Imaging optical system for microlithography

Abstract

An imaging optical system, in particular a projection objective, for microlithography, includes optical elements to guide electromagnetic radiation with a wavelength in a path to image an object field into an image plane. The imaging optical system includes a pupil, having coordinates (p, q), which, together with the image field, having coordinates (x, y) of the optical system, spans an extended 4-dimensional pupil space, having coordinates (x, y, p, q), as a function of which a wavefront W(x, y, p, q) of the radiation passing through the optical system is defined. The wavefront W can therefore be defined in the pupil plane as a function of an extended 4-dimensional pupil space spanned by the image field (x, y) and the pupil (p, q) as W(x, y, p, q)=W(t), with t=(x, y, p, q).

Claims

1. An imaging optical system, comprising: optical elements configured to guide electromagnetic radiation with a wavelength in an imaging beam path to image an object field into an image field, the optical elements comprising a first optical element, wherein: the imaging optical system has a pupil with first and second coordinates; the image field has first and second coordinates; the image field and the pupil span an extended 4-dimensional pupil space having the first and second coordinates of the pupil and the first and second coordinates of the image field; during use of the imaging optical system, a wavefront of the electromagnetic radiation passing through the imaging optical system is defined as a function of the extended 4-dimensional pupil space; the first optical element has a non-rotationally symmetrical surface with a two-dimensional surface deviation relative to every rotationally symmetrical surface; the two-dimensional surface deviation has a difference between its greatest elevation and its deepest valley of at least ; for each point of the object field, a sub-aperture ratio of the non-rotationally symmetrical surface deviates by at least 0.01 from a sub-aperture ratio of every other surface of the optical elements at the point of the object field; the non-rotationally symmetric surface of the first optical element is configured so that, by displacing the first optical element relative to the other optical elements, a change to the wavefront occurs; the change to wavefront has a portion with at least 2-fold symmetry; a maximum value of the wavefront change in the extended 4-dimensional pupil space is at least 110.sup.5 of the wavelength ; and the imaging optical system is a microlithography imaging optical system.

2. The imaging optical system of claim 1, wherein a minimum distance between the first optical element and its adjacent optical elements is five centimeters.

3. The imaging optical system of claim 1, wherein the sub-aperture ratio for each of the optical elements deviates by at least 0.01 from the respective sub-aperture ratio of the other optical elements.

4. The imaging optical system of claim 1, wherein the optical elements are configured such that every combination of two of the optical elements has an optical effect of a non-rotationally symmetrical optical element.

5. The imaging optical system to of claim 1, wherein non-rotationally symmetrical surfaces of the optical system are disposed in planes which are not conjugate to one another.

6. The imaging optical system to of claim 1, wherein the optical elements comprise mirrors.

7. The imaging optical system of claim 1, wherein the electromagnetic radiation is EUV radiation.

8. The imaging optical system of claim 1, wherein at least three of the optical elements have a non-rotationally symmetrical surface.

9. The imaging optical system of claim 1, wherein displacing the first optical element comprises rotating the first optical element.

10. The imaging optical system of claim 1, wherein displacing the first optical element comprises rotating the first optical element relative to a reference axis disposed perpendicular to the image field.

11. The imaging optical system of claim 10, wherein displacing the first optical element further comprises tilting the first optical element relative to the reference axis disposed perpendicular to the image field.

12. The imaging optical system of claim 1, wherein the imaging optical system is configured so that rotating the first optical element changes an astigmatism of the imaging optical system.

13. The imaging optical system of claim 1, wherein displacing the first optical comprises rotating the first optical element relative to an axis of rotation which runs through a center point of a sphere best-adapted to the non-rotationally symmetrical surface.

14. The imaging optical system of claim 1, wherein displacing the first optical element comprises shifting the first optical element.

15. The imaging optical system of claim 1, wherein a non-rotationally symmetrical portion of the non-rotationally symmetric surface of the first optical element has an n-fold symmetry, and a value of n is at least two.

16. The imaging optical system of claim 1, wherein a non-rotationally symmetrical portion of the non-rotationally symmetric surface of the first optical element has an astigmatic form.

17. The imaging optical system of claim 1, wherein the non-rotationally symmetric surface of the first optical element has a rotationally symmetrical portion, and an amplitude of the rotationally symmetrical portion is small in comparison to an amplitude of a non-rotationally symmetrical portion.

18. The imaging optical system of claim 1, wherein the imaging optical system comprises four to eight optical elements with a non-rotationally symmetrical surface.

19. A method, comprising: using an algorithm to determine surface shapes of optical elements of a microlithography system so that a wavefront error of the entire imaging optical system is at most a pre-specified value; and using the algorithm to modify at least one of the surface shapes by additive overlaying with a manipulation form configured so that, when displacing the optical element having the modified surface shape, the wavefront error of the optical system changes, wherein the imaging optical system is an imaging optical system according to claim 1.

20. The method of claim 19, further comprising using a further algorithm to change the non-modified surface shapes to at least partially compensate for a change to the wavefront error of the optical system brought about by the modification of the at least one optical surface shape in the non-displaced state.

21. The method of claim 20, further comprising determining a manipulator quality and a compensation quality with respect to the manipulation form used, wherein: the manipulator quality specifies to what extent the characteristic of the wavefront error can be changed in the desired way by displacing the optical element comprising the manipulation form; and the compensation quality specifies to what extent the change to the wavefront error, which is produced by modifying the at least one optical surface shape with the manipulation form in the non-displaced state, is compensated by the change to the surface shapes of the optical elements not modified by a manipulation form; and the method further comprises, based on the manipulator quality determined and of the compensation quality, deciding whether to use the manipulation form used in the design.

22. The method of claim 19, wherein the imaging optical system is configured to operate with a wavelength , the manipulation form defines a non-rotationally symmetrical surface which has a respective two-dimensional surface deviation in relation to every rotationally symmetrical surface, and the two-dimensional surface deviation has a difference between its greatest elevation and its deepest valley of at least .

23. The method of claim 19, wherein: the manipulation form is configured so that, when displacing the optical element having the modified surface shape, the characteristic of the wavefront error of the optical system changes so that the change to the wavefront error is brought about which has a portion with at least 2-fold symmetry; and a maximum value of the wavefront change in an extended 4-dimensional pupil space is at least 110.sup.5 of the wavelength .

24. The method of claim 19, wherein the manipulation form is configured so that, when displacing the optical element having the modified surface shape, the wavefront error of the optical system changes so that the wavefront error is specifically corrected by a Zernike image error.

25. The method of claim 19, wherein determining the manipulation form comprises: pre-specifying a number of base forms; simulatedly modifying the surface shaped provided for the manipulation form by additively overlaying with a base form; calculating an effect of at least one displacement of the optical element having the modified surface shape upon the wavefront error for each of the base forms; and using a further algorithm to select a set of base forms based on a desired manipulation effect and generation of the manipulation form by combining the selected base forms.

26. A method, comprising: using a merit function of an algorithm to determine surface shapes of optical elements of a microlithography imaging optical system, the merit function comprising as evaluation parameters a wavefront error of the entire imaging optical system and at least one manipulation sensitivity defined by an effect of a displacement of one of the optical elements un an aberration of the imaging optical system defined by a pre-specified characteristic of the wavefront error, wherein the imaging optical system is an imaging optical system according to claim 1.

27. The imaging optical system of claim 1, wherein displacing the first optical element comprises tilting the first optical element relative to a reference axis disposed perpendicular to the image field.

28. An imaging optical system, comprising: optical elements configured to guide electromagnetic radiation with a wavelength in an imaging beam path to image an object field into an image field, the optical elements comprising a first optical element, wherein: the imaging optical system has a pupil with first and second coordinates; the image field has first and second coordinates; the image field and the pupil span an extended 4-dimensional pupil space having the first and second coordinates of the pupil and the first and second coordinates of the image field; during use of the imaging optical system, a wavefront of the electromagnetic radiation passing through the imaging optical system is defined as a function of the extended 4-dimensional pupil space; the first optical element has a non-rotationally symmetrical surface with a two-dimensional surface deviation relative to every rotationally symmetrical surface; the two-dimensional surface deviation has a difference between its greatest elevation and its deepest valley of at least ; for each point of the object field, a sub-aperture ratio of the non-rotationally symmetrical surface deviates by at least 0.01 from a sub-aperture ratio of every other surface of the optical elements at the point of the object field; the non-rotationally symmetric surface of the first optical element is configured so that, by displacing the first optical element relative to the other optical elements, a change to the wavefront occurs; the change to wavefront cannot occur by displacing an optical element of the imaging optical system which has a symmetrical surface; a maximum value of the wavefront change in the extended 4-dimensional pupil space is at least 110.sup.5 of the wavelength ; and the imaging optical system is a microlithography imaging optical system.

29. An imaging optical system, comprising: optical elements configured to guide electromagnetic radiation with a wavelength in an imaging beam path to image an object field from an object plane into an image plane, wherein: at least two of the optical elements have a non mirror-symmetrical surface which deviates at at least one point from each mirror-symmetrical surface by at least /10; at each point of the object field, sub-aperture ratios of the non mirror-symmetrical surfaces deviate from each other by at least 0.01; and the imaging optical system is a microlithography imaging optical system.

30. A mirror element comprising a non-rotationally symmetrical surface configured to change a wavefront of incoming radiation with a wavelength , in an EUV wavelength range, the non-rotationally symmetrical surface having a deviation of at least 500 in relation to each rotationally symmetrical surface at at least one point, the mirror element being configured to be used in a microlithography imaging optical system.

31. An imaging optical system, comprising: optical elements configured to guide electromagnetic radiation with a wavelength in an imaging beam path to image an object field into an image field, the optical elements comprising a first optical element, wherein: the imaging optical system has a pupil with first and second coordinates; the image field has first and second coordinates; the image field and the pupil span an extended 4-dimensional pupil space having the first and second coordinates of the pupil and the first and second coordinates of the image field; during use of the imaging optical system, a wavefront of the electromagnetic radiation passing through the imaging optical system is defined as a function of the extended 4-dimensional pupil space; the first optical element has a non-rotationally symmetrical surface with a two-dimensional surface deviation relative to every rotationally symmetrical surface; the two-dimensional surface deviation has a difference between its greatest elevation and its deepest valley of at least ; for each point of the object field, a sub-aperture ratio of the non-rotationally symmetrical surface deviates by at least 0.01 from a sub-aperture ratio of every other surface of the optical elements at the point of the object field; the non-rotationally symmetric surface of the first optical element is configured so that, by rotating the first optical element relative to the other optical elements by less than 10 arc minutes, a change to the wavefront occurs; the change to wavefront has a portion with at least 2-fold symmetry; a maximum value of the wavefront change in the extended 4-dimensional pupil space is at least 110.sup.5 of the wavelength ; and the imaging optical system is a microlithography imaging optical system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above features, and further advantageous features of the disclosure are illustrated in the following detailed description of exemplary embodiments according to the disclosure with reference to the attached diagrammatic drawings, in which:

(2) FIG. 1 an illustration of the mode of operation of a projection objective of an exposure tool for microlithography when imaging mask structures from an object plane into an image plane with an exemplary illustration of a wavefront distribution in the pupil of the projection objective;

(3) FIG. 2 an exemplary illustration of the shape of an image field of the projection objective according to FIG. 1;

(4) FIG. 3 an exemplary illustration of the shape of a pupil of the projection objective according to FIG. 1;

(5) FIG. 4 an illustration of deviations of the surface of an optical element of the projection objective according to FIG. 1 from a spherical surface;

(6) FIG. 5 a sectional view through an exemplary embodiment of a projection objective according to FIG. 1 with six mirror elements;

(7) FIG. 6 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the third mirror element of the projection objective of FIG. 5;

(8) FIG. 7 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the fourth mirror element of the projection objective of FIG. 5;

(9) FIG. 8 the shape of the image field of the projection objective according to FIG. 5;

(10) FIG. 9 the effects of rotation of the fourth and of the third and fourth mirror upon specific image errors;

(11) FIG. 10 an illustration of the beam path of a disturbed and an undisturbed optical system;

(12) FIG. 11 a grayscale illustration of a height distribution of an optically used region of a mirror element of the projection objective according to FIG. 1 in a further embodiment according to the disclosure;

(13) FIG. 12 a sectional view through a further exemplary embodiment of a projection objective according to FIG. 1 with six mirror elements;

(14) FIG. 13 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the first mirror element of the projection objective of FIG. 12;

(15) FIG. 14 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the second mirror element of the projection objective of FIG. 12;

(16) FIG. 15 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the third mirror element of the projection objective of FIG. 12;

(17) FIG. 16 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the fourth mirror element of the projection objective of FIG. 12;

(18) FIG. 17 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the fifth mirror element of the projection objective of FIG. 12;

(19) FIG. 18 a partial contour diagram of a non-rotationally symmetrical portion of the surface of the sixth mirror element of the projection objective of FIG. 12;

(20) FIG. 19 a rotational configuration of the mirror elements of the projection objective according to FIG. 12;

(21) FIG. 20 the effect of the rotation of the mirror elements according to the rotational configuration of FIG. 19 upon image errors;

(22) FIG. 21 a further rotational configuration of the mirror elements of the projection objective according to FIG. 12;

(23) FIG. 22 the effect of the rotation of the mirror elements according to the rotational configuration of FIG. 21 upon image errors;

(24) FIG. 23 a flow chart illustrating an embodiment of a method according to the disclosure for the optical design of an imaging optical system; and

(25) FIG. 24 an EUV projection exposure tool with an embodiment according to the disclosure of an imaging optical system.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS ACCORDING TO THE DISCLOSURE

(26) In the exemplary embodiments described below, elements which are similar to one another functionally or structurally are provided as far as possible with the same or similar reference numbers. Therefore, in order to understand the features of the individual elements of a specific exemplary embodiment, reference should be made to the description of other exemplary embodiments or to the general description of the disclosure.

(27) In order to facilitate the description of the projection exposure tool a Cartesian xyz coordinate system is specified in the drawing from which the respective relative position of the components shown in the figures is made clear. In FIG. 1 the y direction runs perpendicular to the drawing plane into the latter, the x direction to the right and the z direction upwards.

(28) FIG. 1 illustrates diagrammatically an imaging optical system 10 in the form of a projection objective of a projection exposure tool for microlithography. During operation the optical system 10 images a region to be exposed of a mask disposed in the object plane 12, the so-called object field 13, into an image plane 14, in which a wafer is disposed. The object field 13 is imaged here onto an image field 16, which is pictured in FIG. 2 by way of example for the case of a step and scan projection exposure tool. In this case the image field 16 has a rectangular shape which is shorter in the scanning direction than laterally to the latter. The optical system 10 has a system axis which is disposed perpendicularly to the image plane 14.

(29) FIG. 1 shows as an example the respective imaging beam path 18.sub.1 and 18.sub.2 through the optical system 10 for the imaging of two different points O.sub.1 and O.sub.2 of the object field 13 onto field points B.sub.1 and B.sub.2 of the image field 16. The imaging radiation 19 used here has a wavelength which preferably comes within the EUV wavelength range, in particular with a wavelength of below 100 nm, e.g. approximately 13.5 nm or 6.8 nm. The optical system 10 has a pupil plane 20 in which an aperture diaphragm 22 is disposed.

(30) A pupil plane 20 is characterized in that the local intensity distribution of the imaging radiation 19, which converges onto a specific field point in the image plane 14, corresponds in the pupil plane 20 to the angularly resolved intensity distribution at this field point. This correspondence is guaranteed when the imaging optical system 10 is sinus-corrected, as in the present case. The surface of the pupil plane 20 delimited by the aperture diaphragm 22 is called the pupil 24 of the optical system 10, as illustrated in FIG. 3.

(31) In other words, one generally understands by a pupil 24 of an imaging optical system 10 an image of the aperture diaphragm 22 which delimits the imaging beam path. The planes in which these images come to lie are called pupil planes. Since, however, the images of the aperture diaphragm 22 are not necessarily exactly level, in general the planes which correspond approximately to these images are also called pupil planes. The plane of the aperture diaphragm itself is also called a pupil plane. If the aperture plane is not level, the plane which corresponds best to the aperture diaphragm is called a pupil plane, as with the images of the aperture diaphragm.

(32) An entrance pupil of the imaging optical system 10 is understood as the image of the aperture diaphragm 22 which is produced when the aperture diaphragm 22 is imaged through the part of the imaging optical system 10 which lies between the object plane 12 and the aperture diaphragm 22. Correspondingly, the exit pupil is the image of the aperture diaphragm 22 which is produced when one images the aperture diaphragm 22 through the part of the imaging optical system 10 which lies between the image plane 14 and the aperture diaphragm 22.

(33) In an alternative definition a pupil is the region in the imaging beam path of the imaging optical system 10 in which individual beams originating from the object field points O.sub.n intersect, which individual beams are respectively assigned to the same illumination angle relative to the main beams originating from these object field points. The plane in which the intersection points of the individual beams according to the alternative pupil definition lie, or which come closest to the spatial distribution of these intersection points, which do not necessarily have to lie exactly in a plane, can be called the pupil plane.

(34) The coordinates of the image field 16 in the image plane 14 are identified as (x, y), the coordinates of the pupil 24 in the pupil plane 20 as (p, q). The partial waves T.sub.n of the imaging radiation, which converge at the individual field points B.sub.n of the image field 16, respectively have a particular wavefront distribution W.sub.n (p, q) in the pupil 24. In FIG. 1, for the two image points B.sub.1 with the image field coordinate (x.sub.1, y.sub.1) and B.sub.2 with the image field coordinate (x.sub.2, y.sub.2) exemplary wavefront distributions W.sub.1(p, q) W(x.sub.1, y.sub.1, p, q) and W.sub.2(p, q) W(x.sub.2, y.sub.2, p, q) are shown for the purpose of illustration. These wavefront distributions only serve to illustrate the basic functional principle of a projection exposure tool and are not necessarily representative of wavefront distributions occurring according to the disclosure.

(35) The wavefront W of the imaging radiation 19 passing through the optical system 10 can therefore be defined in the pupil plane 20 as a function of an extended 4-dimensional pupil space spanned by the image field (x, y) and the pupil (p, q) as follows:
W(x,y,p,q)=W(t) with t=(x,y,p,q)(1)

(36) The location coordinates (x, y) and the pupil coordinates (p, q) are standardized to the maximum height of the image field 16 and to the numerical aperture NA so that the coordinates are dimension-less and x.sup.2+y.sup.21 and p.sup.2+q.sup.21.

(37) FIG. 5 shows a sectional view through an exemplary embodiment according to the disclosure of an imaging optical system 10 according to FIG. 1 in the form of a projection objective of a projection exposure tool for microlithography. The latter has exclusively reflective optical elements in the form of six mirrors M1 to M6 which are designed to reflect EUV radiation.

(38) The optical system 10 according to FIG. 5 is a so-called free form surface design. In this the optical surfaces of at least three of the mirrors M1 to M6 are provided with so-called free form surfaces. This type of free form surface 26 is illustrated as an example in FIG. 4. Within the framework of this application a free form surface is understood to be a surface which is not rotationally symmetrical, and deviates at at least one point from every rotationally symmetrical surface by at least the wavelength of the imaging radiation 19. In particular, in relation to every rotationally symmetrical surface, in particular in relation to a best-adapted rotationally symmetrical reference surface 28 or a best-adapted spherical reference surface, the surface 26 has a two-dimensional surface deviation which has a difference between its greatest elevation and its deepest valley of at least . According to one embodiment according to the disclosure this difference is 10, 30, 50 or greater. In the following, these deviations of the surfaces from rotational symmetry are also called asphericities. The term asphericity is often used in a narrower sense in which only a deviation from the spherical shape is meant. In this case, however, the term asphericity should also include deviations from rotational symmetry.

(39) In the embodiment according to FIG. 5 all of the mirrors M1 to M6 are provided with free form surfaces 26. Here respective deviations of the latter from rotationally symmetrical reference surfaces are formed such that the asphericities cancel each other out in the entire optical system 10. Here cancel is to be understood in that the optical effects, which are generated by the single asphericities, respectively, supplement each other collectively to a correction of the wavefront, which correction is small compared to the respective correction effect of the single asphericities. In other words: The superimposed optical effects fall below a prespecified maximum deviation from a spherical wave. In the free form surface design according to FIG. 5 a single element compensating the asphericity of this non-rotationally symmetrical mirror is not assigned to any of the non-rotationally symmetrical mirrors M1 to M6. This is in contrast, for example, to an Alvarez manipulator or to a cylinder compensator wherein a combination of a positive or a negative cylinder lens, as described for example in EP 0 660 169 A1, is provided. As already mentioned above, according to FIG. 5 all of the mirrors M1 to M6 are designed as regards their asphericity such that the non-rotationally symmetrical image errors of the entire optical system 10 caused by the respective deviation of the mirrors from rotational symmetry are compensated. In other words, the asphericity of each mirror M1 to M6 is respectively compensated by the overall asphericity of all of the respectively remaining mirrors.

(40) For each of the mirrors M1 to M6 a sup-aperture diameter is defined. The latter is given by the maximum diameter of a respective surface which is illuminated upon imaging any, but specifically chosen, point of the object field 13 on the corresponding mirror. For the purpose of illustration, in FIG. 5 the sub-aperture diameters d.sub.1.sup.SA and d.sub.2.sup.SA of the two mirrors M1 and M2 are drawn in which identify the diameters of the surfaces illuminated by a point O.sub.1 of the object field 13 on the mirrors. Here the beam path 18.sub.1 of the imaging radiation passing from O.sub.1 to the mirror M1 is marked specially by broken lines. The sub-aperture diameter d.sup.SA can vary from point to point of the object field 13.

(41) Furthermore, for each of the mirrors M1 to M6 an optically free diameter d.sup.CA is defined. The latter is given by the diameter of the smallest circle around a respective reference axis of the corresponding mirror which contains the part of the respective mirror illuminated when imaging the entire object field 13. The respective reference axis is the axis of symmetry with rotationally symmetrical mirror surfaces. With non-rotationally symmetrical mirror surfaces the reference axis is the axis of symmetry of a rotationally symmetrical portion of the surface or the axis of symmetry of a best-adapted rotationally symmetrical reference surface. The reference axis is typically parallel to a normal onto the image plane.

(42) In other words, the optically free diameter d.sup.CA is the maximum diameter of the illuminated portion of the mirror surface when imaging all points of the object field 13 through the beam path when the mirror in question is centrally illuminated. With peripheral illumination the minimum diameter of a mirror surface which fully contains the peripherally illuminated section is used. All of the mirrors M1 to M6 shown in FIG. 5 are illuminated more or less peripherally. The surfaces of the mirrors M1 to M6 respectively illustrated in the figure are decisive surfaces for determining the free diameters d.sup.CA. For the purpose of illustration the respective free diameter d.sub.1.sup.CA or d.sub.2.sup.CA for the mirrors M1 and M2 is also drawn in.

(43) By forming a quotient, a so-called sub-aperture ratio is calculated from the sub-aperture diameter d.sup.SA and the optically free diameter d.sup.CA for each of the mirrors M1 to M6. The sub-aperture ratio can also vary from object point to object point within a mirror. For the exemplary embodiment shown in FIG. 5 this variation within a mirror is negligibly slight. Table 1 below shows the sub-aperture ratios d.sup.SA/d.sup.CA produced for the individual mirrors M1 to M6. Furthermore, the sub-aperture ratios in the object plane 12, the image plane 14 and the pupil plane 20 are also specified.

(44) TABLE-US-00001 TABLE 1 Sub-aperture ratio Position d.sup.SA/d.sup.CA Object plane 0.000 Mirror M1 0.264 Mirror M2 0.470 Pupil plane 1.000 Mirror M3 0.351 Mirror M4 0.230 Mirror M5 0.620 Mirror M6 0.748 Image plane 0.000

(45) As can be seen from Table 1, the sub-aperture ratio of each of the mirrors M1 to M6 deviates considerably from the sub-aperture ratios of the respectively remaining mirrors. The smallest deviation is between the mirrors M1 and M4. However, the deviation here is still greater than 0.03. The design of the optical system 10 is formed such that the deviation at at least one point of the object field 13, in particular at each point of the object field 13, is at least 0.01. In contrast to this, the Alvarez manipulators described above, matched to one another in pairs, have smaller deviations in the sub-aperture ratio.

(46) In the exemplary embodiment according to FIG. 5 the mirrors M3 and M4 for manipulating the wavefront of the optical system 10 are disposed rotatably in relation to a reference axis 30 perpendicular to the image plane 14, as indicated by the double arrows 32 and 34. In the drawing the reference axis is disposed in the z direction. Therefore the mirrors M3 and M4 can be displaced respectively in relation to the other mirrors with regard to their rotation position. In other embodiments of the optical system 10, alternatively or in addition, one or more optical elements can also be mounted displaceably in their position or tiltably relative to the reference axis 30.

(47) As already mentioned above, all of the mirrors M1 to M6 have non-rotationally symmetrical surfaces. The topography of a non-rotationally symmetrical surface of this type can be illustrated by splitting into a rotationally symmetrical and a non-rotationally symmetrical portion. Here in principle the rotationally symmetrical portion can also be zero on all coordinates.

(48) FIGS. 6 and 7 show contour diagrams of the non-rotationally symmetrical portions of the surfaces of the mirrors M3 and M4 of the optical system 10 according to FIG. 5 disposed rotatably for the purpose of manipulation. The respective optically used region is identified by reference number 36.

(49) The surface topography of the optically used regions 36 on the mirrors M3 and M4 respectively has 2-fold symmetry in the lowest order. K-fold symmetry is basically to be understood as meaning that k is the largest natural number, for which the surface topography remains unchanged or is conveyed into itself when rotating the mirror in question in relation to an axis of rotation by the angle 360/k. With the mirrors M3 and M4 the axis of rotation in question 38.sub.3 or 38.sub.4 lies outside of the respective used region 36. In case of rotation of the respective mirror M3 or M4 in relation to the axis of rotation in question 38.sub.3 or 38.sub.4 about an angle of 180 defining the 2-fold symmetry, the contoured region 36 would before its rotation have no overlap with the contoured region rotated by 180. Therefore, the 2-fold symmetry in relation to the mirrors M3 and M4 is characterized via an alternative definition or one extended with respect to the above definition.

(50) According to this definition a surface topography z(x,y), with (x, y)AR.sup.2, extending over the x-y plane R.sup.2 is k-waved or k-fold (with kN, N=set of natural numbers) if the following differential equation is fulfilled:

(51) $\begin{array}{cc}\left(\frac{{}^2}{{}^2}+k^2\right)z\left(r\cos ,r\sin \right)=0& \left(2\right)\end{array}$
for all (x,y)A und (x+r cos , y+r sin )A
wherein (r cos , r sin ) are the polar coordinates for the point (x, y).

(52) The definition according to (2) applies independently of whether the surface z(x,y) includes the z-axis acting as the axis of rotation. The optically used regions 36 of the mirrors M3 and M4 from FIGS. 6 and 7 respectively have according to this definition a 2-fold symmetry in relation to the corresponding axis of rotation 38.sub.3 or 38.sub.4.

(53) Moreover, the surface topography in FIGS. 6 and 7 has mirror symmetry in relation to the xz plane. This mirror symmetry is shown with all of the surfaces of the optical system 10 according to FIG. 5, and so the optical system as a whole is also mirror-symmetrical.

(54) Rotation of one of the two mirrors M3 and M4 or of both mirrors in relation to the reference axis 38.sub.3 or 38.sub.4 means a 2-fold disturbance u of the whole imaging optical system 10. The disturbance u due to the mirror rotation or generally due to displacement of at least one optical element brings about a wavefront change W.sub.u(x,y,p,q) in the extended four-dimensional pupil space, where (x,y,p,q)=t according to equation (1).

(55) In order to give a general illustration of the concept of the wavefront change W.sub.u, FIG. 10 shows under (a) the beam path of an optical system 10 without disturbance which is shown here via two optical lenses. The optical path length OPL from the object plane 12 through the optical system 10 to the image plane 14 is a function of the image field coordinates (x,y) and of the pupil coordinates (p,q). If disturbance u is now introduced into the optical system 10, as illustrated under (b) by tilting the second optical lens, the optical path length (OPL) changes. The difference between the path length OPL (x,y,p,q) of the system with disturbance and the path length OPL(x,y,p,q) of the system without disturbance is the wavefront change W (x,y,p,q).

(56) A disturbance is called k-fold and has k-fold symmetry when k is the largest natural number, so that after a rotation of the optical system 10 by .sub.k=2/k the wavefront change W.sub.u is conveyed into itself:

(57) $\begin{array}{cc}\mathrm{Wu}\left(t^{}\right)=\mathrm{Wu}\left(t\right)\mathrm{mit}{t}^{}={}_{{}_k}t\mathrm{and}& \left(3\right)\\ {}_{{}_k}=\left(\begin{array}{cc}{R}_{{}_k}& 0\\ 0& R_{{}_k}\end{array}\right)=\left(\begin{array}{cccc}\cos {}_k& -\sin {}_k& 0& 0\\ \sin {}_k& \cos {}_k& 0& 0\\ 0& 0& \cos {}_k& -\sin {}_k\\ 0& 0& \sin {}_k& \cos {}_k\end{array}\right)& \left(4\right)\end{array}$

(58) If the wavefront W does not change upon rotation by any arbitrary angle , i.e. when the disturbance u is rotationally symmetrical, one then also talks of disturbance with 0-fold symmetry.

(59) Applied to the 2-fold disturbance produced by mirror rotation in the embodiment of the optical system 10 according to FIG. 5 this produces:

(60) $\begin{array}{cc}{R}_{{}_k}=R_{}=\left(\begin{array}{cccc}-1& 0& 0& 0\\ 0& -1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right)& \left(4a\right)\end{array}$

(61) For k0 a k-fold disturbance v belongs to every k-fold disturbance u which disturbance v is rotated by the angle .sub.k/2=/(2k) relative to the disturbance u. The disturbances u and v are linearly independent upon the basis of k0 in the extended pupil space. Even with regard to the scalar product

(62) $\frac{1}{{}^2}{W}_u{W}_v$
they are orthonormal to one another, the integration in the position and pupil space respectively extending over the unit circle. The phase space vector was standardized here to maximum field height and maximum numerical aperture. The wavefront change for disturbances with small disturbance amplitude and any intermediate angle then reads in linear approximation
W.sub.u.sub.(t)=cos(k)W.sub.u(t)+sin(k)W.sub.u(t).(5)

(63) In the following R.sub. is defined like R.sub..sub. in (4). With a coordinate transformation, which rotates both the wavefront change and the disturbance by the angle , the wavefront does not change:
W.sub.u.sub.+(.sub.t)=W.sub.u.sub.(t)b.z.w.W.sub.u.sub.(.sub.t)=W.sub.u.sub.(t)(6)
and so:

(64) $\begin{array}{cc}\left(\begin{array}{c}{W}_u\left({}_{}t\right)\\ W_{}\left({}_{}t\right)\end{array}\right)=\left(\begin{array}{c}{W_u}_{-}\left(t\right)\\ W_{u_{}/\left(2k\right)-}\left(t\right)\end{array}\right)=R_{k_{}}\left(\begin{array}{c}{W}_u\left(t\right)\\ W_{}\left(t\right)\end{array}\right)& \left(7\right)\end{array}$

(65) This transformation behaviour is generalized in a trivial way for rotationally symmetrical disturbances with k=0. The generalization to negative values of k is just as easy. Here negative values correspond to a disturbance v which has been rotated in the opposite direction with regard to u (and in comparison to a positive k). Therefore, the -fold of the disturbances u and v is |k|.

(66) The Zernike functions known to the person skilled in the art e.g. from section 13.2.3 of the text book Optical Shop Testing, 2.sup.nd Edition (1992) by Daniel Malacara, published by John Wiley & Sons, Inc. are defined in polar coordinates by:

(67) $\begin{array}{cc}{Z}_n^m\left(,\right)=R_n^m\left(\right)\cos \left(m\right)Z_n^{-m}\left(,\right)=R_n^m\left(\right)\sin \left(m\right)fr,,m,n,{}_0\mathrm{und}0mn\mathrm{with}& \left(8\right)\\ R_n^m\left(\right)==\{\begin{array}{cc}\underset{k=0}{\overset{\left(n-m\right)/2}{.Math.}}\frac{{\left(-1\right)}^k\left(n-k\right)!}{k!(\left(n+m/2-k\right)!\left(\left(n-m\right)/2-k\right)!}{}^{n-2k}& \mathrm{for}n-m\mathrm{even}\\ 0& \mathrm{otherwise}\end{array}& \left(9\right)\end{array}$

(68) One can easily convince oneself that the functions Z.sub.n.sup.m defined above at the cross-over from polar coordinates into Cartesian coordinates x= cos and y= sin change into polynomials of the Cartesian coordinates. The Zernike polynomials form an orthonormal function system on the unit circle with the scalar product

(69) $\begin{array}{cc}.Math.f,g.Math.=\frac{1}{2}{}_0^{2}d{}_0^{1}df\left(,\right)g\left(,\right)& \left(10\right)\end{array}$

(70) The transformation behaviour with rotations is given by

(71) $\begin{array}{cc}{Z}_n^0\left(R_{}\left(x,y\right)\right)=Z_n^0\left(x,y\right)\mathrm{for}m=0\mathrm{and}\left(\begin{array}{c}{Z}_n^m\left(R_{}\left(x,y\right)\right)\\ Z_n^{-m}\left(R_{}\left(x,y\right)\right)\end{array}\right)=\left(\begin{array}{c}\cos \left(m\right)Z_n^m\left(x,y\right)-\sin \left(m\right)Z_n^{-m}\left(x,y\right)\\ \sin \left(m\right)Z_n^m\left(x,y\right)+\cos \left(m\right)Z_n^{-m}\left(x,y\right)\end{array}\right)\mathrm{for}m>0& \left(11\right)\end{array}$

(72) The Zernike functions Z.sub.m.sup.n specified above can also be designated in the so-called fringe sorting by Z.sub.j, c.sub.j then being the Zernike coefficients assigned to the respective Zernike functions. The fringe sorting is illustrated, for example, in Table 20-2 on page 215 of the Handbook of Optical Systems, Vol. 2 by H. Gross, 2005 Wiley-VCH Verlag GmbH & Co. KgaA, Weinheim. The wavefront deviation W(,) at a point in the object plane 12 is then developed as follows:

(73) $\begin{array}{cc}W\left(,\right)=\underset{j}{.Math.}{c}_j.Math.Z_j\left(,\right)& \left(12\right)\end{array}$

(74) For the sake of simplicity, here also W was used for designation of the wavefront, although the present relates, in contrast to (1), only to the pupil. Whereas the Zernike functions are designated by Z.sub.j, i.e. with the subscript index j, in the following the Zernike coefficients c.sub.j are also designated, as is customary in the specialist world, by Z.sub.j, i.e. with a normally written index, such as for example Z5 and Z6 for astigmatism.

(75) The surfaces 26.sub.3 and 26.sub.4 of the mirrors M3 and M4 according to FIG. 6 and FIG. 7 are formed with such non-rotationally symmetrical portions that the wavefront change W.sub.u(x,y,p,q) caused by rotation of at least one of the mirrors has an extremal value, the absolute value of which is at least 110.sup.5 of the wavelength , and for =13.5 nm this is at least 0.135 pm. If W.sub.a(x, y, p, q) is the wavefront before the rotation, and W.sub.d(x, y, p, q) is the wavefront after the rotation of the at least one mirror, the following applies:

(76) 0$\begin{array}{cc}\underset{x,yB}{\max }\underset{p,qP}{\max }.Math.W_a\left(x,y,p,q\right)-W_d\left(x,y,p,q\right).Math.1.Math.{10}^{-5}.Math.& \left(13\right)\end{array}$
where B indexes the points of the image field, and P the points of the pupil.

(77) FIG. 9 shows the effect of the disturbance u along a circle segment 42 shown in FIG. 8 brought about by mirror rotation in the optical system 10 according to FIG. 5, the circle segment extending within the image field 16 in the present case being in the form of a ring segment. The effects shown in FIG. 9 relate to Zernike coefficients Z5 and Z6 (astigmatism), Zernike coefficients Z7 and Z8 (coma) and Zernike coefficient Z9 (spherical aberration) in the expansion of the aberration in the pupil on the basis of the Zernike polynomials. The deviations of the aforementioned Zernike coefficients along the circle segment 42 are respectively shown here on the one hand for a rotation of just the mirror M4, and on the other hand for a rotation of both mirrors M3 and M4. When rotating the two mirrors M3 and M4, the rotation is implemented in a fixed and suitably chosen transformation ratio.

(78) As can be gathered from the diagrams of FIG. 9, when rotating the mirror M4 there is high sensitivity with regard to Z5, Z6 and Z7. Rotation of both mirrors M3 and M4 with the aforementioned transformation ratio offers the possibility of manipulating the Zernike coefficient Z6 separately with a constant effect over the image field. As can be seen from FIG. 9, Zernike coefficients Z5, Z7, Z8 and Z9 do not change here, or only change insignificantly, whereas Z6 changes constantly over the whole image field. Therefore the embodiment of the optical system 10 according to FIGS. 5 to 7 includes a roughly pure Z6 astigmatism manipulator.

(79) With the embodiment according to the disclosure of an imaging optical system 10 described above with reference to FIG. 5, as already explained above, the surfaces of the mirrors M5 and M6 are configured such that by rotating one of the aforementioned mirrors, a wavefront change W.sub.u of the optical system 10 with 2-fold symmetry can be produced.

(80) Moreover, the imaging optical system 10 can be configured in a plurality of different embodiments according to the disclosure. These embodiments all satisfy the condition that the surface of one of the optical elements with a non-rotationally symmetrical surface of the optical system is configured such that by displacing this optical element relative to the other optical elements a change W.sub.u to the wavefront, that cannot be brought about by displacement of a rotationally symmetrical optical element, can be produced. The maximum value of the wavefront change W.sub.u (x, y, p, q) is at least 110.sup.5 of the wavelength here. Displacement of the optical element can be brought about for example by rotation, shifting or tilting of the element. For this purpose the optical system 10 has appropriate actuators.

(81) In other words, by displacing the non-rotationally symmetrical optical element one can produce wavefront changes which cannot be produced by displacement of a rotationally symmetrical optical element. An example of this is the wavefront change with 2-fold symmetry which can be produced via the embodiment according to FIG. 5.

(82) In order to define precisely all of the wavefront changes that can be produced via the embodiments according to the disclosure, in the following all of the wavefront changes that can be produced by displacement of a rotationally optical element will first of all be identified.

(83) For this purpose the wavefront change W.sub.u brought about by a disturbance u.sub. with k-fold symmetry (=2/k) is first of all clearly broken down into the following orthonormal function system from products of location Zernike functions Z.sub.n.sup.m (x, y) and pupil Zernike functions Z.sub.n.sup.m(p, q):

(84) $\begin{array}{cc}{W}_{u_{}}\left(x,y,p,q\right)=\underset{n,n^{}=0}{\overset{}{.Math.}}\underset{n-m,n^{}-m^{}\mathrm{even}}{\underset{m,m^{}=-n,-n^{}}{\overset{n,n^{}}{.Math.}}}{w}_{n,m,n^{},m^{}}{Z}_n^m\left(x,y\right)Z_{n^{}}^{m^{}}\left(p,q\right).& \left(14\right)\end{array}$

(85) New base functions are now defined which are better adapted to the k-fold symmetry of the disturbance u.sub.:
A.sub.n,n.sup.m,m(x,y,p,q)=Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)+Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)
B.sub.n,n.sup.m,m(x,y,p,q)=Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)
C.sub.n,n.sup.m,m(x,y,p,q)=Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)
D.sub.n,n.sup.m,m(x,y,p,q)=Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)+Z.sub.n.sup.m(x,y)Z.sub.n.sup.m(p,q)(15)
where m, m0. The index m without a dash specifies the waviness in the field, and the index m with a dash the waviness in the pupil. The following now applies:

(86) $\begin{array}{cc}{W}_{u_{}}\left(x,y,p,q\right)={}^{a}0,0,0,0A_{0,0}^{0,0}\left(x,y,p,q\right)+\underset{n,n^{}=0}{\overset{}{.Math.}}\underset{n,n^{}-m^{}\mathrm{even}}{\underset{m^{}=1}{\overset{n^{}}{.Math.}}}{}^{a}n,0,n^{},m^{}{A}_{n,n^{}}^{0,m^{}}\left(x,y,p,q\right)+{}^{b}n,0,n^{},m^{}{B}_{n,n^{}}^{0,m^{}}\left(x,y,p,q\right)+\underset{n,n^{}=0}{\overset{}{.Math.}}\underset{n-m,n^{}\mathrm{even}}{\underset{m^{}=1}{\overset{n}{.Math.}}}{}^{a}n,m,n^{},0A_{n,n^{}}^{m,0}\left(x,y,p,q\right)+{}^{b}n,m,n^{},0B_{n,n^{}}^{m,0}\left(x,y,p,q\right)+\underset{n,n^{}=0}{\overset{}{.Math.}}\underset{n-m,n^{}-m^{}\mathrm{even}}{\underset{m,m^{}=1,1}{\overset{n,n^{}}{.Math.}}}{}^{a}n,m,n^{},m^{}{A}_{n,n^{}}^{m,m^{}}\left(x,y,p,q\right)+{}^{b}n,m,n^{},m^{}{B}_{n,n^{}}^{m,m^{}}\left(x,y,p,q\right)+{}^{c}n,m,n^{},m^{}{C}_{n,n^{}}^{m,m^{}}\left(x,y,p,q\right)+{}^{d}n,m,n^{},m^{}{D}_{n,n^{}}^{m,m^{}}\left(x,y,p,q\right)\mathrm{with}{}^{a}n,m,n^{},m^{}=\left(w_{n,m,n^{},m^{}}+w_{n,-m,n^{},-m^{}}\right)/2{}^{b}n,m,n^{},m^{}=\left(w_{n,-m,n^{},m^{}}+w_{n,m,n^{},-m^{}}\right)/2{}^{c}n,m,n^{},m^{}=\left(w_{n,m,n^{},m^{}}-w_{n,-m,n^{},-m^{}}\right)/2{}^{d}n,m,n^{},m^{}=\left(w_{n,-m,n^{},m^{}}-w_{n,m,n^{},-m^{}}\right)/2\mathrm{and}{w}_{n,m,n^{},m^{}}=a_{n,m,n^{},m^{}}+c_{n,m,n^{},m^{}}{w}_{n,-m,n^{},-m^{}}=a_{n,m,n^{},m^{}}-c_{n,m,n^{},m^{}}{w}_{n,-m,n^{},m^{}}=b_{n,m,n^{},m^{}}+d_{n,m,n^{},m^{}}{w}_{n,m,n^{},-m^{}}=b_{n,m,n^{},m^{}}-d_{n,m,n^{},m^{}}& \left(16\right)\end{array}$

(87) The new function basis shows the following simple transformation behaviour with rotations by the angle :

(88) $\begin{array}{cc}\left(\begin{array}{c}{A}_{n,n^{}}^{m,m^{}}\left({}_{}t\right)\\ B_{n,n^{}}^{m,m^{}}\left({}_{}t\right)\end{array}\right)=R_{k_1}\left(\begin{array}{c}{A}_{n,n^{}}^{m,m^{}}\left(t\right)\\ B_{n,n^{}}^{m,m^{}}\left(t\right)\end{array}\right)k_1=m-m^{}\mathrm{and}\left(\begin{array}{c}{C}_{n,n^{}}^{m,m^{}}\left({}_{}t\right)\\ D_{n,n^{}}^{m,m^{}}\left({}_{}t\right)\end{array}\right)=R_{k_2}\left(\begin{array}{c}{C}_{n,n^{}}^{m,m^{}}\left(t\right)\\ D_{n,n^{}}^{m,m^{}}\left(t\right)\end{array}\right)\mathrm{with}{k}_2=m+m^{}.& \left(17\right)\end{array}$

(89) Therefore the functions
(A.sub.n,n.sup.m,m,B.sub.n,n.sup.m,m)ansform such as (W.sub.u,W.sub.v).sub.l-wave disturbance, and
(C.sub.n,n.sup.m,m,D.sub.n,n.sup.m,m) such as (W.sub.u,W.sub.v) with a k.sub.2-wave disturbance.

(90) From the transformation behaviour of the symmetry-adapted function system there follows for the corresponding expansion coefficients
a.sub.n,n.sup.m,m,b.sub.n,n.sup.m,m,c.sub.n,n.sup.m,m,und d.sub.n,n.sup.m,m,m=0 . . . n,m=0 . . . n
the following selection rules generally applicable to rotationally symmetrical and non-rotationally symmetrical optical elements:
i) for 0-wave disturbances
a.sub.n,n.sup.m,m=b.sub.n,n.sup.m,m=0 for mm
c.sub.n,n.sup.m,m=d.sub.n,n.sup.m,m=0(18)
(ii) for 1-wave disturbances
a.sub.n,n.sup.m,m=b.sub.n,n.sup.m,m=0 for mm1
c.sub.n,n.sup.m,m=d.sub.n,n.sup.m,m=0(19)
(iii) generally for k-wave disturbances
a.sub.n,n.sup.m,m=b.sub.n,n.sup.m,m=0 for mmk
c.sub.n,n.sup.m,m=d.sub.n,n.sup.m,m=0 for mmk(20)

(91) Proceeding from here, all of the wavefront changes which can be produced by displacement of a rotationally symmetrical optical element are now defined by selection rules. A distinction is made here in the displacement between:

(92) a) a shift of the optical element along its axis of symmetry,

(93) b) a shift of the optical element orthogonally to its axis of symmetry, and

(94) c) tilting of the optical element about an axis orthogonally to its axis of symmetry.

(95) A shift of the optical element along its axis of symmetry according to a) is a zero-wave disturbance which can be described as follows:
W.sub.u(x,y,p,q)=
a.sub.0,0,0,0A.sub.0,0.sup.0,0(x,y,p,q)+constant phase offset (no effect upon imaging)
a.sub.1,1,1,1A.sub.1,1.sup.1,1(x,y,p,q)+scale error
b.sub.1,1,1,1B.sub.1,1.sup.1,1(x,y,p,q)+image field rotation (permitted error, but does not occur de facto),
a.sub.0,2,0,0A.sub.0,2.sup.0,0(x,y,p,q)+field constant Z4 (defocus)
a.sub.2,0,0,0A.sub.2,0.sup.0,0(x,y,p,q)+quadratic phase offset (no effect upon imaging)
a.sub.3,1,1,1A.sub.3,1.sup.1,1(x,y,p,q)+D3 3.sup.rd-order distortion (cushion)
a.sub.1,3,1,1A.sub.1,3.sup.1,1(x,y,p,q)+linear coma
b.sub.3,1,1,1B.sub.3,1.sup.1,1(x,y,p,q)+nameless (permitted distortion error which does not occur de facto)
b.sub.1,3,1,1B.sub.1,3.sup.1,1(x,y,p,q)+nameless (permitted coma error which does not occur de facto)(21)

(96) Terms with mm and terms proportional to C.sub.n,n.sup.m,m or D.sub.n,n.sup.m,m do not occur.

(97) The embodiments according to the disclosure can now be summarized as follows: The surface of one of the non-rotationally symmetrical optical elements of the optical system 10 is configured such that by displacing this optical element relative to the other optical elements, changes W.sub.u to the wavefront can be produced which do not include the wavefront changes mentioned under (19) and (20). These wavefront changes can be brought about by displacing a rotationally symmetrical optical element.

(98) Wavefront changes W.sub.u that can be produced according to the disclosure by the non-rotationally symmetrical optical element cover all wavefront changes with 2-fold and higher number-fold symmetry, but if applicable also some wavefront changes with 1-fold symmetry.

(99) A shift of the optical element orthogonally to its axis of symmetry according to b) and tilting of the optical element about an axis orthogonally to its axis of symmetry according to c) is a one-wave disturbance which can be described as follows:
W.sub.u(x,y,p,q)=
a.sub.1,0,1,0A.sub.1,0.sup.1,0(x,y,p,q)+linear phase offset (no effect upon imaging)
b.sub.1,0,1,0B.sub.1,0.sup.1,0(x,y,p,q)+linear phase offset (not effect upon imaging)
a.sub.0,1,0,1A.sub.0,1.sup.0,1(x,y,p,q)+field displacement in 45 direction
b.sub.0,1,0,1B.sub.0,1.sup.0,1(x,y,p,q)+field displacement in 45 direction
a.sub.2,1,0,1A.sub.2,1.sup.0,1(x,y,p,q)+D2 quadratic distortion
b.sub.2,1,0,1B.sub.2,1.sup.0,1(x,y,p,q)+D2 quadratic distortion
a.sub.1,2,1,0A.sub.1,2.sup.1,0(x,y,p,q)+Z4 tilt (tilt of the image plane)
b.sub.1,2,1,0B.sub.1,2.sup.1,0(x,y,p,q)+Z4 tilt (tilt of the image plane)
a.sub.1,2,1,2A.sub.1,2.sup.1,2(x,y,p,q)+linear astigmatism
b.sub.1,2,1,2B.sub.1,2.sup.1,2(x,y,p,q)+linear astigmatism
a.sub.2,1,2,1A.sub.2,1.sup.2,1(x,y,p,q)+D2 quadratic distortion
b.sub.2,1,2,1B.sub.2,1.sup.2,1(x,y,p,q)+D2 quadratic distortion
a.sub.0,3,0,1A.sub.0,3.sup.0,1(x,y,p,q)+field constant coma in 45 direction(22)

(100) Terms with mm1 and terms proportional to C.sub.n,n.sup.m,m or D.sub.n,n.sup.m,m do not occur.

(101) As already mentioned above, the embodiment of the optical system 10 according to FIGS. 5 to 7 includes a manipulator, which is capable of producing a pure Z6, i.e. a Z6 which is not connected with other Zernike polynomials, and therefore addresses 2.sup.nd-order astigmatism. In the following an embodiment of an optical system is described which is used for the pure manipulation of Z12 and so of 4.sup.th-order astigmatism.

(102) In terms of the new base functions (15) and coefficients (16) a k-fold symmetry of a portion of a general wavefront W.sub.u(x, y, p, q), following the expansion (16), is defined by the following terms:

(103) A wavefront is the to be k-fold symmetric provided that
a.sub.n,n.sup.m,m=b.sub.n,n.sup.m,m=0 if mmk and
c.sub.n,n.sup.m,m=d.sub.n,n.sup.m,m=0 if mmk

(104) A wavefront is the to be at least k-fold symmetric provided that there exists a natural number l such that
a.sub.n,n.sup.m,m=b.sub.n,n.sup.m,m=0 if mmlk and
c.sub.n,n.sup.m,m=d.sub.n,n.sup.m,m=0 if mmlk

(105) A wavefront is the to be containing a portion of k-fold symmetry provided that
a.sub.n,n.sup.m,m0 for at least one m=mk or
b.sub.n,n.sup.m,m0 for at least one m=mk or
c.sub.n,n.sup.m,m0 for at least one m=mk or
d.sub.n,n.sup.m,m0 for at least one m=mk

(106) A wavefront is the to be containing a portion of at least k-fold symmetry provided that there exists a natural number l such that
a.sub.n,n.sup.m,m0 for at least one m=mlk or
b.sub.n,n.sup.m,m0 for at least one m=mlk or
c.sub.n,n.sup.m,m0 for at least one m=mlk or
d.sub.n,n.sup.m,m0 for at least one m=mlk

(107) According to this embodiment the optical system 10 includes an optical element close to the pupil in the form of a mirror element. In this context, close to the pupil means that the sub-aperture ratio d.sup.SA/d.sup.CA of this mirror element is at least 0.9. The optical surface of this element close to the pupil has the following deviation from its rotationally symmetrical basic shape in the z direction, i.e. in the direction perpendicular to the image plane of the optical system:
z(x,y)=cZ13(x,y)(23)

(108) Therefore the optical surface is 2-wave in shape. With a rotation of the element by 6 in relation to the z axis this produces

(109) $\begin{array}{cc}z\left(x.Math.\cos +y.Math.\sin ,y.Math.\cos -x.Math.\sin \right)z\left(x,y\right)+\frac{z\left(x+y.Math.d,y-x.Math.d\right)}{d}{|}_{d=0}=z\left(x,y\right)+2\mathrm{cZ}12\left(x,y\right)& \left(24\right)\end{array}$

(110) The form change upon rotation of the surface is therefore 2-wave. Since the surface is, according to the desired properties, close to the pupil, the primary resulting image error is field constant and proportional to the form change, i.e.

(111) $\begin{array}{cc}\begin{array}{c}W\left(x,y,p,q\right)=Z12\left(p,q\right)\\ =Z1\left(x,y\right)Z12\left(p,q\right)\\ =\frac{}{2}\left(A_{0,4}^{0,2}\left(x,y,p,q\right)+B_{0,4}^{0,2}\left(x,y,p,q\right)\right),\end{array}& \left(25\right)\end{array}$
and so a.sub.0,4.sup.0,2=b.sub.0,4.sup.0,2=/2. All others a.sub.n,n.sup.m,m, b.sub.n,n.sup.m,m, c.sub.n,n.sup.m,m, d.sub.n,n.sup.m,m and so in particular those for mmk and mmk are 0.

(112) In the following a further embodiment of the optical system 10 shown in FIG. 5 is described, wherein M2 has a Z16-type superposition form. In this embodiment the non-rotationally symmetrical portions of the surfaces 26 of the mirrors M1 to M6 are respectively characterized by the combination of a basic deviation from rotational symmetry and a non-rotationally symmetrical superposition form. The basic deviation is defined by the non-rotationally symmetrical portion of a basic shape g of the surface 26 in question. The basic shapes of the surfaces 26, in the following also designated as O.sub.n, are determined by conventional design optimization of the optical system 10. The index n indicates the sequence number of the corresponding mirror M1 to M6. With this type of optimization, within the framework of the optical design the surface shapes are configured such that the optical system obtains desired optical properties. The desired optical properties can, for example, include the minimization of the whole wavefront deviation or of specific image errors.

(113) The basic shapes g.sub.n(x, y) of the surfaces 26 of the mirrors M1 to M6 determined via optical design optimization are modified by superposition forms s.sub.n(x,y). The basic shapes include rotationally symmetrical portions and the aforementioned basic deviations from rotational symmetry. The modification with the superposition forms s.sub.n(x, y) already takes place within the framework of the optics design, i.e. the design data which represent the basic shapes g.sub.n(x, y) are modified by the superposition forms s.sub.n(x, y). The superposition forms s.sub.n(x, y) specify deviations of the mirror surfaces from the basic shapes g.sub.n(x, y) of the latter as a function of the coordinates x and y orthogonal to the reference axis 30. The respective surface O.sub.n(x, y) is determined by addition of the respective basic shape g.sub.n(x, y) to the corresponding superposition form s.sub.n(x, y) as follows:
O.sub.n(x,y)=g.sub.n(x,y)+s.sub.n(x,y)(26)

(114) As already specified above, according to the embodiment now being described, the surface O.sub.2(x, y) of the mirror M2 has a Z16-type superposition form s.sub.2(x, y), i.e. s.sub.2(x, y) is proportional to the Zernike function Z.sub.16 (, ), modulo an adaptation to the diameter of the optically used region. According to one variant, in addition to a portion proportional to the Zernike function Z.sub.16 (, ), the superposition form s.sub.2(x, y) has further portions which follow other distributions. The superposition form s.sub.2(x, y) is configured such that upon displacement of the mirror M2 configured with by the latter, a manipulation effect upon the wavefront error of the optical system 10 is brought about. Therefore the superposition form s.sub.2(x, y) is also called the manipulation form.

(115) Within the framework of the design process the wavefront deviation introduced into the optical system 10 by the superposition form s.sub.2(x, y) is compensated as well as possible by applying superposition forms to the remaining mirrors M1, M3, M4, M5 and M6. The superposition forms s.sub.1(x, y), s.sub.3(x, y), s.sub.4(x, y), s.sub.5(x, y) and s.sub.6(x, y) thus applied are also called compensation forms due to the aforementioned function. If an amplitude, for example, of 75 nm is applied for the manipulation form s.sub.2(x, y), by providing manipulation forms on the remaining mirrors the wavefront error produced by s.sub.2 can be pushed to a non-correctable RMS value of approximately 0.2 nm regarding the Zernike coefficients Z5 to Z37. Here the maxima with Zernike coefficients Z2 to Z8 are approximately 0.05 nm. In this case one obtains as a manipulator a fifth-order polynomial. This corresponds to the derivation of Z.sub.16 in a spatial direction.

(116) According to a further variant the manipulation form s.sub.2(x, y) has at least one portion which is proportional to the Zernike function Z.sub.15 (, ). If an amplitude of 75 nm is also applied to this portion, by providing appropriate compensation forms to the remaining mirrors the wavefront error produced by the Z15-type portion can also be pushed to a non-correctable RMS value of approximately 0.2 nm regarding the Zernike coefficients Z5 to Z37. Here the maxima with Zernike coefficients Z2 to Z36 are smaller than 0.02 nm.

(117) FIG. 11 shows the height profile of an optically used region 36 of a non-rotationally symmetrical surface of a mirror element M in a further embodiment according to the disclosure. In this embodiment the surface in the optically used region 36 has a deviation from the mirror symmetry.

(118) This deviation is displayed as follows: The used surface 36 deviates from every mirror-symmetrical surface in relation to an axis of symmetry 44, in particular from a mirror-symmetrical surface best-adapted to the surface 36, by at least /10. In advantageous embodiments the deviation is at least /2, in particular at least or at least 10. A distinction is made according to the disclosure between imaging optical systems 10 in embodiments wherein there are two or more optical elements having the aforementioned break in symmetry and embodiments with just one optical element having a break in symmetry, in this case the deviation from every mirror symmetrical surface in relation to the axis of symmetry 44 being at least 10.

(119) According to an aspect of the disclosure the aforementioned break in symmetry is already realized in the optical design. Therefore, according to the aspect of the disclosure, with the optical design one deviates from the conventional method. Differently to what has previously been customary, the optical design is no longer completed by mirroring a surface section calculated in the first design step; in fact the entire optically used region 36 is calculated within the framework of the design development. Using this method the design becomes more complex, and, if applicable, also worse in that from the design aspect, the entire optical system is assigned greater image errors, and at the same time the break in symmetry makes it possible to equip the optical element with particularly effective manipulator properties in accordance with the disclosure.

(120) The deviation specified above of the surface region 36 of the completed optical element according to an embodiment of the disclosure from a mirror-symmetrical surface is greater than deviations which are achieved in a conventional manner via mirror-symmetrical design and subsequent mechanical processing. Therefore, the deviation according to the disclosure is not achieved, for example, by the method applied with intrinsically corrected aspheres, also known as ICAs, wherein the optical design supplies mirror-symmetrical data in the conventional way, the optical element is initially produced according to the optical design, and finally the mirror symmetry is broken by ion beam abrasion.

(121) FIG. 12 shows a sectional view through a further exemplary embodiment according to the disclosure of an imaging optical system 10 according to FIG. 1 in the form of a projection objective of a projection exposure tool for microlithography. Like the optical system 10 according to FIG. 5, this projection objective only has reflective elements in the form of six mirrors M1 to M6 which are designed to reflect EUV radiation.

(122) The optical surfaces of all of the mirrors M1 to M6 according to FIG. 12 are respectively in the form of so-called free form surfaces with a non-rotationally symmetrical shape. The deviations of rotationally symmetrical reference surfaces are also formed here such that the asphericities in the entire optical system 10 cancel one another out. FIGS. 13 to 18 show contour diagrams of the non-rotationally symmetrical portions respectively of the optically used region of the surfaces of the mirrors M1 to M6. In FIG. 12, as an example, the optically used region of the mirror M1 is provided with reference number 36. In Table 2 below, the sub-aperture ratios d.sup.SA/d.sup.CA for all of the mirrors M1 to M6, the object plane 12, the pupil plane 20 and the image plane 14 of the optical system 10 according to FIG. 12 are specified.

(123) TABLE-US-00002 TABLE 2 Sub-aperture ratio Position d.sup.SA/d.sup.CA Object plane 0.000 Mirror M1 0.282 Mirror M2 0.461 Pupil plane 1.000 Mirror M3 0.354 Mirror M4 0.144 Mirror M5 0.675 Mirror M6 0.728 Image plane 0.000

(124) As can be seen from Table 2, the sub-aperture ratios deviate considerably from one another. The smallest deviation is between mirrors M5 and M6. However, the deviation is still greater than 0.05 here.

(125) All of the mirrors M1 to M6 are disposed rotatably in relation to a reference axis 30 perpendicular to the image plane 14 in order to manipulate the wavefront of the optical system 10 according to FIG. 12. In the present embodiment all of the mirrors have the same axis of rotation. In other embodiments different axes of rotation can, however, also be assigned to the individual mirrors.

(126) FIG. 19 shows a rotational configuration of the mirrors M1 to M6 which enables partial correction of the Zernike coefficient Z5 in the wavefront W. For this purpose the respective angles of rotation .sub.i for the mirrors M1 to M6 are shown. FIG. 20 shows an image error distribution before and after rotation of mirrors M1 to M6 according to FIG. 19. Here the maximum values occurring in the image field for Zernike coefficients Z2 to Z16 are respectively shown. Furthermore, for the purpose of illustration, the maximum RMS value for all Zernike coefficients (RMS_A) bringing about astigmatism, the maximum RMS value for all Zernike coefficients (RMS.sub.C) bringing about coma, the maximum RMS value for all Zernike coefficients (RMS_3f) bringing about a 3-fold aberration, and the maximum RMS value for Zernike coefficients Z5 to Z36 are specified.

(127) The simply hatched bars show a starting position before rotation in which only Zernike coefficient Z5 is different from zero. The maximum value for Z5 over the field is applied with 1 nm, the values of all other Zernike coefficients with 0 nm. If mirrors M1 to M6 are now rotated by the angle shown in FIG. 19 in arc minutes, the image error distribution changes, as shown in FIG. 20 by the cross-hatched bars.

(128) The value for Z5 decreases to less than half, whereas other Zernike coefficients adopt values different from zero. The RMS value for Z5 to Z36 taken together decreases, however, to approximately half. The rotational configuration shown makes it possible, therefore, to correct an image error in Z5 to a large extent.

(129) FIG. 21 shows a further rotational configuration of mirrors M1 to M6 of the imaging system 10 according to FIG. 12. With this rotational configuration an image error in Z6 can be corrected, as illustrated in FIG. 22.

(130) As already explained via the optical system 10 according to FIG. 5, the surface shape of a mirror of an optical system in one of the embodiments described above can be formed, e.g. by combining a non-rotationally symmetrical basic shape g initially resulting from a design calculation, with a superposition form, which is likewise non-rotationally symmetrical. The shape produced taking into consideration the superposition form forms the basis of the mirror production. A superposition form of this type, serving as a manipulation form, can be configured such that the derivations of the latter produce in certain spatial directions aberrations to be compensated.

(131) FIG. 23 shows a flow chart illustrating an embodiment of a method according to the disclosure for the optical design of an imaging optical system 10 for microlithography in one of the embodiments according to the disclosure described above, which includes mirrors having non-rotationally symmetrical surfaces.

(132) In the design method shown in FIG. 23, in a first step S1 a conventional optical design calculation is first of all implemented with which the wavefront error of the entire optical system 10 is minimized. Here, via a first optimization algorithm the surface shapes of the optical elements in the form of mirrors are determined such that a wavefront error of the entire optical system achieves or falls below a pre-specified threshold characteristic. The threshold characteristic can, for example, specify different thresholds for individual Zernike coefficients, uniform thresholds for the Zernike coefficients, or also just one RMS value for the entire wavefront deviation. Thresholds for values derived from the Zernike coefficients can also be specified. An appropriate threshold for the Zernike coefficients can, dependently upon aperture and the specification for the entire wavefront deviation, be for example 0.2 nm, 0.1 nm or also 0.05 nm for an EUV system.

(133) As a next step a manipulation form for additive overlaying over the surface of a mirror is specified, which is configured such that when displacing this mirror, in the following also called a manipulator mirror, the characteristic of the wavefront error can be manipulated in a desired way. In connection with this one also speaks of a desired manipulation effect. Therefore, the manipulation form can be designed, for example, such that by displacing the mirror acted upon by the latter, a specific Zernike image error, such as for example astigmatism, or a specific combination of Zernike image errors, can be changed. Displacement of the mirror can include a shift, a rotation and/or tilting relative to a reference axis disposed perpendicularly to the image plane.

(134) The selection of a mirror of the imaging optical system for use as a manipulator mirror can be made according to different criteria. According to one embodiment the sub-aperture ratios of all of the mirrors of the optical system are compared with one another, and one or more mirrors are selected as manipulator mirrors, the sub-aperture ratio of which is disposed as close a possible to the sub-aperture ratios of a largest possible number of remaining mirrors of the optical system. The definition of the sub-aperture ratio corresponds here to the definition given above. As can be seen via the exemplary embodiment shown in FIG. 5, the decision for the selection of one or more manipulator mirrors can, however, also depend upon other factors. Table 1 above shows the sub-aperture ratios of mirrors M1 to M6 of the optical system 10 according to FIG. 5. As can easily be seen, the sub-aperture ratios of mirrors M1, M3 and M4, and of mirrors M5 and M6 are respectively relatively similar to one another. In the example described above, mirrors M3 and M4 have been selected as manipulator mirrors. With this selection, in addition to the sub-aperture ratio, other factors, such as for example the available range, setting accuracies, parasitic effects, and the realisability of the desired manipulation forms are taken into consideration.

(135) The manipulation form can, as described in step S2 in FIG. 23, be determined by via a second optimization algorithm. The image error to be corrected, the maximum amplitude to be corrected, and the position of the mirror selected as the manipulator mirror in the beam path are taken into consideration as criteria for the configuration of the manipulation form.

(136) According to a first exemplary embodiment, a number of different base forms are initially specified in order to determine the manipulation form via the second optimization algorithm. The base forms represent base deformations of varying shape on the optical surface of the manipulator mirror. The base forms can be in the form of Zernike coefficients, splines, or functions from other function systems.

(137) First of all the effect of each of the base forms upon the wavefront error of the optical system with a pre-specified displacement of the basic shape of the manipulation mirror overlaid with the base form is calculated. The quotient of this effect and the length of the path of displacement is also called the sensitivity of the respective base form. A path of displacement can designate a distance, as in the case of a translation, an angle interval, as in the case of a rotation or tilt, or also a combination of the latter. The sensitivities can also be calculated for a number of pre-specified displacements of different types. In the simplest case, simple rigid body movements, such as for example translations in all three spatial directions, tilts and rotations relative to a reference axis are considered with the displacement. According to one variant combinations of these rigid body movements can also be made.

(138) In order to calculate the sensitivities, the surface shape of the simulation mirror is first of all modified by additive overlaying with respectively one of the base forms, by simulation, i.e. in the design data set. Then the effect of at least one displacement of the optical element having the modified surface shape upon the wavefront error depending on the displacement path length for each of the base forms is determined. For this purpose, for every base form the wavefront of the optical system in the non-displaced state and in the displaced state of the manipulation mirror is determined. The difference between both wavefronts corresponds to the optical effect of the displacement for the base form in question. The quotient of this difference and the displacement path length is called the sensitivity of the base form. Alternatively, the gradient of the optical effect with displacement of the manipulation form can be determined, and the manipulation form for this can be calculated with the aid of calculus.

(139) Then the manipulation form for a desired manipulation effect is determined via the second optimization algorithm. Here the determined sensitivities of the base forms and general basic conditions, such as for example production possibilities, are used as the basis. The optimization algorithm selects an appropriate set of base forms and forms the manipulation form by an appropriate combination of the selected base forms. The combination is implemented by superposition of the appropriately weighted base forms. Here the Gaussian method of the least squares can be used.

(140) According to a second exemplary embodiment, in order to determine the manipulation form via the second optimization algorithm a standard displacement for a selected manipulator mirror is first of all specified. This standard displacement can include, for example, a translation by a particular distance, for example a length of approximately 0.1 m or 1.0 m, a rotation by a particular angle, for example with a value of approximately 0.1 rad or 1.0 rad, or a displacement along a more complex path, consisting of decentrations and/or tilts in different degrees of freedom. In the case of the optimization of optical systems designed for EUV radiation, it can be advantageous upon the basis of calculation accuracy to choose small standard displacements.

(141) A sensitivity s of the selected manipulation mirror is then determined as a function of the surface shape of the manipulation mirror by displacing the latter by the aforementioned standard displacement. The sensitivity s is a vector with image error sizes such as, for example, Zernike coefficients, for selected field points. The vector elements of s specify for selected image error sizes a difference between the respective image error size for the optical system determined according to step S1 with a non-displaced manipulation mirror and the corresponding image error size for the optical system, with which the manipulation mirror has been displaced by the standard displacement.

(142) The merit function for the second optimization algorithm is then formed according to an exemplary variant via the merit function from step S1, also called the design merit function, and the following additively added term: w(sm).sup.2. Here m is a desired value vector for the sensitivity to be achieved, and w is an appropriate weighting factor for the design merit function. The squaring is to be done in form of a scalar product. The added term brings about a linear regression. When implementing the second optimization algorithm, according to one embodiment only the surface shape of the manipulation mirror is released. The surfaces of the other mirrors are not changed and retain the shapes determined in step S1. The merit function of the second optimization algorithm brings about a combined assessment of the desired correction effect and attainment of the desired correction effect with the desired displacement travel. The term added to the design merit function can also be refined as follows: w(spm).sup.2+qp.sup.2+r/p.sup.2. Here p is an appropriate scaling factor, whereas q and r are corresponding weighting factors.

(143) In step S3 according to FIG. 23 the design data of the surface shape of the selected manipulation mirror are modified by additive overlaying of the manipulation form determined with the surface shape of the mirror selected as a manipulator mirror. According to one variant manipulation forms for a number of mirrors can also be determined, and the design data are correspondingly modified.

(144) In step S4 the surface shapes of the other mirrors, i.e. the mirrors not modified with the manipulation form, are modified via a third optimization algorithm. The aim of this modification is to at least partially compensate again the wavefront deviation introduced into the optical system through the manipulation form in the state in which the manipulation mirror is non-displaced. In other words, in step S4 the non-modified surface shapes are changed via the third optimization algorithm such that a change to the wavefront error of the optical system brought about by the modification of the surface of the manipulation mirror in the non-displaced state is at least partially compensated. The respective change of the surface shapes not acted upon with the manipulation form is also called the compensation form. As a result, for all of the mirrors, apart from the manipulation mirror, compensation forms are determined which are additively overlaid with the surface shape, also called the basic shape, determined under step S1.

(145) As already mentioned above, the manipulation form and the compensation forms now determined are also designated by the generic term superposition forms. The superposition forms of all of the mirrors of the optical system even one another out in total along the light direction so that the imaging quality over the image field is not substantially affected, i.e. remains within predetermined image error specifications. For a single field point there exists for this purpose an infinite diversity of solutions because as the only property, the sum of all superposition forms over the aperture is close to zero. For an expanded image field, or an image field discretized at a number of points, the respective totals, however, disappear over the beam paths of further image field points or come at least within the specifications. These numerous additional conditions for each field point considered restrict the diversity of solutions.

(146) Preferably, the superposition forms for optical systems are configured with aberration progressions varying slowly over the field. In this case a restricted field point number for the calculations is sufficient so that sufficient solution possibilities are available. According to one exemplary embodiment, for example, the aberration progressions vary slowly over the field such that consideration of, for example, 513 field points over a slot-shaped scanner field is sufficient in order to calculate the compensation forms. In this case sixty-five conditions are to be fulfilled for the totals of the superposition form aberrations.

(147) The wavefront error of the optical system achieved by the compensation is quantified by a so-called compensation quality k. The compensation quality k specifies to what extent the change to the wavefront error, which is produced by the modification of the surface shape of the manipulation mirror in the non-displaced state, is compensated by the change to the surface shapes of the mirrors not modified by the manipulation form. Ideally, the wavefront error is pushed below the threshold characteristic achieved in step S1. In particular, since the manipulation mirror opens up, however, the possibility of correcting certain aberrations of the wavefront error again, it can also be acceptable if this threshold characteristic is not totally achieved, as explained in more detail below.

(148) In other words, the compensation quality k constitutes a vector the vector elements of which specify the field point-resolved image error sizes of the design provided with the manipulation form according to which the shapes of the surfaces not modified with the modulation form have been modified via the third optimization algorithm.

(149) In step S5, in addition to the compensation quality achieved, a manipulator quality is evaluated. The manipulator quality specifies to what extent the characteristic of the wavefront error can be changed by displacing the manipulation mirror in the desired way. The evaluation can be implemented, for example, by enquiring whether the manipulator quality and compensation quality achieve predetermined specifications or thresholds. For the compensation quality threshold characteristics reduced in relation to the threshold characteristic pre-specified under step S1 by 5%, 10%, 25%, and in exceptional cases also by 50%, can be applied.

(150) According to one variant, during the evaluation the thresholds can, however, also be formed flexibly for the manipulator quality and the compensation quality. Therefore, for example, in the case where a particularly high manipulator quality is achieved, the desire for the compensation quality can be reduced and vice versa.

(151) The manipulator quality can be specified by a vector f, the individual vector coordinates of which relate to different Zernike coefficients of the wavefront expansions at different selected field points, and so specify the manipulator quality in relation to the corresponding Zernike coefficients. The vector f is determined as follows:
min{f:|spm|f.Math.(h(p)|m|+(p))}(27)

(152) Here, s, p and m are defined as in the second exemplary embodiment under step S2 and h and p are functions, the values of which take the same dimension as f and its components from the positive real numbers. For example functions h and (p) may be used, which are defined component by component h=h.sub.i with h.sub.i (p)=1 or h.sub.i (p)=p and =.sub.i with .sub.i (p)=1/p.

(153) The compensation quality k and the manipulation quality can be combined with methods known to the person skilled in the art to form a merit function, such as, for example, w(spm).sup.2+qp.sup.2+r/p.sup.2+tk.sup.2. Here, s, m, p, q and r are defined as in the second exemplary embodiment under step S2, t is an appropriate scalar, and k the compensation quality. With this merit function steps S2 and S4 can be combined to form an optimization algorithm.

(154) The assessment of the compensation quality can be made according to different criteria. The compensation quality is basically dependent upon the error budget allocated to the design and the overall budget applied during operation of the optical system. In order to assess the compensation quality, the relative ratio of the image error to the sought after design budget or to the sought after overall budget, for example, can be drawn upon. The relative ratio can, for example, be formed respectively for relevant Zernike coefficients. If the ratio from the non-compensatable design image error and the design budget is smaller than or equal to a specific threshold, the design is considered sufficient with regard to the compensation quality. The threshold for the aforementioned ratio can be e.g. 1.05. Ratios of, for example, 0.1, 0.9, 1.0 or 1.05 are therefore accepted. With ratios greater than the threshold, for example 1.06, 1.5 or 2.0, according to one embodiment the budget consumption is considered within the context of the overall budget. If the relative ratio of the non-compensatable design error to the overall budget is clearly greater here than 0.3 or in the region of 0.5 or greater, the design will not be accepted with regard to the compensation quality. Several Zernike-specific exceptions are also conceivable here, however, depending on the application.

(155) The assessment of the manipulator quality f can be made upon the basis of a threshold specified for f. According to one embodiment the manipulator quality is assessed positively if f, component by component, is smaller than a threshold of 0.5. Alternatively, the threshold, component by component, can be 0.1, preferably 0.03 or 0.01.

(156) If the evaluation of the manipulator quality and the compensation quality prove to be positive, the design method is completed. The at least one manipulation form determined, and the compensation forms determined form the basis of the design data of the optical system and are taken into account accordingly when producing the mirrors.

(157) However, if the evaluation of the manipulator quality and the compensation quality prove to be negative, both the at least one manipulation form determined and the compensation forms determined are rejected, and steps S2 to S5 are repeated. Here, in step S2, the parameters decisive for determining the manipulation form are changed so that, as a result, a different manipulation form is determined. This procedure is repeated until there is a manipulation form satisfying the specifications with regard to manipulator quality and compensation quality.

(158) The decisive parameters which are changed when determining the manipulation form in step S2 in the case of negative assessment of the manipulator quality and the compensation quality, can e.g. relate to the distance covered during the displacement. According to the second exemplary embodiment under step S2, the sensitivity s of the selected manipulation mirror relates to the distance covered. By increasing the distance, the design is relaxed, and this makes it easier to find an easily correctable solution.

(159) Alternatively, or in addition, the sought after modulation form sensitivity can also be changed. Therefore, for example, the originally determined manipulation form can be changed such that individual image error parameters are specifically influenced in the resulting wavefront.

(160) Alternatively, or in addition, in the case of negative assessment of the compensation quality the thresholds of the image error sizes observed which form the basis when determining the compensation quality, can be increased. Zernike coefficients smaller than Z10, in particular the Zernike coefficients Z2 and Z3, can easily be corrected by rigid body movements. It can therefore be advantageous, for example, to increase the thresholds for easily correctable Zernike coefficients.

(161) Alternatively, or in addition, in the case of a negative assessment of the compensation quality a greater design contribution to the overall error budget can be permitted.

(162) In the following a further embodiment of a method according to the disclosure for the optical design of an imaging optical system 10 for microlithography with a pre-specified number of optical elements in the form of mirrors is described. According to this method the surface shapes of the mirrors are determined via an optimization algorithm characterized by a merit function, also called a quality function. The merit function used here includes as evaluation values a wavefront error of the entire optical system and at least one so-called manipulation sensitivity. The manipulation sensitivity is defined by an effect of displacement of one of the mirrors, in the following also called the manipulation mirror, upon an aberration of the optical system. An aberration is defined by a pre-specified characteristic of the wavefront error of the optical system, and can be given by an individual Zernike aberration or also by a combination of Zernike aberrations.

(163) In other words, the manipulation sensitivity defines a response behaviour of a wavefront aberration depending on displacement of a mirror designated as a manipulator mirror. Displacement can, as already explained with regard to the above design method, include translation in any spatial direction, rotation about a reference axis and/or tilting relative to the reference axis. The manipulation sensitivity establishes a relationship between the extent of the displacement, such as for example the length of the path of displacement, and the extent of the wavefront aberration changed in this way.

(164) The optimization algorithm then determines design data for the surface shapes of the optical elements. These design data ensure, on the one hand, that the wavefront error of the resulting optical system is minimized such that a pre-specified threshold characteristic is achieved or fallen short of in the same way as in step S1 of the design method according to FIG. 23. On the other hand, at least one surface pattern is formed in the design data such that the mirror in question serves as a manipulation mirror in accordance with the terminology used above. In other words, this mirror is configured such that when the latter is displaced, the characteristic of the wavefront error of the optical system can be changed such that a wavefront aberration can thus be specifically corrected.

(165) In comparison to the design method according to FIG. 23, by incorporating the manipulation sensitivity into the merit function, the design of the optical system with which at least one mirror has a manipulator function, can be produced via a single optimization algorithm.

(166) The optimization algorithms mentioned above can include different algorithms commonly used by the person skilled in the art. This applies in particular to the optimization algorithms in the embodiment according to FIG. 23 and to the optimization algorithm, the merit function of which includes as an evaluation parameter a manipulation sensitivity.

(167) The aforementioned algorithms commonly used by the person skilled in the art include in particular: singular value decomposition, also called SVD, the Gaussian method of the least squares, also called LSQ, attenuated LSQ, linear programming, quadratic programming and convex programming. With regard to details on the aforementioned algorithms, reference is made explicitly to WO 2010/034674 A1. Further optimization algorithms commonly used by the person skilled in the art and suitable for use in the design methods according to the disclosure include genetic algorithms, the ant algorithm, the flood algorithm, simulated annealing, whole number programming, also called integer programming, as well as classical combinatory methods.

(168) FIG. 24 shows an embodiment of a projection exposure tool 50 for microlithography with a further embodiment of an imaging optical system 10 in the form of a projection objective. The projection exposure tool 50 is designed to operate in the EUV wavelength range, and includes an exposure radiation source 52 for producing EUV exposure radiation 54. The exposure radiation source 52 can be designed e.g. in the form of a plasma radiation source. The exposure radiation 54 initially passes through illumination optics 56 and is directed by the latter onto a mask 58. The mask 58 includes mask structures for imaging onto a substrate 62 in the form of a wafer, and is mounted displaceably on a mask movement stage 60, also called a reticle stage.

(169) The exposure radiation 54 is reflected on the mask 58 and then passes through the imaging optical system 10 in the form of a projection objective which is configured to image the mask structures onto the substrate 62. The substrate 62 is displaceably mounted on a substrate movement stage 64, also called a wafer stage. The projection exposure tool 50 can be designed as a so-called scanner, or also as a so-called stepper. The exposure radiation 54 is guided within the illumination optics 56 and the imaging optical system 10 via a plurality of optical elements in the form of reflective optical elementsmirrors. The reflective optical elements are configured in the form of EUV mirrors and are provided with conventional multiple coatings, for example MoSi multiple coatings.

(170) In the embodiment according to FIG. 24 the imaging optical system 10 only includes four reflective optical elements in the form of the mirrors M1 to M4. In this embodiment all of the mirrors are mounted moveably. The mirrors M1, M2 and M3 are mounted displaceably laterally to their respective optical surface, and mirror M4 is mounted tiltably. Therefore all of the mirrors M1 to M4 can be used to manipulate the wavefront. One or more of the mirrors M1 to M4 include one of the manipulation forms described above with a non-rotationally symmetrical shape. Therefore, in the present embodiment, the mirrors not configured with a manipulation form are mounted moveably in order to have additional degrees of freedom in the system. The moveability of these mirrors is optional, however, for the manipulator function of the manipulation forms.

LIST OF REFERENCE NUMBERS

(171) 10 imaging optical system 12 object plane 13 object field O.sub.1, O.sub.2 points of the object field 14 image plane 15 system axis 16 image field B.sub.1, B.sub.2 points of the image field 18.sub.1, 18.sub.2 imaging beam path 19 imaging beam path 20 pupil plane 22 aperture diaphragm 24 pupil T.sub.1, T.sub.2 partial wave M1-M6 mirrors M mirror 26 free form surface 28 reference surface 30 reference axis 32 double arrow 34 double arrow 36 optically used region 36 region rotated by 180 38.sub.3, 38.sub.4 axis of rotation 40 remaining region 42 circle segment 44 axis of symmetry 50 projection exposure tool for microlithography 52 exposure radiation source 54 exposure radiation 56 illumination optics 58 mask 60 mask shifting stage 62 substrate 64 substrate shifting stage