Improvements to lithographic methods and apparatus

Abstract

A method for determining one or more parameters for an imaging system that is for forming an image of an object on a substrate is disclosed. The method comprises determining a value of one or more movement parameters of at least one optical element of the imaging system during the formation of the image. The one or more movement parameters are such that at least one degree of freedom of the at least one optical element has a non-zero acceleration during at least part of the formation of the image. The value of the one or more movement parameters is determined in dependence on an impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined value of the one or more movement parameters.

Description

IMPROVEMENTS TO LITHOGRAPHIC METHODS AND APPARATUS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 24176927.2 which was filed on May 21, 2024 and which is incorporated herein in its entirety by reference. FIELD

[0002] The present invention relates to a method for determining a value of one or more movement parameters for an imaging system that is for forming an image of an object on a substrate. The imaging system may comprise the projection optics of a lithographic apparatus, the object may comprise a reticle and the substrate may comprise a resist-coated silicon wafer. The one or more movement parameters may be such that at least one degree of freedom of the at least optical element has a non-zero acceleration during at least part of the formation of the image. The present invention also relates to an exposure method that uses the determined value(s) of one or more movement parameters of the imaging system. The present invention also relates to a lithographic apparatus operable to carry out one or more of these new methods. The present invention may have particular application to extreme ultraviolet (EUV) lithography. BACKGROUND

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

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

[0005] Radiation that has been patterned by the patterning device is focussed onto the substrate using a projection system. The projection system may introduce optical aberrations, which may cause the image formed on the substrate to deviate from a desired image (for example a diffraction limited image of the patterning device). It is known to measure optical aberrations (for example periodically) and to adjust the projection optics. It is also known to use such measurement to at least partially correct for such optical aberrations in an attempt to minimize optical aberrations.

[0006] It may be desirable to provide methods and apparatus for correcting for such aberrations caused by a projection system that at least partially addresses one or more problems associated with prior art arrangements whether such problems are identified herein or otherwise. SUMMARY

[0007] According to a first aspect of the present disclosure there is provided a method for determining one or more parameters for an imaging system that is for forming an image of an object on a substrate, the method comprising: determining a value of one or more movement parameters of at least one optical element of the imaging system during the formation of the image, the one or more movement parameters being such that at least one degree of freedom of the at least optical element has a non-zero acceleration during at least part of the formation of the image, the value of the one or more movement parameters being determined in dependence on an impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined value of the one or more movement parameters.

[0008] The method of the first aspect of the present disclosure is advantageous, as now discussed. The method may have particular application to an imaging system of a lithographic apparatus.

[0009] In some lithographic apparatus, the radiation beam used to expose the wafer may cause thermal deformation of optical elements in the imaging optics. In turn, this can cause unwanted optical aberrations, degrading optical performance. Note that, in principal there may be other sources of optical aberrations, however, thermally induced aberrations are often the main source of optical aberrations, particularly for intra-wafer aberrations. Various different solutions have been proposed to address this problem including, for example: the use of lens model to optimize the positions of mirrors during lithographic exposure; mirror preheating; mirror sector heaters; and direct cooling water. However, these correction techniques are not able to correct for all optical aberrations. Furthermore, some of these correction techniques are very involved and costly.

[0010] It is also known to use rigid body movements of optical elements in the imaging system to partially correct for optical aberrations. Note that these movements are typically small with respect to the typical dimensions of the optical elements. For example, the optical elements may have a typical dimension of the order of 0.1 m to 1 m whereas the magnitude of the rigid body movements used for aberration correction may be of the order of 1 µm. Furthermore, since the aberrations induced due to thermal load are normally caused by the surface deformation of optical elements, it may be the case that they cannot be completely corrected by simply adjusting positions of the optical element.

[0011] The inventors of the present invention have realized that, due to the finite stiffness of the optical elements (and any associated support structure), when the optical elements accelerate they will be deformed as a result of reaction forces acting on them as they accelerate. Furthermore, the resultantdeformations result in an additional control knob for controlling optical aberrations. As used herein the term “control knob” is intended to mean anything that can be varied to provide control over something.

[0012] The method according to the first aspect involves determining values of one or more movement parameters (for example an acceleration) of at least one optical element of the imaging system in dependence on the impact on imaging performance that would be achieved by a deformation of the at least one optical element when the at least one optical element moves according to the determined value(s) of the one or more movement parameters.

[0013] The method according to the first aspect involves determining an impact on imaging performance that would be achieved when the at least one optical element moves according to the one or more determined movement parameter values. It will be appreciated that this imaging performance may be determined using one or more models. That is, the imaging performance may be a predicted imaging performance, based on such models. Alternatively, the imaging performance may be measured directly.

[0014] The optical system may have m degrees of freedom. Each optical element may have three translational degrees of freedom (x, y and z) and three rotational degrees of freedom (Rx, Ry and Rz). There may be ^ mirrors that can be moved. Therefore, the optical system may have up to 6n degreesof freedom. The degrees of freedom of the optical system may be referred to as ^^, where ^ = 1, … , ^.The one or more movement parameters of at least one optical element are such that at least one degree of freedom of the at least optical element has a non-zero acceleration during at least part of the formationof the image (i.e. such that ^^^^ (^) ≠ 0). For example, the determined value(s) of the one or moremovement parameters may comprise a value or magnitude (for example as a function of time) for the acceleration ^^^^(^) of at least one degree of freedom. In practice, this may involve selecting values of any parameters that parameterize one or more degrees of freedom, ^^(^), of the optical system as a function of time during an exposure time period such that during that time period an acceleration ^^^^(^)of said one or more degrees of freedom is non zero (i.e. ^^^^ (^) ≠ 0). For example, each degree offreedom ^^(^) may be parameterized as a sum of a basis functions weighted by coefficients anddetermining one or more movement parameters of an optical element may comprise determining a set of coefficients for at least one degree of freedom ^^associated with that optical element.

[0015] In general, such an acceleration will cause deformation of the optical surface of that optical element (due to mass inertia and finite stiffness of the optical element). Optionally, the one or more movement parameters of at least one optical element may also comprise an additional time dependence (in addition to that resulting from the acceleration) of the position ^^(^) of at least one degree of freedom associated with that optical element.

[0016] The determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for an optical aberration of the imaging optics.

[0017] That is, the determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for a contribution to the imaging performance from a deformation of surface(s) of one or more optical elements of the imaging optics from other sources.

[0018] Such other sources may, for example, include thermal loads (i.e. thermal deformations). For example, the determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to the movement at least partially corrects for a contribution to the imaging performance from a thermal deformation of a surface of one or more optical elements of the imaging optics.

[0019] In some embodiments, each mirror may be moved in such a way that it has minimal deformations.

[0020] Optical aberrations describe a departure from perfect imaging performance. Perfect imaging performance may be achieved by spherical wavefronts converging to a point at each point in the image plane. Put differently, perfect optical performance is achieved when the optical path length is the same for all parts of the converging light cone at the image plane. Optical aberrations may be described as a departure of the wavefront from such perfect imaging (e.g. a perfect spherical wavefront). Optical aberrations may be well described by a wavefront (or relative phase) map in a pupil plane of the imaging system. Such a wavefront map may be expressed as a linear combination of Zernike / Tatian polynomials (which form a complete orthonormal set on a unit circle).

[0021] As used here “an optical aberration of the imaging optics” may mean one or more coefficients in such a Zernike / Tatian polynomial expansion.

[0022] In some embodiments, a subset of the optical elements may be moved so as to cause deformation of the optical surfaces of that subset which at least partially correct for a contribution to one or more aberrations from the thermal deformations of all of the optical elements (i.e. including the optical elements that do not move).

[0023] In some embodiments, the determined value(s) of the one or more movement parameters are such that one or more optical aberrations of the imaging system are optimized.

[0024] The determined value(s) of the one or more movement parameters may be such that one or more optical aberrations of the imaging system are minimized.

[0025] It will be appreciated that, minimizing one or more optical aberrations of the imaging system may use any suitable optimization merit function. For example, in some embodiments, it may be desirable to minimize variation in the wavefront map in the pupil plane. In some embodiments, certain components of optical aberrations (for example certain Zernike / Tatian components) may have a particularly large effect on imaging performance and so it may be particularly desirable to minimize these components and the merit function may reflect this.

[0026] It will be appreciated that minimizing one or more optical aberrations of the imaging system may comprise the use of any optimization method (for example to minimize a merit function) as desiredor required. Examples of such optimization methods may include, for example, any of the following: genetic optimization algorithms; Newton’s method in optimization (also known as the Newton-Raphson method); simulated annealing; a least squares method; a quadratic programming active set method; an interior-point method; and / or a quadratic constrained quadratic programing method.

[0027] The determined values(s) of the one or more movement parameters may be such that one or more optical aberrations of the imaging system are reduced relative to an exposure in which the optical elements do not move.

[0028] In particular, the determined values(s) of the one or more movement parameters may be such that one or more optical aberrations of the imaging system are reduced relative to an exposure in which the optical elements do not accelerate.

[0029] The method may use a thermal model to map, for the or each of one or more of the optical elements, a thermal load of an optical element to a corresponding thermal deformation of that optical element.

[0030] Such a thermal model may be able to quantify a thermal deformation of any of the optical elements (for example mirrors) in the imaging system. Note that, in general, the thermal model may also include thermal effects on supporting structures (for example frames) of the optical elements.

[0031] The method may use a model to map the one or more movement parameters of each of the at least one optical element to at least one optical aberration of the imaging system.

[0032] Such a model may take into account both: (a) a mechanical model that can quantify a deformation of all of the moving optical elements (for example mirrors) in the imaging system that is due to said movement (for example due to acceleration of the optical elements); and (b) an optical model that can map such deformations to optical aberrations.

[0033] If a degree of freedom ^^(^) is moved with acceleration ^^^^(^), then a time dependence of a wavefront aberration ^^to this degree of freedom, ^^;^(^), willform of:^(^) = ^ ^^^;^ ^,^ ∙ ^^(^) + ^^,^ ∙ ^^ (^). (1)

[0034] The first term describes how the position or value of that degree of freedom will affect the aberration and the second term describes how deformation of an optical surface of the degree of freedom (caused by acceleration) will affect the aberration.

[0035] The method may use a mechanical model to map one or more movement parameters of each of the at least one optical element to a corresponding movement deformation of that optical element.

[0036] Such a mechanical model may be able to quantify a deformation of all of the moving optical elements (for example mirrors) in the imaging system that is due to said movement (for example due to acceleration of the optical elements).

[0037] The method may use an optical model to map deformation of one or more of the optical elements of the imaging system to optical aberrations of the imaging system.

[0038] For example, the optical model may allow for a deformation of an optical element (which maybe from any source) into a wavefront (relative phase) map.

[0039] The value(s) of the one or more movement parameters may be determined for forming an image of an object on a substrate a plurality of times in succession.

[0040] It will be appreciated that a substrate used in a lithographic apparatus (e.g. a resist-coated silicon wafer) typically comprises a plurality of target regions. The same image (as defined by a reticle or mask) may be formed on each of the target regions. There may be, for example, of the order of 100 target regions or more.

[0041] In some embodiments, it may be desirable for at least one of the optical elements to undergo an acceleration during formation of the image (i.e. during an exposure of a target region on a wafer). However, it may be the case that the cumulative effect of accelerating the optical element in the same way for all exposures results in that optical element moving a sufficiently large distance that it starts to impact on imaging performance. It may therefore be desirable to move the optical element back to a nominal position between each exposure.

[0042] The determined value(s) of the one or more movement parameters may comprise: a first set of determined values to be used during the formation of at least a part of each image of the object on the substrate; and a second set of determined values to be used at different times.

[0043] The second set of determined values may be be used in between the formation of each pair of successive images.

[0044] The second set of determined value(s) of the movement parameters may, for example, be such that the optical element is moved back to a nominal position between each exposure.

[0045] In some embodiments, it may be desirable to move one or more other optical elements in such a way so as to at least partially compensate for the movement of an optical element that is being accelerated.

[0046] The determined value(s) of the one or more movement parameters may comprise: a third set of determined values to be used by at least one optical element that are determined in dependence on the impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined third set of values of the movement parameters; and a fourth set of determined values to be used by at least one other optical element such that the movement of the at least one other optical element at least partially corrects for a change in a contribution to one or more optical aberrations that results from a change of position of the at least one optical element.

[0047] The time dependence, ^^;^(^), of a wavefront aberration ^^to a degree of freedom ^^will be of the form given in equation (1). As previously explained, the present disclosure relates in particular to the use of non-zero acceleration of at least one optical element to cause a surface of that opticalelement to deform so as to at least partially correct for one or more aberrations. When one of the opticalelements is accelerated during an exposure process (|^^^^ (^)| > 0) to exploit the second term in equation(1) (i.e. obtain ^^,^ ∙ ^^^^ (^)), then the first term (i.e. ^^,^ ∙ ^^(^)) will vary during the exposure processdue to the non-zero acceleration (|^^^^ (^)| > 0). Furthermore, the fact that the first term also variesduring thecan limit the correction of optical aberrations.

[0048] However, in some embodiments it may be desirable to be able use the second term of equation (1) independently of the first term of equation (1). In order to achieve this, another degree of freedom, ^^, may be used. Note that a time dependence, ^^;^(^), of a wavefront aberration ^^to this degree of freedom ^^will be of the form of: ^(^) ^^^;^ = ^^,^ ∙ ^^(^) + ^^,^ ∙ ^^ (^). (2)

[0049] If these two^^ then the total time dependence of the aberration ^^ is given by ^^;^(^) + ^^;^(^). For simplicity,assume that degree of freedom ^^is only suitable for generating the first term of equation (2) with thisaberration ^^ (i.e. ^^,^ = 0). Therefore, the total time dependence of the aberration ^^ is given by:^ (^) = ^ ∙ ^ (^) + ^ ^^^ ^,^ ^ ^,^ ∙ ^^(^) + ^^,^ ∙ ^^ (^). (3)

[0050] In this simple example, the third set of determined values may comprise the values of the position, ^^(^), and the acceleration, ^^^^(^), of degree of freedom D and the fourth set of determined values the position, ^^(^), of degree of freedom ^^. It is useful to for each degree of freedom which is accelerating (for example, in this example degree of freedom ^^) to express the degree of freedom as a function of time as: ^^(^) = ^^(0) + ^^,var(^), (4)where ^^(0) is an initial position or value of the degree of freedom, ^^, and ^^,var(^) is a time-varying contribution to the position.

[0051] For this simple example, the fourth set of determined values being such that the movement of the at least one other optical element at least partially corrects for a change in a contribution to one or more optical aberrations that results from a change of position of the at least one optical element may be expressed as requiring that: ^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^(^) = 0. (5)

[0052] In this way, the additional degree of freedom, ^^, is selected so that the movement of the additional optical element corrects for optical aberrations that result from a change in the position of the first degree of freedom, ^^.

[0053] In practice, it may not be possible to ensure that equation (5) is satisfied exactly. Therefore, in some embodiments, the movement of the second degree of freedom may be such that it at least partially cancels out a contribution to an aberration ^^from the time-varying contribution of the position ^^,var(^) from a degree of freedom which is accelerating. In order to achieve such partial contribution,it may be desirable to minimize |^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^(^)|. For example, it may be desirable toensure that: |^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^(^)| < |^^,^ ∙ ^^,var(^)|. (6)

[0054] Inof a plurality of other optical elements, rather than just one additional optical element. In practice, this is typically possible, as actuations in one degree of freedom can usually be compensated well by a linear combination of other degrees of freedom. In general, a set of second degrees of freedom "^^# may be actuated such that they at least partially cancel out a contribution to an aberration ^^the time-varying contribution of the position ^^,var(^) from a degree of freedom which is accelerating. This may be achieved by minimizing:|^^,^ ∙ ^^,var(^) + $ ^^,^ ∙ ^^(^) |.(7)where the sum is over all members of the set "^^#.

[0055] Therefore, by moving another degree of freedom ^^to compensate for variation of the position of the first degree of freedom, ^^, a "pure" acceleration effect can be achieved without the (potentially significantly larger) effect from the change in the position of the first degree of freedom, ^^.

[0056] According to a second aspect of the present disclosure there is provided an exposure method comprising: patterning a radiation beam using a patterning device so as to form patterned radiation; using imaging optics to collect the patterned radiation and to form an image of the patterning device on a substrate; wherein at least one optical element of the imaging optics moves during the formation of the image according to a value of one or more movement parameters determined by the method of the first aspect of the present disclosure.

[0057] The method of the second aspect of the present disclosure is advantageous, as it may allow for thermal distortions to be at least partially cancelled by mechanical distortions, resulting in reduced optical aberrations and optimized imaging performance.

[0058] The exposure method may further comprise carrying out the method of the first aspect of the present disclosure.

[0059] The exposure method may further comprising reading an output of the method of the first aspect of the present disclosure from a storage medium and using this output to control movement of the at least one optical element.

[0060] According to a third aspect of the present disclosure there is provided a lithographic apparatus or a lithographic system comprising: imaging optics; and a controller operable to perform the method of the first aspect of the present disclosure.

[0061] The time dependence, ^^;^(^), of a wavefront aberration ^^to a degree of freedom ^^will be of the form given in equation (1). In some embodiments, at least one optical element of the lithographic apparatus may be designed so that a stiffness distribution of that optical element has been selected so as to achieve a desired response for one or more aberrations to acceleration(s) of its degrees of freedom. From equation (1), a response for an aberration ^^to acceleration(s) of a degree of freedom ^^is ^^,^. However, note that, in general, there will be a different response for each different Zernike / Tatian. That is, the response of the wavefront to acceleration(s) of a degree of freedom ^^is not a scalar value but a complex wavefront signature, for example a set of various Zernike / Tatian components at various field-points. That is, at least one optical element of the lithographic apparatus may be designed so that a stiffness distribution of that optical element has been selected so as to achieve a desired set of response coefficients, "^^,^#.

[0062] By varying a stiffness distribution of at least one optical element in a design-phase (e.g. by changing shape or adding / subtracting material at various parts of the mirror) the set of response coefficients, "^^,^# can be varied. By optimizing the stiffness distributions of the optical elements the acceleration induced deformation effects on the wavefront can be controlled. For example, the set of response coefficients, "^^,^# may be selected so as to allow for correction of aberrations that are of the form of the (e.g. thermally induced) aberrations that are expected in the lithographic apparatus.

[0063] Note that this is contrary to conventional wisdom wherein typically the optical elements are designed so as to be as stiff as possible (so that the response coefficients, "^^,^# are as small as possible).

[0064] Note that the coefficients, "^^,^# , that describe the response for aberrations ^^ toacceleration(s) of degrees of freedom ^^also depend on the positions of mounting points (or bushes) for the relevant optical element (or mirror). Therefore, in some embodiments, the positions of the mounting points of one or more optical elements may be varied in order to achieve a desired set of response coefficients, "^^,^#.

[0065] The imaging optics may comprise at least one optical element having an anisotropic stiffness distribution.

[0066] For example, a mirror support may be provided by ribs or comparable structural features lateral surfaces of the mirror have a highly anisotropic rigidity distribution.

[0067] The imaging optics may comprise at least one optical element having a stiffness distribution such that a response of a wavefront of radiation to an acceleration of the at least one optical element in at least one direction generally matches optical aberrations that are expected in use.

[0068] According to a fourth aspect of the present disclosure there is provided a computer comprising: one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the method of the first aspect of the present disclosure.

[0069] The one or more processors may be configured to store on the storage media value(s) of one or more movement parameters determined by the method of the first aspect of the present disclosure.

[0070] According to a fifth aspect of the present disclosure there is provided a computer-readable medium having instructions for carrying out the method of the first aspect of the present disclosure.

[0071] The computer-readable medium may be a non-transitory computer-readable medium. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which: - Figure 1 depicts a lithographic system comprising a lithographic apparatus and a radiation source; - Figure 2 schematically shows a new method for determining a value of one or more parameters for an imaging system according to an embodiment of the present disclosure that receives as an input atarget wavefront map %&(', ();- Figure 3 is a schematic diagram of a first embodiment of the new method for determining value(s) of the one or more movement parameters shown in Figure 2; - Figure 4 is a schematic diagram of a second embodiment of the new method for determining value(s) of the one or more movement parameters shown in Figure 2; - Figure 5 schematically shows an embodiment of the present disclosure in which optical elements are moved back to a nominal position between each exposure, showing the displacement of two optical elements (for example relative to a nominal position of those optical elements) as a function of time and also showing three time periods during which the wafer is exposed and time periods between successive exposures (shown shaded); - Figure 6A schematically shows: (i) the ^)components of an optical aberration (solid lines); (ii) the contributions to this aberration from the movement of a single degree of freedom, ^^, (dotted line, dashed line and shaded region); and (iii) a difference between the ^)component of the opticalaberration and the contribution to the ^)component from the single degree of freedom, ^^, (dot-dashed line and striped-shaded region); - Figure 6B schematically shows: (i) the ^*components of an optical aberration (solid lines); (ii) the contributions to this aberration from the movement of the same degree of freedom, ^^, shown in Figure 6A (dotted line and dashed line); and (iii) a difference between the ^*component of the optical aberration and the contribution to the ^*component from the single degree of freedom, ^^, (dot-dashed line); - Figure 7A schematically shows: (i) the ^)components of an optical aberration (solid lines); (ii) the contributions to this aberration from the movement of two degrees of freedom ^^, ^^(dotted line, dashed line and shaded regions); and (iii) a difference between the ^)component of the optical aberration and the contribution to the ^)component from the single degree of freedom, ^^(dot-dashed line); - Figure 7B schematically shows: (i) the ^*components of an optical aberration (solid lines); (ii) the contributions to this aberration from the movement one of the degrees of freedom, ^^, shown in Figure 7A (dotted lines and dashed lines); and (iii) a difference between the ^*component of the optical aberration and the contribution to the ^*component from this degree of freedom, ^^, (dot-dashed line); and - Figure 8 schematically shows a new exposure method according to an embodiment of the present disclosure wherein at least one optical element of the imaging optics moves during the formation of an image according to a value of one or more movement parameters determined by the new method(s) shown in Figures 2 to 4. DETAILED DESCRIPTION

[0073] Figure 1 shows a lithographic system comprising a radiation source SO and a lithographic apparatus LA. The radiation source SO is configured to generate an EUV radiation beam B and to supply the EUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT configured to support a patterning device MA (e.g., a mask), a projection system PS and a substrate table WT configured to support a substrate W.

[0074] The illumination system IL is configured to condition the EUV radiation beam B before the EUV radiation beam B is incident upon the patterning device MA. Thereto, the illumination system IL may include a facetted field mirror device 10 and a facetted pupil mirror device 11. The faceted field mirror device 10 and faceted pupil mirror device 11 together provide the EUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to, or instead of, the faceted field mirror device 10 and faceted pupil mirror device 11.

[0075] After being thus conditioned, the EUV radiation beam B interacts with the patterning device MA. As a result of this interaction, a patterned EUV radiation beam B’ is generated. The projection system PS is configured to project the patterned EUV radiation beam B’ onto the substrate W. For that purpose, the projection system PS may comprise a plurality of mirrors 13, 14 which are configured to project the patterned EUV radiation beam B’ onto the substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV radiation beam B’, thus forming an image with features that are smaller than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated as having only two mirrors 13, 14 in Figure 1, the projection system PS may include a different number of mirrors (e.g. six or eight mirrors).

[0076] The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus LA aligns the image, formed by the patterned EUV radiation beam B’, with a pattern previously formed on the substrate W.

[0077] A relative vacuum, i.e. a small amount of gas (e.g. hydrogen) at a pressure well below atmospheric pressure, may be provided in the radiation source SO, in the illumination system IL, and / or in the projection system PS.

[0078] The radiation source SO shown in Figure 1 is, for example, of a type which may be referred to as a laser produced plasma (LPP) source. A laser system 1, which may, for example, include a CO2laser, is arranged to deposit energy via a laser beam 2 into a fuel, such as tin (Sn) which is provided from, e.g., a fuel emitter 3. Although tin is referred to in the following description, any suitable fuel may be used. The fuel may, for example, be in liquid form, and may, for example, be a metal or alloy. The fuel emitter 3 may comprise a nozzle configured to direct tin, e.g. in the form of droplets, along a trajectory towards a plasma formation region 4. The laser beam 2 is incident upon the tin at the plasma formation region 4. The deposition of laser energy into the tin creates a tin plasma 7 at the plasma formation region 4. Radiation, including EUV radiation, is emitted from the plasma 7 during de- excitation and recombination of electrons with ions of the plasma.

[0079] The EUV radiation from the plasma is collected and focused by a collector 5. Collector 5 comprises, for example, a near-normal incidence radiation collector 5 (sometimes referred to more generally as a normal-incidence radiation collector). The collector 5 may have a multilayer mirror structure which is arranged to reflect EUV radiation (e.g., EUV radiation having a desired wavelength such as 13.5 nm). The collector 5 may have an ellipsoidal configuration, having two focal points. A first one of the focal points may be at the plasma formation region 4, and a second one of the focal points may be at an intermediate focus 6, as discussed below.

[0080] The laser system 1 may be spatially separated from the radiation source SO. Where this is the case, the laser beam 2 may be passed from the laser system 1 to the radiation source SO with the aid of a beam delivery system (not shown) comprising, for example, suitable directing mirrors and / or abeam expander, and / or other optics. The laser system 1, the radiation source SO and the beam delivery system may together be considered to be a radiation system.

[0081] Radiation that is reflected by the collector 5 forms the EUV radiation beam B. The EUV radiation beam B is focused at intermediate focus 6 to form an image at the intermediate focus 6 of the plasma present at the plasma formation region 4. The image at the intermediate focus 6 acts as a virtual radiation source for the illumination system IL. The radiation source SO is arranged such that the intermediate focus 6 is located at or near to an opening 8 in an enclosing structure 9 of the radiation source SO.

[0082] Although Figure 1 depicts the radiation source SO as a laser produced plasma (LPP) source, any suitable source such as a discharge produced plasma (DPP) source or a free electron laser (FEL) may be used to generate EUV radiation.

[0083] The faceted field mirror device 10 and the faceted pupil mirror device 11 are arranged to provide a desired angular distribution of the radiation beam B, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. The illumination system IL may be arranged to provide Kohler illumination of an illumination region IR (that the patterning device MA may be moved through during exposure of a substrate W) such that the plasma at the plasma formation region 4 is out of focus (and therefore does not influence properties of the radiation beam) at the patterning device MA and in the conjugate plane of the substrate W. As used herein, the illumination region IR may also be referred to as the illumination slit or the slit.

[0084] The illumination region IR is in a field plane in which the reticle MA is disposed during a lithographic exposure. Therefore, the illumination region IR may be referred as a reticle-level or object- level illumination region IR. It will be appreciated that projection system PS forms an image IR’ of the illumination region IR in the plane of the substrate W. The image IR’ of the illumination region IR in the plane of the substrate W may be referred to as a wafer-level or image-level illumination region IR’. As used herein, the wafer-level illumination region IR’ may also be referred to as the slit.

[0085] The lithographic apparatus LA may be a scanning lithographic apparatus (also referred to as a scanner) and the image (of a reticle MA) may be formed during a scanning exposure. In such an exposure, the reticle MA may be moved in a scanning direction through the reticle-level illumination region IR. It will be appreciated that, as a result of this movement of the reticle MA, the image of the reticle MA will move at wafer level. Therefore, during the scanning exposure, the wafer W is also moved through the wafer-level illumination region IR’. In particular, the wafer W is moved so that the image of reticle MA is substantially static with respect to the wafer W. The movement of the reticle MA and the substrate W are therefore synchronized. The movement (speed and direction) of the substrate W will be dependent on the movement of the reticle and the imaging performed by the projection system PS. In some embodiments, the projection system PS may form an inverted image of the reticle MA and therefore the substrate W may be moved in an opposite direction to the reticle MA. In some embodiments, the projection system PS may apply a reduction factor to the patterned EUVradiation beam B’ in the scanning direction and therefore the substrate W may move at a speed that is smaller than the speed of the reticle MA by this reduction factor.

[0086] In lithography, the illumination of the patterning device MA is very important. In particular, it is desirable to control the angular distribution of the radiation at the illumination region IR where the patterning device MA is exposed to radiation. This angular distribution of the radiation is conveniently described in terms of the spatial distribution of the radiation in an illumination pupil plane, which describes how a cone of light that is incident on each point on the patterning device MA is filled.

[0087] The uniformity of the illumination is also very important. The uniformity of illumination affects the uniformity of dose to which the target portion of the substrate W is exposed, which affects critical dimension uniformity (CDU), an important measure of the uniformity of the dimension of features formed on the substrate W. For example, it may be desirable to maintain a desired spatial intensity distribution of radiation across the illumination region IR. As used herein the spatial intensity distribution of radiation across the illumination region IR may be referred to as the slit profile.

[0088] The collector 5 is generally of the form of a concave mirror, which is arranged to collect the radiation which is emitted from the plasma formation region 4 into a solid angle subtended by the collector 5. This radiation is reflected and focused at the intermediate focus 6. As a result, within the housing, the radiation beam B is generally of the form of a converging cone of radiation, which converges at the intermediate focus 6, an outer edge of this cone being indicated in Figure 1 by two lines. Downstream of the intermediate focus 6, the radiation beam B is generally of the form of a diverging cone of radiation, which is incident on the generally circular field facet mirror device 10. However, the radiation source SO may comprise an obscuration that will block a portion of this radiation cone such that there will be some portion of the diverging cone of radiation that which will not receive radiation from the collector 5. For example, the radiation source SO may comprise a shield (not shown) which may be arranged to prevent the laser beam 2 from propagating through the opening 8 and into the lithographic apparatus LA (where it may damage optical components). This shield may be supported by the enclosing structure via a support (not shown). Together, the shield and the support form an obscuration of the radiation source SO. It will be appreciated that the obscuration may have any shape or configuration.

[0089] Typically, the intensity distribution of the radiation in field planes of a lithographic apparatus has the following general shape in a scanning direction of the lithographic apparatus: there is a central portion which is generally flat and two peripheral portions on either side of the central portion in which the intensity falls to zero. For example, the intensity distribution in the scanning direction may be generally of the shape of a trapezium.

[0090] In general, the projection system PS has an optical transfer function which may be non- uniform, which can affect the pattern which is imaged on the substrate W. For unpolarized radiation such effects can be fairly well described by two scalar maps, which describe the transmission (apodization) and relative phase (aberration) of radiation exiting the projection system PS as a functionof position in a pupil plane thereof. These scalar maps, which may be referred to as the transmission map and the relative phase map, may be expressed as a linear combination of a complete set of basis functions. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials defined on a unit circle. A determination of each scalar map may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be obtained from a measured scalar map by calculating the inner product of the measured scalar map with each Zernike polynomial in turn and dividing this by the square of the norm of that Zernike polynomial. In the following, unless stated otherwise, any reference to Zernike coefficients will be understood to mean the Zernike coefficients of a relative phase map (also referred to herein as an aberration map). It will be appreciated that in alternative embodiments other sets of basis functions may be used. For example, some embodiments may use Tatian Zernike polynomials, for example for obscured aperture systems.

[0091] Optical aberrations describe a departure from perfect imaging performance. Perfect imaging performance may be achieved by spherical wavefronts converging to a point at each point in the image plane. Put differently, perfect optical performance is achieved when the optical path length is the same for all parts of the converging light cone at the image plane. Optical aberrations may be described as a departure of the wavefront from such perfect imaging (e.g. a perfect spherical wavefront). Optical aberrations may be well described by a wavefront (or relative phase) map in a pupil plane of the imaging system.

[0092] The wavefront aberration map represents the distortions of the wavefront of light approaching a point in an image plane of the projection system PS from a spherical wavefront (as a function of position in the pupil plane or, alternatively, the angle at which radiation approaches theimage plane of the projection system PS). As discussed, this wavefront aberration map %(', () maybe expressed as a linear combination of Zernike polynomials: %(', () = $ ^+ ∙ ,+(', () ,(8)where ' and ( are coordinates in the pupil plane, ,+(', () is the ^th Zernike polynomial and ^+ is acoefficient. It will be appreciated that in the following, Zernike polynomials and coefficients arelabelled with an index, which is commonly referred to as a Noll index. Therefore, ,+(', () is theZernike polynomial having a Noll index of ^ and ^+is a coefficient having a Noll index of ^. The wavefront aberration map may then be characterized by the set of coefficients ^ in such an expansion,which may be referred to as Zernike coefficients. Note that %(', () may alternatively be expressed asa linear combination of Zernike-Tatian polynomials (also referred to herein as Tatian polynomials) in a similar way (i.e. a similar expansion to that expressed in equation (8)) and when used below anyreference to Zernike coefficients ^+ may alternatively mean similarly defined Zernike-Tatiancoefficients (or simply Tatian coefficients.

[0093] It will be appreciated that only a finite number of Zernike orders are taken into account. Different Zernike coefficients of the phase map may provide information about different forms of aberration which are caused by the projection system PS. The Zernike coefficient having a Noll index of 1 may be referred to as the first Zernike coefficient, the Zernike coefficient having a Noll index of 2 may be referred to as the second Zernike coefficient and so on.

[0094] The first Zernike coefficient, ^-, relates to a mean value (which may be referred to as a piston) of a measured wavefront. The first Zernike coefficient may be irrelevant to the performance of the projection system PS and as such may not be corrected for using the methods described herein. The second Zernike coefficient, ^), relates to the tilt of a measured wavefront in the x-direction. The tilt of a wavefront in the x-direction is equivalent to a placement in the x-direction. The third Zernike coefficient, ^., relates to the tilt of a measured wavefront in the y-direction. The tilt of a wavefront in the y-direction is equivalent to a placement in the y-direction. The fourth Zernike coefficient, ^ / , relates to a defocus of a measured wavefront. The fourth Zernike coefficient is equivalent to a placement in the z-direction. Higher order Zernike coefficients relate to other forms of aberration which are caused by the projection system (e.g. astigmatism, coma, spherical aberrations and other effects).

[0095] Throughout this description the term “aberrations” should be intended to include all forms of deviation of a wavefront from a perfect spherical wavefront. That is, the term “aberrations” may relate to the placement of an image (e.g. the second, third and fourth Zernike coefficients) and / or to higher order aberrations such as those which relate to Zernike coefficients having a Noll index of 5 or more. Furthermore, any reference to an aberration map for a projection system PS may include all forms of deviation of a wavefront from a perfect spherical wavefront, including those due to image placement.

[0096] The transmission map and the relative phase map are field and system dependent. That is, in general, each projection system PS will have a different Zernike expansion for each field point (i.e. for each spatial location in its image plane).

[0097] As will be known to the skilled person, the relative phase of the projection system PS in its pupil plane may be determined by projecting radiation from an object plane of the projection system PS (i.e. the plane of the patterning device MA), through the projection system PS and using a shearing interferometer to measure a wavefront (i.e. a locus of points with the same phase). The shearing interferometer may comprise a diffraction grating, for example a two dimensional diffraction grating, in an image plane of the projection system (i.e. the substrate table WT) and a detector arranged to detect an interference pattern in a plane that is conjugate to a pupil plane of the projection system PS.

[0098] Some embodiments of the present disclosure relate to new methods for determining a value of one or more parameters for an imaging system that is for forming an image of an object on a substrate. The method may have particular application to an imaging system of a lithographic apparatus. Theimaging system may be a projection system PS of a lithographic apparatus LA of the type shown schematically in Figure 1 and described above. The object may be a reticle or patterning device MA and the substrate may be a resist-coated silicon wafer W.

[0099] The method comprises determining a value of one or more movement parameters of at least one optical element of the imaging system PS during the formation of the image. The one or more movement parameters are such that at least one degree of freedom of the at least optical element has a non-zero acceleration during at least part of the formation of the image. The one or more movement parameters may, for example, comprise at least one acceleration parameter. Alternatively, the one or more parameters may comprise any parameters that parameterize one or more degrees of freedom of one or more optical elements, the values of which are determined such that at least one optical element of the imaging system PS undergoes a non-zero acceleration during the formation of the image. [000100] The value of the one or more movement parameters is / are determined in dependence on an impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined value of the one or more movement parameters. Note that such deformation of the optical surface of optical elements is caused by mass inertia and limited (finite) stiffness of the optical element. For example, as shown schematically in Figure 2, the new method 100 for determining a value of oneor more parameters for an imaging system PS may receive as an input a target wavefront map %&(', ().In the method 100, the determination of value of the one or more movement parameters may be made so as to result in a deformation of the at least one optical element (caused by mass inertia and finite stiffness of the optical element) that results in a distortion of the wavefront of the radiation B’ passingthrough the imaging system PS that generally matches the target wavefront map %&(', () . Forexample, the target wavefront map %&(', () may be given by:%&(', () = −%1(', () (9)where %1(', () is measured wavefront map (resulting from other sources of aberration).[000101] The method 100 is advantageous, as now discussed. In some lithographic apparatus, the radiation beam B’ used to expose the wafer may cause thermal deformation of optical elements 13, 14 in the imaging optics PS. Additionally or alternatively, the radiation beam B, B’ may cause thermal deformation of the reticle (patterning device MA) and / or the wafer (substrate W). In turn, all such thermal deformations can cause unwanted optical aberrations, degrading optical performance. Note that, in principle there may be other sources of optical aberrations, however, thermally induced aberrations are often the main source of optical aberrations, particularly for intra-wafer aberrations. Various different solutions have been proposed to address this problem including, for example: the use of lens model to optimize the positions of mirrors during lithographic exposure; mirror preheating; mirror sector heaters; and direct cooling water. However, these correction techniques are not able tocorrect for all optical aberrations. Furthermore, some of these correction techniques are very involved and costly. [000102] It is also known to use rigid body movements of optical elements in the imaging system to partially correct for optical aberrations. Note that these movements are typically small with respect to the typical dimensions of the optical elements. For example, the optical elements may have a typical dimension of the order of 0.1 m to 1 m whereas the magnitude of the rigid body movements used for aberration correction may be of the order of 1 µm. Furthermore, since the aberrations induced due to thermal load are normally caused by the surface deformation of optical elements, it may be the case that they cannot be completely corrected by simply adjusting positions of the optical element. [000103] The inventors of the present invention have realized that, due to the finite stiffness of the optical elements (and any associated support structure), when the optical elements accelerate they will be deformed as a result of reaction forces acting on them as they accelerate. Furthermore, the resultant deformations result in an additional control knob for controlling optical aberrations. As used herein the term “control knob” is intended to mean anything that can be varied to provide control over something. [000104] The method 100 involves determining values of one or more movement parameters (for example an acceleration) of at least one optical element of the imaging system in dependence on the impact on imaging performance that would be achieved by a deformation of the at least one optical element when the at least one optical element moves according to the determined value(s) of the one or more movement parameters. [000105] The method 100 involves determining an impact on imaging performance that would be achieved when the at least one optical element moves according to the one or more determined movement parameter values. It will be appreciated that this imaging performance may be determined using one or more models. That is, the imaging performance may be a predicted imaging performance, based on such models. Alternatively, the imaging performance may be measured directly. [000106] The optical system PS may have m degrees of freedom. Each optical element may have three translational degrees of freedom (x, y and z) and three rotational degrees of freedom (Rx, Ry and Rz). There may be ^ mirrors that can be moved. Therefore, the optical system may have upto 6^degrees of freedom. The degrees of freedom of the optical system may be referred to as ^^, where ^ =1, … , ^. It will be appreciated that the method 100 comprises determining a value of one or moremovement parameters of at least one optical element of the imaging system PS during the formation of the image and that this means that, in general, at least one degree of freedom,^^(^), of the optical system will be actuated continuously during the exposure process, leading to non-zero velocities and / or accelerations of at least some of the optical elements. In general, each degree of freedom may be parameterized by a plurality of parameters. Therefore, more than 6^ parameters may be selected. For example, if degree of freedom ^^is parameterized as a function of time by 2^parameters then, in total,there will be 2^ parameters, values of which may be determined using the method 100.[000107] As used herein ^^^(^) is intended to mean the first differential of ^^with respect to time, i.e.^^^(^) = 6^^⁄ 6^ and ^^^^ (^) is intended to mean the second differential of ^^ with respect to time, i.e.^^^(^) = 6) ⁄ )^ ^^ 6^ .[000108] Note that as used herein when it is stated that the method comprises determining a value of one or more movement parameters of at least one optical element of the imaging system PS during the formation of the image, said movement parameters may be any parameters that parameterize movement of the at least one optical element. For example, when stated herein that the one or more movement parameters are such that at least one degree of freedom of the at least optical element has a non-zero acceleration during at least part of the formation of the image, this is intended to mean at least one parameter that parameterizes movement of the at least one optical element such that it accelerates. Note that this does not necessarily mean that the acceleration is determined directly. For example, this may involve selecting values of any parameters that parameterize one or more degrees of freedom, ^^(^), of the optical system as a function of time during an exposure time period such that during that time periodan acceleration ^^^^ (^) of said one or more degrees of freedom is non zero (i.e. ^^^^ (^) ≠ 0).[000109] The one or more movement parameters of the at least one optical element may comprise an acceleration ^^^at least one degree of freedom associated with that optical element (or, typically, a set of parameters that parameterize the acceleration ^^^^(^)). That is, the determined value(s) of the one or more movement parameters may comprise a value or magnitude (for example as a function of time) for the acceleration ^^^^(^) of at least one degree of freedom. In general, such an acceleration will cause deformation of the optical surface of that optical element (due to mass inertia and finite stiffness of the optical element). [000110] In some embodiments, each degree of freedom ^^(^) may be parameterized as a sum of a basis functions or basis splines (also known as B-splines). For example, a degree of freedom ^^may be parameterized as follows: ^^(^) = $ 8^ ∙ ^^(^)(10)where ^^(^) are a set of 9 basis functions or B-splines and 8^are a set of 9 coefficients. For such embodiments, determining one or more movement parameters of an optical element may comprise determining a set of coefficients 8^in an expansion of the type shown in equation (10) for at least one degree of freedom ^^associated with that optical element. Therefore, for such embodiments the determinedparameters will, in general, not be accelerations, however, the combination of B-spline coefficients 8^will determine the acceleration of the optical element over an entire trajectory during formation of the image.[000111] Figure 3 is a schematic diagram showing how the value(s) of the one or more movement parameters determined using the new method 100 can be used in practice. [000112] As shown schematically in Figure 3, the optical aberrations 120 of an imaging system PS can be influenced by deformation 130 of the optical elements of the imaging system PS. In turn, such deformation 130 of the optical elements of the imaging system PS can be caused by thermal effects 140 and accelerations of the optical elements as determined using the new method 100. [000113] The optical aberrations 120 of an imaging system PS can also be influenced by any aberration requests or requirements 150 imposed by a user of the imaging optics PS. For example, a desired or set point relative phase map may have some non-zero aberrations. [000114] A mechanical model 160 may allow for accelerations ^^^^(^) of one or more degrees of freedom to be mapped onto deformation 130 of the optics of the imaging system PS. That is, the mechanical model 160 may be able to predict how the one or moreelements that are accelerating will be deformed based on the acceleration of those optical elements. [000115] An optical model 170 may allow for deformation 130 of the optics of the imaging system PS to be mapped onto the optical aberrations 120. That is, the optical model 170 may be able to predict the optical aberrations that will result from a given deformation of the optical elements. Such an optical model 170 may involve ray tracing methods. In some embodiments, such an optical model 170 may also take into account deformation of the reticle (patterning device MA) and / or the wafer (substrate W). For example, the optical model 170 be used to map, for each of the reticle (patterning device MA) and the wafer (substrate W), a deformation of that object onto the optical aberrations 120. [000116] In general imaging quality may be assessed, for example, by aberration measurements 180. For example, such measurements may be made using a shearing interferometer within the lithographicapparatus LA. Such measurements may involve determining a measured wavefront map, %1(', ().[000117] The acceleration of one or more degrees of freedom ^^will, in general, give rise to a change in the position of the degree or freedom ^^(i.e. rigid body movement of the degree of freedom). Optionally, the one or more movement parameters of at least one optical element may also comprise an additional time dependence (i.e. a time dependence in addition to that which results from the acceleration) of the position ^^(^) of at least one degree of freedom associated with that optical element (i.e. additional rigid body movements). Such an arrangement is shown schematically in Figure 4. Some benefits of such embodiments are discussed below with reference to Figures 7A and 7B. [000118] The determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for an optical aberration of the imaging optics. For example, the determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for a contribution to the imaging performance from a deformation of surface(s) of one or more optical elements of the imaging optics from other sources.[000119] Such other sources may, for example, include thermal loads (i.e. thermal deformations). For example, the determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to the movement at least partially corrects for a contribution to the imaging performance from a thermal deformation of a surface of one or more optical elements of the imaging optics. [000120] As used here “an optical aberration of the imaging optics” may mean one or more coefficients in a Zernike / Tatian polynomial expansion of the form of equation (8). For example, the determined value(s) of the one or more movement parameters may be such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for certain Zernike / Tatian contributions to the relative phase map of the imaging optics PS. [000121] In some embodiments, each optical element (e.g. mirror) may be moved in such a way that it has minimal deformations. In some embodiments, a subset of the optical elements may be moved so as to cause deformation of the optical surfaces of that subset which at least partially correct for a contribution to one or more aberrations from the thermal deformations of all of the optical elements (i.e. including the optical elements that do not move). [000122] In some embodiments, the determined value(s) of the one or more movement parameters are such that one or more optical aberrations of the imaging system are optimized. [000123] In some embodiments of the method 100, the determined value(s) of the one or more movement parameters is / are such that one or more optical aberrations of the imaging system are minimized. It will be appreciated that, minimizing one or more optical aberrations of the imaging system may use any suitable optimization merit function. For example, in some embodiments, it may be desirable to minimize variation in the wavefront map in the pupil plane. In some embodiments, certain components of optical aberrations (for example certain Zernike / Tatian components) may have a particularly large effect on imaging performance and so it may be particularly desirable to minimize these components and the merit function may reflect this. [000124] It will be appreciated that minimizing one or more optical aberrations of the imaging system may comprise the use of any optimization method (for example to minimize a merit function) as desired or required. Examples of such optimization methods may include, for example, any of the following: genetic optimization algorithms; Newton’s method in optimization (also known as the Newton-Raphson method); simulated annealing; a least squares method; a quadratic programming active set method; an interior-point method; and / or a quadratic constrained quadratic programing method. [000125] In some embodiments, the determined values(s) of the one or more movement parameters is / are such that one or more optical aberrations of the imaging system are reduced relative to an exposure in which the optical elements do not move. In particular, the determined values(s) of the one or more movement parameters may be such that one or more optical aberrations of the imaging system are reduced relative to an exposure in which the optical elements do not accelerate.[000126] In some embodiments, a thermal model may be used to map, for the or each of one or more of the optical elements, a thermal load of an optical element to a corresponding thermal deformation of that optical element. Such a thermal model may be able to quantify a thermal deformation of any of the optical elements (for example mirrors) in the imaging system. Note that, in general, the thermal model may also include thermal effects on supporting structures (for example frames) of the optical elements. In some embodiments, such a thermal model may also take into account heating of the reticle (patterning device MA) and / or the wafer (substrate W). For example, a thermal model be used to map, for each of the reticle (patterning device MA) and the wafer (substrate W), a thermal load of that object to a thermal deformation of that object. [000127] In some embodiments, the method 100 may use a model to map the one or more movement parameters of each of the at least one optical element to at least one optical aberration of the imaging system. Such a model may take into account both: (a) a mechanical model 160 that can quantify a deformation 130 of all of the moving optical elements (for example mirrors) in the imaging system PS that is due to said movement (for example due to acceleration of the optical elements); and (b) an optical model 170 that can map such deformations to optical aberrations 120. [000128] If a degree of freedom ^^(^) is moved with velocity ^^^(^) and acceleration ^^^^(^), then a time dependence of a wavefront aberration ^^to this degree of freedom, ^^;^(^), will form of:^^;^(^) = ^ ^^^,^ ∙ ^^ (^) + ^^,^ ∙ ^^ (^), (11)where ^^,^describes the response to a or of freedom ^^(^) and ^^,^describes the response of wavefront aberration to acceleration of that degree of freedom ^^(^). Note that in general, ^^,^and ^^,^are not merely scalars but may be functions of position within a field plane. In particular, ^^,^and ^^,^may be functions of position within a field plane in a direction that corresponds to a non-scanning direction of the lithographic apparatus. [000129] The first term of equation (11) will vary due to any change in the position of that degree of freedom ^^(^), which will affect the aberration ^^, and the second term describes how deformation of an of the degree of freedom ^^(^) (caused by acceleration) will affect the aberration ^^. [000130] In some embodiments, the method 100 may use a mechanical model 160 to map one or more movement parameters of each of the at least one optical element to a corresponding movement deformation 130 of that optical element. Such a mechanical model 160 may be able to quantify a deformation of all of the moving optical elements (for example mirrors) in the imaging system PS that is due to said movement (for example due to acceleration of the optical elements). [000131] In some embodiments, the method 100 may use an optical model 170 to map deformation 130 of one or more of the optical elements of the imaging system to optical aberrations 120 of the imaging system. For example, the optical model may allow for a deformation of an optical element(which may be from any source) into a wavefront (relative phase) map. In some embodiments, such an optical model 170 may also take into account deformation of the reticle (patterning device MA) and / or the wafer (substrate W). For example, the optical model 170 be used to map, for each of the reticle (patterning device MA) and the wafer (substrate W), a deformation of that object onto the optical aberrations 120 of the imaging system. [000132] In some embodiments, the value(s) of the one or more movement parameters is / are determined for forming an image of an object MA on a substrate a plurality of times in succession. It will be appreciated that a substrate W used in a lithographic apparatus (e.g. a resist-coated silicon wafer) typically comprises a plurality of target regions. The same image (as defined by a reticle or mask MA) may be formed on each of the target regions. There may be, for example, of the order of 100 target regions or more. [000133] As explained above, the lithographic apparatus LA may be a scanning lithographic apparatus LA and the image (of a reticle MA) may be formed during a scanning exposure. After the formation of an image on a first one of the plurality of target regions, the wafer W may be moved such that a second target region is ready to be moved through the wafer-level illumination region IR’ so as to form an image on the second target region and so on. The plurality of target regions may be sequentially exposed using a movement of the substrate W that may be referred to as a meander scan. [000134] In some embodiments, it may be desirable for at least one of the optical elements to undergo an acceleration during formation of the image (i.e. during an exposure of a target region on a wafer W). However, it may be the case that the cumulative effect of accelerating the optical element in the same way for all exposures results in that optical element moving a sufficiently large distance that it starts to impact on imaging performance. It may therefore be desirable to move the optical element back to a nominal position between each exposure. [000135] An embodiment of the present disclosure wherein the optical elements are moved back to a nominal position between each exposure is illustrated schematically in Figure 5, which shows the displacement of two optical elements (for example relative to a nominal position of those optical elements) as a function of time. Three time periods 210 during which the wafer W is exposed are shown. The time periods 220 between two successive exposures are also shown (and are shaded in Figure 5). The displacement of a first optical element is shown as a dashed line 230 and the displacement of a second optical element is shown as a dotted line 240. As can be seen from the dashed line 230, the first optical element accelerates during the exposure time periods 210 and returns back to its nominal position during the time periods 220 between two successive exposures. Similarly, as can be seen from the dotted line 240, the second optical element moves with uniform velocity during the exposure time periods 210 and returns back to its nominal position during the time periods 220 between two successive exposures. It will be appreciated, in such embodiments, that the values of the movement parameters (position and acceleration) of each optical element may, in general, be different during the exposure time periods 210 and the time periods 220 between two successive exposures.[000136] Therefore, in some embodiments, the determined value(s) of the one or more movement parameters may comprise: (i) a first set of determined values to be used during the formation of at least a part of each image of the object on the substrate (i.e. during time periods 210); and (ii) a second set of determined values to be used at different times. For example, the second set of determined values may be used in between the formation of each pair of successive images (i.e. during time periods 220). The second set of determined value(s) of the movement parameters may, for example, be such that the optical element is moved back to a nominal position between each exposure. [000137] In some embodiments of the present disclosure, it may be desirable to move another optical element in such a way so as to at least partially compensate for the movement of an optical element that is being accelerated, as now discussed with reference to Figures 6A to 7B. [000138] The time dependence, ^^;^(^), of a wavefront aberration ^^to a degree of freedom ^^will be of the form given in equation (11). As previously explained, the present disclosure relates in particular to the use of non-zero acceleration of at least one optical element to cause a surface of that optical element to deform so as to at least partially correct for one or more aberrations. When one ofthe optical elements is accelerated during an exposure process (|^^^^ (^)| > 0) to exploit the second termin equation (11) (i.e. to obtain a contribution to the aberration of the form of ^ ^^^,^ ∙ ^^ (^)), then the firstterm (i.e. ^^,^ ∙ ^^ (^)) will also vary with time, since the position ^^ (^) will change during theexposure time period due to the non-zero acceleration (|^^^^ (^)| > 0). The variation of the first termwill during the exposure time period, which can limit the correction of optical aberrations, is now discussed with reference to Figures 6A and 6B. [000139] Note that in Figures 6A to 7B the following convention is used: the components 300a, 300b of the optical aberration (solid lines, which it is desired to correct) and the contributions to these aberrations from degrees of freedom (dotted and dashed lines and shaded areas, which are used to correct the optical aberrations) are shown with the same sign. However, a residual or total aberration (dot-dashed lines and striped-shaded regions) for a given aberration should be found as follows: all of the contributions to this aberration from degrees of freedom (dotted and dashed lines and shaded areas) should be summed and then this sum should be subtracted from the optical aberration (solid lines) which is being corrected. [000140] Figures 6A and 6B schematically show the ^)and ^*components 300a, 300b of an optical aberration (solid lines). Also shown are the contributions to these aberrations from the movement of a single degree of freedom, ^^. The contributions from to the position or value of this degree of freedom^^, i.e. ^),^ ∙ ^^(^) and ^*,^ ∙ ^^(^) are shown as dotted lines and the contributions from acceleration ofthis degree of freedom ^^, i.e. ^),^ ∙ ^^^^ (^) and ^*,^ ∙ ^^^^ (^) are shown as dashed lines.[000141] In this simple example, as can be seen in Figure 6A, the contribution to the ^)component from position (^),^) is non-zero and so any movement (which will vary the amplitude, ^^(^)) can be used to reduce the ^)aberration significantly. The difference between the ^)component of the opticalaberration 300a (solid line) and the contribution to the ^) component from position (^),^ ∙ ^^(^); dottedline) is shown as a corrected aberration 310 (dot-dashed line). The contribution to the ^)componentfrom acceleration of this degree of freedom is negligible (i.e. ^),^ ≈ 0).[000142] As can be seen in Figure 6B, the contribution to the ^*component of the optical aberration300b from the position or value of this degree of freedom ^^ is negligible (i.e. ^*,^ ≈ 0). However, thecontribution to the ^*component from acceleration (^*,^) of this degree of freedom is non-zero and sosuch movement (with an appropriate amplitude ^^^^ (^) ) can be used to reduce the ^* aberrationsignificantly. The difference between the ^*component of the optical aberration 300b (solid line) andthe contribution to the ^* component from acceleration (^*,^ ∙ ^^^^ (^); dashed line) is shown as acorrected aberration 320 (dot-dashed line).[000143] However, since this degree of freedom is(^^^^ (^) ≠ 0), the positionor value of this degree of freedom ^^(^) will change during the exposure. In turn, this means that the correction of the ^)aberration will be affected. For example, it is no longer possible for the rigid body movement of this degree of freedom to be as indicated by the dotted line of Figure 6A. Rather, this contribution will vary during the exposure time and will be spread out, as indicated by the shaded region surrounding the dotted line. As a result, the difference between the ^)component of the optical aberration 300a (solid line) and the contribution to the ^)component from the position or value of thisdegree of freedom ^^ (^),^ ∙ ^^(^); dotted line) is not the dot-dashed line but rather is spread out asindicated by the striped- surrounding the dot-dashed line.[000144] In some it may be desirable to be able use the second term of equation (11) independently of the first term of equation (11). In order to achieve this, another degree of freedom, ^^, may be used. Note that a time dependence, ^^;^(^), of a wavefront aberration ^^to this degree of freedom ^^will be of the form of: ^^;^(^) = ^^,^ ∙ ^^(^) + ^^,^ ∙ ^^^^ (^). (12)[000145] If these two degrees of freedom are the only degrees of freedom which affect this aberration^^ then the total time dependence of the aberration ^^ is given by ^^;^(^) + ^^;^(^). For simplicity,assume that degree of freedom ^^is only used to generate the first term of equation (12) for thisaberration ^^ (i.e. ^^,^ = 0). Therefore, the total time dependence of the aberration ^^ is given by:^^(^) = ^^,^ ∙ ^^(^) + ^ ^^^,^ ∙ ^^(^) + ^^,^ ∙ ^^ (^). (13)[000146] It is useful to for each degree of freedom which is accelerating (for example, in this example degree of freedom ^^) to express the degree of freedom as a function of time as:^^(^) = ^^(0) + ^^,var(^), (14)where ^^(0) is an initial position or value of the degree of freedom and ^^,var(^) is a time-varying contribution to the position (which arises due to the non-zero acceleration of this degree of freedom). [000147] In this simple example, the additional degree of freedom, ^^, is selected so that the movement of the additional optical element corrects for optical aberrations that result from a change in the first degree of freedom, ^^. This is achieved when: ^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^(^) = 0 (for all t). (15)[000148] Such an arrangement is shown schematically in Figure 7A, as now discussed. Figures 7A and 7B schematically show the ^)and ^*components 300a, 300b of an optical aberration (solid lines). Also shown are the contributions to these aberrations from the movement of two degrees of freedom, ^^and ^^. A first degree of freedom ^^is the same degree of freedom shown in Figures 6A and 6B. A second degree of freedom ^^is actuated so as to satisfy equation (15). In Figure 7A, the contributionto aberration ^) from: (i) the position or value of degree of freedom ^^, i.e. ^),^ ∙ ^^(^), is shown as ashaded region; (ii) the position or value of degree of freedom ^^, i.e. ^),^ ∙ ^^(^), is shown as anothershaded region; and (iii) acceleration of degree of freedom ^ ^^^, i.e. ^),^ ∙ ^^ (^), is shown as a dashed line.Figure 7B is the same as Figure 6B and shows the contributions to aberration ^*from the position orvalue of degree of freedom ^^, i.e. ^*,^ ∙ ^^(^), as a dotted line and from acceleration of this degree offreedom ^^ , i.e. ^*,^ ∙ ^^^^ (^) , as aAs in Figure 6B, the difference between the ^*component of the optical aberration 300b (solid line) and the contribution to the ^*component fromacceleration (^*,^ ∙ ^^^^ (^); dashed line) is shown as a corrected aberration 320 (dot-dashed line).[000149] The arrows provided in the shaded regions of Figure 7A indicate how the two position contributions (^^and ^^) vary with time. For example, at the start of the exposure process, the contribution to aberration ^)from the position or value of degree of freedom ^^is given by a loweredge of the shaded region labelled ^),^ ∙ ^^(^); and at the end of the exposure process the contributionto aberration ^)from the position or value of degree of freedom ^^is given by an upper edge of theshaded region labelled ^),^ ∙ ^^(^). Similarly, at the start of the exposure process, the contribution toaberration ^)from the position or value of degree of freedom ^^is given by an upper edge of theshaded region labelled ^),^ ∙ ^^(^); and at the end of the exposure process the contribution to aberration^)from the position or value of degree of freedom ^^is given by a lower edge of the shaded regionlabelled ^),^ ∙ ^^(^).[000150] Since the second degree of freedom ^^is actuated so as to satisfy equation (15), the sum of the contributions to ^)from the positions of the two degrees of freedom (i.e. ^^and ^^) remainsconstant and is given by ^),^ ∙ ^^(0) and is shown by the dotted line in Figure 7A. Therefore, with suchan arrangement the difference between the ^)component of the optical aberration 300a (solid line) and the contribution to the ^)component from the positions of the two degrees of freedom (^^and ^^) is shown as the corrected aberration 310 (dot-dashed line). [000151] In practice, it may not be possible to ensure that equation (15) is satisfied exactly. Therefore, in some embodiments, the movement of the second degree of freedom may be such that it at least partially cancels out a contribution to an aberration ^^from the time-varying contribution of the position ^^,var(^)from a degree of freedom which is accelerating. In order to achieve such partial contribution,it may be desirable to minimize |^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^ (^)|. For example, it may be desirable toensure that: ^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^ (^) ≈ 0, (16)or that: |^^,^ ∙ ^^,var(^) + ^^,^ ∙ ^^ (^)| < |^^,^ ∙ ^^ (^)|. (17)[000152] In practice, may a of a plurality of other optical elements, rather than just one additional optical element. In practice, this is typically possible, as actuations in one degree of freedom can usually be compensated well by a linear combination of other degrees of freedom. [000153] In general, a set of second degrees of freedom "^^# may be actuated such that they at least partially cancel out a contribution to an aberration ^^from the time-varying contribution of the position ^^,var(^) from a degree of freedom which is accelerating. This may be achieved by minimizing: ∙(^) + $ ∙ ^^(^)(18)where the sum is over all members of the set "^^#. [000154] In some embodiments of the new method 100, the determined value(s) of the one or more movement parameters may comprise: (a) a third set of determined values to be used by at least one optical element that are determined in dependence on the impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when theat least one optical element moves according to the determined third set of values of the movement parameters; and (b) a fourth set of determined values to be used by at least one other optical element such that the movement of the at least one other optical element at least partially corrects for a change in a contribution to one or more optical aberrations that results from a change of position of the at least one optical element. [000155] For example, in the simple example described above with reference to Figures 7A and 7B, the third set of determined values may comprise the values of the position, ^^(^), and the acceleration, ^^^^(^), of degree of freedom ^^and the fourth set of determined values may comprise the position, ^^(^), of degree of freedom ^^. Some embodiments of the present disclosure relate to a new exposure method wherein at least one optical element of the imaging optics moves during the formation of an image according to a value of one or more movement parameters determined by the new method 100 described above. An example of such an exposure method 400 is shown schematically in Figure 8. [000157] The new exposure method 400 comprises a step 410 of patterning a radiation beam using a patterning device MA so as to form patterned radiation. [000158] The new exposure method 400 comprises a step 420 of using imaging optics to collect the patterned radiation B’ and to form an image of the patterning device MA on a substrate W. [000159] The new exposure method 400 shown in Figure 8 is advantageous as it may allow for thermal distortions to be at least partially cancelled by mechanical distortions, resulting in reduced optical aberrations and optimized imaging performance. [000160] In some embodiments, optionally, the exposure method 400 may comprise a step of carrying out the new method 100 described above. [000161] Additionally or alternatively, the exposure method 400 may comprise step 405 of reading an output of the new method 100 described above from a storage medium and using this output to control movement of the at least one optical element. [000162] Some embodiments of the present disclosure relate to a lithographic apparatus or a lithographic system, which may be generally of the form shown in Figure 1. In general, the lithographic apparatus LA comprises: imaging optics PS; and a controller CN operable to perform the new methods 100, 400 described above. [000163] The time dependence, ^^;^(^), of a wavefront aberration ^^to a degree of freedom ^^will be of the form given in equation (11). In some embodiments, at least one optical element of the lithographic apparatus LA may be designed so that a stiffness distribution of that optical element has been selected so as to achieve a desired response for one or more aberrations to acceleration(s) of its degrees of freedom. From equation (11), a response for an aberration ^^to acceleration(s) of a degree of freedom ^^is ^^,^. However, note that, in general, there will be a different response for each different Zernike / Tatian component. That is, the response of the wavefront to acceleration(s) of a degree offreedom ^^is not a scalar value but a complex wavefront signature, for example a set of various Zernike / Tatian components at various field-points. That is, at least one optical element of the lithographic apparatus LA may be designed so that a stiffness distribution of that optical element has been selected so as to achieve a desired set of response coefficients, "^^,^#. [000164] By varying a stiffness distribution of at least one optical element in a design-phase (e.g. by changing a shape or adding / subtracting material at various parts ofthe mirror) the set of response coefficients, "^^,^# can be varied. By optimizing the stiffness distributions of the optical elements the acceleration induced deformation effects on the wavefront can be controlled. For example, the set of response"^^,^# may be selected so as to allow for correction of aberrations that are of the form of the (e.g. thermally induced) aberrations that are expected in the lithographic apparatus. [000165] Note that this is contrary to conventional wisdom wherein typically the optical elements are designed so as to be as stiff as possible (so that the response coefficients, "^^,^# are as small as possible). [000166] In some embodiments of the lithographic apparatus LA, the imaging optics PS may comprise at least one optical element having an anisotropic stiffness distribution. For example, a mirror support may be provided by ribs or comparable structural features lateral surfaces of the mirror have a highly anisotropic rigidity distribution. [000167] In some embodiments of the lithographic apparatus LA, the imaging optics PS may comprise at least one optical element having a stiffness distribution such that a response of a wavefront of radiation to an acceleration of the at least one optical element in at least one direction generally matches optical aberrations that are expected in use.[000168] Note that the coefficients, "^^,^# , that describe the response for aberrations ^^ toacceleration(s) of degrees of freedom ^^also depend on the positions of mounting points (or bushes) for the relevant optical element (or mirror). Therefore, in some embodiments, the positions of the mounting points of one or more optical elements may be varied in order to achieve a desired set of response coefficients, "^^,^#. [000169] Some embodiments of the present disclosure relate to a computer comprising: one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the new methods 100, 400 described above. In some embodiments, the one or more processors may be configured to store on the storage media value(s) of one or more movement parameters determined by the new method 100 described above. [000170] Some embodiments of the present disclosure relate to a computer-readable medium having instructions for carrying out the methods 100, 400 described above. The computer-readable medium may be a non-transitory computer-readable medium. [000171] 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 mayhave other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid- crystal displays (LCDs), thin-film magnetic heads, etc. [000172] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non-vacuum) conditions. [000173] Where the context allows, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g. carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world. [000174] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

Claims

1. CLAIMS 1. A method for determining one or more parameters for an imaging system that is for forming an image of an object on a substrate, the method comprising: determining a value of one or more movement parameters of at least one optical element of the imaging system during the formation of the image, the one or more movement parameters being such that at least one degree of freedom of the at least one optical element has a non-zero acceleration during at least part of the formation of the image, the value of the one or more movement parameters being determined in dependence on an impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined value of the one or more movement parameters.

2. The method of claim 1 wherein the determined value(s) of the one or more movement parameters is / are such that a contribution to the imaging performance from a deformation of the at least one optical element due to such movement at least partially corrects for an optical aberration of the imaging optics.

3. The method of any preceding claim wherein the determined value(s) of the one or more movement parameters is / are such that one or more optical aberrations of the imaging system are minimized.

4. The method of any preceding claim wherein the determined values(s) of the one or more movement parameters is / are such that one or more optical aberrations of the imaging system are reduced relative to an exposure in which the optical elements do not move.

5. The method of any preceding claim wherein the method uses a thermal model to map, for the or each of one or more of the optical elements, a thermal load of an optical element to a corresponding thermal deformation of that optical element.

6. The method of any preceding claim wherein the method uses a model to map the one or more movement parameters of each of the at least one optical element to at least one optical aberration of the imaging system.

7. The method of any preceding claim wherein the method uses a mechanical model to map one or more movement parameters of each of the at least one optical element to a corresponding movement deformation of that optical element.

8. The method of any preceding claim wherein the method uses an optical model to map deformation of one or more of the optical elements of the imaging system to optical aberrations of the imaging system.

9. The method of any preceding claim wherein the value(s) of the one or more movement parameters is / are determined for forming an image of an object on a substrate a plurality of times in succession.

10. The method of claim 9 wherein the determined value(s) of the one or more movement parameters comprise: a first set of determined values to be used during the formation of at least a part of each image of the object on the substrate; and a second set of determined values to be used at different times.

11. The method of claim 10 wherein the second set of determined values are to be used in between the formation of each pair of successive images.

12. The method of any preceding claim wherein the determined value(s) of the one or more movement parameters comprise: a third set of determined values to be used by at least one optical element that are determined in dependence on the impact on imaging performance that would be achieved by a deformation of an optical surface of the at least one optical element caused when the at least one optical element moves according to the determined third set of values of the movement parameters; and a fourth set of determined values to be used by at least one other optical element such that the movement of the at least one other optical element at least partially corrects for a change in a contribution to one or more optical aberrations that results from a change of position of the at least one optical element.

13. An exposure method comprising: patterning a radiation beam using a patterning device so as to form patterned radiation; using imaging optics to collect the patterned radiation and to form an image of the patterning device on a substrate; wherein at least one optical element of the imaging optics moves during the formation of the image according to a value of one or more movement parameters determined by the method of any preceding claim.

14. The exposure method of claim 13 further comprising carrying out the method of any one of claims 1 to 12.

15. The exposure method of claim 13 or claim 14 further comprising reading an output of the method of any one of claims 1 to 12 from a storage medium and using this output to control movement of the at least one optical element.

16. A lithographic apparatus or a lithographic system comprising: imaging optics; and a controller operable to perform the method according to any preceding claim.

17. The lithographic apparatus of claim 16 wherein the imaging optics comprises at least one optical element having an anisotropic stiffness distribution.

18. The lithographic apparatus of claim 16 or claim 17 wherein the imaging optics comprises at least one optical element having a stiffness distribution such that a response of a wavefront of radiation to an acceleration of the at least one optical element in at least one direction generally matches optical aberrations that are expected in use.

19. A computer comprising: one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the method of any one of claims 1 to 12.

20. The computer of claim 19 wherein the one or more processors are configured to store on the storage media value(s) of one or more movement parameters determined by the method of any one of claims 1 to 12.

21. A computer-readable medium having instructions for carrying out the method of any one of claims 1 to 12.

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