Abstract:
Another approach to decrease the resolution is to introduce an immersion liquid having high refractive index into the gap that remains between a final lens element on the image side of the projection objective and the photoresist or another photosensitive layer to be exposed. Projection objectives that are designed for immersion operation and are therefore also referred to as immersion objective may reach numerical apertures of more than 1, for example 1.3 or 1.4. The term “immersion liquid” shall, in the context of this application, relate also to what is commonly referred to as “solid immersion”. In the case of solid immersion, the immersion liquid is in fact a solid medium that, however, does not get in direct contact with the photoresist but is spaced apart from it by a distance that is only a fraction of the wavelength used. This ensures that the laws of geometrical optics do not apply such that no total reflection occurs.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The invention relates to microlithographic projection exposure apparatuses as are used to manufacture large-scale integrated electrical circuits and other microstructured components. More particular, the invention relates to a projection objective of such an apparatus that is designed for immersion operation. 
         [0003]    2. Description of Related Art 
         [0004]    Integrated electrical circuits and other microstructured components are normally produced by applying a plurality of structured layers to a suitable substrate, which may be, for example, a silicon wafer. To structure the layers, they are first covered with a photoresist that is sensitive to light of a certain wavelength range. The wafer coated in this way is then exposed in a projection exposure apparatus. In this operation, a pattern of structures contained in a mask is imaged on the photoresist with the aid of a projection objective. Since the imaging scale is generally smaller than 1, such projection objectives are frequently also referred to as reduction objectives. 
         [0005]    After the development of the photoresist, the wafer is subjected to an etching or deposition process, as a resuit of which the uppermost layer is structured in accordance with the pattern on the mask. The photoresist still remaining is then removed from the remaining parts of the layer. This process is repeated until all the layers have been applied to the wafer. 
         [0006]    One of the most prominent objects in the design of projection exposure apparatuses is to be able to define lithographically structures having increasingly smaller dimensions on the wafer. Small structures result in high integration densities, which generally have a favorable effect on the performance of the microstructured components produced with the aid of such apparatuses. 
         [0007]    One of the most important parameters that determine the minimum size of the structures to be lithographically defined is the resolution of the projection objective. 
         [0008]    Since the resolution of the projection objectives decreases as the wavelength of the projection light becomes smaller, one approach to achieve smaller resolutions is to use projection light with ever-shorter wavelengths. The shortest currently used wavelengths are in the deep ultraviolet (DUV) spectral range and are 193 nm and 157 nm. 
         [0009]    Another approach to decrease the resolution is to introduce an immersion liquid having high refractive index into the gap that remains between a final lens element on the image side of the projection objective and the photoresist or another photosensitive layer to be exposed. Projection objectives that are designed for immersion operation and are therefore also referred to as immersion objective may reach numerical apertures of more than 1, for example 1.3 or 1.4. The term “immersion liquid” shall, in the context of this application, relate also to what is commonly referrd to as “solid immersion”. In the case of solid immersion, the immersion liquid is in fact a solid medium that, however, does not get In direct contact with the photoresist but is spaced apart from it by a distance that is only a fraction of the wavelength used. This ensures that the laws of geometrical optics do not apply such that no total reflection occurs. 
         [0010]    Immersion operation, however, does not only allow to achieve very high numerical apertures and, consequently, a smaller resolution, but it also has a favorable effect on the depth of focus. The higher the depth of focus is, the lower are the requirements imposed on an exact positioning of the wafer in the image plane of the projection objective. Apart from that, it has been found out that immersion operation considerably relaxes certain design constraints and simplifies the correction of aberrations if the numerical aperture is not increased. 
         [0011]    In the meantime, immersion liquids have been developed whose refractive index is significantly above that of deionized water (n H2O =1.43) and that are nevertheless also highly transparent and resistant to projection light of the wavelength 193 nm. When using immersion liquids with such high refractive indices, it may happen that the refractive index of the immersion liquid is greater than the refractive index of the material of which the last optical element on the image side is composed. In conventional projection objectives having a last optical element with a plane surface on the image side, the maximum numerical aperture is restricted by the refractive index of this last optical element. If this optical element is, for example, made of quartz glass, an increase in the numerical aperture beyond the refractive index of quartz glass (n SiO2 =1.56) is not possible although the refractive index of the immersion liquid is even higher. 
         [0012]    Document JP 2000-058436 A discloses a projection exposure apparatus having a projection objective can be used both in dry and in immersion operation. When switching to immersion operation, an additional lens element having a concave surface on the image side is introduced into the gap between the last optical element of the projection objective and the wafer. The interspace between the additional lens element and the wafer may be filled with an immersion liquid, for example an oil. This document does not disclose the refractive indices of the immersion liquid and the additional lens element. 
       SUMMARY OF THE INVENTION 
       [0013]    It is therefore an object of the present invention to provide an immersion projection objective in which the refractive index of the last optical element on the image side is larger is smaller than the refractive index of the immersion liquid, but having a numerical aperture that is not restricted by the refractive index of the last optical element. 
         [0014]    This object is achieved in that, during immersion operation, the immersion liquid is convexly curved towards the object plane. 
         [0015]    As a result of the convex curvature of the immersion liquid towards the object plane, the angles of incidence at which projection light rays impinge on the interface between an adjoining medium, e.g. the last optical element on the image side, and the immersion liquid are reduced. Thus a light ray that would be totally reflected by a flat interface can now contribute to the image, and this, in turn, allows higher numerical apertures that can also be above the refractive index of the last optical element on the image side. In this way the numerical aperture is limited only by the refractive index of the immersion liquid, but not by the refractive index of the medium that adjoins the immersion liquid on the object side. 
         [0016]    The simplest way of achieving an immersion liquid that is convexly curved towards the object plane is to allow the immersion liquid to adjoin directly a concavely curved image-side surface of the last optical element of the projection objective. The curvature of the immersion liquid is then unalterably fixed by the curvature of this surface. 
         [0017]    In order to prevent an undesired drainage of the immersion liquid from the cavity that is formed by the concavely curved image-side surface of the last optical element, this surface may be surrounded circumferentially by a drainage barrier. This may, for example, be a ring that is joined to the last optical element and/or a housing of the projection objective. The ring, which may be composed, for example, of a standard lens material such as quartz glass or calcium fluoride (CaF 2 ), but also of a ceramic or of hardened steel, is preferably provided on the inside with a coating that prevents contamination of the immersion liquid by the ring. Such a ring is also advantageous if the refractive index of the immersion liquid is equal to or smaller than the refractive index of the medium that adjoins the immersion liquid on the object side. 
         [0018]    The image-side surface of the last optical element may be spherical. Calculations have shown that the radius of curvature may advantageously be selected to be between 0.9 times and 1.5 times and preferably 1.3 times the axial distance (i.e. vertex distance) between the this surface and the image plane. Such a configuration, which is also advantageous if the refractive index of the immersion liquid is equal to or smaller than the refractive index of the medium that adjoins the immersion liquid on the object side, has the advantage the high angles of incidence at the object side interface of the immersion liquid are avoided. Such high angles usually result in a strong sensitivity of the interface to design and manufacturing deficiencies. From this point of view, the angles of incidence should be as small as possible. This generally requires a very large curvature (i.e. a small radius of curvature) of the object-side interface of the immersion liquid. 
         [0019]    Another way of obtaining an interface of the immersion liquid that is convexly curved toward the object plane is to introduce an intermediate liquid between the last optical element and the immersion liquid. This intermediate liquid is not miscible with the immersion liquid and forms a curved interface in an electric field during immersion operation. Such a configuration is also advantageous if the refractive index of the immersion liquid is equal to or smaller than the refractive index of the medium that adjoins the immersion liquid on the object side. 
         [0020]    This approach makes use of an effect that is also known as “electrowetting”. If the magnitude of the electric field is altered, this is accompanied by an alteration in the curvature of the interface. This effect has hitherto been used, however, only for autofocus lenses for CCD or CMOS sensors on components that are produced by Varioptic, France. 
         [0021]    The more the electrical conductivities of the two liquids differ from one another, the greater is the curvature of the interface. A large difference may be achieved if one of the two liquids, for example the intermediate liquid, is electrically conductive and the other liquid, for example the immersion liquid, is electrically insulating. 
         [0022]    It is furthermore advantageous if the intermediate liquid has substantially the same density as the immersion liquid since no buoyancy forces can occur and, consequently, the shape of the interface is independent, of the position of the arrangement in space. 
         [0023]    The refractive index of the intermediate liquid should be less than the refractive index of the immersion liquid, but it may be less or greater than the refractive index of the last optical element on the image side. 
         [0024]    Preferably, the electric field that is necessary to form the curved interface is generated by an electrode. A symmetrical formation of the interface can be achieved, for example, by using an annular cone electrode that is disposed between the last optical element and the image plane. The curvature of the interface can be continuously varied in this way by varying a voltage applied to the electrode. This can be exploited in order to correct certain imaging properties of the projection objective. 
         [0025]    Above it has been mentioned that it may be desirable to have a strongly curved interface between the immersion liquid and the medium adjoining to the object side, because this simplifies the correction, of imaging aberrations. However, it has also significant advantages if the curvature of this interface is small. This is because a large curvature generally leads to the formation of a cavity within the last optical element. Such a cavity has several drawbacks. For example, it favors the occurrence of undesired turbulences within the cavity if a flow of the immersion liquid has to maintained, for example for reasons of temperature stability and for purifying the liquid. Furthermore, highly refractive immersion liquids have a somewhat higher absorption than lens materials. For that reasons the maximum geometrical path lengths within the immersion liquid should be kept small. Finally, a small curvature simplifies the access to the image side surface of the last optical element for cleaning purposes. 
         [0026]    Therefore it is generally preferred if the immersion liquid forms a convexly curved interface with a medium adjoining the immersion liquid towards the object plane such that light rays pass the interface with a maximum angle of incidence whose sine is between 0.98 and 0.5, more preferably between 0.95 and 0.85, and even more preferably between 0.94 and 0.87. The latter values correspond to angles of incidence of 60° and 70°, respectively. The angle of incidence here denotes the angle between the light ray and a surface normal at the point where the light ray impinges on the surface. These configurations are also advantageous if the refractive index of the immersion liquid is equal to, or smaller than the refractive index of the medium that adjoins the immersion liquid on the object side. 
         [0027]    The very high numerical apertures possible according to the invention, which may be, for example, 1.6 and above, require, under some circumstances, a novel design of the projection objective. In this connection, a catadioptric projection objective comprising at least two imaging mirrors in which at least two intermediate images may be advantageous. Such a configuration is also advantageous if the refractive index of the immersion liquid is equal to or smaller than the refractive index of the medium that adjoins the immersion liquid on the object side. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]    Various features and advantages of the present invention may be more readily understood with reference to the following detailed description taken in conjunction with the accompanying drawing in which: 
           [0029]      FIG. 1  shows a meridian section through a microlithographic projection exposure apparatus having a projection objective according to the invention in a considerably simplified view that is not to scale; 
           [0030]      FIG. 2  shows an enlarged view of the image-side end of the projection objective shown in  FIG. 1 ; 
           [0031]      FIG. 3  shows an enlarged view similar to  FIG. 2  for an alternative embodiment with a drainage barrier; 
           [0032]      FIG. 4  shows the image-side end of a projection objective in accordance with another exemplary embodiment in which an intermediate liquid has been introduced between the immersion liquid and the last optical element on the image side; 
           [0033]      FIG. 5  shows details of the geometrical conditions at the image-side end of a projection objective according to the invention; 
           [0034]      FIG. 6  shows a meridian section through a catadioptric projection objective in accordance, with an embodiment the present invention; 
           [0035]      FIG. 7  shows a meridian section through a catadioptric projection objective in accordance with a further embodiment the present invention; 
           [0036]      FIG. 8  shows a meridian section through a catadioptric projection objective in accordance with another embodiment the present invention; 
           [0037]      FIG. 9  shows a meridian section through a complete catadioptric projection objective in accordance with still another embodiment the present invention. 
       
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0038]      FIG. 1  shows a meridian section through a microlithographic projection exposure apparatus denoted in its entirety by  110  in a considerably simplified view that is not to scale. The projection exposure apparatus  110  comprises an illuminating system  112  for generating projection light  113  including a light source  114 , illumination optics indicated by  116  and a diaphragm  118 . In the exemplary embodiment shown, the projection light  113  has a wavelength of 193 nm. 
         [0039]    The projection exposure apparatus  110  furthermore includes a projection objective  120  that comprises a multiplicity of lens elements, of which, for the sake of clarity, only a few are indicated by way of example in  FIG. 1  and are denoted by L 1  to L 5 . The projection objective  120  images a mask  124  disposed in an object plane  122  of the projection objective  120  on a reduced scale on a photosensitive layer  126 . The layer  126 , which may be composed of a photoresist, is disposed in an image plane  128  of the projection objective  120  and is applied to a substrate  130 . The photosensitive layer  126  may itself be composed of a plurality of layers and may also comprise antireflection layers, as is known in the art as such. 
         [0040]    An immersion liquid  134  has been introduced into a gap  132  that remains between the last lens element L 5  on the image side and the photosensitive layer  126 . 
         [0041]    This can be seen more clearly in  FIG. 2  that shows the image-side end of the projection objective  120  on an enlarged scale. The last lens element L 5  on the image side has, on the image side, a surface  136  that is concavely curved. The gap  132  between the last lens element L 5  on the image side and the photosensitive layer  126 , which is usually flat at both ends, now transforms into a kind of cavity. 
         [0042]    The surface  136  is approximately of spherical shell shape, the radius of curvature being denoted in  FIG. 2  by R. In this arrangement, the radius of curvature R is about 1.3 times the axial distance s between, the last lens element L 5  on the image side and the photosensitive layer  126 . 
         [0043]    The immersion liquid  134  has a refractive index n L  that is greater than the refractive index of the material n 1  of which the last lens element L 5  on the image side is composed. If, for example, quartz glass or calcium fluoride is used as material, a liquid should be chosen whose refractive index n L  is above 1.56 or 1.5. This can be achieved, for example, by adding sulphates, alkalis such as caesium, or phosphates to water, as is described on Internet page www.eetimes.com/semi/news/OEG20040128S0017. These immersion liquids have sufficient transparency and stability even at wavelengths in the deep ultraviolet spectral range. If the projection exposure apparatus  110  is designed for longer wavelengths, for example for wavelengths in the visible spectral range, conventional immersion liquids having high refractive index, such as, for example, cedarwood oil, carbon disulphide or monobromonaphthalene may also be used as immersion liquid. 
         [0044]    Since the immersion liquid forms, with respect to the object plane  122 , a convexly curved interface  139  with the last lens element L 5  on the image side, only relatively small beam incidence angles occur at said interface  139 . This is shown in  FIG. 2  by way of example for aperture rays  113   a  and  113   b  having a maximum aperture angles α. As a result, reflection losses at said interface are correspondingly small. Thus rays having large aperture angles with respect to an optical axis OA of the projection objective  120  may also contribute to forming an image of the mask  124 , with the result that it is possible to achieve with the projection objective  120  numerical apertures that extend up to the refractive index n L  of the immersion liquid  134 . If, on the other hand, the interface  139  were plane, as is usual in the prior art, said rays would be totally reflected at the interface between the last lens element L 5  and the immersion liquid. 
         [0045]      FIG. 3  shows a projection objective  120  in accordance with another exemplary embodiment in a view along the lines of  FIG. 2 . Identical parts are characterized in the figure by identical reference numerals. 
         [0046]    The projection objective  120 ′ differs from the projection objective  120  shown in  FIGS. 1 and 2  only in that a ring  140  is tightly joined to the last lens element L 5  and a housing  141  of the projection objective  120 . The ring  140  functions as a drainage barrier for the immersion liquid  134 . Such a drainage barrier may be particularly advantageous if the surface  136  of the last lens element L 5  on the image side is strongly curved since then the gap  132  has a large maximum extension along the optical axis OA. Accordingly, the hydrostatic pressure of the immersion liquid  134  is relatively high. Without a drainage barrier, said pressure may ultimately have the result that the immersion liquid  134  is forced out of the cavity into the surrounding gap  132  between the projection objective  120  and the photosensitive layer  126  so that a surrounding gas may enter the cavity. 
         [0047]    The ring  140  may be composed, for example, of a standard lens material such as quartz glass or calcium chloride, but also of other materials, such as Invar™ nickel alloy, stainless steel or (glass) ceramic. 
         [0048]      FIG. 4  shows an image-side end of a projection objective  120 ″ in accordance with a further exemplary embodiment in which a curvature of the immersion liquid  134  is achieved in another way. 
         [0049]    In the projection objective  120 ″, the immersion liquid  134  does not directly adjoin a last lens element L 5 ″ on the image side. Instead, a further liquid, which is referred to in the following as intermediate liquid  142 , is situated between the last lens element L 5 ″ on the image side and the immersion liquid  134 . The intermediate liquid  142  is, in the embodiment shown, water to which ions have been added. Due to the ions the water becomes electrically conductive. The immersion liquid  134 , which also in this case has a greater refractive index than the last lens element L 5 ″, is electrically insulating. For wavelengths of the projection light that are in the visible spectral range, the oils and naphthalenes already mentioned above are, for example, suitable as immersion liquid  134 . 
         [0050]    The intermediate liquid  142  completely fills the space that remains between an image-side surface  136 ″ of the last lens element L 5 ″ on the image side and the immersion liquid  134 . The surface  136 ″ is convexly curved in the exemplary embodiment shown, but the latter may also be a plane surface. Adjacent to a ring  140 ″ that, as in the exemplary embodiment described above, has the function of a drainage barrier, a likewise annular conical electrode  146  is provided that is connected to a controllable voltage source  147 . Applied to the conical electrode  146  is an insulator layer  148  that, together with the photosensitive layer  126 , ensures continuous insulation of the immersion liquid  134  with respect to the image plane. The voltage source  147  generates an alternating voltage whose frequency is between 100 kHz and 500 kHz. The voltage applied to the conical electrode  146  is in the order of magnitude of about 40 V. 
         [0051]    When the alternating voltage is applied to the conical electrode  146 , the electrowetting effect known as such has the result that the interface  139  between the immersion liquid  134  and the intermediate liquid  142  convexly curves towards the object plane  122 . The cause of this curvature is capillary forces that, together with the unalterability of the total volume and the tendency to the formation of a minimum surface, generate, to a good approximation, a spherical interface  139  if a sufficiently high alternating voltage is applied to electrode  146 . 
         [0052]    If the alternating voltage is now reduced, the curvature of the interface  139  decreases. In  FIG. 4  this is indicated by an interface  139 ′ shown as a broken line. The refractive index of the liquid lens formed by the immersion liquid  134  can consequently be continuously varied in a simple way, namely by altering the electrical alternating voltage applied to the conical electrode  146 . For the sake of completeness, it may also be mentioned at this point that the curvature of the interface  139  does not necessarily require an alternating voltage, but may also be achieved with a direct voltage. 
         [0053]    Also in this embodiment, the interface of the immersion liquid  134  that is convexly curved towards the object plane  122  has the effect that a numerical aperture can be achieved that is limited not by the refractive index of the last lens element L 5 ″ but only by the refractive index of the immersion liquid  134 . 
         [0054]    The continuous variability of the refractive power of the liquid lens formed by the immersion liquid  134  can advantageously also be used at other locations in the projection objective. Advantageously, such a liquid lens can be used at positions inside the projection objective that are exposed to particularly high light intensities. Degradation phenomena, such as occur in the case of conventional solid lenses, can be suppressed in this way or at least be repaired by simply replacing the immersion liquid. Incidentally, corresponding remarks also apply to the embodiments shown in  FIGS. 2 and 3 . 
         [0055]      FIG. 5  shows an image-side end of a projection objective according to a still further exemplary embodiment. Here the last lens element L 205  has a spherical surface  236  facing towards the image plane that has a smaller concave curvature, i.e. a larger&#39;radius R, than the lens element L 5  in the embodiments shown in  FIGS. 2 and 3 . In the following the geometrical conditions at the interface between the last lens element L 205  and the immersion liquid  134  will be discussed in further detail. 
         [0056]    Reference numeral AR denotes an aperture ray having a maximum aperture angle φ. The aperture ray AR impinges on the photosensitive layer  126  at a peripheral point of the image field at a height h with respect to the optical axis OA. The aperture ray AR has an angle of incidence α and an angle of refraction β at the interface between the last lens element L 205  and the immersion liquid  134 . The distance between the vertex of the last surface  236  of the lens element L 205  and the image plane in which the photosensitive layer  126  is positioned is denoted by s. 
         [0057]    Projection objectives are basically characterized by two quantities, namely the image-side numerical aperture 
         [0000]        NA=n ·sin(φ)
 
         [0000]    and the quantity 2 h, i.e. the diameter of a circle around the optical axis OA on which an image can be formed. 
         [0058]    From the image-side numerical aperture NA certain geometrical properties can be derived which ensure that the light can propagate through the last lens element and immersion liquid without being reflected at the interfaces. However, the design requirements applied to the last lens element are, in practice, somewhat stricter than those that can be derived solely from the image-side numerical aperture. For example, the angle of incidence α should not exceed a certain value that is, for example, about 75°, and more preferably 70°. This is because experience shows that projection objectives having larger angles of incidence α require very complex measures to achieve a good aberration correction and a reduced sensitivity to manufacturing tolerances and changing environmental conditions. 
         [0059]    At present projection objectives for dry operation achieve an image-side NA close to about 0.95. This means that the numerical aperture NA does not exceed 95% of the refractive index of the medium (usually a gas or a mixture of gases such as air) that immediately precedes the image plane. In such dry projection objectives the maximum angles of incidence are in the order of about 70°, in particular at the last surfaces close to the image plane but also at other surfaces of lens elements. 
         [0060]    Since these considerations also apply to immersion objectives, the angles of incidence should be kept below these values. From geometrical considerations it becomes clear that the stronger the curvature of the surface  236  is, the smaller are the angles of incidence. Thus a strong curvature ensures that the angles of incidence do not go beyond these values. 
         [0061]    The surface  236  of the lens element L 205  should, on the other hand, not be too severely curved. This is due to the fact that a too severely curvature may result in increased problems with respect to flow mechanics, contamination and temperature sensitivity of the immersion liquid  134 . For example, it may be difficult to achieve a homogenous and constant temperature of the immersion liquid  134 , and, the immersion liquid  134  may be enclosed in such a way within a strongly convex cavity that replacing the immersion liquid, for example for purging reasons, becomes a very complex task. 
         [0062]    It has been found out that a good compromise is achieved if the following condition holds for the maximum angle of incidence α: 
         [0000]      0.95&gt;sin(α)&gt;0.85.
 
         [0063]    In the following a formula is derived that specifies a suitable curvature ρ as a function of NA=n.sin(φ), distance s, image height h and the refractive indices n′, n of the last lens element L 205  and the immersion liquid  134 , respectively, so that the sine of the angle of incidence α does not exceed a certain advantageous and practicable value. Such a value was found to be sin(α)&lt;κ, where κ=0.95. Using the law of refraction, it follows that 
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         [0000]    According to simple geometrical considerations, it can be deduced therefrom that 
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         [0000]    is the condition for minimum surface curvature. For the radius R=1/ρ this gives 
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         [0064]    For an exemplary numerical aperture NA=1.5 and SiO 2  as material for the last lens element L 205  with n′=1.56, this results in 
         [0000]    
       
      
       R&gt;m·s  
      
     
         [0000]    with m≈83. For s=2 mm, this leads to a radius R of about 167 mm for the maximum radius of curvature. 
         [0065]    If, in addition, the aperture rays of the outermost image point are taken into account in the case of a finite image field, it is sufficient for this purpose to substitute the distance s by s′ according to 
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         [0000]    in the above formulae. For a maximum field height h, it then follows for the minimum curvature ρ 
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         [0066]    If one starts with a projection objective having the above mentioned parameters, i.e. NA=1.5 and n′=1.56, and if one further assumes that the maximum field height h is 15 mm, the maximum radius of curvature R should be below m=83 times (s−5.57 mm). For s=8 mm, this results in a maximum radius of curvature R of approximately 200 mm, and for s=10 mm R is approximately 375 mm. 
         [0067]    If, for example, κ is selected to be&#39;0.95 and an immersion liquid with a refractive index of n=1.43 is used, a numerical aperture NA=1.35 may be realized with a last lens element L 205  that is made of SiO 2  and which has a distance s=2 mm to the image plane and has a maximum radius of curvature below approximately 80 mm. The aforementioned detrimental effects that occur in the case of large curvatures can be minimized if the maximum radius of the surface is not only below the given values, but at least substantially identical to these values. 
         [0068]    Apart from the fact that the maximum angle of incidence should not exceed certain upper and lower limits as is explained above, it should be ensured that the light rays rather quickly converge if one looks from a point on the image plane towards the object plane. Otherwise optical elements with very large diameters would be required. 
         [0069]    This qualitative design rule can be mathematically expressed in the following way: If k, l, m are the three direction cosines of an aperture ray and n is the refractive within a medium with k 2 +l 2 +m 2 =n 2 , there should be no volume in the objective (particularly in the vicinity of the image plane) in which (k 2 +l 2 )/n 2 &gt;K 0 . The limit K 0  may be selected to be K 0 =0.95 or even better K 0 =0.85. 
         [0070]      FIG. 6  shows a meridian section through a first exemplary embodiment of the projection objective  120  shown in  FIGS. 1 and 2 . The design data of the projection objective are listed in Table 1; radii and thicknesses are specified in millimeters. The numerals above the projection objective point to selected surfaces of optical elements. Surfaces that are characterized by groups of short bars are aspherically curved. The curvature of said surfaces is described by the aspherical formula below: 
         [0000]    
       
         
           
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                   h 
                   12 
                 
               
               + 
               
                 F 
                  
                 
                     
                 
                  
                 
                   h 
                   14 
                 
               
             
           
         
       
     
         [0071]    In this equation, z is the saggita of the respective surface parallel to the optical axis, h is the radial distance from the optical axis, c=1/R is the curvature at the vertex of the respective surface where R is the radius of curvature, k is the conical constant and A, B, C, D, E and F are the aspherical constants listed in Table 2. In the exemplary embodiment, the spherical constant k equals zero. 
         [0072]    The projection objective  120  contains two aspherical mirrors S 1  and S 2  between which two (not optimally corrected) intermediate images are produced. The projection objective  120  is designed for a wavelength of 193 nm and a refractive index n L  of the immersion liquid of 1.60. The linear magnification of the projection objective  120  is β=−0.25 and the numerical aperture is NA=1.4. Some additional improvements, however, make it possible to achieve without difficulty also a numerical aperture NA that just reaches the refractive index of the immersion medium and is, consequently, only slightly less than 1.6. 
         [0073]      FIGS. 7 to 9  show meridian sections through three furthey exemplary embodiments of the projection objective  120  shown in  FIGS. 1 and 2 . The design data and aspherical constants of the projection objective shown in  FIG. 7  are listed in Tables 3 and 4; Tables 5, 6 and Tables 7, 8 list the design data and aspherical constants for the embodiments shown in  FIGS. 8 and 9 , respectively. 
         [0074]    The projection objectives shown in  FIGS. 7 to 9  all have an image-side numerical aperture NA=1.40 and an immersion liquid with a refractive index of n L =1.60. Thus this refractive index is always greater than the refractive index of the last lens element made of CaF 2 , i.e. n L &gt;n CaF2 . 
         [0075]    The projection objective shown in  FIG. 7 , which is designed for a wavelength λ=193 nm, is non-achromatized and has a last lens element LL 7  with a strongly concavely curved image-side surface that forms a kind of cavity for the immersion liquid  134 . The wavefront is corrected to about 2/100λ. 
         [0076]    The projection objective shown in  FIG. 8  is designed for a wavelength λ=157 nm and is achromatized. The image-side surface of the last lens element LL 8  is even stronger concavely curved; apart from that, the radius of curvature is almost identical with the axial distance between the last lens element LL 8  and the image plane, i.e. the center of curvature lies substantially within the image plane. As a result, the immersion liquid  134  has a large maximum thickness. Although the refractive index of CaF 2  is about n CaF2 =1.56 at λ=157 nm, the refractive index of the immersion liquid is still assumed to be larger (n L =1.60). The wavefront is corrected to about 4/100λ. 
         [0077]    The projection objective shown in  FIG. 9  is designed for a wavelength λ=193 nm and is non-achromatized. The image-side surface of the last lens element LL 9  has only a small concave curvature so that the immersion liquid  934  forms almost a flat layer. The radius of curvature is significantly (about a factor  10 ) greater than the axial distance between the last lens element LL 9  and the image plane, i.e. there is a substantial distance between the center of curvature and the image plane. The maximum angel of incidence at the interface between the last lens element LL 9  and the immersion liquid  934  is about 67° (i.e. sin α=0.92). The wavefront is corrected to about 5/100λ. 
         [0078]    When comparing the wavefront errors in the similar embodiments shown in  FIGS. 7 and 9 , it becomes clear that the design of  FIG. 7  with its greater curvature of the image-side surface of the last lens element LL 7  allows to achieve a much better wavefront correction (2/100λ vs. 5/100λ). However, although the projection objective shown in  FIG. 9  is not as well corrected as the projection objective shown in  FIG. 7 , due to the comparatively large radius of curvature there is only a small cavity underneath the last lens element LL 9  which is advantageous for the reasons that have been mentioned above. 
         [0079]    It goes without saying that the present invention is not restricted to the use in catadioptric projection objectives as have been described above. The invention can also advantageously be used in projection objectives having a smaller or larger number of intermediate images than in the embodiments shown, and also in dioptric projection objectives with or without any intermediate images. In addition, the optical axis may also extend through the center of the image field. Examples of further suitable lens designs are to be found, for example, in US 2002/0196533 A1, WO 01/050171 A1, WO 02/093209 A2 and U.S. Pat. No. 6,496,306A. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Design data 
               
             
          
           
               
                 SURFACE 
                 RADIUS 
                 ASPHERICAL 
                 THICKNESS 
                 MATERIAL 
               
               
                   
               
             
          
           
               
                 Object plane 
                 ∞ 
                   
                 37.648 
                   
               
               
                 1 
                 210.931 
                   
                 21.995 
                 SiO 2   
               
               
                 2 
                 909.02 
                   
                 1.605 
               
               
                 3 
                 673.572 
                   
                 22.728 
                 SiO 2   
               
               
                 4 
                 −338.735 
                 x 
                 33.19 
               
               
                 5 
                 130.215 
                 x 
                 8.994 
                 SiO 2   
               
               
                 6 
                 119.808 
                   
                 36.001 
               
               
                 7 
                 216 
                   
                 40.356 
                 SiO 2   
               
               
                 8 
                 −210.59 
                   
                 0.939 
               
               
                 9 
                 97.24 
                   
                 49.504 
                 SiO 2   
               
               
                 10 
                 216.208 
                 x 
                 8.164 
               
               
                 12 
                 −65.704 
                   
                 49.734 
                 SiO 2   
               
               
                 Diaphragm 
                 ∞ 
                   
                 49.302 
               
               
                 13 
                 −113.325 
                   
                 55.26 
               
               
                 14 
                 −6210.149 
                 x 
                 70.31 
                 SiO 2   
               
               
                 15 
                 −195.536 
                   
                 0.962 
               
               
                 16 
                 3980.16 
                   
                 65.997 
                 SiO 2   
               
               
                 17 
                 −473.059 
                   
                 277.072 
               
               
                 18 
                 −225.942 
                 x 
                 246.731 
                 Mirror 
               
               
                 19 
                 193.745 
                 x 
                 294.329 
                 Mirror 
               
               
                 20 
                 −338.56 
                 x 
                 17.389 
                 SiO 2   
               
               
                 21 
                 −206.244 
                   
                 8.884 
               
               
                 22 
                 −148.97 
                   
                 34.064 
                 SiO 2   
               
               
                 23 
                 129.921 
                 x 
                 40.529 
               
               
                 24 
                 −2704.885 
                   
                 33.192 
                 SiO 2   
               
               
                 25 
                 −195.599 
                   
                 0.946 
               
               
                 26 
                 −794.214 
                 x 
                 30.169 
                 SiO 2   
               
               
                 27 
                 −479.39 
                   
                 24.236 
               
               
                 28 
                 −311.778 
                 x 
                 100.056 
                 SiO 2   
               
               
                 29 
                 −159.333 
                   
                 28.806 
               
               
                 30 
                 309.839 
                   
                 43.609 
                 SiO 2   
               
               
                 31 
                 836.077 
                 x 
                 0.951 
               
               
                 32 
                 225.096 
                   
                 55.667 
                 SiO 2   
               
               
                 33 
                 687.556 
                   
                 0.945 
               
               
                 34 
                 154.575 
                   
                 64.278 
                 SiO 2   
               
               
                 35 
                 911.8 
                 x 
                 0.932 
               
               
                 36 
                 89.986 
                   
                 44.143 
                 SiO 2   
               
               
                 37 
                 199.475 
                 x 
                 0.878 
               
               
                 38 
                 61.984 
                   
                 9.635 
                 SiO 2   
               
               
                 39 
                 35.475 
                   
                 34.43 
                 Liquid 
               
               
                 40 
                 ∞ 
                   
                   
                 Resist 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Aspherical constants 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Surface 4 
                 Surface 5 
                 Surface10 
                 Surface 14 
               
               
                   
               
             
          
           
               
                 A 
                 5.36225288E−08 
                 A 
                 2.53854010E−08 
                 A 
                 4.51137087E−07 
                 A 
                 −8.48905023E−09 
               
               
                 B 
                 −5.17992581E−12 
                 B 
                 −1.22713179E−11 
                 B 
                 2.46833840E−11 
                 B 
                 1.45061822E−13 
               
               
                 C 
                 8.49599769E−16 
                 C 
                 1.21417341E−15 
                 C 
                 5.78496960E−15 
                 C 
                 −6.34351367E−18 
               
               
                 D 
                 −7.57832730E−20 
                 D 
                 −1.92474180E−19 
                 D 
                 −4.39101683E−18 
                 D 
                 2.84301572E−22 
               
               
                 E 
                 3.59228710E−24 
                 E 
                 2.08240691E−23 
                 E 
                 −5.64853356E−22 
                 E 
                 −8.24902650E−27 
               
               
                 F 
                 −9.16722201E−29 
                 F 
                 −9.29539601E−28 
                 F 
                 4.95744749E−26 
                 F 
                 1.27798308E−31 
               
               
                   
               
             
          
           
               
                   
                 Surface 18 
                 Surface 19 
                 Surface 20 
               
               
                   
                   
               
             
          
           
               
                   
                 A 
                 1.04673033E−08 
                 A 
                 −4.11099367E−09 
                 A 
                 1.14749646E−07 
               
               
                   
                 B 
                 1.34351117E−13 
                 B 
                 −9.91828838E−14 
                 B 
                 −8.19248307E−12 
               
               
                   
                 C 
                 1.03389626E−18 
                 C 
                 −7.93614779E−19 
                 C 
                 8.78420843E−16 
               
               
                   
                 D 
                 5.16847878E−23 
                 D 
                 −1.66363646E−22 
                 D 
                 −1.39638210E−19 
               
               
                   
                 E 
                 −1.23928686E−27 
                 E 
                 5.56486530E−27 
                 E 
                 2.09064504E−23 
               
               
                   
                 F 
                 3.09904827E−32 
                 F 
                 −1.79683490E−31 
                 F 
                 −2.15981914E−27 
               
               
                   
                   
               
             
          
           
               
                   
                 Surface 23 
                 Surface 26 
                 Surface 28 
               
               
                   
                   
               
             
          
           
               
                   
                 A 
                 −2.87603531E−08 
                 A 
                 −4.35420789E−08 
                 A 
                 −2.70754285E−08 
               
               
                   
                 B 
                 −9.68432739E−12 
                 B 
                 −6.70429494E−13 
                 B 
                 −1.36708653E−12 
               
               
                   
                 C 
                 6.88099059E−16 
                 C 
                 −4.05835225E−17 
                 C 
                 −2.46085956E−17 
               
               
                   
                 D 
                 −8.70009838E−20 
                 D 
                 −1.10658303E−20 
                 D 
                 2.26651081E−21 
               
               
                   
                 E 
                 9.59884320E−24 
                 E 
                 4.80978147E−25 
                 E 
                 −1.20009586E−25 
               
               
                   
                 F 
                 −5.07639229E−28 
                 F 
                 −5.35014389E−29 
                 F 
                 9.28622501E−30 
               
               
                   
                   
               
             
          
           
               
                   
                 Surface 31 
                 Surface 35 
                 Surface 37 
               
               
                   
                   
               
             
          
           
               
                   
                 A 
                 4.38707762E−09 
                 A 
                 1.73743303E−08 
                 A 
                 1.04975421E−07 
               
               
                   
                 B 
                 −3.69893805E−13 
                 B 
                 1.60994523E−12 
                 B 
                 1.94141448E−11 
               
               
                   
                 C 
                 −4.93747026E−18 
                 C 
                 −1.71036162E−16 
                 C 
                 −2.31145732E−15 
               
               
                   
                 D 
                 4.05461849E−22 
                 D 
                 1.26964535E−20 
                 D 
                 4.57201996E−19 
               
               
                   
                 E 
                 −7.59674606E−27 
                 E 
                 −5.77497378E−25 
                 E 
                 −3.92356845E−23 
               
               
                   
                 F 
                 5.58403314E−32 
                 F 
                 1.55390733E−29 
                 F 
                 2.35233647E−27 
               
               
                   
                   
                   
                 G 
                 −1.78430224E−34 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Design data 
               
             
          
           
               
                 SUR- 
                   
                 THICK- 
                 MATE- 
                   
                   
               
               
                 FACE 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 SEMIDIAM 
               
               
                   
               
             
          
           
               
                 0 
                 ∞ 
                 32.0000 
                   
                   
                 65.50 
               
               
                 1 
                 ∞ 
                 0.0000 
                   
                   
                 80.45 
               
               
                 2 
                 332.4480 
                 18.9959 
                 SiO 2   
                 1.560318 
                 84.22 
               
               
                 3 
                 27083.8930 
                 17.5539 
                   
                   
                 85.42 
               
               
                 4 
                 −253.5666 
                 26.7129 
                 SiO 2   
                 1.560318 
                 86.06 
               
               
                 5 
                 −179.3607 
                 164.1318 
                   
                   
                 90.72 
               
               
                 6 
                 1920.0084 
                 34.5089 
                 SiO 2   
                 1.560318 
                 111.13 
               
               
                 7 
                 −279.4103 
                 0.9461 
                   
                   
                 111.59 
               
               
                 8 
                 213.6767 
                 34.3917 
                 SiO 2   
                 1.560318 
                 103.48 
               
               
                 9 
                 17137.3629 
                 26.7484 
                   
                   
                 100.67 
               
               
                 10 
                 −208.9766 
                 9.4997 
                 SiO 2   
                 1.560318 
                 99.22 
               
               
                 11 
                 −609.1513 
                 0.9500 
                   
                   
                 97.67 
               
               
                 12 
                 734.0560 
                 18.8742 
                 SiO 2   
                 1.560318 
                 95.00 
               
               
                 13 
                 −1380.9253 
                 24.2008 
                   
                   
                 93.32 
               
               
                 14 
                 ∞ 
                 231.0887 
                   
                   
                 81.98 
               
               
                 15 
                 252.7510 
                 74.6720 
                 SiO 2   
                 1.560318 
                 126.43 
               
               
                 16 
                 1098.5274 
                 0.9492 
                   
                   
                 121.38 
               
               
                 17 
                 268.9906 
                 50.1845 
                 SiO 2   
                 1.560318 
                 119.28 
               
               
                 18 
                 −463.5300 
                 1.0915 
                   
                   
                 117.08 
               
               
                 19 
                 697.8278 
                 30.0054 
                 SiO 2   
                 1.560318 
                 106.59 
               
               
                 20 
                 292.0140 
                 120.0163 
                   
                   
                 94.90 
               
               
                 21 
                 ∞ 
                 9.9914 
                   
                   
                 82.23 
               
               
                 22 
                 ∞ 
                 −100.0083 
                 Mirror 
                 1.560318 
                 142.10 
               
               
                 23 
                 −178.0803 
                 −45.0048 
                 SiO 2   
                 1.560318 
                 115.52 
               
               
                 24 
                 −663.9291 
                 −95.3149 
                   
                   
                 113.38 
               
               
                 25 
                 −237.9404 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 115.72 
               
               
                 26 
                 −166.3412 
                 −152.4364 
                   
                   
                 111.11 
               
               
                 27 
                 222.8026 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 127.22 
               
               
                 28 
                 539.8416 
                 −94.3687 
                   
                   
                 138.91 
               
               
                 29 
                 364.8709 
                 94.3687 
                 Mirror 
                   
                 167.04 
               
               
                 30 
                 539.8416 
                 15.0000 
                 SiO 2   
                 1.560318 
                 138.91 
               
               
                 31 
                 222.8026 
                 152.4364 
                   
                   
                 127.22 
               
               
                 32 
                 −166.3412 
                 15.0000 
                 SiO 2   
                 1.560318 
                 111.11 
               
               
                 33 
                 −237.9404 
                 95.3149 
                   
                   
                 115.72 
               
               
                 34 
                 −663.9291 
                 45.0048 
                 SiO 2   
                 1.560318 
                 113.38 
               
               
                 35 
                 −178.0803 
                 100.0083 
                   
                   
                 115.52 
               
               
                 36 
                 ∞ 
                 94.5942 
                   
                   
                 122.31 
               
               
                 37 
                 ∞ 
                 −23.8903 
                   
                   
                 91.10 
               
               
                 38 
                 ∞ 
                 20.0000 
                   
                   
                 179.89 
               
               
                 39 
                 254.8239 
                 29.5175 
                 SiO 2   
                 1.560318 
                 96.82 
               
               
                 40 
                 −2985.0549 
                 36.7407 
                   
                   
                 96.62 
               
               
                 41 
                 200.4128 
                 45.9683 
                 SiO 2   
                 1.560318 
                 106.20 
               
               
                 42 
                 −666.1976 
                 170.5500 
                   
                   
                 105.01 
               
               
                 43 
                 −95.1516 
                 15.0000 
                 SiO 2   
                 1.560318 
                 77.96 
               
               
                 44 
                 −643.9252 
                 55.6492 
                   
                   
                 95.09 
               
               
                 45 
                 −175.8508 
                 −55.6492 
                 Mirror 
                   
                 109.51 
               
               
                 46 
                 −643.9252 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 95.09 
               
               
                 47 
                 −95.1516 
                 −170.5500 
                   
                   
                 77.96 
               
               
                 48 
                 −666.1976 
                 −45.9683 
                 SiO 2   
                 1.560318 
                 105.01 
               
               
                 49 
                 200.4128 
                 −12.1735 
                   
                   
                 106.20 
               
               
                 50 
                 ∞ 
                 −24.5646 
                   
                   
                 90.83 
               
               
                 51 
                 −2985.0549 
                 −29.5175 
                 SiO 2   
                 1.560318 
                 96.62 
               
               
                 52 
                 254.8239 
                 −20.0000 
                   
                   
                 96.82 
               
               
                 53 
                 ∞ 
                 180.1673 
                 Mirror 
                   
                 134.73 
               
               
                 54 
                 −148.5117 
                 25.7491 
                 SiO 2   
                 1.560318 
                 95.86 
               
               
                 55 
                 327.9861 
                 43.1843 
                   
                   
                 116.84 
               
               
                 56 
                 −496.1113 
                 30.0070 
                 SiO 2   
                 1.560318 
                 124.28 
               
               
                 57 
                 −252.6773 
                 19.1777 
                   
                   
                 130.89 
               
               
                 58 
                 1365.3904 
                 68.1411 
                 SiO 2   
                 1.560318 
                 165.17 
               
               
                 59 
                 −284.3746 
                 73.5313 
                   
                   
                 172.58 
               
               
                 60 
                 754.4880 
                 93.5313 
                 SiO 2   
                 1.560318 
                 234.19 
               
               
                 61 
                 −588.1067 
                 54.2510 
                   
                   
                 235.10 
               
               
                 62 
                 357.9132 
                 85.3268 
                 SiO 2   
                 1.560318 
                 221.99 
               
               
                 63 
                 −762.8649 
                 0.9929 
                   
                   
                 220.72 
               
               
                 64 
                 304.8598 
                 57.6484 
                 SiO 2   
                 1.560318 
                 181.91 
               
               
                 65 
                 1098.9629 
                 0.9340 
                   
                   
                 177.48 
               
               
                 66 
                 143.0811 
                 62.6047 
                 SiO 2   
                 1.560318 
                 127.33 
               
               
                 67 
                 347.6273 
                 0.9010 
                   
                   
                 177.47 
               
               
                 68 
                 79.6669 
                 50.1800 
                 CaF 2   
                 1.501403 
                 73.25 
               
               
                 69 
                 36.1540 
                 21.2194 
                 Liquid 
                 1.600000 
                 31.82 
               
               
                 70 
                 ∞ 
                   
                   
                   
                 19.38 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Aspherical constants 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 SURFACE 
                 3 
                 19 
                 24 
                 28 
                 30 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 4.047232E−09 
                 −4.175853E−08 
                 −3.889430E−08 
                 6.661869E−09 
                 6.661869E−09 
               
               
                 B 
                 8.449241E−13 
                 −5.621416E−13 
                 2.260825E−13 
                 2.899240E−13 
                 2.899240E−13 
               
               
                 C 
                 5.603175E−17 
                 −2.909466E−19 
                 9.880822E−18 
                 −1.932302E−17 
                 −1.932302E−17 
               
               
                 D 
                 −4.004583E−21 
                 3.690043E−22 
                 −2.672567E−22 
                 1.602360E−21 
                 1.602360E−21 
               
               
                 E 
                 −8.168767E−25 
                 2.119217E−26 
                 4.717688E−26 
                 −6.342246E−26 
                 −6.342246E−26 
               
               
                 F 
                 2.123279E−29 
                 −9.535588E−31 
                 −3.817055E−30 
                 1.183564E−30 
                 1.183564E−30 
               
               
                   
               
               
                 SURFACE 
                 34 
                 39 
                 44 
                 46 
                 52 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −3.889430E−08 
                 −2.037803E−08 
                 −1.157857E−08 
                 −1.157857E−08 
                 −2.037803E−08 
               
               
                 B 
                 2.260825E−13 
                 −6.612137E−13 
                 1.455623E−12 
                 1.455623E−12 
                 −6.612137E−13 
               
               
                 C 
                 9.880822E−18 
                 2.840028E−17 
                 −5.746524E−17 
                 −5.746524E−17 
                 2.840028E−17 
               
               
                 D 
                 −2.672567E−22 
                 −4.931922E−21 
                 1.261354E−21 
                 1.261354E−21 
                 −4.931922E−21 
               
               
                 E 
                 4.717688E−26 
                 4.142905E−25 
                 4.054615E−25 
                 4.054615E−25 
                 4.142905E−25 
               
               
                 F 
                 −3.817055E−30 
                 −1.562251E−29 
                 −2.761361E−29 
                 −2.761361E−29 
                 −1.562251E−29 
               
               
                   
               
             
          
           
               
                 SURFACE 
                 58 
                 62 
                 65 
                 67 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −1.679180E−08 
                 −1.483428E−08 
                 −9.489171E−09 
                 −1.782977E−08 
               
               
                 B 
                 −5.846864E−14 
                 −2.269457E−14 
                 5.001612E−13 
                 9.574096E−13 
               
               
                 C 
                 7.385649E−18 
                 4.944523E−18 
                 −1.283531E−17 
                 7.878477E−17 
               
               
                 D 
                 −5.142028E−22 
                 −1.410026E−22 
                 −8.674473E−23 
                 −7.167182E−21 
               
               
                 E 
                 1.479187E−26 
                 1.643655E−27 
                 7.103644E−27 
                 2.682224E−25 
               
               
                 F 
                 −2.189903E−31 
                 −7.668842E−33 
                 −7.251904E−32 
                 −3.423260E−30 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Design data 
               
             
          
           
               
                 SUR- 
                   
                 THICK- 
                 MATE- 
                   
                   
               
               
                 FACE 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 SEMIDIAM 
               
               
                   
               
             
          
           
               
                 0 
                 ∞ 
                 32.0000 
                   
                   
                 65.50 
               
               
                 1 
                 ∞ 
                 0.0000 
                   
                   
                 80.46 
               
               
                 2 
                 3568.5495 
                 29.3610 
                 CAF 2   
                 1.555560 
                 80.77 
               
               
                 3 
                 −306.4778 
                 50.8080 
                   
                   
                 84.99 
               
               
                 4 
                 −495.7015 
                 32.5298 
                 CAF 2   
                 1.555560 
                 97.37 
               
               
                 5 
                 −161.1181 
                 81.4155 
                   
                   
                 99.50 
               
               
                 6 
                 188.0753 
                 36.2525 
                 CAF 2   
                 1.555560 
                 93.00 
               
               
                 7 
                 −1013.7352 
                 6.1886 
                   
                   
                 90.93 
               
               
                 8 
                 288.3482 
                 26.9703 
                 CAF 2   
                 1.555560 
                 82.17 
               
               
                 9 
                 872.7887 
                 32.5801 
                   
                   
                 74.60 
               
               
                 10 
                 ∞ 
                 47.8395 
                   
                   
                 57.76 
               
               
                 11 
                 −76.3176 
                 12.9591 
                 CAF 2   
                 1.555560 
                 65.40 
               
               
                 12 
                 −82.8195 
                 72.8834 
                   
                   
                 71.21 
               
               
                 13 
                 494.0581 
                 30.0025 
                 CAF 2   
                 1.555560 
                 105.98 
               
               
                 14 
                 500.2689 
                 0.9499 
                   
                   
                 109.01 
               
               
                 15 
                 210.1705 
                 55.9335 
                 CAF 2   
                 1.555560 
                 115.54 
               
               
                 16 
                 −462.2471 
                 0.9442 
                   
                   
                 114.96 
               
               
                 17 
                 191.5029 
                 28.1484 
                 CAF 2   
                 1.555560 
                 104.19 
               
               
                 18 
                 469.5739 
                 3.8083 
                   
                   
                 100.65 
               
               
                 19 
                 313.4359 
                 9.4935 
                 CAF 2   
                 1.555560 
                 99.24 
               
               
                 20 
                 161.6230 
                 115.1964 
                   
                   
                 91.07 
               
               
                 21 
                 ∞ 
                 14.7967 
                   
                   
                 90.40 
               
               
                 22 
                 ∞ 
                 −100.0183 
                 Mirror 
                   
                 206.37 
               
               
                 23 
                 −247.2670 
                 −56.5211 
                 CAF 2   
                 1.555560 
                 148.25 
               
               
                 24 
                 1546.1350 
                 −403.3917 
                   
                   
                 147.84 
               
               
                 25 
                 500.0000 
                 −25.0000 
                 CAF 2   
                 1.555560 
                 142.88 
               
               
                 26 
                 −2059.5717 
                 −87.3199 
                   
                   
                 147.68 
               
               
                 27 
                 173.4701 
                 −25.0000 
                 CAF 2   
                 1.555560 
                 148.30 
               
               
                 28 
                 823.5657 
                 −65.7941 
                   
                   
                 193.66 
               
               
                 29 
                 295.8639 
                 65.7941 
                 Mirror 
                   
                 204.70 
               
               
                 30 
                 823.5657 
                 25.0000 
                 CAF 2   
                 1.555560 
                 193.66 
               
               
                 31 
                 173.4701 
                 87.3199 
                   
                   
                 148.30 
               
               
                 32 
                 −2059.5717 
                 25.0000 
                 CAF 2   
                 1.555560 
                 147.68 
               
               
                 33 
                 500.0000 
                 403.3917 
                   
                   
                 142.88 
               
               
                 34 
                 1546.1350 
                 56.5211 
                 CAF 2   
                 1.555560 
                 147.84 
               
               
                 35 
                 −247.2670 
                 100.0183 
                   
                   
                 148.25 
               
               
                 36 
                 ∞ 
                 49.8789 
                   
                   
                 125.86 
               
               
                 37 
                 ∞ 
                 20.8278 
                   
                   
                 89.12 
               
               
                 38 
                 ∞ 
                 20.0000 
                   
                   
                 149.02 
               
               
                 39 
                 215.5222 
                 38.8898 
                 CAF 2   
                 1.555560 
                 91.59 
               
               
                 40 
                 −548.9606 
                 360.6137 
                   
                   
                 90.02 
               
               
                 41 
                 −126.6780 
                 15.0000 
                 CAF 2   
                 1.555560 
                 120.92 
               
               
                 42 
                 −567.9480 
                 48.8335 
                   
                   
                 169.01 
               
               
                 43 
                 −224.2817 
                 −48.8335 
                 Mirror 
                   
                 171.87 
               
               
                 44 
                 −567.9480 
                 −15.0000 
                 CAF 2   
                 1.555560 
                 169.01 
               
               
                 45 
                 −126.6780 
                 −314.8668 
                   
                   
                 120.92 
               
               
                 46 
                 ∞ 
                 −45.7487 
                   
                   
                 81.94 
               
               
                 47 
                 −548.9606 
                 −38.8898 
                 CAF 2   
                 1.555560 
                 90.02 
               
               
                 48 
                 215.5222 
                 −20.0000 
                   
                   
                 91.59 
               
               
                 49 
                 ∞ 
                 195.8787 
                 Mirror 
                   
                 133.74 
               
               
                 50 
                 −121.2718 
                 15.1499 
                 CAF 2   
                 1.555560 
                 97.18 
               
               
                 51 
                 529.2614 
                 24.3014 
                   
                   
                 127.08 
               
               
                 52 
                 −8438.5548 
                 64.5537 
                 CAF 2   
                 1.555560 
                 137.42 
               
               
                 53 
                 −202.6253 
                 25.2464 
                   
                   
                 142.97 
               
               
                 54 
                 −1447.9251 
                 63.0634 
                 CAF 2   
                 1.555560 
                 168.91 
               
               
                 55 
                 −254.3816 
                 80.5189 
                   
                   
                 174.93 
               
               
                 56 
                 783.5550 
                 57.0370 
                 CAF 2   
                 1.555560 
                 203.06 
               
               
                 57 
                 −939.7625 
                 70.4486 
                   
                   
                 203.12 
               
               
                 58 
                 358.1334 
                 55.4484 
                 CAF 2   
                 1.555560 
                 186.96 
               
               
                 59 
                 5861.2627 
                 0.9614 
                   
                   
                 184.33 
               
               
                 60 
                 259.9889 
                 36.5173 
                 CAF 2   
                 1.555560 
                 161.62 
               
               
                 61 
                 371.5128 
                 0.8975 
                   
                   
                 156.47 
               
               
                 62 
                 134.7936 
                 77.4909 
                 CAF 2   
                 1.555560 
                 127.53 
               
               
                 63 
                 767.8631 
                 0.7967 
                   
                   
                 119.07 
               
               
                 64 
                 72.9080 
                 48.3195 
                 CAF 2   
                 1.555560 
                 70.97 
               
               
                 65 
                 29.7284 
                 27.0563 
                 IMMO16 
                 1.600000 
                 31.25 
               
               
                 66 
                 ∞ 
                   
                   
                   
                 19.39 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Aspherical constants 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 SURFACE 
                 3 
                 9 
                 19 
                 24 
                 26 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 2.172737E−08 
                 8.983641E−08 
                 −5.825972E−08 
                 −1.605889E−08 
                 −2.779244E−10 
               
               
                 B 
                 1.718631E−12 
                 −5.996759E−12 
                 −6.306762E−13 
                 4.504977E−16 
                 −3.062909E−14 
               
               
                 C 
                 1.514127E−16 
                 6.363808E−16 
                 −2.783920E−17 
                 3.596627E−21 
                 1.861506E−18 
               
               
                 D 
                 −2.716770E−22 
                 −3.998733E−20 
                 −1.594705E−21 
                 2.792862E−22 
                 −2.425072E−22 
               
               
                 E 
                 −1.008203E−24 
                 −5.130142E−24 
                 2.956685E−25 
                 −1.885291E−26 
                 1.114443E−26 
               
               
                 F 
                 −1.157181E−28 
                 1.266998E−28 
                 −1.064251E−29 
                 3.351694E−31 
                 −2.553147E−31 
               
               
                   
               
             
          
           
               
                 SURFACE 
                 28 
                 30 
                 32 
                 34 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 4.632690E−09 
                 4.632690E−09 
                 −2.779244E−10 
                 −1.605889E−08 
               
               
                 B 
                 −3.213384E−14 
                 −3.213384E−14 
                 −3.062909E−14 
                 4.504977E−16 
               
               
                 C 
                 7.229632E−20 
                 7.229632E−20 
                 1.861506E−18 
                 3.596627E−21 
               
               
                 D 
                 2.100335E−23 
                 2.100335E−23 
                 −2.425072E−22 
                 2.792862E−22 
               
               
                 E 
                 −5.592560E−28 
                 −5.592560E−28 
                 1.114443E−26 
                 −1.885291E−26 
               
               
                 F 
                 6.249291E−33 
                 6.249291E−33 
                 −2.553147E−31 
                 3.351694E−31 
               
               
                   
               
               
                 SURFACE 
                 39 
                 42 
                 44 
                 48 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −1.815667E−08 
                 −9.514646E−09 
                 −9.514646E−09 
                 −1.815667E−08 
               
               
                 B 
                 −2.488991E−13 
                 1.336864E−13 
                 1.336864E−13 
                 −2.488991E−13 
               
               
                 C 
                 2.824306E−17 
                 −4.722253E−18 
                 −4.722253E−18 
                 2.824306E−17 
               
               
                 D 
                 −4.697303E−21 
                 1.120165E−22 
                 1.120165E−22 
                 −4.697303E−21 
               
               
                 E 
                 3.415362E−25 
                 −1.895395E−27 
                 −1.895395E−27 
                 3.415362E−25 
               
               
                 F 
                 −9.509214E−30 
                 1.489410E−32 
                 1.489410E−32 
                 −9.509214E−30 
               
               
                   
               
             
          
           
               
                   
                 SURFACE 
                 54 
                 59 
                 61 
                 63 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 A 
                 −1.031964E−08 
                 8.72E−09 
                 −2.45E−08 
                 4.37E−08 
               
               
                   
                 B 
                 −1.081794E−13 
                 −2.71E−13 
                 6.62E−13 
                 −8.96E−13 
               
               
                   
                 C 
                 6.909628E−18 
                 1.07E−17 
                 −1.32E−17 
                 4.21E−17 
               
               
                   
                 D 
                 −3.648077E−22 
                 −6.07E−22 
                 6.68E−22 
                 −3.88E−21 
               
               
                   
                 E 
                 9.693996E−27 
                 1.40E−26 
                 −1.47E−26 
                 2.01E−25 
               
               
                   
                 F 
                 −1.380442E−31 
                 −1.10E−31 
                 1.14E−31 
                 −3.84E−30 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Design data 
               
             
          
           
               
                 SUR- 
                   
                 THICK- 
                 MATE- 
                   
                   
               
               
                 FACE 
                 RADIUS 
                 NESS 
                 RIAL 
                 INDEX 
                 SEMIDIAM. 
               
               
                   
               
             
          
           
               
                 0 
                 ∞ 
                 32.0000 
                   
                   
                 65.50 
               
               
                 1 
                 ∞ 
                 0.0000 
                   
                   
                 80.45 
               
               
                 2 
                 361.5503 
                 30.0063 
                 SiO 2   
                 1.560318 
                 83.87 
               
               
                 3 
                 3766.1854 
                 29.9775 
                   
                   
                 86.87 
               
               
                 4 
                 −313.0243 
                 17.3177 
                 SiO 2   
                 1.560318 
                 90.72 
               
               
                 5 
                 −211.2930 
                 182.7697 
                   
                   
                 93.19 
               
               
                 6 
                 −709.0001 
                 29.1631 
                 SiO 2   
                 1.560318 
                 120.83 
               
               
                 7 
                 −255.7121 
                 13.1321 
                   
                   
                 122.28 
               
               
                 8 
                 261.1325 
                 45.4463 
                 SiO 2   
                 1.560318 
                 118.65 
               
               
                 9 
                 −728.3260 
                 29.9790 
                   
                   
                 116.70 
               
               
                 10 
                 −209.1405 
                 18.3161 
                 SiO 2   
                 1.560318 
                 113.35 
               
               
                 11 
                 −2675.8307 
                 4.7872 
                   
                   
                 113.10 
               
               
                 12 
                 421.7508 
                 25.2987 
                 SiO 2   
                 1.560318 
                 112.42 
               
               
                 13 
                 −5576.5014 
                 21.4392 
                   
                   
                 111.29 
               
               
                 14 
                 ∞ 
                 355.5491 
                   
                   
                 103.93 
               
               
                 15 
                 249.8044 
                 71.3667 
                 SiO 2   
                 1.560318 
                 163.42 
               
               
                 16 
                 −4441.8089 
                 32.5158 
                   
                   
                 161.31 
               
               
                 17 
                 247.2422 
                 37.4261 
                 SiO 2   
                 1.560318 
                 135.08 
               
               
                 18 
                 797.4045 
                 43.7199 
                   
                   
                 130.81 
               
               
                 19 
                 665.9047 
                 30.0078 
                 SiO 2   
                 1.560318 
                 108.60 
               
               
                 20 
                 318.3673 
                 120.0233 
                   
                   
                 96.83 
               
               
                 21 
                 ∞ 
                 9.9881 
                   
                   
                 79.40 
               
               
                 22 
                 ∞ 
                 −100.0079 
                 Mirror 
                   
                 122.85 
               
               
                 23 
                 −145.3105 
                 −45.0039 
                 SiO 2   
                 1.560318 
                 107.21 
               
               
                 24 
                 −705.3999 
                 −7.6524 
                   
                   
                 104.90 
               
               
                 25 
                 −149.2286 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 100.69 
               
               
                 26 
                 −107.5358 
                 −125.6003 
                   
                   
                 91.50 
               
               
                 27 
                 398.2665 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 101.84 
               
               
                 28 
                 419.3212 
                 −44.0802 
                   
                   
                 104.16 
               
               
                 29 
                 398.6744 
                 44.0802 
                 Mirror 
                   
                 107.66 
               
               
                 30 
                 419.3212 
                 15.0000 
                 SiO 2   
                 1.560318 
                 104.16 
               
               
                 31 
                 398.2665 
                 125.6003 
                   
                   
                 101.84 
               
               
                 32 
                 −107.5358 
                 15.0000 
                 SiO 2   
                 1.560318 
                 91.50 
               
               
                 33 
                 −149.2286 
                 7.6524 
                   
                   
                 100.69 
               
               
                 34 
                 −705.3999 
                 45.0039 
                 SiO 2   
                 1.560318 
                 104.90 
               
               
                 35 
                 −145.3105 
                 100.0079 
                   
                   
                 107.21 
               
               
                 36 
                 ∞ 
                 103.9571 
                   
                   
                 130.84 
               
               
                 37 
                 ∞ 
                 −33.2893 
                   
                   
                 99.43 
               
               
                 38 
                 ∞ 
                 20.0000 
                   
                   
                 210.81 
               
               
                 39 
                 250.9147 
                 31.5356 
                 SiO 2   
                 1.560318 
                 101.23 
               
               
                 40 
                 −1057.0829 
                 21.3930 
                   
                   
                 102.52 
               
               
                 41 
                 202.0288 
                 47.3927 
                 SiO 2   
                 1.560318 
                 111.71 
               
               
                 42 
                 −941.7186 
                 197.8094 
                   
                   
                 110.48 
               
               
                 43 
                 −88.9067 
                 15.0000 
                 SiO 2   
                 1.560318 
                 72.67 
               
               
                 44 
                 −573.5619 
                 23.1569 
                   
                   
                 88.88 
               
               
                 45 
                 −142.4338 
                 −23.1569 
                 Mirror 
                   
                 89.38 
               
               
                 46 
                 −573.5619 
                 −15.0000 
                 SiO 2   
                 1.560318 
                 88.88 
               
               
                 47 
                 −88.9067 
                 −197.8094 
                   
                   
                 72.67 
               
               
                 48 
                 −941.7186 
                 −47.3927 
                 SiO 2   
                 1.560318 
                 110.48 
               
               
                 49 
                 202.0288 
                 −11.3868 
                   
                   
                 111.71 
               
               
                 50 
                 ∞ 
                 −9.9896 
                   
                   
                 92.32 
               
               
                 51 
                 −1057.0829 
                 −31.5356 
                 SiO 2   
                 1.560318 
                 102.52 
               
               
                 52 
                 250.9147 
                 −20.0000 
                   
                   
                 101.23 
               
               
                 53 
                 ∞ 
                 209.4519 
                 Mirror 
                   
                 135.07 
               
               
                 54 
                 −133.90811 
                 9.4987 
                 SiO 2   
                 1.560318 
                 97.71 
               
               
                 55 
                 406.9979 
                 48.9711 
                   
                   
                 119.82 
               
               
                 56 
                 −523.9173 
                 41.1332 
                 SiO 2   
                 1.560318 
                 135.89 
               
               
                 57 
                 −224.0541 
                 29.8664 
                   
                   
                 142.55 
               
               
                 58 
                 1367.6570 
                 94.8234 
                 SiO 2   
                 1.560318 
                 191.42 
               
               
                 59 
                 −271.7647 
                 8.1788 
                   
                   
                 198.87 
               
               
                 60 
                 667.9279 
                 83.6854 
                 SiO 2   
                 1.560318 
                 232.81 
               
               
                 61 
                 −808.5395 
                 140.7841 
                   
                   
                 233.01 
               
               
                 62 
                 286.6775 
                 82.6895 
                 SiO 2   
                 1.560318 
                 201.18 
               
               
                 63 
                 −1096.4782 
                 0.9668 
                   
                   
                 198.76 
               
               
                 64 
                 350.5350 
                 35.6242 
                 SiO 2   
                 1.560318 
                 164.87 
               
               
                 65 
                 884.2685 
                 0.9173 
                   
                   
                 159.58 
               
               
                 66 
                 115.9293 
                 64.9068 
                 SiO 2   
                 1.560318 
                 108.97 
               
               
                 67 
                 412.6826 
                 0.8041 
                   
                   
                 99.04 
               
               
                 68 
                 57.1792 
                 41.0408 
                 CaF 2   
                 1.501403 
                 55.06 
               
               
                 69 
                 99.9106 
                 10.1713 
                 Liquid 
                 1.600000 
                 30.68 
               
               
                 70 
                 ∞ 
                   
                   
                   
                 19.40 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Aspherical constants 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 SURFACE 
                 3 
                 19 
                 24 
                 28 
                 30 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −1.001534E−09 
                 −4.128786E−08 
                 −4.510495E−08 
                 1.339665E−08 
                 1.339665E−08 
               
               
                 B 
                 6.144615E−13 
                 −4.980750E−13 
                 6.742821E−13 
                 1.482582E−12 
                 1.482582E−12 
               
               
                 C 
                 1.247768E−16 
                 2.649167E−18 
                 3.004246E−17 
                 −1.857530E−16 
                 −1.857530E−16 
               
               
                 D 
                 −1.048854E−20 
                 5.315992E−22 
                 2.453737E−21 
                 3.433994E−20 
                 3.433994E−20 
               
               
                 E 
                 −4.463818E−25 
                 −6.165935E−27 
                 −3.687563E−25 
                 −2.905941E−24 
                 −2.905941E−24 
               
               
                 F 
                 6.154983E−30 
                 1.945950E−32 
                 −1.491146E−30 
                 1.237374E−28 
                 1.237374E−28 
               
               
                   
               
               
                 SURFACE 
                 34 
                 39 
                 44 
                 46 
                 52 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −4.510495E−08 
                 −2.582589E−08 
                 −1.589920E−08 
                 −1.589920E−08 
                 −2.582589E−08 
               
               
                 B 
                 6.742821E−13 
                 −4.336537E−13 
                 1.112204E−12 
                 1.112204E−12 
                 −4.336537E−13 
               
               
                 C 
                 3.004246E−17 
                 5.153775E−17 
                 −2.537422E−17 
                 −2.537422E−17 
                 5.153775E−17 
               
               
                 D 
                 2.453737E−21 
                 −7.829187E−21 
                 −5.148293E−21 
                 −5.148293E−21 
                 −7.829187E−21 
               
               
                 E 
                 −3.687563E−25 
                 5.696031E−25 
                 8.322199E−25 
                 8.322199E−25 
                 5.696031E−25 
               
               
                 F 
                 −1.491146E−30 
                 −1.711252E−29 
                 −2.485886E−29 
                 −2.485886E−29 
                 −1.711252E−29 
               
               
                   
               
             
          
           
               
                 SURFACE 
                 58 
                 62 
                 65 
                 67 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
               
               
                 A 
                 −1.313863E−08 
                 −1.809441E−08 
                 −1.821041E−09 
                 −4.599046E−10 
               
               
                 B 
                 1.817234E−14 
                 −2.428724E−14 
                 4.495016E−13 
                 3.983791E−12 
               
               
                 C 
                 2.355838E−18 
                 1.168088E−17 
                 −7.637258E−18 
                 −1.382332E−16 
               
               
                 D 
                 −1.447425E−22 
                 −4.545469E−22 
                 −1.610477E−21 
                 −2.858839E−21 
               
               
                 E 
                 3.333235E−22 
                 7.354258E−27 
                 7.379400E−26 
                 4.614539E−25 
               
               
                 F 
                 −4.355238E−32 
                 −4.766510E−32 
                 −9.483899E−31 
                 −1.411510E−29