Abstract:
A projection lens for use with LCD or DMD panels is provided. The lens has three lens units, the first unit having a weak power and at least one aspheric surface, the second unit having a positive power, a high dispersion negative lens element, and a low dispersion positive lens element, and the third unit having a negative power, a positive meniscus lens element and a negative lens element. The projection lens satisfies the following relationships: 
     f 0 /|f 1 |&lt;0.6; and 
     BFL/f 0 &gt;0.3 
     where (i) f 0  is the effective focal length of the combination of the first, second, and third lens units; (ii) f 1  is the effective focal length of the first lens unit; and (iii) BFL is the back focal length of the combination of the first, second, and third lens units for an object located at infinity along the long conjugate side of the projection lens.

Description:
CROSS REFERENCE TO RELATED PROVISIONAL APPLICATION 
     This application claims the benefit under 35 USC §119(e) of U.S. Provisional Application Ser. No.60/118,288 filed Feb. 2, 1999, 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 LCD or DMD. 
     BACKGROUND OF THE INVENTION 
     Projection lens systems (also referred to herein as “projection systems”) are used to form an image of an object on a viewing screen. The basic structure of such a system is shown in FIG. 5, 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 “output” of the illumination system),  14  is the object which is to be projected (e.g., a matrix of on and off pixels), and  13  is a projection lens, composed of multiple lens elements, which forms an enlarged image of object  14  on viewing screen  16 . The system can also include a field lens, e.g., a Fresnel lens, in the vicinity of the pixelized panel to direct the exit pupil of the illumination system towards the entrance pupil of the projection lens. 
     FIG. 5 is drawn for the case of a LCD panel where the output of the illumination system strikes the back of the panel and passes through those pixels of the panel which are transparent. DMDs, on the other hand, work by reflection and thus the output of the illumination system is routed to the front of the panel by a prism or similar device. 
     Projection lens systems in which the object is a 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. In some cases, two panels are used, one for two colors, e.g., red and green, and the other for one color, e.g., blue. A spinning filter wheel or similar device is associated with the panel for the two colors and the panel is alternately fed information for the two colors in synchrony with the rotating filter. 
     There exists a need for a projection lens for use with a pixelized panel which simultaneously has at least the following properties: (1) a long focal length; (2) a long back focal length; (3) the ability to operate (focus) at various magnifications (conjugates) while maintaining an efficient coupling to the output of the illumination system and a high level of aberration correction (hereinafter referred to as the “lens&#39; focus range”); (4) a relatively small size, including a small number of lens elements, a relatively small barrel length, and a relatively small maximum lens diameter; (5) a high level of color correction; and (6) low distortion. 
     A long focal length is needed for projection systems which are to be used in theaters, conference halls, and the like. In such settings, the projection system is typically located at the back of the hall so that the throw distance from the lens to the viewing screen is long. For a given panel size and screen size, i.e., a given magnification, the longer the focal length, the longer the throw distance. Accordingly, for a given range of magnifications, the focal length of the lens must increase as the throw distance increases. 
     A long back focal length, i.e., the distance from the last lens surface to the pixelized panel, is needed, especially where multiple panels are used, to accommodate the optical elements, e.g., filters, beam splitters, prisms, and the like, used in combining the light from the different color optical paths which the lens system projects towards the viewing screen. In addition, a long back focal length allows the output of the illumination system to be in the vicinity of the projection lens for output distances which are relatively large. Relatively large output distances are desirable since they provide relatively shallow entrance angles for the light at the pixelized panel which is especially important in the case of LCD panels. 
     A projection lens which can efficiently operate at various magnifications, i.e., a lens which has a large focus range, is desirable since it allows the projection system to be used with screens of different sizes and halls of different dimensions without the need to change any of the components of the system. Only the object and image conjugates need to be changed which can be readily accomplished by moving the lens relative to the pixelized panel. The challenge, of course, is to provide efficient coupling to the output of the illumination system and a high level of aberration correction throughout the operative range of magnifications. 
     A relatively small projection lens is desirable from a cost, weight, and size point of view. Large numbers of lens elements and elements having large diameters consume more raw materials, weigh more, and are more expensive to build and mount. Long barrel lengths normally increase the overall size of the projection system, which again leads to increased cost and weight. Accordingly, a lens with a minimum number of relatively small lens elements, located relatively close to one another, is desired. 
     A high level of color correction is important because color aberrations can be easily seen in the image of a pixelized panel as a smudging of a pixel or, in extreme cases, the complete dropping of a pixel from the image. These problems are typically most severe at the edges of the field. In general terms, the color correction, as measured at the pixelized panel, should be better than about a pixel and, preferably, better than about a half a pixel to avoid these problems. 
     All of the chromatic aberrations of the system need to be addressed, with lateral color, chromatic variation of coma, and chromatic aberration of astigmatism typically being most challenging. Lateral color, i.e., the variation of magnification with color, is particularly troublesome since it manifests itself as a decrease in contrast, especially at the edges of the field. In extreme cases, a rainbow effect in the region of the full field can be seen. 
     In projection systems employing cathode ray tubes (CRTs) a small amount of (residual) lateral color can be compensated for electronically by, for example, reducing the size of the image produced on the face of the red CRT relative to that produced on the blue CRT. With a pixelized panel, however, such an accommodation cannot be performed because the image is digitized and thus a smooth adjustment in size across the full field of view is not possible. A higher level of lateral color correction is thus needed from the projection lens. 
     It should be noted that color aberrations become more difficult to correct as the focal length of the projection lens increases. Thus, the first and fifth criteria discussed above, i.e., a long focal length and a high level of color correction, work against one another in arriving at a suitable lens design. 
     The use of a pixelized panel to display data leads to stringent requirements regarding the correction of distortion. This is so because good image quality is required even at the extreme points of the field of view of the lens when viewing data. As will be evident, an undistorted image of a displayed number or letter is just as important at the edge of the field as it is at the center. Moreover, projection lenses are often used with offset panels, the lenses of FIGS. 1-4 being, for example, designed for such use. In such a case, the distortion at the viewing screen does not vary symmetrically about a horizontal line through the center of the screen but can increase monotonically from, for example, the bottom to the top of the screen. This effect makes even a small amount of distortion readily visible to the viewer. 
     The projection lenses described below achieve all of the above requirements and can be successfully used in producing relatively low cost projection lens systems capable of forming a high quality color image of a pixelized panel on a viewing screen. 
     DESCRIPTION OF THE PRIOR ART 
     Projection lenses for use with pixelized panels are described in various patents including Taylor, U.S. Pat. No. 4,189,211, Tanaka et al., U.S. Pat. No. 5,042,929, Yano et al., U.S. Pat. No. 5,179,473, Moskovich, U.S. Pat. No. 5,200,861, Moskovich, U.S. Pat. No. 5,218,480, Iizuka et al., U.S. Pat. No. 5,278,698, Betensky, U.S. Pat. No. 5,313,330, Yano, U.S. Pat. No. 5,331,462, Moskovich, U.S. Pat. No. 5,625,495, Moskovich, 5,841,587, EPO Patent Publication No. 0809407, and PCT Patent Publications Nos. WO97/41461 and WO98/34134. Discussions of LCD systems can be found in Gagnon et al., U.S. Pat. No. 4,425,028, Gagnon, U.S. Pat. No. 4,461,542, Ledebuhr, U.S. Pat. No. 4,826,311, and EPO Patent Publication No. 311,116. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, it is an object of the present invention to provide improved projection lenses for use with a pixelized panel which simultaneously have each of the six desired properties discussed above. This object is achieved by means of a projection lens which, in order from its image side to its object side (i.e., from its long conjugate side to its short conjugate side), comprises: 
     (A) a first lens unit having a weak power and comprising at least one aspheric surface; 
     (B) a second lens unit having a positive power and comprising a negative lens element composed of a high dispersion material and a positive lens element composed of a low dispersion material; 
     (C) a third lens unit having a negative power and comprising a positive meniscus lens element and a negative lens element; and 
     (D) an optional field lens which is nearer to the object than to the third lens unit. 
     Preferably, the projection lens consists of just the foregoing three lens units and optional field lens. Most preferably, the first lens unit consists of a single lens element and the second and third lens units each consists of two lens elements having the above specified powers. Even more preferably, the two lens elements of the second lens unit are in the order negative/positive, while those of the third lens unit are in the order positive/negative. 
     In further preferred embodiments, the projection lens satisfies at least some and preferably all of the following numerical limitations: 
     f 0 /|f 1 |&lt;0.6 (1) 
     BFL/f 0 &gt;0.3 (2) 
     D2 12 &lt;D 12  (3) 
     D2 12 &lt;D 23  (4) 
     D3 12 &lt;D 23  (5) 
      where: 
     (i) f 0  is the effective focal length of the combination of the first, second, and third lens units; 
     (ii) f 1  is the effective focal length of the first lens unit; 
     (iii) BFL is the back focal length of the combination of the first, second, and third lens units for an object located at infinity along the long conjugate side of the projection lens; 
     (iv) D 12  is the distance between the first and second lens units measured from the last surface of the first unit to the first surface of the second unit; 
     (v) D 23  is the distance between the second and third lens units measured from the last surface of the second unit to the first surface of the third unit; 
     (vi) D2 12  is the distance between the negative and positive lens elements of the second lens unit measured between the facing surfaces of those elements; and 
     (vii) D3 12  is the distance between the negative and positive lens elements of the third lens unit measured between the facing surfaces of those elements. 
     In still further preferred embodiments, f 0 |f 1 | is less than about 0.2, BFL/f 0 is greater than about 0.5, and D2 12  is less than both 0.5•D 12  and 0.5•D 23 . Even more preferably, D2 12  is less than both 0.3•D 12  and 0.3•D 23 . 
     In certain embodiments, the projection lenses of the invention are designed using the location of the output of the illumination system as a pseudo-aperture stop/entrance pupil of the projection lens (see Betensky, U.S. Pat. No. 5,313,330, the relevant portions of which are incorporated herein by reference). In this way, efficient coupling is achieved between the light output of the illumination system and the projection lens. The projection lenses of FIGS. 1-4 were designed in this way. 
     In accordance with these embodiments, the invention provides a projection lens system which forms an image of an object and comprises: 
     (a) an illumination system comprising a light source and illumination optics which forms an image of the light source, said image being the output of the illumination system; 
     (b) a pixelized panel which comprises the object; and 
     (c) a projection lens of the type described above, said projection lens having an entrance pupil whose location substantially corresponds to the location of the output of the illumination system. 
     In connection with other aspects of the invention, the magnification of the projection lens is varied by changing the distance between the pixelized panel and the first, second, and third lens units while (a) holding constant the distance between the second and third lens units, and (b) varying the distance between the first lens unit and the second lens unit. The lenses of FIGS. 2-4 are of this type. 
     If desired, for a particular magnification, a limited amount of zooming can be performed by varying the distance between the second and third lens units, the lens of FIG. 1 being of this type. Although not illustrated in the prescriptions set forth below, this feature can also be employed in the lens systems of FIGS.  2 - 4 . 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a schematic side view of a projection lens constructed in accordance with the invention. FIG. 1B shows the projection lens of FIG. 1A in combination with a pixelized panel (PP). 
     FIGS. 2-4 are schematic side views of further projection lenses constructed in accordance with the invention. These lenses are combined with a pixelized panel in the same manner as illustrated in FIG. 1B for the lens of FIG.  1 A. 
     FIG. 5 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 
     The projection lenses of the present invention have the general form of a corrector unit (unit  1 ) on the long conjugate side of a telephoto lens (units  2  and  3 ). 
     The corrector unit has a weak power, i.e., its power is less than 60%, and preferably less than 20%, of the combined power of first, second, and third lens units. The unit has at least one aspheric surface which contributes to the correction of the system&#39;s distortion which, as discussed above, needs to be highly corrected for lens systems used with pixelized panels. The distortion correction is generally better than about one percent at the image, and preferably better than about 0.5 percent. The aspheric surface(s) also contribute to the correction of spherical aberration, astigmatism, and coma. 
     In addition to correcting aberrations, the first lens unit also plays an important role in focusing of the lens system. In particular, the first lens unit is moved relative to the pixelized panel at a different rate than the second and third lens units to vary the magnification of the system while maintaining a high image quality. The first lens unit can thus be viewed as a front, focusing, aspherical corrector. 
     The second and third lens units have the form of a telephoto lens. Thus, the second lens unit has a positive power, the third lens unit has a negative power, and the two units are relatively widely spaced apart. The magnitude of the power of the second lens unit is greater than that of the third lens unit and both are substantially greater than the magnitude of the power of the first lens unit. 
     The output of the illumination system is generally located between the second and third lens units and thus these units preferably include only glass elements which can withstand the heat generated in the vicinity of that output. In particular, by using glass in these units and plastic in the front unit, a lens system whose optical properties are substantially insensitive to temperature variations is achieved. 
     As indicated above and discussed in more detail below, relative movement between the second and third units can be used to provide the lens with at least some zoom capabilities. 
     Color correction for the projection lens is provided by the second lens unit which comprises a negative lens element composed of a high dispersion material and a positive lens element composed of a low dispersion material. As discussed above, these elements are preferably composed of glass, although plastic materials can be used if desired. 
     In general terms, a high dispersion material is a material having a dispersion like flint glass and a low dispersion material is a material having a dispersion like crown glass. More particularly, high dispersion materials are those having V-values ranging from 20 to 50 for an index of refraction in the range from 1.85 to 1.5, respectively, and low dispersion materials are those having V-values ranging from 35 to 75 for the same range of indices of refraction. 
     For plastic lens elements, the low and high dispersion materials of choice are acrylic and styrene, respectively. Other plastics can, of course, be used if desired. For example, in place of styrene, polycarbonates and copolymers of polystyrene and acrylic (e.g., NAS) having flint-like dispersions can be used. See  The Handbook of Plastic Optics , U.S. Precision Lens, Inc., Cincinnati, Ohio, 1983, pages 17-29. 
     Since the negative lens element and the positive lens element of the second lens unit have a combined power which is positive, the V-value of the high dispersion material of the negative lens element needs to be smaller than the V-value of low dispersion material of the positive lens element to achieve the desired color correction. 
     FIGS. 1 to  4  illustrate various projection lenses constructed in accordance with the invention. Corresponding prescriptions and optical properties appear in Tables 1 to 4, respectively. 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 plastic elements. 
     The aspheric coefficients set forth in the tables are for use in the following equation:        z   =         cy   2       1   +       [     1   -       (     1   +   k     )          c   2          y   2         ]       1   /   2           +     Dy   4     +     Ey   6     +     Fy   8     +     Gy   10     +     Hy   12     +     Iy   14                              
     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, which is zero except where indicated in the prescriptions of Tables 1-4. 
     The abbreviations used in the tables are as follows: 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 EFL 
                 effective focal length 
               
               
                   
                 FVD 
                 front vertex distance 
               
               
                   
                 f/ 
                 f-number 
               
               
                   
                 ENP 
                 entrance pupil as seen from the long conjugate 
               
               
                   
                 EXP 
                 exit pupil as seen from the long conjugate 
               
               
                   
                 BRL 
                 barrel length 
               
               
                   
                 OBJ HT 
                 object height 
               
               
                   
                 MAG 
                 magnification 
               
               
                   
                 STOP 
                 location of aperture stop 
               
               
                   
                 IMD 
                 image distance 
               
               
                   
                 OBD 
                 object distance 
               
               
                   
                 OVL 
                 overall length. 
               
               
                   
                   
               
             
          
         
       
     
     The designation “a” 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; and the designation “c” indicates a surface for which k in the above equations is not zero. 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 pixelized panel will be on the right, and light will travel from right to left. In particular, the references in the tables to objects and images are reversed from that used in the rest of the specification and in the claims. 
     The pixelized panel is shown by the designation “PP” in FIG.  1 B. The panel for which the lenses were designed, specifically, an LCD panel, had an effective diagonal of 218 millimeters when the offset of the panel from the lens system&#39;s optical axis is included. 
     In all of the tables, the first lens unit (U 1 ) comprises surfaces 1-2, and the second lens unit (U 2 ) comprises surfaces 3-6. In Tables 1-3, the third lens unit (U 3 ) comprises surfaces 7-10, while in Table 4, it comprises surfaces 7-11, surface 9 being an optional vignetting surface. 
     As discussed above, the projection lenses of FIGS. 1-4 were designed using the pseudo-aperture stop/entrance pupil technique of Betensky, U.S. Pat. No. 5,313,330. In accordance with this approach, the illumination system is used to define the entrance pupil for the projection lens, with the entrance pupil being located at a constant position relative to the pixelized panel for all lens focal lengths and conjugates. The location of this pupil is determined by the substantially parallel light (substantially telecentric light) which passes through the pixelized panel from the illumination system. 
     The surface labeled “aperture stop” in Tables 1-4 constitutes the pseudo-aperture stop of the above Betensky patent. Its location corresponds to the location of the output of the illumination system. As can be seen in the subtables labeled “Variable Spaces,” the distance from the pseudo-aperture stop to the pixelized panel is essentially constant for all magnifications of the projection lens systems of FIGS. 1-4 (see the column labeled “Image Distance”). For the magnifications shown, the variable space which defines the location of the aperture stop relative to the back surface of the projection lens is negative for each of Tables 1-4 corresponding to the illumination output being located within the space defined by the lens&#39; front and back lens surfaces. It should be noted that although preferred, the pseudo-aperture stop approach does not have to be used in the design of the lenses of the invention. Rather, the lenses can be designed using a conventional aperture stop. 
     As also discussed above, the projection lenses of FIGS. 2-4 can be focused by changing the distance between the pixelized panel and the first, second, and third lens units while (a) holding constant the distance between the second and third lens units, and (b) varying the distance between the first lens unit and the second lens unit. As shown in the prescriptions for these lenses, the amount of movement of the first lens unit relative to the second lens unit is small compared to the overall movement of the lens system relative to the pixelized panel. 
     The projection lens of Example 1 has both focusing and zooming capabilities, the zooming capability being achieved by varying the spacing between the second and third units. The inclusion of a zooming capability allows for fine tuning of the image to, for example, fully fill a viewing screen. 
     Conventional mechanisms known in the art are used, to move the lens and its component parts during focusing and/or zooming. 
     Although focusing and zooming both involve magnification changes, the magnification changes are achieved in fundamentally different ways. Thus, during focusing, the focal length of the lens remains substantially constant as the image and object conjugates change, and the magnification change is a result of the change in the ratio of those conjugates. During zooming, on the other hand, the focal length changes while the image and object conjugates remain constant, and the magnification change is a result of the change in the focal length. 
     Positions 1-5 in Table 1 illustrate this difference with positions 1, 2, and 3 illustrate focusing of the lens, while positions 3, 4, and 5 illustrate zooming. It should be noted that the lens of this example includes means for accommodating for changes in the focus of the lens resulting from zooming. In particular, Table 1 shows some changes in conjugates during zooming which achieve these focus corrections. 
     The lens of Table 1 has a focus range (F) of 0.09, where the focus range is given by: 
     
       
         F=max|h O /h I |−min|h O /h I |, 
       
     
     where ho is the object height, h I  is the magnified image height, and max |h O /h I | and min |h O /h I | are the maximum and minimum magnitudes, respectively, of the image-to-object magnification (minification) which the projection lens can achieve while maintaining a desired level of image quality. 
     The lens also has a zoom range (Z) of 0.12, where the zoom range is given by: 
     
       
         Z=2*(max|h I |−min|h I |)/(max|h I |+min|h I |), 
       
     
     where max |h I | and min |h I | are the maximum and minimum magnitudes, respectively, of the image height as a result of zooming about a |h O /h I | ratio in the focus range. 
     As is well known in the art, any lens which is capable of zooming can be “pushed” beyond its intended zoom range. Such “pushing”, of course, leads to a degradation in the performance of the lens. The degradation, however, is generally not precipitous and generally does not affect all performance parameters at the same rate. Accordingly, as used herein, the zoom range is that range for which the image quality does not fall below a specified criterion. In the case of the lens of Table 1, the criterion used for the zoom range was an MTF exceeding 65% at 5.6 cycles/mm through 85% of the field of the lens. This criterion, as opposed to, for example, distortion or lateral color, was used for this lens because the field of view for the lens is narrow. 
     Tables 5 and 6 summarize various properties of the lens systems of the invention. The BFL values are calculated for an object at infinity along the long conjugate of the system. As shown in Table 6, numerical limitations (1) and (2) are satisfied by the lens systems of FIGS. 1-4. 
     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 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                   
                 1634.3740 
                 20.00000 
                 ACRYLIC 
                 142.49 
               
               
                 2 
                 ac 
                 1106.5900 
                 Space 1 
                   
                 140.38 
               
               
                 3 
                   
                 6000.0001 
                 12.00000 
                 FD14 
                 151.86 
               
               
                 4 
                   
                  301.7851 
                 11.37822 
                   
                 153.30 
               
               
                 5 
                   
                 322.8628 
                 33.60000 
                 BACD18 
                 159.78 
               
               
                 6 
                   
                 −195.1980 
                 Space 2 
                   
                 160.53 
               
               
                 7 
                   
                 −263.7858 
                 13.00000 
                 BACD18 
                 128.67 
               
               
                 8 
                   
                 −194.8775 
                 54.52309 
                   
                 130.32 
               
               
                 9 
                   
                 −159.2364 
                  9.00000 
                 FC5 
                 120.74 
               
               
                 10 
                   
                 3900.0001 
                 Space 3 
                   
                 123.95 
               
             
          
           
               
                 11 
                 Aperture stop Image distance 
                 112.87 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
               
                 Conics 
               
             
          
           
               
                 Surface 
                   
                   
               
               
                 Number 
                 Constant 
               
               
                   
               
               
                 2 
                 −5.0000E−01 
               
               
                   
               
             
          
           
               
                 Even Polynomial Aspheres 
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 2 
                 5.4286E−08 
                 2.0878E−12 
                 −6.0772E−16 
                 2.8570E−19 
                 −4.7940E−23 
                 2.9585E−27 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
               
             
          
           
               
                 Pos. 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
               
               
                 No. 
                 T(2) 
                 T(6) 
                 T(10) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 93.600 
                 90.628 
                 −160.000 
                 0.375 
                 503.973 
               
               
                 2 
                 95.100 
                 90.628 
                 −108.143 
                 −0.112 
                 503.989 
               
               
                 3 
                 94.530 
                 90.628 
                 −131.193 
                 0.104 
                 503.986 
               
               
                 4 
                 94.530 
                 74.500 
                 −74.620 
                 1.520 
                 504.004 
               
               
                 5 
                 94.530 
                 103.890 
                 −172.691 
                 −0.762 
                 503.963 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
               
               
                 OBJ. HT: −5100.0   f/ 4.50   MAG: −0.0200 
               
               
                 STOP: 0.00 after surface 11.   DIA: 112.54 
               
             
          
           
               
                 EFL: 
                 582.058 
                 FVD: 
                 681.703 
                 ENP: 
                 73.2134 
               
               
                 IMD: 
                 503.973 
                 BRL: 
                 177.730 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −29718.4 
                 OVL: 
                 30400.1 
               
             
          
           
               
                 POS 2 System First Order Properties 
               
               
                 OBJ. HT: −940.00   f/ 4.66   MAG: −0.1100 
               
               
                 STOP: 0.00 after surface 11.   DIA: 108.77 
               
             
          
           
               
                 EFL: 
                 581.922 
                 FVD: 
                 735.076 
                 ENP: 
                 155.811 
               
               
                 IMD: 
                 503.989 
                 BRL: 
                 231.087 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −5903.86 
                 OVL: 
                 6638.93 
               
             
          
           
               
                 POS 3 System First Order Properties 
               
               
                 OBJ. HT: −1456.0   f/ 4.50   MAG: −0.0700 
               
               
                 STOP: 0.00 after surface 11.   DIA: 112.64 
               
             
          
           
               
                 EFL: 
                 581.974 
                 FVD: 
                 711.452 
                 ENP: 
                 116.957 
               
               
                 IMD: 
                 503.986 
                 BRL: 
                 207.467 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8928.25 
                 OVL: 
                 9639.70 
               
             
          
           
               
                 POS 4 System First Order Properties 
               
               
                 OBJ. HT: −1366.0   f/ 5.00   MAG: −0.0745 
               
               
                 STOP: 0.00 after surface 11.   DIA: 100.94 
               
             
          
           
               
                 EFL: 
                 618.995 
                 FVD: 
                 751.916 
                 ENP: 
                 63.4684 
               
               
                 IMD: 
                 504.005 
                 BRL: 
                 247.912 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8950.51 
                 OVL: 
                 9702.43 
               
             
          
           
               
                 POS 5 System First Order Properties 
               
               
                 OBJ. HT: −1540.0   f/ 4.50   MAG: −0.0663 
               
               
                 STOP: 0.00 after surface 11.   DIA: 112.86 
               
             
          
           
               
                 EFL: 
                 554.690 
                 FVD: 
                 683.193 
                 ENP: 
                 63.4684 
               
               
                 IMD: 
                 503.963 
                 BRL: 
                 179.231 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8960.51 
                 OVL: 
                 9643.71 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
               
             
          
           
               
                 Element 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.14229E−03 
                 −7027.9 
               
               
                 2 
                 3 
                 4 
                 −0.24165E−02 
                 −413.83 
               
               
                 3 
                 5 
                 6 
                  0.51380E−02 
                 194.63 
               
               
                 4 
                 7 
                 8 
                  0.92299E−03 
                 1083.4 
               
               
                 5 
                 9 
                 10  
                 −0.31995E−02 
                 −312.55 
               
               
                   
               
             
          
           
               
                 First Order Properties of Groups 
               
             
          
           
               
                 Group 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.14229E−03 
                 −7027.9 
               
               
                 2 
                 3 
                 6 
                  0.30208E−02 
                 331.04 
               
               
                 3 
                 7 
                 10  
                 −0.21764E−02 
                 −459.47 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
               
             
          
           
               
                 Positon 
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.17180E−02 
                 582.06 
               
               
                 2 
                 0.17184E−02 
                 581.92 
               
               
                 3 
                 0.17183E−02 
                 581.97 
               
               
                 4 
                 0.16155E−02 
                 618.99 
               
               
                 5 
                 0.18028E−02 
                 554.70 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
             
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                   
                 −185148.7093 
                 14.97000 
                 ACRYLIC 
                 122.09 
               
               
                 2 
                 ac 
                 550.2681 
                 Space 1 
                   
                 122.36 
               
               
                 3 
                   
                 483.8345 
                 11.00000 
                 F8 
                 140.74 
               
               
                 4 
                   
                 192.2149 
                  4.73853 
                   
                 141.01 
               
               
                 5 
                   
                 207.6194 
                 33.60000 
                 FCD1 
                 143.22 
               
               
                 6 
                   
                 −184.7353 
                 Space 2 
                   
                 143.78 
               
               
                 7 
                   
                 −274.0555 
                 12.00000 
                 BACD5 
                 120.65 
               
               
                 8 
                   
                 −160.3742 
                 57.42358 
                   
                 121.40 
               
               
                 9 
                   
                 −135.8544 
                  8.00000 
                 FC5 
                 108.72 
               
               
                 10 
                   
                 3900.0001 
                 Space 3 
                   
                 111.90 
               
             
          
           
               
                 11 
                 Aperture stop Image distance 
                  98.01 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
               
                 Conics 
               
             
          
           
               
                 Surface 
                   
                   
               
               
                 Number 
                 Constant 
               
               
                   
               
               
                 2 
                 −5.0000E−01 
               
               
                   
               
             
          
           
               
                 Even Polynomial Aspheres 
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 2 
                 6.1378E−08 
                 2.4418E−12 
                 −5.5060E−16 
                 3.2694E−19 
                 −7.2524E−23 
                 5.7428E−27 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
               
             
          
           
               
                 Pos. 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
               
               
                 No. 
                 T(2) 
                 T(6) 
                 T(10) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 89.735 
                 108.498 
                 −160.000 
                  0.104 
                 503.021 
               
               
                 2 
                 90.505 
                 108.498 
                 −108.335 
                 −0.415 
                 503.990 
               
               
                 3 
                 90.347 
                 108.498 
                 −131.356 
                 −0.206 
                 503.994 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
               
               
                 OBJ. HT: −5100.0   f/ 5.17   MAG: −0.0200 
               
               
                 STOP: 0.00 after surface 11.   DIA: 97.951 
               
             
          
           
               
                 EFL: 
                 582.607 
                 FVD: 
                 683.986 
                 ENP: 
                 62.9351 
               
               
                 IMD: 
                 504.021 
                 BRL: 
                 179.965 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −29756.9 
                 OVL: 
                 30440.9 
               
             
          
           
               
                 POS 2 System First Order Properties 
               
               
                 OBJ. HT: −940.00   f/ 5.33   MAG: −0.1100 
               
               
                 STOP: 0.00 after surface 11.   DIA: 95.056 
               
             
          
           
               
                 EFL: 
                 581.102 
                 FVD: 
                 736.390 
                 ENP: 
                 144.385 
               
               
                 IMD: 
                 503.990 
                 BRL: 
                 232.400 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −5915.35 
                 OVL: 
                 6651.74 
               
             
          
           
               
                 POS 3 System First Order Properties 
               
               
                 OBJ. HT: −1460.0   f/ 5.17   MAG: −0.0700 
               
               
                 STOP: 0.00 after surface 11.   DIA: 98.006 
               
             
          
           
               
                 EFL: 
                 582.973 
                 FVD: 
                 713.215 
                 ENP: 
                 106.047 
               
               
                 IMD: 
                 503.994 
                 BRL: 
                 209.221 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8940.83 
                 OVL: 
                 9654.04 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
               
             
          
           
               
                 Element 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.90003E−03 
                 −1111.1 
               
               
                 2 
                 3 
                 4 
                 −0.18521E−02 
                 −539.93 
               
               
                 3 
                 5 
                 6 
                  0.49537E−02 
                 201.87 
               
               
                 4 
                 7 
                 8 
                  0.15897E−02 
                 629.04 
               
               
                 5 
                 9 
                 10  
                 −0.37283E−02 
                 −268.22 
               
               
                   
               
             
          
           
               
                 First Order Properties of Groups 
               
             
          
           
               
                 Group 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.90003E−03 
                 −1111.1 
               
               
                 2 
                 3 
                 6 
                  0.32150E−02 
                 311.05 
               
               
                 3 
                 7 
                 10  
                 −0.18578E−02 
                 −538.26 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
               
             
          
           
               
                 Positon 
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.17164E−02 
                 582.61 
               
               
                 2 
                 0.17183E−02 
                 581.97 
               
               
                 3 
                 0.17179E−02 
                 582.10 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
             
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                   
                 1252.8200 
                 14.97000 
                 ACRYLIC 
                 122.30 
               
               
                 2 
                 ac 
                 787.0785 
                 Space 1 
                   
                 121.63 
               
               
                 3 
                   
                 1406.0749 
                 11.00000 
                 FD8 
                 131.79 
               
               
                 4 
                   
                 224.1674 
                  9.24000 
                   
                 132.24 
               
               
                 5 
                   
                 259.5466 
                 28.50000 
                 BACD5 
                 136.46 
               
               
                 6 
                   
                 −193.9218 
                 Space 2 
                   
                 137.10 
               
               
                 7 
                   
                 −239.8299 
                 12.00000 
                 BACD18 
                 116.94 
               
               
                 8 
                   
                 −157.8392 
                 51.18000 
                   
                 118.09 
               
               
                 9 
                   
                 −143.1680 
                  8.00000 
                 FC5 
                 110.00 
               
               
                 10 
                   
                 3900.0001 
                 Space 3 
                   
                 113.00 
               
             
          
           
               
                 11 
                 Aperture stop Image distance 
                  97.96 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
               
                 Conics 
               
             
          
           
               
                 Surface 
                   
                   
               
               
                 Number 
                 Constant 
               
               
                   
               
               
                 2 
                 −5.0000E−01 
               
               
                   
               
             
          
           
               
                 Even Polynomial Aspheres 
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 2 
                 5.2242E−08 
                 2.1791E−12 
                 −7.1572E−16 
                 3.7111E−19 
                 −7.7946E−23 
                 6.0410E−27 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
               
             
          
           
               
                 Pos. 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
               
               
                 No. 
                 T(2) 
                 T(6) 
                 T(10) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 97.240 
                 101.191 
                 −160.030 
                  0.062 
                 503.997 
               
               
                 2 
                 98.383 
                 101.191 
                 −107.978 
                 −0.243 
                 503.995 
               
               
                 3 
                 98.079 
                 101.191 
                 −131.096 
                 −0.089 
                 503.996 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
               
               
                 OBJ. HT: −5100.0   f/ 5.17   MAG: −0.0200 
               
               
                 STOP: 0.00 after surface 11.   DIA: 97.925 
               
             
          
           
               
                 EFL: 
                 582.174 
                 FVD: 
                 677.288 
                 ENP: 
                 71.6279 
               
               
                 IMD: 
                 503.997 
                 BRL: 
                 173.291 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −29725.5 
                 OVL: 
                 30402.8 
               
             
          
           
               
                 POS 2 System First Order Properties 
               
               
                 OBJ. HT: −940.00   f/ 5.33   MAG: −0.1100 
               
               
                 STOP: 0.00 after surface 11.   DIA: 95.014 
               
             
          
           
               
                 EFL: 
                 581.997 
                 FVD: 
                 730.481 
                 ENP: 
                 154.107 
               
               
                 IMD: 
                 503.995 
                 BRL: 
                 226.486 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −5906.22 
                 OVL: 
                 6636.70 
               
             
          
           
               
                 POS 3 System First Order Properties 
               
               
                 OBJ. HT: −1460.0   f/ 5.17   MAG: −0.0700 
               
               
                 STOP: 0.00 after surface 11.   DIA: 97.964 
               
             
          
           
               
                 EFL: 
                 582.044 
                 FVD: 
                 707.060 
                 ENP: 
                 115.424 
               
               
                 IMD: 
                 503.996 
                 BRL: 
                 203.064 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8930.65 
                 OVL: 
                 9637.71 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
               
             
          
           
               
                 Element 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.23074E−03 
                 −4333.8 
               
               
                 2 
                 3 
                 4 
                 −0.25930E−02 
                 −385.66 
               
               
                 3 
                 5 
                 6 
                  0.52040E−02 
                 192.16 
               
               
                 4 
                 7 
                 8 
                  0.14684E−02 
                 681.01 
               
               
                 6 
                 9 
                 10  
                 −0.35443E−02 
                 −282.15 
               
               
                   
               
             
          
           
               
                 First Order Properties of Groups 
               
             
          
           
               
                 Group 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.23074E−03 
                 −4333.8 
               
               
                 2 
                 3 
                 6 
                  0.28606E−02 
                 349.57 
               
               
                 3 
                 7 
                 10  
                 −0.18778E−02 
                 −532.54 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
               
             
          
           
               
                 Position 
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.17177E−02 
                 582.17 
               
               
                 2 
                 0.17182E−02 
                 582.00 
               
               
                 3 
                 0.17181E−02 
                 582.04 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
             
               
               
               
             
               
             
               
               
               
             
               
             
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                 ac 
                 152.0189 
                 23.90000 
                 ACRYLIC 
                 155.65 
               
               
                 2 
                 a 
                 144.8473 
                 Space 1 
                   
                 145.34 
               
               
                 3 
                   
                 −3900.0001 
                 12.00000 
                 FD14 
                 142.29 
               
               
                 4 
                   
                 323.5706 
                 17.50377 
                   
                 143.92 
               
               
                 5 
                   
                 374.5398 
                 31.00000 
                 BACD18 
                 152.91 
               
               
                 6 
                   
                 −184.9560 
                 Space 2 
                   
                 153.78 
               
               
                 7 
                   
                 −266.9933 
                 12.50000 
                 BACD18 
                 120.79 
               
               
                 8 
                   
                 −198.9568 
                 12.51129 
                   
                 121.83 
               
               
                 9 
                   
                 ∞ 
                 30.00000 
                   
                 116.40 
               
               
                 10 
                   
                 −184.7593 
                 Space 3 
                 FC5 
                 113.86 
               
               
                 11 
                   
                 3900.0001 
                 Space 3 
                   
                 116.57 
               
             
          
           
               
                 12 
                 Aperture stop Image distance 
                 112.99 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
               
                 Conics 
               
             
          
           
               
                 Surface 
                   
                   
               
               
                 Number 
                 Constant 
               
               
                   
               
               
                 2 
                 −5.0000E−01 
               
               
                   
               
             
          
           
               
                 Even Polynomial Aspheres 
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 1 
                 9.3495E−09 
                 −7.0233E−12 
                 −6.5200E−16 
                  5.8269E−21 
                 −1.2053E−24 
                  3.0711E−28 
               
               
                 2 
                 4.8705E−08 
                 −8.3045E−12 
                 −7.3948E−16 
                 −7.2417E−20 
                  1.2320E−23 
                 −9.8789E−29 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
               
             
          
           
               
                 Pos. 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
               
               
                 No. 
                 T(2) 
                 T(6) 
                 T(10) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 78.210 
                 98.959 
                 −160.000 
                 −0.177 
                 503.994 
               
               
                 2 
                 79.754 
                 98.959 
                 −108.039 
                 −0.729 
                 503.862 
               
               
                 3 
                 79.420 
                 98.959 
                 −131.082 
                 −0.344 
                 504.010 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
               
               
                 OBJ. HT: −5100.0   f/ 4.50   MAG: −0.0200 
               
               
                 STOP: 0.00 after surface 12.   DIA: 112.66 
               
             
          
           
               
                 EFL: 
                 582.000 
                 FVD: 
                 669.578 
                 ENP: 
                 86.5199 
               
               
                 IMD: 
                 503.994 
                 BRL: 
                 165.584 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −29701.2 
                 OVL: 
                 30370.8 
               
             
          
           
               
                 POS 2 System First Order Properties 
               
               
                 OBJ. HT: −940.00   f/ 4.60   MAG: −0.1100 
               
               
                 STOP: 0.00 after surface 12.   DIA: 110.29 
               
             
          
           
               
                 EFL: 
                 582.015 
                 FVD: 
                 722.951 
                 ENP: 
                 169.357 
               
               
                 IMD: 
                 503.862 
                 BRL: 
                 219.089 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −5890.56 
                 OVL: 
                 6613.51 
               
             
          
           
               
                 POS 3 System First Order Properties 
               
               
                 OBJ. HT: −1460.0   f/ 4.50   MAG: −0.0700 
               
               
                 STOP: 0.00 after surface 12.   DIA: 112.73 
               
             
          
           
               
                 EFL: 
                 582.012 
                 FVD: 
                 699.722 
                 ENP: 
                 130.767 
               
               
                 IMD: 
                 504.010 
                 BRL: 
                 195.711 
                 EXP: 
                 0.000000 
               
               
                 OBD: 
                 −8914.33 
                 OVL: 
                 9614.05 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
               
             
          
           
               
                 Element 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                  0.16340E−04 
                 61199. 
               
               
                 2 
                 3 
                 4 
                 −0.25756E−02 
                 −388.26 
               
               
                 3 
                 5 
                 6 
                  0.50673E−02 
                 197.34 
               
               
                 4 
                 7 
                 8 
                  0.88032E−03 
                 1135.9 
               
               
                 5 
                 10  
                 11  
                 −0.27749E−02 
                 −360.38 
               
               
                   
               
             
          
           
               
                 First Order Properties of Groups 
               
             
          
           
               
                 Group 
                   
                   
                   
                   
               
               
                 Number 
                 Surface Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                  0.16340E−04 
                 61199. 
               
               
                 2 
                 3 
                 6 
                  0.28956E−02 
                 345.35 
               
               
                 3 
                 7 
                 11  
                 −0.18408E−02 
                 −543.24 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
               
             
          
           
               
                 Position 
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.17182E−02 
                 582.00 
               
               
                 2 
                 0.17182E−02 
                 582.01 
               
               
                 3 
                 0.17182E−02 
                 582.01 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Example 
                 f 0   
                 f 1   
                 f 2   
                 f 3   
                 BFL 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 1 
                 582.1 
                 −7027.9 
                 331.04 
                 −459.47 
                 332.4 
               
               
                   
                 2 
                 582.6 
                 −1111.1 
                 311.05 
                 −538.26 
                 332.5 
               
               
                   
                 3 
                 582.2 
                 −4333.8 
                 349.57 
                 −532.54 
                 332.4 
               
               
                   
                 4 
                 582.0 
                 61199.0 
                 345.35 
                 −543.24 
                 332.6 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Example 
                 f 0 /|f 1 | 
                 BFL/f 0   
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 0.083 
                 0.57 
               
               
                 2 
                 0.52 
                 0.57 
               
               
                 3 
                 0.13 
                 0.57 
               
               
                 4 
                 0.01 
                 0.57