Abstract:
The disclosure relates a projection objective of a microlithographic projection exposure apparatus, as well as a related microlithographic projection exposure apparatus and method. The projection objective can include a lens of a cubically crystalline material whose crystal orientation is oriented at an angle of at most 15° relative to the optical axis of the projection objective. The projection objective can also include a polarization correction element which has at least two subelements of birefringent, optically uniaxial material and having at least one respective aspheric surface. During use of the projection objective, the polarization correction element at least partially compensates for an intrinsic birefringence of the lens.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation of, and claims benefit under 35 USC 120 to, international application PCT/EP2008/052736, filed Mar. 6, 2008, which claims benefit of German Application No. 10 2007 012 563.3, filed Mar. 13, 2007. International application PCT/EP2008/052736 is hereby incorporated by reference in its entirety. 
     
    
     FIELD 
       [0002]    The disclosure relates to a projection objective of a microlithographic projection exposure apparatus, as well as a related microlithographic projection exposure apparatus and method. 
       BACKGROUND 
       [0003]    Microlithographic projection exposure apparatuses can be used for the production of microstructured components such as for example integrated circuits or LCDs. Such a projection exposure apparatus typically has an illumination system and a projection objective. In the microlithography process, the image of a mask (=reticle) illuminated by the illumination system is projected by the projection objective onto a substrate (for example silicon wafer) which is coated with a light-sensitive layer (photoresist) and arranged in the image plane of the projection objective to transfer the mask structure onto the light-sensitive layer. 
         [0004]    In microlithography objectives, such as immersion objectives with a value with respect to the numerical aperture (NA) of more than 1.5, it can be desirable to use materials with a high refractive index, in particular for the last optical element at the image side. The term “high refractive index” is used herein to denote a refractive index if its value at the given wavelength exceeds that of quartz, with a value of about 1.56 at a wavelength of 193 nm. An example of such a materialis lutetium aluminum garnet (Lu 3 Al 5 O 12 , LuAG), which has a refractive index at 193 nm is about 2.14. In some cases, such materials, due to their cubic crystal structure, have intrinsic birefringence (═IBR) which rises with a low wavelength. For example, measurements for lutetium aluminum garnet have given a maximum IBR-induced retardation of 30.1 nm/cm. The term “retardation” is used herein to denote the difference in the optical paths of two orthogonal (mutually perpendicular) polarization states. 
       SUMMARY 
       [0005]    In some embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, which permits the use of high-refraction crystal materials while limiting an undesirable influence of intrinsic birefringence. 
         [0006]    In certain embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, which is configured to project a mask which can be positioned in an object plane of the projection objective onto a light-sensitive layer which can be positioned in an image plane of the projection objective. The projection objective includes at least one lens of a cubically crystalline material whose [110] crystal orientation is oriented at an angle of at most 15° relative to the optical axis of the projection objective. The projection objective also includes at least one polarization correction element which has at least two subelements of birefringent, optically uniaxial material and having at least one respective aspheric surface. The polarization correction element at least partially compensates for an intrinsic birefringence of the at least one lens. 
         [0007]    Reference to the optical axis denotes a straight line or a succession of straight line portions, which extends through the centers of curvature of the rotationally symmetrical optical components of the projection objective. 
         [0008]    In some embodiments, the [110] crystal orientation of the at least one lens of cubically crystalline material is oriented at an angle of at most 10° (e.g., at most 5°, at most 3°) relative to the optical axis of the projection objective. 
         [0009]    The disclosure is based, in part at least, on the realization that the field-dependent residual retardation remaining in the case of polarization-optical compensation of an intrinsically birefringent lens (and in particular a lens which is the last at the image plane side) by a polarization correction element depends on the crystal orientation of that lens. The disclosure makes use of the realization that a reduction in that residual retardation can be achieved if the crystal orientation of the lens to be compensated with respect to its intrinsic birefringence is so selected that the maximum retardation values in the field distribution of that lens occur on or in the proximity of the optical lens of the projection objective. 
         [0010]    The [110] crystal orientation that is selected for the lens to be compensated with respect to its intrinsic birefringence has the property that light beams which pass in axis-parallel relationship through the [110] lens experience the maximum retardation (in contrast, for example, to the situation with a [100] lens which does not have any retardation for light beams passing thereto in axis-parallel relationship). In addition the disclosure makes use of the fact that, by using a suitable polarization correction element, it is possible to completely compensate for the intrinsic birefringence for any field point (for example a field point on the optical axis) while that compensation only takes place partially for the other field points. 
         [0011]    When designing the polarization correction element for optimum polarization-optical compensation of the retardation of the lens to be compensated with respect to its intrinsic birefringence, in the field center, it is possible by the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation which is to be compensated with respect to its intrinsic birefringence on the other hand, to create a situation in which the maximum retardation of the [110] lens is optimized for axis-parallel beams in the field center. 
         [0012]    In some embodiments, the polarization correction element includes a crystal material with a non-cubic crystal structure. For example, the polarization correction element can include an optically uniaxial crystal material, such as magnesium fluoride (MgF 2 ), lanthanum fluoride (LaF 3 ), sapphire (Al 2 O 3 ) or crystalline quartz (SiO 2 ). 
         [0013]    In certain embodiments, the polarization correction element can have at least three subelements (optionally, precisely three subelements) of birefringent material and with at least one respective aspheric surface. With such a polarization correction element it is possible to achieve at least almost complete compensation of intrinsic birefringence for any field point (for example the field center). 
         [0014]    More generally, the polarization correction element can have at least two subelements of birefringent material, with each sublement having at least one aspheric surface. 
         [0015]    In some embodiments, the birefringent material of the subelements of the polarization correction element is an optically uniaxial crystal material. The birefringent material of the subelements of the polarization correction element can be, for example, magnesium fluoride (MgF 2 ), lanthanum fluoride (LaF 3 ), sapphire (Al 2 O 3 ) or crystalline quartz (SiO 2 ). 
         [0016]    In certain embodiments, the lens is the last lens of the projection objective on the image plane side of the projection objective. For the field center, it is possible to minimize a field-dependent residual error with respect to polarization-optical compensation, that is caused by the typically planoconvex geometry of the last lens on the image plane side, as (in contrast to the situation for example in the case of the coma rays or edge rays of the different field beams) the principal rays which are in axis-parallel relationship in the image plane and which are near the axis pass through substantially the same optical travel length in the last lens on the image plane side. 
         [0017]    In some embodiments, the projection objective has precisely one lens of a cubically crystalline material whose [110] crystal orientation is oriented at an angle of at most 15° relative to the optical axis of the projection objective. The disclosure makes use of the fact that the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation on the other hand, in regard to the polarization-optical compensation which can be achieved, possibly makes the presence of further [110] lenses with lens clocking dispensable. 
         [0018]    In certain embodiments, the optical crystal axes of all three subelements are oriented differently from each other. 
         [0019]    In some embodiments, the optical crystal axes of at least two subelements of the polarization correction element are oriented in a plane perpendicular to the optical axis of the projection objective. 
         [0020]    In certain embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, for projecting a mask which can be positioned in an object plane onto a light-sensitive layer which can be positioned in an image plane. The projection objective includes precisely one lens of a cubically crystalline material that has its [110] crystal orientation oriented at an angle of at most of 15° relative to the optical axis the projection objective. The projection objective also includes a polarization correction element which has an optically uniaxial crystal material and at least partially compensates for an intrinsic birefringence of the lens. 
         [0021]    The disclosure makes use of the realization that the combination of a polarization correction element on the one hand and a lens with [110] crystal orientation on the other hand, in regard to the polarization-optical compensation which can be achieved, possibly makes the presence of further [110] lenses with lens clocking dispensable. 
         [0022]    In some embodiments, the disclosure provides a projection objective of a microlithographic projection exposure apparatus, for projecting a mask which can be positioned in an object plane onto a light-sensitive layer which can be positioned in an image plane. All lenses of cubically crystalline material in the projection objective have their [110] crystal orientation oriented at an angle of at most 15° relative to the optical axis of the projection objective. The projection objective also includes a polarization correction element which has an optically uniaxial crystal material and at least partially compensates for an intrinsic birefringence of the one or more lenses. 
         [0023]    The disclosure also relates to a microlithographic projection exposure apparatus, a process for the production of microlithographic components, and a microlithographic component. 
         [0024]    Further configurations of the disclosure are to be found in the description and the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0025]      FIG. 1  shows an overall meridional section through a complete catadioptric projection objective; 
           [0026]      FIGS. 2   a - b  show a diagrammatic view of the typical configuration of partial rays of different beams in a first lens on the object plane side and a last lens on the image plane side of a projection objective; 
           [0027]      FIG. 3  shows an overall meridional section through a complete catadioptric projection objective; 
           [0028]      FIGS. 4   a - b  show the residual retardation (in nm) obtained for the projection objective of  FIG. 1  without polarization correction element in the case of a [100] crystal orientation of the last lens on the image plane side ( FIG. 4   a ) and for the case of a [110] crystal orientation of the last lens on the image plane side ( FIG. 4   b ); 
           [0029]      FIGS. 5   a - c  show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [100] crystal orientation; 
           [0030]      FIGS. 6   a - b  show the residual retardation (in nm) obtained with a polarization correction element as shown in  FIGS. 5   a - c  for the field center ( FIG. 6   a ) and the field edge ( FIG. 6   b ); 
           [0031]      FIGS. 7   a - c  show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [110] crystal orientation; 
           [0032]      FIGS. 8   a - b  show the residual retardation (in nm) obtained with a polarization correction element as shown in  FIGS. 7   a - c  for the field center ( FIG. 8   a ) and the field edge ( FIG. 8   b ); 
           [0033]      FIGS. 9   a - b  show the residual retardation (in nm) obtained for the projection objective of  FIG. 3  without polarization correction element in the case of a [100] crystal orientation of the last lens on the image plane side ( FIG. 9   a ) and for the case of a [110] crystal orientation of the last lens on the image plane side ( FIG. 9   b ); 
           [0034]      FIGS. 10   a - c  show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [100] crystal orientation; 
           [0035]      FIGS. 11   a - b  show the residual retardation (in nm) obtained with a polarization correction element as shown in  FIGS. 10   a - c  for the field center ( FIG. 11   a ) and the field edge ( FIG. 11   b ), 
           [0036]      FIGS. 12   a - c  show height profiles (in μm) of the respective subelements of a polarization correction element used for IBR compensation of the last lens on the image plane side with [110] crystal orientation; and 
           [0037]      FIGS. 13   a - b  show the residual retardation (in nm) obtained with a polarization correction element as shown in  FIGS. 12   a - c  for the field center ( FIG. 13   a ) and the field edge ( FIG. 13   b ). 
       
    
    
     DETAILED DESCRIPTION 
       [0038]      FIG. 1  shows an exemplary projection objective  100 . The design data of exemplary projection objective  100  are set out in Table 1, where column 1 represents the number of the respective refracting or in some other fashion distinguished optical surface, column 2 specifies the radius r of that surface (in mm), column 3 gives a reference to an asphere present on that surface, column 4 specifies the spacing, identified as thickness, of that surface relative to the following surface (in mm), column 5 specifies the material following the respective surface, column 6 specifies the refractive index of that material at λ=193 nm and column 7 specifies the optically useable free half diameter of the optical component. The radii, thicknesses and half diameters are specified in millimeters. 
         [0039]    The surfaces identified by thick dots in  FIG. 1  and specified in Tables 1 and 2 are aspherically curved, wherein the curvature of those surfaces is given by the following asphere formula: 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                      
                     
                       ( 
                       h 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             / 
                             r 
                           
                           ) 
                         
                         · 
                         
                           h 
                           2 
                         
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   cc 
                                 
                                 ) 
                               
                                
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     r 
                                   
                                   ) 
                                 
                                 2 
                               
                                
                               
                                 h 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         C 
                         1 
                       
                        
                       
                         h 
                         4 
                       
                     
                     + 
                     
                       
                         C 
                         2 
                       
                        
                       
                         h 
                         6 
                       
                     
                     + 
                     … 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    P denotes the camber height of the surface in question parallel to the optical axis, h denotes the radial spacing from the optical axis, r denotes the radius of curvature of the surface in question, cc denotes the conical constant (identified by K in Table 2) and C 1 , C 2 , . . . denote the asphere constants set out in Table 2. 
         [0040]    Referring to  FIG. 1  the projection objective  100  has a catadioptric structure with a first optical subsystem  110 , a second optical subsystem  120  and a third optical subsystem  130 . As used herein, “subsystem” always denotes such an arrangement of optical elements, by which a real object is projected into a real image or intermediate image. In other words each subsystem, starting from a given object or intermediate image plane, always includes all optical elements to the next real image or intermediate image. 
         [0041]    The first optical subsystem  110  includes an arrangement of refractive lenses  111 - 118  and reproduces the object plane “OP” in a first intermediate image IMI 1 , the approximate position of which is indicated in  FIG. 1  by an arrow. That first intermediate image IMI 1  is reproduced by the second optical subsystem  120  in a second intermediate image IMI 2 , the approximate position of which is also indicated in  FIG. 1  by an arrow. 
         [0042]    The second optical subsystem  120  includes a first concave mirror  121  and a second concave mirror  122  which are each “cut off” in a direction perpendicular to the optical axis in such a way that light propagation can occur from the respective reflecting surfaces of the concave mirrors  121 ,  122  to the image plane “IP”. The second intermediate image IMI 2  is reproduced in the image plane IP by the third optical subsystem  130 . 
         [0043]    The third optical subsystem  130  includes an arrangement of refractive lenses  131 - 143 . In regard to the last lens  143  at the image plane side this involves a planoconvex lens with a lens surface which is convexly curved on the object plane side. Lens  143  is a [110] lens with its [110] crystal orientation that is oriented at an angle of at most 15° relative to the optical axis (OA). 
         [0044]    Between the light exit surface of the lens  143  and the light-sensitive layer arranged in the image plane IP in the region of the projection objective  100  is an immersion liquid which in the illustrated embodiment, at a working wavelength of 193 nm, has a refractive index of n Imm ≈1.65. An immersion liquid which is suitable for example for that purpose bears the designation “Dekalin”. A further suitable immersion liquid is cyclohexane (n Imm ≈11.57 at 193 nm). 
         [0045]    Disposed in the pupil plane PP 1  is a polarization correction element  105 , the structure of which is described in greater detail hereinafter with reference to  FIGS. 4 through 8 . 
         [0046]    The reduction or minimization achieved with respect to the field-dependent residual retardation as a consequence of the combination of a polarization correction element with a lens which is last on the image plane side with [110] crystal orientation is described in greater detail hereinafter with reference to  FIGS. 2   a - b.    
         [0047]      FIGS. 2   a  and  2   b  diagrammatically show the typical configuration of three respective subrays of three individual light beams in a lens which is first on the object plane side ( FIG. 2   a ) and the lens which is last on the image plane side ( FIG. 2   b ) on an enlarged scale. The coma rays of those beams A, B and C are denoted in  FIGS. 2   a  and  2   b  by A 1 , A 3 , B 1 , B 3 , C 1  and C 3 . The principal rays of the beams A, B and C are denoted in  FIGS. 2   a  and  2   b  by A 2 , B 2  and C 2 . Those principal rays extend substantially parallel to the optical axis OA with double-side (and thus in particular image-side) telecentry of the projection objective within the last lens on the image plane side. As is further apparent from  FIG. 2   b  the optical travel lengths of those principal rays A 2 , B 2  and C 2  within the last lens on the image plane side are almost equal so that those subrays also experience substantially the same retardation and can be equally well compensated by a polarization correction element. 
         [0048]    In contrast for example the subray C 3  of the beam C within the last lens on the image plane side as shown in  FIG. 2   b  covers a substantially greater optical distance than the subray C 1  of the same beam C. That difference is responsible for the above-mentioned field-dependent residual error of the polarization-optical compensation effect which can be achieved by a polarization correction element, or the residual retardation achieved, and is correspondingly greater, the greater the spread angle of the individual beams. 
         [0049]    It follows from the foregoing description that the polarization-optical compensation which can be achieved by the polarization correction element with respect to the last lens on the image plane side is particularly effective, in the field center. The fact that the last lens is in the [110] crystal orientation means that the particular effectiveness of a polarization correction element which is optimized for the field center is advantageously combined with a maximum retardation in the intrinsically birefringent [110] crystal material of that last lens. 
         [0050]    The effect of that advantageous combination is clear from a comparison of  FIGS. 4 through 8 . 
         [0051]      FIGS. 4   a  and  b  show the residual retardation (in nm) obtained for the projection objective of  FIG. 1  without polarization correction element, more specifically in the case of a [100] crystal orientation of the last lens on the image plane side ( FIG. 4   a ) and for the case of a [110] crystal orientation of the last lens on the image plane side ( FIG. 4   b ). It will be seen that the residual retardations are respectively approximately at 200 nm, wherein the maximum residual retardation is achieved in the case of the [100] crystal orientation at the field edge and in the case of the [110] crystal orientation in the field center. In this respect, here and hereinafter the respective axes are specified in the diagrams for representing the residual retardation, in pupil coordinates, that is to say in the value range of −NA through +NA (NA=numerical aperture). 
         [0052]      FIG. 5   a - c  show the height profiles (in μm) of three subelements of a polarization correction element for IBR compensation in the case of the [100] lens of  FIG. 4   a . In this case, here and hereinafter, the respective axes are specified in mm in the diagrams for representing height profiles. 
         [0053]    The three subelements are respectively made from sapphire (Al 2 O 3 ). The optical crystal axes in those three subelements are respectively disposed in a plane perpendicular to the optical axis OA of the projection objective and are so oriented that the optical crystal axis of the second subelement in the light propagation direction is arranged rotated through 45° about the optical axis OA with respect to the optical crystal axis of the first subelement while the optical crystal axis of the third subelement in the light propagation direction is again arranged parallel to the optical crystal axis of the first subelement. In some embodiments, the third subelement can also be arranged rotated for example through an angle of 90° about the optical axis OA with respect to the optical crystal axis of the first subelement (and through 45° about the optical axis OA with respect to the optical crystal axis of the second subelement) so that then the optical crystal axes of all three subelements are differently oriented. 
         [0054]    The positive or negative height data contained in the height profiles of  FIGS. 5   a - c  of the three subelements are respectively specified relative to the thickness of a plane plate with an effective retardation of a wavelength (or generally an integral multiple of the wavelength, that is to say relative to a plane plate of the thickness D=N*λ/Δn with Δn=n e −n o ). 
         [0055]    A further quantitative description of the height profiles of the three subelements is shown in Table 5 which contains the Zernike coefficients of the surfaces so scaled that a respective height profile in micrometers is afforded, more specifically in accordance with the relationship: 
         [0000]    
       
         
           
             
               
                 
                   
                     height 
                      
                     
                         
                     
                      
                     profile 
                   
                   = 
                   
                     
                       ∑ 
                       i 
                     
                      
                     
                         
                     
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                       ( 
                       
                         
                           C 
                           i 
                         
                         * 
                         
                           
                             Z 
                             i 
                           
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                             ( 
                             
                               
                                 r 
                                 / 
                                 
                                   r 
                                   max 
                                 
                               
                               , 
                               phi 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0056]    C i  denotes the Zernike coefficients in Table 5, phi denotes the azimuth angle, r/r max  denotes the standardized radial coordinate and Z i  denotes the i-th standard Zernike polynomial, where the maximum radii r max  in the projection objective  100  are 55.47800 mm for the first subelement, 55.48200 mm for the second subelement and 55.48500 mm for the third subelement. 
         [0057]    The residual retardation achieved by that polarization correction element is shown in  FIG. 6   a  for the field center and in  FIG. 6   b  for the field edge. While  FIG. 6   a  shows almost complete compensation for the field center,  FIG. 6   b  shows that there is still a maximum residual retardation of 24 nm for the field edge. 
         [0058]    Similarly  FIGS. 7   a - c  show the height profiles (in μm) of the subelements of a polarization correction element used for IBR compensation of the [110] lens as shown in  FIG. 4   b , where Table 6 contains the corresponding Zernike coefficients in accordance with the foregoing description.  FIG. 8   a  shows the residual polarization obtained by that polarization correction element for the field center ( FIG. 8   a ) and the residual retardation obtained for the field edge ( FIG. 8   b ). While in  FIG. 8   a  optimum compensation is still obtained for the field center the residual retardation for the field edge is only still a maximum of 18 nm as shown in  FIG. 8   b.    
         [0059]    Of the subelements of the polarization correction element two or more (in particular all) of those subelements can also be assembled seamlessly (for example by wringing). In addition compensation elements (for example of optically isotropic material) for compensation of a beam deflection can also be associated with one or more (in particular all) of those subelements. 
         [0060]      FIG. 3  shows a complete projection objective  300  in meridional section in accordance. The design data of that projection objective  300  are set out in Table 3 (in a similar fashion to Table 1) and the aspheric constants are to be found in Table 4. 
         [0061]    The projection objective  300  includes a first refractive subsystem  310 , a second catadioptric subsystem  320  and a third refractive subsystem  330  and is therefore also referred as a “RCR system”. 
         [0062]    The first refractive subsystem  310  includes refractive lenses  311  through  319 , after which a first intermediate image IMI 1  is produced in the beam path. The second subsystem  320  includes a double-folding mirror with two mirror surfaces  321  and  322  arranged at an angle relative to each other, where light incident from the first subsystem is reflected firstly at the mirror surface  321  in the direction towards lenses  323  and  324  and a subsequent concave mirror  325 . The light reflected at the concave mirror  325  is reflected after again passing through the lenses  323  and  324  at the second mirror surface  322  of the double-fold mirror so that as the outcome the optical axis OA is folded twice through 90°. The second subsystem  320  produces a second intermediate image IMI 2  and the light from that intermediate image IMI 2  is incident on the third refractive subsystem  330  which includes refractive lenses  331  through  345 . The second intermediate image IMI 2  is reproduced on the image plane IP by the third refractive subsystem  330 . 
         [0063]    The concave mirror  325  of the second catadioptric subsystem permits in per se known manner effective compensation of the image field curvature produced by the subsystems  310  and  330 . 
         [0064]    A polarization correction element  305  is disposed in the first pupil plane PP 1  of the projection objective  300 . The structure of the element  305  is described in greater detail hereinafter with reference to  FIGS. 9 through 13 . 
         [0065]      FIGS. 9   a  and  9   b  show residual retardation (in nm) obtained for the projection objective  300  of  FIG. 3  without polarization correction element, in the case of a [100] crystal orientation of the last lens on the image plane side ( FIG. 9   a ) and in the case of a [110] crystal orientation of the last lens on the image plane side ( FIG. 9   b ). 
         [0066]    The optical crystal axes in those three subelements are again respectively disposed in a plane perpendicularly to the optical axis OA of the projection objective and are oriented similarly to the optical crystal axes in the three subelements of the polarization correction element in the exemplary embodiment of  FIG. 1  and  FIGS. 4 through 8 , respectively. 
         [0067]      FIGS. 10   a - c  show the height profiles (in μm) of three subelements of a polarization correction element for IBR compensation in the case of the [100] lens of  FIG. 9   a.    
         [0068]    A further quantitative description of the height profiles of the three subelements is set forth in Table 7 which contains the Zernike coefficients of the surfaces so scaled that a respective height profile in micrometers is afforded, in accordance with foregoing relationship (2). In that case the maximum radii r max  in the projection objective  300  are 10.50640 mm for the first subelement, 10.51220 mm for the second subelement and 10.51810 mm for the third subelement. 
         [0069]    The residual retardation obtained by that polarization correction element is shown in  FIG. 11   a  for the field center and in  FIG. 11   b  for the field edge. While  FIG. 11   a  shows almost complete compensation for the field center,  FIG. 11   b  shows that there is still a maximum residual retardation of 16 nm for the field edge. 
         [0070]    Similarly  FIGS. 12   a - c  show the height profiles (in μm) of the subelements of a polarization correction element used for IBR compensation of the [110] lens shown in  FIG. 9   b , where Table 8 contains the corresponding Zernike coefficients in accordance with the foregoing description.  FIGS. 13   a  and  13   b  show the residual polarization obtained by that polarization correction element for the field center ( FIG. 13   a ) and the residual retardation obtained for the field edge  FIG. 13   b ). While an optimum compensation is still obtained in  FIG. 13   a  for the field center, the residual retardation for the field edge is only still a maximum of 12 nm. 
         [0071]    Although the disclosure has been described certain embodiments, numerous variations and alternative embodiments will be apparent to one man skilled in the art, for example by combination and/or exchange of features of individual embodiments. Accordingly, it will be appreciated that such variations and alternative embodiments are also embraced by the present disclosure and the scope of the disclosure is limited only in the sense of the accompanying claims and equivalents thereof. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 (DESIGN DATA for FIG. 1): 
               
               
                 (NA = 1.55; field size 26 mm * 5.5 mm; wavelength 193 nm) 
               
             
          
           
               
                   
                   
                   
                   
                   
                 REFRACTIVE 
                 HALF 
               
               
                 SURFACE 
                 RADIUS 
                   
                 THICKNESS 
                 MATERIAL 
                 INDEX 
                 DIAMETER 
               
               
                   
               
             
          
           
               
                 0 
                 0.000000 
                   
                 29.999023 
                   
                 1.00000000 
                 63.700 
               
               
                 1 
                 0.000000 
                   
                 −0.293904 
                   
                 1.00000000 
                 76.311 
               
               
                 2 
                 116.967388 
                 AS 
                 33.971623 
                 SIO2V 
                 1.56078570 
                 93.710 
               
               
                 3 
                 268.858710 
                   
                 45.405733 
                   
                 1.00000000 
                 92.342 
               
               
                 4 
                 −252.724978 
                 AS 
                 58.607153 
                 SIO2V 
                 1.56078570 
                 92.157 
               
               
                 5 
                 −152.905212 
                   
                 0.986967 
                   
                 1.00000000 
                 102.264 
               
               
                 6 
                 100.588881 
                   
                 94.936165 
                 SIO2V 
                 1.56078570 
                 89.748 
               
               
                 7 
                 480.541211 
                 AS 
                 22.683526 
                   
                 1.00000000 
                 61.038 
               
               
                 8 
                 −151.461922 
                   
                 9.967307 
                 SIO2V 
                 1.56078570 
                 58.676 
               
               
                 9 
                 −1104.178549 
                 AS 
                 2.998283 
                   
                 1.00000000 
                 54.598 
               
               
                 10 
                 0.000000 
                   
                 0.000000 
                   
                 1.00000000 
                 53.972 
               
               
                 11 
                 0.000000 
                   
                 26.000000 
                   
                 1.00000000 
                 53.972 
               
               
                 12 
                 −4615.634680 
                   
                 9.983258 
                 SIO2V 
                 1.56078570 
                 77.043 
               
               
                 13 
                 −7648.187834 
                   
                 9.234701 
                   
                 1.00000000 
                 82.010 
               
               
                 14 
                 −625.750713 
                   
                 48.866298 
                 SIO2V 
                 1.56078570 
                 85.509 
               
               
                 15 
                 −110.073136 
                 AS 
                 47.938753 
                   
                 1.00000000 
                 90.434 
               
               
                 16 
                 693.459276 
                   
                 15.566986 
                 SIO2V 
                 1.56078570 
                 114.997 
               
               
                 17 
                 2225.036283 
                   
                 111.995402 
                   
                 1.00000000 
                 115.765 
               
               
                 18 
                 −209.012550 
                   
                 24.611839 
                 SIO2V 
                 1.56078570 
                 126.681 
               
               
                 19 
                 −181.333947 
                 AS 
                 37.469604 
                   
                 1.00000000 
                 129.924 
               
               
                 20 
                 0.000000 
                   
                 238.315935 
                   
                 1.00000000 
                 129.948 
               
               
                 21 
                 −214.798316 
                 AS 
                 −238.315935 
                 REFL 
                 1.00000000 
                 151.231 
               
               
                 22 
                 186.831531 
                 AS 
                 238.315935 
                 REFL 
                 1.00000000 
                 153.712 
               
               
                 23 
                 0.000000 
                   
                 37.462671 
                   
                 1.00000000 
                 111.274 
               
               
                 24 
                 297.174670 
                   
                 29.574318 
                 SIO2V 
                 1.56078570 
                 123.808 
               
               
                 25 
                 1191.420870 
                   
                 35.484494 
                   
                 1.00000000 
                 123.384 
               
               
                 26 
                 4081.914442 
                   
                 22.323161 
                 SIO2V 
                 1.56078570 
                 122.901 
               
               
                 27 
                 273.503277 
                 AS 
                 0.998916 
                   
                 1.00000000 
                 122.715 
               
               
                 28 
                 231.074591 
                 AS 
                 9.994721 
                 SIO2V 
                 1.56078570 
                 108.656 
               
               
                 29 
                 162.434674 
                   
                 7.329878 
                   
                 1.00000000 
                 100.728 
               
               
                 30 
                 173.924185 
                   
                 9.996236 
                 SIO2V 
                 1.56078570 
                 100.278 
               
               
                 31 
                 147.324038 
                   
                 39.865421 
                   
                 1.00000000 
                 96.038 
               
               
                 32 
                 517.833939 
                 AS 
                 9.994259 
                 SIO2V 
                 1.56078570 
                 95.918 
               
               
                 33 
                 418.975568 
                   
                 18.691694 
                   
                 1.00000000 
                 97.853 
               
               
                 34 
                 402.609022 
                   
                 9.991838 
                 SIO2V 
                 1.56078570 
                 103.816 
               
               
                 35 
                 225.169608 
                 AS 
                 18.474719 
                   
                 1.00000000 
                 105.756 
               
               
                 36 
                 350.705440 
                 AS 
                 25.452147 
                 SIO2V 
                 1.56078570 
                 107.818 
               
               
                 37 
                 −3388.791523 
                   
                 12.488356 
                   
                 1.00000000 
                 110.250 
               
               
                 38 
                 1008.270218 
                 AS 
                 41.022442 
                 SIO2V 
                 1.56078570 
                 119.521 
               
               
                 39 
                 −314.632041 
                   
                 3.943706 
                   
                 1.00000000 
                 121.832 
               
               
                 40 
                 1442.963243 
                 AS 
                 12.476333 
                 SIO2V 
                 1.56078570 
                 126.022 
               
               
                 41 
                 −1002.829857 
                   
                 14.096377 
                   
                 1.00000000 
                 126.891 
               
               
                 42 
                 194.591039 
                   
                 81.128704 
                 SIO2V 
                 1.56078570 
                 132.890 
               
               
                 43 
                 −264.895277 
                 AS 
                 −22.880987 
                   
                 1.00000000 
                 131.108 
               
               
                 44 
                 0.000000 
                   
                 −0.362185 
                   
                 1.00000000 
                 132.343 
               
               
                 45 
                 0.000000 
                   
                 24.001275 
                   
                 1.00000000 
                 132.533 
               
               
                 46 
                 159.644367 
                   
                 50.327970 
                 SIO2V 
                 1.56078570 
                 109.736 
               
               
                 47 
                 494.742901 
                 AS 
                 0.961215 
                   
                 1.00000000 
                 105.155 
               
               
                 48 
                 328.066727 
                   
                 14.868291 
                 SIO2V 
                 1.56078570 
                 92.427 
               
               
                 49 
                 −3072.231603 
                 AS 
                 0.927658 
                   
                 1.00000000 
                 86.384 
               
               
                 50 
                 84.317525 
                   
                 69.022697 
                 LuAG 
                 2.15000000 
                 64.842 
               
               
                 51 
                 0.000000 
                   
                 3.100000 
                 HINDLIQ 
                 1.65002317 
                 24.540 
               
               
                 52 
                 0.000000 
                   
                 0.000000 
                   
                   
                 15.928 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 (ASPHERIC CONSTANTS for FIG. 1): 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                 2 
                 4 
                 7 
                 9 
                 15 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 −4.353148e−08 
                 −9.800573e−08 
                 2.666231e−07 
                 1.295769e−07 
                 1.774606e−08 
               
               
                 C2 
                 −1.948518e−13 
                 5.499401e−13 
                 −1.471516e−11 
                 1.032347e−11 
                 1.042043e−13 
               
               
                 C3 
                 −3.477204e−16 
                 −1.499103e−16 
                 −1.385474e−15 
                 5.718200e−15 
                 2.794961e−17 
               
               
                 C4 
                 2.346643e−20 
                 −1.967686e−20 
                 2.138176e−18 
                 −4.988183e−18 
                 −3.892158e−21 
               
               
                 C5 
                 −2.078112e−24 
                 4.517642e−24 
                 −1.482225e−22 
                 1.949505e−21 
                 4.464755e−25 
               
               
                 C6 
                 −8.347999e−31 
                 −2.738209e−28 
                 −8.304062e−27 
                 −2.335999e−25 
                 4.773462e−30 
               
               
                 C7 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                 19 
                 21 
                 22 
                 27 
                 28 
               
               
                   
               
               
                 K 
                 0 
                 −2.01691 
                 −1.35588 
                 0 
                 0 
               
               
                 C1 
                 −1.294881e−08 
                 −1.791441e−08 
                 1.799581e−08 
                 −2.305522e−07 
                 −5.364751e−08 
               
               
                 C2 
                 2.960445e−14 
                 1.393731e−13 
                 6.604119e−14 
                 −2.977863e−12 
                 2.985313e−12 
               
               
                 C3 
                 −3.744673e−18 
                 −1.959652e−18 
                 1.091967e−18 
                 1.067601e−15 
                 1.185542e−16 
               
               
                 C4 
                 3.872183e−22 
                 3.972150e−23 
                 3.177716e−23 
                 −7.036742e−20 
                 −5.029250e−20 
               
               
                 C5 
                 −1.724706e−26 
                 −6.577183e−28 
                 −5.281159e−28 
                 2.314154e−24 
                 3.896020e−24 
               
               
                 C6 
                 4.346424e−31 
                 6.141114e−33 
                 1.575655e−32 
                 −3.151486e−29 
                 −1.479810e−28 
               
               
                 C7 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                 32 
                 35 
                 36 
                 38 
                 40 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 2.753990e−08 
                 1.438723e−07 
                 4.030346e−08 
                 4.491651e−08 
                 −9.637167e−08 
               
               
                 C2 
                 −2.426854e−11 
                 −2.226044e−11 
                 −6.610222e−12 
                 −5.791619e−12 
                 3.256893e−12 
               
               
                 C3 
                 1.360579e−15 
                 1.482620e−15 
                 2.501723e−16 
                 5.024169e−16 
                 −9.241857e−17 
               
               
                 C4 
                 −1.150640e−19 
                 −5.040252e−20 
                 −2.574681e−21 
                 −3.768862e−20 
                 9.112235e−21 
               
               
                 C5 
                 7.525459e−24 
                 1.831772e−24 
                 −7.619628e−25 
                 1.711080e−24 
                 9.519978e−26 
               
               
                 C6 
                 −2.203312e−30 
                 −8.726413e−29 
                 1.815817e−29 
                 −3.990765e−29 
                 −1.423818e−29 
               
               
                 C7 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                   
                 43 
                 47 
                 49 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 5.213696e−08 
                 −1.687244e−07 
                 1.276858e−07 
               
               
                   
                 C2 
                 −2.852489e−13 
                 1.277072e−11 
                 1.143276e−12 
               
               
                   
                 C3 
                 6.349974e−17 
                 −5.376139e−16 
                 −2.525252e−16 
               
               
                   
                 C4 
                 −4.223029e−21 
                 1.564911e−20 
                 9.197266e−20 
               
               
                   
                 C5 
                 1.155960e−25 
                 −3.759137e−25 
                 −8.401499e−24 
               
               
                   
                 C6 
                 −1.415349e−30 
                 1.266337e−29 
                 6.171793e−28 
               
               
                   
                 C7 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 (DESIGN DATA for FIG. 3): 
               
             
          
           
               
                   
                   
                   
                   
                   
                 REFRACTIVE 
                 HALF 
               
               
                 SURFACE 
                 RADIUS 
                   
                 THICKNESS 
                 MATERIAL 
                 INDEX 
                 DIAMETER 
               
               
                   
               
             
          
           
               
                 0 
                 0.000000 
                   
                 56.505360 
                   
                 1.00000000 
                 61.600 
               
               
                 1 
                 0.000000 
                   
                 0.628593 
                   
                 1.00000000 
                 84.411 
               
               
                 2 
                 0.000000 
                   
                 9.999465 
                 SIO2V 
                 1.56078570 
                 84.665 
               
               
                 3 
                 0.000000 
                   
                 1.018383 
                   
                 1.00000000 
                 87.136 
               
               
                 4 
                 267.687560 
                   
                 23.051668 
                 SIO2V 
                 1.56078570 
                 94.506 
               
               
                 5 
                 2076.339784 
                   
                 3.011269 
                   
                 1.00000000 
                 95.214 
               
               
                 6 
                 195.468828 
                   
                 118.243767 
                 SIO2V 
                 1.56078570 
                 99.907 
               
               
                 7 
                 213.465552 
                   
                 65.301393 
                   
                 1.00000000 
                 87.739 
               
               
                 8 
                 233.154018 
                   
                 24.923341 
                 SIO2V 
                 1.56078570 
                 92.865 
               
               
                 9 
                 −1992.179958 
                 AS 
                 1.169743 
                   
                 1.00000000 
                 91.232 
               
               
                 10 
                 397.921478 
                   
                 69.915906 
                 SIO2V 
                 1.56078570 
                 91.709 
               
               
                 11 
                 505.661172 
                   
                 17.194249 
                   
                 1.00000000 
                 95.812 
               
               
                 12 
                 −735.689494 
                   
                 9.999732 
                 SIO2V 
                 1.56078570 
                 96.173 
               
               
                 13 
                 887.983169 
                   
                 8.242783 
                   
                 1.00000000 
                 100.163 
               
               
                 14 
                 0.000000 
                   
                 0.000000 
                   
                 1.00000000 
                 101.571 
               
               
                 15 
                 0.000000 
                   
                 42.782393 
                   
                 1.00000000 
                 101.571 
               
               
                 16 
                 −410.552179 
                 AS 
                 78.848881 
                 SIO2V 
                 1.56078570 
                 128.012 
               
               
                 17 
                 −163.270786 
                   
                 336.654237 
                   
                 1.00000000 
                 134.938 
               
               
                 18 
                 237.665945 
                   
                 66.291266 
                 SIO2V 
                 1.56078570 
                 153.690 
               
               
                 19 
                 −1317.124240 
                 AS 
                 86.415659 
                   
                 1.00000000 
                 152.243 
               
               
                 20 
                 222.206724 
                   
                 27.565105 
                 SIO2V 
                 1.56078570 
                 112.997 
               
               
                 21 
                 921.104852 
                 AS 
                 68.984477 
                   
                 1.00000000 
                 110.393 
               
               
                 22 
                 0.000000 
                   
                 0.000000 
                   
                 1.00000000 
                 82.262 
               
               
                 23 
                 0.000000 
                   
                 −223.984401 
                 REFL 
                 1.00000000 
                 82.262 
               
               
                 24 
                 112.393927 
                 AS 
                 −9.995120 
                 SIO2V 
                 1.56078570 
                 93.383 
               
               
                 25 
                 618.177768 
                   
                 −30.194887 
                   
                 1.00000000 
                 110.198 
               
               
                 26 
                 180.843143 
                   
                 −9.993434 
                 SIO2V 
                 1.56078570 
                 111.320 
               
               
                 27 
                 459.728303 
                   
                 −49.418013 
                   
                 1.00000000 
                 131.268 
               
               
                 28 
                 166.364160 
                   
                 49.418013 
                 REFL 
                 1.00000000 
                 133.173 
               
               
                 29 
                 459.728303 
                   
                 9.993434 
                 SIO2V 
                 1.56078570 
                 130.248 
               
               
                 30 
                 180.843143 
                   
                 30.194887 
                   
                 1.00000000 
                 106.184 
               
               
                 31 
                 618.177768 
                   
                 9.995120 
                 SIO2V 
                 1.56078570 
                 102.211 
               
               
                 32 
                 112.393927 
                 AS 
                 223.984401 
                   
                 1.00000000 
                 87.128 
               
               
                 33 
                 0.000000 
                   
                 0.000000 
                   
                 1.00000000 
                 69.972 
               
               
                 34 
                 0.000000 
                   
                 −63.976352 
                 REFL 
                 1.00000000 
                 69.972 
               
               
                 35 
                 412.103957 
                   
                 −20.679211 
                 SIO2V 
                 1.56078570 
                 92.437 
               
               
                 36 
                 203.153828 
                   
                 −0.998595 
                   
                 1.00000000 
                 95.263 
               
               
                 37 
                 −1996.505583 
                   
                 −25.026685 
                 SIO2V 
                 1.56078570 
                 104.114 
               
               
                 38 
                 387.517974 
                   
                 −0.999117 
                   
                 1.00000000 
                 105.544 
               
               
                 39 
                 −217.409028 
                   
                 −35.834400 
                 SIO2V 
                 1.56078570 
                 112.665 
               
               
                 40 
                 −1732.046627 
                   
                 −89.753105 
                   
                 1.00000000 
                 111.738 
               
               
                 41 
                 −432.227186 
                   
                 −24.454670 
                 SIO2V 
                 1.56078570 
                 100.002 
               
               
                 42 
                 −429.393785 
                 AS 
                 −61.820584 
                   
                 1.00000000 
                 96.269 
               
               
                 43 
                 127.267221 
                 AS 
                 −9.998963 
                 SIO2V 
                 1.56078570 
                 96.639 
               
               
                 44 
                 −354.132669 
                   
                 −7.868044 
                   
                 1.00000000 
                 110.880 
               
               
                 45 
                 −523.720649 
                   
                 −14.975470 
                 SIO2V 
                 1.56078570 
                 112.701 
               
               
                 46 
                 −341.520890 
                 AS 
                 −0.997791 
                   
                 1.00000000 
                 118.281 
               
               
                 47 
                 −411.353502 
                   
                 −48.777625 
                 SIO2V 
                 1.56078570 
                 120.957 
               
               
                 48 
                 342.083102 
                   
                 −8.810353 
                   
                 1.00000000 
                 122.794 
               
               
                 49 
                 514.961229 
                 AS 
                 −14.987375 
                 SIO2V 
                 1.56078570 
                 123.090 
               
               
                 50 
                 291.403757 
                   
                 −79.216652 
                   
                 1.00000000 
                 128.222 
               
               
                 51 
                 826.480933 
                 AS 
                 −24.931069 
                 SIO2V 
                 1.56078570 
                 151.976 
               
               
                 52 
                 388.289534 
                   
                 −1.073107 
                   
                 1.00000000 
                 155.772 
               
               
                 53 
                 1460.275628 
                   
                 −24.262791 
                 SIO2V 
                 1.56078570 
                 162.233 
               
               
                 54 
                 543.277065 
                   
                 −0.999651 
                   
                 1.00000000 
                 163.887 
               
               
                 55 
                 −4320.460965 
                   
                 −27.112870 
                 SIO2V 
                 1.56078570 
                 168.245 
               
               
                 56 
                 901.554468 
                   
                 −0.999423 
                   
                 1.00000000 
                 168.871 
               
               
                 57 
                 −227.624376 
                   
                 −78.149238 
                 SIO2V 
                 1.56078570 
                 170.522 
               
               
                 58 
                 −2243.544699 
                   
                 −9.897025 
                   
                 1.00000000 
                 167.855 
               
               
                 59 
                 0.000000 
                   
                 0.000000 
                   
                 1.00000000 
                 165.919 
               
               
                 60 
                 0.000000 
                   
                 −43.822974 
                   
                 1.00000000 
                 165.919 
               
               
                 61 
                 −193.437748 
                   
                 −56.826827 
                 SIO2V 
                 1.56078570 
                 128.975 
               
               
                 62 
                 4852.914186 
                 AS 
                 −1.258966 
                   
                 1.00000000 
                 124.642 
               
               
                 63 
                 −126.542916 
                   
                 −25.022273 
                 SIO2V 
                 1.56078570 
                 89.797 
               
               
                 64 
                 −202.284936 
                 AS 
                 −0.996510 
                   
                 1.00000000 
                 78.587 
               
               
                 65 
                 −95.520347 
                   
                 −72.724717 
                 LUAG 
                 2.10000000 
                 70.909 
               
               
                 66 
                 0.000000 
                   
                 −6.000000 
                 HIINDLIQ 
                 1.64000000 
                 28.915 
               
               
                 67 
                 0.000000 
                   
                 0.000000 
                   
                   
                 15.401 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 (ASPHERIC CONSTANTS for FIG. 3): 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                 9 
                 16 
                 19 
                 21 
                 24 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 1.993155e−07 
                 7.648792e−08 
                 1.310449e−08 
                 1.499407e−08 
                 −1.140413e−07 
               
               
                 C2 
                 −2.965837e−11 
                 −1.147476e−12 
                 −1.473288e−13 
                 4.898569e−13 
                 −1.405657e−12 
               
               
                 C3 
                 7.084938e−15 
                 −1.620016e−16 
                 1.789597e−18 
                 −4.831673e−18 
                 −6.422308e−16 
               
               
                 C4 
                 −1.108567e−18 
                 1.291519e−20 
                 −3.347563e−23 
                 5.603761e−22 
                 9.595133e−20 
               
               
                 C5 
                 1.294384e−22 
                 −4.536509e−25 
                 7.855804e−28 
                 1.107164e−28 
                 −1.651690e−23 
               
               
                 C6 
                 −8.666805e−27 
                 8.063130e−30 
                 −1.561895e−32 
                 −1.720748e−31 
                 1.285598e−27 
               
               
                 C7 
                 2.821071e−31 
                 −5.992411e−35 
                 1.565488e−37 
                 3.402783e−35 
                 −5.054656e−32 
               
               
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                 32 
                 42 
                 43 
                 46 
                 49 
               
               
                   
               
               
                 K 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 C1 
                 −1.140413e−07 
                 −4.189168e−08 
                 −1.685701e−07 
                 6.336319e−09 
                 5.280703e−08 
               
               
                 C2 
                 −1.405657e−12 
                 −3.147936e−13 
                 9.635698e−12 
                 4.071242e−12 
                 1.157060e−12 
               
               
                 C3 
                 −6.422308e−16 
                 −1.294082e−18 
                 −1.217963e−15 
                 −3.577670e−16 
                 −7.824880e−17 
               
               
                 C4 
                 9.595133e−20 
                 −2.828644e−22 
                 1.012583e−19 
                 2.732048e−20 
                 7.171704e−21 
               
               
                 C5 
                 −1.651690e−23 
                 4.489648e−26 
                 −8.858422e−24 
                 −1.655966e−24 
                 −3.888551e−26 
               
               
                 C6 
                 1.285598e−27 
                 −1.468171e−29 
                 4.866371e−28 
                 6.535740e−29 
                 −2.007284e−29 
               
               
                 C7 
                 −5.054656e−32 
                 1.147294e−33 
                 −1.337836e−32 
                 −1.353076e−33 
                 4.237726e−34 
               
               
                 C8 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                 C9 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
                 0.000000e+00 
               
               
                   
               
             
          
           
               
                   
                 Surface 
               
             
          
           
               
                   
                   
                 51 
                 62 
                 64 
               
               
                   
                   
               
               
                   
                 K 
                 0 
                 0 
                 0 
               
               
                   
                 C1 
                 −6.339317e−09 
                 4.857833e−08 
                 −2.139384e−07 
               
               
                   
                 C2 
                 9.839286e−13 
                 −8.830803e−12 
                 1.525695e−11 
               
               
                   
                 C3 
                 −3.557535e−17 
                 7.521403e−16 
                 −4.799207e−15 
               
               
                   
                 C4 
                 2.050828e−21 
                 −4.932093e−20 
                 1.286852e−18 
               
               
                   
                 C5 
                 −7.703006e−26 
                 2.223792e−24 
                 −3.670356e−22 
               
               
                   
                 C6 
                 2.045013e−30 
                 −5.700404e−29 
                 7.133596e−26 
               
               
                   
                 C7 
                 −2.770838e−35 
                 −3.566708e−35 
                 −9.239454e−30 
               
               
                   
                 C8 
                 0.000000e+00 
                 4.807714e−38 
                 6.969720e−34 
               
               
                   
                 C9 
                 0.000000e+00 
                 −1.056980e−42 
                 −2.499170e−38 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Zernike coefficients for FIG. 1 with [100] lens: 
               
             
          
           
               
                   
                 Zernike 
                 Element 1 
                 Element 2 
                 Element 3 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 8.28E−02 
                 −3.48E−03 
                 8.15E−02 
               
               
                   
                 2 
                 −1.12E−02 
                 1.62E−01 
                 −1.16E−02 
               
               
                   
                 3 
                 3.22E−01 
                 1.50E−02 
                 3.21E−01 
               
               
                   
                 4 
                 4.08E−03 
                 −3.98E−03 
                 −3.13E−05 
               
               
                   
                 5 
                 −1.19E+01 
                 −1.64E−03 
                 −1.19E+01 
               
               
                   
                 6 
                 1.48E−02 
                 −5.22E+00 
                 1.47E−02 
               
               
                   
                 7 
                 1.53E−03 
                 4.36E−03 
                 1.00E−03 
               
               
                   
                 8 
                 1.65E−01 
                 −2.19E−03 
                 1.29E−01 
               
               
                   
                 9 
                 1.58E−02 
                 2.05E−03 
                 8.85E−03 
               
               
                   
                 10 
                 1.43E−02 
                 5.89E−02 
                 1.38E−02 
               
               
                   
                 11 
                 −4.02E−01 
                 2.37E−02 
                 −3.74E−01 
               
               
                   
                 12 
                 3.61E+00 
                 9.78E−05 
                 3.54E+00 
               
               
                   
                 13 
                 −1.11E−02 
                 3.62E+00 
                 −1.12E−02 
               
               
                   
                 14 
                 4.76E−03 
                 −8.69E−02 
                 4.05E−03 
               
               
                   
                 15 
                 8.91E−02 
                 −5.32E−03 
                 5.26E−02 
               
               
                   
                 16 
                 2.96E−02 
                 1.58E−03 
                 1.98E−02 
               
               
                   
                 17 
                 −1.37E−02 
                 1.56E−02 
                 −2.85E−02 
               
               
                   
                 18 
                 −3.63E−03 
                 −4.99E−02 
                 −3.67E−03 
               
               
                   
                 19 
                 −9.41E−03 
                 −3.82E−03 
                 −1.04E−02 
               
               
                   
                 20 
                 −8.93E−02 
                 −1.38E−02 
                 −6.41E−02 
               
               
                   
                 21 
                 6.83E−01 
                 8.84E−05 
                 5.92E−01 
               
               
                   
                 22 
                 2.80E−04 
                 −7.95E−01 
                 1.24E−05 
               
               
                   
                 23 
                 −1.02E−04 
                 −6.01E−02 
                 −1.04E−03 
               
               
                   
                 24 
                 1.99E−01 
                 4.05E−04 
                 1.56E−01 
               
               
                   
                 25 
                 3.86E−02 
                 5.00E−04 
                 2.58E−02 
               
               
                   
                 26 
                 7.30E−03 
                 1.39E−01 
                 6.66E−03 
               
               
                   
                 27 
                 −5.21E−02 
                 −9.22E−03 
                 −5.42E−02 
               
               
                   
                 28 
                 3.64E−02 
                 −7.62E−03 
                 1.65E−02 
               
               
                   
                 29 
                 2.39E−03 
                 3.00E−02 
                 2.45E−03 
               
               
                   
                 30 
                 −1.57E−04 
                 1.53E−01 
                 −1.37E−03 
               
               
                   
                 31 
                 −2.10E−01 
                 1.63E−03 
                 −1.81E−01 
               
               
                   
                 32 
                 5.43E−01 
                 1.08E−04 
                 4.37E−01 
               
               
                   
                 33 
                 −3.73E−04 
                 3.08E−01 
                 −6.85E−04 
               
               
                   
                 34 
                 4.18E−04 
                 −7.80E−02 
                 −6.80E−04 
               
               
                   
                 35 
                 2.37E−01 
                 −1.77E−03 
                 1.89E−01 
               
               
                   
                 36 
                 4.47E−02 
                 1.06E−03 
                 2.88E−02 
               
               
                   
                 37 
                 6.12E−01 
                 3.30E−04 
                 6.10E−01 
               
               
                   
                 38 
                 −6.88E−03 
                 2.32E+00 
                 −7.15E−03 
               
               
                   
                 39 
                 −6.13E−03 
                 −9.59E−02 
                 −7.05E−03 
               
               
                   
                 40 
                 4.76E−02 
                 6.55E−03 
                 4.83E−02 
               
               
                   
                 41 
                 4.20E−02 
                 −1.60E−03 
                 1.70E−02 
               
               
                   
                 42 
                 −4.14E−04 
                 4.15E−03 
                 −4.74E−04 
               
               
                   
                 43 
                 −2.68E−04 
                 4.10E−02 
                 −1.70E−03 
               
               
                   
                 44 
                 −2.32E−01 
                 −2.25E−03 
                 −2.01E−01 
               
               
                   
                 45 
                 6.83E−01 
                 3.67E−04 
                 5.68E−01 
               
               
                   
                 46 
                 −9.34E−04 
                 2.81E−01 
                 −1.27E−03 
               
               
                   
                 47 
                 7.97E−04 
                 −9.23E−02 
                 −4.25E−04 
               
               
                   
                 48 
                 2.45E−01 
                 −1.38E−03 
                 1.97E−01 
               
               
                   
                 49 
                 5.38E−02 
                 9.61E−04 
                 3.49E−02 
               
               
                   
                 50 
                 −7.00E−03 
                 −2.09E−01 
                 −7.84E−03 
               
               
                   
                 51 
                 5.02E−02 
                 −1.02E−02 
                 3.60E−02 
               
               
                   
                 52 
                 −9.15E−01 
                 −1.47E−04 
                 −9.20E−01 
               
               
                   
                 53 
                 8.34E−03 
                 −2.09E+00 
                 8.02E−03 
               
               
                   
                 54 
                 4.16E−04 
                 6.56E−02 
                 −6.87E−04 
               
               
                   
                 55 
                 −3.27E−02 
                 6.41E−04 
                 −3.93E−02 
               
               
                   
                 56 
                 4.80E−02 
                 −1.64E−03 
                 1.91E−02 
               
               
                   
                 57 
                 3.82E−04 
                 7.56E−03 
                 3.41E−04 
               
               
                   
                 58 
                 −8.37E−04 
                 6.39E−02 
                 −2.40E−03 
               
               
                   
                 59 
                 −2.43E−01 
                 −2.07E−03 
                 −2.14E−01 
               
               
                   
                 60 
                 7.38E−01 
                 3.59E−04 
                 6.21E−01 
               
               
                   
                 61 
                 −1.01E−03 
                 1.48E−01 
                 −1.37E−03 
               
               
                   
                 62 
                 8.11E−04 
                 −9.84E−02 
                 −4.80E−04 
               
               
                   
                 63 
                 2.57E−01 
                 −1.20E−03 
                 2.12E−01 
               
               
                   
                 64 
                 6.27E−02 
                 9.17E−04 
                 4.10E−02 
               
               
                   
                 65 
                 5.29E−03 
                 −4.88E−03 
                 −9.60E−03 
               
               
                   
                 66 
                 2.19E−03 
                 2.67E−02 
                 1.29E−03 
               
               
                   
                 67 
                 7.61E−03 
                 7.87E−02 
                 6.75E−03 
               
               
                   
                 68 
                 −3.80E−02 
                 9.28E−03 
                 −4.76E−02 
               
               
                   
                 69 
                 4.11E−01 
                 −3.66E−04 
                 4.02E−01 
               
               
                   
                 70 
                 −2.97E−03 
                 6.57E−01 
                 −3.24E−03 
               
               
                   
                 71 
                 4.34E−04 
                 2.99E−02 
                 −7.66E−04 
               
               
                   
                 72 
                 −1.37E−02 
                 2.47E−04 
                 −1.92E−02 
               
               
                   
                 73 
                 5.73E−02 
                 −1.79E−03 
                 2.55E−02 
               
               
                   
                 74 
                 3.79E−04 
                 1.46E−02 
                 3.16E−04 
               
               
                   
                 75 
                 −9.06E−04 
                 7.68E−02 
                 −2.54E−03 
               
               
                   
                 76 
                 −2.51E−01 
                 −1.72E−03 
                 −2.27E−01 
               
               
                   
                 77 
                 7.47E−01 
                 3.78E−04 
                 6.34E−01 
               
               
                   
                 78 
                 −9.70E−04 
                 1.98E−01 
                 −1.32E−03 
               
               
                   
                 79 
                 7.88E−04 
                 −9.81E−02 
                 −5.24E−04 
               
               
                   
                 80 
                 2.55E−01 
                 −1.31E−03 
                 2.17E−01 
               
               
                   
                 81 
                 7.13E−02 
                 9.31E−04 
                 4.71E−02 
               
               
                   
                 82 
                 −2.47E−03 
                 −4.91E−02 
                 −4.14E−03 
               
               
                   
                 83 
                 3.09E−02 
                 8.09E−04 
                 3.79E−02 
               
               
                   
                 84 
                 −1.89E−02 
                 4.93E−03 
                 −3.54E−02 
               
               
                   
                 85 
                 −2.05E−03 
                 −3.05E−02 
                 −3.11E−03 
               
               
                   
                 86 
                 −2.42E−03 
                 −6.97E−02 
                 −3.48E−03 
               
               
                   
                 87 
                 3.88E−02 
                 −1.76E−03 
                 2.53E−02 
               
               
                   
                 88 
                 −1.16E−01 
                 −3.49E−04 
                 −1.24E−01 
               
               
                   
                 89 
                 9.09E−04 
                 −2.37E−01 
                 5.50E−04 
               
               
                   
                 90 
                 −5.29E−04 
                 3.01E−02 
                 −1.82E−03 
               
               
                   
                 91 
                 −6.03E−03 
                 8.78E−04 
                 −1.50E−02 
               
               
                   
                 92 
                 6.45E−02 
                 −1.69E−03 
                 3.08E−02 
               
               
                   
                 93 
                 2.82E−04 
                 1.48E−02 
                 1.95E−04 
               
               
                   
                 94 
                 −8.48E−04 
                 6.89E−02 
                 −2.47E−03 
               
               
                   
                 95 
                 −2.44E−01 
                 −1.88E−03 
                 −2.27E−01 
               
               
                   
                 96 
                 7.69E−01 
                 3.82E−04 
                 6.69E−01 
               
               
                   
                 97 
                 −9.48E−04 
                 2.10E−01 
                 −1.27E−03 
               
               
                   
                 98 
                 7.56E−04 
                 −9.46E−02 
                 −5.20E−04 
               
               
                   
                 99 
                 2.40E−01 
                 −1.28E−03 
                 2.12E−01 
               
               
                   
                 100 
                 7.96E−02 
                 8.77E−04 
                 5.34E−02 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Zernike coefficients for FIG. 1 with [110] lens: 
               
             
          
           
               
                   
                 Zernike 
                 Element 1 
                 Element 2 
                 Element 3 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.23E+00 
                 7.07E−03 
                 1.23E+00 
               
               
                   
                 2 
                 1.51E−02 
                 3.33E−01 
                 1.50E−02 
               
               
                   
                 3 
                 −3.38E−01 
                 −2.41E−02 
                 −3.41E−01 
               
               
                   
                 4 
                 −6.89E+00 
                 6.38E−03 
                 −6.91E+00 
               
               
                   
                 5 
                 −1.71E+00 
                 1.19E−03 
                 −1.71E+00 
               
               
                   
                 6 
                 −1.67E−02 
                 6.23E+00 
                 −1.66E−02 
               
               
                   
                 7 
                 −5.77E−04 
                 8.01E−02 
                 −4.05E−04 
               
               
                   
                 8 
                 −3.40E−01 
                 −6.04E−04 
                 −3.11E−01 
               
               
                   
                 9 
                 1.12E+00 
                 −2.82E−03 
                 1.08E+00 
               
               
                   
                 10 
                 −1.20E−02 
                 1.14E−01 
                 −1.21E−02 
               
               
                   
                 11 
                 −3.64E−01 
                 −3.74E−02 
                 −3.63E−01 
               
               
                   
                 12 
                 −6.80E−01 
                 4.97E−04 
                 −7.01E−01 
               
               
                   
                 13 
                 1.18E−02 
                 −3.47E+00 
                 1.15E−02 
               
               
                   
                 14 
                 −1.12E−02 
                 −1.59E−01 
                 −1.10E−02 
               
               
                   
                 15 
                 −2.66E−02 
                 1.27E−02 
                 1.93E−03 
               
               
                   
                 16 
                 7.67E−01 
                 −3.42E−03 
                 7.17E−01 
               
               
                   
                 17 
                 3.27E+00 
                 −1.44E−02 
                 3.29E+00 
               
               
                   
                 18 
                 2.25E−03 
                 2.15E+00 
                 2.41E−03 
               
               
                   
                 19 
                 1.04E−02 
                 2.14E−02 
                 1.02E−02 
               
               
                   
                 20 
                 −1.53E−01 
                 1.86E−02 
                 −1.34E−01 
               
               
                   
                 21 
                 2.99E−01 
                 −1.18E−04 
                 2.68E−01 
               
               
                   
                 22 
                 7.32E−03 
                 −1.98E+00 
                 7.10E−03 
               
               
                   
                 23 
                 −1.36E−03 
                 4.31E−03 
                 −1.31E−03 
               
               
                   
                 24 
                 −5.88E−02 
                 1.53E−03 
                 −2.90E−02 
               
               
                   
                 25 
                 6.73E−01 
                 1.02E−04 
                 6.19E−01 
               
               
                   
                 26 
                 −6.31E−03 
                 2.36E−01 
                 −6.29E−03 
               
               
                   
                 27 
                 1.68E−02 
                 −1.50E−02 
                 −1.09E−02 
               
               
                   
                 28 
                 −2.91E−01 
                 8.19E−03 
                 −2.56E−01 
               
               
                   
                 29 
                 5.01E−04 
                 −1.26E+00 
                 4.32E−04 
               
               
                   
                 30 
                 2.47E−03 
                 −4.86E−02 
                 2.46E−03 
               
               
                   
                 31 
                 5.65E−03 
                 7.46E−03 
                 2.64E−02 
               
               
                   
                 32 
                 4.69E−01 
                 2.57E−04 
                 4.35E−01 
               
               
                   
                 33 
                 −4.78E−03 
                 1.21E+00 
                 −4.78E−03 
               
               
                   
                 34 
                 4.70E−03 
                 1.89E−01 
                 4.78E−03 
               
               
                   
                 35 
                 −1.64E−01 
                 −2.44E−03 
                 −1.36E−01 
               
               
                   
                 36 
                 1.10E−01 
                 1.82E−04 
                 5.24E−02 
               
               
                   
                 37 
                 1.10E+00 
                 −4.48E−03 
                 1.10E+00 
               
               
                   
                 38 
                 3.80E−03 
                 9.45E−01 
                 3.89E−03 
               
               
                   
                 39 
                 8.83E−03 
                 4.43E−02 
                 8.72E−03 
               
               
                   
                 40 
                 4.85E−02 
                 4.99E−03 
                 2.12E−02 
               
               
                   
                 41 
                 −1.01E+00 
                 1.56E−03 
                 −9.75E−01 
               
               
                   
                 42 
                 −9.55E−04 
                 −1.55E−01 
                 −9.21E−04 
               
               
                   
                 43 
                 −3.48E−03 
                 −9.44E−02 
                 −3.51E−03 
               
               
                   
                 44 
                 −8.20E−02 
                 −4.91E−03 
                 −6.76E−02 
               
               
                   
                 45 
                 1.83E−01 
                 4.28E−04 
                 1.46E−01 
               
               
                   
                 46 
                 −2.21E−03 
                 2.08E−01 
                 −2.29E−03 
               
               
                   
                 47 
                 4.48E−04 
                 7.32E−02 
                 6.45E−04 
               
               
                   
                 48 
                 −2.40E−01 
                 1.43E−03 
                 −2.10E−01 
               
               
                   
                 49 
                 1.54E−01 
                 −8.40E−04 
                 9.17E−02 
               
               
                   
                 50 
                 3.42E−04 
                 1.70E−01 
                 4.41E−04 
               
               
                   
                 51 
                 2.23E−03 
                 −1.11E−02 
                 −8.28E−03 
               
               
                   
                 52 
                 −3.83E−01 
                 2.41E−03 
                 −3.77E−01 
               
               
                   
                 53 
                 −3.97E−03 
                 −1.09E−01 
                 −3.90E−03 
               
               
                   
                 54 
                 −2.13E−03 
                 −1.04E−01 
                 −2.08E−03 
               
               
                   
                 55 
                 1.09E−01 
                 1.24E−03 
                 8.29E−02 
               
               
                   
                 56 
                 −4.97E−02 
                 −1.62E−03 
                 −1.63E−02 
               
               
                   
                 57 
                 −1.52E−03 
                 3.20E−01 
                 −1.41E−03 
               
               
                   
                 58 
                 −9.75E−05 
                 −3.73E−02 
                 −2.30E−04 
               
               
                   
                 59 
                 −2.32E−01 
                 7.66E−05 
                 −2.19E−01 
               
               
                   
                 60 
                 8.14E−02 
                 3.06E−04 
                 4.00E−02 
               
               
                   
                 61 
                 2.64E−03 
                 −4.45E−01 
                 2.42E−03 
               
               
                   
                 62 
                 −3.50E−03 
                 1.32E−02 
                 −3.29E−03 
               
               
                   
                 63 
                 −1.91E−01 
                 2.70E−03 
                 −1.65E−01 
               
               
                   
                 64 
                 4.63E−01 
                 −1.03E−03 
                 4.03E−01 
               
               
                   
                 65 
                 3.09E−01 
                 −2.72E−03 
                 3.00E−01 
               
               
                   
                 66 
                 −7.11E−04 
                 1.42E+00 
                 −7.17E−04 
               
               
                   
                 67 
                 8.68E−04 
                 1.23E−02 
                 8.75E−04 
               
               
                   
                 68 
                 −5.05E−02 
                 8.70E−04 
                 −5.85E−02 
               
               
                   
                 69 
                 −4.86E−01 
                 −4.72E−04 
                 −4.82E−01 
               
               
                   
                 70 
                 2.16E−03 
                 −4.33E−01 
                 2.18E−03 
               
               
                   
                 71 
                 −4.26E−03 
                 −8.66E−02 
                 −4.26E−03 
               
               
                   
                 72 
                 1.07E−01 
                 −8.27E−04 
                 7.51E−02 
               
               
                   
                 73 
                 1.86E−01 
                 3.73E−04 
                 2.23E−01 
               
               
                   
                 74 
                 −7.72E−05 
                 −1.07E−01 
                 −3.66E−05 
               
               
                   
                 75 
                 2.02E−03 
                 −2.59E−02 
                 1.91E−03 
               
               
                   
                 76 
                 −1.94E−01 
                 3.12E−03 
                 −1.82E−01 
               
               
                   
                 77 
                 2.46E−01 
                 1.31E−04 
                 2.02E−01 
               
               
                   
                 78 
                 2.75E−03 
                 −3.73E−01 
                 2.59E−03 
               
               
                   
                 79 
                 −2.22E−03 
                 4.60E−02 
                 −2.10E−03 
               
               
                   
                 80 
                 −1.25E−01 
                 2.12E−03 
                 −1.08E−01 
               
               
                   
                 81 
                 5.09E−01 
                 −8.99E−04 
                 4.56E−01 
               
               
                   
                 82 
                 −3.15E−03 
                 −4.73E−02 
                 −3.14E−03 
               
               
                   
                 83 
                 −2.38E−02 
                 −8.56E−03 
                 −1.34E−02 
               
               
                   
                 84 
                 5.25E−02 
                 5.96E−04 
                 4.59E−02 
               
               
                   
                 85 
                 −7.38E−04 
                 −2.87E−01 
                 −7.86E−04 
               
               
                   
                 86 
                 −3.16E−05 
                 −2.48E−02 
                 4.81E−05 
               
               
                   
                 87 
                 5.58E−02 
                 2.82E−03 
                 5.17E−02 
               
               
                   
                 88 
                 1.95E−01 
                 −8.12E−04 
                 1.99E−01 
               
               
                   
                 89 
                 6.58E−04 
                 −5.77E−02 
                 7.71E−04 
               
               
                   
                 90 
                 1.62E−03 
                 −1.03E−02 
                 1.51E−03 
               
               
                   
                 91 
                 7.50E−02 
                 1.40E−04 
                 4.29E−02 
               
               
                   
                 92 
                 −2.87E−01 
                 1.00E−03 
                 −2.51E−01 
               
               
                   
                 93 
                 7.64E−04 
                 −2.63E−01 
                 7.62E−04 
               
               
                   
                 94 
                 9.85E−04 
                 −5.21E−02 
                 9.45E−04 
               
               
                   
                 95 
                 −8.10E−02 
                 2.64E−03 
                 −7.63E−02 
               
               
                   
                 96 
                 3.40E−01 
                 9.13E−05 
                 2.98E−01 
               
               
                   
                 97 
                 1.27E−04 
                 −1.69E−01 
                 1.02E−04 
               
               
                   
                 98 
                 3.25E−04 
                 7.54E−02 
                 3.96E−04 
               
               
                   
                 99 
                 −1.33E−01 
                 1.66E−03 
                 −1.28E−01 
               
               
                   
                 100 
                 3.68E−01 
                 −8.69E−04 
                 3.25E−01 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Zernike coefficients for FIG. 3 with [100] lens: 
               
             
          
           
               
                   
                 Zernike 
                 Element 1 
                 Element 2 
                 Element 3 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −5.20E−02 
                 −1.98E−02 
                 −5.16E−02 
               
               
                   
                 2 
                 −1.15E−02 
                 1.82E−01 
                 −1.15E−02 
               
               
                   
                 3 
                 1.50E−01 
                 1.16E−02 
                 1.51E−01 
               
               
                   
                 4 
                 −1.07E−01 
                 −2.20E−02 
                 −1.06E−01 
               
               
                   
                 5 
                 −1.34E+01 
                 −2.71E−03 
                 −1.34E+01 
               
               
                   
                 6 
                 1.41E−03 
                 −5.60E+00 
                 1.45E−03 
               
               
                   
                 7 
                 1.47E−03 
                 −2.81E−02 
                 1.43E−03 
               
               
                   
                 8 
                 1.08E−01 
                 −4.12E−03 
                 9.92E−02 
               
               
                   
                 9 
                 −4.27E−02 
                 5.85E−04 
                 −4.05E−02 
               
               
                   
                 10 
                 1.41E−02 
                 8.59E−02 
                 1.42E−02 
               
               
                   
                 11 
                 −4.65E−01 
                 2.26E−02 
                 −4.60E−01 
               
               
                   
                 12 
                 4.58E+00 
                 −6.33E−04 
                 4.57E+00 
               
               
                   
                 13 
                 −3.52E−03 
                 3.65E+00 
                 −3.43E−03 
               
               
                   
                 14 
                 3.28E−03 
                 −2.67E−02 
                 3.21E−03 
               
               
                   
                 15 
                 −1.29E−03 
                 −3.64E−03 
                 −8.29E−03 
               
               
                   
                 16 
                 −2.37E−02 
                 1.69E−03 
                 −2.09E−02 
               
               
                   
                 17 
                 −1.58E−01 
                 9.09E−02 
                 −1.56E−01 
               
               
                   
                 18 
                 −1.67E−02 
                 −1.31E−01 
                 −1.68E−02 
               
               
                   
                 19 
                 −9.00E−03 
                 −9.34E−03 
                 −8.96E−03 
               
               
                   
                 20 
                 3.17E−02 
                 −1.15E−02 
                 3.42E−02 
               
               
                   
                 21 
                 −3.46E−01 
                 −3.18E−04 
                 −3.60E−01 
               
               
                   
                 22 
                 8.48E−04 
                 −1.59E+00 
                 9.43E−04 
               
               
                   
                 23 
                 −1.25E−03 
                 −3.60E−02 
                 −1.36E−03 
               
               
                   
                 24 
                 1.27E−01 
                 7.76E−04 
                 1.17E−01 
               
               
                   
                 25 
                 −3.31E−02 
                 9.62E−04 
                 −2.98E−02 
               
               
                   
                 26 
                 9.70E−03 
                 7.57E−02 
                 9.79E−03 
               
               
                   
                 27 
                 −4.80E−02 
                 −3.29E−04 
                 −4.88E−02 
               
               
                   
                 28 
                 −3.12E−02 
                 −1.76E−02 
                 −2.89E−02 
               
               
                   
                 29 
                 5.07E−03 
                 7.34E−03 
                 5.09E−03 
               
               
                   
                 30 
                 1.77E−03 
                 1.11E−01 
                 1.89E−03 
               
               
                   
                 31 
                 −1.16E−01 
                 4.07E−03 
                 −1.12E−01 
               
               
                   
                 32 
                 8.53E−02 
                 8.68E−05 
                 7.06E−02 
               
               
                   
                 33 
                 −4.51E−04 
                 5.63E−01 
                 −3.42E−04 
               
               
                   
                 34 
                 1.74E−04 
                 −3.33E−02 
                 5.81E−05 
               
               
                   
                 35 
                 1.33E−01 
                 −2.08E−03 
                 1.21E−01 
               
               
                   
                 36 
                 −3.65E−02 
                 2.91E−03 
                 −3.29E−02 
               
               
                   
                 37 
                 6.20E−01 
                 4.55E−03 
                 6.26E−01 
               
               
                   
                 38 
                 −5.12E−04 
                 2.56E+00 
                 −5.97E−04 
               
               
                   
                 39 
                 −6.99E−03 
                 −4.66E−02 
                 −6.93E−03 
               
               
                   
                 40 
                 2.52E−02 
                 6.82E−03 
                 2.53E−02 
               
               
                   
                 41 
                 −2.95E−02 
                 1.05E−03 
                 −2.69E−02 
               
               
                   
                 42 
                 −3.08E−03 
                 −2.54E−02 
                 −3.17E−03 
               
               
                   
                 43 
                 −1.83E−04 
                 −1.04E−02 
                 −7.27E−05 
               
               
                   
                 44 
                 −1.15E−01 
                 −2.59E−03 
                 −1.11E−01 
               
               
                   
                 45 
                 2.88E−01 
                 3.57E−04 
                 2.71E−01 
               
               
                   
                 46 
                 −3.54E−04 
                 7.37E−02 
                 −2.30E−04 
               
               
                   
                 47 
                 4.01E−04 
                 −4.84E−02 
                 2.74E−04 
               
               
                   
                 48 
                 1.37E−01 
                 −1.15E−03 
                 1.24E−01 
               
               
                   
                 49 
                 −3.79E−02 
                 2.15E−03 
                 −3.42E−02 
               
               
                   
                 50 
                 −7.02E−03 
                 −2.04E−01 
                 −7.08E−03 
               
               
                   
                 51 
                 5.09E−02 
                 −9.05E−03 
                 5.25E−02 
               
               
                   
                 52 
                 −1.00E+00 
                 −8.40E−05 
                 −9.93E−01 
               
               
                   
                 53 
                 1.17E−03 
                 −2.40E+00 
                 1.05E−03 
               
               
                   
                 54 
                 2.77E−03 
                 3.21E−02 
                 2.88E−03 
               
               
                   
                 55 
                 −2.37E−02 
                 −4.55E−04 
                 −2.56E−02 
               
               
                   
                 56 
                 −2.73E−02 
                 −3.95E−03 
                 −2.44E−02 
               
               
                   
                 57 
                 1.73E−03 
                 −4.84E−03 
                 1.70E−03 
               
               
                   
                 58 
                 −6.60E−04 
                 4.85E−02 
                 −5.38E−04 
               
               
                   
                 59 
                 −1.20E−01 
                 −1.33E−03 
                 −1.15E−01 
               
               
                   
                 60 
                 2.82E−01 
                 3.92E−04 
                 2.62E−01 
               
               
                   
                 61 
                 −2.60E−04 
                 1.81E−02 
                 −1.14E−04 
               
               
                   
                 62 
                 2.84E−04 
                 −5.74E−02 
                 1.50E−04 
               
               
                   
                 63 
                 1.63E−01 
                 −1.49E−03 
                 1.50E−01 
               
               
                   
                 64 
                 −4.08E−02 
                 2.56E−03 
                 −3.74E−02 
               
               
                   
                 65 
                 2.14E−02 
                 −3.63E−02 
                 2.58E−02 
               
               
                   
                 66 
                 1.53E−02 
                 1.19E−01 
                 1.53E−02 
               
               
                   
                 67 
                 7.88E−03 
                 1.32E−01 
                 7.81E−03 
               
               
                   
                 68 
                 −4.64E−02 
                 7.68E−03 
                 −4.27E−02 
               
               
                   
                 69 
                 6.28E−01 
                 −5.30E−05 
                 6.37E−01 
               
               
                   
                 70 
                 −1.17E−03 
                 1.28E+00 
                 −1.28E−03 
               
               
                   
                 71 
                 1.20E−04 
                 1.27E−02 
                 2.28E−04 
               
               
                   
                 72 
                 −1.17E−02 
                 6.03E−04 
                 −1.24E−02 
               
               
                   
                 73 
                 −3.05E−02 
                 −4.10E−03 
                 −2.74E−02 
               
               
                   
                 74 
                 5.12E−04 
                 −5.97E−03 
                 4.65E−04 
               
               
                   
                 75 
                 −5.85E−04 
                 5.53E−02 
                 −4.59E−04 
               
               
                   
                 76 
                 −1.46E−01 
                 −1.44E−03 
                 −1.42E−01 
               
               
                   
                 77 
                 2.91E−01 
                 4.82E−04 
                 2.70E−01 
               
               
                   
                 78 
                 −2.85E−04 
                 1.42E−01 
                 −1.21E−04 
               
               
                   
                 79 
                 2.54E−04 
                 −5.57E−02 
                 1.01E−04 
               
               
                   
                 80 
                 1.71E−01 
                 −1.65E−03 
                 1.57E−01 
               
               
                   
                 81 
                 −4.08E−02 
                 2.91E−03 
                 −3.78E−02 
               
               
                   
                 82 
                 −5.64E−03 
                 −4.41E−02 
                 −5.71E−03 
               
               
                   
                 83 
                 2.45E−03 
                 −4.80E−03 
                 1.97E−03 
               
               
                   
                 84 
                 −5.55E−04 
                 2.12E−02 
                 4.58E−03 
               
               
                   
                 85 
                 −8.43E−03 
                 −3.86E−02 
                 −8.41E−03 
               
               
                   
                 86 
                 −4.36E−03 
                 −9.15E−02 
                 −4.46E−03 
               
               
                   
                 87 
                 5.15E−02 
                 −4.47E−03 
                 5.44E−02 
               
               
                   
                 88 
                 −3.55E−01 
                 −4.58E−04 
                 −3.45E−01 
               
               
                   
                 89 
                 7.27E−04 
                 −5.43E−01 
                 5.93E−04 
               
               
                   
                 90 
                 −3.63E−04 
                 5.57E−03 
                 −2.48E−04 
               
               
                   
                 91 
                 −5.94E−03 
                 1.26E−03 
                 −7.76E−03 
               
               
                   
                 92 
                 −3.39E−02 
                 −4.09E−03 
                 −3.06E−02 
               
               
                   
                 93 
                 4.93E−04 
                 −9.61E−03 
                 4.45E−04 
               
               
                   
                 94 
                 −5.44E−04 
                 4.51E−02 
                 −4.06E−04 
               
               
                   
                 95 
                 −1.54E−01 
                 −1.82E−03 
                 −1.50E−01 
               
               
                   
                 96 
                 3.42E−01 
                 5.55E−04 
                 3.20E−01 
               
               
                   
                 97 
                 −3.27E−04 
                 1.19E−01 
                 −1.64E−04 
               
               
                   
                 98 
                 2.87E−04 
                 −6.36E−02 
                 1.12E−04 
               
               
                   
                 99 
                 1.80E−01 
                 −1.60E−03 
                 1.66E−01 
               
               
                   
                 100 
                 −3.94E−02 
                 3.04E−03 
                 −3.71E−02 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 Zernike coefficients for FIG. 3 with [110] lens: 
               
             
          
           
               
                   
                 Zernike 
                 Element 1 
                 Element 2 
                 Element 3 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 4.83E−01 
                 2.93E−02 
                 4.79E−01 
               
               
                   
                 2 
                 1.68E−02 
                 1.92E−01 
                 1.67E−02 
               
               
                   
                 3 
                 −2.79E−01 
                 −1.85E−02 
                 −2.81E−01 
               
               
                   
                 4 
                 −7.03E+00 
                 3.27E−02 
                 −7.04E+00 
               
               
                   
                 5 
                 −2.49E+00 
                 1.79E−02 
                 −2.49E+00 
               
               
                   
                 6 
                 1.19E−02 
                 5.86E+00 
                 1.15E−02 
               
               
                   
                 7 
                 −2.46E−03 
                 6.03E−03 
                 −2.48E−03 
               
               
                   
                 8 
                 −2.78E−01 
                 2.94E−03 
                 −2.72E−01 
               
               
                   
                 9 
                 2.13E+00 
                 −6.50E−03 
                 2.13E+00 
               
               
                   
                 10 
                 −7.36E−03 
                 6.11E−02 
                 −7.31E−03 
               
               
                   
                 11 
                 −3.00E−01 
                 −3.06E−02 
                 −3.01E−01 
               
               
                   
                 12 
                 −6.65E−01 
                 4.38E−03 
                 −6.67E−01 
               
               
                   
                 13 
                 3.12E−03 
                 −4.56E+00 
                 1.95E−03 
               
               
                   
                 14 
                 −1.08E−02 
                 −1.30E−01 
                 −1.08E−02 
               
               
                   
                 15 
                 1.17E−01 
                 8.74E−03 
                 1.19E−01 
               
               
                   
                 16 
                 5.53E−01 
                 −7.61E−03 
                 5.45E−01 
               
               
                   
                 17 
                 3.72E+00 
                 −4.84E−02 
                 3.73E+00 
               
               
                   
                 18 
                 5.10E−02 
                 2.15E+00 
                 5.14E−02 
               
               
                   
                 19 
                 1.11E−02 
                 8.31E−02 
                 1.12E−02 
               
               
                   
                 20 
                 −3.69E−02 
                 1.90E−02 
                 −3.38E−02 
               
               
                   
                 21 
                 4.46E−01 
                 −1.55E−03 
                 4.43E−01 
               
               
                   
                 22 
                 −3.18E−03 
                 −6.97E−01 
                 −4.58E−03 
               
               
                   
                 23 
                 3.97E−03 
                 5.38E−02 
                 3.92E−03 
               
               
                   
                 24 
                 −2.50E−02 
                 −2.92E−03 
                 −2.22E−02 
               
               
                   
                 25 
                 1.07E−01 
                 5.30E−03 
                 9.70E−02 
               
               
                   
                 26 
                 −5.33E−03 
                 1.78E−01 
                 −5.35E−03 
               
               
                   
                 27 
                 7.08E−02 
                 −1.94E−02 
                 6.51E−02 
               
               
                   
                 28 
                 −9.66E−01 
                 3.20E−02 
                 −9.62E−01 
               
               
                   
                 29 
                 −1.98E−02 
                 −1.48E+00 
                 −1.96E−02 
               
               
                   
                 30 
                 −1.14E−03 
                 −2.60E−02 
                 −1.04E−03 
               
               
                   
                 31 
                 5.01E−02 
                 2.29E−04 
                 5.19E−02 
               
               
                   
                 32 
                 2.07E−01 
                 1.67E−03 
                 2.02E−01 
               
               
                   
                 33 
                 3.24E−03 
                 1.98E+00 
                 1.69E−03 
               
               
                   
                 34 
                 5.34E−03 
                 1.25E−01 
                 5.24E−03 
               
               
                   
                 35 
                 −1.14E−01 
                 −6.94E−04 
                 −1.10E−01 
               
               
                   
                 36 
                 −3.41E−01 
                 3.97E−04 
                 −3.51E−01 
               
               
                   
                 37 
                 1.29E+00 
                 −8.80E−03 
                 1.29E+00 
               
               
                   
                 38 
                 3.27E−02 
                 1.20E+00 
                 3.41E−02 
               
               
                   
                 39 
                 1.08E−02 
                 1.17E−02 
                 1.07E−02 
               
               
                   
                 40 
                 −3.49E−03 
                 8.00E−03 
                 −7.33E−03 
               
               
                   
                 41 
                 −7.60E−01 
                 −3.03E−03 
                 −7.52E−01 
               
               
                   
                 42 
                 −5.82E−04 
                 4.20E−01 
                 −8.98E−05 
               
               
                   
                 43 
                 −2.67E−03 
                 −7.35E−02 
                 −2.53E−03 
               
               
                   
                 44 
                 −8.45E−02 
                 −5.13E−03 
                 −8.43E−02 
               
               
                   
                 45 
                 −1.73E−01 
                 1.31E−03 
                 −1.79E−01 
               
               
                   
                 46 
                 4.18E−03 
                 −5.21E−01 
                 2.16E−03 
               
               
                   
                 47 
                 −4.32E−03 
                 −3.76E−02 
                 −4.48E−03 
               
               
                   
                 48 
                 −1.04E−01 
                 3.54E−03 
                 −9.82E−02 
               
               
                   
                 49 
                 1.92E−01 
                 −4.14E−03 
                 1.82E−01 
               
               
                   
                 50 
                 −7.42E−04 
                 5.07E−02 
                 −8.61E−04 
               
               
                   
                 51 
                 9.49E−03 
                 −1.09E−02 
                 9.43E−03 
               
               
                   
                 52 
                 −6.69E−01 
                 9.88E−03 
                 −6.68E−01 
               
               
                   
                 53 
                 −9.34E−03 
                 −3.79E−01 
                 −7.65E−03 
               
               
                   
                 54 
                 −6.83E−03 
                 −7.66E−02 
                 −6.92E−03 
               
               
                   
                 55 
                 3.19E−02 
                 −1.12E−03 
                 2.73E−02 
               
               
                   
                 56 
                 5.60E−01 
                 −6.94E−03 
                 5.68E−01 
               
               
                   
                 57 
                 7.43E−03 
                 3.40E−01 
                 8.02E−03 
               
               
                   
                 58 
                 3.67E−03 
                 3.54E−02 
                 3.86E−03 
               
               
                   
                 59 
                 −1.35E−01 
                 3.56E−03 
                 −1.33E−01 
               
               
                   
                 60 
                 −1.47E−03 
                 −9.18E−04 
                 −7.85E−03 
               
               
                   
                 61 
                 −1.72E−03 
                 −5.02E−01 
                 −4.13E−03 
               
               
                   
                 62 
                 −4.12E−03 
                 6.37E−03 
                 −4.32E−03 
               
               
                   
                 63 
                 −3.67E−02 
                 2.06E−03 
                 −3.14E−02 
               
               
                   
                 64 
                 3.71E−01 
                 −2.01E−03 
                 3.59E−01 
               
               
                   
                 65 
                 3.96E−01 
                 −1.31E−02 
                 3.99E−01 
               
               
                   
                 66 
                 1.62E−02 
                 1.66E+00 
                 1.55E−02 
               
               
                   
                 67 
                 1.53E−03 
                 1.38E−03 
                 1.27E−03 
               
               
                   
                 68 
                 −5.96E−02 
                 3.90E−03 
                 −5.77E−02 
               
               
                   
                 69 
                 −1.56E−01 
                 −5.63E−03 
                 −1.52E−01 
               
               
                   
                 70 
                 2.32E−04 
                 −3.04E−01 
                 2.23E−03 
               
               
                   
                 71 
                 −1.51E−03 
                 −5.28E−03 
                 −1.57E−03 
               
               
                   
                 72 
                 4.45E−02 
                 −1.84E−03 
                 3.75E−02 
               
               
                   
                 73 
                 4.54E−02 
                 4.67E−03 
                 5.26E−02 
               
               
                   
                 74 
                 −3.69E−03 
                 −3.03E−01 
                 −3.14E−03 
               
               
                   
                 75 
                 2.66E−03 
                 −2.61E−03 
                 2.93E−03 
               
               
                   
                 76 
                 −2.91E−02 
                 2.51E−03 
                 −2.63E−02 
               
               
                   
                 77 
                 2.11E−01 
                 −6.93E−04 
                 2.03E−01 
               
               
                   
                 78 
                 −6.88E−04 
                 9.83E−02 
                 −3.22E−03 
               
               
                   
                 79 
                 1.83E−03 
                 6.74E−02 
                 1.56E−03 
               
               
                   
                 80 
                 −5.99E−02 
                 1.58E−03 
                 −5.59E−02 
               
               
                   
                 81 
                 8.73E−02 
                 −1.09E−03 
                 7.31E−02 
               
               
                   
                 82 
                 −4.97E−03 
                 −9.09E−02 
                 −4.70E−03 
               
               
                   
                 83 
                 −8.53E−03 
                 −9.63E−03 
                 −4.26E−03 
               
               
                   
                 84 
                 −5.39E−02 
                 4.49E−03 
                 −5.13E−02 
               
               
                   
                 85 
                 7.83E−04 
                 −6.40E−01 
                 −1.20E−04 
               
               
                   
                 86 
                 −3.20E−03 
                 −5.82E−04 
                 −3.52E−03 
               
               
                   
                 87 
                 4.35E−02 
                 1.13E−03 
                 4.60E−02 
               
               
                   
                 88 
                 4.54E−01 
                 −1.08E−03 
                 4.57E−01 
               
               
                   
                 89 
                 9.66E−04 
                 2.35E−01 
                 3.33E−03 
               
               
                   
                 90 
                 6.07E−03 
                 3.56E−02 
                 6.01E−03 
               
               
                   
                 91 
                 1.33E−02 
                 5.63E−04 
                 6.51E−03 
               
               
                   
                 92 
                 −5.06E−01 
                 2.07E−03 
                 −4.97E−01 
               
               
                   
                 93 
                 −4.84E−03 
                 −8.16E−02 
                 −4.19E−03 
               
               
                   
                 94 
                 2.11E−05 
                 −3.62E−02 
                 4.06E−04 
               
               
                   
                 95 
                 −2.61E−02 
                 7.66E−04 
                 −2.55E−02 
               
               
                   
                 96 
                 9.27E−02 
                 1.12E−04 
                 8.33E−02 
               
               
                   
                 97 
                 3.17E−03 
                 9.43E−02 
                 5.00E−04 
               
               
                   
                 98 
                 1.19E−03 
                 4.57E−02 
                 7.97E−04 
               
               
                   
                 99 
                 −1.26E−01 
                 2.23E−03 
                 −1.22E−01 
               
               
                   
                 100 
                 3.55E−02 
                 −2.26E−03 
                 2.17E−02