regions 15a-g and the detector regions 25a-g can be aligned in different configurations.

[00095] Moving the sensor apparatus 21 and/or the measurement patterning device MA’ may comprise stepping the sensor apparatus by a distance in the first direction which is approximately equal to a separation between detector regions in the first direction. Moving the sensor apparatus 21 and/or the measurement patterning device MA’ may comprise stepping the patterning device by a distance in the first direction which is approximately equal to a separation between patterning regions in the first direction. Either way, this is beneficial in that only a small movement of the sensor apparatus 21 and/or the measurement patterning device MA’ is carried out between configurations which can reduce the thermal effects of moving these parts of the system.

[00096] In figures 5A-5C, the sensor apparatus 21 is stepped in the first direction a distance approximately equal to a separation between detector regions in the first direction. As the distance between the detector regions 25a-g and the patterning regions 15a-g are corresponding, when the sensor apparatus 21 is stepped by a distance approximately equal to a separation between detector regions, many of the patterning regions 15a-g still align with the detector regions 25a-g, albeit in a different combination. This allows measurements to be made, then moving to another configuration which moves each measurement beam to an adjacent detector region (in the x-direction) for the next set of measurements.

[00097] Although Figures 5A-C show patterning regions 15a-g and detector regions 25a-g spaced apart in the x-direction (the first direction), the patterning regions and/or detector regions 25a- g could additionally or alternatively be spaced apart in the y-direction (the second direction).

[00098] In further detail, at least some of the patterning regions of the measurement patterning device MA’ may be spaced apart from each other in the second direction (the y-direction). An embodiment is shown in figure 6 A in which the patterning regions 15 are spaced apart in the first direction and the second direction. At least some of the detector regions may be spaced apart from each other in the second direction (the y direction). An embodiment is shown in figure 6B in which the detector regions 25 are spaced apart in the first direction and the second direction. The patterning regions and the detector regions may be spaced apart in the second direction by corresponding amounts. In other words, the patterning regions and the detector regions may be spaced apart in the second direction such that a plurality of the patterning regions and the detector regions can be aligned in different configurations, e.g. as shown in figures 6A and B. Thus, the detector regions and the patterning regions are aligned in the second direction when the measurement patterning device MA’ and the sensor apparatus 21 are in a specific configuration.

[00099] Moving the sensor apparatus 21 and/or the measurement patterning device MA’ may comprise stepping the sensor apparatus by a distance in the second direction which is approximately equal to a separation between detector regions in the second direction. Moving the sensor apparatus 21 and/or the measurement patterning device MA’ may comprise stepping the patterning device by a distance in the second direction which is approximately equal to a separation between patterning regions in the second direction. Either way, this is beneficial in that only a small movement of the sensor apparatus 21 and/or the measurement patterning device MA’ is carried out between configurations which can reduce the thermal effects of moving these parts of the system.

[000100] The sensor apparatus 21 may be stepped in the second direction a distance approximately equal to a separation between detector regions in the second direction. If the distance between the detector regions 25a-g and the patterning regions 15a-g are corresponding, when the sensor apparatus 21 is stepped by a distance approximately equal to a separation between detector regions, many of the patterning regions still align with the detector regions, albeit in a different combination. This allows measurements to be made, then moving to another configuration which moves each measurement beam to an adjacent detector region (in the y-direction) for the next set of measurements.

[000101] One or other of the sensor apparatus 21 and/or the measurement patterning device MA’ may be moved across the whole field of the projection system with relatively minimal movements between configurations. For example, the sensor apparatus 21 may take measurements and be moved one step in the first direction sequentially between configurations without moving in the second direction until measurements have been taken for all configurations at that position in the second direction. Then the sensor apparatus may be moved one step in the second direction. The sensor apparatus 21 may take measurements and be moved one step in the first direction sequentially between configurations without moving in the second direction until measurements have been taken for all configurations at that position in the second direction, and then the sensor apparatus may be moved one step in the second direction again. Thus, the sensor apparatus can be stepped through all the desired positions to take measurements whilst only carrying out small steps between each configuration and thus maintaining thermal equilibrium or at least improving negative effects on thermal equilibrium which may otherwise be caused from larger movement of the sensor apparatus 21. [000102] Diffraction gratings which form the patterned regions 15a-15c may each share a common grid such that the pitch of each of the diffraction gratings is the same. Additionally or alternatively, diffraction gratings which form the detector regions 25a-25c may each share a common grid such that the pitch of each of the diffraction gratings is the same. In some embodiments, the patterned regions 15a-15c and the detector regions 25a-g share a common grid. That is, the spacing between patterned regions 15a-g may correspond with the spacing between the detector regions 25a- 25g in the first and/or second direction. This is shown in the embodiment in figures 6A and B.

[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. In general, any number and configuration of patterned regions 15a-15c and detector regions 25a-25c may be used which modify the measurement beams 17a-17c such that measurements made at the radiation sensor 23 provides information about aberrations which are caused by the projection system. Preferably there are more than three patterned regions 15 and detector regions 25.

[000104] There may be fewer detector regions 25 than patterned regions 15. This may be beneficial in that having a larger number of patterned regions allows for patterned regions 25 to be more spread out across the field of the projection system PL. This is preferred as it provides more information on the aberrations caused by the projection system PL. Having fewer detector regions is beneficial in that it provides greater design freedom because the detector regions 25 can take up a smaller amount of space and may be incorporated on other detector systems which may be used for other functions.

[000105] The detector regions 25 and a subset of the patterning regions 15 may be aligned in the first direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations. The detector regions 25 and a subset of the patterning regions 15 are aligned in the second direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations.

[000106] The detector regions 25 may be provided in an array and the patterning regions 15 are provided in an array, for example as shown in figures 6A and 6B. The array of detector regions 25 may be smaller than the array of patterning regions. This may provide greater design freedom. It may be relatively easy to move the sensor apparatus 21 into a number of different positions relative to the measurement patterning device MA’ such that providing a smaller array of detectors which are moved around to make additional measurements is more beneficial than providing a larger array of detector regions 25.

[000107] The array of detector regions 25 may form a uniform grid pattern. This may be beneficial in more easily matching the measurement beams. Preferably, the array may be provided with 3 rows of detectors and 5 columns. However, the exact number of rows or columns may be selected depending on a variety of factors, including how many detector regions may fit into a space available. The array of detector regions 25 may include at least 3 rows and 3 columns of detector regions to allow for stitching of measurements taken in the z-direction. The sensor apparatus 21 may comprises additional sensing portions 50, for example, as shown in figure 7. The additional sensing portions 50 may be provided on the sensor apparatus surrounding the detector regions 25. Thus, the additional sensing portions 50 may all be positioned outwards of the detector regions 25 as shown in figure 7.

[000108] Having a uniform grid pattern and stepping the sensor apparatus 21 and/or the measurement patterning device MA’ along by one detector region 25 and or patterning region 15 is particularly beneficial in reducing the thermal impact of the measurement process. This may be particularly advantageous compared to a system which is required to move the sensor apparatus 21 and/or the measurement patterning device MA’ over large distances and/or more frequently.

[000109] Each projection system will have different aberrations across the whole field. This means that each field point (i.e. for each spatial location in its image plane), a different measurement could be taken. Preferably, the projection system PL is configured to project the measurement beams 17 and the measurement system is configured to take measurements across a whole field of the projection system PL. Thus, preferably measurements are taken across the whole projection system. This may mean that measurements are taken across the full width and height of the field. Each field point may correspond to a location of a radiation beam projected through the projection system PL. Preferably, a measurement is taken for each field point. Thus, preferably a measurement is taken for each measurement beam 17. Lor example, in the context of figure 8, at least one measurement may be taken for each field point of the projection system. In some instances, it may be preferable to take multiple measurements for at least one field point of the projection system. In other words, preferably multiple measurements are taken for at least one measurement beam. Lor example, the measurement patterning device is moved between figures 8A-C and figure 8D-L. Ligures 8A-8C show the first three measurements taken sequentially in a first configuration, which are indicated by the locations labelled X. It will be understood that additional measurements are taken in the first configuration for each detector region which is aligned with a patterned region. Ligures 8D-8E show the first three measurements taken sequentially in a second configuration, which are indicated by the locations labelled X. It will be understood that additional measurements are taken in the second configuration for each detector region which is aligned with a patterned region. However, there is some overlap of field points which will be measured in the first configuration shown in Ligures 8A-C and in the second configuration shown in figures 8D-E. Thus, multiple measurement will be taken for field points which are measured in both configurations.

[000110] Measuring a measurement beam multiple times, e.g. at a plurality of detector regions and/or via a plurality of patterned regions may provide more information about the measurement beam (when compared to only measuring a measurement beam being received at a single detector region 25a-25g). For example, measuring a measurement beam multiple times at a plurality of detector regions may provide information about the measurement beam which is less dependent on the positioning, orientation and configuration of the sensor apparatus 21. Measuring a measurement beam multiple times and being received at a plurality of detector regions may allow aberrations which are caused by the projection system PL to be separated from aberrations which are a result of errors in the positioning and/or the configuration of the sensor apparatus 21. Similarly, measuring a measurement beam multiple times and being patterned by a plurality of patterned regions may allow aberrations which are caused by the projection system PL to be separated from aberrations which are a result of errors in the positioning and/or the configuration of the measurement patterning device MA’. This advantageously allows data relating to aberrations caused by the projection system PL and which relate to lower order Zernike coefficients (in addition to data relating to aberrations which relate to higher order Zernike coefficients) to be determined.

[000111] Above it is described that the sensor apparatus 21 and the measurement patterning device MA’ are provided in a first configuration and a second configuration. The sensor apparatus 21 and the measurement patterning device MA’ may be provided in various additional configurations, e.g. at least a third configuration and optionally more additional configurations. As described above, the positioning apparatus PW is configured to move at least one of the measurement patterning device MA’ and the sensor apparatus 21 so as to change the relative configuration to provide the measurement patterning device MA’ and the sensor apparatus 21 in a third configuration. In this embodiment, the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus 21 to make a measurement of radiation at each detector region 25a-c which aligns with a patterned region 15a-c when the patterning device and the sensor apparatus are in the third configuration. Each additional configuration provides measurement information which can be used to more accurately determine data relating to aberrations of the projection system PL. The specific modes of movement described above may be used between different configurations.

[000112] In a given configuration, each detector region is preferably aligned with a subset of patterned regions. Thus, for a given configuration each detector region is lined up with a respective patterned region and is to be illuminated with a measurement beam which has been patterned by the respective patterned region. Preferably, adjacent measurement beams are patterned by the subset of patterned regions. This is shown for example in figure 2, in which adjacent measurement beams 17a, 17b and 17c are patterned by patterned regions 15a, 15b and 15c respectively and are detected at detector regions 25a, 25b and 25c respectively. As the measurement beams are projected sequentially, in the embodiment shown in figure 2, patterned measurement beam 17a may be projected onto detector region 25a, followed by patterned measurement beam 17b being projected onto detector region 25b, followed by patterned measurement beam 17c being projected onto detector region 25c.

[000113] The measurement system is configured to use the radiation measurements to determine data relating to aberrations caused by the projection system. For any given measurement, there may be a number of different factors which affect the measurement. Thus, it is not possible to determine the contribution from the projection system PL from a single measurement and the data relating to aberrations caused by the projection system PL cannot be determined from individual measurements.

[000114] The value measured by each detector region of the sensor apparatus is a sum of contributions from projector system PL aberrations, patterning region placement errors (which may be of the order of approximately Inm), support structure MT placement errors (which may be of the order of approximately Inm), detector region placement errors (which may be of the order of approximately Inm), substrate table (if that is the support provided for the sensor apparatus 21) placement errors (which may be of the order of approximately Inm) as well as other errors. As will be understood, without further analysis of the measurements, this will not provide an accurate measurement, e.g. of the order of approximately 20, or 50 or 100 pm, of the aberrations introduced from the projector system PL because the other errors affect the measurement and are generally larger. Thus, determining the data relating to aberrations involves steps of separating the projector system PL aberrations from the other errors.

[000115] The radiation measurements can be used to determine the data relating to aberrations using known stitching techniques. Any known mechanism for stitching can be used to isolate the data relating to aberrations caused by the projection system PL. For example, the aberrations may be determined from the measurements as described in WO 2016/169890 which is hereby incorporated by reference.

[000116] The measurement system may be configured to use at least the first and second measurements to determine the placement of the patterned regions and/or the detector regions to determine data relating to aberrations caused by the projection system. Determining the placement of the patterned regions and/or the detector regions may comprise deriving Zernike coefficients having a Noll index of 4 or less. The measurement system may be configured to use at least the first and second measurements to derive Zernike coefficients.

[000117] Determining data relating to aberrations caused by the projection system may comprise determining the placement of a wavefront which is projected by the projection system. For example, determining data relating to aberrations caused by the projection system may comprise determining data relating to aberrations related to second, third, fourth and/or fifth Zernike coefficients. Determining data relating to aberrations may include determining data relating to higher order aberrations, e.g. related to sixth or higher Zernike coefficients. However, higher-order aberrations (e.g. greater than or equal to sixth Zernike coefficients) are much less sensitive to positions errors, therefore typically, the desired accuracy may be reached without using the present stitching method for these higher-order aberrations.

[000118] Data relating to aberrations may be the value of the Zernike coefficient at a given field point compared to the value of the same Zernike coefficient at another field point, i.e. the difference of a specific Zernike coefficient between different field points. Preferably, the data relating to the aberrations is the difference between a Zernike coefficient between adjacent field points. For example, the data relating to the aberrations may be the determined difference between the second Zernike coefficient at adjacent field points, and/or the data relating to the aberrations may be the determined difference between the third Zernike coefficient at adjacent field points, etc.. The data relating to the aberrations may be the value of the Zernike coefficient at a given field point. Determining a value for a Zernike coefficient at a given field point may require additional assumptions than determining the difference of a Zernike coefficient between different field points. The value of the Zernike coefficient at a given location may be determined by fitting measurements made to Zernike polynomials in order to obtain Zernike coefficients, for example, as described in WO 2016/169890 which is hereby incorporated by reference in its entirety.

[000119] Different Zernike coefficients may provide information about different forms of aberration which are caused by the projection system PL. 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, 3 A and 3B, Zernike coefficients may be determined for each measurement beam 17a- 17c.

[000120] As was mentioned above different Zernike coefficients may provide information about different forms of aberration which are caused by the projection system PL. Determining data relating to aberrations which are caused by the projection system PL may comprise fitting the measurements which are made by the sensor apparatus 21 to Zernike polynomials in order to obtain Zernike coefficients. Typically, Zernike polynomials are considered to comprise a plurality of orders, each order having an associated Zernike coefficient. The orders and coefficients may be labelled with an index, which is commonly referred to as a Noll index. 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.

[000121] 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 not be relevant to the performance of the projection system PL 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. The fifth Zernike coefficient relates to astigmatism of the projection system. 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).

[000122] The measurement system may be configured to use at least the first and second measurements to derive second, third, fourth and/or fifth Zernike coefficients. In particular, the measurement system may be configured to determine the Zernike coefficients using a stitching method based on at least the first and second measurements.

[000123] An example of the stitching method is described below based on a simplified model shown in figure 9. In the example shown in figure 9, nine measurements are taken by 3 sensors at 5 field points of the projection system. The three sensors are moved between a first configuration (the top row of sensors), a second configuration (the middle row of sensors), and a third configuration (the bottom row of sensors). Measurements are taken by each sensor in each configuration. As the sensors are moved between the different configurations, the sensors measure different field points/measurement beams in each configuration. Each measurement includes errors introduced by the sensor (Ax_sen) and errors introduced by the projection system PL (AXPOB) as well as other errors (accounted for by the setpoints included in equation 1 below).

[000124] The first measurement (Ax_mea(l)) is taken by sensor 1 in relation to the first field point/measurement beam (AXPOB(I)). The second measurement (Ax_mea(2)) is taken by sensor 2 in relation to second field point/measurement beam (AXPOB(2)). The third measurement (Ax_mea(3)) is taken by sensor 3 in relation to the third field point/measurement beam (AXPOB(3)). The fourth measurement (Ax_mea(4)) is taken by sensor 1 in relation to the second field point/measurement beam (AXPOB(2)). The fifth measurement (Ax_mea(5)) is taken by sensor 2 in relation to third field point/measurement beam (AXPOB(3)). The sixth measurement (Ax_mea(6)) is taken by sensor 3 in relation to the fourth field point/measurement beam (AXPOB(4)). The seventh measurement (Ax_mea(7)) is taken by sensor 1 in relation to the third field point/measurement beam (AXPOB(3)). The eighth measurement (Ax_mea(8)) is taken by sensor 2 in relation to fourth field point/measurement beam (AXPOB(4)). The ninth measurement (Ax_mea(9)) is taken by sensor 3 in relation to the fifth field point/measurement beam (AXPOB(5)).

[000125] The measurements can be represented by the following stitching equation (1): Equation 1

[000126] Setpoint 1 is shown as Ax_setp(l), setpoint 2 is shown as Ax_set_P(2), setpoint 3 is shown as Ax_setp(3). The setpoints are included to account for errors other than those introduced by the sensor or the projection system PL. The setpoints represent the unknowns in the position of the sensor as a whole.

[000127] In equation (1), AXPOB, Ax_sen and Ax_set_P are unknown. The aim is to determine at least AXPOB from the measured values Ax_mea. However, equation (1) does not have a unique solution.

[000128] Equation 1 is shown in short in equation 2:

Ax_mea — M Ax_unk

Equation 2

[000129] The design matrix M in equation 2 represents the matrix shown in Equation 1. The design matrix in Equation 1 is based on Figure 9, however, this design matrix will depend on which measurements are made by each sensor in a each configuration.

[000130] The design matrix is described in further detail below in relation to the detector regions 25a-gand measurement beams 17a- 17g as shown in Figures 5A-C. The design matrix represents measurements taken when the sensor apparatus 21 and the measurement patterning device MA’ are in different configurations (i.e. are moved relative to each other between measurements). Each shift position described below corresponds to a specific configuration sensor apparatus 21 and the measurement patterning device MA’ . For example, the 0 x-shift position may be the configuration shown in figure 5B. The +1 x-shift position may be the configuration shown in figure 5 A. The -1 x- shift position may be the configuration shown in figure 5C. Other shift positions may represent additional configurations where the sensor apparatus 21 and/or measurement patterning device MA’ are moved related to each other between different configurations.

[000131] Figure 10A is a schematic representation of the information which can be obtained by the measurements such as those described above. The representation which is shown in Figure 10A may be referred to as a design matrix. The design matrix corresponds to M in equation 2. Each row of the design matrix represents a sub-measurement and each column of the design matrix represents information relating to an unknown variable of the measurement system.

[000132] The unknown variables of the measurement system relate to properties of the sensor apparatus 21, the measurement patterning device MA’ and the projection system PL. As will be described below the sub-measurements which are represented in the design matrix of Figure 10A allow the unknown variables which relate to the sensor apparatus to be separated from the unknown variables which relate to the measurement patterning device MA’ and the projection system PL. The unknown variables are therefore represented in Figure 10A as 14 columns where each column relates an unknown. The first 7 columns in Figure 10A each relate to an unknown which is associated with one of the seven detector regions 25a-25g of the sensor apparatus 21 as shown in Figures 5A-C. The second 7 columns in Figure 10A each relate to an unknown which is associated with one of the seven measurement beams 17a- 17g as shown in Figures 5A-C. Unknowns which are associated with the measurement beams 17a-17g may relate to unknown variables of the measurement patterning device MA’ and/or unknown variables of the projection system PL.

[000133] As is indicated in Figure 10A the first three rows of the design matrix relate to sub-measurements which are made when the sensor apparatus 21 is in a +4 x-shift position. In the +4 x-shift position three of the measurement beams 17a-17g are received at three of the detector regions 25a-25g. Three sub-measurements are therefore made when the sensor apparatus 21 is in the +4 x- shift position and hence the first three rows of the design matrix relate to the sensor apparatus 21 in the +4 x-shift position.

[000134] As can be seen from Figure 10A, the next four rows of the design matrix relate to four sub-measurements which are made when the sensor apparatus 21 is in a +3 x-shift position, the next five rows relate to five sub-measurement which are made when the sensor apparatus 21 is in a +2 x-shift position and so on. When the sensor apparatus is in a 0 x- shift position all seven measurement beams 17a-17g are received at a respective detector region 25a-25g (as shown in figure 5B). Seven sub-measurements are therefore made when the sensor apparatus 21 is in the 0 x-shift position and accordingly seven rows of the design matrix relate to the 0 x-shift position.

[000135] Each sub-measurement (and hence each row of the design matrix) relates to the measurement of a single measurement beam 17a-17g at a single detector region. Each row of the design matrix therefore contains information which is related to an unknown associated with a single detector region 25a-25g and information which is related to an unknown associated with a single measurement beam 17a-17g. Accordingly each row of the design matrix contains two non-zero values. Non-zero values which are associated with a detector region 25a-25g are represented in Figure 10A with white shaded regions. Non-zero values which are associated with a measurement beam 17a- 17g are represented in Figure 10A with black shaded regions. Zero values are represented in Figure 10A with grey shaded regions. Grey shaded regions denote unknowns about which a given sub-measurement does not provide any information.

[000136] The design matrix which is shown in Figure 10A may equivalently be thought of as a series of equations, where each row of the design matrix relates to a single equation. The equations may be solved simultaneously so as to find the unknowns which relate to the sensor apparatus 21 and the measurement beams. Finding the unknowns may allow data relating to aberrations which are caused by the projection system PL to be determined. By separately finding the unknowns which are associated with the sensor apparatus 21, the influence of uncertainties associated with the sensor apparatus 21 on the determination of the data relating to aberrations which are caused by the projection system may be advantageously reduced. [000137] In the example, which is shown in Figure 10A there are more equations than there are unknowns. This may allow the unknowns to be found from the equations. However the equations may be under constrained and therefore extra constraints may need to be added to the design matrix in order to solve for the unknowns. This is represented in Figure 10A with an extra row at the bottom of the design matrix. The extra constraints may relate to a physical assumption which is made about the measurement system. For example, in one embodiment it may be assumed that the sum of the offsets of the detector regions 25a-25g from their presumed positions is equal to zero. This assumption may be added to the design matrix by adding the following equation (3): kd_k = 0 where k is an index which denotes the detector regions 25a-25g and dk is the offset of the k* detector region. This assumption is shown in the bottom row of the design matrix which is shown in Figure 10A in which the elements relating to the sensor apparatus unknowns have non-zero values.

[000138] Adding the extra constraint that the average offset of the detector regions 25a-25g from their presumed positions is equal to zero may allow the equations to be solved and the data relating to aberrations which are caused by the projection system PL to be determined. In other embodiments different and/or additional physical assumptions may be added to the design matrix in order to solve the equations and determine data relating to aberrations which are caused by the projection system PL.

[000139] In the design matrix which is represented in Figure 10A, the only unknowns which are included relate to the sensor apparatus 21 and the measurement beams 17a-17g. These unknowns are presumed to be the same during each relative configuration of the sensor apparatus 21 and the measurement patterning device MA’. That is, at each shift position of the sensor apparatus 21 and at each row of the design matrix the unknowns are assumed to be the same. Such a formulation of the design matrix effectively assumes that no errors are made in the shifting of the sensor apparatus 21 between shift positions and that any uncertainties associated with the sensor apparatus 21 are constant and equal at each shift position. As will be described below, this may be a reasonable assumption to make for the purposes of determining data relating to some aberrations which are caused by the projection system PL but not for determining data relating to other aberrations which are caused by the projection system PL.

[000140] Aberrations which relate to higher order Zernike coefficients (e.g. having a Noll index in the range of 5 to about 50) relate to forms of aberration which are likely to be caused by optical elements which form the projection system and are not likely to be caused by the measurement patterning device MA’ and/or the sensor apparatus 21. For example, higher order Zernike coefficients may relate to effects such as astigmatism, coma and/or spherical aberrations. In particular, uncertainties in the shifting of the sensor apparatus 21 are unlikely to introduce aberrations such as astigmatism, coma and/or spherical aberrations into measurements made by the sensor apparatus 21. Uncertainties in the shifting of the sensor apparatus 21 may not therefore affect the determination of higher order Zernike coefficients. An assumption that no errors are made in the shifting of the sensor apparatus 21 between shift positions may therefore be a reasonable assumption to make when determining higher order Zernike coefficients since accounting for shift uncertainties may not affect the determination of higher order Zernike coefficients. The design matrix which is shown in Figure 10A may therefore be suitable for determining data relating to aberrations which relate to higher order Zernike coefficients (e.g. having a Noll index in the range of 5 to about 50).

[000141] The determination of lower order Zernike coefficients (e.g. having a Noll index which is less than about 5) may be affected by uncertainties in the shifting of the sensor apparatus 21. As was described above, lower order Zernike coefficients relate to aberrations such as placement and focus. Errors in the shifting of the sensor apparatus 21 between shift positions may introduce placement and focus aberrations into the measurements made by the sensor apparatus 21 and thus uncertainties in the shifting of the sensor apparatus 21 may affect the determination of lower order Zernike coefficients. Accordingly, it may not be reasonable, for the purposes of determining lower order coefficients, to assume that no errors are made in the shifting of the sensor apparatus 21 between different shift positions.

[000142] Errors in the shifting of the sensor apparatus 21 between shift positions may be accounted for by introducing further unknowns to the design matrix. Figure 10B is a schematic representation of a design matrix in which further unknowns have been included. The further unknowns are shown in Figure 10B as extra columns added to the right hand side of the design matrix. In the embodiment which is shown in Figure 10B the further unknowns relate to offsets in the shift of the sensor apparatus 21 between different shift positions. Each shift position of the sensor apparatus 21 has an associated unknown related to the shift offset of the sensor apparatus 21 at that shift position. Therefore, for each shift position an extra unknown column is added to the design matrix.

[000143] At each shift position of the sensor apparatus 21, the sub-measurements which are made at that shift position contain information related to the shift offset of the sensor apparatus 21 at that shift position. For example, the three sub-measurements which are made at the +4 x-shift position each contain information related to the shift offset of the sensor apparatus 21 at the +4 shift position. This can be seen in Figure 10B since the first shift offset column of the design matrix (which relates to the shift offset of the sensor apparatus 21 at the +4 shift position) contains non-zero values in the top three rows which relate to the sub-measurements which are made in the +4 shift position.

[000144] Since the design matrix which is shown in Figure 10B contains extra unknowns (when compared with the design matrix which is shown in Figure 10A) further extra constraints may need to be added to the design matrix in order to solve for all of the unknowns. This is shown in Figure 10B with two extra rows which are added to the bottom of the design matrix when compared with the design matrix which is shown in Figure 10A. The two extra rows relate to further physical assumptions which are made about the measurement system. The design matrix of Figure 10B contains the assumptions that the sum of the offsets of the detector regions 25a-25g from their presumed positions is equal to zero (first row of extra constraints), that the sum of the offsets of the patterned regions 15a-15g from their presumed positions is equal to zero (second row of extra constraints) and that the sensor apparatus 21 no magnification is introduced by shifting the sensor apparatus 21 in the x-direction (third row of extra constraints).

[000145] The assumption that the sum of the offsets of the detector regions 25a-25g from their presumed positions is equal to zero may be added to the design matrix in the form of equation (3). The assumption that the sum of the offsets of the patterned regions 15a-15g from their presumed positions is equal to zero may be added to the design matrix by adding the following equation (4): iPi = o where 1 is an index which denotes the patterned regions 15a-15g and pi is the offset of the 1* patterned region. The assumption that no magnification is introduced by shifting the sensor apparatus 21 in the x-direction may be added to the design matrix by adding the following equation (5):

HfcXcl] — 0 where x is a position on the x-axis of the detector regions 25a-25g. When this assumption is applied to the calculation of the second Zernike coefficient it is equivalent to assuming that the magnification of the sensor apparatus 21 is equal to a desired (or design) magnification.

[000146] The addition of equations (3), (4) and (5) to the design matrix may allow data relating to aberrations which are caused by the projection system PL to be determined whilst accounting for uncertainties related to offsets in the shift of the sensor apparatus 21 between shift positions. The design matrix which is shown in Figure 10B may, for example, be used to determine one or more lower order Zernike coefficients (e.g. having a Noll index of 4 or less). The design matrix which is shown in Figure 10B may, for example, be used to determine the second Zernike coefficients for each measurement beam 17a-17g. The design matrix may be resolved to determine the data relating to the aberrations, i.e. to rethe value of the Zernike coefficient at a given field point and/or the difference of a specific Zernike coefficient between different field points.

[000147] As was described above, the design matrix which is shown in Figure 10B includes extra unknowns which relate to the offsets in the shift of the sensor apparatus 21 between shift positions and thus uncertainties in the shift offsets are accounted for. This approach assumes that the only uncertainties which are associated with the shifting of the sensor apparatus 21 relate to offsets in the shifting. The design matrix of Figure 10B therefore includes an assumption that no rotation of the sensor apparatus 21 occurs in the shifting. For example, the design matrix of Figure 10B assumes that no rotation of the sensor apparatus 21 about the y or the z-axis occurs. This assumption may be a reasonable assumption to make when determining the second Zernike coefficients relating to each measurement beam 17a-17g since rotations of the sensor apparatus 21 about the y and/or the z-axis are unlikely to affect the determination of the second Zernike coefficients. The second Zernike coefficient relates to a placement of a measured wavefront in the x-direction. Rotation of the sensor apparatus 21 about the y and/or the z-axis are unlikely to introduce a magnification to the measurements made by the sensor apparatus 21. Not accounting for such rotations in the sensor apparatus 21 may therefore be a reasonable assumption to make when determining the second Zernike coefficients.

[000148] As was described above the third Zernike coefficient relates to the placement of a measured wavefront in the y-direction and the fourth Zernike coefficient relates to a focus of a measured wavefront or equivalently to the placement in the z-direction of a measured wavefront. A rotation of the sensor apparatus 21 which occurs during shifting of the sensor apparatus 21 may introduce a placement error in the y-direction and/or may change the focus of radiation which is measured by the sensor apparatus 21. Rotation of the sensor apparatus 21 may therefore affect a determination of the third and/or fourth Zernike coefficients. In order to determine data relating to aberrations which are caused by the projection system PL and which relate to the third and fourth Zernike coefficients, uncertainties in the tilt of the sensor apparatus which occur during shifting of the sensor apparatus 21 may therefore be included as extra unknowns in the design matrix.

[000149] Figure 10C is a schematic representation of a design matrix which may be used to determine third and/or fourth Zernike coefficients. The design matrix which is shown in Figure 10C includes extra columns (when compared to the design matrix of Figure 10B) which relate to unknowns associated with the tilt of the sensor apparatus which occurs during shifting of the sensor apparatus 21. Each shift position of the sensor apparatus 21 has an associated unknown related to the tilt of the sensor apparatus 21 at that shift position. Therefore, for each shift position an extra unknown column is added to the design matrix. At each shift position of the sensor apparatus 21, the sub-measurements which are made at that shift position contain information related to the tilt of the sensor apparatus 21 at that shift position. For example, the three sub-measurements which are made at the +4 x-shift position each contain information related to the tilt of the sensor apparatus 21 at the +4 shift position. This can be seen in Figure 10C since the first shift tilt column of the design matrix (which relates to the tilt of the sensor apparatus 21 at the +4 shift position) contains non-zero values in rows which relate to the sub-measurements which are made in the +4 shift position. The submeasurements which are made in each shift position each provide different information about the tilt of the sensor apparatus 21 in that shift position. This can be seen in Figure 10C by the different values which appear in each shift tilt column at a given shift position. [000150] Since the design matrix which is shown in Figure 10C contains extra unknowns (when compared with the design matrix which is shown in Figure 10B) further extra constraints may need to be added to the design matrix in order to solve for all of the unknowns. This is shown in Figure 10C with two extra rows which are added to the bottom of the design matrix when compared with the design matrix which is shown in Figure 10B. The two extra rows relate to further physical assumptions which are made about the measurement system. The design matrix of Figure 10C contains the assumptions that the sum of the offsets of the detector regions 25a-25g from their presumed positions is equal to zero (first row of extra constraints), that the sum of the offsets of the patterned regions 15a-15g from their presumed positions is equal to zero (second row of extra constraints), no magnification is introduced by shifting the sensor apparatus 21 in the x -direction (third row of extra constraints), that the measurement patterning device MA’ is not tilted in the x- direction (fourth row of extra constraints) and that the sensor apparatus 21 does not include any curvature (fifth row of extra constraints).

[000151] The first three constraints (which were also included in the design matrix which is shown in Figure 10B) may be added to the design matrix in the form of equations (3), (4) and (5) as was described above. The assumption that the measurement patterning device is not tilted in the x- direction may be added to the design matrix by adding the following equation (6): ixpi = 0 where 1 is an index which denotes the patterned regions 15a-15g, p_t is the offset of the 1* patterned region and x is a position on the x-axis of the patterned regions 15a-15g. The assumption that the sensor apparatus 21 does not include any curvature may be added to the design matrix by adding the following equation (7): kx²d_k = 0 where the variables in equation (7) are the same as was described above with reference to equation (5).

[000152] The addition of the extra constraints to the design matrix may allow data relating to aberrations which are caused by the projection system PL to be determined whilst accounting for uncertainties related to offsets in the shift of the sensor apparatus 21 between shift positions and for uncertainties related to tilt of the sensor apparatus 21 which occurs during shifting of the sensor apparatus 21 between shift positions. The design matrix which is shown in Figure 10C may, for example, be used to determine one or more lower order Zernike coefficients (e.g. having a Noll index of 4 or less). The design matrix which is shown in Figure 10C may, for example, be used to determine the third and/or the fourth Zernike coefficients for each measurement beam 17a-17g. [000153] Some or all of the physical assumptions which are made in order to add the extra constraints to the design matrix of Figure 10C are reasonable assumptions to make. For example, the position and/or tilt of the sensor apparatus in the x-direction may be closely controlled and calibrated and thus the assumptions of equations (3)-(6) may hold true to a reasonable accuracy. However, in some embodiments it may be desirable to not include the assumption that the sensor apparatus 21 does not include any curvature (equation (7)). In some embodiments the sensor apparatus 21 may include some curvature. For example, regions of the sensor apparatus 21 may be heated locally which may introduce curvature to the sensor apparatus 21. If the sensor apparatus 21 is assumed to include no curvature then the determination of data relating to aberrations which are caused by the projection system PL may be affected by curvature of the sensor apparatus 21 thereby introducing uncertainties in the determination of data relating to aberrations. In some embodiments, it may therefore be desirable to determine data relating to aberrations which are caused by the projection system PL whilst accounting for any curvature of the sensor apparatus 21. In particular it may be desirable to provide a method which enables the curvature of the sensor apparatus 21 to be determined whilst simultaneously determining data relating to aberrations which are caused by the projection system PL. [000154] Embodiments have been described above in which patterned regions 15a-15g of a measurement patterning device MA’ are spaced apart in the x-direction, detector regions 25a-25g of a sensor apparatus 21 are spaced apart in the x-direction and the sensor apparatus 21 is shifted relative to the measurement patterning device MA’ in the x-direction. In some embodiments, a measurement patterning device MA’ may include patterned regions which are also spaced apart in the y-direction. A sensor apparatus may include detector regions which are additionally or alternatively spaced apart in the y-direction and the sensor apparatus 21 may be shifted relative to the measurement patterning device MA’ in both the x and y-directions. The spacing between detector regions in the y-direction may be the same as the spacing between detector regions in the x-direction or may be different to the spacing between detector regions in the x-direction.

[000155] As was described above, in general measurements made at different shift positions are added to a design matrix and the design matrix is solved in order to derive data relating to aberrations caused by the projection system. Typically, in order to solve the design matrix a number of constraints are added to the design matrix in the form of extra equations (or equivalently extra rows are added to the matrix). The constraints allow singularities to be removed from the design matrix so as to allow a solution to be found.

[000156] The constraints are based on physical assumptions related to the measurement patterning device MA’, the sensor apparatus 21 and the relative movement of the measurement patterning device MA’ and the sensor apparatus 21. Constraints may relate to offsets of features. For example, constraints may relate to the offset of patterned regions 25, detector regions 25 and/or offsets in the relative movement of the measurement patterning device MA’ and the sensor apparatus 21. Some constraints may relate to a tilt or magnification of components. For example, constraints may relate to a tilt of the measurement patterning device MA’, the sensor apparatus 21 and/or tilts in the movement of the measurement patterning device MA’ and the sensor apparatus 21. In some embodiments, constraints may be used which include quadratic terms, for example, constraints which relate to a curvature of components.

[000157] In some embodiments, different constraints may be used in order to determine different Zernike coefficients. For example, different constraints may be used in order to determine the fourth Zernike coefficient to constraints which are used to determine the second and third Zernike coefficients. In particular, it may be desirable not to use constraints related to a curvature of components (e.g. constraints which include quadratic terms) in order to determine the second and third Zernike coefficients. Constraints related to a curvature of components may however, be used to determine the fourth Zernike coefficient (and/or other Zernike coefficients).

[000158] The constraints which are chosen in order to determine one or more Zernike coefficients may be made based on the physical assumptions which underlie the constraints and the effects of the physical assumptions on the one or more Zernike coefficients to be determined. In general, in embodiments in which at least one of the patterning device and the sensor apparatus are moved relative to each other in two different directions (e.g. the x and y-directions) in order to perform measurements, and in which data relating to aberrations are determined in three dimensions, a total of nine different constraints may be added to a design matrix in order to determine each Zernike coefficient at each field point.

[000159] In some embodiments, the same set of constraints may be used in order to determine the second and third Zernike coefficients and a different set of constraints may be used to determine the fourth Zernike coefficient.

[000160] In some embodiments the constraints used to determine the second and/or the third Zernike constraints may include constraints in the form of assuming that a sum of offsets of the patterned regions 15 are equal to zero in both the x and y-directions (i.e. this assumption forms two separate constraints, one in the x-direction and one in the y-direction). Such constraints may have a form similar to the constraint described above with reference to equation (4). The constraints may further include constraints in the form of assuming that a sum of offsets of the detector regions 25 are equal to zero in both the x and y-directions (i.e. this assumption forms two separate constraints, one in the x-direction and one in the y- direction). Such constraints may further include constraints similar to the constraint described above with reference to equation (3).

[000161] The constraints may further include constraints in the form of linear terms in x and y, which relate to the tilt or magnification of measurement patterning device MA’ . For example, the constraints may include constraints in the form of assuming that the magnification of the sensor apparatus is substantially equal to a design magnification in both the x and y-directions (i.e. this assumption forms two separate constraints, one in the x- direction and one in the y-direction). Such constraints may have a form similar to the constraint described above with reference to equation (6). The constraints may further include constraints in the form of assuming that the measurement sensor apparatus 21 is not tilted in the x-direction or in the y-direction (i.e. this assumption forms two separate constraints, one in the x-direction and one in the y-direction).

[000162] The constraints may further include a constraint in the form of assuming that relative movement of the measurement patterning device MA’ and the sensor apparatus 21 do not include any offsets in the form of a rotation about the z-axis.

[000163] In some embodiments, the above described constraints may form the nine constraints added to the design matrix used to determine the second and third Zernike coefficients.

[000164] A set of constraints used to determine the fourth Zernike coefficient may be different to the above described constraints. In some embodiments, the constraints used to determine the fourth Zernike coefficient may include a constraint in the form of an assumption that a sum of offsets of the patterned regions 15 in the z-direction is equal to zero. The constraints may further include a constraint in the form of an assumption that a sum of offsets of the detector regions 25 in the z- direction is equal to zero.

[000165] The constraints may further include constraints in the form of linear terms in x and y, which relate to changes in position in the z-direction as a function of position in x and y. For example, the constraints may include constraints in the form of an assumption that the position of the detector regions 25 in the z-direction do not change as a function of x or y (i.e. this assumption forms two separate constraints, one in the x-direction and one in the y- direction).

[000166] The constraints may further include constraints in the form of assuming that relative movements of the measurement patterning device MA’ and the sensor apparatus 21 do not include any offsets in the form of a rotation about the x-axis or rotation about the y- axis (i.e. these assumptions form two separate constraints, one related to rotation about the x-axis and one related to rotation about the y-axis).

[000167] The constraints may further include constraints in the form of quadratic terms. For example, the constraints may include constraints in the form of an assumption that relative movements of the measurement patterning device MA’ and the sensor apparatus 21 do not include any curvature in the x-direction or in the y-direction and do not include offsets as a function of x times y (i.e. this assumption forms three separate constraints).

[000168] In some embodiments, the above described constraints may form the nine constraints added to the design matrix used to determine the second and third Zernike coefficients.

[000169] In other embodiments constraints other than those described above may be used. However, the constraints described above have been found to be particularly advantageous for use in deriving the second, third and fourth Zernike coefficients (as described above).

[000170] In some embodiments, as an alternative to using constraints in the form of physical assumptions, one or more of the constraints may be replaced with information derived from measurements taken by another sensor. For example, one or more alignment sensors may be used in a lithographic apparatus and the results of measurements made by the one or more alignment sensors may be added to a design matrix in place of a constraint based upon a physical assumption. In some embodiments, a separate alignment sensor may be used to measure offsets and/or magnifications associated with the sensor apparatus 21 and detector regions 25. These measurements may be added to a design matrix in place of constraints related to assumptions involving offsets and/or magnifications of the sensor apparatus 21 and detector regions 25. Use of information derived from measurements as opposed to being based on assumptions may advantageously lead to an increase in accuracy of the determined data relating to aberrations.

[000171] As an aside, there are some “non-stitching” parameters, which are parameters which cannot be solved in the above equation (i.e. the lower order parameters). Fortunately, some of these non-stitching parameters are considered unimportant, or non-interesting, e.g. corresponding to an error relating to the projection system PL which is very easy to correct for during exposure. This error can be measured, together with all other sources for translation, just before exposure, and can be corrected by appropriate adaptation of the substrate table WT position. However, for some nonstitching parameters, this is not true. For example, magnification errors relating to the projection system PL may not be corrected without introducing parasitic higher order aberrations. At present, it is assumed that the magnitude of the non-stitching parameters are small enough and so the nonresolution of these parameters is not considered further here.

[000172] Thus, in the analysis all non-stitching parameters are disregarded. It is worth noting that the non-stitching parameters are not necessarily set to 0.

[000173] The above model can be applied to more complex systems comprising additional dimensions, degrees of freedom, to account for stitching at the measurement patterning device MA’, and to account for more complex relations between unknowns and measurement results.

[000174] The above can be resolved (with the selection of specific constraints) to obtain the data relating to the aberrations, e.g. to obtain Zernike coefficients representative of the aberrations caused by the projection system. It will be noted that it is not necessary to resolve to obtain the values of each individual Zernike coefficient at each field point. Instead, resolving the above model may result in an indication of the difference in respective Zernike coefficients between two field points, and preferably, between adjacent field points. Obtaining this data (i.e. relating to the difference rather than a value at each field point) is enough to be able to qualify the projection system PL. For example, the projection system may have an acceptable level of error (i.e. cause an acceptable amount of aberration) as long as all the data is below a predetermined threshold (e.g. as long as the differences in a given coefficient between adjacent field points are below a predetermined level). The predetermined level may be set by the user depending on the acceptable degree of error.

[000175] Thus, the measurement system can use the model described above, or other known stitching methods to derive the Zernike coefficients to determine the contribution of the projection system, i.e. to determine data relating to the aberrations caused by the projection system. [000176] It is described above that the measurement system is configured to determine the data relating to aberrations, more specifically, this may be the controller, or any processor which is configured to obtain the measurement information from the detector regions and is configured to carry out the relevant calculations to determine the data relating to aberrations.

[000177] The present invention can also be described or characterised by the following clauses:

1. A method of determining data relating to aberrations caused by a projection system, the method comprising: providing a patterning device with a plurality of patterned regions and a sensor apparatus with a plurality of detector regions; illuminating the patterning device with radiation, wherein each patterned region patterns a measurement beam; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in a first configuration; moving at least one of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a second configuration; sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the second configuration; and determining, from the radiation measurements, data relating to aberrations caused by the projection system.

2. The method of any preceding clause, further comprising moving at least one of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a third configuration, and sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the third configuration.

3. The method of any preceding clause, wherein moving at least one of the patterning device and the sensor apparatus comprises moving at least one of the patterning device and the sensor apparatus in a first direction or a second direction, substantially perpendicular to the first direction.

4. The method of clause 3, wherein at least some of the patterning regions of the patterning device are spaced apart from each other in the first direction.

5. The method of clause 3 or 4, wherein at least some of the detector regions of the sensor apparatus are spaced apart from each other in the first direction.

6. The method of any one of clauses 3 to 5, wherein moving at least one of the patterning device and the sensor apparatus comprises: i) stepping the sensor apparatus by a distance in the first direction which is approximately equal to a separation between detector regions in the first direction; and/or ii) stepping the patterning device by a distance in the first direction which is approximately equal to a separation between patterning regions in the first direction.

7. The method of any one of clauses 3 to 6, wherein the detector regions and a subset of the patterning regions are aligned in the first direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations.

8. The method of any one of clauses 3 to 7, wherein at least some of the detector regions of the sensor apparatus are spaced apart from each other in the second direction.

9. The method of any one of clauses 3 to 8, wherein at least some of the patterning regions of the patterning device are spaced apart from each other in the second direction.

10. The method of any one of clauses 3 to 9, wherein moving at least one of the patterning device and the sensor apparatus comprises: i) stepping the sensor apparatus by a distance in the second direction which is approximately equal to a separation between detector regions in the second direction; and/or ii) stepping the patterning device by a distance in the second direction which is approximately equal to a separation between patterning regions in the second direction.

11. The method of any one of clauses 3 to 10, wherein the detector regions and a subset of the patterning regions are aligned in the second direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations.

12. The method of any preceding clause, wherein there are fewer detector regions than patterned regions.

13. The method of any preceding clause, wherein in a given configuration, each detector region is aligned with a subset of patterned regions, and adjacent measurement beams are patterned by the subset of patterned regions.

14. The method of any preceding clause, wherein the detector regions are provided in an array and the patterning regions are provided in an array.

15. The method of clause 14, wherein the array of detector regions is smaller than the array of patterning regions.

16. The method of either of clauses 14 or 15, wherein the array of detector regions forms a uniform grid pattern.

17. The method of any preceding clause, wherein the sensor apparatus comprises additional sensing portions, preferably wherein the additional sensing portions are provided on the sensor apparatus surrounding the detector regions.

18. The method of any preceding clause, wherein the measurement beams are projected by the projection system and the method takes measurements across a whole field of the projection system. 19. The method of any preceding clause, wherein at least one measurement is taken for each measurement beam.

20. The method of any preceding clause, wherein multiple measurements are taken for at least one measurement beam.

21. The method of any preceding clause, wherein the method comprises using at least the first and second measurements to determine the placement of the patterned regions and/or the detector regions to determine data relating to aberrations caused by the projection system.

22. The method of any preceding clause, wherein the method comprises using at least the first and second measurements to derive Zernike coefficients.

23. The method of any preceding clause, wherein the method comprises using at least the first and second measurements to derive second, third, fourth and/or fifth Zernike coefficients.

24. The method of clause 22 or 23, wherein the Zernike coefficients are derived using a stitching method based on at least the first and second measurements.

25. The method of any preceding clause, wherein sequentially projecting individual patterned measurement beams comprises illuminating a single patterned region of the patterning device at a time.

26. The method of any one of clauses 1 to 25, wherein sequentially projecting individual patterned measurement beams comprises illuminating multiple patterned regions of the patterning device at a time, and masking the patterned measurement beams to allow for one patterned measurement beam to reach the sensor apparatus at a time.

27. The method of any preceding clause, wherein the data relating to aberrations caused by the projection system comprises (i) the difference of a Zernike coefficient between different field points, and/or (ii) a value of a Zernike coefficient at a given field point.

28. A measurement system for determining data relating to aberrations caused by a projection system, the measurement system comprising: a patterning device comprising a plurality of patterned regions, wherein each patterned region is configured to pattern a measurement beam when illuminated with radiation; an illumination system arranged to illuminate the patterning device with radiation; a sensor apparatus comprising a plurality of detector regions, wherein the sensor apparatus is configured to measure radiation at the detector regions; a projection system configured to project the patterned measurement beam onto the sensor apparatus, wherein the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region in a given configuration; a positioning apparatus configured to move at least one of the patterning device and the sensor apparatus so as to change the relative configuration of the patterning device and the sensor apparatus between a first configuration and a second configuration; and a controller configured to: receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the first configuration; receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the second configuration; and determine, from the radiation measurements, data relating to aberrations caused by the projection system.

29. The measurement system of clause 28, wherein the positioning apparatus is configured to move at least one of the patterning device and the sensor apparatus so as to change the relative configuration of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a third configuration, and wherein the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the third configuration.

30. The measurement system of either of clause 28 or 29, wherein the positioning apparatus is configured to move at least one of the patterning device and the sensor apparatus comprises in a first direction or a second direction, substantially perpendicular to the first direction.

31. The measurement system of clause 30, wherein at least some of the patterning regions of the patterning device are spaced apart from each other in the first direction.

32. The measurement system of either of clause 30 or 31 , wherein at least some of the detector regions of the sensor apparatus are spaced apart from each other in the first direction.

33. The measurement system of any one of clauses 30 to 32, wherein the positioning apparatus is configured to: i) step the sensor apparatus by a distance in the first direction which is approximately equal to a separation between detector regions in the first direction; and/or ii) step the patterning device by a distance in the first direction which is approximately equal to a separation between patterning regions in the first direction.

34. The measurement system of any one of clauses 30 to 33, wherein the detector regions and a subset of the patterning regions are aligned in the first direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations. 35. The measurement system of any one of clauses 30 to 34, wherein at least some of the detector regions of the sensor apparatus are spaced apart from each other in the second direction.

36. The measurement system of any one of clauses 30 to 35, wherein at least some of the patterning regions of the patterning device are spaced apart from each other in the second direction.

37. The measurement system of any one of clauses 30 to 36, wherein the positioning apparatus is configured to: i) step the sensor apparatus by a distance in the second direction which is approximately equal to a separation between detector regions in the second direction; and/or ii) step the patterning device by a distance in the second direction which is approximately equal to a separation between patterning regions in the second direction.

38. The measurement system of any one of clauses 30 to 37, wherein the detector regions and a subset of the patterning regions are aligned in the second direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations.

39. The measurement system of any one of clauses 28 to 38, wherein there are fewer detector regions than patterned regions.

40. The measurement system of any one of clauses 28 to 39, wherein in a given configuration, each detector region is aligned with a subset of patterned regions, and adjacent measurement beams are patterned by the subset of patterned regions.

41. The measurement system of any one of clauses 28 to 40, wherein the detector regions are provided in an array and the patterning regions are provided in an array.

42. The measurement system of clause 41, wherein the array of detector regions is smaller than the array of patterning regions.

43. The measurement system of either of clauses 41 or 42, wherein the array of detector regions forms a uniform grid pattern.

44. The measurement system of any one of clauses 28 to 43, wherein the sensor apparatus comprises additional sensing portions, preferably wherein the additional sensing portions are provided on the sensor apparatus surrounding the detector regions

45. The measurement system of any one of clauses 28 to 44, wherein the projection system is configured to project the measurement beams and the measurement system is configured to take measurements across a whole field of the projection system.

46. The measurement system of any one of clauses 28 to 45, wherein the measurement system is configured to take at least one measurement for each measurement beam.

47. The measurement system of any one of clauses 28 to 46, wherein the measurement system is configured to take multiple measurements for at least one measurement beam. 48. The measurement system of any one of clauses 28 to 47, wherein the measurement system is configured to use at least the first and second measurements to determine the placement of the patterned regions and/or the detector regions to determine data relating to aberrations caused by the projection system.

49. The measurement system of any one of clauses 28 to 48, wherein the measurement system is configured to use at least the first and second measurements to derive Zernike coefficients.

50. The measurement system of any one of clauses 28 to 49, wherein the measurement system is configured to use at least the first and second measurements to derive second, third, fourth and/or fifth Zernike coefficients.

51. The measurement system of either of clauses 49 or 50, wherein the measurement system is configured to derive the Zernike coefficients using a stitching method based on at least the first and second measurements.

52. The measurement system of any one of clauses 28 to 51, wherein the illumination system is configured to illuminate a single patterned region of the patterning device at a time.

53. The measurement system of any one of clauses 28 to 51, further comprising a masking device configured to mask the patterned measurement beams to allow for one patterned measurement beam to reach the sensor apparatus at a time.

54. The measurement system of any one of clauses 28 to 53, wherein the data relating to aberrations caused by the projection system comprises (i) the difference of a Zernike coefficient between different field points, and/or (ii) a value of a Zernike coefficient at a given field point.

55. A lithographic apparatus comprising the measurement system of any one of clauses 28 to 54. [000178] 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.

[000179] Although the patterning device MA’ is described above as being supported by a support structure MT, any appropriate patterning device may be used to pattern the measurement beams. For example, the patterning device may be provided by a fiducial comprising the patterned regions, with the fiducial being mounted on the support structure MT.

[000180] Whilst embodiments have been described above in which a measurement system is of a transmissive type, in other embodiments a reflective type measurement system may be used. For example, the patterning device may comprise reflective patterned regions, the projection system may include one or more reflective optics and/or the detector regions may include reflective optics.

[000181] 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 description is not intended to limit the invention.

Claims

2. The method of any preceding claim, further comprising moving at least one of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a third configuration, and sequentially projecting individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the third configuration.

3. The method of any preceding claim, wherein moving at least one of the patterning device and the sensor apparatus comprises moving at least one of the patterning device and the sensor apparatus in a first direction or a second direction, substantially perpendicular to the first direction.

4. The method of claim 3, wherein moving at least one of the patterning device and the sensor apparatus comprises: i) stepping the sensor apparatus by a distance in the first direction which is approximately equal to a separation between detector regions in the first direction; and/or ii) stepping the patterning device by a distance in the first direction which is approximately equal to a separation between patterning regions in the first direction.

5. The method of any one of claims 3 to 4, wherein moving at least one of the patterning device and the sensor apparatus comprises: i) stepping the sensor apparatus by a distance in the second direction which is approximately equal to a separation between detector regions in the second direction; and/or ii) stepping the patterning device by a distance in the second direction which is approximately equal to a separation between patterning regions in the second direction.

6. The method of any one of claims 3 to 5, wherein the detector regions and a subset of the patterning regions are aligned in the second direction when the patterning device and the sensor apparatus are in the first, second and/or third configurations.

7. The method of any preceding claim, wherein in a given configuration, each detector region is aligned with a subset of patterned regions, and adjacent measurement beams are patterned by the subset of patterned regions.

8. The method of any preceding claim, wherein the detector regions are provided in an array and the patterning regions are provided in an array.

9. The method of any preceding claim, wherein the measurement beams are projected by the projection system and the method takes measurements across a whole field of the projection system.

10. The method of any preceding claim, wherein the method comprises using at least the first and second measurements to derive Zernike coefficients.

11. A measurement system for determining data relating to aberrations caused by a projection system, the measurement system comprising: a patterning device comprising a plurality of patterned regions, wherein each patterned region is configured to pattern a measurement beam when illuminated with radiation; an illumination system arranged to illuminate the patterning device with radiation; a sensor apparatus comprising a plurality of detector regions, wherein the sensor apparatus is configured to measure radiation at the detector regions; a projection system configured to project the patterned measurement beam onto the sensor apparatus, wherein the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region in a given configuration; a positioning apparatus configured to move at least one of the patterning device and the sensor apparatus so as to change the relative configuration of the patterning device and the sensor apparatus between a first configuration and a second configuration; and a controller configured to: receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the first configuration; receive measurements of radiation from the detector regions when the patterning device and the sensor apparatus are positioned in the second configuration; and determine, from the radiation measurements, data relating to aberrations caused by the projection system.

12. The measurement system of claim 11, wherein the positioning apparatus is configured to move at least one of the patterning device and the sensor apparatus so as to change the relative configuration of the patterning device and the sensor apparatus to provide the patterning device and the sensor apparatus in a third configuration, and wherein the measurement system is configured to sequentially project individual patterned measurement beams onto the sensor apparatus to make a measurement of radiation at each detector region which aligns with a patterned region when the patterning device and the sensor apparatus are in the third configuration.

13. The measurement system of either of claim 11 or 12, wherein the positioning apparatus is configured to move at least one of the patterning device and the sensor apparatus comprises in a first direction or a second direction, substantially perpendicular to the first direction.

14. The measurement system of any one of claims 11 to 13, wherein the measurement system is configured to use at least the first and second measurements to determine the placement of the patterned regions and/or the detector regions to determine data relating to aberrations caused by the projection system.

15. A lithographic apparatus comprising the measurement system of any one of claims 11 to 14.