Abstract:
A lens system is provided. The lens system includes a first lens system moveable between a first position removed from an optical axis and a second position on the optical axis. The first lens system includes a first lens element, an aperture stop, and a second lens element positioned in order from an object side to an image side of the lens system. The first lens system has a first focal length. A second lens system is moveable between a first position on the optical axis and a second position removed from the optical axis. The second lens system has a second focal length with the second focal length being greater than the first focal length such that a magnification ratio change results from interchanging the first lens system and the second system on the optical axis.

Description:
FIELD OF THE INVENTION 
   This invention relates generally to lens systems, and in particular to variable focal length lens systems. 
   BACKGROUND OF THE INVENTION 
   Variable focal length lens systems are known. For example, U.S. Pat. No. 6,873,473 B2, issued Mar. 29, 2005, to Lewis et al., discloses a two position variable focal length lens. The variable focal length lens includes a common lens element moveably positioned on an optical axis; a wide angle lens element moveable between a first location removed from the optical axis and a first position on the optical axis on an image side of the common lens element; and a telephoto lens element moveable between a second location removed from the optical axis and a second position on the optical axis on the image side of the common lens element. A magnification ratio change occurs by moving the common lens element along the optical axis and switching between the wide angle lens element located at the first position on the optical axis and the telephoto lens element located at the second position on the optical axis. 
   U.S. Pat. No. 6,449,430 B1, issued Sep. 10, 2002, to Tasaka et al., discloses a lens-fitted photo film unit having a rotatable lens holder that supports first and second taking lenses arranged perpendicularly to a photographic optical axis. The first and second taking lenses have different focal lengths. An externally operable button rotates the lens holder to selectively position the first and second taking lenses on the photographic optical axis. 
   The first lens, a wide-angle taking lens, is located on an object side of a first aperture, and consists of two lens elements. The second lens, a telephoto taking lens, is located on an object side of a second aperture, and consists of a single lens element. When compared to the wide-angle taking lens, the telephoto taking lens is positioned offset toward the object side along the photographic optical axis. The second aperture is also positioned offset toward the object side along the photographic optical axis when compared to the first aperture. 
   SUMMARY OF THE INVENTION 
   According to a feature of the present invention, a lens system includes a first lens system moveable between a first position removed from an optical axis and a second position on the optical axis. The first lens system includes a first lens element, an aperture stop, and a second lens element positioned in order from an object side to an image side of the lens system. The first lens system has a first focal length. A second lens system is moveable between a first position on the optical axis and a second position removed from the optical axis. The second lens system has a second focal length with the second focal length being greater than the first focal length such that a magnification ratio change results from interchanging the first lens system and the second system on the optical axis. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the detailed description of the preferred embodiments of the invention presented below, reference is made to the accompanying drawings, in which: 
       FIGS. 1A and 1B  are cross sectional views of a first example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 1C and 1D  are aberration diagrams of the example embodiment shown in  FIGS. 1A and 1B , respectively; 
       FIGS. 1E and 1F  are through focus MTF plots for the example embodiment shown in  FIGS. 1A and 1B , respectively; 
       FIGS. 2A and 2B  are cross sectional views of a second example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 2C and 2D  are aberration diagrams of the example embodiment shown in  FIGS. 2A and 2B , respectively; 
       FIGS. 2E and 2F  are through focus MTF plots for the example embodiment shown in  FIGS. 2A and 2B , respectively; 
       FIGS. 3A and 3B  are cross sectional views of a third example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 3C and 3D  are aberration diagrams of the example embodiment shown in  FIGS. 3A and 3B , respectively; 
       FIGS. 3E and 3F  are through focus MTF plots for the example embodiment shown in  FIGS. 3A and 3B , respectively; 
       FIGS. 4A and 4B  are cross sectional views of a fourth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 4C and 4D  are aberration diagrams of the example embodiment shown in  FIGS. 4A and 4B , respectively; 
       FIGS. 4E and 4F  are through focus MTF plots for the example embodiment shown in  FIGS. 4A and 4B , respectively; 
       FIGS. 5A and 5B  are cross sectional views of a fifth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 5C and 5D  are aberration diagrams of the example embodiment shown in  FIGS. 5A and 5B , respectively; 
       FIGS. 5E and 5F  are through focus MTF plots for the example embodiment shown in  FIGS. 5A and 5B , respectively; 
       FIGS. 6A and 6B  are cross sectional views of a sixth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 6C and 6D  are aberration diagrams of the example embodiment shown in  FIGS. 6A and 6B , respectively; 
       FIGS. 6E and 6F  are through focus MTF plots for the example embodiment shown in  FIGS. 6A and 6B , respectively; 
       FIGS. 7A and 7B  are cross sectional views of a seventh example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 7C and 7D  are aberration diagrams of the example embodiment shown in  FIGS. 7A and 7B , respectively; 
       FIGS. 7E and 7F  are through focus MTF plots for the example embodiment shown in  FIGS. 7A and 7B , respectively; 
       FIGS. 8A and 8B  are cross sectional views of an eighth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 8C and 8D  are aberration diagrams of the example embodiment shown in  FIGS. 8A and 8B , respectively; 
       FIGS. 8E and 8F  are through focus MTF plots for the example embodiment shown in  FIGS. 8A and 8B , respectively; 
       FIGS. 9A and 9B  are cross sectional views of a ninth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively; 
       FIGS. 9C and 9D  are aberration diagrams of the example embodiment shown in  FIGS. 9A and 9B , respectively; 
       FIGS. 9E and 9F  are through focus MTF plots for the example embodiment shown in  FIGS. 9A and 9B , respectively; and 
       FIGS. 10A and 10B  are schematic cross sectional views of an embodiment made in accordance with the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present description will be directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance with the present invention. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art. 
   Referring to  FIGS. 10A and 10B , a lens system  10  having a plurality of interchangeable component lens systems  20 ,  30  is shown. Component lens systems  20 ,  30  are designed to be moved on and off of an optical axis  40  using a switching mechanism (not shown). The switching mechanism can be any known mechanism suitable for this purpose, see, for example, commonly assigned U.S. patent application Ser. No. 10/949,616, entitled “CAMERA ASSEMBLIES HAVING OVERLAPPING ROCKER AND LINK PROJECTIONS” filed, Sep. 24, 2004, in the name of DiRisio; commonly assigned U.S. patent application Ser. No. 10/949,596, entitled “CAMERA ASSEMBLY HAVING LENS TURRET AND INDEPENDENTLY MOVABLE ROCKER” field Sep. 24, 2004, in the name of DiRisio, et al.; etc. 
   Each of component lens systems  20 ,  30  (which can be referred to as a first lens system  20  and a second lens system  30 ) has design characteristics that affect an image produced on a cylindrically curved image plane  50 . For example, component lens systems  20 ,  30  can have different focal lengths which magnify (zoom in, zoom out) the image produce at image plane  50  differently depending on which component lens system is positioned in optical axis  40 . Component lens systems  20  and  30  each produce an acceptable image on image plane  50  independently of the other. As such, preferred implementations of component lens systems  20 ,  30  do not have to have a lens element(s) that is common to both lens systems  20 ,  30  in order to produce an acceptable image at image plane  50 . 
   Specific embodiments of component lens systems  20 ,  30  include at least one lens element and can include additional components such as aperture stops, baffles, spacers, etc., depending on the application contemplated. Additionally, lens system  10  can include more than two component lens systems  20 ,  30  depending on the application contemplated. 
   Example embodiments of lens system  10  will now be discussed with like elements having like reference signs with reference to  FIGS. 1A–9F . In  FIGS. 1A–9F , the object side of lens system  10  is viewed from the left hand side of the figure while the image side of lens system  10  is viewed from the right hand side of the figure and lens element surfaces are spherical unless otherwise noted. In Tables  1 A– 9 B, back focus (BF) and front focus (FF) values are shown for an object at infinity while best focus values are shown for the finite object distance design criteria associated with each lens system of each example embodiment. The image format is cylindrically curved with a radius of −90 mm in each example embodiment. 
   Referring to  FIGS. 1A and 1B , cross sectional views of a first example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  102  and a rear lens element  104  as viewed from an object side. Front lens element  102  is biconvex. Rear lens element  104  is meniscus and convex toward image plane  50 . Both lens elements  102  and  104  are made from acrylic plastic. An aperture stop  106  is located between lens elements  102  and  104  and a shutter  108  is located on an image side of lens element  104 . Rear lens element  104  includes an aspheric surface located on its object side surface. 
   Second lens system  30  includes a positive power meniscus lens element  110  convex toward an object side. Lens element  110  has spherical surfaces and is made of acrylic plastic. An aperture stop  112  is located on an image side of lens element  110 . A shutter  114  is located on an image side of aperture stop  112 . 
   Tables  1 A and  1 B provide additional design characteristics for the example embodiment shown in  FIGS. 1A and 1B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 1A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   13.95   83.3240   1.700   1.492   57.4       2   12.94   −69.1030   5.230           2.61   DIAPHRAGM   0.250       3   2.74   ASPHERE   2.857   1.492   57.4       4   4.78   −6.52570   1.820           6.79   SHUTTER                    
LENS LENGTH: 10.037
 
BF: 31.21
 
FF: 21.66
 
BEST FOCUS: 0.800
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       1 
                       - 
                       
                         ( 
                         
                           k 
                           + 
                           1 
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     C 
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
           
         
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 3: 
               C = 
               D = −0.5354778E−02 
               F = −0.3703106E−02 
             
             
                 
               −0.1250000 
               E = 0.6458337E−02 
               G = 0.7872486E−03 
             
             
                 
               k = 0 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = −8.000 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 1B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   9.96   9.26560   3.200   1.492   57.4       2   7.53   14.5545   3.771           2.88   DIAPHRAGM   3.750           6.79   SHUTTER                    
LENS LENGTH: 3.200
 
BF: 38.12
 
FF: 46.16
 
BEST FOCUS: −0.708
 
   Referring to  FIGS. 1C and 1D , lateral color diagrams of the example embodiment shown in  FIGS. 1A and 1B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 1E and 1F , through focus MTF performance plots for the example embodiment shown in  FIGS. 1A and 1B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 2A and 2B , cross sectional views of a second example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  202  and a rear lens element  204  as viewed from an object side. Front lens element  202  is biconvex. Rear lens element  204  is meniscus and convex toward image plane  50 . Both lens elements  202  and  204  are made from acrylic plastic. An aperture stop  206  is located between lens elements  202  and  204  and a shutter  208  is located on an image side of lens element  204 . Front lens element  202  includes an aspheric surface on its object side surface. Rear lens element  204  includes an aspheric surface located on its image side surface. 
   Second lens system  30  includes a positive power meniscus lens element  210  convex toward an object side. Lens element  210  has spherical surfaces and is made of acrylic plastic. An aperture stop  212  is located on an image side of lens element  210 . A shutter  214  is located on an image side of aperture stop  212 . 
   Tables  2 A and  2 B provide additional design characteristics for the example embodiment shown in  FIGS. 2A and 2B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                             TABLE 2A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V               1   8.24   ASPHERE   2.110   1.492   57.4       2   6.49   −64.9367   1.980           2.57   DIAPHRAGM   0.592       3   3.02   −7.11880   2.245   1.492   57.4       4   4.67   ASPHERE   1.820           6.79   SHUTTER                    
LENS LENGTH: 6.927
 
BF: 29.38
 
FF: 24.64
 
BEST FOCUS: 0.836
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
           
         
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 1: 
               C = 
               D = −0.19438227E−03 
               F = −0.10943439E−05 
             
             
                 
               0.031680454 
               E = 0.19146213E−04 
               G = 0.24513379E−07 
             
             
                 
               k = 0 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = 31.5652045 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 4: 
               C = −0.152938639 
               D = −0.10034969E−01 
               F = −0.18974151E−03 
             
             
                 
               k = −27.1224987 
               E = 0.16763751E−02 
               G = 0.93583407E−05 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = −6.53857003 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 2B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   9.56   8.35126   3.000   1.492   57.4       2   7.22   12.4770   3.513           2.78   DIAPHRAGM   4.002           6.79   SHUTTER                    
LENS LENGTH: 3.000
 
BF: 36.34
 
FF: 44.51
 
BEST FOCUS: −0.700
 
   Referring to  FIGS. 2C and 2D , lateral color diagrams of the example embodiment shown in  FIGS. 2A and 2B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 2E and 2F , through focus MTF performance plots for the example embodiment shown in  FIGS. 2A and 2B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 3A and 3B , cross sectional views of a third example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  302  and a rear lens element  304  as viewed from an object side. Front lens element  302  is biconvex. Rear lens element  304  is meniscus and convex toward image plane  50 . Both lens elements  302  and  304  are made from acrylic plastic. An aperture stop  306  is located between lens elements  302  and  304  and a shutter  308  is located on an image side of lens element  304 . 
   Second lens system  30  includes a positive power meniscus lens element  310  convex toward an object side. Lens element  310  has spherical surfaces and is made of acrylic plastic. An aperture stop  312  is located on an image side of lens element  310 . A shutter  314  is located on an image side of aperture stop  312 . 
   Tables  3 A and  3 B provide additional design characteristics for the example embodiment shown in  FIGS. 3A and 3B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 3A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.19   105.824   1.639   1.492   57.4       2   11.14   −46.1229   3.877           2.62   DIAPHRAGM   0.521       3   2.81   −8.00000   3.751   1.492   57.4       4   5.31   −6.86460   1.350           6.79   SHUTTER                    
LENS LENGTH: 9.788
 
BF: 31.92
 
FF: 21.43
 
BEST FOCUS: −0.519
 
                                                                       TABLE 3B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.56   9.28710   3.000   1.492   57.4       2   8.37   14.5761   4.480           2.89   DIAPHRAGM   4.000           6.79   SHUTTER                    
LENS LENGTH: 3.000
 
BF: 38.99
 
FF: 46.62
 
BEST FOCUS: −0.781
 
   Referring to  FIGS. 3C and 3D , lateral color diagrams of the example embodiment shown in  FIGS. 3A and 3B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 3E and 3F , through focus MTF performance plots for the example embodiment shown in  FIGS. 3A and 3B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 4A and 4B , cross sectional views of a fourth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  402  and a rear lens element  404  as viewed from an object side. Front lens element  402  is meniscus and convex toward image plane  50 . Rear lens element  404  is meniscus and convex toward image plane  50 . Both lens elements  402  and  404  are made from acrylic plastic. An aperture stop  406  is located between lens elements  402  and  404  and a shutter  408  is located on an image side of lens element  404 . Front lens element  402  includes an aspheric surface on its image side surface. 
   Second lens system  30  includes a positive power meniscus lens element  410  convex toward an object side. Lens element  410  has spherical surfaces and is made of acrylic plastic. An aperture stop  412  is located on an image side of lens element  410 . A shutter  414  is located on an image side of aperture stop  412 . 
   Tables  4 A and  4 B provide additional design characteristics for the example embodiment shown in  FIGS. 4A and 4B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 4A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.76   −232.718   1.629   1.492   57.4       2   11.79   ASPHERE   3.989           2.62   DIAPHRAGM   0.521       3   2.81   −8.00000   3.751   1.492   57.4       4   5.26   −6.86460   1.350           6.79   SHUTTER                    
LENS LENGTH: 9.890
 
BF: 32.15
 
FF: 21.20
 
BEST FOCUS: −0.756
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
           
         
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 2: 
               C = −0.0349157288 
               D = −0.22651633E−03 
               F = −0.39501434E−07 
             
             
                 
               k = −52.53574309 
               E = 0.45422977E−05 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = −28.6403874 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 4B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.37   9.28710   3.000   1.492   57.4       2   8.16   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.00
 
BF: 38.99
 
FF: 46.62
 
BEST FOCUS: −0.441
 
   Referring to  FIGS. 4C and 4D , lateral color diagrams of the example embodiment shown in  FIGS. 4A and 4B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 4E and 4F , through focus MTF performance plots for the example embodiment shown in  FIGS. 4A and 4B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 5A and 5B , cross sectional views of a fifth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  502  and a rear lens element  504  as viewed from an object side. Front lens element  502  is biconvex. Rear lens element  504  is meniscus and convex toward image plane  50 . Both lens elements  502  and  504  are made from acrylic plastic. An aperture stop  506  is located between lens elements  502  and  504  and a shutter  508  is located on an image side of lens element  504 . Front lens element  502  includes an aspheric surface on its object side surface. 
   Second lens system  30  includes a positive power meniscus lens element  510  convex toward an object side. Lens element  510  has spherical surfaces and is made of acrylic plastic. An aperture stop  512  is located on an image side of lens element  510 . A shutter  514  is located on an image side of aperture stop  512 . 
   Tables  5 A and  5 B provide additional design characteristics for the example embodiment shown in  FIGS. 5A and 5B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 5A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.09   ASPHERE   1.610   1.492   57.4       2   11.05   −52.2346   3.908           2.62   DIAPHRAGM   0.521       3   2.81   −8.00000   3.751   1.492   57.4       4   5.26   −6.86460   1.350           6.79   SHUTTER                    
LENS LENGTH: 9.790
 
BF: 31.84
 
FF: 21.46
 
BEST FOCUS: −0.442
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
           
         
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 
               C = .012114119475 
               D = .15704399E−03 
               F = 
             
             
               1: 
               k = −1146.1888082 
               E = −.32087938E−05 
               .27346388E−07 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = 82.54830259 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 5B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.37   9.28710   3.000   1.492   57.4       2   8.16   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.00
 
BF: 38.99
 
FF: 46.62
 
BEST FOCUS: −0.441
 
   Referring to  FIGS. 5C and 5D , lateral color diagrams of the example embodiment shown in  FIGS. 5A and 5B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 5E and 5F , through focus MTF performance plots for the example embodiment shown in  FIGS. 5A and 5B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/i 5, 40%/26, 60%/33, 75%/18, 90%/ 8  and the wavelengths and weights described above. 
   Referring to  FIGS. 6A and 6B , cross sectional views of a sixth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  602  and a rear lens element  604  as viewed from an object side. Front lens element  602  is biconvex. Rear lens element  604  is meniscus and convex toward image plane  50 . Both lens elements  602  and  604  are made from acrylic plastic. An aperture stop  606  is located between lens elements  602  and  604  and a shutter  608  is located on an image side of lens element  204 . Front lens element  602  includes an aspheric surface on its image side surface. Rear lens element  604  includes an aspheric surface located on its image side surface. 
   Second lens system  30  includes a positive power meniscus lens element  610  convex toward an object side. Lens element  610  has spherical surfaces and is made of acrylic plastic. An aperture stop  612  is located on an image side of lens element  610 . A shutter  614  is located on an image side of aperture stop  612 . 
   Tables  6 A and  6 B provide additional design characteristics for the example embodiment shown in  FIGS. 6A and 6B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 6A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.68   63.2004   1.893   1.492   57.4       2   11.63   ASPHERE   4.746           2.66   DIAPHRAGM   0.995       3   3.42   −7.08950   2.156   1.492   57.4       4   4.93   ASPHERE   1.350           6.79   SHUTTER                    
LENS LENGTH: 9.790
 
BF: 30.74
 
FF: 25.54
 
BEST FOCUS: 0.610
 
ASPHERIC EQUATION:
 
           X   =         CY   2       1   +           1   -       (     k   +   1     )     ⁢   C         2     ⁢     Y   2           +     DY   4     +     EY   6     +     FY   8     +     GY   10             
SURFACE 2:
 
                                             C = −0.0249247767   D = 0.23710700E−04   F = 0.28706026E−07       k = −31.59187578   E = −0.11472204E−05   G = −0.30987401E−09            VERTEX RADIUS = (1/C) = −40.12072045                    
SURFACE 4:
 
   
     
       
             
             
             
           
             
           
         
             
                 
             
           
           
             
               C = −0.1546638525 
               D = −0.77426813E−02 
               F = −0.92957799E−04 
             
             
               k = −19.29138454 
               E = 0.10141176E−02 
               G = 0.37603631E−05 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = −6.46563489 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 6B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.37   9.28710   3.000   1.492   57.4       2   8.16   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.00
 
BF: 38.99
 
FF: 46.62
 
BEST FOCUS: −0.441
 
   Referring to  FIGS. 6C and 6D , lateral color diagrams of the example embodiment shown in  FIGS. 6A and 6B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 6E and 6F , through focus MTF performance plots for the example embodiment shown in  FIGS. 6A and 6B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 7A and 7B , cross sectional views of a seventh example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  702  and a rear lens element  704  as viewed from an object side. Front lens element  702  is biconvex. Rear lens element  704  is meniscus and convex toward image plane  50 . Both lens elements  702  and  704  are made from acrylic plastic. An aperture stop  706  is located between lens elements  702  and  704  and a shutter  708  is located on an image side of lens element  704 . 
   Second lens system  30  includes a positive power meniscus lens element  710  convex toward an object side. Lens element  710  has spherical surfaces and is made of acrylic plastic. An aperture stop  712  is located on an image side of lens element  710 . A shutter  714  is located on an image side of aperture stop  712 . 
   Tables  7 A and  7 B provide additional design characteristics for the example embodiment shown in  FIGS. 7A and 7B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 7A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.19   105.824   1.639   1.492   57.4       2   11.14   −46.1229   3.877           2.62   DIAPHRAGM   0.521       3   2.81   −8.00000   3.751   1.492   57.4       4   5.31   −6.86460   1.350           6.79   SHUTTER                    
LENS LENGTH: 9.788
 
BF: 31.92
 
FF: 21.43
 
BEST FOCUS: −0.519
 
                                                                       TABLE 7B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.37   9.28710   3.000   1.492   57.4       2   8.16   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.00
 
BF: 38.99
 
FF: 46.62
 
BEST FOCUS: −0.441
 
   Referring to  FIGS. 7C and 7D , lateral color diagrams of the example embodiment shown in  FIGS. 7A and 7B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 7E and 7F , through focus MTF performance plots for the example embodiment shown in  FIGS. 7A and 7B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 8A and 8B , cross sectional views of an eighth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  802  and a rear lens element  804  as viewed from an object side. Front lens element  802  is biconvex. Rear lens element  804  is meniscus and convex toward image plane  50 . Both lens elements  802  and  804  are made from acrylic plastic. An aperture stop  806  is located between lens elements  802  and  804  and a shutter  808  is located on an image side of lens element  804 . Front lens element  802  includes aspheric surfaces on its object side and image side surfaces (biaspheric). Rear lens element  804  includes an aspheric surface located on its image side surface. 
   Second lens system  30  includes two lens elements, a front lens element  810  and a rear lens element  816  as viewed from an object side. Front lens element  810  and rear lens element  816  are meniscus and convex toward the object side. Both lens elements  810  and  816  are made from acrylic plastic. An aperture stop  812  is located between lens elements  810  and  816  and a shutter  814  is located on an image side of rear lens element  816 . Rear lens element  816  includes aspheric surfaces on its object side and image side surfaces (biaspheric). 
   Tables  8 A and  8 B provide additional design characteristics for the example embodiment shown in  FIGS. 8A and 8B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 8A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   12.42   ASPHERE   2.232   1.492   57.4       2   10.69   ASPHERE   4.027           2.51   DIAPHRAGM   0.983       3   3.61   −5.49365   2.500   1.492   57.4       4   5.94   ASPHERE   1.350           8.72   SHUTTER                    
LENS LENGTH: 9.742
 
BF: 30.47
 
FF: 18.69
 
BEST FOCUS: +0.900
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
             + 
             
               HY 
               12 
             
             + 
             
               IY 
               14 
             
           
         
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 1: 
               C = 0.0020000 
               D = 3.99734886552E−4 
               G = −9.93835415796E−10 
             
             
                 
               k = 3500.000 
               E = −9.79975631821E−6 
               H = 0. 
             
             
                 
                 
               F = 1.52460655566E−7 
               I = 0. 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = 500.0000 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
             
           
         
             
                 
                 
             
           
           
             
                 
               SURF. 2: 
               C = −0.0227927 
               D = 0. 
               G = 0. 
             
             
                 
                 
               k = −462.03856654 
               E = 0. 
               H = 0. 
             
             
                 
                 
                 
               F = 0. 
               I = 0. 
             
           
        
         
             
                 
               VERTEX RADIUS = (1/C) = −43.8737729753 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 4: 
               C = −0.2043465 
               D = −0.0188601226631 
               G = 1.03481246067E−4 
             
             
                 
               k = −21.249032504 
               E = 0.00449273235856 
               H = −6.84328365961E−6 
             
             
                 
                 
               F = −8.58719072584E−4 
               I = 1.8782811385E−7 
             
           
        
         
             
               VERTEX RADIUS = (1/C) = −4.89364805421 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 8B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.16   9.28710   3.000   1.492   57.4       2   8.08   14.5761   4.847           2.71   DIAPHRAGM   1.565       3   4.66   ASPHERE   1.347   1.492   57.4       4   5.43   ASPHERE   3.240           8.91   SHUTTER                    
LENS LENGTH: 10.759
 
BF: 33.72
 
FF: 56.15
 
BEST FOCUS: −0.900
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
             + 
             
               HY 
               12 
             
             + 
             
               IY 
               14 
             
           
         
       
     
   
   
     
       
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 3: 
               C = 0.0915783 
               D = 0. 
               F = 0. 
               H = 0. 
             
             
                 
               k = −12.2711702 
               E = 0. 
               G = 0. 
               I = 0. 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 10.9196145445 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 4: 
               C = 0.1049791 
               D = 0.1456182E−01 
               F = 0.1490086E−02 
               H = 0.1993857E−04 
             
             
                 
               k = −141.6509677 
               E = −0.5686506E−02 
               G = −0.2353026E−03 
               I = −0.6927936E−06 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 9.5257023402 
             
             
                 
             
           
        
       
     
   
   Referring to  FIGS. 8C and 8D , lateral color diagrams of the example embodiment shown in  FIGS. 8A and 8B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 8E and 8F , through focus MTF performance plots for the example embodiment shown in  FIGS. 8A and 8B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Referring to  FIGS. 9A and 9B , cross sectional views of a ninth example embodiment made in accordance with the invention in wide angle and telephoto zoom positions, respectively, are shown. Light are shown going through first and second lens systems  20 ,  30  on axis, at 40%, 60%, 75%, 90%, 100% relative field (20.58 mm), and at 105% relative field (21.63 mm). 
   Lens system  10  includes a first lens system  20  and a second lens system  30 . First and second lens systems  20 ,  30  are interchangeably positionable on optical axis  40 . Second lens system  30  has a longer focal length than first lens system  20 . 
   First lens system  20  includes two positive power lens elements, a front lens element  902  and a rear lens element  904  as viewed from an object side. Front lens element  902  is meniscus and convex toward the object side. Rear lens element  904  is meniscus and convex toward image plane  50 . Front lens element  902  is made from styrene plastic and rear lens element  904  is made from acrylic plastic. An aperture stop  906  is located between lens elements  902  and  904  and a shutter  908  is located on an image side of lens element  904 . Front lens element  902  includes aspheric surfaces on its object side and image side surfaces (biaspheric). Rear lens element  804  also includes aspheric surfaces on its object side and image side surfaces (biaspheric). 
   Second lens system  30  includes two lens elements, a front lens element  910  and a rear lens element  916  as viewed from an object side. Front lens element  910  and rear lens element  916  are meniscus and convex toward the object side. Both lens elements  910  and  916  are made from acrylic plastic. An aperture stop  912  is located between lens elements  910  and  916  and a shutter  914  is located on an image side of rear lens element  916 . Rear lens element  916  includes aspheric surfaces on its object side and image side surfaces (biaspheric). 
   Tables  9 A and  9 B provide additional design characteristics for the example embodiment shown in  FIGS. 9A and 9B . In both tables, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system; surfaces  3  and  4  refer to the object side surface and image side surface of the next lens element; etc. 
                                                                       TABLE 9A                   first lens system 20                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   14.40   ASPHERE   2.547   1.590   30.9       2   11.81   ASPHERE   4.432           2.31   DIAPHRAGM   0.396       3   2.72   ASPHERE   3.212   1.492   57.4       4   5.86   ASPHERE   1.350           8.73   SHUTTER                    
LENS LENGTH: 10.587
 
BF: 30.24
 
FF: 13.54
 
BEST FOCUS: +1.250
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
             + 
             
               HY 
               12 
             
             + 
             
               IY 
               14 
             
             + 
             
               JY 
               16 
             
             + 
             
               KY 
               18 
             
           
         
       
     
   
   
     
       
             
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF.1: 
               C = 0.0043907 
               D = 0.7247961E−03 
               F = 0.5765921E−06 
               H = 0.1527704E−09 
               J = −0.1850309E−13 
             
             
                 
               k = 0. 
               E = −0.1845085E−04 
               G = −0.1321436E−07 
               I = 0.8976964E−13 
               K = 0.1219260E−15 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 277.752157854 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 2: 
               C = 0.0004259 
               D = 0.8903960E−03 
               F = 0.5547956E−06 
               H = −0.2815706E−10 
               J = 0. 
             
             
                 
               k = 0. 
               E = −0.2898818E−04 
               G = −0.4091017E−08 
               I = 0.50339403E−12 
               K = 0. 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 2347.98191304 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 3: 
               C = −0.1865951 
               D = 0. 
               F = 0. 
               H = 0. 
               J = 0. 
             
             
                 
               k = 1.3857597 
               E = 0. 
               G = 0. 
               I = 0. 
               K = 0. 
             
           
        
         
             
               VERTEX RADIUS = 1/C = −5.35919818597 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 4: 
               C = −0.2193030 
               D = −0.2022930E−01 
               F = −0.8839514E−03 
               H = −0.6975969E−05 
               J = 0. 
             
             
                 
               k = −18.3457766 
               E = −0.4655701E−02 
               G = 0.1057644E−03 
               I = 0.1911695E−06 
               K = 0. 
             
           
        
         
             
               VERTEX RADIUS = 1/C = −4.55990072211 
             
             
                 
             
           
        
       
     
   
                                                                       TABLE 9B                   second lens system 30                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.16   9.28710   3.000   1.492   57.4       2   8.08   14.5761   4.847           2.71   DIAPHRAGM   1.565       3   4.66   ASPHERE   1.347   1.492   57.4       4   5.43   ASPHERE   3.240           8.91   BAFFLE                    
LENS LENGTH: 10.759
 
BF: 33.72
 
FF: 56.15
 
BEST FOCUS: −0.900
 
ASPHERIC EQUATION:
 
   
     
       
         
           X 
           = 
           
             
               
                 CY 
                 2 
               
               
                 1 
                 + 
                 
                   
                     
                       
                         1 
                         - 
                         
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           C 
                         
                       
                     
                     2 
                   
                   ⁢ 
                   
                     Y 
                     2 
                   
                 
               
             
             + 
             
               DY 
               4 
             
             + 
             
               EY 
               6 
             
             + 
             
               FY 
               8 
             
             + 
             
               GY 
               10 
             
             + 
             
               HY 
               12 
             
             + 
             
               IY 
               14 
             
           
         
       
     
   
   
     
       
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 3: 
               C = 0.0915783 
               D = 0. 
               F = 0. 
               H = 0. 
             
             
                 
               k = −12.2711702 
               E = 0. 
               G = 0. 
               I = 0. 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 10.9196145445 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
           
             
           
         
             
                 
             
           
           
             
               SURF. 4: 
               C = 0.1049791 
               D = 0.1456182E−01 
               F = 0.1490086E−02 
               H = 0.1993857E−04 
             
             
                 
               k = −141.6509677 
               E = −0.5686506E−02 
               G = −0.2353026E−03 
               I = −0.6927936E−06 
             
           
        
         
             
               VERTEX RADIUS = 1/C = 9.5257023402 
             
             
                 
             
           
        
       
     
   
   Referring to  FIGS. 9C and 9D , lateral color diagrams of the example embodiment shown in  FIGS. 9A and 9B , respectively, are shown. Lateral color was measured along the image format diagonal using a maximum field height of 20.58 mm. The dotted line shows primary lateral color, defined here as the height of the blue (440 nm) image minus the height of the red (650 nm) image. Positive lateral color in this situation means that the blue image is larger than the red image. The solid line shows secondary lateral color, defined here as the height of the blue (440 nm) image minus the height of the green (546.1 nm) image. Positive secondary lateral color in this situation means that the blue image is larger than the green image. 
   Referring to  FIGS. 9E and 9F , through focus MTF performance plots for the example embodiment shown in  FIGS. 9A and 9B , respectively, are shown. The MTF performance plots were measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nm at 35%) at a frequency of 5.00 cycles per millimeter with a full field (100%) being 20.58 mm and centered along the image format diagonal. The area weighted average MTF numbers shown were calculated along the image format diagonal using obliquities/weights of axis/15, 40%/26, 60%/33, 75%/18, 90%/8 and the wavelengths and weights described above. 
   Tables 10 and 11 provide additional design characteristics for the example embodiments shown in  FIGS. 1A through 9F . 
   In example embodiments 8 and 9, lens system  30  includes two lens elements. In a preferred implementation, front lens element  810 ,  910  as viewed from the object side of the lens system is lens element  610  of example embodiment 6. As such, the shape of rear lens element  816 ,  916  is provided in TABLE 11. Rear lens element  816 ,  916  has negative power, meniscus in shape, and concave toward the image side of the lens system. 
   In TABLES 10 and 11, units are in millimeters where applicable. Surface types and materials are listed from object side to image side of the lens system. Surface types having an “S” are spherical, while surface types having an “A” are aspheric. “PMMA” is an acrylic plastic (polymethyl-methacrylate) and “PS” is a styrene plastic. 
   “% LINEBOW, HOR/VERT” is the horizontal and vertical linebow distortion over the top and side of the full image format (24 mm×36 mm in example embodiments 1 through 9). A negative linebow distortion is often referred to as “barrel” distortion in which the corners of the image are bowed in. A positive linebow distortion is often referred to as “pincushion” distortion in which the corners of the image are bowed out. 
   The values for area weighted average MTF (AWA MTF) (heterochromatic) are taken along the image format diagonal with wavelength/weights of 650 nm/35; 546.1 nm/50; 440 nm/15; and obliquities/weights of axis/15; 40%/26; 60%/33; 75%/18; 90%/8. The values are shown at 5 c/mm and 10 c/mm at the image. A 100% field is an image height of 20.58 mm. “FVFD” is a front vertex to film distance or dimension where film is placed at a best image position using the object distance design criteria for each lens. Image distances shown are from the rear lens vertex for the associated object distance and include the best focus shifts of each lens system. 
   
     
       
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 10 
             
             
                 
             
             
                 
                 
                 
               SHUTTER 
                 
                 
               SURFACE 
               AWA 
               % LINEBOW 
             
             
                 
               EFL 
               EFF. FNO. 
               TO FILM 
               FVFD 
               MATERIALS 
               TYPES 
               MTF 5/10 
               HOR/VERT 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               EX. 1 
                 
                 
                 
                 
                 
                 
                 
                 
             
             
               LENS 20 
               31.03 
               F/11.11 
               30.507 
               42.364 
               PMMA/PMMA 
               SSAS 
               90/74 
               −1.47/.60 
             
             
               LENS 30 
               43.03 
               F/12.17 
               30.507 
               41.228 
               PMMA 
               SS 
               82/63 
                −.31/.39 
             
             
               EX. 2 
             
             
               LENS 20 
               29.99 
               F/11.01 
               28.691 
               37.438 
               PMMA/PMMA 
               ASAS 
               92/79 
               −1.80/.26 
             
             
               LENS 30 
               41.24 
               F/12.02 
               28.691 
               39.206 
               PMMA 
               SS 
               81/63 
                −.31/1.47 
             
             
               EX. 3 
             
             
               LENS 20 
               30.90 
               F/11.11 
               30.363 
               41.501 
               PMMA/PMMA 
               SSSS 
               88/70 
               −1.73/.41 
             
             
               LENS 30 
               43.65 
               F/12.17 
               30.363 
               41.843 
               PMMA 
               SS 
               81/62 
                −.38/1.32 
             
             
               EX. 4 
             
             
               LENS 20 
               30.90 
               F/11.21 
               30.360 
               41.600 
               PMMA/PMMA 
               SASS 
               89/72 
               −1.56/.70 
             
             
               LENS 30 
               43.65 
               F/13.19 
               30.363 
               42.183 
               PMMA 
               SS 
               81/63 
                −.38/1.29 
             
             
               EX. 5 
             
             
               LENS 20 
               30.90 
               F/11.13 
               30.360 
               41.500 
               PMMA/PMMA 
               ASSS 
               89/72 
               −1.65/.49 
             
             
               LENS 30 
               43.65 
               F/13.19 
               30.363 
               42.183 
               PMMA 
               SS 
               81/63 
                −.38/1.29 
             
             
               EX. 6 
             
             
               LENS 20 
               32.90 
               F/11.22 
               30.360 
               41.50 
               PMMA/PMMA 
               SASA 
               92/79 
                −.31/1.70 
             
             
               LENS 30 
               43.65 
               F/13.19 
               30.363 
               42.183 
               PMMA 
               SS 
               81/63 
                −.38/1.29 
             
             
               EX. 7 
             
             
               LENS 20 
               30.90 
               F/11.11 
               30.363 
               41.501 
               PMMA/PMMA 
               SSSS 
               88/70 
               −1.73/.41 
             
             
               LENS 30 
               43.65 
               F/13.19 
               30.363 
               42.183 
               PMMA 
               SS 
               81/63 
                −.38/1.29 
             
             
               EX. 8 
             
             
               LENS 20 
               28.81 
               F/11.02 
               30.363 
               41.455 
               PMMA/PMMA 
               AASA 
               86/66 
                −.48/1.51 
             
             
               LENS 30 
               48.50 
               F/14.32 
               30.363 
               44.362 
               PMMA/PMMA 
               SSAA 
               79/61 
                  .10/1.69 
             
             
               EX. 9 
             
             
               LENS 20 
               25.75 
               F/11.02 
               30.363 
               42.300 
               PS/PMMA 
               AAAA 
               85/66 
                −.48/1.64 
             
             
               LENS 30 
               48.50 
               F/14.32 
               30.363 
               44.362 
               PMMA/PMMA 
               SSAA 
               79/61 
                  .10/1.69 
             
           
        
         
             
               ADDITIONAL EXAMPLES USING ALTERNATIVE MATERIALS 
             
           
        
         
             
               LENS 
                 
                 
                 
                 
                 
                 
                 
                 
             
             
               A 
               43.70 
               F/13.16 
               30.363 
               42.183 
               ZEONOR1600R 
               SS 
               81/63 
                −.35/1.32 
             
             
               B 
               43.70 
               F/13.16 
               30.363 
               42.183 
               TOPAS6017 
               SS 
               81/64 
                −.35/1.32 
             
             
               C 
               43.65 
               F/12.17 
               30.363 
               41.843 
               K10 (Glass) 
               SS 
               81/62 
                −.36/1.33 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 11 
             
             
                 
                 
             
             
                 
                 
               DESIGNED 
                 
                 
                 
               CENTER 
                 
             
             
                 
                 
               OBJECT 
               IMAGE 
               COMPONENT 
               FRONT 
               SPACE AS 
               IMAGE 
             
             
                 
               EFL 
               DISTANCE 
               DISTANCE 
               EFL&#39;S 
               ELEMENT SHAPE 
               A % OF EFL 
               DIST/EFT 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               EX. 1 
                 
                 
                 
                 
                 
                 
                 
             
             
               LENS 20 
               31.03 
               −3048 
               32.327 
                76.79/43.71 
               BICONVEX ( ) 
               5.48/31.03 = 17.7% 
               1.04 
             
             
               LENS 30 
               43.03 
               −3048 
               38.028 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .88 
             
             
               EX. 2 
             
             
               LENS 20 
               29.99 
               −3048 
               30.511 
                43.33/71.29 
               BICONVEX ( ) 
               2.572/29.99 = 8.6% 
               1.02 
             
             
               LENS 30 
               41.24 
               −3048 
               36.206 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .88 
             
             
               EX. 3 
             
             
               LENS 20 
               30.90 
               −3048 
               31.713 
                65.29/46.82 
               BICONVEX ( ) 
               4.398/30.90 = 14.2% 
               1.03 
             
             
               LENS 30 
               43.65 
               −3048 
               38.843 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .89 
             
             
               EX. 4 
             
             
               LENS 20 
               30.90 
               −3048 
               31.710 
                65.97/46.82 
               MENISCUS )) 
               4.510/30.90 = 14.6% 
               1.03 
             
             
               LENS 30 
               43.65 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               EX. 5 
             
             
               LENS 20 
               30.90 
               −3048 
               31.710 
                65.05/46.82 
               BICONVEX ( ) 
               4.429/30.90 = 14.3% 
               1.03 
             
             
               LENS 30 
               43.65 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               EX. 6 
             
             
               LENS 20 
               32.90 
               −3048 
               31.710 
                50.00/69.47 
               BICONVEX ( ) 
               5.741/32.90 = 17.4% 
               .96 
             
             
               LENS 30 
               43.65 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               EX. 7 
             
             
               LENS 20 
               30.90 
               −3048 
               31.713 
                65.29/46.82 
               BICONVEX ( ) 
               4.398/30.90 = 14.2% 
               1.03 
             
             
               LENS 30 
               43.65 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               EX. 8 
             
             
               LENS 20 
               28.81 
               −2438.4 
               31.713 
                81.80/38.17 
               BICONVEX ( ) 
               5.010/28.81 = 17.4% 
               1.01 
             
             
               LENS 30 
               48.50 
               −3048 
               33.603 
                43.65/−222.07 
               MENISCUS (( 
               6.412/48.50 = 13.2% 
               .69 
             
             
               EX. 9 
             
             
               LENS 20 
               25.75 
               −3048 
               31.713 
               423.74/26.59 
               MENISCUS (( 
               4.828/25.75 = 18.7% 
               1.23 
             
             
               LENS 30 
               48.50 
               −3048 
               33.603 
                43.65/−222.07 
               MENISCUS (( 
               6.412/48.50 = 13.2% 
               .69 
             
           
        
         
             
               ADDITIONAL EXAMPLES USING ALTERNATIVE MATERIALS: 
             
           
        
         
             
               LENS 
                 
                 
                 
                 
                 
                 
                 
             
             
               A 
               43.70 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               B 
               43.70 
               −3048 
               39.183 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .90 
             
             
               C 
               43.65 
               −3048 
               38.843 
               (SINGLET) 
               MENISCUS (( 
               (SINGLET) 
               .89 
             
             
                 
             
           
        
       
     
   
   In TABLES 10 and 11, example lens made from materials other than PMMA and PS plastics are shown. Lens A is made from ZEONOR brand plastic. Lens B is made from TOPAS brand plastic. Lens C is made from “K-10” glass. ZEONOR (cyclo-olefin polymers) and TOPAS (cyclic olefin copolymers) are brand names of “special” plastics having lower water absorbing characteristics than other types of plastics, for example, PMMA or PS plastics. “K-10” is a commercially available type of glass, taken from the Schott glass catalog (2000). Using lens elements made from “special” plastics and/or glass instead of or in addition to lens elements made from PMMA and/or PS plastics can help to improve environmental stability. For example, lens elements made from “special” plastics and/or glass can help to reduce the thermal and/or humidity effects associated with environmental changes on lens elements made from PMMA and/or PS plastics. 
   A lens or lenses made from any of these materials can be substituted for any of the lens elements described above with reference to example embodiments 1 through 9 in order to improve environmental stability of lens system  10 . For example, any one of lenses A, B, or C can be directly substituted for meniscus lens element  610  of second lens system  30  in example embodiment 6 described above. However, depending on the specific application contemplated, it may be desirable to make additional minor design changes, for example, changes in lens element thickness, spacing, radius of curvature, surface type, etc., in order to improve the overall performance of lens system  10  when these types of materials are used. 
   Tables A, B, and C provide additional design characteristics for the alternative material example embodiments described above. In each table, surfaces are viewed from an object side toward an image side. As such, surfaces  1  and  2  refer to the object side surface and image side surface, respectively, of the lens element located closest to the object side of the lens system. 
                                                                       TABLE A                   lens A                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.42   9.64047   3.000   1.535   55.8       2   8.18   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.000
 
BF: 38.95
 
FF: 46.84
 
BEST FOCUS: −0.400
 
                                                                       TABLE B                   lens B                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.42   9.62661   3.000   1.533   56.7       2   8.18   14.5761   4.480           2.67   DIAPHRAGM   4.340           6.79   SHUTTER                    
LENS LENGTH: 3.000
 
BF: 38.95
 
FF: 46.83
 
BEST FOCUS: −0.400
 
                                                                       TABLE C                   lens C                CLEAR                       SURF.   APER.   RADIUS   THICKNESS   INDEX   V                    1   10.57   9.40858   3.000   1.501   56.4       2   8.38   14.6949   4.480           2.89   DIAPHRAGM   4.000           6.79   SHUTTER                    
LENS LENGTH: 3.000
 
BF: 38.99
 
FF: 46.63
 
BEST FOCUS: −0.781
 
   Referring back to  FIGS. 1A–9F , each lens system  20  includes an aperture stop positioned between the front and rear lens elements with a shutter located on an image side of the second lens element as viewed from an object side of the lens system. Positioning the aperture stop between the front and rear elements helps to improve the ability to correct or control aberrations, for example, lateral color, occurring in the upper and lower portions of the off-axis (away from the optical axis) light ray bundles when compared to other aperture stop locations (for example, on an object side of the front lens element or on an image side of the rear lens element). 
   The front and rear lens elements of each lens system  20  described with reference to  FIGS. 1A–9F  are quasi-symmetrical. This also helps to improve the ability to correct or control aberrations, for example, lateral color, occurring in the upper and lower portions of the off-axis light ray bundles when compared to non-symmetrical lens elements. The term quasi-symmetrical is broadly defined to mean that a degree of symmetry exists between the front and rear lens elements that helps to reduce at least some off-axis aberrations. This degree of symmetry can vary as is described in more detail in the numerical design characteristics of example embodiments 1 through 9. As used herein, the term quasi-symmetrical is defined to mean that at least three lens surfaces out of the four lens surfaces of the first lens system  20  have a center of curvature in a direction toward the aperture stop such that lens surfaces on the object side of the aperture stop (left of the aperture stop in  FIGS. 1A–10B ) have a positive curvature (vertex radius) and lens surfaces on the image side of the aperture stop (right of the aperture stop in  FIGS. 1A–10B ) have a negative curvature (vertex radius). 
   Again referring back to  FIGS. 1A–9F , lens system  20  includes two lens elements which provides a longer image distance when compared to single element designs. The longer image distance of each lens system  20  allows lens system  20  and lens system  30  to have a common shutter location which simplifies manufacturing of cameras incorporating lens system  10 . 
   There are two types of linebow distortion—horizontal and vertical. When present, horizontal linebow distortion can be seen throughout the entire image, whereas vertical linebow is present only at the edges of the image. As such, and again referring back to  FIGS. 1A–9F , in preferred implementations of example embodiments 1 through 9, lens system  20  has an absolute value of % horizontal linebow distortion of less than 0.50, and more preferably, less than 0.35 while the absolute value of % vertical linebow distortion is less than 1.75, and more preferably, less than 1.65. 
   In preferred implementations of example embodiments 1 through 9, lens system  30  has an absolute value of % horizontal linebow distortion of less than 0.40, and more preferably, less than 0.15 while the absolute value of % vertical linebow distortion of less than 1.70, and more preferably, less than 1.30. 
   The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.