Patent Publication Number: US-8528461-B2

Title: Force actuator

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit under 35 USC §119 of German patent application 10 0 2007 040 363.3, filed Aug. 24, 2007, and German patent application 10 2007 063 293.4, filed Dec. 27, 2007. The entire disclosure of both of these applications is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention concerns an actuator arrangement which allows a defined force to be applied to a body and which can be employed in particular in connection with an optical imaging apparatus. The invention can be employed in the field of microlithography, which is used in connection with the manufacture of microelectronic circuits. The invention further extends to an optical imaging method which can be performed, among other processes, with the optical imaging apparatus according to the invention. 
     Particularly in the realm of microlithography it is imperative, among other requirements besides using components of the highest possible precision, that the position and geometry of the components of the imaging apparatus, i.e. for example the optical elements such as lenses, mirrors or reticles be kept as constant as possible in order to achieve a high image quality. The high requirements for accuracy in the microscopic range at an order of magnitude of a few nanometers and below are in large part a consequence of the constant need to increase the resolution of the optical systems that are used in the manufacture of microelectronic circuits, in order to further advance the miniaturization of the microelectronic components being manufactured. 
     As a means to achieve an increased resolution, one can either use light of a shorter wavelength, as is the case in systems operating in the extreme UV range (EUV) at operating wavelengths in the range of 13 nm, or one can increase the numerical aperture of the projection system. One possibility to significantly increase the numerical aperture above a value of 1.0 is realized with so-called immersion systems, where the space between the last optical element of the projection system and the substrate that is to be exposed is occupied by an immersion medium whose refractive index is larger than 1.0. A further increase of the numerical aperture is possible with optical elements of a particularly high refractive index. 
     With a shorter operating wavelength as well as with a higher numerical aperture, not only will the optical elements that are being used have to meet more stringent requirements on positioning accuracy and on the ability to hold their dimensions over the entire operating life, but there will of course also be increased requirements to minimize the imaging errors of the entire optical arrangement. 
     A known concept to minimize imaging errors is to subject the optical elements involved to an active deformation in order to change their optical characteristics in such a way as to counteract one or more specific imaging errors of the optical system (even to the extent of completely correcting the imaging error). In order to achieve the desired deformation of the optical element, suitable forces are applied to the optical element through a diversity of actuators. 
     In many cases, so-called N-wave deformations (where N is an integer larger than 1) are generated in order to effect the correction of imaging errors. Normally, this involves subjecting the optical element to actuator forces (normally parallel to the optical axis of the optical system) which are applied at N locations distributed (in most cases evenly) on the circumference of the optical element. In between the points of application of the actuator forces, the optical element is seated against support elements or further actuators (which are normally set along the circumferential direction halfway between every two neighboring points of application of the actuator forces). The result is, accordingly, a deformation with an undulating shape in the circumferential direction of the optical element. An arrangement of the kind has been described for example in DE 198 27 603 A1 (Holderer et al.), whose entire disclosure is incorporated herein by reference. 
     This wave-shaped deformation can be used to compensate for imaging errors of the kinds which are caused for example when optical elements of optical systems are heating up. It is normally necessary to superimpose deformations of different order N on each other in order to achieve a desired corrective effect. With an arrangement designed for a certain maximum order N, it is also possible to produce deformations of a lower order. For example, with an arrangement for a 4-wave deformation, it is also possible to produce a 2-wave deformation. 
     This concept is often implemented with fluidic actuators, which allow a desired actuator force to be generated by setting a corresponding pressure in an actuator chamber. Such fluidic actuators have the advantage that there is an exactly defined relationship between the pressure in the actuator chamber and the actuator force generated by the actuator, so that the actuator force can be regulated simply by regulating the pressure in the actuator chamber. 
     This arrangement poses the problem that, depending on the geometry of the optical element, a significantly smaller actuator force may be required for a lower-order deformation than for a higher-order deformation. Accordingly, if this is the case, a lower-order deformation will be significantly more sensitive than a higher-order deformation in regard to errors that may occur in setting the actuator force. 
     Thus, it is possible for example in lenses that are thick at the border, that a 4-wave deformation will require a 20 times larger actuator force than a 2-wave deformation of the same amplitude. This represents a disadvantage in that the pressure regulation has to be designed for the maximum pressure to be generated in the actuator chamber and consequently, if the relative accuracy of the pressure regulation is assumed to be approximately constant, the absolute accuracy of the setting for the smaller actuator forces for the 2-wave deformation is reduced by a corresponding factor. 
     Finally, besides the aforementioned actuator arrangements, an actuator arrangement for deforming a lens is described in DE 198 27 603 A1 among other subjects, wherein two identical actuators, arranged in diametrically opposite locations (relative to the optical axis of the lens) and acting parallel to the plane of the lens, are introducing bending moments into the lens by way of the lens mount. This arrangement, too, suffers from the aforementioned drawbacks. 
     BRIEF SUMMARY OF THE INVENTION 
     It is therefore the object of the present invention to provide an actuator arrangement, an optical arrangement with an actuator arrangement, an optical imaging apparatus with an actuator arrangement, and an optical imaging process which uses an actuator arrangement, wherein the aforementioned disadvantages are absent or at least occur only to a lesser degree and wherein in particular the actuator force can be set more accurately for different levels of magnitude of the force. 
     The present invention is based on the observation that a higher accuracy in setting the actuator force at different levels of force can be achieved easily through a concept where the actuator force that is called for is generated by separately producing individual actuator forces of different levels of magnitude through separate actuator arrangements and superimposing these individual actuator forces on each other to produce the desired resultant actuator force. This opens a simple way to design each of the separate actuator devices for the respective level of force, so that in each case the setting accuracy is optimized for the respective level of force. 
     As is self-evident, the invention can be used in connection with any desired actuator principles. For example, any electrical and/or fluidic actuators can be used to realize the two actuator arrangements. Of course, it is also possible to use any combination of different actuator principles. Particularly advantageous versions are obtained by using fluidic actuators. 
     In fluidic actuators, the setting accuracy can be optimized through the components of the actuator chamber and/or the components of the pressure regulation. For example, while using identical components of the pressure regulation (i.e. with the same maximum pressure level), an adaptation to different levels of force is possible simply through an adaptation of the effective surface area of the actuator chamber. Likewise with the exact opposite concept, if identical components are used for the actuator chamber, the adaptation to the required level of force is possible simply through an adaptation of the pressure level of the pressure regulation. Finally, it is also possible with identical components for the actuator chamber and the pressure regulation to achieve an adaptation to the required force level by using a commensurate amount of force reduction (for example by way of a transmitting mechanism) which is arranged downstream of the actuator chamber. 
     Therefore, one object of the present invention is an actuator arrangement, serving in particular to introduce a deformation in an optical element with a first, specifically fluidic-based actuator device, which is designed to exert on a body associated with the first actuator device a first actuator force in an amount up a first maximum force value. The actuator arrangement further includes a second, specifically fluidic-based actuator device, which is designed to exert on the body associated with the first actuator device a second actuator force in an amount up a second maximum force value. The second actuator device is arranged in such a way in relation to the first actuator device that the respective lines of action of the first actuator force and the second actuator force have at most a small distance from each other in the area of the their respective points of application on the body. Furthermore, the second maximum value of the second actuator force is smaller than the first maximum value of the first actuator force. 
     A further object of the present invention is an optical arrangement, specifically for the field of microlithography, with an optical element and a supporting structure, wherein the supporting structure supports the optical element and includes at least one actuator arrangement functioning as a force actuator according to the invention, which is connected to the optical element. 
     A further object of the present invention is an optical imaging arrangement, specifically for the field of microlithography, with an illumination device, a mask device designed to receive a mask that includes a design pattern to be projected, a projection device with a plurality of optical elements, and a substrate device serving to receive a substrate, wherein the illumination device is designed to illuminate the design pattern and the optical elements are designed to project an image of the design pattern onto the substrate, and wherein the projection device includes an optical arrangement according to the invention, which in turn includes one of the optical elements. 
     A further object of the present invention is a method of exerting forces on a body by means of at least one force actuator, specifically for the purpose of causing a deformation of the body, wherein by means of a first, specifically fluidic-based actuator device of a force actuator a first actuator force of a magnitude up to a first maximum force value is exerted on the body. Furthermore, a second actuator force in an amount up a second maximum force value is exerted on the body by means of a second, specifically fluidic-based actuator device, wherein the respective lines of action of the first actuator force and the second actuator force have at most a small distance from each other in the area of the their respective points of application on the body, and the second maximum value of the second actuator force is smaller than the first maximum value of the first actuator force. 
     A further object of the present invention is a an optical imaging method, in particular for the field of microlithography, wherein an image of a design pattern is projected onto a substrate by means of a plurality of optical elements, wherein an imaging error in the projection of the design pattern onto the substrate is registered, and wherein based on the registered imaging error at least one of the optical elements is subjected to a deformation by way of a method according to the invention in order to change the optical properties of said element and to thereby reduce the imaging error. 
     A further object of the present invention is an actuator arrangement, serving in particular to cause a deformation in an optical element with a first, specifically fluidic-based actuator device, wherein the first actuator device includes a first actuator chamber, and the first actuator device is designed to exert a first actuator force on a body associated with the first actuator device. The actuator arrangement further includes a second, specifically fluidic-based actuator device, wherein the second actuator device includes a second actuator chamber. The second actuator device which is designed to exert on the body associated with the first actuator device a second actuator force. The first actuator chamber and the second actuator chamber are arranged so that they are nested inside each other. 
     Further preferred embodiments of the invention are presented in the subordinate claims and in the following description of examples of preferred embodiments with references to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic representation of a preferred embodiment of the imaging apparatus according to the invention, which includes a preferred embodiment of the optical arrangement according to the invention with a preferred embodiment of the actuator arrangement according to the invention. 
         FIG. 2  is a schematic, in part sectional view of a portion of the imaging apparatus of  FIG. 1 ; 
         FIG. 3  represents a schematic partial cross-section of the detail III of  FIG. 2 ; 
         FIG. 4  represents a strongly simplified perspective view of the optical arrangement shown in  FIG. 2 ; 
         FIG. 5  represents a flowchart diagram of a preferred embodiment of the optical imaging method according to the invention, which can be carried out with the optical imaging apparatus of  FIG. 1 , using a preferred embodiment of the method according to the invention for generating and applying forces; 
         FIG. 6  represents a schematic partial cross-section of a part of a further preferred embodiment of the optical arrangement according to the invention; 
         FIG. 7  represents a schematic partial cross-section of a part of a further preferred embodiment of the optical arrangement according to the invention; and 
         FIG. 8  represents a strongly simplified perspective view of a further preferred embodiment of the optical arrangement according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     First Example 
     Making reference to  FIGS. 1 to 5 , following is a description of a preferred embodiment of the optical imaging apparatus according to the invention for use in microlithography. 
       FIG. 1  shows a schematic representation, not drawn to scale, of a preferred embodiment of the optical imaging apparatus according to the invention in the form of a microlithography apparatus  101  which operates with light in the UV range with a wavelength of 193 nm. However, it should be understood that the invention can also find application in connection with any other optical imaging apparatus which may operate at any desired different wavelengths. 
     The microlithography apparatus  101  includes an illumination system  102 , a mask device in the form of a mask stage  103 , an optical projection system in the form of an objective  104 , and a substrate device in the form of a wafer stage  105 . The illumination system  102  illuminates a mask  103 . 1  which is arranged on the mask stage  103  with a projection light bundle (not shown in the drawing) with a wavelength of 193 nm. The mask  103 . 1  carries a design pattern that is to be projected by the projection light bundle through the optical elements arranged in the objective  104  onto a substrate in the form of a wafer  105 . 1  which is arranged on the wafer stage  105 . 
     The illumination system  102  and the objective  104  each contain an optical element group  106 ,  107 , respectively, wherein each group is formed by a series of optical modules  106 . 1  and  107 . 1 , whose optical elements are arranged along an optical axis  101 . 1  (which may be folded) of the microlithography apparatus  101 . The optical modules  107 . 1  are secured in the housing  104 . 1  of the objective  104 . To work at an operating wavelength of 193 nm, the optical elements selected for the optical modules  106 . 1  and  107 . 1  are refractive optical elements, i.e. lenses or the like. However, it should be understood that in other embodiments of the invention, it is also possible to use any other desired optical elements. One could in particular use refractive, reflective or diffractive optical elements by themselves or in any desired combination. 
       FIG. 2  illustrates a preferred embodiment of the optical arrangement according to the invention in the form of an optical module  107 . 1 . As can be seen in  FIG. 2 , the optical module  107 . 1  includes a first optical element in the form of a lens  108  which is held by a supporting structure  109 . The supporting structure  109  includes a ring-shaped lens holder  109 . 1  which is in contact with the lens  108 . The lens holder  109 . 1 , in turn, is supported by a ring-shaped support device  109 . 2  which is connected, in turn, to the housing  104 . 1  of the objective  104 . 
     The lens holder  109  is connected by way of four holder elements  109 . 3  to an upper ring-shaped support element  109 . 4 . The holder elements  109 . 3  in the neutral state shown in  FIG. 2  take up the weight force G of the subassembly consisting of the lens holder  109 . 1  and the lens  108 . 
     The holder elements  109 . 3  are evenly distributed over the circumference of the lens holder  109 . 1 . They define the position (location and/or orientation) of the subassembly consisting of the lens holder  109 . 1  and the lens  108 . To perform this function, the holder elements  109 . 3  can be configured as simple passive elements. However, it is also possible that the holder elements  109 . 3  are configured as active elements which allow the position of the subassembly consisting of the lens holder  109 . 1  and the lens  108  to be actively adjusted under the control of a controller device connected to the holder elements. 
     The supporting structure  109  further includes four actuator arrangements of identical design conforming to the invention, in the form of fluidic force actuators  110 ,  111 ,  112  and  113  which are arranged at uniform intervals over the circumference of the lens holder  109 . 1 . However, it should be understood that different embodiments of the invention could also be equipped with any other desired number of force actuators, wherein the number of force actuators, as will be explained in detail hereinafter, depends on a desired mode of deformation of the optical element  108 . The holder elements  109 . 3  and the force actuators  110  are distributed in alternating sequence and at essentially equal intervals over the circumference of the lens holder  109 . 1 , so that each holder element  109 . 3  is rotated (relative to the optical axis  101 . 1 ) by an angle of about 45° relative to a neighboring force actuator  110 . 
     As can be seen in particular in  FIG. 3 , the force actuator  110  is connected at a first end to a lower ring-shaped support element  109 . 5  of the support device  109 . 2 . The force actuator  110  is further connected at its second end to the lower surface of the lens holder  109 . 1  in order to exert along a thrust axis  110 . 1  a resultant actuator force F res  on the lens holder  109 . 1 . 
     The force actuator  110  includes among other things a first fluidic actuator device  110 . 3  and a second fluidic actuator device  110 . 4 . These devices are implemented in the force actuator  110  through a generally cylindrical, thin-walled first wall element  110 . 5  and a likewise generally cylindrical, thin-walled second wall element  110 . 6 , an upper actuator element  110 . 7 , and a bottom element  110 . 8 . The upper actuator element  110 . 7  is solidly connected in a suitable way to the lens holder  109 . 1 , while the bottom element  110 . 8  is solidly connected in a suitable way to the lower support element  109 . 5 , so that the force actuator  110  can transmit along its thrust axis  110 . 1  the tensile forces as well as compressive forces between the lens holder  109 . 1  and the lower support element  109 . 5 . 
     It should be understood that the first and/or the second wall element need not necessarily have a cylindrical geometry. In other embodiments of the invention, one may also select any other desired geometry, for example a prismatic geometry with a polygonal cross-section perpendicular to the thrust axis. 
     The cylinder axis of the first wall element  110 . 3  defines a first thrust axis  110 . 9 , while the cylinder axis of the second first wall element  110 . 4  defines a second thrust axis  110 . 10 . The first wall element  110 . 5  and the second wall element  110 . 6  are concentric relative to each other. Accordingly, the first thrust axis  110 . 9  and the second thrust axis  110 . 10  coincide with the thrust axis  110 . 1  of the force actuator  110 . However, it should be understood that in other embodiments of the invention the respective thrust axes of the two wall elements could also be spaced apart from each other. 
     The first wall element  110 . 5  is connected gas-tight to the actuator element  110 . 7  and the bottom element  110 . 8  and thus defines a ring-shaped first actuator chamber  110 . 11  of the first actuator device  110 . 3 . The second wall element is likewise connected gas-tight to the actuator element  110 . 7  and the bottom element  110 . 8  and thus defines a second actuator chamber  110 . 12  of the second actuator device  110 . 4 , which is surrounded by the first actuator chamber  110 . 9 . 
     Accordingly, the first actuator chamber  110 . 11  and the second actuator chamber  110 . 12 , and thus the first actuator device  110 . 3  and the second actuator device  110 . 4  are arranged kinematically parallel and nested inside each other, whereby a particularly compact arrangement is achieved. 
     However, it should be understood that such a nested arrangement of the kinematically parallel actuator devices is not a necessary requirement in other embodiments of the invention. For example, with a suitable design of the actuator element a configuration can be achieved where the actuator chambers are not nested inside each other even with a kinematically parallel arrangement and collinear thrust axes of the two actuator chambers. This is possible for example with an arrangement where the outer, ring-shaped actuator chamber only encloses a bottom element, which extends completely through the space enclosed by the ring-shaped actuator chamber and on which the second actuator chamber is supported only outside of said space. 
     The first actuator device  110 . 3  includes a pressure regulation device  110 . 13  which supplies the first actuator chamber  110 . 11  with a first actuator fluid at a first pressure p 1 , so that in the first actuator chamber  110 . 11  a first relative pressure Δp 1  establishes itself relative to the pressure p a  of the atmosphere surrounding the force actuator  112 , which may be expressed as
 
Δ p   1   =p   1   −p   a .  (1)
 
     The second actuator device  110 . 4  includes a pressure regulation device  110 . 14  which supplies the second actuator chamber  110 . 12  with a second actuator fluid at a second pressure p 2 , so that in the second actuator chamber  110 . 12  a second relative pressure Δp 2  establishes itself relative to the pressure p a  of the atmosphere surrounding the force actuator  112 , which may be expressed as
 
 Δp   2   =p   2   −p   a .  (2)
 
     The first pressure-regulating device  110 . 13  and the second pressure-regulating device  110 . 14  belong to a pressure-regulating unit  110 . 15 . The first pressure-regulating device  110 . 13  is designed so that it regulates the first pressure in the first actuator chamber  110 . 11  up to a first maximum pressure p max1 . The second pressure-regulating device  110 . 14  is of analogous configuration, so that it regulates the second pressure in the second actuator chamber  110 . 12  up to a second maximum pressure p max2 . 
     Each of the first actuator fluid and the second actuator fluid in the present example is a gaseous medium, for example air. However, it is considered self-evident that in different versions of the invention one could also use a liquid medium. It is also possible to use different media for the first actuator fluid and the second actuator fluid. 
     The first wall element  110 . 3  and the second wall element  110 . 4  are both configured (at least in sections) in the form of a bellows, so that the force actuator  110  can achieve a relatively large displacement stroke along its thrust axis  110 . 1  without being opposed to any significant extent by elastic counter forces within the wall elements. The elastic restoring forces are normally of the order of 1% to 5% of the actuator force, i.e. of a magnitude that needs to be taken into account in practice, but can still be controlled. 
     Depending on the first pressure p 1  in the first actuator chamber  110 . 11 , the first actuator device  110 . 3  by way of the actuator element  110 . 7  exerts a first actuator force F 1  on the lens holder  108 . With the effective first thrust surface area A 1  of the first actuator chamber  110 . 11 , the first actuator force F 1  can be calculated as
 
 F   1   =Δp   1   ·A   1 ,  (3)
 
wherein the line of action of the first actuator force F 1  lies on the first thrust axis  110 . 9  of the first actuator device  110 . 3 .
 
     Analogously, depending on the second pressure p 1  in the second actuator chamber  110 . 12 , the second actuator device  110 . 4  by way of the actuator element  110 . 7  exerts a second actuator force F 2  on the lens holder  108 . With the effective second thrust surface area A 2  of the second actuator chamber  110 . 12 , the second actuator force F 2  can be calculated as
 
 F   2   =Δp   2   ·A   2 ,  (4)
 
wherein the line of action of the second actuator force F 2  lies on the second thrust axis  110 . 10  of the second actuator device  110 . 4 .
 
     In the neutral state illustrated in  FIGS. 2 and 3 , the first pressure p 1  and the second pressure p 2  are both equal to the pressure p a , so that the first actuator device  110 . 3  and the second actuator device  110 . 4  exert no actuator force on the lens holder  109 . 1 . 
     The effective second thrust surface area A 2  of the second actuator chamber  110 . 12  can be calculated for the illustrated example with the second effective radius R 2  of the second actuator chamber  110 . 12  (wherein R 2  can be calculated for the specific actuator device for example through sufficiently well known approximation formulas) as
 
 A   2   =R   2   2 ·π,  (5)
 
while the effective first thrust surface area A 1  of the first actuator chamber  110 . 11  can be calculated with good approximation for the illustrated example with the first effective radius R 1  of the first actuator chamber  110 . 11  (wherein R 1  can be calculated for the specific actuator device for example through sufficiently well known simplified formulas) as
 
 A   1 =( R   1   2   −R   2   2 )·π.  (6)
 
     In the foregoing example, the ratio between the second effective thrust surface area and the first effective thrust surface area is accordingly 
     
       
         
           
             
               
                 
                   
                     
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     In terms of the ratio of the effective radii 
                   x   =       R   1       R   2               (   8   )               
equation (7) can be rewritten as:
 
     
       
         
           
             
               
                 
                   
                     
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     Thus, one obtains for the ratio between the second actuator force F 2  and the first actuator force F 1 : 
     
       
         
           
             
               
                 
                   
                     
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     In the example shown, the first effective radius R 1  is three times as large as the second effective radius R 2 , so that x=3. Thus, the second effective thrust surface area A 2  is 12.5% of the first effective thrust surface area A 1 . Consequently, assuming an equal pressure (p 1 =p 2 ) in the two actuator chambers  110 . 11  and  110 . 12 , the second actuator force F 2  is likewise only 12.5% of the first actuator force F 1 . 
     This leads to the conclusion that with identical amounts of pressure in the two actuator chambers  110 . 11  and  110 . 12 , almost any desired ratio between the two actuator forces F 1  and F 2  can be selected by way of the ratio x between the effective radii. 
     In particular, this shows clearly that with a ratio of x&lt;√{square root over (2)} the first effective thrust surface area A 1  is smaller than the second effective thrust surface area A 2 , so that with identical pressure levels in the two actuator chambers the actuator force in the outer, ring-shaped chamber is smaller than the actuator force in the inner, cylindrical chamber. Accordingly, it is also possible to switch the spatial arrangement of the actuator devices, so that the actuator device that is to produce a higher-level actuator force is arranged on the inside and the actuator device that is to produce a lower-level actuator force is arranged on the outside. 
     Due to the concentric arrangement of the two actuator devices  110 . 3  and  110 . 4 , the distance is zero between the respective lines of action of the first and second actuator forces F 1  and F 2  in the area of their points of application on the lens holder  108 , and the lines of action are in parallel alignment. Consequently, the two actuator forces F 1  and F 2  simply superimpose themselves on each other, adding up to a resultant actuator force F res , or expressed as an equation
 
 F   res   =F   1   +F   2 ,  (11)
 
wherein this arrangement has the added advantage that no torque is introduced into the lens holder  109 . 1 .
 
     As a means to largely prevent bending moments even if the lens holder  109 . 1  has been deformed by the resultant actuator force F res  (whereby the point of application of the actuator force F res  has been shifted), the actuator element  110 . 7  has in the area of contact with the lens holder  109 . 1  a protrusion  110 . 16  with a circular (ring-shaped) constriction  110 . 17 . As a result, the protrusion  110 . 16  allows the force actuator  110  and the lens holder  109 . 1  to assume a tilted position relative to each other and thus prevents the transfer of a torque between them. 
     In this context, it should be understood that in other embodiments of the invention one could also envision a design concept where the thrust axes of the two actuator devices and thus the lines of action of the first and the second actuator force have a certain distance from each other at their respective points of application on the lens holder. This can be of advantage if a desired deformation of the lens holder is to be achieved or assisted by way of a torque which occurs as a result of the distance between the thrust axes and which is then introduced into the lens holder. However, the distance of the lines of action of the first and the second actuator force at their respective points of application on the lens holder is smaller than 50% (and with higher preference smaller than 10%) of the sum of the two effective radii R 1  and R 2  (more generally: of the sum of the maximum transverse dimensions of the actuator chamber at a right angle to its thrust axis), in order to keep the moment associated with this distance within a reasonable range. 
     As shown in  FIG. 4  (which illustrates the force actuators  110  to  113 , the holder elements  109 . 3  and the lens holder  109 . 1  in a strongly simplified perspective view from above) each of the force actuators  110  to  113  allows a first actuator force F 1  and second actuator force F 2  which are directed parallel to the optical axis  101 . 1  to be applied to the lens holder  109 . 1 . In this arrangement, all first actuator forces F 1  of all force actuators  110  to  113  can have the same direction, as shown in  FIG. 4 , so that the actuator forces in cooperation with the reactive forces of the holder elements  109 . 3  will cause a so-called 4-wave deformation of the lens holder  109 . 1  and thus of the lens  108 . 
     In contrast, the second actuator forces F 2  of the force actuators  110  and  112  can have the opposite direction of the second actuator forces F 2  of the force actuators  111  and  113  (by setting a corresponding sub-ambient pressure in the second actuator chamber  110 . 12  relative to the surrounding atmosphere), so that the actuator forces in cooperation with the reactive forces of the holder elements  109 . 3  will cause a so-called 2-wave deformation of the lens holder  109 . 1  and thus of the lens  108 . 
     The setting of the actuator forces is controlled by way of the first and second pressure-regulating devices  110 . 13 ,  110 . 14 , wherein the first pressure-regulating device  110 . 13  includes a pressure regulation loop which sets the same first pressure p 1  in all first actuator chambers  110 . 11  of the force actuators  110  to  113 . The second pressure-regulating device  110 . 13  has two pressure regulation loops, wherein the first pressure regulation loop serves to set an above-ambient pressure in the second actuator chambers of the force-actuators  110  and  112 , and the second pressure regulation loop serves to set a sub-ambient pressure in the second actuator chambers of the force-actuators  111  and  113 . 
     The 2-wave deformation of the lens  108  requires markedly smaller actuator forces than the 4-wave deformation, so that the second actuator forces F 2  are of significantly smaller absolute magnitude than the first actuator forces F 1 . In the present example, the force required for a 4-wave deformation of the lens  108  is about eight times as large as the force required for a 2-wave deformation with the same maximum displacement amplitude. 
     As the different effective thrust surface areas A 1  and A 2  already by themselves ensure a corresponding force ratio between the respective first actuator force F 1  and the second actuator force F 2  and thus a commensurate difference in the force levels for the 2-wave deformation and the 4-wave deformation, the embodiment according to this example offers the advantageous possibility to use components of identical design for the two pressure-regulating devices  110 . 13  and  110 . 14 . 
     Accordingly, the first maximum pressure p max1  for which the first pressure-regulating device  110 . 13  is designed is equal to the second maximum pressure p max2  for which the second pressure-regulating device  110 . 14  is designed. With an appropriate choice of the effective thrust surface areas A 1  and A 2 , this therefore opens an advantageous possibility to operate each of the pressure-regulating devices in an optimum range where its setting accuracy has its maximum, so that errors in setting the pressure in the respective actuator chambers  110 . 11 ,  110 . 12  and thus controlling the deformation of the lens  108  are minimized. 
     By arranging the actuator devices  110 . 3  and  110 . 4  so that their respective kinematic actions are parallel and as a result the separately generated first actuator force F 1  and second actuator force F 2  are superimposed on each other, it is possible (unlike in the prior-art concept of superimposing the pressures on each other within a single actuator chamber) to achieve for both actuator forces F 1  and F 2 , in spite of the different respective force levels, an optimum in the absolute accuracy of setting the respective pressure in each of the actuator chambers  110 . 11  and  110 . 12  and thus setting the respective actuator forces F 1  and F 2 . 
     However, it should be understood that in other versions of the invention, actuator forces of different levels of magnitude could also be generated —in addition or as an alternative to setting the levels through the effective thrust surfaces A 1  and A 2 —through a suitable choice of the pressure level of the respective pressure-regulating device (i.e. of the maximum pressure p max  for which the respective pressure-regulating device is designed). Finally, in addition or as an alternative to these two concepts, the force level could also be set by way of a suitable force-reduction device that is interposed between each actuator chamber and the lens. 
     During the projection of the design pattern of the mask  103 . 1  onto the substrate  105 . 1 , the geometry or, more specifically, the deformation of the lens  108  is actively adjusted through the force actuators  110  to  113  under feedback control (or only open-loop control) by a controller in the form of a regulating device  114 . The active adjustment of the deformation by way of the force actuators  110  to  113  is made in response to at least one imaging error of the imaging apparatus  101  and/or in response to at least one other operating quantity of the imaging apparatus  101  which is capable of being influenced by a deformation of the lens  108 . 
     Of course, there is also the additional possibility of an active feedback regulation (or only an open-loop control) of the position (i.e. location and orientation) of the lens  108  by way of the holder elements  109 . 3 . To perform this function, the holder elements  109 . 3  are connected likewise to the regulating device  114 . The active adjustment of the position can again occur in response to at least one imaging error of the imaging apparatus  101  and/or in response to at least one other operating quantity of the imaging apparatus  101  which is capable of being influenced by a position change of the lens  108 . 
     The current value of this imaging error and/or the at least one other operating quantity of the imaging apparatus  101  is captured by means of a transducer device  115  and transmitted to the regulating device  114 . From this signal, the regulating device  114  generates corresponding control signals for the first and second pressure-regulating devices  110 . 13  and  110 . 14  which, in turn, set the corresponding pressure in the actuator chambers of the force actuators  110  to  113 . 
     However, it should be understood that in other embodiments of the invention there does not have to be a direct detection of the imaging error and/or of the at least one other operating quantity of the imaging apparatus. Instead, the regulating device can operate with suitable models (established beforehand) of the imaging apparatus, which allow the control signals for the pressure-regulating devices to be determined on the basis of current values of variables and/or parameters of the imaging apparatus. 
     With the imaging apparatus  101  of  FIG. 1  a preferred embodiment of the optical imaging method according to the invention can be performed, wherein a preferred embodiment of the method of generating and applying forces according to the invention is implemented, as will be explained in more detail in the following, making reference to  FIG. 5  as well as  FIGS. 1 to 4 . 
     First, in a step  116 . 1 , the components of the imaging apparatus  101 , in particular the lens  108  and the supporting structure  109 , are made available and are brought into their spatial arrangement with a resultant configuration as described above in  FIGS. 1 to 4 . 
     Next, in a step  116 . 2 , the design pattern of the mask  103 . 1  is projected onto the substrate  105 . 1  (this operation may be divided into several steps and/or cycles). In a step  116 . 3 , simultaneously with this exposure process of the substrate  105 . 1 , the current value of an imaging error or of another operating quantity of the imaging apparatus  101  is registered by way of the transducer device  115 , as has been described above. 
     In a step  116 . 4 , the lens  108  is being actively deformed by the force actuators  110  to  113  (in response to control signals of the regulating device  114 ), meaning that the geometry of the lens  108  is actively regulated, as has also been described above. Furthermore, the position of the lens  108  can likewise be actively regulated, as has also been described above. 
     In step  116 . 5 , a test is made as to whether or not the process is to be terminated. In the negative case, (for example if a further substrate  105 . 1  is to be exposed), the process loops back to step  116 . 2 . In the affirmative case, the process ends in a step  116 . 6 . 
     In the foregoing description, the invention has been presented through an example in which two actuator chambers are nested inside each other. However, it should be understood that in other versions of the invention, there could also be more than two actuator chambers for (possibly more than two) different levels of force, which could again be nested inside each other. 
     Furthermore, the invention has been described above through an example where the second wall element  110 . 6  delimits the first actuator chamber  110 . 11  as well as the second actuator chamber  110 . 12 . It should however be understood that other versions of the invention are also possible, where there is no such coupling link between the chambers. For example, there could be a separate wall element set up which forms the inner wall of the ring-shaped first actuator chamber. 
     Second Example 
     In the following a further preferred embodiment in the form of a fluidic force actuator  210  within the actuator arrangement according to the invention is described with references to  FIGS. 1 and 6 . The view presented in  FIG. 6  is analogous to  FIG. 3 . 
     In its principal design and function, the force actuator  210  is analogous to the force actuator  110  of  FIGS. 1 to 4 . In particular, the force actuator  210  can be used in place of the force actuator  110  in the imaging apparatus  101 . Consequently, the following description will only cover the features in which the force actuator  210  differs from the force actuator  110 . Components that are identical are identified by the same reference symbols raised by 100 and (unless there are expressly different explanations given in the following), the reader is referred to the previous description of those components. 
     The force actuator  210  differs from the force actuator  110  only in the sense that the first pressure-regulating device  210 . 13  and the second pressure-regulating device  210 . 14  are both designed for the function of generating in the respective actuator chambers only an above-ambient pressure relative to the surrounding atmosphere. Starting from the neutral state represented in  FIG. 6  (where there is no pressure differential between any of the actuator chambers and the surrounding atmosphere and thus no force is applied by the force actuator  210 ), in order to be able to deform the lens  108  in both directions along the optical axis  101 . 1 , i.e. along the thrust axis  210 . 1  of the force actuator  210 , the first actuator device  210 . 3  of the force actuator  210 , besides including a first actuator subassembly  210 . 19  with the first actuator chamber  210 . 11  and the second actuator chamber  210 . 12 , also comprises an identically configured second actuator subassembly  210 . 20  with a third actuator chamber  210 . 21  and a fourth actuator chamber  210 . 22 . 
     The respective thrust axes of the actuator chambers  210 . 11 ,  210 . 12 ,  210 . 21  and  210 . 22  are collinear with the thrust axis  210 . 1  of the force actuator  210 . While the first actuator subassembly  210 . 19  is arranged between the lower supporting element  109 . 5  and the lens holder  109 . 1 , the second actuator subassembly  210 . 20  is arranged between the upper supporting element  210 . 4  and the lens holder  109 . 1 , so that in the presence of an above-ambient pressure in all actuator chambers  210 . 11 ,  210 . 12 ,  210 . 21  and  210 . 22 , the first actuator subassembly  210 . 19  and the second actuator subassembly  210 . 20  produce actuator forces that oppose each other. 
     The first actuator chamber  210 . 11  is connected to a first pressure-regulating loop  210 . 23  of the first pressure-regulating device  210 . 13 , while the second actuator chamber  210 . 12  is connected to a second pressure-regulating loop of the second pressure-regulating device  210 . 14 . The third actuator chamber  210 . 21 , in turn, is connected to a third pressure-regulating loop  210 . 25  of the first pressure-regulating device  210 . 13 , while the fourth actuator chamber  210 . 22  is connected to a fourth pressure-regulating loop of the second pressure-regulating device  210 . 14 . The pressure-regulating loops  210 . 23  to  210 . 26  regulate the pressure again in response to control signals of the regulating device  114 . The latter again generates the control signals in response to signals of the transducer device  115 , as has been explained above in the context of the first example. 
     Under an above-ambient pressure relative to the surrounding atmosphere, the third actuator chamber  210 . 21  generates a third actuator force F 3  that is opposed to the first actuator force F 1 , while the fourth actuator chamber  210 . 22  generates a fourth actuator force F 4  that is opposed to the second actuator force F 2 . The actuator forces F 1  to F 4 , superimposed on each other, produce the resultant actuator force F res  which causes the deformation of the lens holder  109 . 1  and thus of the lens  108 . Depending on the pressure setting in the actuator chambers  210 . 11 ,  210 . 12 ,  210 . 21  and  210 . 22 , the resultant actuator force F res  can take either direction along the thrust axis  210 . 1  of the force actuator  210 , so that a deformation of the lens holder  109 . 1 , and thus of the lens  108 , can be achieved in both directions along the optical axis  101 . 1 . 
     It is evident that with this force actuator  210 , too, the imaging method according to the invention, as described above in the context of  FIG. 5 , can be carried out, wherein the afore-described method of generating and applying a force according to the invention is used. 
     Third Example 
     In the following, a further preferred embodiment in the form of a fluidic force actuator  310  within the actuator arrangement according to the invention is described with references to  FIGS. 1 and 7 . The view presented in  FIG. 7  is analogous to  FIG. 3 . However, the drawing plane in  FIG. 7  is oriented in the tangential direction of the circumference of the lens  108 . Of course, in other embodiments of the invention the arrangement illustrated in  FIG. 7  could also lie in a drawing plane with any other desired orientation (particularly in a plane oriented in a radial direction of the lens  108 ). 
     In the principal design of its components and in its function, the force actuator  310  is analogous to the force actuator  110  of  FIGS. 1 to 4 . In particular, the force actuator  310  can be used in place of the force actuator  110  in the imaging apparatus  101 . Consequently, the following description will only cover the features in which the force actuator  310  differs from the force actuator  110 . Components that are identical are identified by the same reference symbols raised by  200  and (unless there are expressly different explanations given in the following), the reader is referred to the previous description of those components. 
     The force actuator  310  differs from the force actuator  110  only in the sense that instead of the actuator devices nested inside each other, the force actuator  310  has two actuator devices  310 . 3  and  310 . 4  arranged kinematically parallel to each other, with actuator chambers  310 . 11  and  310 . 12  arranged side by side. The first actuator chamber  310 . 11  and the second actuator chamber  310 . 12  are coupled by way of a coupling device  310 . 27  with parallel-guiding linkages  310 . 28  and  310 . 29  (which are sufficiently well known and therefore not further explained here) to the actuator element  310 . 7  which, in turn, is connected directly to the lens  108 . In this arrangement, the coupling device  310 . 27  is, in turn, movably constrained through parallel-guiding linkages (which are sufficiently well known and therefore not further explained here) to the supporting element  109 . 5 . 
     The parallel-guiding linkages  310 . 28 ,  310 . 29  in the illustrated example are tied to the actuator element  310 . 7  in such a way that the actuator element  310 . 7  has to sustain no bending moment. It should be understood, however, that the parallel-guiding linkages  310 . 28 ,  310 . 29  in other embodiments of the invention could also be tied to the actuator element  310 . 7  in a way that causes a bending moment. For example, the respective left arms of the two parallel-guiding linkages  310 . 28 ,  310 . 29  could be tied to the same point on the actuator element  310 . 7 , while the respective right arms of the two parallel-guiding linkages  310 . 28 ,  310 . 29  could also be tied to the same point on the actuator element  310 . 7 . 
     The first actuator chamber  310 . 11  is connected to a first pressure-regulating device  310 . 13 , while the second actuator chamber  310 . 12  is connected to a second pressure-regulating device  310 . 14 . The pressure-regulating devices  310 . 13  and  310 . 14  regulate the pressure in the respective actuator chambers  310 . 11  and  310 . 12  again in response to control signals of the regulating device  114  which, in turn, generates the control signals in response to signals of the transducer device  115 , as has been explained above in the context of the first example. 
     When they are subjected to a certain pressure differential relative to the surrounding atmosphere, the first actuator chamber  310 . 11  and the second actuator chamber  310 . 12 , along their respective thrust axes  310 . 9  and  310 . 10 , generate pressure-dependent forces which are converted, respectively, into a first actuator force F 1  and a second actuator force F 2  which are transferred to the lens  108  in the area where the actuator element  310 . 7  makes contact with the lens  108 . 
     The actuator forces F 1  and F 2 , superimposed on each other, produce the resultant actuator force F res  which causes the deformation of the lens  108 . In this case, too, the resultant actuator force F res  can take either direction along the thrust axis  310 . 1  of the force actuator  310 , depending on the pressure that was set in the actuator chambers  310 . 11  and  310 . 12 , so that a deformation of the lens  108  can be achieved in both directions along the optical axis  101 . 1 . 
     It is evident that with this force actuator  310 , too, the imaging method according to the invention, as described above in the context of  FIG. 5 , can be carried out, wherein the afore-described method of generating and applying a force according to the invention is used. 
     As can be seen in  FIG. 7 , the first actuator chamber  310 . 11  and the second actuator chamber  310 . 12  are configured identically so that, among other shared traits, they have identical effective thrust surface areas. The different force levers of the first and the second actuator force F 1 , F 2  in this embodiment can also be achieved through different pressure levels of the pressure-regulating devices  310 . 13  and  310 . 14  (i.e. by designing the pressure-regulating devices  310 . 13  and  310 . 14  for different respective maximum pressures p max ). 
     It should again be understood that in other embodiments of the invention an adaptation to different force levels of the actuator forces F 1  and F 2  could be achieved through the effective thrust surface areas of the actuator chambers, as has been described above in the context of the first example. 
     The present example also offers the possibility to achieve an adaptation to different force levels of the actuator forces F 1  and F 2  through a specific design of the coupling device  310 . 27  or by shifting the location of the thrust axes  310 . 9  and  310 . 10  of the actuator chambers relative to the thrust axis  310 . 1  of the force actuator  310 . For example, the distance between the thrust axis  310 . 1  of the force actuator  310  and the thrust axis  310 . 10  of the second actuator chamber  310 . 12  can be increased further in order to commensurately lower the force level of the second actuator force F 2 . 
     Fourth Example 
     In the following a further preferred embodiment in the form of an optical module  407 . 1  within the actuator arrangement according to the invention is described with references to  FIGS. 1 and 6 . The view presented in  FIG. 8  is analogous to  FIG. 4 . 
     In its principal design and function, the optical module  407 . 1  is analogous to the optical module  107 . 1  of  FIGS. 1 to 4 . In particular, the optical module  407 . 1  can be used in place of the optical module  107 . 1  in the imaging apparatus  101 . Consequently, the following description will only cover the features in which the optical module  407 . 1  differs from the optical module  107 . 1 . In particular, components that are identical are identified by the same reference symbols raised by 300 and (unless there are expressly different explanations given in the following), the reader is referred to the previous description of those components. 
     The optical module  407 . 1  differs from the optical module  107 . 1  only in the sense that the supporting structure  109  has only two, rather than four, identically configured actuator arrangements in the form of fluidic force actuators  410  and  411 , which are offset by 90° relative to each other on the circumference of the lens holder  109 . 1 . However, it should be understood that other embodiments of the invention can also have any other desired number of force actuators, wherein the number of force actuators depends on a desired mode of deformation of the optical element  108 , as will be explained in detail at a later point. 
     The force actuators  410  and  411  are of identical configuration as the force actuators  110  and  111 . In contrast to the first example, the force actuators  410  and  411  are not acting directly on the supporting structure  109  (shown for the lens  108  in  FIG. 2 ) but through respective transmitting mechanisms  417  and  418 , which will be described subsequently in more detail. The first transmitting mechanism  417  acts on the optical element  108  through the points of application  417 . 1  and  417 . 2 , while the second transmitting mechanism  418  acts on the optical element  108  through the points of application  418 . 1  and  418 . 2 . The points of application  417 . 1  and  417 . 2  are arranged (relative to the optical axis  101 . 1 ) with an angular offset of about 180°, meaning that they lie diametrically opposite each other across the center point of the lens  108 . 
     The holder elements  109 . 3  and the points of application of the transmitting mechanisms  417  and  418  are arranged on the circumference of the lens holder  109 . 1  in alternating order and with essentially uniform spacing, so that each holder element  109 . 3  is offset or rotated against a neighboring point of application of one of the transmitting mechanisms  417  and  418  by an angle of about 45° about the optical axis  101 . 1 . 
     Each of the transmitting mechanisms  417  and  418  in the illustrated example is configured as a fork-shaped lever arm which is rotatably constrained in bearing elements  417 . 3  and  418 . 3 , respectively, on the lower supporting ring  109 . 5 . The swiveling axis which is thereby defined for each of the lever arms  417  and  418  runs parallel to the main plane in which the optical element  108  principally extends (i.e. perpendicular to the optical axis  101 . 1 ). Furthermore, the swiveling axis of each lever arm  417 ,  418  and the respectively associated points of application  417 . 1 ,  417 . 2  and  418 . 1 ,  418 . 2  are each arranged at least approximately in a common plane that extends parallel to the principal plane of the optical element, so that the forces F 1 , F 2  exerted, respectively, on the points of application  417 . 1 ,  417 . 2  and  418 . 1 ,  418 . 2 , are directed essentially parallel to the optical axis. 
     Depending on the amount of pressure p 1 , p 2  in the respective actuator chambers of the force actuators  410  and  411 , the force actuators  410  and  411  exert on the respectively associated lever arm  417  and  418  a first actuator force F A1  and a second actuator force F A2 . With the respective transmission ratios g of the lever arms  417  and  418 , effective forces F 1  and F 2  are therefore exerted at the points of application  417 . 1 ,  417 . 2  and  418 . 1 ,  418 . 2  on the lens holder  108 , wherein because of the symmetrical configuration (relative to the thrust plane of the actuator forces F A1  and F A2 ) of the lever arms  417  and  418 , the forces F 1  and F 2  conform to the relationships: 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       1 
                     
                     = 
                     
                       
                         g 
                         · 
                         
                           F 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     F 
                     2 
                   
                   = 
                   
                     
                       
                         g 
                         · 
                         
                           F 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       2 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     As can be seen in  FIG. 8 , first and second effective forces F 1  and F 2  directed parallel to the optical axis  101 . 1  can be applied to the lens holder  109 . 1  by way of the force actuators  410  and  411  and the lever arms  417  and  418 , respectively. In this arrangement, the first effective forces F 1  can have the same direction, so that in cooperation with the reactive forces of the holder elements  109 . 3 , the first effective forces F 1  produce a so-called 4-wave deformation of the lens holder  109 . 1 , and accordingly of the lens  108 . 
     In contrast, the second effective forces F 2  of the one force actuator  410  (with an appropriate sub-ambient pressure setting relative to the surrounding atmosphere) can have the opposite direction of the second effective forces F 2  of the other force actuator  411 , so that they generate in cooperation with the reactive forces of the holder elements  109 . 3  a so-called 2-wave deformation of the lens holder  109 . 1  and, consequently, of the lens  108 . 
     The setting of the actuator forces and thus of the effective forces on the lens holder  109 . 1  is performed again by way of the pressure-regulating unit  110 . 15 , as described in detail in the context of the first embodiment. 
     The present configuration with only one force actuator  410  and  411 , respectively, for generating effective forces at diametrically opposite points of application  417 . 1 ,  417 . 2  and  418 . 1 ,  418 . 2  has the advantage over the embodiment of  FIG. 4  that due to the achievable manufacturing accuracy of the respective transmitting mechanisms  417  and  418 , it is easy to ensure that the effective forces at the diametrially opposite points of application  417 . 1 ,  417 . 2  and  418 . 1 ,  418 . 2  have the same absolute magnitude. With the embodiment of  FIG. 4 , this is more difficult to achieve, as the two diametrically opposed force actuators  110  and  112  as well as  111  and  113  have to be either precisely matched or have to be equipped with separate pressure-regulating loops. 
     In other words, by generating with a single actuator multiple effective forces that are in a precisely defined ratio to each other (which can be easily realized through the transmitting mechanism), it is possible to significantly reduce the manufacturing cost of the optical module. In this context, it should be understood that in other embodiments of the invention (dependent in particular on the deformation mode that is to be produced) it is also possible with a single actuator to generate more than two effective forces (by way of a suitably configured transmitting mechanism) with a precisely defined ratio. 
     It should be expressly noted here that the foregoing concept of producing a plurality of effective forces of a precisely defined ratio by means of a single actuator represents an inventive concept capable of being protected by itself, independent of the design of the force actuator. 
     While the design pattern of the mask  103 . 1  is being projected onto the substrate  105 . 1 , the geometry or, more specifically, the deformation of the lens  108  is actively set by way of the force actuators  410  and  411  under feedback regulation (or also merely with open-loop control) by a controller device in the form of a regulating device  114 . The active setting of the deformation by way of the force actuators  410  and  411  occurs in a way that is dependent on at least one imaging error of the imaging device  101  and/or at least one other operating quantity of the imaging device  101  that is capable of being influenced by a deformation of the lens  108 . 
     Of course, there is also the additional possibility of an active feedback regulation (or only an open-loop control) of the position (i.e. location and orientation) of the lens  108  by way of the holder elements  109 . 3 . To perform this function, the holder elements  109 . 3  are connected likewise to the regulating device  114 . The active adjustment of the position can again occur in response to at least one imaging error of the imaging apparatus  101  and/or in response to at least one other operating quantity of the imaging apparatus  101  which is capable of being influenced by a position change of the lens  108 . 
     The current value of this imaging error and/or the at least one other operating quantity of the imaging apparatus  101  is captured by means of a transducer device  115  and transmitted to the regulating device  114 . From this signal, the regulating device  114  generates corresponding control signals for the pressure-regulating device  110 . 15  which, in turn, set the corresponding pressure in the actuator chambers of the force actuators  410  and  411 . 
     However, it should be understood that in other embodiments of the invention there does not have to be a direct detection of the imaging error and/or of the at least one other operating quantity of the imaging apparatus. Instead, the regulating device can operate with suitable models (established beforehand) of the imaging apparatus, which allow the control signals for the pressure-regulating devices to be determined on the basis of current values of variables and/or parameters of the imaging apparatus. 
     It is evident that in this example, too, the imaging method according to the invention, as described above in the context of  FIG. 5 , can be carried out, wherein the afore-described method of generating and applying a force according to the invention is used. 
     The foregoing description of the present invention is based primarily on examples (first and second example) where the optical element (lens  108 ) is held by a holder device (lens holder  109 . 1 ) which is firmly connected to the optical element and which is being deformed by force actuators, whereby due to the connection between the holder device and the optical element, a corresponding deformation is also imparted to the optical element. However, it should be understood that one could also envision an arrangement in other embodiments of the invention where the force actuators are connected directly to the optical element, as in the third example, so that the force actuators deform the optical element itself. 
     Furthermore, the foregoing description of the present invention involves only examples in which the resultant actuator force F res  of the force actuators produces a deformation of an optical element. However, it should be understood that one could also envision arrangements in other embodiments of the invention where the resultant actuator force F res  is used for purposes other than causing a deformation of a body. In particular, the possibility exists to use the resultant actuator force F res  for effecting a change in position (i.e. location and/or orientation) of the body. It should further be understood that the resultant actuator force F res  can be applied to bodies other than optical elements and/or their mounting elements. 
     Furthermore, the foregoing description of the present invention involves only examples in which a 2-wave deformation and a 4-wave deformation are produced through a plurality of force actuators. It should be understood, however, that other embodiments of the invention could be envisioned with only a single force actuator exerting a corresponding force on a body of any kind. 
     Furthermore, one could of course also use any other number of force actuators. For the correction of image errors, one could for example generate any desired N-wave deformation (with the maximum order N being an integer larger than 1) by means of a corresponding number N of force actuators exerting their actuator forces on the optical element (normally parallel to the optical axis of the optical system) at N positions distributed (in particular with uniform spacing) along the circumference of the optical element. Between every two neighboring points of application of the actuator forces, the optical element is normally supported by a passive support element or an active support element (i.e. a further actuator) arranged in particular midway in the circumferential direction between the points of application of the actuator. In this context it should be understood that only in special cases (for example 2- and 4-wave deformation) are passive support elements arranged between each two actuators. If the optical element is supported exclusively by actuators, there are consequently at least 2N actuators required for a maximum order N of the wave-shaped deformation. 
     Expressed in more general terms, in an arrangement which is designed for a maximum order N of the wave-shaped deformation, all deformation orders can be realized which are obtained by prime factorization of the maximum order N and by multiplying any of the resultant prime factors N i  either with a value of 1 or with one or more of the other prime factors N i . Consequently, with a maximum order of
 
 N= 12=2·2·3  (14)
 
it is possible to realize wave deformations of the orders 2, 3, 4, 6 and 12.
 
     Furthermore, the foregoing description of the present invention is based exclusively on examples with fluidic actuators. It is therefore noted once more that to put the invention into practice one could select any actuator principles for the two actuator devices. Accordingly, any electrical and/or fluidic actuators could be used in order to realize the two actuator devices. Of course, it is also possible to arbitrarily combine different actuator principles with each other. 
     As a last remark, the present invention has been described herein exclusively in connection with a microlithography apparatus which operates with a wavelength of 193 nm. It is however considered self-evident that the invention can also be used in connection with any other optical apparatus operating at different wavelengths. In particular, the invention can also be used in connection with so-called EUV systems which operate at wavelengths below 20 nm (typically in the range of 13 nm).