Abstract:
The invention relates to a method for the targeted deformation of an optical element, in particular a mirror that is positioned in an optical system. The optical element or a support element, on which the optical element is placed in such a way that forces acting on the support element cause a deformation of the optical element itself, are connected to a fixed structure indirectly by means of fixing elements or connecting members. The desired deformation of the optical element is achieved by a targeted variation of the fixing elements to modify the forces exerted in the fixing process on the optical element or the support element and/or the action of the moment of force and/or torque of the connecting members on the fixing elements.

Description:
PRIORITY CLAIM  
       [0001]     Priority under 35 U.S.C. §365(c) is hereby claimed to PCT/EP03/05113 filed May 15, 2003 which claims priority to German Patent Application No. DE 102 22 331.9, filed May 18, 2002. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1.74 Field of the Invention  
         [0003]     The invention relates to a method for the targeted deformation of an optical element, in particular a mirror, that is arranged in an optical system, the optical element or a carrier element, on which the optical element is mounted in such a way that forces acting on the carrier element cause a deformation of the optical element itself, being connected via fastening means directly or via joining means to a fixed structure. The invention also relates to a method for adjusting an optical element in accordance with the preamble of Claim  16 .  
         [0004]     2. Description of the Related Art  
         [0005]     Aberrations caused, for example, by heat, environmental conditions, positional deviations of mirrors, deviation in the shape of the optical surface from the desired shape, by layer stresses and tightening torques of screws, deformations induced in mounts and by manufacturing defects substantially impair the image quality of an optical system, for example of a projection exposure machine for microlithography. These problems are particularly compounded in the EUV region, where manipulators and the optical system are no longer adequately decoupled. An aberration correction, for example in order to balance out manufacturing inaccuracies in the projection objective is carried out by means of manipulating the optical elements via special manipulators or actuators. The disadvantage of this is that the very movements of the manipulator do not generally act on the optical element in a fashion free from deformation. The aberrations owing to the parasitic deformation of the surface of the optical element on the basis of the manipulator movements could in individual cases even be greater than the aberrations that were actually to be corrected by the movement. There is the risk that adjusting the objective without taking account of these deformations is no longer reliably possible. These problems are further compounded by so-called parasitic movements of the manipulators, that is to say by undesired additional movements of the manipulators, in particular in other degrees of freedom. The adjustment process of the newly fabricated projection objective is thereby rendered substantially longer and more complicated.  
         [0006]     Also known to date are measures for correcting aberrations that are based on the introduction of forces or torques to optical elements, particularly mirrors. In the case of all previously used optical elements and mounts, this introduction of forces or torques is always performed via actuators, adjusting screws or the like that are specifically designed therefor.  
         [0007]     However, with regard to the required design space in the objectives or imaging devices, this frequently constitutes a very complicated and expensive solution that causes a not inconsiderable outlay on construction if the aim is to find room in the objective for all requisite components for the purpose. Moreover, it must be ensured that all adjusting screws also remain accessible for manipulation or that, in the case of the use of actuators, there is always the possibility of electrical, pneumatic or other connection to an actuating medium.  
       SUMMARY OF THE INVENTION  
       [0008]     It is therefore the object of the present invention to provide methods of the type mentioned at the beginning that cancel the disadvantages of the prior art, the particular aim being to enable targeted correction of aberrations of an optical system in an adjustment process that is as simple and short as possible by means of accurate manipulations and/or targeted deformations of the optical elements, in which case the use of special and expensive actuators is to be dispensed with for this purpose.  
         [0009]     This object is achieved according to the invention by means of the characterizing features of claim  1 . It is likewise achieved by means of the features of claim  9  and it is likewise achieved by means of the features of claim  16 .  
         [0010]     Forces and/or torques are introduced in a simple and advantageous way by means of these measures in the region of holding means, such as clamps, adhesives or screws, that are required in any case for fastening optical elements, for the purpose of targeted deformation of the optical element. This saves the use of complicated actuators whose main function would be to deform the optical element. There is no need for additional design space, and no additional substantial outlay on construction is caused. Consequently, manipulation of an active optical element is enabled in a favorable way.  
         [0011]     It is advantageous when the image of the optical system in the image plane or on the substrate stage is influenced by the targeted deformation of the optical element, and aberrations of the optical system in the image plane or on the substrate stage are removed at least approximately by the targeted deformation of the optical element.  
         [0012]     Consequently, a simple method is provided for compensating aberrations of an optical system without high outlay by deformations of an optical element. This can be performed without high outlay only with the aid of the holding and/or fastening elements required in any case by the optical element.  
         [0013]     It is advantageous when a mirror is used as optical element. Both coated and uncoated mirrors can be deformed to correct the aberrations of an optical system. It is also possible to use a reticle mask as optical element.  
         [0014]     Advantages with reference to claim  8  result from the fact that the optical element can advantageously be adjusted more accurately and more quickly with incorporation of the additional parasitic effects to be expected from the manipulation itself.  
         [0015]     Advantageous refinements and developments of the invention follow from the further subclaims and from the exemplary embodiments described in principle in what follows with the aid of the drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]      FIG. 1  shows a sketch of the principle of an optical system having six mirrors;  
         [0017]      FIG. 2  shows a plan view of a mirror having a carrier element;  
         [0018]      FIG. 3  shows a side view of a mirror with a link to a fixed structure in a first embodiment;  
         [0019]      FIG. 4   a  shows a side view of a mirror with a link to a fixed structure in a second embodiment by means of a manipulator;  
         [0020]      FIG. 4   b  shows a further side view of a mirror with a link to a fixed structure in a second embodiment by means of a manipulator;  
         [0021]      FIG. 5  shows a graphical representation of a possible deformation of the optical surface of a mirror;  
         [0022]      FIG. 6   a  shows a sketch of the principle of a parasitic movement of a Z manipulator;  
         [0023]      FIG. 6   b  shows a compensation of the parasitic movement of the Z manipulator from  FIG. 6   a  by means of a movement in x- and in rotx-directions; and  
         [0024]      FIG. 7  shows a design principle of an EUV projection exposure machine having a light source, an illumination system and a projection objective. 
     
    
     DETAILED DESCRIPTION  
       [0025]     As may be seen from  FIG. 1 , an optical system  1  has six mirrors  2   a,    2   b,    2   c,    2   d,    2   e,    2   f.  The beam path  3  of the light is sketched in principle. As illustrated in  FIG. 7 , such an optical system  1  can be used as projective objective  1  in an EUV projection exposure machine  11  for microlithography.  
         [0026]      FIG. 2  shows the mirror  2   d,  which is fastened on a carrier element  4 . In the present exemplary embodiment, the carrier element  4  is connected directly ( FIG. 3 ) or via manipulators  10  ( FIGS. 4   a  and  4   b ) via screws  5 ,  5   a,    5   b,    5   c  to a fixed structure  6  that is illustrated in more detail in  FIGS. 3, 4   a  and  4   b,  and can be a fixed part of the projection exposure objective. It is particularly important that a fixed connection not decoupled with regard to forces exists between the mirror  2   d,  that is to say the optically active surface, and the carrier element  4 . It would be optimal to use a single block mirror, however, it is likewise possible to bond the mirror  2   d  onto the carrier element  4  although this is attended by a corresponding damping of the force actions. The forces, stresses and torques occurring during tightening of the screws  5 ,  5   a,    5   b,    5   c  for the carrier element  4  are consequently passed on to the mirror  2   d.  These forces, stresses and torques are actively used in order to manipulate and/or deform the mirror  2   d  or the optically active surface thereof indirectly via the carrier element  4  so as to reduce aberrations of the optical system  1 . In addition to the simple possibility of modifying the tightening torque of the individual screws  5 ,  5   a,    5   b,    5   c,  there is the possibility, in addition, of achieving this via active elements, in particular longitudinally modifiable actuators such as piezoelectric stacks. Such a mode of operation is outlined in  FIGS. 3, 4   a  and  4   b  in particular.  
         [0027]     As may be seen from  FIG. 3 , the mirror  2   d  is mounted on the carrier element  4  and connected to the fixed structure  6  via screws  5 ,  5   a  by means of a mount  7 . Piezoelectric elements  8  are inserted between metal shins  9  and around the screws  5 ,  5   a  in such a way that given a modification of the length of the piezoelectric elements  8  in the direction of the carrier element  4  the pressure exerted thereon strengthens the holding or clamping force of the screws  5 ,  5   a  and therefore introduces forces onto the carrier element  4  with the mirror  2   d.  In order to modify the holding or clamping force of the screws  5 ,  5   a,  it is also possible, of course, in another exemplary embodiment to use other means than piezoelectric elements  8 . The electrical connections of the piezoelectric elements  8  are not illustrated. Consequently, the force can easily and advantageously occur in the region of the screws  5 ,  5   a  required in any case for fastening the carrier element  4  with the mirror  2   d  on the mount  7  or the fixed structure  6 .  
         [0028]     In  FIGS. 4   a  and  4   b  a manipulator  10  ensures that the carrier element  4  with the mirror  2   d  is linked to the fixed structure  6 . Manipulators  10  permit the translatory and rotary motion of the carrier element  4  with the mirror  2   d.  In addition, the manipulator  10  can also be used in order to exert forces or torques on the screws  5 ,  5   a  or on the carrier element  4 , and thus on the mirror  2   d.    
         [0029]      FIG. 4   b  shows a side view of the embodiment illustrated in  FIG. 4   a.    
         [0030]      FIG. 5  illustrates by way of example a possible form of the deformation of the optically active surface of the mirror  2   d  after introduction of forces.  
         [0031]      FIG. 6   a  shows parasitic movements of a Z manipulator  10   a:  undesired movements occur in the X-direction P x  and in the rotX-direction P rotx . For this purpose, use was made in the present exemplary embodiment of a X-manipulator  10   b  and a rotx-manipulator  10   c  for compensating the parasitic movements P x , P rotx  ( FIG. 6   b ). It is advantageously possible in further exemplary embodiments to use the remaining manipulators  10 , in particular in 5 degrees of freedom, for compensating the parasitic movements of a manipulator  10 .  
         [0032]     As may be seen from  FIG. 7 , the EUV projection exposure machine  11  has a light source  12 , an EUV illumination system  13  for illuminating a field in a plane  14  in which a structure-bearing mask is arranged, as well as the projection objective  1  for imaging the structure-bearing mask in the plane  14  onto a photosensitive substrate  15 . Reference may be made to EP 1 123 195 A1 as regards the EUV illumination system  13 .  
         [0033]     The main aim of the deformations and movements caused by the introduction of forces or torques via the screws  5 ,  5   a,    5   b,    5   c  or the manipulators  10  is to balance out aberrations of the optical system  1 . Such aberrations are produced, for example, by manufacturing inaccuracies (shape errors—deviation of the shape of the optical surface from the desired shape, deformations induced by layer stresses, deformations caused by screw tightening torques), positional deviations, heat and environmental conditions. This main aim is intended to be achieved by introducing forces onto the mirror  2   d  or the carrier element  4  thereof, or by moving the mirror  2   d  or the carrier element  4  thereof by the manipulators  10  in all 6 degrees of freedom. In order to correct aberrations, the image of the optical system  1  in the image plane or on a substrate stage is influenced by deformations produced in the optical surface of the mirror  2   d  and by a possible change in tilting/position. It is also possible to correct short term aberrations caused by heat or temperature variations in the environment. It is true that the deformations induced by the manipulators  10  or the screws  5 ,  5   a,    5   b,    5   c  likewise constitute perturbations of the optical system  1 , but these, as it were, artificial perturbations or their strength or amplitude can be controlled. For this reason, these controlled deformations constitute a very effective means of improving the image quality or of adapting the properties of the optical system  1 . Consequently, these controlled deformations caused by the tightening torque of the screws  5 ,  5   a,    5   b,    5   c  and by the action of force or the action of torque on the manipulators  10  form degrees of freedom for correcting the aberrations in the optical system  1 . It is conceivable to use a described method both for correcting static aberrations when adjusting the optical system  1 , and for correcting dynamically occurring aberrations (for example owing to heat, temperature drift, or the like). As already addressed above, there is still the problem of parasitic effects of the manipulators  10  which occur in an undesired fashion in addition to the targeted movements and actions of forces and torques. Both additional induced deformations and movements along other directions are involved here. The aberrations owing to the parasitic deformation of the surface of the optical elements could even become greater in individual cases than the aberrations that are actually to be corrected by the movement. These parasitic effects of the manipulators  10  (and also, possibly, of the screws  5 ,  5   a,    5   b,    5   c ) are now also already incorporated, according to the invention, in the calculation of the adjusting positioning travels and in selection of the manipulators  10  or the screws  5 ,  5   a,    5   b,    5   c  to be readjusted, that is to say they are incorporated in the adjustment algorithm. This integration is enabled by a mathematical description. The aberrations of the optical system  1  can be determined from a measured image, and the requisite movements of the manipulators  10  can be calculated. The deformations to be expected of the optical surfaces are indicated in the adjustment algorithm as pseudo-manipulators coupled to the real manipulators  10 , as it were.  
         [0034]     The deformations produced in a targeted manner on the optical surface cover the nanometer range (for a force of 1 N and torques of 10 Nmm at the manipulators  10 ) and permit virtually all types of corrections of aberration. Rotationally symmetrical deformations for example can be produced by the use of the manipulators  10  or by the variation of the screws  5 ,  5   a,    5   b,    5   c  which, as illustrated in  FIG. 2 , are arranged approximately symmetrically about the mirror  2   d  on the carrier element  4 . These are, for example, changed in radius in the x- or y-direction owing to radial compression of the carrier element  4  with the mirror  2   d  (astigmatism for the correction of image offset). The correction of three-leaf clover can be performed, for example, by torques introduced onto the mirror  2   d.  Of course, a symmetrical arrangement is not mandatory. Asymmetric aberrations could also be corrected with the aid of an asymmetric arrangement of the manipulators  10  or of the screws  5 ,  5   a,    5   b,    5   c.    
         [0035]     The following method is applied to correct the aberrations in the optical system  1 :  
         [0036]     in a first step, there is an analysis of the modifications, with reference to the image or the aberrations, that can be induced by the screws  5 ,  5   a,    5   b,    5   c  and also by the manipulators  10  in the image plane or on the substrate stage of the optical system  1 ;  
         [0037]     in a second step, there is an analysis (by calculation, measurement or simulation) of the current perturbations of the optical system  1  in the image plane; and 
        in a third step there is a minimization of the aberrations determined in step two by means of a linear combination of the inducible image modifications, determined in step  1  with the aid of suitable mathematical methods (for example SVD or the like) in accordance with which the aberrations that are caused by the perturbations of the optical system  1  are corrected by modifications of the forces or torques on the screws  5 ,  5   a,    5   b,    5   c,  the respective intensities or amplitudes of the forces or torques respectively to be used being specified by the coefficients of the linear combination.        
 
         [0039]     The following exemplary embodiment shows that aberrations of the optical system  1  can be corrected, and the optical quality of the system can be improved, with the aid of the variation of the tightening torque of the screws  5   a,    5   b,    5   c  of the mirror  2   d  on the carrier element  4 . The modification of the tightening torque of the screws  5   a,    5   b,    5   c  is equivalent to a modification of the pressure on the contact point of the screws  5   a,    5   b,    5   c  with the carrier element  4  or with the mirror  2   d.  In this exemplary embodiment, only three screws  5   a,    5   b  or  5   c  were used as adjustable degrees of freedom, as it were, and it was possible to provide nine degrees of freedom when using all the screws  5 ,  5   a,    5   b,    5   c.  The number of possibilities for reducing the aberrations rises, of course, with the use of as many degrees of freedom as possible.  
         [0040]     Only a few specific aberrations were treated by way of example, for the sake of simplicity. These are: distortion (DIST.), field curvature (FC), astigmatism (AST), wave front errors (WFE), coma and spherical aberration (SPA). These aberrations relate largely to the optical system  1 .  
         [0041]     The above method was used as follows in a first exemplary embodiment:  
         [0042]     The tightening torques of the screws  5   a,    5   b,    5   c  (see  FIG. 2 ) of the mirror  2   d  of the optical system  1  were temporarily increased in a first step by 500 N in each case, in order to determine the aberrations inducible thereby.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    Screw 5a   10.493   147,881   114.333   0.931   1.257   0.430       Screw 5b   7.271   97.655   79.468   0.656   0.873   −0.291       Screw 5c   7.377   97.127   79.130   0.655   0.885   −0.275                  
 
         [0043]     Subsequently, the aberrations of the optical system  1  were determined in a second step by means of induced perturbations.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    opt.   5.94   102.6   80.1   0.652   0.829   −0.377       system 1                  
 
         [0044]     In the last step, a minimization of the aberrations of the optical system  1  determined in step two was calculated by a linear combination of the inducible image modifications determined in step one, this being done by varying the tightening torque of the screws  5   a,    5   b,    5   c  by 500 N. The factor specifies the reduction of the respective aberration by the linear combination. The coefficients in front of the reference symbols of the screws  5   a,    5   b,    5   c  specify the linear coefficient that is required in order to achieve a minimum aberration. Consequently, the aberrations are minimized for the screw  5   a  given a strengthening of the tightening torque by 2.9×500 N, the figure for screw  5   b  being 3.3×500 N, and that for screw  5   c  being 2.5×500 N.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    1.44 (5a) + 1.82   6.43   82.2   51.39   0.389   0.522   −0.288       (5b) + 0.94 (5c)       Factor   0.9   1.2   1.6   1.7   1.6   1.3       2.9 (5a) + 3.3   5.1   70.9   50.7   0.398   0.557   −0.318       (5b) + 2.5 (5c)       Factor   1.2   1.4   1.6   1.7   1.5   1.2                  
 
         [0045]     In a second exemplary embodiment, an attempt was made to use an appropriate correction of the tightening torques of the screws  5   b,    5   c  in order to balance out the instances of image interference of the optical system  1  caused by an increase in the tightening torque of the screw  5   a  of the mirror  2   d  on the carrier element  4 .  
         [0046]     The effects of the variation of the tightening torque of the screws  5   b  and  5   c  by 500 N were determined in the first step in the process.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    Screw 5b   7.271   97.655   79.468   0.656   0.873   −0.291       Screw 5c   7.377   97.127   79.130   0.655   0.885   −0.275                  
 
         [0047]     The aberrations caused by the increase in the tightening torque of the screw  5   a  were determined in a second step.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    Screw 5a   10.493   147.881   114.333   0.931   1.257   0.430                  
 
         [0048]     A minimization of the error determined in step two was carried out with the aid of the results from step  1  in the third step, once again by means of the linear combination. As in the above exemplary embodiment, the factor specifies the reduction in the respective aberration.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    5a, 5b, 5c   1.06   25.9   11.6   0.113   0.19   0.06       (5a) + 1.036(5b) +   0.76   16.04   10.27   0.078   0.133   0.073       1.037(5c)       Factor   1.4   1.6   1.1   1.4   1.4   0.8                  
 
         [0049]     In a third exemplary embodiment, aberration corrections were introduced by manipulators  10  in accordance with  FIGS. 4   a  and  4   b.  Use was made of eight degrees of freedom in the form of manipulators  10  that act on the points of the screws  5   a,    5   b.  Here, only eight degrees of freedom were used, but when the basis is twelve degrees of freedom per mirror  2   a,    2   b,    2   c,    2   d,    2   e,    2   f  the result is a total maximum number of 72 degrees of freedom for the optical system  1  that are admittedly available in principle for correcting aberrations, but of which not all can be used owing to mechanical and physical reasons.  
         [0050]     In the first step, the effects of the variation of the actions of the forces of the manipulators on the sites formed by the screws  5   a  and  5   b  of the mirror  2   d  on the carrier element  4  were measured once again. The following forces and torques were fundamentally applied to the mirror  2   f  in this process: radial force (RF), radial torque (RT), tangential torque (TT), torque along or in the direction of the optical axis (ZT).  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    RF 5a 2f   0.72   6.52   6.52   0.007   0.001   0.044       RT 5a 2f   0.56   13.98   13.98   0.002   −0.0002   0.093       TT 5a 2f   0.11   1.38   1.35   0.008   0.001   0.013       ZT 5a 2f   0.02   0.57   0.56   0.001   0.0002   0.004       RF 5b 2f   0.88   7.11   7.11   0.007   0.003   0.048       RT 5b 2f   0.83   15.16   15.16   0.002   0.0004   0.100       TT 5b 2f   0.35   3.20   3.20   0.009   0.002   0.023       ZT 5b 2f   0.03   0.46   0.46   0.001   −0.0001   0.003                  
 
         [0051]     The present image interference of the optical system  1 , which were induced by a deformation of the mirror  2   d,  were determined in the second step.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    2d   0.86   13.45   11.08   0.086   0.103   −0.046                  
 
         [0052]     The optimum image corrections were calculated in the third step on the basis of the manipulations shown in step one.  
                                                                                                 DIST.   FC   AST   WFE   COMA   SPA                                    Mirror 2d   0.47   9.94   4.77   0.058   0.063   −0.042       Factor   1.8   1.4   2.3   1.6   1.1   1.5                  
 
         [0053]     Targeted movements of the manipulators can approximately produce changes in radius by 5×10 −8  m Δr/r per mirror  2   a,    2   b,    2   c,    2   d,    2   e,    2   f  and thereby correct the following aberrations with orders of magnitude as follows:  
         [0054]      2   a:  100 Nm FC and AST, and 1 nm coma  
         [0055]      2   b:  negligible  
         [0056]      2   c:  negligible  
         [0057]      2   d:  200 nm DIST., 300 nm FC and AST, 2 nm WFE, 1 nm coma, 0.2 nm SPA  
         [0058]      2   e:  negligible  
         [0059]      2   f:  100 nm DIST., 0.2 nm SPA.  
         [0060]     There follows an examination of the principle of an adjusting algorithm in which the parasitic effects of the manipulators  10  of an optical system are additionally incorporated into the calculation of the adjusting positioning travels, and into the selection of the manipulators to be readjusted.  
         [0061]     Given a perfectly adjusted optical system, a movement of the manipulators produces aberrations by the change in position of the optical elements, on the one hand, and by their deformation, on the other hand. The deformation is a function of the magnitude of the forces and torques that act on the optical elements, and these are a function, in turn, of the setting of the manipulators.  
         [0062]     The effects can be described as {overscore (b)} D =A D ·{overscore (x)} in a linear approximation, {overscore (b)} D  representing the aberrations that result from the pure manipulation {overscore (x)}. The sensitivity matrix A D  produces the relationship between {overscore (b)} D  and {overscore (x)} in accordance with the design of the optical-system.  
         [0063]     In the same way, {overscore (b)} V =A V ·{overscore (x)} describes the aberrations {overscore (b)} v  that result from the additional parasitic deformations during the manipulation {overscore (x)}. Here, the sensitivity matrix A V  takes account only of the effects of the additional deformations.  
         [0064]     The correction of these aberrations {overscore (b)} V  depending on deformation requires a number of degrees of freedom that can be achieved either by an additional movement of the same manipulator, or by the movement of one or more other manipulators.  
         [0065]     An actual effect of a manipulation on the aberrations is yielded by adding the two effects {overscore (b)} D  and {overscore (b)} V .  
           b   _     =           b   _     D     +       b   _     V       =         (       A   D     +     A   V       )     ·     x   _       =     A   ·     x   _             ,     A   =     (           a     1   ,   1             a     1   ,   2           ⋯         a     1   ,   m                 a     2   ,   1             a     2   ,   2           ⋯         a     2   ,   m               ⋮       ⋯       ⋯       ⋮             a     n   ,   1             a     n   ,   2           ⋯         a     n   ,   m             )           
 
         [0066]     a 1,1  to a a,m  represent the factors determined for the purpose of describing the relationship between the positioning travels to be covered and the aberrations resulting therefrom.  
         [0067]     The actual adjustment problem can be solved in a known manner by means of singular-value analysis methods.  
         [0068]     The fact that the imaging optics for EUV lithography place extremely stringent requirements on the image quality and thus on the magnitude of the residual errors requires the use of very many manipulators. Consequently, all the optical elements (except for the reference element) are manipulated in all six degrees of freedom. However, in conjunction with a finite measuring accuracy of the aberrations this can lead to instabilities in the method, resulting, for example, in extremely high positioning travels (possibly not capable of implementation) of some manipulators, while others would not be moved at all. According to the prior art, it would therefore be necessary to select manipulators. In other words, attempts would be made to use a minimum number of manipulators sufficient for adjustment, while other manipulators carrying out similar tasks would be ignored. However, the residual level of the aberrations after adjustment would thereby be raised and in some circumstances precisely the manipulators ignored for a specific problem would be decisive, in particular given the stringent requirements in the EUV field.  
         [0069]     The inventors solve this contradiction by means of a so-called self-conditioning method that avoids instabilities and at the same time uses all the manipulators. For this purpose the matrix A is expanded to A sk  so that the positioning travels are shifted to the aberration side. 
 
 G·{overscore (b)}   sk   =G·A   sk   ·{overscore (x)}, where  
 
  
           A   sk     =     (           a     1   ,   1             a     1   ,   2           ⋯         a     1   ,     m   -   1               a     1   ,   m               ⋮       ⋯       ⋯       ⋯       ⋮             a     n   ,   1             a     n   ,   2           ⋯         a     n   ,     m   -   1               a     n   ,   m               1       0       ⋯       0       0           ⋮       ⋯       ⋯       ⋯       ⋮           0       0       ⋯       0       1         )       ,     
     ⁢         b   _     sk     =     (       b   _     0     )       ,     G   =     (           g   1         ⋯       0       0       ⋯       0           ⋮       ⋯       ⋯       ⋯       ⋯       ⋮           0       ⋯         g   n         0       ⋯       0           0       ⋯       0         g     n   +   1           ⋯       0           ⋮       ⋯       ⋯       ⋯       ⋯       ⋮           0       ⋯       0       0       ⋯         g     n   +   m             )           
 
         [0070]     That is to say, an aberration vector {overscore (b)} sk  expanded by the positioning travels is defined. At the same time, weighting factors g i  that permit positioning travels and aberrations to be weighted at different strengths are introduced. If a measurement of the aberrations is now expanded by the positioning travels 0, optimization by means of singular-value analysis yields a result that automatically uses only those ones of all manipulators that lead in specific instances to an improvement of the aberrations, and simultaneously require manipulator paths (positioning travels) that are as small as possible. All the optical elements (apart from the reference element) can be used in this way for manipulation and simultaneously ensure a stable process. The optimum selection of the weighting factors g i  has proved to be very important in practice. If a measurement of the aberrations is expanded by the deflection of the manipulators, then optimization by means of singular-value analysis yields a result that automatically minimizes the absolute deflection of the manipulators in addition to minimizing the aberrations. This ensures observance of the physically possible positioning ranges of the manipulators (range control).