Abstract:
A projection lens for use with a pixelized panel (LCD) is provided. The lens has two positive lens units with an aperture stop between them. The optical powers of each of the units are such that f1 is substantially shorter than f2, where f1 and f2 are the focal lengths of the first lens unit and the second lens unit, respectively, the first lens unit being on the system&#39;s long conjugate side and the second lens unit being on the short conjugate side. The ratio of f1 to f2 is preferably less than about 0.75.

Description:
CROSS REFERENCE TO RELATED PROVISIONAL APPLICATION 
     This application claims the benefit under 35 USC §119(e) of U.S. Provisional Application No. 60/016,447 filed Apr. 29, 1996 the content of which in its entirety is hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to projection lenses and, in particular, to projection lenses which can be used, inter alia, to form an image of an object composed of pixels, such as, a liquid crystal display (LCD). 
     BACKGROUND OF THE INVENTION 
     Projection lens systems (also referred to herein as &#34;projection systems&#34;) are used to form an image of an object on a viewing screen. The basic structure of such a system is shown in FIG. 7, wherein 10 is a light source (e.g., a tungsten-halogen lamp), 12 is illumination optics which forms an image of the light source (hereinafter referred to as the &#34;output&#34; of the illumination system), 14 is the object which is to be projected (e.g., a matrix of on and off pixels of a LCD panel), and 13 is a projection lens, composed of multiple lens elements, which forms an enlarged image of object 14 on viewing screen 16. 
     Projection lens systems in which the object is a LCD or other pixelized panel are used in a variety of applications, including data display systems. Such projection lens systems preferably employ a single projection lens which forms an image of either a single panel having, for example, red, green, and blue pixels, or three individual panels, one for each color. For ease of reference, the following discussion will be in terms of a projection lens system that employs a single LCD panel, it being understood that the invention can also be used in systems which employ multiple panels and/or other types of pixelization. 
     SUMMARY OF THE INVENTION 
     The projection lenses of the invention comprise two positive lens units with an aperture stop between them. The optical powers of each of the units are such that f1 is substantially shorter than f2, where f1 and f2 are the focal lengths of the first lens unit and the second lens unit, respectively, the first lens unit being on the system&#39;s long conjugate side and the second lens unit being on the short conjugate side. In particular, the ratio of f1 to f2 is less than about 0.75. (See Table 7 and note that when the second unit includes a field lens, e.g., a Fresnel field lens, the value of f2 is calculated without the field lens.) In contrast, for a classical double gauss form, f1 is about the same as f2, or longer than f2. 
     The projection lenses of the invention are capable of covering a wide field of view. They have a back focal length approximately equal to the focal length of the lens. Each of the first and second lens units has at least one aspherical surface. 
     The first lens unit on the long conjugate side of the stop may consist of a single positive element. However, to obtain a better correction of residual astigmatism and chromatic aberrations, this unit may include a leading negative element closely followed by a positive component which may be a color correcting doublet. As illustrated in Tables 1-5, the spacing between the leading negative element and the positive component is at most about 5% of the focal length of the first lens unit. 
     The second lens unit behind the aperture stop includes a color correcting doublet and a single positive element with at least one aspherical surface. Most of the correction of spherical aberration is obtained in the first lens unit, while off-axis aberrations including coma and distortion, as well as chromatic aberrations, are corrected predominantly in the second lens unit. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1-6 are schematic side views of projection lenses constructed in accordance with the invention. 
     FIG. 7 is a schematic diagram showing an overall projection lens system in which the projection lens of the present invention can be used. 
     The foregoing drawings, which are incorporated in and constitute part of the specification, illustrate the preferred embodiments of the invention, and together with the description, serve to explain the principles of the invention. It is to be understood, of course, that both the drawings and the description are explanatory only and are not restrictive of the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIGS. 1 to 6 illustrate various projection lenses constructed in accordance with the invention. Corresponding prescriptions and optical properties appear in Tables 1 to 6, respectively. The correspondence between the lens units discussed above and the various elements and surfaces of the lenses of Tables 1-6 is set forth in Table 7. 
     HOYA or SCHOTT designations are used for the glasses employed in the lens systems. Equivalent glasses made by other manufacturers can be used in the practice of the invention. Industry acceptable materials are used for the styrene and acrylic elements. 
     The aspheric coefficients set forth in the tables are for use in the following equation: ##EQU1## where z is the surface sag at a distance y from the optical axis of the system, c is the curvature of the lens at the optical axis, and k is a conic constant. 
     The designation &#34;a&#34; associated with various surfaces in the tables represents an aspheric surface, i.e., a surface for which at least one of D, E, F, G, H, or I in the above equation is not zero. The designation &#34;c&#34; represents a conic surface for which the k value in the above equation is not zero. The designation &#34;f&#34; represents a Fresnel lens surface (the Fresnel lens is identified by the designation &#34;FL&#34; in FIGS. 1 and 3). All dimensions given in the tables are in millimeters. The tables are constructed on the assumption that light travels from left to right in the figures. In actual practice, the viewing screen will be on the left and the LCD panel will be on the right, and light will travel from right to left. 
     Although specific embodiments of the invention have been described and illustrated, it is to be understood that a variety of modifications which do not depart from the scope and spirit of the invention will be evident to persons of ordinary skill in the art from the foregoing disclosure. 
     
                                           TABLE 1__________________________________________________________________________Lens DataSurf.                             Clear ApertureNo.  Type   Radius Thickness Glass                             Diameter__________________________________________________________________________ 1   a      -1770.1750              8.00000   ACRYLIC                             84.11 2   a      72.5195              10.00000       71.77 3          63.3660              25.00000  SK18 68.98 4          -63.3660              4.00000   KF6  65.89 5          762.9749              9.16228        60.48 6          Aperture stop              35.18800       57.72 7          -38.4192              5.00000   SF14 63.38 8          -81.9407              1.00000        80.13 9   a      -77.4031              18.00000  ACRYLIC                             83.6010   a      -57.0000              Space 1        93.6511   c      -927.4539              29.50000  ACRYLIC                             119.7712   a      -79.0000              Space 2        124.9913   cf     185.6000              4.00000   ACRYLIC                             237.0614          ∞              Image distance 236.86__________________________________________________________________________Symbol Description            a -- Polynomial asphere            c -- Conic section            f -- Fresnel__________________________________________________________________________Conics      Surface      Number          Constant__________________________________________________________________________      11  -7.1739E+01      13  -1.7000E+00__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________ 1 -7.0051E-08     -6.3254E-12            -2.9530E-14                    7.5364E-19                           9.4792E-21                                 -3.0013E-24 2  7.7762E-08      1.2679E-11             1.0260E-13                   -3.2966E-17                          -1.6803E-21                                  1.6991E-23 9  4.1171E-07      2.1244E-10             1.0122E-14                    4.0619E-18                           4.4932E-21                                 -1.0666E-2410  2.4362E-07      1.2454E-10             1.2955E-14                    1.0067E-17                           1.8340E-21                                  3.0151E-2412  1.3759E-07      5.0414E-11            -2.7910E-15                    1.1423E-18                           3.9343E-23                                 -3.3950E-27__________________________________________________________________________Variable SpacesZoom       Space 1          Space 2      Focal                           ImagePos.       T(10)          T(12)        Shift                           Distance__________________________________________________________________________1          1.500          182.411      -1.425                           10.0212          0.500          190.200      -1.000                           10.0153          2.000          175.350      -1.800                           10.013__________________________________________________________________________First-Order Data          Zoom Position          1           2    3__________________________________________________________________________f/number       3.50        3.50 3.50Magnification  -0.0645     -0.1000                           -0.0322Object Height  -1830.8     -1180.0                           -3660.0Object Distance          -3048.7     -1998.8                           -6010.2Effective Focal Length          198.28      202.52                           194.61Image Distance 10.021      10.015                           10.013Overall Length 3391.4      2348.3                           6346.5Forward Vertex Distance          342.78      349.56                           336.21Barrel Length  332.76      339.55                           326.20Stop Surface Number          6           6    6Distance to Stop          0.00        0.00 0.00Stop Diameter  55.244      56.621                           54.042Entrance Pupil Distance          40.838      40.838                           40.838Exit Pupil Distance          -2564.2     -2859.8                           -2270.8__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1       1  2   -0.70980E-02                 -140.88                        5.1374 -0.210472       3  4    0.18681E-01                 53.532 8.2520 -8.25203       4  5   -0.88988E-02                 -112.38                        0.20149                               -2.42614       7  8   -0.10095E-01                 -99.059                        -2.6268                               -5.60255       9 10    0.29494E-02                 339.06 35.393 26.0636      11 12    0.57837E-02                 172.90 21.342 1.81797      13 14    0.26604E-02                 375.88 -0.51716E-08                               -2.6778__________________________________________________________________________First-Order Properties of DoubletsElement  SurfaceNumbers  Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________2 3    3 5      0.11187E-01                 89.389 1.5277 -16.542__________________________________________________________________________First Order Properties of GroupsGroup  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1       1 10   -0.26248E-03                 -3809.7                        495.35 349.412      11 12    0.57837E-02                 172.90 21.342 1.81793      13 14    0.26604E-02                 375.88 -0.51716E-08                               -2.6778__________________________________________________________________________First Order Properties of the LensZoom PositionNumber         Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1               0.50433E-02                 198.28 223.78 -199.632               0.49377E-02                 202.52 228.97 -211.763               0.51385E-02                 194.61 218.81 -189.07__________________________________________________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________Lens DataSurf.                             Clear ApertureNo.  Type   Radius Thickness Glass                             Diameter__________________________________________________________________________ 1   a      -3501.6551              8.00000   ACRYLIC                             83.97 2   a      73.8047              10.00000       72.07 3          63.9262              25.00000  SK18 69.86 4          -63.9262              4.00000   KF6  67.04 5          570.3825              2.53228        60.39 6          ∞              41.97092       59.72 7          -39.0852              5.00000   SF14 64.45 8          -83.4350              1.00000        80.90 9   a      -77.4031              18.00000  ACRYLIC                             83.8810   a      -57.0000              0.50000        94.2611   c      -927.4539              30.50000  ACRYLIC                             119.0412   a      -79.0000              194.22819      124.60__________________________________________________________________________Symbol Description            a -- Polynomial asphere            c -- Conic section            Focal Shift = -1.97869__________________________________________________________________________Conics      Surface      Number          Constant__________________________________________________________________________      11  -7.5322E+01__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________ 1 -8.1680E-08     -9.0415E-12            -2.8846E-14                    9.7292E-19                           9.4877E-21                                 -2.8507E-24 2  6.1549E-08      5.4266E-12             9.8518E-14                   -3.4835E-17                          -1.5392E-21                                  1.7744E-23 9  3.8615E-07      1.8759E-10             1.0984E-14                    7.6281E-18                           5.6048E-21                                 -1.6720E-2410  2.7112E-07      1.4686E-10             1.7530E-14                    1.0200E-17                           1.4695E-21                                  2.8348E-2412  1.1260E-07      4.4374E-11            -2.9777E-15                    1.1981E-18                           4.3134E-23                                 -6.5187E-27__________________________________________________________________________First-Order Dataf/number    3.50       Overall Length                             3505.33Magnification       -0.0645    Forward Vertex Distance                             340.731Object Height       -1830.8    Barrel Length                             146.503Object Distance       -3164.60   Entrance Pupil Distance                             40.9073Effective Focal Length       198.998    Exit Pupil Distance                             -145.903Image Distance       194.228    Stop Diameter                             57.224Stop Surface Number       6          Distance to Stop                             6.43__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1       1  2   -0.68364E-02                 -146.28                        5.2411 -0.110472       3  4    0.18530E-01                 53.965 8.2460 -8.24603       4  5   -0.90617E-02                 -110.35                        0.26468                               -2.36164       7  8   -0.99405E-02                 -100.60                        -2.6199                               -5.59265       9 10    0.29494E-02                 339.06 35.393 26.0636      11 12    0.57859E-02                 172.83 22.057 1.8788__________________________________________________________________________First Order Properties of DoubletElement  SurfaceNumbers  Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________2 3    3 5      0.10898E-01                 91.762 1.1692 -6.833__________________________________________________________________________First Order Properties of the Lens          Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________          0.50252E-02                 199.00 119.64 -15.627__________________________________________________________________________FIRST ORDER DATA, SURF 1 TO 5K           PP1           PP2  f&#39;__________________________________________________________________________0.490176E-02       30.3186       -1.10148                          204.00__________________________________________________________________________FIRST ORDER DATA, SURF 7 TO 12K           PP1           PP2  f&#39;__________________________________________________________________________0.232360E-02       147.569       172.803                          430.37__________________________________________________________________________ 
    
     
                                           TABLE 3__________________________________________________________________________Lens DataSurf.                             Clear ApertureNo.  Type   Radius Thickness Glass                             Diameter__________________________________________________________________________1    a      -148.4666              6.00000   ACRYLIC                             51.922    a      54.4747              0.50000        45.043           40.0292              15.00000  SK18 45.074           -130.3723              6.26676        42.155           Aperture stop              21.40605       34.586           -23.1527              3.00000   SF13 39.967           -64.2034              1.50000        54.398           -54.0449              16.67610  ACRYLIC                             54.699    a      -35.8273              0.50000        63.6810   a      -3465.3279              24.66862  ACRYLIC                             93.0911   a      -54.7193              121.94030      95.7412   cf     120.0000              4.00000   ACRYLIC                             166.7913          ∞              9.99997        166.48__________________________________________________________________________Symbol Description            a -- Polynomial asphere            c -- Conic section            f -- Fresnel            Focal Shift = -1.94463__________________________________________________________________________Conics      Surface      Number          Constant__________________________________________________________________________      12  -2.0085E+00__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________ 1 -1.0532E-06     -1.0364E-09             1.3079E-12                   -2.2637E-15                           4.0754E-18                                 -2.4681E-21 2 -1.0077E-06      1.3853E-10            -5.4208E-12                    1.3555E-14                          -3.2354E-18                                 -5.1055E-21 9 -7.2513E-07      1.8571E-09            -2.8477E-12                    1.3532E-1S                           6.7032E-19                                 -5.6155E-2210 -2.1332E-07      2.4887E-11             3.2458E-14                    8.2905E-18                           2.9285E-22                                 -1.2661E-2511  5.7413E-07      4.5720E-11             4.8259E-14                    2.5315E-17                          -1.5472E-20                                  9.1310E-24__________________________________________________________________________First-Order Dataf/number    3.50       Overall Length                             1401.46Magnification       -0.1083    Forward Vertex Distance                             231.458Object Height       -762.00    Barrel Length                             221.458Object Distance       -1170.00   Entrance Pupil Distance                             20.3913Effective Focal Length       129.271    Exit Pupil Distance                             5729.90Image Distance       9.99997    Stop Diameter                             34.576Stop Surface Number       5          Distance to Stop                             0.00__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1       1  2   -0.12511E-01                 -79.928                        2.9100 -1.06772       3  4    0.20219E-01                 49.458 2.2234 -7.24143       6  7   -0.19987E-01                 -50.032                        -0.99970                               -2.77224       8  9    0.60514E-02                 165.25 25.425 16.8555      10 11    0.89025E-02                 112.33 16.739 0.264326      12 13    0.41148E-02                 243.03 -0.82019E-08                               -2.6778__________________________________________________________________________First Order Properties of the Lens          Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________           0.77357E-02                 129.27 152.58 -131.33__________________________________________________________________________ 
    
     
                                           TABLE 4__________________________________________________________________________Lens DataSurf.                             Clear ApertureNo.  Type   Radius Thickness Glass                             Diameter__________________________________________________________________________ 1   a      -143.9480              6.00000   ACRYLIC                             52.57 2   a      54.0933              0.50000        46.45 3          39.9766              15.00000  SK18 47.01 4          -138.3967              6.26676        44.55 5          ∞              23.26477       37.09 6          -23.3945              3.00000   SF13 41.34 7          -57.7517              1.50000        55.58 8          -50.6040              16.57162  ACRYLIC                             56.00 9   a      -36.2946              0.50000        64.8910   a      -2367.8999              24.39444  ACRYLIC                             92.9211   a      -54.6713              134.17166      95.59__________________________________________________________________________Symbol Description            a -- Polynomial asphere            Focal Shift = -1.24114__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________ 1 -7.8786E-07     -7.4301E-10             1.2284E-12                   -2.6558E-15                           3.7917E-18                                 -1.8308E-21 2 -4.9688E-07      6.2284E-10            -5.5378E-12                    1.2528E-14                          -4.7256E-18                                 -2.2320E-21 9 -6.7035E-07      1.6035E-09            -2.8384E-12                    1.4275E-15                           6.5802E-19                                 -6.1437E-2210 -2.4379E-07      2.3325E-11             3.2535E-14                    8.2976E-18                           2.0542E-22                                 -2.1158E-2511  6.0221E-07      5.9205E-11             4.6922E-14                    2.3851E-17                          -1.6076E-20                                  8.9490E-24__________________________________________________________________________First-Order Dataf/number    3.50       Overall Length                             1473.17Magnification       -0.1083    Forward Vertex Distance                             231.169Object Height       -762.00    Barrel Length                             96.9976Object Distance       -1242.00   Entrance Pupil Distance                             20.8429Effective Focal Length       129.736    Exit Pupil Distance                             -136.607Iinage Distance       134.172    Stop Diameter                             36.897Stop Surface Number       5          Distance to Stop                             0.45__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1       1  2   -0.12684E-01                 -78.838                        2.8906 -1.08622       3  4    0.19996E-01                 50.010 2.1178 -7.33183       6  7   -0.18289E-01                 -54.677                        -1.2146                               -2.99834       8  9    0.53197E-02                 187.98 28.371 20.3495      10 11    0.88539E-02                 112.94 16.659 0.38462__________________________________________________________________________First Order Properties of the Lens          Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________          0.77080E-02                 129.74 85.332 -8.3775__________________________________________________________________________FIRST ORDER DATA, SURF 1 TO 4K           PP1           PP2  f&#39;__________________________________________________________________________0.825105E-02       11.8672       -1.63760                          121.20__________________________________________________________________________FIRST ORDER DATA, SURF 6 TO 11K           PP1           PP2  f&#39;__________________________________________________________________________0.412919E-02       105.968       138.422                          242.18__________________________________________________________________________ 
    
     
                                           TABLE 5__________________________________________________________________________Lens DataSurf.                             Clear ApertureNo.  Type   Radius Thickness Glass                             Diameter__________________________________________________________________________ 1   a      -215.0838              6.00000   ACRYLIC                             50.10 2   a      51.3941              0.50000        44.84 3          39.5202              15.00000  SK18 45.08 4          -204.0199              6.26676        41.86 5          ∞              24.70386       37.34 6          -23.5819              3.00000   SF13 42.80 7          -54.9838              17.48359  SK5  58.11 8          -38.5513              0.50000        68.16 9   a      -442.7462              22.96924  ACRYLIC                             93.1810   a      -54.6936              133.38308      95.54__________________________________________________________________________Symbol Description            a -- Polynomial asphere            Focal Shift = -1.06757__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________ 1 -6.2558E-07     -6.6007E-10             1.3377E-12                   -2.7764E-15                           3.6207E-18                                 -1.7047E-21 2 -4.7729E-07      2.8390E-10            -5.2520E-12                    1.3608E-14                          -6.5024E-18                                 -3.3618E-21 9 -4.6643E-08      3.6819E-11             2.8968E-14                    8.8163E-18                           1.7148E-21                                  2.3288E-2510  5.3589E-07      1.0862E-10             4.8657E-14                    2.7503E-17                          -1.4201E-20                                  9.3743E-24__________________________________________________________________________First-Order Dataf/number    3.50       Overall Length                             1471.80Magnification       -0.1083    Forward Vertex Distance                             229.807Object Reight       -762.00    Barrel Length                             96.4234Object Distance       -1241.99   Entrance Pupil Distance                             19.6498Effective Focal Length       129.598    Exit Pupil Distance                             -136.742Image Distance       133.383    Stop Diameter                             37.137Stop Surface Number       5          Distance to Stop                             -0.86__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1      1  2    -0.11992E-01                 -83.389                        3.2180 -0.768952      3  4     0.18904E-01                 52.899 1.5196 -7.84493      6  7    -0.17354E-10                 -57.623                        -1.3444                               -3.13474      7  8     0.63978E-02                 156.30 26.344 18.4715      9 10     0.80676E-02                 123.95 17.207 2.1256__________________________________________________________________________First Order Properties of DoubletsElement  SurfaceNumbers  Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________3 4    6 8     -0.76835E-02                 -130.15                        -25.890                               -48.110__________________________________________________________________________First Order Properties of the Lens          Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________          0.77162E-02                 129.60 83.934 -9.1868__________________________________________________________________________FIRST ORDER DATA, SURF 1 TO 4K                    PP1  PP2__________________________________________________________________________0.754490E-02         10.2057                     -3.41220__________________________________________________________________________FIRST ORDER DATA, SURF 6 TO 10K                    PP1  PP2__________________________________________________________________________0.446394E-02         93.0606                     115.413__________________________________________________________________________ 
    
     
                                           TABLE 6__________________________________________________________________________Lens DataSurf.                              Clear ApertureNo.  Type   Radius Thickness Glass Diameter__________________________________________________________________________1    a      94.4760              15.00000  STYRENE                              42.782    a      -528.9612              0.50000         37.323           ∞              21.29889        36.844           -27.7690              3.00000   STYRENE                              40.465    a      -407.8987              4.00000         53.216           -74.3345              12.15783  BK7   53.557           -42.4453              0.50000         61.028    a      164.4718              26.97190  ACRYLIC                              92.869    a      -62.3055              135.01787       95.37__________________________________________________________________________Symbol Description            a -- Polynomial asphere            Focal Shift = -0.74200__________________________________________________________________________Even Polynomial AspheresSurf.No.   D      E      F      G      H      I__________________________________________________________________________1  -2.1948E-07     -3.1161E-09             7.4142E-12                   -1.0377E-14                          -2.2299E-17                                  3.2858E-202  -1.5111E-06     -5.1899E-09            -8.6485E-12                    2.3336E-14                           2.8430E-17                                 -1.0133E-195  -3.9131E-07     -6.8333E-10             5.5582E-13                    6.5433E-16                           1.3386E-20                                 -7.1347E-228  -2.9686E-07     -3.7064E-12             9.5859E-15                    4.9355E-18                           1.5459E-21                                  5.8285E-259   5.6173E-07      1.1183E-10             1.3209E-14                    1.5832E-17                          -1.7718E-20                                  7.9237E-24__________________________________________________________________________First-Order Dataf/number    3.50       Overall Length                             1460.42Magnification       -0.1083    Forward Vertex Digtance                             218.446Object Height       -762.00    Barrel Length                             83.4286Object Distance       -1241.97   Entrance Pupil Distance                             14.3855Effective Focal Length       128.370    Exit Pupil Distance                             -110.515Image Distance       135.018    Stop Diameter                             35.707Stop Surface Number       3          Distance to Stop                             3.27__________________________________________________________________________First Order Properties of ElementsElement  SurfaceNumber Numbers Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________1      1 2      0.73555E-02                 135.95 1.4381 -8.05182      4 5     -0.19908E-01                 -50.232                        -0.13781                               -2.02433      6 7      0.59254E-02                 168.76 16.511 9.42764      8 9      0.10498E-01                 95.259 13.631 -5.1638__________________________________________________________________________First Order Properties of the Lens          Power  f&#39;     lpp    l&#39;pp__________________________________________________________________________          0.77900E-02                 128.37 71.383 -7.9999__________________________________________________________________________FIRST ORDER DATA, SURF 4 TO 9K                    PP1  PP2__________________________________________________________________________0.444232E-02         92.8040                     107.813__________________________________________________________________________ 
    
     
                       TABLE 7______________________________________  Unit 1   Unit 2Ex. No.  Surf. Nos.           Surf. Nos.                    f1    f2    f     f1/f2______________________________________1      1 to 5   7 to 12  199.16                          448.33*                                198.99*                                      0.4442      1 to 5   7 to 12  204.00                          430.37                                199.00                                      0.4743      1 to 4   6 to 11  115.38                          257.84*                                129.60*                                      0.4474      1 to 4   6 to 11  121.20                          242.18                                129.74                                      0.5005      1 to 4   6 to 10  132.56                          224.02                                129.60                                      0.5926      1 to 2   4 to 9   135.95                          225.11                                128.37                                      0.604______________________________________ *Value calculated without the Fresnel lens since the Fresnel lens is primarily a field lens which serves to couple the lens&#39; entrance pupil to the exit pupil of the illumination system. As such, the Fresnel lens has minimal effect on the overall focal length of the lens, but a large effec on the value of f2, which effect is not representative of the actual functioning of the f2 unit.