PATENT ABSTRACT
The disclosure generally relates to imaging optical systems that include a plurality of mirrors, which image an object field lying in an object plane in an image field lying in an image plane, where at least one of the mirrors has a through-hole for imaging light to pass through. The disclosure also generally relates to projection exposure installations that include such imaging optical systems, methods of using such projection exposure installations, and components made by such methods.

PATENT DESCRIPTION
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 13/205,278, filed Aug. 8, 2011, which is a continuation of U.S. application Ser. No. 11/971,640, filed Jan. 9, 2008, which claims priority under 35 U.S.C. §119(e)(1) to U.S. Ser. No. 60/885,261, filed Jan. 17, 2007, which claims priority under 35 U.S.C. §119 to German patent application serial number 10 2007 003 305.4, filed Jan. 17, 2007. These applications are incorporated herein by reference in their entirety. 
    
    
     FIELD 
     The disclosure generally relates to imaging optical systems that include a plurality of mirrors, which image an object field lying in an object plane in an image field lying in an image plane, where at least one of the mirrors has a through-hole for imaging light to pass through. The disclosure also generally relates to projection exposure installations that include such imaging optical systems, methods of using such projection exposure installations, and components made by such methods. 
     BACKGROUND 
     Imaging optical systems are known as projection optical systems as a component of projection exposure installations for microlithography. Imaging optical systems are also known in conjunction with microscope lenses for inspecting masks or wafers. 
     SUMMARY 
     In one aspect, the disclosure features an imaging optical system that includes a plurality of mirrors configured to image an object field lying in an object plane in an image field lying in an image plane. At least one of the mirrors has a through-hole configured so that imaging light can pass therethrough. A reflection surface of at least one mirror is in the form of a free-form surface which cannot be described by a rotationally symmetrical function. 
     In another aspect, the disclosure provides a projection exposure installation that includes an imaging optical system as described in the preceding paragraph, and a lens system configured to direct illumination light to the object field of the imaging optical system. The projection exposure installation is a projection exposure installation for microlithography. 
     In a further aspect, the disclosure provides a method that includes using the projection exposure installation described in the preceding paragraph to produce a microstructure on a wafer. 
     In some embodiments, the disclosure provides an imaging optical system wherein a reflection surface of at least one mirror is in the form of a free-form surface which cannot be described by a rorationally symmetrical function. 
     It has been recognized that using free-form surfaces instead of reflection surfaces having a rotationally symmetrical axis provides a new level of design freedom which results in imaging optical systems with combinations of properties which are not possible with rotationally symmetrical reflection surfaces. The free-form surface cannot be described by a function which is rotationally symmetrical about a marked axis representing a normal axis to a surface portion of the optical surface. The free-form surface thus cannot be defined in particular by a conic section-aspheric equation. Aspheres of this conic type deviate from spherical symmetry but can be described, however, by a rotationally symmetrical function, namely a function which is dependent on only one parameter, namely the distance to an optical axis, whereas the free-form surfaces require at least two parameters which are independent of one another to describe the surface. Conic section-aspheric surfaces are therefore not free-form surfaces. The shape of a boundary of the optically effective surface is not significant. Optically effective surfaces which are not bounded in a rotationally symmetrical manner are known. Optically effective surfaces of this type can nevertheless be described by a rotationally symmetrical function, a non-rotationally-symmetrically bounded portion of this optical surface being used. The free-form surface may be a static free-form surface. The term “static free-form surface” refers to a free-form surface, the shape of which is not actively modified during use of projection in the projection optical system. A static free-form surface can of course be displaced for adjustment purposes. The free-form surface can, in particular, be constructed on the basis of a planar reference surface or basic shape, a concave reference surface or a convex reference surface. In particular, at least one free-form surface may be used which is constructed on the basis of a curved reference surface. In this case, a reference surface with a vertex curvature which is constant over the entire reference surface can be used. A conic section-asphere may also be used as a reference surface. In conventional imaging optical systems including a through-hole, which are known as pupil-obscured systems, the use of this type of free-form surfaces can enable compact imaging optical systems with a low level of imaging errors to be achieved and, in particular, a high light throughput to be produced. According to the number of mirrors in the imaging optical system, a single mirror, or a plurality of mirrors, or all of the mirrors of the imaging optical system may be in the form of free-form surfaces. The free-form surfaces can have a maximum deviation from a rotationally symmetrical surface, which is best-fitted on the free-form surface and which does not necessarily match a designed reference surface, of at least the value of the wavelength of the imaging light. The deviation of, in particular, at least the value of a wavelength of the imaging light is, in practice, always markedly greater than the manufacturing tolerances during production of optical components for microlithography which, in absolute terms, are conventionally 0.1 nm and, in relative terms, are conventionally 1/50 or 1/100 of the wavelength of the illumination light used. In the case of illumination with EUV wavelengths, the deviation is at least several tens of nm, for example 50 nm. Larger deviations, for example 100 nm, 500 nm or 1,000 nm or even larger deviations are also possible. When using systems with imaging light of higher wavelengths, even greater deviations are possible. A free-form surface may be provided, for example, by a biconical surface, i.e. an optical surface with two different basic curves and two different conical constants in two directions perpendicular to one another, by a toric surface or an anamorphic and, at the same time, in particular, aspheric surface. A cylindrical surface therefore also represents a free-form surface of this type. The free-form surfaces may be mirror symmetrical to one or more planes of symmetry. The free-form surface can be a surface with n-fold symmetry, n being a whole number and greater than or equal to 1. The free-form surface may also have no axis of symmetry and no plane of symmetry at all. 
     Different ways of describing optical surfaces, in particular anamorphic surfaces, are described in U.S. Pat. No. 6,000,798, for example, which is hereby incorporated by reference. Analytical formulae for describing non-rotationally-symmetrical surfaces, in particular anamorphic aspherical surfaces, toric surfaces or biconical aspherical surfaces, are also described in WO 01/88597, which is hereby incorporated by reference. Some optical design programmes such as Oslo® and Code V® allow optical systems to be described and designed through mathematical functions, by which it is also possible to set non-rotationally-symmetrical optical surfaces. The aforementioned mathematical descriptions relate to mathematical surfaces. An actually optically used optical surface, i.e. the physical surface of an optical element, which surface is acted upon by an illumination beam and can be described with this type of mathematical description, generally contains only a portion of the actual mathematical surface, also known as the parent surface. The mathematical surface thus extends beyond the physical optically effective surface. In so far as an optical system can be described with the aid of a reference axis, some or all of the optically used surface portions may be arranged beyond this reference axis in such a way that the reference axis divides the mathematical surface, but not, however, the actual optically used portion of this mathematical surface. 
     Field planes arranged parallel to one another facilitate the integration of the imaging optical system into constructional surroundings. This advantage can be particularly significant when the imaging optical system is used in a scanning projection exposure installation, since the scan directions can then be guided parallel to one another. 
     A maximum angle of reflection of 25° (e.g., a maximum angle of reflection of 20°, a maximum angle of reflection of 16°) can allow the imaging optical system to be used in a highly effective manner as a projection optical system for an EUV projection exposure installation, since the mirrors, over the entire aperture, i.e. the entire usable reflective surface, thereof, may then be covered with consistently highly reflective layers. This advantage can be important in particular for the p-polarisation components of reflected radiation, since the reflectivity of p-polarisation components decreases rapidly in the case of elevated angles of reflection. 
     An imaging optical system, wherein the quotient of a maximum angle of reflection of the imaging light within the imaging optical system and the numerical aperture thereof on the image side is at most 40°, can allow a good compromise to be achieved between high EUV throughput and optimised pattern resolution in an EUV projection exposure installation. 
     A mirror arranged before the last mirror in the imaging light path in the region of a pupil plane and having a convex basic shape allows good Petzval correction of the imaging optical system to be achieved. 
     An imaging optical system having at least four mirrors (e.g., six mirrors) can be particularly suitable for the construction of an imaging optical system that is both compact and well-corrected in terms of its imaging errors. 
     Imaging optical systems having mirrors with angular magnification of the principal ray, wherein at least two of the mirrors have a negative angular magnification of the principal ray, and wherein a mirror with positive angular magnification of the principle ray is arranged between two mirrors with negative angular agnification of the principal ray, can allow systems with low maximum angles of reflection to be achieved. Imaging optical systems with three mirrors and a negative angular magnification of the principal ray are also possible. The angular magnification of the principal ray is defined as the angle between a principal ray belonging to a central field point and a reference axis. The reference axis is perpendicular to the object plane of the projection exposure installation and extends through the centre point of the object field. 
     A beam angle of a central imaging beam, directed through the last mirror and essentially through a pupil, of a central object point of greater than 85° relative to the image plane produces merely a low lateral image shift in the image plane when defocusing. 
     An imaging optical system, wherein the imaging light path directed through the last mirror has an intermediate image being arranged in an intermediate image plane in the region of the through-hole in the mirror, a portion of the optical system between the object plane and the intermediate image plane having a reducing magnification level of at least 2× can allow a relatively large penultimate mirror in the light path before the image field to be used. This can reduce the maximum angle of reflection and can also reduce the extent of pupil obscuration if the penultimate mirror is obscured. It is also possible to achieve magnification of the portion of the optical system of greater than 2× (e.g., greater than 2.5×, greater than 3.0×, 3.2×). 
     An arrangement, wherein a mirror, which is arranged so as to be the penultimate mirror in the imaging light path, has a through-hole for imaging light to pass through, the image plane being arranged behind the penultimate mirror so as to be off-centre by not more than a fifth of the diameter of the penultimate mirror (e.g., to be central) relative to the penultimate mirror, can allow a penultimate mirror with a relatively small through-hole to be used. This can ensure a stable penultimate mirror and low pupil obscuration. 
     A slightly curved penultimate mirror having a radius of curature greater than 500 mm (e.g., greater than 1,000 mm, greater than 1,500 mm) can allow a small through-hole relative to the diameter of the mirror to be achieved in the penultimate mirror at a given image-side numerical aperture. 
     An image field greater than 1 mm 2  can lead to good throughput when the imaging optical system is used in a projection exposure installation. 
     An image-side numerical aperture on the image side of at least 0.4 (e.g., at least 0.45, at least 0.5, at least 0.55, at least 0.6, at least 0.65, at least 0.7) can allow high resolution of the imaging optical system to be achieved. 
     An image-side telecentric imaging optical system can allow, for example, the system to refocus in the image plane without thereby changing the imaging magnification and thus can increase the flexibility of use of the imaging optical system. On the object-side, the imaging optical system can be formed in such a way that individual rays which are associated with different object field points but with the same exposure direction, enter the imaging optical system from the object field in a convergent manner. Alternatively, it is also possible for the individual rays of this type to enter the imaging optical system in a divergent or parallel manner. The latter case results in an object-side telecentric imaging optical system. 
     A low object-image shift of less than 100 mm (e.g., less than 10 mm, less than 1 mm) can lead to a compact imaging optical system and, in addition, facilitates optical system test methods, in which the imaging optical system is rotated about an axis extending through the object or image field and located perpendicular to the corresponding field plane, since the object or image field then does not shift too far during rotation. 
     At least one pair of adjacent mirrors, wherein the mirrors are at a distance from one another, perpendicular to the object plane and/or to the image plane, of more than 40% of the distance between the object field and the image field, can allow small angles of incidence to be observed in the light path of the imaging light through the imaging optical system. Due to the small angles of incidence, it is also possible to achieve highly reflective mirrors in the EUV wavelength range. In particular, 2, 3, 4 or more pairs of mirrors may satisfy the distance condition. 
     Having in the imaging optical system at least one mirror with a minimum distance of less than 25 mm from the reflection surface used to the closest imaging light path not acting upon the mirror results in an imaging optical system in which the angle of incidence on the mirrors is kept as small as possible. The advantages of small angles of incidence on mirrors has previously been discussed. In particular 2, 3 or 4 mirrors of the imaging optical system may be at the minimum distance. This minimum distance can be less than 25 mm, but optionally greater than 5 mm so the constructional demands on the mirrors are not too great. 
     An imaging optical system, wherein the imaging light is reflected to the image field by the mirror including the through-hole for the imaging light to pass through, in which the last mirror in the imaging light path includes the through-hole, can allow a high numerical aperture to be achieved in a compact construction with minimised imaging errors. 
     The advantages of a projection exposure installation including an imaging optical system, including a light source for the illumination and imaging light, and including a lens system for directing the illumination light to the object field of the imaging optical system, and wherein the light source for generating the illumination light is formed with a wavelength of between 10 and 30 mm, can correspond to those previously discussed with regard to the imaging optical system. The light source of the projection exposure installation may be in the form of a broadband light source and may have, for example, a bandwidth greater than 1 nm (e.g., greater than 10 nm, greater than 100 nm). In addition, the projection exposure installation may be constructed in such a way that it can be operated with light sources of different wavelengths. 
     Corresponding advantages can also apply to the production method including the steps of providing a reticle and a wafer, projecting a structure on the reticle onto a light-sensitive layer of the wafer by using the projection exposure installation and producing a microstructure on the wafer, and the microstructured component produced thereby. 
     Using the imaging optical system as a microlens, wherein the arrangement of the optical components when used in this way correspond to those on the condition that object plane and image plane are exchanged, and when inspecting a substrate which is to be exposed or has already been exposed with respect to projection exposure with a lithographic projection exposure instrallation, can result in the advantage that, in the region of the intermediate image, drilling through any very small mirrors can be avoided. 
     Embodiments of the disclosure will be described in the following in greater detail with reference to the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  schematically shows a projection exposure installation for microlithography; 
         FIG. 2  shows a cross-section through a projection optical system of the projection exposure installation in  FIG. 1  containing field points spaced from one another along an imaging light path; 
         FIG. 3  shows a plan view of an image field of the projection optical system in  FIG. 2  viewed from direction III in  FIG. 2 ; 
         FIG. 4  shows a cross-section through a non-rotationally-symmetrical free-form surface and through a rotationally symmetrical surface; 
         FIG. 5  shows a cross-section through a portion of a mirror of the projection optical system in  FIG. 2 ; 
         FIG. 6  schematically shows a light path onto a mirror in the projection optical system in  FIG. 2  with positive angular magnification of the principal ray; 
         FIG. 7  schematically shows a light path onto a mirror in the projection optical system in  FIG. 2  with a negative angular magnification of the principal ray; 
         FIG. 8  shows a similar view to  FIG. 1  of a projection exposure installation for microlithography; 
         FIG. 9  shows an enlarged partial detail of a wafer exposed with the projection exposure installation in  FIG. 1  or  8 , and a mirror adjacent thereto; 
         FIG. 10  shows a view similar to that of  FIG. 2  of a projection optical system; 
         FIG. 11  shows a view similar to that of  FIG. 2  of a projection optical system; 
         FIG. 12  shows a view similar to that of  FIG. 2  of a projection optical system; 
         FIG. 13  shows a view similar to that of  FIG. 11  of a microscope lens for inspecting wafers; 
         FIGS. 14 and 15  show two further views similar to that of  FIG. 2  of a projection optical system; and 
         FIGS. 16 and 17  show views similar to that of  FIG. 13  of a microscope lens for inspecting wafers. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , a projection exposure installation  1  for microlithography has a light source  2  for illumination light. The light source  2  is an EUV light source which produces light in a wavelength range of between 10 nm and 30 nm. Other EUV wavelengths are also possible. In general, even any desired wavelengths, for example visible wavelengths, are possible for the illumination light guided in the projection exposure installation  1 . A light path of the illumination light  3  is very schematically shown in  FIG. 1 . 
     A lens system  5  serves to guide the illumination light  3  to an object field in an object plane  4 . The object field is imaged by a projection optical system  6  in an image field  7  (cf.  FIG. 3 ) in an image plane  8  with a predetermined reduction scale. The projection optical system  6  reduces the size by a factor of 8. Other imaging magnification levels are also possible, for example 4×, 5×, 6× or even imaging magnification levels greater than 8×. An imaging magnification level of 8× is particularly suitable for illumination light with an EUV wavelength, since the object-side angle of incidence on a reflection mask can thereby remain small. An image-side aperture of the projection optical system of NA=0.5 produces an illumination angle of less than 6° on the object-side. An image magnification level of 8× does not require, in addition, unnecessarily large masks to be used. In the projection optical system  6  according to  FIG. 2 , the image plane  8  is arranged parallel to the object plane  4 . A portion of a reflective mask  9 , also known as a reticle, coinciding with the object field is hereby imaged. Imaging is achieved on the surface of a substrate  10  in the form of a wafer which is supported by a substrate holder  11 . In  FIG. 1 , a light beam  12  of the illumination light  3  entering the projection optical system  6  is shown schematically between the reticle  9  and the projection optical system, and a ray beam  13  of the illumination light  3  exiting from the projection optical system  6  is shown schematically between the projection optical system  6  and the substrate  10 . The image field-side numerical aperture of the projection optical system  6  in accordance with  FIG. 2  is 0.50. The projection optical system  6  is telecentric on the image side. 
     In order to aid the description of the projection exposure installation  1  an xyz cartesian coordinate system is provided in the drawings and shows the respective locations of the components represented in the figures. In  FIG. 1  the x direction extends perpendicularly into the drawing plane, the y direction extends to the right and the z direction extends downwards. 
     The projection exposure installation  1  is a scanner-type device. Both the reticle  9  and the substrate  10  are scanned in the y direction during operation of the projection exposure installation  1 . 
       FIG. 2  shows the optical construction of the projection optical system  6 . The light path of each of three individual rays  14 , coming from five object field points which, in  FIG. 2 , are on top of one another and are at a distance from one another in the y direction, is shown, the three individual rays  14  which belong to one of the five object field points each being associated to three different illumination directions for the five object field points. 
     From object field  4 , the individual rays  14  are initially reflected by a first mirror  15 , which is denoted in the following as mirror M 1 , and are subsequently reflected by further mirrors  16 ,  17 ,  18 ,  19 ,  20 , which are also denoted in the following as mirrors M 2 , M 3 , M 4 , M 5  and M 6  in the sequence of the light path. The projection optical system  6  in  FIG. 2  therefore has 6 reflective mirrors. The mirrors have a coating which is highly reflective for the wavelength of the illumination light, if required due to the wavelength, for example with EUV wavelengths. Radiation of greatly differing wavelengths may also be guided in the lens system  5  and the projection optical system  6 , since these optical systems have substantially achromatic properties. In these optical systems it is therefore possible, for example, to direct an adjusting laser or to operate an autofocusing system, at the same time using a wavelength for the illumination light that differs greatly from the operating wavelengths of the adjusting laser or the autofocusing system. An adjusting laser can thus operate at 632.8 nm, 248 nm or 193 nm, while, at the same time, an illumination light is operated in the range between 10 and 30 nm. 
     The mirrors  15 ,  17  and  19  have a convex basic shape and can thus be described by a convex best-fitted surface. The third mirror  17  in particular has a convex basic shape. The mirrors  16 ,  18  and  20  have a concave basic shape and can thus be described by a concave best-fitted surface. In the following description, this type of mirror is referred to in a simplified manner merely as convex or concave. The concave mirror  17  provides good Petzval correction in the projection optical system  6 . 
     The individual rays  14 , which come from spaced object field points and are associated with the same illumination direction, enter the projection optical system  6  in a convergent manner between the object plane  4  and the first mirror M 1 . The design of the projection optical system  6  can be adapted in such a way that the same illumination directions for the individual rays  14  associated with the object field points also extend in a divergent manner from, or in a parallel manner to, one another between these components. The latter variant corresponds to a telecentric light path on the object side. 
     The individual rays  14  belonging to a particular illumination direction of the five object field points  3  merge in a pupil plane  21  of the projection optical system  6 , adjacent to which the mirror  17  is arranged. The mirror  17  is therefore also known as a pupil mirror. An aperture stop may be arranged in the pupil plane  21  for limiting the illumination light ray beam. The aperture stop may be provided by a mechanical and removable stop or in the form of an appropriate coating applied directly to the mirror M 3 . 
     The mirrors  15  to  18  image the object plane  4  in an intermediate image plane  22 . The intermediate image-side numerical aperture of the projection optical system  6  is 0.2. The mirrors  15  to  18  form a first portion of the imaging optical system of the projection optical system  6  with a reducing magnification level of 3.2×. The following mirrors  19  and  20  form a further portion of the imaging optical system of the projection optical system  6  with a reducing magnification level of 2.5×. In the sixth mirror  20 , in the region of the intermediate image plane  22 , a through-hole  23  is formed, through which the illumination or imaging light  3  passes after reflection by the fourth mirror  18  towards the fifth mirror  19 . In turn, the fifth mirror  19  has a central through-hole  24  through which the ray beam  13  passes between the sixth mirror  20  and the image field  8 . 
     The fifth mirror  19 , which, together with the sixth mirror  20 , images the illumination or imaging light  3  from the intermediate image plane  22  in the image plane  8 , is arranged in the vicinity of a further pupil plane  25 , conjugate to the first pupil plane  21 , of the projection optical system  6 . The further pupil plane  25  is typically located in the light path of the imaging light  3  between the fifth mirror  19  and the sixth mirror  20 , so there is a physically accessible stop plane at the location of the further pupil plane  25 . An aperture stop can alternatively or additionally be arranged in this diaphragm plane, as previously described with respect to the aperture stop in the region of the pupil plane  21 . 
     The projection optical system  6  has an obscuration stop arranged centrally in one of the pupil planes  20 ,  25 . By this means the beam portions of the projection light path, associated with the central through-holes  23 ,  24  in the mirrors  20 ,  19 , are obscured. The construction of the projection optical system  6  can therefore also be termed construction with central pupil obscuration. 
     A marked individual ray  14 , which connects a central object field point to a centrally illuminated point in the entrance pupil of the projection optical system  6  in the entrance pupil plane  21 , will also be referred to in the following as the principal ray  26  of a central field point. The principal ray  26  of the central field point makes approximately a right angle with the image plane  8  after reflection on the sixth mirror  20  and thus extends approximately parallel to the z-axis of the projection exposure installation  1 . The angle is greater than 85° in any case. 
     The image field  7  is rectangular. The aspect ratio of the image field  7  is not shown to scale in  FIG. 3 . The image field  7  extends by 13 mm parallel to the x direction. The image field  7  extends by 1 mm parallel to the y direction. The image field  7  is located centrally behind the fifth mirror  19 , as shown in  FIG. 3 . A radius R of the through-hole  24  can be calculated from:
 
 R= 1/2 ·D+d   w   ·NA.  
     D is the diagonal of the image field  7 . d w  is the working distance of the mirror  19  from the image plane. NA is the numerical aperture on the image side.   

     All six mirrors  15  to  20  of the projection optical system  6  are in the form of free-form surfaces which cannot be described by a rotationally symmetrical function. Other configurations of the projection optical system  6  are also possible, in which at least one of the mirrors  15  to  20  includes a free-form reflection surface of this type. 
     Production of a free-form surface  27  of this type from a rotationally symmetrical reference surface  28  will be described in the following with reference to  FIG. 4 . First of all, information on the characterisation of the free-form surface under consideration is obtained. The reference surface  28  can, for example, be a rotationally symmetrical asphere. Part of the design information may be the radius of curvature of the reference surface  28 , which is also referred to as 1/c, c denoting the vertex curvature of the reference surface  28 . A conical constant k of the reference surface  28  and polynomial coefficients which describe the reference surface  28  are also part of the information. 
     Alternatively or additionally, the information characterising the reference surface  28  can also be obtained from a surface measurement of a reference mirror surface, for example, by using an interferometer. This type of surface measurement produces a function z′(x′, y′), which describes the reference surface  28 , z′ denoting the rising height of the reference surface  28  along the z′-axis for different (x′, y′) coordinates, as shown in  FIG. 4 . 
     This first step in designing the free-form surface also includes determining the portion of the mirror surface, which is only defined by the surface description and is initially unlimited, that will actually be used for reflecting illumination or imaging light  3  during imaging of the object field in the image field  7 . The region is also referred to as the footprint. The footprint of the mirror can be at least approximately determined by ray tracing of the projection optical system  6 . Examples for a possible footprint in the x dimension are provided in  FIG. 4 . x min  refers to the lower limit and x max  refers to the upper limit for the exemplary footprint. The data above x max  and below x min  are similarly calculated within specific limits so that no undesired edge effects arise when determining the free-form surface  27 . 
     After the information characterising the reference surface  28  has been determined, a local coordinate system for the reference surface  28  is introduced, in which both decentration and tilting of the reference surface  28  are zero. The z′-axis is thus the axis of rotational symmetry of the aspherical reference surface  28  or, if the reference surface was obtained by a surface measurement, the optical axis of the measuring device, for example the interferometer. The z′-axis is generally displaced parallel to and tilted relative to the z-axis of the xyz coordinate system of the projection exposure installation  1 . This also applies to the other coordinate axes x′, y′. This parallel displacement or tilting is determined in the initial step in the optical design of the free-form surface. 
     As an alternative to an asphere, the reference surface  28  may also be a spherical surface. The origin of the coordinates x c , y c , z c  for describing the spherical reference surface  28  generally differs from the origin of the xyz coordinate system of the projection exposure installation  1 . 
     After the reference surface  28  has been determined, a local distance d i  (i=1 . . . N) between a number of points on the reference surface  28  and points on the free-form surface  27  parallel to the z′-axis is determined. The different local distances d i  are then varied until a set of secondary conditions is satisfied. The secondary conditions are predetermined limit values for specific imaging errors and/or illumination properties of the projection optical system  6 . 
     The free form surface can be mathematically described by the following equation: 
     
       
         
           
             Z 
             = 
             
               
                 
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                     j 
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                   66 
                 
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                     C 
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                     X 
                     m 
                   
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                     Y 
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             in 
             ⁢ 
             
                 
             
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             ⁢ 
             
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             j 
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                         m 
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         Z is the rising height of the free-form surface parallel to a Z-axis which can, for example be parallel to the z′-axis in  FIG. 4 . 
         c is a constant corresponding to the vertex curvature of a corresponding asphere. k corresponds to a conical constant of a corresponding asphere. C j  are the coefficients of the monomials X m  Y n  . The values of c, k and C j  are generally determined on the basis of the desired optical properties of the mirror inside the projection optical system  6 . The order of the monomial, m+n, can be varied as desired. A monomial of a higher order can lead to a design of the projection optical system with improved image error correction, but is, however, more complex to calculate. m+n can have values of between 3 and more than 20. 
       
    
     Free-form surfaces can also be described mathematically by Zernike polynomials, which are described, for example, in the manual of the optical design program CODE V®. Alternatively, free-form surfaces can be described with two-dimensional spline surfaces. Examples thereof are Bezier curves or non-uniform rational basis splines (NURBS). Two-dimensional spline surfaces can be described, for example, by a grid of points in an xy-plane and related z-values, or by the points and their related gradients. Depending on the respective type of spline surface, the complete surface will be obtained by interpolating between the grid points by using, for example, polynomials or functions which have specific properties with respect to their continuity and differentiability. Examples thereof include analytical functions. 
     The mirrors  15  to  20  have multiple reflective coatings for optimising the reflection thereof for the incident EUV illumination light  3 . Reflection is better the closer the angle of incidence of the individual rays  14  on the mirror surface is to the perpendicular incidence. The projection optical system  6  has very small angles of reflection for all of the individual rays  14 . Half of the angle between the individual ray  14  striking a point on one of the mirrors  15  to  20  and the individual ray  14  reflected from this point will be referred to in the following as the angle of reflection of this point. 
     The maximum angle of reflection in the projection optical system  6  is the angle of the individual ray  14  at the outer edge of the fifth mirror  19 . This angle α is approximately 16° in the projection optical system  6 . The quotient of the maximum angle of reflection α and the numerical aperture is thus 32° in the projection optical system  6  shown in  FIG. 2 . The dependence of the size of the angle of reflection on the position of the point of incidence on the reflection mirror will be explained schematically in the following with an example of a sample reflection mirror  29 , shown in  FIG. 5 . In the picture a divergent beam of individual rays  14   a ,  14   b ,  14   c  strikes a reflection surface  30  of the sample reflection mirror  29 . The reflection surface  30  is convex. Due to the collective effect of the reflection surface  30 , the incident descending beam made of individual rays  14   a ,  14   b  and  14   c  is deflected forming a reflected convergent beam. The individual ray  14   a  striking closest to the edge on the reflection surface  30  is deflected with the largest angle of reflection α, the centre individual ray  14   b  is deflected with an angle of reflection β which is smaller in comparison thereto and the individual ray  14   c  furthest from the edge of the sample reflection mirror  29  is deflected by the smallest angle of reflection γ. 
     The light path within the projection optical system  6  can additionally be characterised by the sequence of angular magnification of the principal ray. This will be explained in the following with reference to the schematic drawings  6  and  7 . In  FIG. 6 , the principal ray  26  is radiated onto a sample reflection mirror  31  at an angle α to a reference axis  32  extending perpendicular to the object plane  4  of the projection exposure installation  1 . On the side of the object field, i.e. up to and inclusive of the mirror M 4 , the reference axis  32  is additionally defined by the centre of the object field. The reference axis  32  generally does not coincide with the z-axis but runs parallel to the axis. After being reflected by the sample reflection mirror  31 , the principal ray  26  is reflected back at an angle β to the reference axis  32 . Since both angles α, β are between 0 and 90°, the quotient tan α/tan β is positive. The sample reflection mirror  31  therefore has a positive angular magnification of the principal ray. 
       FIG. 7  shows the case of negative angular magnification of the principal ray. The incident principal ray  26  intersects the reference axis  32  at an angle α which is between 0 and 90°. The principal ray  26  reflected by a sample reflection mirror  33  virtually encloses an angle β between 90 and 180° with the reference axis  32 . In this case the quotient tanα/tanβ is thus negative. 
     In the projection optical system  6 , the first mirror  15  has negative angular magnification of the principal ray. The second mirror  16  has positive angular magnification of the principal ray. The third mirror  17  has negative angular magnification of the principal ray. The angular magnification of the fourth mirror  18  is infinite, since the angle β is 180° at that location. 
       FIG. 8  again shows a slightly modified representation of the projection exposure installation  1  for clearly showing a further characterising value of the projection optical system  6 , namely the object-image shift d ois . This is defined as the distance between a perpendicular projection of the central object point onto the image plane  8  and the central image point. In the projection optical system  6  shown in  FIG. 2 , the object-image shift d ois  is less than 1 mm. 
       FIG. 9  demonstrates a further characteristic of the projection optical system  6 , namely the free working distance d w . This is defined as the distance between the image plane  8  and the closest portion  34  thereto of one of the mirrors of the projection optical system  6 , i.e. mirror  19  in the embodiment shown in  FIG. 2 . 
     In the projection optical system  6 , the free working distance d w  is 40 mm. The fifth mirror  19 , which is closest to the image plane  8 , can therefore be constructed having a thickness that provides sufficient stability of the fifth mirror  19 . Materials for mirrors of this type include, for example, quartz, zerodur or silicon carbide compounds. Other materials with ultra low expansion properties may also be used. Examples of materials of this type are known from products sold by Corning, USA, under the name “ULE”. 
     The optical data of the projection optical system  6  are summarised in the following: 
     The image-side numerical aperture NA is 0.5. The size of the image field is 1×13 mm 2 . The reducing magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light is 13.5 nm. The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is NPNPNP. Principal rays enter the projection optical system in a convergent manner from the object plane. An aperture stop is arranged on the mirror M 3  for limiting the illumination light at the edge. The z-distance between the object plane  4  and the image plane  8  is 1,500 mm. The object-image shift is 0.42 mm. 5.9% of the illuminated surfaces in the pupil planes are obscured. The projection optical system has a wave front error (rms) of 0.02 in units of the wavelength of the illumination light  3 . The distortion is 12 nm. The field curvature is 9 nm. The angle of the principal ray at the central object field point is 5.9°. The mirror M 1  has dimensions (x/y) of 117×61 mm 2 . The mirror M 2  has dimensions of 306×143 mm 2 . The mirror M 3  has dimensions of 80×77 mm 2 . The mirror M 4  has dimensions of 174×126 mm 2 . The mirror M 5  has dimensions of 253×245 mm 2 . The mirror M 6  has dimensions of 676×666 mm 2 . The sequence of the principal ray angle of incidence, of the principal ray  26  of the central object field point, on the mirrors M 1  to M 6  is 16.01°, 7.14° 13.13°, 7.21°, 0.0° and 0.0°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 22.55°, 9.62°, 13.90°, 10.16°, 16.23°, 4.37°. The sequence of bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 13.12°, 5.07°, 1.58°, 6.10°, less than 16.23° and less than 4.37°. The working distance in the object plane  4  is 100 mm. The working distance in the image plane  8  is 40 mm. The ratio of the distance between the object plane  4  and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 4.25. Between each of the adjacent mirrors M 2 -M 3 , M 4 -M 5 , M 5 -M 6  and also between the mirror M 6  and the image plane  8  there is a distance of greater than 40% of the z-distance between the object plane  4  and the image plane  8 . The mirrors M 1  and M 4  have a minimum distance from the used reflection surface to the closest imaging light path not acting on the mirror (free board) of less than 25 mm. 
     The optical design data of the reflection surfaces of the mirrors M 1  to M 6  of the projection optical system  6  can be gathered from the following tables. The first of the tables shows the respective reciprocal value of the vertex curvature (radius) and a distance value (thickness), which corresponds to the z-distance of adjacent elements in the light path, starting from the object plane, for the optical components and the aperture stop. The second table shows the coefficients C j  of the monomials X m Y n  in the aforementioned free-form surface equation for the mirrors M 1  to M 6 . At the end of the second table the value by which the respective mirror is decentred (Y-decenter) and rotated (X-rotation) from a mirror reference design is given in millimeters. This corresponds to the parallel displacement and tilting in the free-form surface design method described above. Displacement thus takes place in the y direction and tilting takes place about the x axis. The angle of rotation is given in degrees. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 425.420 
                   
               
               
                   
                 Mirror 1 
                 294.947 
                 −325.420 
                 REFL 
               
               
                   
                 Mirror 2 
                 681.039 
                 690.757 
                 REFL 
               
               
                   
                 Mirror 3 
                 319.431 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 −244.337 
               
               
                   
                 Mirror 4 
                 396.876 
                 913.580 
                 REFL 
               
               
                   
                 Mirror 5 
                 1749.322  
                 −620.710 
                 REFL 
               
               
                   
                 Mirror 6 
                 834.214 
                 660.710 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Coefficient 
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
               
             
             
               
                 K 
                 −8.972907E−01   
                 −2.722153E−01   
                 6.009025E+00 
                 −2.083103E−01   
                 3.438760E+01 
                 3.027724E−01 
               
               
                 Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2 
                 −6.723739E−04   
                 −9.397624E−05   
                 −5.616960E−04   
                 −1.596929E−04   
                 9.008585E−06 
                 3.436254E−05 
               
               
                 Y2 
                 −7.259542E−04   
                 −1.245430E−04   
                 −4.962660E−04   
                 −1.209634E−04   
                 2.711820E−06 
                 3.328586E−05 
               
               
                 X2Y 
                 −2.611787E−07   
                 9.438147E−09 
                 −6.471824E−07   
                 −1.397345E−07   
                 −3.166886E−08   
                 4.403654E−10 
               
               
                 Y3 
                 1.848873E−07 
                 2.540415E−08 
                 4.939085E−07 
                 −1.842875E−07   
                 5.311486E−09 
                 6.726500E−10 
               
               
                 X4 
                 −5.585253E−10   
                 −3.707750E−11   
                 −2.414232E−08   
                 −1.057114E−10   
                 9.436063E−10 
                 1.898115E−12 
               
               
                 X2Y2 
                 −1.454988E−09   
                 −1.447610E−10   
                 −4.434814E−08   
                 −5.420267E−11   
                 1.946694E−09 
                 4.974829E−12 
               
               
                 Y4 
                 −5.523329E−09   
                 −2.392090E−11   
                 −1.815299E−08   
                 4.380159E−10 
                 9.997897E−10 
                 3.488151E−12 
               
               
                 X4Y 
                 −1.364069E−12   
                 1.084325E−15 
                 −3.114225E−11   
                 −1.197000E−12   
                 5.182403E−14 
                 4.428526E−16 
               
               
                 X2Y3 
                 6.732062E−12 
                 1.382697E−13 
                 9.802932E−11 
                 −1.950774E−12   
                 4.779360E−13 
                 1.769320E−16 
               
               
                 Y5 
                 3.635430E−11 
                 0.000000E+00 
                 7.767198E−11 
                 −1.559300E−12   
                 3.401358E−13 
                 4.373202E−16 
               
               
                 X6 
                 −2.750390E−15   
                 −9.087823E−17   
                 −9.415776E−13   
                 −4.463189E−16   
                 1.620585E−15 
                 9.932173E−19 
               
               
                 X4Y2 
                 2.324635E−14 
                 −5.352295E−17   
                 −3.094331E−12   
                 7.684993E−15 
                 5.526453E−15 
                 3.332327E−18 
               
               
                 X2Y4 
                 3.956161E−15 
                 −2.030722E−16   
                 −3.217471E−12   
                 3.107748E−15 
                 5.847027E−15 
                 3.759258E−18 
               
               
                 Y6 
                 −1.092384E−13   
                 −8.567898E−17   
                 −7.281446E−13   
                 −7.204126E−16   
                 1.552120E−15 
                 1.038153E−18 
               
               
                 X6Y 
                 −1.179589E−16   
                 4.377060E−19 
                 −1.789065E−16   
                 −1.451963E−19   
                 3.245847E−19 
                 1.324484E−22 
               
               
                 X4Y3 
                 −2.570887E−16   
                 0.000000E+00 
                 1.023466E−14 
                 −4.269245E−17   
                 1.564405E−18 
                 −9.051915E−22   
               
               
                 X2Y5 
                 −8.917936E−17   
                 7.695621E−21 
                 1.492914E−14 
                 −1.217398E−17   
                 2.326082E−18 
                 −1.811267E−22   
               
               
                 Y7 
                 1.236168E−16 
                 0.000000E+00 
                 4.771084E−15 
                 5.163018E−18 
                 7.533041E−19 
                 2.904675E−22 
               
               
                 X8 
                 7.305784E−20 
                 −2.087892E−22   
                 −4.992347E−17   
                 −9.852110E−22   
                 5.510114E−21 
                 −9.878544E−26   
               
               
                 X6Y2 
                 6.107242E−19 
                 −8.775175E−22   
                 −2.298856E−16   
                 −2.713369E−20   
                 2.453885E−20 
                 6.254655E−25 
               
               
                 X4Y4 
                 5.443174E−19 
                 −2.629666E−22   
                 −3.296922E−16   
                 3.809184E−20 
                 3.817638E−20 
                 4.270350E−24 
               
               
                 X2Y6 
                 −6.091249E−19   
                 −8.692919E−23   
                 −1.689920E−16   
                 3.730606E−21 
                 2.483560E−20 
                 4.657493E−24 
               
               
                 Y8 
                 −2.536724E−19   
                 8.059798E−24 
                 −2.318537E−17   
                 −7.839829E−21   
                 6.692413E−21 
                 1.504196E−24 
               
               
                 X8Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y9 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Nradius 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
               
               
                 Y-decenter 
                 68.139 
                 −264.855 
                 176.907 
                 −28.983 
                 101.914 
                 97.590 
               
               
                 X-rotation 
                 −1.258 
                 25.000 
                 1.304 
                 25.000 
                 0.098 
                 0.498 
               
               
                   
               
             
          
         
       
     
       FIG. 10  shows a projection optical system  35 , which can be used, instead of the projection optical system  6 , in the projection exposure installation  1 . Components or reference quantities which correspond to those which have previously been described with reference to  FIGS. 1 to 9  have the same reference numerals and will not be discussed in detail again. 
     The projection optical system  35  also has a total of six reflective mirrors, which, starting from the object plane  4  in the light path sequence, have reference numerals  36  to  41 , and will also be referred to in the following as mirrors M 1  to M 6 . The mirrors  36  to  41  all have reflective free-form surfaces which cannot be described by a rotationally symmetrical function. The mirrors  36 ,  38  and  40  have a convex basic shape and the mirrors  37 ,  39 ,  41  have a concave basic shape. 
     The projection optical system  35  has a reduction factor of 8. The projection optical system  36  has an image-side numerical aperture of 0.5. The dimensions of the image field  7  of the projection optical system  35  are exactly the same as those of the projection optical system  6 . The intermediate image-side numerical aperture is 0.28. 
     The first mirror  36  has negative angular magnification of the principal ray. The second mirror  37  has positive angular magnification of the principal ray. The third mirror  38  has negative angular magnification of the principal ray. The fourth mirror  39  has infinite angular magnification of the principal ray since the principal ray  26  extends from the fourth mirror  39  so as to be perpendicular to the image plane  8 . 
     In the projection optical system  35 , the object-image shift is markedly greater than in the projection optical system  6  and is 134 mm. 
     The maximum angle of reflection α, which is also achieved by the rays at the edge of the fifth mirror  40  in the projection optical system  35 , is 17°. The quotient of the maximum angle of reflection α and the image-side numerical aperture is 34°. 
     At 42 mm, the free working distance d w  in the projection optical system  35  is comparable with the free working distance of the projection optical system  6 . 
     The optical data of the projection optical system  35  are summarised again in the following: 
     The image-side numerical aperture NA is 0.5. The dimensions of the image field  7  are 1×13 mm 2 . The reducing magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light  3  is 13.5 nm. The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is PPNPNP. At the image-side, the projection optical system  35  is virtually telecentric. An aperture stop for limiting the illumination light at the edge is arranged on mirror M 3 . The z-distance between the object plane  4  and the image plane  8  is 1,823 mm. The object-image shift is 134 mm. 9.2% of the surfaces illuminated in the pupil planes are obscured. The angle of the principal ray at the central object field point is 6°. The mirror M 1  has dimensions (x/y) of 241×138 mm 2 . The mirror M 2  has dimensions of 377×269 mm 2 . The mirror M 3  has dimensions of 80×75 mm 2 . The mirror M 4  has dimensions of 246×197 mm 2 . The mirror M 5  has dimensions of 352×304 mm 2 . The mirror M 6  has dimensions of 776×678 mm 2 . The sequence of the angle of incidence of the principal ray of the central object field point on the mirrors M 1  to M 6  is 7.10°, 5.19°, 13.66°, 4.60°, 0.0° and 0.02°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 12.23°, 5.53°, 15.43°, 7.33°, 16.98° and 5.51°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 9.93°, 0.78°, 2.98°, 5.27°, less than 16.98° and less than 5.51°. The working distance in the object plane  4  is 336 mm. The working distance in the image plane  8  is 42 mm. The ratio of the distance between the object plane  4  and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 3.04. The mirrors M 1  to M 4  have a minimum distance between the used reflection surface and the closest imaging light path which does not act upon the mirror (free board) of less than 25 mm. The distance between the object plane  4  and the mirror M 1  and the distances between the pairs of mirrors M 2 -M 3  and M 4 -M 5  is greater than 40% of the distance between the object plane and the image plane. 
     The optical design data of the reflection surfaces of the mirrors M 1  to M 6  of the projection optical system  35  can be gathered from the following tables, which correspond to the tables for the projection optical system in accordance with  FIG. 2 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 1023.157 
                   
               
               
                   
                 Mirror 1 
                 −50610.892 
                 −686.714 
                 REFL 
               
               
                   
                 Mirror 2 
                 1171.238 
                 828.471 
                 REFL 
               
               
                   
                 Mirror 3 
                 318.004 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 −378.086 
               
               
                   
                 Mirror 4 
                 413.560 
                 994.620 
                 REFL 
               
               
                   
                 Mirror 5 
                 2997.146 
                 −612.464 
                 REFL 
               
               
                   
                 Mirror 6 
                 817.300 
                 654.356 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Coeff. 
                   
                   
                   
                   
                   
                   
               
               
                 K 
                 4.156869E+03 
                 4.620221E−02 
                 9.990462E+00 
                 −9.081861E−03   
                 −2.372322E−01   
                 6.789706E−03 
               
               
                 Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2 
                 4.219939E−05 
                 −7.203705E−05   
                 −2.856541E−04   
                 −1.831594E−04   
                 −4.114605E−05   
                 2.674563E−06 
               
               
                 Y2 
                 −2.952066E−04   
                 −8.835077E−05   
                 1.576757E−04 
                 −1.812758E−04   
                 −3.733421E−05   
                 7.346415E−06 
               
               
                 X2Y 
                 −2.987815E−08   
                 1.958263E−08 
                 4.843132E−07 
                 −7.966262E−08   
                 −5.183892E−08   
                 −3.629397E−09   
               
               
                 Y3 
                 5.768104E−07 
                 8.430075E−08 
                 −7.326854E−08   
                 −9.457440E−08   
                 −2.814518E−08   
                 9.209304E−11 
               
               
                 X4 
                 2.110770E−10 
                 2.081353E−11 
                 1.569949E−08 
                 −3.236129E−10   
                 3.542926E−11 
                 1.915378E−12 
               
               
                 X2Y2 
                 3.100857E−10 
                 −1.622544E−11   
                 3.080477E−08 
                 −6.357050E−10   
                 8.409285E−11 
                 4.860251E−12 
               
               
                 Y4 
                 −2.322578E−10   
                 −4.348550E−11   
                 −9.859142E−09   
                 −1.882466E−10   
                 −2.084652E−11   
                 6.490959E−14 
               
               
                 X4Y 
                 0.000000E+00 
                 −7.908907E−15   
                 0.000000E+00 
                 1.810068E−13 
                 1.675236E−13 
                 −2.002515E−15   
               
               
                 X2Y3 
                 0.000000E+00 
                 1.426458E−14 
                 0.000000E+00 
                 −2.244745E−13   
                 1.806451E−13 
                 −1.799322E−15   
               
               
                 Y5 
                 0.000000E+00 
                 −1.321548E−14   
                 0.000000E+00 
                 −2.730307E−13   
                 −1.337121E−14   
                 3.920622E−16 
               
               
                 X6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y9 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Nradius 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
               
               
                 Coefficient 
               
               
                 Y-decenter 
                 −242.949 
                 −116.015 
                 15.485 
                 −94.370 
                 162.630 
                 −15.854 
               
               
                 X-rotation 
                 −2.051 
                 4.274 
                 −4.892 
                 10.143 
                 −3.797 
                 −2.652 
               
               
                   
               
             
          
         
       
     
       FIG. 11  shows a further configuration of a projection optical system  42  which may be used, instead of the projection optical system  6 , in the projection exposure installation  1 . 
     Components or reference quantities which correspond to those which have previously been explained with reference to  FIGS. 1 to 10  have the same reference numerals and will not again be discussed in detail. 
     The projection optical system  42  also has six reflection mirrors which are denoted by the reference numerals  43  to  48  in accordance with their sequence in the imaging light path, starting from the object plane  4 . The mirrors will also be referred to in the following as M 1  to M 6 . In the projection optical system  42 , all of the reflection surfaces are formed as free-form surfaces which cannot be described by a rotationally symmetrical function. 
     The first mirror  43  is concave, but has only a very slight curve so that it can be simply modified to form a mirror with a zero base curve or to form a convexly curved mirror. The second mirror  44  is concave and the third mirror  45  is convex. The fourth mirror  46  is concave. The fifth mirror  47  is convex. The sixth mirror  48  is concave. 
     Each of the first three mirrors  43  to  45  has negative angular magnification of the principal ray. The angular magnification of the principal ray of the fourth mirror  46  is infinite since the principal ray  26  extends perpendicular to the image plane  8  after reflection by the fourth mirror  46 . 
     The projection optical system  42  has an image-side numerical aperture of 0.5. The projection optical system  42  has an intermediate image-side numerical aperture of 0.11. 
     In the projection optical system  42 , the free working distance d w  is 20 mm. 
     The projection optical system  42  has a reduction factor of 8. 
     The dimensions of the image field in the projection optical system  42  correspond to those of the projection optical systems  6  and  35 . 
     In the projection optical system  42 , the maximum angle of reflection also occurs in the outer edge rays reflected on the fifth mirror  47  and is α=16°. The quotient of the maximum angle of reflection of the illumination light  3  within the projection optical system  42  and the image-side numerical aperture is  32 . 
     The optical data of the projection optical system  42  are again summarised in the following: 
     The image-side numerical aperture NA is 0.5. The dimensions of the image field are 1×13 mm 2 . The reducing imaging magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light  3  is 13.5 nm. The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is PPNPNP. Principal rays enter convergently into the projection optical system  42  from the object plane  4 . An aperture stop is arranged on the mirror M 2  for limiting the illumination light at the edge. The z-distance between the object plane  4  and the image plane  8  is 1,700 mm. The object-image shift is 393 mm. 17.0% of the surfaces illuminated in the pupil planes are obscured. The projection optical system  42  has a wavefront error (rms) of 0.100 in units of the wavelength of the illumination light  3 . The distortion is 16 nm. The image field curvature is 35 nm. The angle of the principal ray at the central object field point is 6°. The mirror M 1  has dimensions (x/y) of 164×134 mm 2 . The mirror M 2  has dimensions of 312×170 mm 2 . The mirror M 3  has dimensions of 147×155 mm 2 . The mirror M 4  has dimensions of 354×196 mm 2 . The mirror M 5  has dimensions of 103×96 mm 2 . The mirror M 6  has dimensions of 457×444 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point on the mirrors M 1  to M 6  is 3.54°, 5.15°, 9.11°, 4.45°, 0.01° and 0.01°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 6.18°, 5.62°, 9.80°, 6.85°, 15.94°, and 2.36°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 5.16°, 1.08°, 1.52°, 4.63°, less than 15.94° and less than 2.38°. The working distance in the object plane  4  is 200 mm. The working distance in the image plane  8  is 20 mm. The ratio of the distance between the object plane  4  and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 5.07. The mirrors M 1  and M 2  have a minimum distance between the used reflection surface and the closest imaging light path which does not act upon the mirror (free board) of less than 25 mm. The distance between the object plane  4  and the mirror M 1  and the distances between the pairs of mirrors M 1 -M 2 , M 2 -M 3 , M 3 -M 4  and M 4 -M 5  are greater than 40% of the distance between the object plane and the image plane. 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 6  of the projection optical system  42  can be gathered from the following tables, which correspond to the tables previously provided for the projection optical system  6  in accordance with  FIG. 2 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 1014.317 
                   
               
               
                   
                 Mirror 1 
                 −2704.152    
                 −814.317 
                 REFL 
               
               
                   
                 Mirror 2 
                 531.833 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 935.139 
               
               
                   
                 Mirror 3 
                 491.748 
                 −718.533 
                 REFL 
               
               
                   
                 Mirror 4 
                 870.221 
                 1263.419 
                 REFL 
               
               
                   
                 Mirror 5 
                 245.485 
                 −424.886 
                 REFL 
               
               
                   
                 Mirror 6 
                 495.477 
                 444.861 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Coeff. 
                   
                   
                   
                   
                   
                   
               
               
                 K 
                 1.144605E+01 
                 −9.050341E−01   
                 −1.089239E+00   
                 −6.248739E−01   
                 2.948620E+00 
                 1.091603E−01 
               
               
                 Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2 
                 2.857150E−04 
                 −5.920234E−04   
                 −2.610462E−04   
                 −1.368396E−04   
                 −4.475618E−04   
                 1.730506E−05 
               
               
                 Y2 
                 9.176083E−05 
                 −8.321210E−04   
                 −7.892918E−04   
                 −2.573840E−04   
                 −4.405714E−04   
                 1.563424E−05 
               
               
                 X2Y 
                 7.455682E−07 
                 −9.307510E−09   
                 4.809832E−08 
                 3.116002E−08 
                 4.341012E−09 
                 −3.269435E−09   
               
               
                 Y3 
                 4.605832E−08 
                 −1.943924E−07   
                 −2.212409E−07   
                 7.169569E−09 
                 −4.274845E−07   
                 −4.266065E−09   
               
               
                 X4 
                 −3.659110E−10   
                 −1.644174E−11   
                 8.510237E−10 
                 1.713005E−11 
                 2.190981E−09 
                 1.081076E−11 
               
               
                 X2Y2 
                 −1.689952E−09   
                 −3.435735E−10   
                 6.957800E−12 
                 −9.146320E−12   
                 −5.946668E−09   
                 2.690241E−11 
               
               
                 Y4 
                 −2.561746E−10   
                 −6.556489E−10   
                 1.590530E−10 
                 3.880664E−13 
                 −1.024229E−08   
                 −1.427930E−12   
               
               
                 X4Y 
                 −3.302144E−12   
                 −1.451447E−13   
                 −3.859663E−12   
                 4.923124E−14 
                 −2.729947E−11   
                 −2.149830E−14   
               
               
                 X2Y3 
                 −2.296129E−12   
                 2.463662E−13 
                 4.902075E−12 
                 4.230604E−14 
                 −2.255029E−11   
                 5.867643E−15 
               
               
                 Y5 
                 4.869118E−13 
                 2.042378E−12 
                 −5.901335E−13   
                 −2.503638E−15   
                 −1.535539E−11   
                 1.362505E−14 
               
               
                 X6 
                 2.532299E−14 
                 3.607331E−16 
                 −3.635906E−15   
                 −1.910942E−17   
                 5.572070E−14 
                 1.020771E−17 
               
               
                 X4Y2 
                 1.050746E−14 
                 3.556935E−15 
                 6.819544E−14 
                 1.635726E−16 
                 4.514505E−13 
                 3.413101E−17 
               
               
                 X2Y4 
                 2.215727E−14 
                 8.029448E−15 
                 −1.161921E−14   
                 −1.548212E−17   
                 −4.560072E−13   
                 −1.111206E−17   
               
               
                 Y6 
                 −9.649794E−16   
                 7.587037E−15 
                 4.555774E−16 
                 1.222675E−17 
                 −3.875470E−13   
                 −2.539409E−17   
               
               
                 X6Y 
                 −1.936844E−16   
                 −4.478100E−19   
                 9.189317E−17 
                 3.837055E−19 
                 −3.689123E−15   
                 −6.718113E−20   
               
               
                 X4Y3 
                 5.354672E−17 
                 1.140666E−17 
                 −4.339139E−16   
                 2.254755E−19 
                 −3.854918E−15   
                 7.351666E−20 
               
               
                 X2Y5 
                 −3.646598E−17   
                 3.260549E−17 
                 −2.644153E−17   
                 −8.425001E−20   
                 9.184510E−16 
                 1.186287E−19 
               
               
                 Y7 
                 6.063079E−19 
                 9.615056E−17 
                 1.324974E−18 
                 −1.850786E−21   
                 −2.798829E−15   
                 6.587133E−20 
               
               
                 X8 
                 5.617315E−19 
                 1.744698E−21 
                 8.327575E−19 
                 2.970358E−21 
                 4.324289E−18 
                 5.187555E−23 
               
               
                 X6Y2 
                 5.094397E−19 
                 3.594344E−20 
                 −9.344050E−19   
                 2.069107E−21 
                 4.500525E−17 
                 3.412692E−23 
               
               
                 X4Y4 
                 −2.079112E−19   
                 1.260510E−19 
                 1.229358E−18 
                 −7.743007E−23   
                 −2.240628E−17   
                 6.720118E−23 
               
               
                 X2Y6 
                 −1.595633E−20   
                 1.627768E−19 
                 −2.763971E−20   
                 1.708991E−22 
                 −4.013864E−17   
                 2.519384E−23 
               
               
                 Y8 
                 1.940634E−21 
                 4.827783E−19 
                 5.031625E−21 
                 −1.299209E−23 
                 −6.317984E−18   
                 −9.073694E−23   
               
               
                 X8Y 
                 −3.793003E−21   
                 2.116730E−23 
                 −7.801057E−21   
                 1.432927E−23 
                 −4.043104E−19   
                 −8.431854E−26   
               
               
                 X6Y3 
                 −6.345560E−22   
                 2.804678E−22 
                 4.289367E−21 
                 2.349972E−24 
                 −4.743148E−19   
                 5.385876E−25 
               
               
                 X4Y5 
                 −1.925796E−22   
                 9.316727E−22 
                 −1.053643E−21   
                 −3.225767E−25   
                 1.860041E−19 
                 1.381096E−24 
               
               
                 X2Y7 
                 8.214685E−23 
                 2.388724E−21 
                 8.375537E−22 
                 2.766796E−25 
                 1.013965E−19 
                 1.617787E−24 
               
               
                 Y9 
                 1.703546E−24 
                 4.526481E−21 
                 −2.966098E−23   
                 1.800745E−26 
                 3.422243E−22 
                 6.810995E−25 
               
               
                 X10 
                 1.991274E−24 
                 5.335545E−26 
                 1.741970E−24 
                 7.205669E−28 
                 0.000000E+00 
                 −5.791957E−28   
               
               
                 X8Y2 
                 6.491228E−24 
                 1.977752E−24 
                 1.571441E−23 
                 1.716942E−26 
                 0.000000E+00 
                 −1.179271E−26   
               
               
                 X6Y4 
                 4.259954E−25 
                 7.623140E−24 
                 −1.086567E−23   
                 0.000000E+00 
                 0.000000E+00 
                 −1.124411E−26   
               
               
                 X4Y6 
                 8.190088E−25 
                 1.642262E−23 
                 −1.531617E−24   
                 0.000000E+00 
                 0.000000E+00 
                 −6.908146E−27   
               
               
                 X2Y8 
                 −3.305040E−26   
                 2.718356E−23 
                 −1.734683E−24   
                 4.000570E−29 
                 0.000000E+00 
                 −4.575592E−27   
               
               
                 Y10 
                 −5.699224E−27   
                 2.657964E−23 
                 5.982496E−26 
                 4.841412E−30 
                 0.000000E+00 
                 −1.211899E−27   
               
               
                 Nradius 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
                   1.00E+00 
               
               
                 Coefficient 
               
               
                 Y-decenter 
                 −262.562 
                 −14.529 
                 −294.373 
                 184.266 
                 −286.525 
                 −283.609 
               
               
                 X-rotation 
                 −5.767 
                 −4.073 
                 2.602 
                 −13.391 
                 0.685 
                 0.041 
               
               
                   
               
             
          
         
       
     
       FIG. 12  shows a projection optical system  49  which can be used in the projection exposure installation  1  in the case of UV illumination instead of the projection optical system  6 . Components or reference quantities which correspond to those which have been previously explained with reference to  FIGS. 1 to 11  have the same reference numerals and will not be discussed in detail again. 
     The projection optical system  49  also has six reflection mirrors which are denoted with the reference numerals  50  to  55  in accordance with their sequence in the imaging light path, from the object plane  4 . The mirrors will also be referred to in the following as M 1  to M 6 . In the projection optical system  49 , all of the reflection surfaces are formed as free-form surfaces which cannot be described by a rotationally symmetrical function. 
     In the configuration shown in  FIG. 12 , the sequence of the base curves of the mirror is the same as in the configuration of  FIG. 11 . Again, the first mirror is only very slightly curved and can thus be simply converted into a mirror with a zero base curve (planar base curve) or to a mirror with a convex base curve. 
     Each of the first three mirrors  50  to  52  has negative angular magnification of the principal ray. The angular magnification of the principal ray of the fourth mirror  53  is infinite since the principal ray  26  extends perpendicular to the image plane  8  after reflection on the fourth mirror  53 . 
     The projection optical system  49  has an image-side numerical aperture of 0.7. The projection optical system  49  has an intermediate image numerical aperture of 0.14. 
     In the projection optical system  49 , the free working distance d w  is 20 mm. 
     The projection optical system  49  has a reduction factor of 8. 
     In the projection optical system  49 , the image field dimensions correspond to those of the projection optical systems  6 ,  35  and  42 . The image field dimensions are 13×1 mm 2 . 
     In the projection optical system  49 , the maximum angle of reflection also occurs in the outer edge rays reflected on the fifth mirror  54  and is α=23.8°. The quotient of the maximum angle of reflection of the imaging light  3  within the projection optical system and the image-side numerical aperture is 34°. 
     The optical data for the projection optical system  49  are again summarised in the following: 
     The image-side numerical aperture NA is 0.7. The dimensions of the image field  7  are 1×13 mm 2 . The reducing magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light  3  is 193.0 nm. The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is PPNPNP. Principal rays enter the projection optical system  49  in a convergent manner from the object plane  4 . An aperture stop is arranged on the mirror M 2  for limiting the illumination light at the edge. The z-distance between the object plane  4  and the image plane  8  is 1,700 mm. The object-image shift is 549 mm. 11.6% of the surfaces illuminated in the pupil planes are obscured. The projection optical system  49  has wavefront error (rms) of 0.053 in units of the wavelength of the illumination light. The distortion is 400 nm. The image field curvature is 130 nm. The angle of the principal ray on the central object field point is 6°. The mirror M 1  has dimensions (x/y) of 204×184 mm 2 . The mirror M 2  has dimensions of 652×271 mm 2 . The mirror M 3  has dimensions of 192×260 mm 2 . The mirror M 4  has dimensions of 515×347 mm 2 . The mirror M 5  has dimensions of 162×153 mm 2 . The mirror M 6  has dimensions of 643×619 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point on the mirrors M 1  to M 6  is 5.40°, 8.76°, 11.83°, 5.37°, 0.01° and 0.02°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 9.70°, 10.06°, 13.22°, 8.94°, 24.01° and 3.62°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 8.23°, 2.81°, 3.10°, 6.95°, less than 24.01° and less than 3.62°. 
     The working distance in the object plane  4  is 200 mm. The working distance in the image plane  8  is 20 mm. The ratio of the distance between the object plane  4  and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 5.11. The mirrors M 1  to M 3  have a minimum distance between the used reflection surface and the closest imaging light path which does not act upon the mirrors (free board) of less than 25 mm. The distance between the object plane  4  and the mirror M 1  and the distances between the pairs of mirrors M 1 -M 2 , M 2 -M 3 , M 3 -M 4 , M 4 -M 5  are greater than 40% of the distance between the object and the image plane. 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 6  can be gathered from the following tables which correspond to those of the projection optical system  6  of  FIG. 2  described above. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 1022.710 
                   
               
               
                   
                 Mirror 1 
                 −7390.359    
                 −822.710 
                 REFL 
               
               
                   
                 Mirror 2 
                 513.847 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 942.710 
               
               
                   
                 Mirror 3 
                 501.145 
                 −842.710 
                 REFL 
               
               
                   
                 Mirror 4 
                 843.206 
                 1380.024 
                 REFL 
               
               
                   
                 Mirror 5 
                 578.181 
                 −417.314 
                 REFL 
               
               
                   
                 Mirror 6 
                 496.039 
                 437.290 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Coeff. 
                   
                   
                   
                   
                   
                   
               
               
                 K 
                   3.481687E+02 
                 −9.241869E−01 
                 −7.566344E−01 
                 −5.019615E−01 
                   1.965937E+01 
                   1.267270E−01 
               
               
                 Y 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X2 
                   6.555377E−04 
                 −5.511453E−04 
                   2.158158E−04 
                 −1.699472E−04 
                   2.894217E−04 
                   5.126962E−06 
               
               
                 Y2 
                   3.295088E−05 
                 −8.776483E−04 
                 −9.084036E−04 
                 −2.883162E−04 
                   3.472889E−04 
                   1.671956E−05 
               
               
                 X2Y 
                 −4.245568E−07 
                   3.113324E−08 
                   7.395458E−07 
                   7.821775E−08 
                 −4.476295E−07 
                 −6.764774E−09 
               
               
                 Y3 
                   1.390824E−08 
                 −1.918862E−07 
                   8.435308E−08 
                 −2.628080E−08 
                   5.451515E−08 
                 −2.659596E−09 
               
               
                 X4 
                 −3.307013E−10 
                 −1.191040E−11 
                   3.063977E−09 
                 −3.668514E−11 
                   5.377968E−09 
                   8.032524E−12 
               
               
                 X2Y2 
                   3.290269E−09 
                 −6.921528E−11 
                   1.233667E−11 
                   1.187534E−10 
                   2.249411E−08 
                   2.023497E−11 
               
               
                 Y4 
                 −1.463471E−10 
                   5.786874E−11 
                 −6.021292E−12 
                 −1.106757E−10 
                   7.037151E−09 
                 −5.631157E−12 
               
               
                 X4Y 
                   2.736617E−12 
                   4.032934E−15 
                 −6.984058E−13 
                 −8.039415E−14 
                 −1.260298E−12 
                 −5.006977E−15 
               
               
                 X2Y3 
                   3.522297E−13 
                 −1.166725E−13 
                 −2.454747E−12 
                   5.957814E−13 
                 −1.250078E−11 
                 −5.698119E−15 
               
               
                 Y5 
                 −2.490692E−13 
                   2.590308E−12 
                 −3.745572E−13 
                 −1.408338E−14 
                 −2.442407E−11 
                 −7.179108E−15 
               
               
                 X6 
                 −1.862455E−14 
                   6.281324E−18 
                 −2.148629E−14 
                 −6.004672E−17 
                   1.997946E−13 
                 −1.011352E−17 
               
               
                 X4Y2 
                 −7.981936E−14 
                   4.496399E−17 
                 −1.242837E−14 
                 −6.611499E−16 
                   2.590470E−13 
                 −6.909855E−17 
               
               
                 X2Y4 
                 −4.901925E−14 
                 −3.029567E−16 
                 −3.758114E−15 
                   9.515240E−16 
                 −2.673556E−13 
                 −1.224111E−16 
               
               
                 Y6 
                   2.434885E−16 
                   1.266995E−14 
                   1.367511E−16 
                   6.466128E−17 
                   2.511816E−13 
                 −4.838450E−17 
               
               
                 X6Y 
                   2.013361E−16 
                   1.162633E−19 
                   1.149857E−17 
                 −3.125791E−19 
                 −1.332065E−15 
                 −1.469592E−20 
               
               
                 X4Y3 
                   3.552832E−16 
                   1.010087E−18 
                 −1.441396E−16 
                 −1.842092E−18 
                 −2.995433E−15 
                 −1.117419E−19 
               
               
                 X2Y5 
                 −9.924040E−19 
                 −2.022287E−19 
                 −1.400280E−17 
                   1.100935E−18 
                 −2.362122E−15 
                 −1.093754E−19 
               
               
                 Y7 
                   1.950700E−18 
                 −1.249257E−17 
                   6.126115E−19 
                   3.018212E−20 
                   2.029387E−15 
                 −2.279935E−20 
               
               
                 X8 
                 −1.816371E−19 
                   8.241847E−23 
                   1.607901E−19 
                 −2.596493E−23 
                   6.322415E−18 
                 −1.205865E−22 
               
               
                 X6Y2 
                 −1.231881E−18 
                   1.602604E−21 
                   2.552251E−19 
                 −7.939427E−22 
                   1.136621E−17 
                 −2.391492E−22 
               
               
                 X4Y4 
                 −1.457234E−19 
                   1.343999E−20 
                 −6.277420E−19 
                 −2.461049E−21 
                 −7.995361E−19 
                 −1.719723E−22 
               
               
                 X2Y6 
                   5.627869E−19 
                   1.086725E−20 
                   2.371593E−20 
                   9.514060E−22 
                 −3.361939E−17 
                 −2.245468E−22 
               
               
                 Y8 
                   3.626451E−21 
                 −2.072810E−20 
                 −3.369745E−21 
                 −6.523915E−23 
                 −4.042492E−18 
                 −1.070962E−22 
               
               
                 X8Y 
                   1.644403E−21 
                   5.521298E−25 
                   7.387878E−22 
                 −4.934005E−26 
                 −4.739358E−20 
                   1.327526E−25 
               
               
                 X6Y3 
                   2.012939E−21 
                   1.839641E−23 
                   6.948031E−22 
                 −5.010250E−25 
                 −3.213699E−19 
                   8.788103E−25 
               
               
                 X4Y5 
                 −9.196304E−22 
                   1.613032E−22 
                 −7.384331E−22 
                 −1.017620E−24 
                 −4.869993E−19 
                   1.435145E−24 
               
               
                 X2Y7 
                 −8.444082E−22 
                   4.724249E−22 
                   1.160142E−22 
                   5.807469E−25 
                 −3.565433E−19 
                   5.071171E−25 
               
               
                 Y9 
                 −1.391751E−24 
                 −1.535204E−22 
                 −1.540508E−24 
                   3.217510E−27 
                 −5.879640E−20 
                 −1.515906E−26 
               
               
                 X10 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X8Y2 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X6Y4 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X4Y6 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X2Y8 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 Y10 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 Nradius 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
               
               
                 Coefficient 
               
               
                 Y-decenter 
                 −197.752 
                 −67.646 
                 −76.378 
                 −20.289 
                 −432.652 
                 −422.877 
               
               
                 X-rotation 
                 −1.837 
                 −3.960 
                 −2.990 
                 −9.847 
                 −0.659 
                 −1.856 
               
               
                   
               
             
          
         
       
     
       FIG. 13  shows a microscope lens  56  which can be used for inspecting projection masks required for projection exposure or lithography or for inspecting of exposed wafers  10 . The microscope lens images a microscope object plane or substrate plane  57 , which coincides with the image plane  8  during projection of the projection exposure installation  1 , on a microscope image plane  58 . The construction of the microscope lens  56  is similar, for example, to that of the projection object  6  in  FIG. 2 , with the difference that, in the microscope lens  56 , the object and image planes are exchanged in comparison to the projection optical system  6 . The object to be analysed is therefore located at the high aperture portion of the microscope lens  56  and an image-recording device, for example a CCD camera is located at the low aperture portion of the microscope lens  56 . In the light path between the microscope image plane  58  and the substrate plane  57 , the microscope lens  56  has a total of four mirrors  59  to  62  which are numbered in this order and are also referred to as M 1  to M 4 . The third mirror  61  and the fourth mirror  62  of the microscope lens  56  correspond to the mirrors M 5 , M 6  of the previously discussed projection optical systems in terms of their design positions and the through-holes  23 ,  24 . The four mirrors  59  to  62  are configured as free-form surfaces which cannot be described by a rotationally symmetrical function. Alternatively, it is also possible for at least one of the mirrors  59  to  62  to have a free-form reflection surface of this type. 
     The first mirror  59  has negative angular magnification of the principal ray. The second mirror  60  has infinite angular magnification of the principal ray, since the principal ray  26  extends perpendicularly to the substrate plane  57  from the second mirror  60 . The angular magnifications of the principal ray of the third mirror  61  and the fourth mirror  62  are correspondingly undefined. 
     The microscope lens  56  has a numerical aperture of 0.7. The microscope lens  56  has an intermediate image-side numerical aperture of 0.17. 
     In the microscope lens  56 , the maximum angle of reflection α is again achieved by the outer edge rays of the mirror  57  including the through-hole  24  and is 24°. Correspondingly, the quotient of this angle of reflection and the numerical aperture is 34°. 
     The projection optical systems  6 ,  35 ,  42 ,  49  and the microscope lens  56  may be operated using wavelengths of the illumination or imaging light  3  other than EUV wavelengths. For example, it is also possible to use the free-form constructions for visible wavelengths. 
     The projection optical systems  6 ,  35 ,  42 ,  49 , the microscope lens  56  and the optical systems described in the following in relation to  FIGS. 14 to 17  can be constructed in such a way that, with the exception of the light path in the region of the through-holes  23 ,  24 , there is always a distance of less than 25 mm, but greater than 1 mm (e.g., greater than 5 mm) maintained between the individual rays  14  and the respective mirror M 1  to M 6  not acted upon, or  59  to  62  when acted upon by reflection of the illumination light  3  in the desired manner. This simplifies the constructional requirements of the respective optical system. 
       FIG. 14  shows a further configuration of a projection optical system  63  which can be used in the projection exposure installation  1 , again with EUV illumination, instead of the projection optical system  6 . Components or reference quantities which correspond to those previously discussed in relation to the projection optical systems  6 ,  35 ,  42 ,  49  of  FIGS. 1 to 12  have the same reference numerals and will not be discussed in detail again. In the following only the substantial differences between the projection optical system  63  and the previously explained projection optical systems  6 ,  35 ,  42 ,  49  will be discussed. 
     The optical data for the projection optical system  63  are as follows: 
     The image-side numerical aperture NA is 0.6. The dimensions of the image field  7  are 1×13 mm 2 . The reducing magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light  3  is 13.5 nm. The projection optical system  63  has six mirrors M 1  to M 6 . The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is NPNPNP. The single intermediate image of the projection optical system  63  is present between the mirrors M 4  and M 5 . Principal rays enter the projection optical system  63  in a convergent manner from the object plane  4 . An aperture stop for limiting the illumination light at the edge is arranged on mirror M 3 . The z-distance between the object plane  4  and the image plane is 1,500 mm. The object-image shift is 7.07 mm. 5.7% of the surfaces illuminated in the pupil planes are obscured. The projection optical system  63  has a wavefront error (rms) of 0.034 in units of the wavelength of the illumination light  3 . The distortion is 15 nm. The image field curvature is 10 nm. The angle of the principal ray at the central object field point is 5.9°. The mirror M 1  has dimensions (x/y) of 126×73 mm 2 . The mirror M 2  has dimensions of 339×164 mm 2 . The mirror M 3  has dimensions of 100×96 mm 2 . The mirror M 4  has dimensions of 196×150 mm 2 . The mirror M 5  has dimensions of 307×298 mm 2 . The mirror M 6  has dimensions of 814×806 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point on the mirrors M 1  to M 6  is 18.61°, 8.76°, 15.44°, 8.53°, 0.00° and 0.00°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 26.60°, 11.80°, 15.98°, 12.32°, 20.14° and 5.11°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 16.06°, 6.30°, 1.03°, 7.87°, less than 20.14° and less than 5.11°. The sequence of the angular magnification of the principal ray of the mirrors M 1  to M 3  (negative N; positive P) is NPN. The working distance in the object plane  4  is 102 mm. The working distance in the image plane is 40 mm. The ratio of the distance between the object plane  4  and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 4.13. The mirrors M 1  and M 4  have a minimum distance between the used reflection surfaces and the closest imaging light path which does not act on the mirror (free board) of less than 25 mm. The distances between the pairs of mirrors M 2 -M 3 , M 4 -M 5 , M 5 -M 6  and the distance between the mirror M 6  and the image plane  8  are less than 40% of the distance between the object plane  4  and the image plane  8 . 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 6  of the projection optical system  63  can be gathered from the following tables, which correspond to the tables provided for the projection optical system  6  in accordance with  FIG. 2 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 423.049 
                   
               
               
                   
                 Mirror 1 
                 291.429 
                 −320.693 
                 REFL 
               
               
                   
                 Mirror 2 
                 682.291 
                 698.472 
                 REFL 
               
               
                   
                 Mirror 3 
                 327.553 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 −250.085 
               
               
                   
                 Mirror 4 
                 398.721 
                 909.257 
                 REFL 
               
               
                   
                 Mirror 5 
                 1753.638  
                 −620.641 
                 REFL 
               
               
                   
                 Mirror 6 
                 834.258 
                 660.641 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Coeff. 
                   
                   
                   
                   
                   
                   
               
               
                 K 
                 −9.797768E−01 
                 −2.654407E−01 
                   3.633187E+00 
                 −2.607926E−01 
                   3.367484E+01 
                   3.003345E−01 
               
               
                 Y 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X2 
                 −6.757907E−04 
                 −9.897313E−05 
                 −6.055737E−04 
                 −1.712326E−04 
                   8.316524E−06 
                   3.449849E−05 
               
               
                 Y2 
                 −6.711750E−04 
                 −1.286106E−04 
                 −5.464279E−04 
                 −1.127817E−04 
                   1.666997E−06 
                   3.303139E−05 
               
               
                 X2Y 
                 −1.718471E−07 
                   8.106102E−09 
                   3.559721E−08 
                 −1.625547E−07 
                 −3.433987E−08 
                 −5.594447E−10 
               
               
                 Y3 
                   8.441316E−08 
                   2.066449E−08 
                   2.993241E−07 
                 −2.438542E−07 
                 −5.340235E−09 
                   2.648587E−10 
               
               
                 X4 
                 −4.235340E−10 
                 −6.184068E−11 
                 −1.590557E−08 
                 −5.148175E−11 
                   9.293663E−10 
                   1.431375E−12 
               
               
                 X2Y2 
                 −2.833593E−10 
                 −1.232739E−10 
                 −2.294580E−08 
                   6.076202E−11 
                   1.884838E−09 
                   4.501941E−12 
               
               
                 Y4 
                 −6.283000E−09 
                 −1.538541E−11 
                 −7.807703E−09 
                   4.592939E−10 
                   9.735975E−10 
                   3.169895E−12 
               
               
                 X4Y 
                   5.216941E−13 
                   1.355055E−14 
                 −4.125213E−11 
                 −5.236068E−13 
                 −6.108177E−14 
                   4.760532E−16 
               
               
                 X2Y3 
                 −5.462082E−12 
                   1.539145E−13 
                   5.882108E−11 
                 −7.857103E−13 
                   5.606699E−14 
                 −1.383433E−15 
               
               
                 Y5 
                   3.841515E−11 
                 −4.826907E−15 
                   6.536341E−11 
                 −1.173929E−12 
                   6.122980E−14 
                 −1.198686E−15 
               
               
                 X6 
                 −2.961655E−14 
                 −5.649609E−16 
                 −5.319482E−13 
                   1.037860E−15 
                   1.575126E−15 
                   5.280799E−19 
               
               
                 X4Y2 
                 −6.986732E−15 
                   1.523728E−17 
                 −1.125923E−12 
                   4.138161E−15 
                   5.066143E−15 
                   3.110524E−18 
               
               
                 X2Y4 
                   5.755669E−14 
                 −1.992110E−16 
                 −9.962349E−13 
                 −5.642387E−15 
                   5.364157E−15 
                   3.810873E−18 
               
               
                 Y6 
                 −7.476803E−14 
                 −3.652597E−17 
                 −1.721064E−13 
                 −2.311791E−16 
                   1.498586E−15 
                   9.716738E−19 
               
               
                 X6Y 
                   8.136042E−16 
                   1.347989E−18 
                   1.560712E−15 
                 −3.431381E−17 
                   1.006276E−18 
                 −1.255738E−22 
               
               
                 X4Y3 
                   1.102636E−17 
                   9.697709E−22 
                   2.841374E−15 
                 −6.361244E−17 
                 −5.733345E−19 
                 −1.261922E−21 
               
               
                 X2Y5 
                   1.331907E−16 
                 −1.331590E−20 
                   2.163234E−15 
                   2.657780E−17 
                 −1.545019E−18 
                 −3.386914E−22 
               
               
                 Y7 
                   3.093492E−17 
                   0.000000E+00 
                   2.304330E−15 
                   1.049058E−19 
                   3.738255E−20 
                   1.710371E−22 
               
               
                 X8 
                   1.506508E−18 
                   5.810497E−21 
                   1.133674E−17 
                   6.127110E−21 
                   3.186325E−21 
                   1.107455E−24 
               
               
                 X6Y2 
                 −1.013674E−17 
                   6.179938E−22 
                 −5.629342E−17 
                   3.657501E−19 
                   2.411205E−20 
                   2.133982E−24 
               
               
                 X4Y4 
                 −1.366007E−18 
                 −3.261229E−22 
                 −8.750490E−17 
                   4.374764E−19 
                   3.931624E−20 
                   4.739463E−24 
               
               
                 X2Y6 
                 −1.047171E−18 
                 −1.345299E−22 
                 −1.260161E−17 
                 −6.674633E−20 
                   2.052091E−20 
                   3.396921E−24 
               
               
                 Y8 
                 −9.482484E−19 
                 −7.567828E−23 
                 −3.447928E−18 
                 −3.054349E−21 
                   6.173346E−21 
                   9.678311E−25 
               
               
                 X8Y 
                 −5.877725E−20 
                 −1.822355E−23 
                 −4.253705E−19 
                 −1.365311E−22 
                 −1.472429E−23 
                   2.361551E−27 
               
               
                 X6Y3 
                   4.790823E−20 
                 −3.116535E−24 
                 −6.154610E−19 
                 −1.894833E−21 
                 −3.675978E−23 
                   1.990878E−27 
               
               
                 X4Y5 
                   8.584886E−21 
                 −9.980946E−26 
                   2.375768E−19 
                 −1.854722E−21 
                 −2.816555E−23 
                 −4.075851E−27 
               
               
                 X2Y7 
                 −1.694967E−20 
                 −4.093120E−26 
                   7.589434E−19 
                 −4.379199E−23 
                 −6.563563E−24 
                 −5.800819E−27 
               
               
                 Y9 
                   2.326792E−21 
                   0.000000E+00 
                   1.307119E−19 
                 −2.515286E−23 
                   2.606727E−24 
                 −1.858737E−28 
               
               
                 X10 
                   1.401272E−22 
                   6.373969E−27 
                   2.615474E−22 
                   2.577682E−25 
                   4.145747E−26 
                 −1.274796E−31 
               
               
                 X8Y2 
                   3.458862E−22 
                   1.154175E−26 
                 −7.752079E−21 
                   5.165996E−25 
                   1.524801E−25 
                 −2.154682E−30 
               
               
                 X6Y4 
                 −6.486950E−23 
                 −8.465791E−29 
                 −1.437881E−20 
                   3.499212E−24 
                   2.916563E−25 
                   4.867171E−30 
               
               
                 X4Y6 
                 −2.005656E−23 
                 −2.584491E−28 
                 −1.352099E−21 
                   3.142335E−24 
                   3.587746E−25 
                   1.828109E−29 
               
               
                 X2Y8 
                   6.434247E−23 
                 −5.536465E−29 
                   7.452494E−21 
                   3.871445E−25 
                   2.307038E−25 
                   1.576792E−29 
               
               
                 Y10 
                   1.692634E−24 
                   0.000000E+00 
                   1.578385E−21 
                   1.350146E−25 
                   2.372597E−26 
                   1.664967E−30 
               
               
                 Nradius 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
               
               
                 Coefficient 
               
               
                 Y-decenter 
                 72.424 
                 −276.725 
                 184.767 
                 −26.657 
                 97.145 
                 97.828 
               
               
                 X-rotation 
                 −3.803 
                 24.855 
                 1.633 
                 24.917 
                 0.012 
                 −0.062 
               
               
                   
               
             
          
         
       
     
       FIG. 15  shows a further configuration of a projection optical system  64  which can be used in the projection exposure installation  1 , again with EUV illumination, instead of the projection optical system  6 . Components or reference quantities corresponding to those which have previously been explained with reference to  FIG. 1 to 12  or  14  have the same reference numerals and will not be discussed in detail again. 
     The optical data of the projection optical system  64  are summarised in the following: 
     The image-side numerical aperture NA is 0.7. The dimensions of the image field  7  are 1×13 mm 2 . The reducing magnification level is 8×. The image field  7  is rectangular. The wavelength of the illumination light  7  is 13.5 nm. The projection optical system  64  has six mirrors M 1  to M 6 . The sequence of the optical effects of the mirrors M 1  to M 6  (negative N; positive P) is NPNPNP. The single intermediate image plane of the projection optical system  64  is present between the mirrors M 4  and M 5 . Principal rays enter the projection optical system  64  in a convergent manner from the object plane  4 . An aperture stop for limiting the illumination light at the edge is arranged on mirror M 3 . The z-distance between the object plane  4  and the image plane  8  is 1,483 mm. The object-image shift is 13.86 mm. 6.4% of the surfaces illuminated in the pupil planes are obscured. The projection optical system  64  has a wavefront error (rms) of 0.062 in units of the wavelength of the illumination light  3 . The distortion is 18 nm. The image field curvature is 10 nm. The angle of the principal ray at the central object field point is 5.9°. The mirror M 1  has dimensions (x/y) of 134×84 mm 2 . The mirror M 2  has dimensions of 365×174 mm 2 . The mirror M 3  has dimensions of 121×114 mm 2 . The mirror M 4  has dimensions of 220 ×176 mm 2 . The mirror M 5  has dimensions of 363×354 mm 2 . The mirror M 6  has dimensions of 956×952 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point on the mirrors M 1  to M 6  is 20.86°, 10.26°, 17.50°, 9.84°, 0.00° and 0.00°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 6  is 29.83°, 13.67°, 18.09°, 14.40°, 24.60° and 5.70°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 6  is 18.23°, 7.18°, 1.06°, 9.50°, less than 16.98° and less than 5.51°. The sequence of the angular magnification of the principal ray of the mirrors M 1  to M 3  (negative N; positive P) is NPN. The working distance in the object plane  4  is 100 mm. The working distance in the image plane  8  is 40 mm. The ratio of the distance between the object plane and the mirror M 1  and the distance between the object plane  4  and the mirror M 2  is 4.13. The mirrors M 1  and M 4  have a minimum distance between the used reflection surface and the closest imaging light path not acting upon the mirrors (free board) of less than 25 mm. The distances between the pairs of mirrors M 2 -M 3 , M 4 -M 5 , M 5 -M 6  and the distance between the mirror M 6  and the image plane  8  are greater than 40% of the distance between the object plane  4  and the image plane  8 . 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 6  of the projection optical system  64  can be inferred from the following tables, which correspond to the tables provided for the projection optical system  6  according to  FIG. 2 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 413.264 
                   
               
               
                   
                 Mirror 1 
                 289.172 
                 −313.264 
                 REFL 
               
               
                   
                 Mirror 2 
                 680.603 
                 689.549 
                 REFL 
               
               
                   
                 Mirror 3 
                 333.217 
                 0.000 
                 REFL 
               
               
                   
                 STOP 
                 INFINITY 
                 −255.285 
               
               
                   
                 Mirror 4 
                 400.498 
                 908.331 
                 REFL 
               
               
                   
                 Mirror 5 
                 1757.579  
                 −620.526 
                 REFL 
               
               
                   
                 Mirror 6 
                 834.338 
                 660.526 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Coeff. 
                   
                   
                   
                   
                   
                   
               
               
                 K 
                 −1.030576E+00 
                 −2.635304E−01 
                   4.190202E+00 
                 −2.532242E−01 
                   3.343958E+01 
                   2.989093E−01 
               
               
                 Y 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
                   0.000000E+00 
               
               
                 X2 
                 −6.535480E−04 
                 −9.651094E−05 
                 −6.315149E−04 
                 −1.860891E−04 
                   6.210957E−06 
                   3.467308E−05 
               
               
                 Y2 
                 −6.703313E−04 
                 −1.285085E−04 
                 −5.894828E−04 
                 −1.055800E−04 
                   3.848982E−07 
                   3.293719E−05 
               
               
                 X2Y 
                 −1.109153E−07 
                   9.418989E−09 
                   5.191842E−07 
                 −1.736028E−07 
                 −3.604297E−08 
                 −1.901465E−09 
               
               
                 Y3 
                 −1.849968E−07 
                   1.804370E−08 
                   1.052875E−08 
                 −3.008104E−07 
                 −1.255871E−08 
                 −7.306681E−10 
               
               
                 X4 
                 −3.455652E−10 
                 −6.435672E−11 
                 −1.959503E−08 
                 −1.181975E−10 
                   9.251123E−10 
                   9.219996E−13 
               
               
                 X2Y2 
                   8.907151E−11 
                 −1.169230E−10 
                 −2.854507E−08 
                   3.223161E−11 
                   1.828013E−09 
                   3.292930E−12 
               
               
                 Y4 
                 −6.694084E−09 
                 −1.746102E−11 
                 −1.100719E−08 
                   5.508116E−10 
                   9.590508E−10 
                   2.723624E−12 
               
               
                 X4Y 
                 −6.682583E−13 
                   6.169836E−15 
                 −4.579394E−11 
                 −4.554803E−13 
                 −1.075058E−13 
                 −9.398044E−17 
               
               
                 X2Y3 
                 −3.764773E−12 
                   1.837427E−13 
                   8.072483E−13 
                 −1.108837E−12 
                   1.733346E−14 
                 −1.372960E−15 
               
               
                 Y5 
                   3.946729E−11 
                   1.501209E−15 
                   4.522011E−11 
                 −1.761285E−12 
                   5.059303E−14 
                 −1.418313E−15 
               
               
                 X6 
                 −2.950759E−14 
                   5.555342E−16 
                 −4.772179E−13 
                   2.049340E−16 
                   1.249728E−15 
                   6.302080E−19 
               
               
                 X4Y2 
                 −3.981976E−14 
                   7.309283E−17 
                 −1.369581E−12 
                   2.599849E−15 
                   4.180701E−15 
                   1.406199E−18 
               
               
                 X2Y4 
                   6.662007E−14 
                 −1.567936E−16 
                 −1.344358E−12 
                 −6.991042E−15 
                   4.324958E−15 
                   9.589967E−19 
               
               
                 Y6 
                 −6.296271E−14 
                   5.254697E−18 
                 −3.274586E−13 
                 −1.365187E−15 
                   1.317067E−15 
                   4.531531E−19 
               
               
                 X6Y 
                   9.572567E−16 
                 −4.550481E−18 
                 −2.349696E−17 
                 −2.327425E−17 
                   1.147404E−18 
                 −5.815673E−22 
               
               
                 X4Y3 
                   1.729544E−15 
                 −5.168321E−21 
                 −6.343836E−16 
                 −6.844084E−17 
                   1.396280E−18 
                 −1.101533E−21 
               
               
                 X2Y5 
                   2.003151E−16 
                 −1.086056E−20 
                   7.211912E−17 
                   3.651614E−17 
                   2.129037E−19 
                 −6.825077E−22 
               
               
                 Y7 
                 −6.259873E−17 
                   0.000000E+00 
                   1.314567E−15 
                   4.966906E−18 
                   4.944608E−20 
                 −3.674224E−22 
               
               
                 X8 
                   8.514832E−19 
                   5.499001E−21 
                 −1.315946E−17 
                   1.431441E−20 
                   5.935619E−21 
                   2.351396E−25 
               
               
                 X6Y2 
                 −1.930952E−17 
                   1.021410E−20 
                 −3.809772E−17 
                   2.893679E−19 
                   2.146809E−20 
                   1.941034E−24 
               
               
                 X4Y4 
                 −2.629657E−17 
                 −5.261250E−22 
                 −4.023107E−17 
                   4.708584E−19 
                   2.844557E−20 
                   3.285122E−24 
               
               
                 X2Y6 
                 −7.113538E−18 
                 −2.063344E−22 
                 −3.710671E−17 
                 −1.202904E−19 
                   1.718587E−20 
                   6.947595E−25 
               
               
                 Y8 
                 −6.688170E−19 
                 −9.807129E−23 
                 −1.246348E−17 
                 −1.007426E−20 
                   5.947625E−21 
                   5.352899E−25 
               
               
                 X8Y 
                 −2.167642E−20 
                 −1.475245E−23 
                 −4.375451E−20 
                 −3.593805E−22 
                 −6.272355E−24 
                 −6.386618E−29 
               
               
                 X6Y3 
                   1.577014E−19 
                 −7.541034E−24 
                   1.407216E−21 
                 −1.733010E−21 
                 −1.503182E−23 
                 −2.378905E−27 
               
               
                 X4Y5 
                   1.475476E−19 
                   2.828164E−25 
                   2.164416E−19 
                 −1.819583E−21 
                 −5.558949E−24 
                 −4.818316E−27 
               
               
                 X2Y7 
                   2.386767E−20 
                   2.916090E−26 
                   4.037031E−19 
                   1.506408E−22 
                   1.500592E−23 
                 −2.782420E−27 
               
               
                 Y9 
                   2.686189E−21 
                 −3.808616E−26 
                   1.365101E−19 
                   2.759985E−23 
                   9.373049E−24 
                   3.697377E−29 
               
               
                 X10 
                   6.880195E−23 
                   4.028878E−27 
                 −3.684363E−22 
                   3.684053E−25 
                   8.977447E−27 
                   1.376079E−31 
               
               
                 X8Y2 
                   1.028653E−22 
                   7.179210E−27 
                 −5.946953E−21 
                   1.412893E−24 
                   6.817863E−26 
                 −3.343096E−30 
               
               
                 X6Y4 
                 −4.423830E−22 
                 −2.428875E−28 
                 −1.431825E−20 
                   3.370257E−24 
                   1.794556E−25 
                 −8.790772E−30 
               
               
                 X4Y6 
                 −2.798064E−22 
                   1.268239E−28 
                 −9.083451E−21 
                   2.674694E−24 
                   2.401259E−25 
                 −2.285964E−30 
               
               
                 X2Y8 
                 −1.113049E−23 
                 −1.289425E−30 
                   4.131039E−22 
                 −1.824536E−27 
                   1.599496E−25 
                   5.901778E−30 
               
               
                 Y10 
                   1.536113E−24 
                   0.000000E+00 
                   9.866128E−22 
                   9.363641E−28 
                   1.894848E−26 
                   1.501949E−30 
               
               
                 Nradius 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
                     1.00E+00 
               
               
                 Coefficient 
               
               
                 Y- 
                 76.368 
                 −281.911 
                 194.003 
                 −24.759 
                 94.122 
                 96.437 
               
               
                 decenter 
               
               
                 X-rotation 
                 −6.675 
                 24.349 
                 2.204 
                 25.034 
                 −0.109 
                 −0.453 
               
               
                   
               
             
          
         
       
     
     In the following more optical data for two further microscope lenses  65 ,  66  are summarised which, like the microscope lens  56 , can be used for inspecting projection masks required for projection exposure or lithography or for inspecting exposed wafers. Both of these further microscope lenses  65 ,  66  are shown in  FIGS. 16 and 17 . The basic four-mirror construction of the two further microscope lens  65 ,  66  corresponds to that of  FIG. 13 . 
     Components in these further microscope lenses  65 ,  66 , which correspond to those which have previously been explained in relation to the microscope lens  56 , have the same reference numerals or designations. 
     The first of the two further microscope lenses  65 ,  66 , the microscope lens  65 , shown in  FIG. 16 , has an object-side numerical aperture of 0.8. The dimensions of the square object field are 0.8×0.8 mm 2 . The increasing magnification level is 10×. The wavelength of the illumination light  3  is 193.0 nm. Other illumination light wavelengths are also possible, for example a visible wavelength or an EUV wavelength. The sequence of the optical effects of the mirrors M 1  to M 4  (negative N; positive P) is NPNP. The single intermediate image is located between the mirrors M 2  and M 3  at the location of the through-hole  23  in the mirror M 4 . Principal rays travel out of the microscope lens  65  in a divergent manner from the microscope image plane  58 . The z-distance between the substrate plane  57  and the image plane  58  is 1,933 mm. The object-image shift is 477 mm. 21.5% of the illuminated surfaces in the pupil planes are obscured. The microscope lens  65  has a wavefront error (rms) of 0.004 in units of the wavelength of the illumination light  3 . The angle of the principal ray at the central object field point is 13.8°. The mirror M 1  has dimensions (x/y) of 219×216 mm 2 . The mirror M 2  has dimensions of 520×502 mm 2 . The mirror M 3  has dimensions of 202×189 mm 2 . The mirror M 4  has dimensions of 742×699 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point on the mirrors M 1  to M 4  is 10.48°, 3.53°, 0.04° and 0.02°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 4  is 15.70°, 5.58°, 27.79° and 3.19°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 4  is 11.93°, 4.46°, 27.79° and 3.19°. The working distance in the microscope image plane  58  is 240 mm. The working distance in the substrate plane  57  is 40 mm. The ratio of the distance between the microscope image plane  58  and the mirror M 1  and the distance between the microscope image plane  58  and the mirror M 2  is 5.63. The distance between the substrate plane  57  and the mirror M 1  and the distances between the pairs of mirrors M 1 -M 2  and M 2 -M 3  are greater than 40% of the distance between the substrate plane  57  and the image plane  58 . 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 4  of the microscope lens  65  can be gathered from the following tables, which correspond to the tables for the previously described projection optical systems. In these tables “object” refers to the microscope image plane  58 . “Image” refers to the substrate plane  57 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 1350.229 
                   
               
               
                   
                 Mirror 1 
                 240.546 
                 −1110.493 
                 REFL 
               
               
                   
                 Mirror 2 
                 435.560 
                 1653.485 
                 REFL 
               
               
                   
                 Mirror 3 
                 756.829 
                 −422.992 
                 REFL 
               
               
                   
                 Mirror 4 
                 530.970 
                 462.991 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Coefficient 
                 M1 
                 M2 
                 M3 
                 M4 
               
               
                   
               
             
             
               
                 K 
                 −1.387402E+00   
                 −9.186277E−01   
                 2.479623E+01 
                 1.846234E−01 
               
               
                 Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2 
                 −1.972513E−03   
                 −8.152652E−04   
                 4.304599E−04 
                 3.443510E−05 
               
               
                 Y2 
                 −2.046135E−03   
                 −8.219532E−04   
                 4.280214E−04 
                 3.442623E−05 
               
               
                 X2Y 
                 4.924422E−07 
                 1.043274E−08 
                 1.420911E−07 
                 −1.467857E−09   
               
               
                 Y3 
                 3.892760E−07 
                 1.233789E−08 
                 1.433179E−07 
                 −1.285787E−09   
               
               
                 X4 
                 2.843271E−09 
                 −8.849537E−11   
                 5.644150E−09 
                 5.790124E−12 
               
               
                 X2Y2 
                 6.307229E−09 
                 −1.868473E−10   
                 1.095525E−08 
                 1.192799E−11 
               
               
                 Y4 
                 3.357640E−09 
                 −9.886660E−11   
                 5.323173E−09 
                 6.015673E−12 
               
               
                 X4Y 
                 3.303637E−13 
                 1.821786E−14 
                 −9.065558E−13   
                 2.636707E−15 
               
               
                 X2Y3 
                 4.517153E−13 
                 3.654773E−14 
                 −1.999032E−12   
                 4.573973E−15 
               
               
                 Y5 
                 −1.472281E−14   
                 1.913697E−14 
                 −1.039223E−12   
                 1.907361E−15 
               
               
                 X6 
                 −1.567647E−14   
                 −2.778349E−17   
                 3.227077E−14 
                 6.941174E−18 
               
               
                 X4Y2 
                 −4.271994E−14   
                 −8.658416E−17   
                 9.037002E−14 
                 1.569376E−17 
               
               
                 X2Y4 
                 −3.766656E−14   
                 −8.931045E−17   
                 8.435334E−14 
                 1.111043E−17 
               
               
                 Y6 
                 −1.062731E−14   
                 −3.096033E−17   
                 2.620546E−14 
                 2.369368E−18 
               
               
                 X6Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y9 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Nradius 
                 1.000000E+00 
                 1.000000E+00 
                 1.000000E+00 
                 1.000000E+00 
               
               
                 Y-decenter 
                 −419.012 
                 −607.162 
                 −478.467 
                 −476.646 
               
               
                 X-rotation 
                 −2.721 
                 8.467 
                 0.209 
                 −0.024 
               
               
                   
               
             
          
         
       
     
     The optical data for the second microscope lens  66 , which is shown in  FIG. 17  and can also be used instead of the microscope lens  56  in  FIG. 13 , are summarised in the following; 
     The object-side numerical aperture NA is 0.8. The dimensions of the square object field are 0.8×0.8 mm 2 . The increasing magnification level is 40×. The wavelength of the illumination light  3  is 193.0 nm. Other illumination light wavelengths may also be used, for example visible or EUV wavelengths. The sequence of the optical effects of the mirrors M 1  to M 4  (negative N; positive P) is NPNP. The single intermediate image is located between the mirrors M 2  and M 3  in the region of the through-hole  23  in the mirror M 4 . On the image-side, principal rays travel out of the microscope lens  66  in a divergent manner. The z-distance between the substrate plane  57  and the image plane  58  is 2,048 mm. The object-image shift is 522 mm. 24.6% of the surfaces illuminated in the pupil planes are obscured. The microscope lens  66  has a wavefront error (rms) of 0.016 in units of the wavelength of the illumination light  3 . The angle of the principal ray at the central object field point is 17.1°. The mirror M 1  has dimensions (x/y) of 59×58 mm 2 . The mirror M 2  has dimensions of 222×197 mm 2 . The mirror M 3  has dimensions of 180×163 mm 2 . The mirror M 4  has dimensions of 736×674 mm 2 . The sequence of the principal ray angle of incidence of the principal ray  26  of the central object field point to the mirrors M 1  to M 4  is 12.23°, 3.81°, 0.10° and 0.14°. The sequence of the maximum angle of incidence on the mirrors M 1  to M 4  is 18.94°, 5.66°, 24.95° and 2.75°. The sequence of the bandwidths of the angle of incidence on the mirrors M 1  to M 4  is 10.17°, 1.81°, 24.95° and 2.75°. The working distance in the microscope image plane  58  is 996 mm. The working distance in the substrate plane  57  is 40 mm. The ratio of the distance between the microscope image plane  58  and the mirror M 1  and the distance between the microscope image plane  58  and the mirror M 2  is 1.46. The distance between the substrate plane  57  and the mirror M 1  and the distance between the pair of mirrors M 2 -M 3  is less than 40% of the distance between the substrate plane  57  and the image plane  58 . 
     The optical design data for the reflection surfaces of the mirrors M 1  to M 4  of the microscope lens  66  can be gathered from the following tables, which correspond to the tables for the previously described microscope lens  65 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Surface 
                 Radius 
                 Thickness 
                 Mode 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 INFINITY 
                 1458.431 
                   
               
               
                   
                 Mirror 1 
                 138.358 
                 −462.391 
                 REFL 
               
               
                   
                 Mirror 2 
                 352.350 
                 1011.807 
                 REFL 
               
               
                   
                 Mirror 3 
                 521.060 
                 −429.417 
                 REFL 
               
               
                   
                 Mirror 4 
                 523.773 
                 469.415 
                 REFL 
               
               
                   
                 Image 
                 INFINITY 
                 0.000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Coefficient 
                 M1 
                 M2 
                 M3 
                 M4 
               
               
                   
               
             
             
               
                 K 
                 2.186021E−01 
                 −8.967130E−01   
                 1.353344E+01 
                 1.426428E−01 
               
               
                 Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2 
                 −2.119566E−03   
                 −6.122040E−04   
                 3.598902E−04 
                 2.150055E−05 
               
               
                 Y2 
                 −1.870353E−03   
                 −6.339662E−04   
                 4.023778E−04 
                 2.187467E−05 
               
               
                 X2Y 
                 −2.390768E−05   
                 6.494155E−08 
                 −2.453628E−07   
                 3.235225E−09 
               
               
                 Y3 
                 −2.981028E−05   
                 5.780210E−08 
                 −6.744637E−08   
                 4.604016E−09 
               
               
                 X4 
                 1.923306E−08 
                 2.795937E−10 
                 2.925492E−09 
                 −1.313710E−12   
               
               
                 X2Y2 
                 4.121148E−07 
                 5.095698E−10 
                 1.819466E−09 
                 −5.092789E−12   
               
               
                 Y4 
                 4.757534E−07 
                 2.387275E−10 
                 −6.547683E−10   
                 −2.809211E−12   
               
               
                 X4Y 
                 −1.446899E−09   
                 5.301791E−13 
                 −9.735433E−12   
                 −3.703196E−15   
               
               
                 X2Y3 
                 −7.970490E−09   
                 8.235778E−13 
                 −4.591548E−11   
                 −1.311139E−14   
               
               
                 Y5 
                 −6.911626E−09   
                 5.427574E−13 
                 −3.434264E−11   
                 −8.056144E−15   
               
               
                 X6 
                 −6.957804E−12   
                 4.031055E−16 
                 4.869018E−14 
                 −2.032419E−18   
               
               
                 X4Y2 
                 −6.520224E−12   
                 3.388642E−15 
                 1.730353E−13 
                 −5.277652E−18   
               
               
                 X2Y4 
                 5.785767E−11 
                 4.106532E−15 
                 8.768509E−14 
                 −5.976002E−18   
               
               
                 Y6 
                 5.002226E−11 
                 −2.665419E−15   
                 −1.533312E−14   
                 3.256782E−19 
               
               
                 X6Y 
                 3.978450E−14 
                 −3.458637E−18   
                 2.808257E−16 
                 −2.974086E−21   
               
               
                 X4Y3 
                 1.060921E−15 
                 −5.135846E−18   
                 1.062927E−15 
                 −1.985462E−20   
               
               
                 X2Y5 
                 −2.907745E−13   
                 1.367522E−17 
                 1.248668E−15 
                 −1.673351E−20   
               
               
                 Y7 
                 −1.895272E−13   
                 2.948597E−17 
                 4.722358E−16 
                 −2.273773E−22   
               
               
                 X8 
                 0.000000E+00 
                 9.742461E−21 
                 −1.224565E−19   
                 −5.498909E−24   
               
               
                 X6Y2 
                 0.000000E+00 
                 −1.149790E−22   
                 −8.469691E−19   
                 −3.121995E−23   
               
               
                 X4Y4 
                 0.000000E+00 
                 −3.605842E−20   
                 −9.612391E−19   
                 −9.354588E−23   
               
               
                 X2Y6 
                 0.000000E+00 
                 −8.956173E−20   
                 3.862422E−20 
                 −1.029099E−22   
               
               
                 Y8 
                 0.000000E+00 
                 −6.962503E−20   
                 1.096441E−19 
                 −3.729022E−23   
               
               
                 X8Y 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y3 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y5 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y7 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y9 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X8Y2 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X6Y4 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X4Y6 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 X2Y8 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y10 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Nradius 
                 1.000000E+00 
                 1.000000E+00 
                 0.000000E+00 
                 0.000000E+00 
               
               
                 Y-decenter 
                 −473.594 
                 −625.447 
                 −517.418 
                 −517.782 
               
               
                 X-rotation 
                 −2.590 
                 13.500 
                 −1.408 
                 −0.608 
               
               
                   
               
             
          
         
       
     
     Other embodiments are in the claims.