Abstract:
A two position variable focal length lens is provided. 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 is effected 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.

Description:
FIELD OF THE INVENTION  
         [0001]    This invention relates generally to lens design, and in particular to a variable focal length lens for use in a camera.  
         BACKGROUND OF THE INVENTION  
         [0002]    Zoom lens system in which the rear or image side lens units switch out of and into an optical path are known. For example, U.S. Pat. No. 4,871,238, which issued to Sato et al., on Oct. 3, 1989, discloses a photographic optical device including a master lens unit having a positive refractive power; a first auxiliary lens unit having a positive refractive power capable of being placed on and off the optical path; and a second auxiliary lens unit having a negative refractive power capable of being placed on and off the optical path. The first auxiliary lens unit is attached to an image-plane side of the master lens unit to form a photographic unit giving a low ratio of magnification. The second auxiliary lens unit is attached to an image-plane side of the master lens unit to form another photographic unit giving a high ratio of magnification. The first and second auxiliary lens units are placed outside of the optical path to form another photographic unit giving a middle ratio of magnification. The zoom lens system disclosed in U.S. Pat. No. 4,871,238 is disadvantaged in that each lens unit requires many individual lens components which increases manufacturing costs associated with building the zoom lens system and increases the complexity of the design of the zoom lens system. Additionally, the zoom lens system disclosed in U.S. Pat. No. 4,871,238 includes a wide angle, mid-range, and telephoto format (lens position) which increases the cost and complexity associated with the lens driving mechanism.  
           [0003]    Lens systems having a reduced number of individual lens components are also known. For example, U.S. Pat. No. 5,677,798, which issued to Hirano et al., on Oct. 14, 1997, discloses an image forming lens system including a positive front lens group, a diaphragm, and a rear lens group, in order from an object to be imaged. The front lens group is made of optical glass. The rear lens group is made of a single meniscus plastic lens having opposed aspheric lens surfaces with a concave surface adjacent to the diaphragm. Additionally, U.S. Pat. No. 5,067,803, which issued to Ohno, on Nov. 26, 1991, discloses a photographic wide angle lens which is composed of, from an object side thereof, a first lens of positive meniscus having a convex surface on the object side, and a second lens of positive meniscus having a concave surface on the object side. The wide angle lens has an aspheric surface at least on one of the four lens surfaces provided by the first and second lenses. While the lens systems disclosed in U.S. Pat. Nos. 5,677,798 and 5,067,803 have a reduced number of individual lens elements, each lens system is disadvantaged in that the ratio of magnification of the lens system can not be changed.  
           [0004]    Recent surveys of picture taking consumers using a zoom lens indicated that over 90% of all photographs are shot in either a wide angle format or a telephoto format. As such, there is a need for a variable focal length lens system having a reduced number of individual lens components capable of switching between a wide angle format and a telephoto format.  
         SUMMARY OF THE INVENTION  
         [0005]    According to one feature of the present invention, a two position variable focal length lens includes a common lens element moveably positioned on an optical axis. A wide angle lens element is 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. A telephoto lens element is 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 is effected 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. The two position variable focal length lens satisfies the following condition: |f c −f zt |&lt;|f c −f zw |, where f c  is a focal length of the common lens element, f zt  is a focal length of the two position variable focal length lens in a telephoto position, and f zw  is a focal length of the two position variable focal length lens in a wide angle position.  
           [0006]    According to another feature of the present invention, a two position variable focal length lens includes a common lens element moveably positioned on an optical axis. The common lens element has an image side surface with the image side surface having a curvature. The common lens element satisfies the following condition: (1/−20.8)≦c≦(1/5), where c is the curvature of the image side surface. A wide angle lens element is 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. A telephoto lens element is 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 is effected 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.  
           [0007]    According to another feature of the present invention, a two position variable focal length lens includes a common lens element moveably positioned on an optical axis. A wide angle lens element is 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. A first aperture stop is moveably positioned with the wide angle lens element on an object side of the wide angle lens element. A telephoto lens element is 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 second aperture stop is moveably positioned with the telephoto lens element on an object side of the telephoto lens element. A magnification ratio change is effected by moving the common lens element along the optical axis and switching between the first aperture stop and the wide angle lens element located at the first position on the optical axis and the second aperture stop and the telephoto lens element located at the second position on the optical axis such that a distance between the common lens element and the first aperture stop is equivalent to a distance between the common lens element and the second aperture stop.  
           [0008]    According to another feature of the present invention, a two position variable focal length lens includes a common lens element moveably positioned on an optical axis. A wide angle lens element having aspheric surfaces is 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. A telephoto lens element having aspheric surfaces is 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 is effected 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. The aspheric surfaces of the telephoto lens element have base radii that are larger than corresponding base radii of the aspheric surfaces of the wide angle lens element.  
           [0009]    According to another feature of the present invention, a two position variable focal length lens includes a common lens element moveably positioned on an optical axis. A wide angle lens element is 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. A telephoto lens element is 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, wherein a magnification ratio change is effected 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. The two position variable focal length lens satisfies the following condition: f C &gt;((f ZW +f ZT )/2), where f C  is a focal length of the common lens element, f ZW  is a focal length of the two position variable focal length lens in a wide angle position, and f ZT  is a focal length of the two position variable focal length lens in a telephoto position.  
           [0010]    According to another feature of the present invention, a method of changing a magnification ratio from a wide angle position to telephoto angle position includes providing a common lens element positioned at a first location on an optical axis; providing a wide angle lens element located at a first position on the optical axis on an image side of the common lens element; providing a telephoto lens element located at a location removed from the optical axis; moving the common lens element toward an object plane; moving the telephoto lens element to a second position on the optical axis on the image side of the common lens element; and removing the wide angle lens from the optical axis. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]    In the detailed description of the embodiments of the invention presented below, reference is made to the accompanying drawings, in which:  
         [0012]    [0012]FIGS. 1A and 1B are schematic cross sectional views of an embodiment made in accordance with the present invention in a wide angle zoom position and telephoto zoom position;  
         [0013]    [0013]FIGS. 2A and 2B are cross sectional views of first and second numerical examples made in accordance with the present invention in a wide angle zoom position and a telephoto zoom position;  
         [0014]    FIGS.  3 A- 3 C are MTF performance plots of the first and second examples shown in FIGS. 2A and 2B;  
         [0015]    FIGS.  4 A- 4 C are lateral color aberration curves for the first and second examples shown in FIGS. 2A and 2B;  
         [0016]    [0016]FIGS. 5A and 5B are cross sectional views of third and fourth numerical examples made in accordance with the present invention in a wide angle zoom position and a telephoto zoom position;  
         [0017]    FIGS.  6 A- 7 B are MTF performance plots of the third and fourth examples, respectively, shown in FIGS. 5A and 5B;  
         [0018]    FIGS.  8 A- 9 B are lateral color aberration curves for the third and fourth examples, respectively, shown in FIGS. 5A and 5B;  
         [0019]    [0019]FIGS. 10A and 10B are cross sectional views of fifth and sixth numerical examples made in accordance with the present invention in a wide angle zoom position and a telephoto zoom position;  
         [0020]    FIGS.  1 A- 12 B are MTF performance plots of the third and fourth examples, respectively, shown in FIGS. 10A and 10B; and  
         [0021]    FIGS.  13 A- 14 B are lateral color aberration curves for the third and fourth examples, respectively, shown in FIGS. 10A and 10B. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0022]    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.  
         [0023]    Referring to FIGS. 1A and 1B, a two position variable focal length lens  20  is shown. The two position variable focal length lens  20  includes a first lens unit  22  and a second lens unit  24 , as viewed from an object side of the two position variable focal length lens  20 . As shown in FIG. 1A, the first lens unit  22  includes a common lens element  26  while the second lens unit  24  includes a wide angle lens element  28 . An aperture stop  30  is positioned between common lens element  26  and wide angle lens element  28 . As shown in FIG. 1B, the first lens unit  22  includes the common lens element  26  while the second lens unit  24  includes a telephoto lens element  32 . A second aperture stop  34  is positioned between the common lens element  26  and the telephoto lens element  32 . Image plane  36  is cylindrically curved.  
         [0024]    Zooming in and zooming out are accomplished by moving the common lens element  26  along a optical axis  38  while switching between wide angle lens element  28  and telephoto lens element  32 . For example, as shown in FIG. 1A, two position variable focal length lens  20  is in a wide angle position. As such, two position variable focal length lens  20  includes aperture stop  30  positioned between common lens element  26  and wide angle lens element  28 . When a telephoto position is desired, common lens element  26  moves toward object plane  40  in a direction as indicated by arrow  42  while wide angle lens  28  moves out of the optical axis  38  in a direction as indicated by arrow  44 . As this is occurring, telephoto lens element  32  (shown in phantom in FIG. 1A) moves into optical axis  38  in a direction as indicated by arrow  46  after common lens element  26  is located on the object side of telephoto lens element  32 . This completes the zoom in process which results in the two position variable focal length lens  20  being in a telephoto position, as shown in FIG. 1B.  
         [0025]    When a wide angle position is desired, the telephoto lens element  32  moves out of the optical axis  38  in a direction as indicated by arrow  48  while common lens element  26  moves toward image plane  36  in a direction as indicated by arrow  50 . Wide angle lens element  28  moves into optical axis  38  in a direction as indicated by arrow  52  such that common lens element  26  is on the object side of wide angle lens element  32 . This completes the zoom out process which results in the two position variable focal length lens  20  being in the wide angle position as shown in FIG. 1A.  
         [0026]    While the motion of the wide angle lens element  28  and the telephoto lens element  32  is generally perpendicular to the optical axis  38 , other motion angles can be incorporated with substantially similar results. The motion of common lens element  26  is generally parallel to optical axis  38 . Additionally, aperture stop  30  moves into and out of optical axis  38  with wide angle lens element  28  while second aperture stop  34  moves into and out of optical axis  38  with telephoto lens element  32 . Finally, common lens element  26  does not stop at a mid-range position. The movement of two position variable focal length lens  20  is from a wide angle position directly to a telephoto position or directly from a telephoto position to a wide angle position.  
         [0027]    Referring to FIGS. 2A and 2B, a first example of the two position variable focal length lens  20  is shown. FIG. 2A shows two position variable focal length lens  20  in a wide angle format or position while FIG. 2B show two position variable focal length lens  20  in a telephoto format or position. Common lens element  26  is glass and includes surface S 1  which is spherical and convex toward the object plane  40  while surface S 2  is plano. Wide angle lens element  28  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (styrene) and includes surfaces S 5A  and S 6A  which are both aspheric.  
         [0028]    A second example is also shown in FIGS. 2A and 2B. In this example, common lens element  26  is glass and includes surface S 1  which is spherical and convex toward the object plane  40  while surface S 2  is plano. Wide angle lens element  28  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (for example, acrylic or PMMA, etc.) and includes surfaces S 5B  and S 6B  which are both aspheric.  
       EXAMPLES 1 AND 2 (FIGS.  2 A- 2 B)  
       [0029]    [0029]                                                                                                                                                                                                                                                                                                                                                                                             Surface   Radius   Thickness   Index   V                                                   S 1     20.7488   2.499   1.517   64.2           S 2     plano   2.161           STOP   diaphragm   1.664           wide angle           S 3     asphere   2.500   1.492   57.4           S 4     asphere           telephoto 1           S 5A     asphere   2.500   1.590   30.9           S 6A     asphere           telephoto 2           S 5B     asphere   2.500   1.492   57.4           S 6B     asphere                        ASPHERIC EQUATION for surfaces S 3 -S 6A :                       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                                                         Surface S 3 :                                                C =   −0.15420764   D =   −0.6102268E−03   F =   −0.5459696E−04   H =   0.2136513E−05       k =   0   E =   0.1320045E−03   G =   0.5290771E−05   I =   −0.4709130E−06                               J =   0.2424784E−07            Surface S 4 :                                                C =   −0.16406247   D =   0.4134610E−04   F =   0.5126819E−05   H =   −0.1939498E−08       k =   0   E =   −0.1706174E−04   G =   −0.4149921E−06    I =   0.2729591E−08                               J =   −0.1170938E−09            Surface S 5A :                                                C =   −0.1122254   D =   0.3331735E−03   F =   0.2060900E−04   H =   −0.1077000E−06       k =   0   E =   −0.2999852E−04   G =   −0.3665477E−05    I =   0.1144493E−06                               J =   −0.9815623E−08            Surface S 6A :                                                C =   −0.0995002   D =   0.2473666E−03   F =   0.3904813E−05   H =   0.2350041E−07       k =   0   E =   −0.5835636E−05   G =   −0.4983947E−06   I =   0.5129185E−09                               J =   −0.5786020E−10            ASPHERIC EQUATION for surfaces S 3B  and S 6B :               X   =                CY   2       1   +       1   -       (     k   +   1     )          C   2          Y   2               +     DY   4     +     EY   6     +     FY   8     +     GY   10                                                      Surface S 5B :                                                C =   −0.11651826   D =   0.3604447E−03   F =   0.4611370E−05           k =   0   E =   −0.1543348E−06   G =   −0.2947564E−06                Surface S 6B :                                                C =   −0.10340955   D =   0.2667438E−03   F =   0.0           k =   0   E =   0.1049829E−04   G =   0.0                Focal   Back   Front   Best   Lens   Exit Pupil   Relative           Length   Focus   Focus   Focus   Length   Diameter   Aperture                                                            Wide angle   28.80   26.82   22.50   −0.008   8.824   3.15   10       Telephoto 1   46.53   42.54   42.56   −0.147   8.824   4.31   11       Telephoto 2   46.47   42.03   42.89   0.138   8.824   4.27   11                    
         [0030]    In wide angle format, Examples 1 and 2 have a cylindrically curved image plane with a radius=−120.0; a semi-field of 36.45°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  28  has a focal length of 65.834 mm.  
         [0031]    In telephoto 1 format, Example 1 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.66°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  32  has a focal length of-727.007 mm.  
         [0032]    In telephoto 2 format, Example 2 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.64°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000, and the second lens element  32  has a focal length of −642.625.  
         [0033]    Referring to FIGS.  3 A- 3 C, MTF performance plots are measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nanometers at 35%) at a frequency of 4.45 cycles per millimeter with full field (100%) being 20.58 mm. FIG. 3A shows MTF plots for Examples 1 and 2 in wide angle format. FIG. 3B shows MTF plots for Example 1 in telephoto (telephoto 1) format. FIG. 3C shows MTF plots for Example 2 in an alternative telephoto (telephoto 2) format. MTF plots are centered along the diagonal of the film cylinder (long dimension of 24×36 mm image format is measured along cylinder radius of curvature in all examples).  
         [0034]    FIGS.  4 A- 4 C describe additional performance characteristics of the variable focal length lens  20  of Examples 1 and 2. FIG. 4A shows lateral color correction for Examples 1 and 2 in wide angle format. FIG. 4B shows lateral color correction for Example 1 in telephoto (telephoto 1) format. FIG. 4C shows lateral color correction for Example 1 in the alternative telephoto (telephoto 2) format.  
         [0035]    Referring to FIGS. 5A and 5B, a third example of the two position variable focal length lens  20  is shown. FIG. 5A shows two position variable focal length lens  20  in a wide angle format or position while FIG. 5B show two position variable focal length lens  20  in a telephoto format or position. Common lens element  26  is a meniscus glass lens and includes spherical surfaces S 1  and S 2  with surface S 1  being convex toward the object plane  40 . Wide angle lens element  28  is plastic (for example, acrylic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (for example, acrylic or PMMA, etc.) and includes surfaces S 5  and S 6  which are both aspheric.  
       EXAMPLE 3 (FIGS.  5 A AND  5 B)  
       [0036]    [0036]                                                                                                                                                                                                                                                                       Surface   Radius   Thickness   Index   V                                                   S 1     11.8245   2.5080   1.517   64.2           S 2     25.5000   0.3000           STOP   diaphragm   3.3692           wide angle           S 3     asphere   1.7241   1.492   57.4           S 4     asphere           telephoto           S 5     asphere   1.7241   1.492   57.4           S 6     asphere                        ASPHERIC EQUATION for surfaces S 3 -S 6 :               X   =                CY   2       1   +       1   -       (     k   +   1     )          C   2          Y   2               +     DY   4     +     EY   6     +     FY   8     +     GY   10                                             Surface S 3 :                                        C =   −0.13847405   D =   −0.428189E−03   F =   −0.101596E−04       k =   0   E =   0.426948E−04   G =   0.350162E−06            Surface S 4 :                                        C =   −0.15511068   D =   −0.113785E−03   F =   −0.322740E−05       k =   0   E =   0.358426E−04   G =   0.731344E−07            Surface S 5 :                                        C =   −0.0597393   D =   0.377504E−03   F =   0.383276E−06       k =   0   E =   −0.123211E−04   G =   −0.232214E−08            Surface S 6 :                                        C =   −0.05134647   D =   0.401549E−03   F =   0       k =   0   E =   −0.394677E−06   G =   0                Focal   Back   Front   Best   Lens   Exit Pupil   Relative           Length   Focus   Focus   Focus   Length   Diameter   Aperture                                                            Wide   28.81   25.15   24.91   −0.233   7.9013   3.11   10       angle       Tele-   46.46   38.81   47.44   −0.126   7.9013   4.05   11       photo                    
         [0037]    In wide angle, Example 3 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 36.55°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  28  has a focal length of 70.131 mm.  
         [0038]    In telephoto, Example 3 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.38°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  32  has a focal length of-304.786 mm.  
         [0039]    Referring to FIGS.  6 A- 6 B, MTF performance plots are measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nanometers at 35%) at a frequency of 4.45 cycles per millimeter with full field (100%) being 20.58 mm. FIG. 6A shows MTF plots for Example 3 in wide angle format. FIG. 6B shows MTF plots for Example 3 in telephoto format. MTF plots are centered along the diagonal of the film cylinder (long dimension of 24×36 mm image format is measured along cylinder radius of curvature in all examples).  
         [0040]    FIGS.  8 A- 8 B describe additional performance characteristics of the variable focal length lens  20  of Example 3. FIG. 8A shows lateral color correction for Example 3 in wide angle format. FIG. 8B shows lateral color correction for Example 3 in telephoto format.  
         [0041]    Again referring to FIGS. 5A and 5B, a fourth example is shown. Common lens element  26  is a meniscus glass lens and includes spherical surfaces S 1  and S 2  with surface S 1  being convex toward the object plane  40 . Wide angle lens element  28  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (styrene) and includes surfaces S 5  and S 6  which are both aspheric.  
       EXAMPLE 4 (FIGS.  5 A AND  5 B)  
       [0042]    [0042]                                                                                                                                                                                                                                                                                                             Surface   Radius   Thickness   Index   V                                                   S 1     10.2817   2.4831   1.517   64.2           S 2     18.700   0.3000           STOP   diaphragm   2.4529           wide angle           S 3     asphere   1.6785   1.492   57.4           S 4     asphere           telephoto           S 5     asphere   1.6785   1.590   30.9           S 6     asphere                        ASPHERIC EQUATION for surfaces S 3  and S 4 :                       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                                                         Surface S 3 :                                                C =   −0.12452800   D =   −0.105809E−02   F =   −0.880093E−04   H =   0.368912E−05       k =   0   E =   0.426807E−03   G =   −0.689681E−05   I =   −0.395997E−06                               J =   0.142000E−07            Surface S 4 :                                                C =   −0.14260139   D =   0.333729E−03   F =   0.698542E−04   H =   0.957627E−06       k =   0   E =   −0.216354E−03   G =   −0.115044E−04   I =   −0.398302E−07                               J =   0.6655202E−09            ASPHERIC EQUATION for surfaces S 5  and S 6 :               X   =                CY   2       1   +       1   -       (     k   +   1     )          C   2          Y   2               +     DY   4     +     EY   6     +     FY   8     +     GY   10                                                      Surface S 5 :                                                C =   −0.03705074   D =   0.235494E−03   F =   0.360128E−06           k =   0   E =   −0.765443E−06   G =   −0.927079E−07                Surface S 6 :                                                C =   −0.03041180   D =   0.345056E−03   F =   0.467614E−06           k =   0   E =   0.931367E−07   G =   −0.395775-07                Focal   Back   Front   Best   Lens   Exit Pupil   Relative           Length   Focus   Focus   Focus   Length   Diameter   Aperture                                                            Wide angle   28.80   25.32   25.93   0.183   7.9144   2.92   10       Telephoto   46.45   39.12   48.37   −0.018   7.9144   3.98   11                    
         [0043]    In wide angle, Example 4 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 36.52°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  28  has a focal length of 72.521 mm.  
         [0044]    In telephoto, Example 4 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.35°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  32  has a focal length of-283.278 mm.  
         [0045]    Referring to FIGS.  7 A- 7 B, MTF performance plots are measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nanometers at 35%) at a frequency of 4.45 cycles per millimeter with full field (100%) being 20.58 mm. FIG. 7A shows MTF plots for Example 4 in wide angle format. FIG. 7B shows MTF plots for Example 4 in telephoto format. MTF plots are centered along the diagonal of the film cylinder (long dimension of 24×36 mm image format is measured along cylinder radius of  30  curvature in all examples).  
         [0046]    FIGS.  9 A- 9 B describe additional performance characteristics of the variable focal length lens  20  of Example 4. FIG. 9A shows lateral color correction for Example 4 in wide angle format. FIG. 9B shows lateral color correction for Example 4 in telephoto format.  
         [0047]    Referring to FIGS. 10A and 10B, a fifth example of the two position variable focal length lens  20  is shown. FIG. 10A shows two position variable focal length lens  20  in a wide angle format or position while FIG. 10B shows two position variable focal length lens  20  in a telephoto format or position. Common lens element  26  is glass, biconvex, and includes spherical surfaces S 1  and S 2 . Wide angle lens element  28  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 5  and S 6  which are both aspheric.  
       EXAMPLE 5 (FIGS.  10 A AND  10 B)  
       [0048]    [0048]                                                                                                                                                                                                                                                                       Surface   Radius   Thickness   Index   V                                                   S 1       28.2156   2.5355   1.517   64.2           S 2     −76.0000   2.1037           STOP   diaphragm   1.2977           wide angle           S 3     asphere   2.5000   1.492   57.4           S 4     asphere           telephoto           S 5     asphere   2.5000   1.492   57.4           S 6     asphere                        ASPHERIC EQUATION for surfaces S 3 -S 6 :               X   =                CY   2       1   +       1   -       (     k   +   1     )          C   2          Y   2               +     DY   4     +     EY   6     +     FY   8     +     GY   10                                             Surface S 3 :                                        C =   −0.16827865   D =   −0.784385E−03   F =   0.323412E−04       k =   0   E =   0.140733E−04   G =   −0.506861E−05            Surface S 4 :                                        C =   −0.17451256   D =   0.127490E−03   F =   0.586203E−05       k =   0   E =   −0.164813E−04   G =   −0.177061E−06            Surface S 5 :                                        C =   −0.13923392   D =   0.450399E−03   F =   0.996882E−06       k =   0   E =   −0.176693E−04   G =   −0.660403E−06            Surface S 6 :                                        C =   −0.12294855   D =   0.275038E−03   F =   0       k =   0   E =   0.133983E−04   G =   0                Focal   Back   Front   Best   Lens   Exit Pupil   Relative           Length   Focus   Focus   Focus   Length   Diameter   Aperture                                                            Wide   28.81   27.81   22.19   0.166   8.4369   3.20   10       angle       Tele-   46.46   43.86   41.51   −0.167   8.4369   4.40   11       photo                    
         [0049]    In wide angle, Example 5 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 36.51°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  28  has a focal length of 66.395 mm.  
         [0050]    In telephoto, Example 5 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.83°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  32  has a focal length of-946.925 mm.  
         [0051]    Referring to FIGS.  11 A- 11 B, MTF performance plots are measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nanometers at 35%) at a frequency of 4.45 cycles per millimeter with full field (100%) being 20.58 mm. FIG. 11A shows MTF plots for Example 5 in wide angle format. FIG. 11B shows MTF plots for Example 5 in telephoto format. MTF plots are centered along the diagonal of the film cylinder (long dimension of 24×36 mm image format is measured along cylinder radius of curvature in all examples).  
         [0052]    FIGS.  13 A- 13 B describe additional performance characteristics of the variable focal length lens  20  of Example 5. FIG. 13A shows lateral color correction for Example 5 in wide angle format. FIG. 13B shows lateral color correction for Example 5 in telephoto format.  
         [0053]    Again referring to FIGS. 10A and 10B, a sixth example is shown. Common lens element  26  is glass, biconvex, and includes spherical surfaces S 1  and S 2 . Wide angle lens element  28  is plastic (for example, acrylic plastic or PMMA, etc.) and includes surfaces S 3  and S 4  which are both aspheric. Telephoto lens element  32  is plastic (styrene) and includes surfaces S 5  and S 6  which are both aspheric.  
       EXAMPLE 6 (FIGS.  10 A AND  10 B)  
       [0054]    [0054]                                                                                                                                                                                                                                                                                                                                       Surface   Radius   Thickness   Index   V                                                        S 1     25.9540   2.5382   1.517   64.2           S 2     −100.0000   2.161           STOP   diaphragm   1.664           wide angle           S 3     asphere   2.500   1.492   57.4           S 4     asphere           telephoto           S 5     asphere   2.500   1.590   30.9           S 6     asphere                        ASPHERIC EQUATION for surfaces S 3  and S 4 :                       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                                                         Surface S 3 :                                                C =   −0.16514207   D =   −0.141911E−02   F =   −0.886266E−03   H =   −0.885040E−04       k =   0   E =   0.125105E−02   G =   0.383751E−03   I =   0.105047E−04                               J =   −0.53105E−06            Surface S 4 :                                                C =   −0.17251917   D =   0.378557E−03   F =   0.451695E−04   H =   0.157973E−06       k =   0   E =   −0.168890E−03   G =   −0.481651E−06    I =   0.115974E−07                               J =   −0.764399E−09            ASPHERIC EQUATION for surfaces S 5  and S 6 :               X   =                CY   2       1   +       1   -       (     k   +   1     )          C   2          Y   2               +     DY   4     +     EY   6     +     FY   8     +     GY   10                                                      Surface S 5 :                                                C =   −0.13066330   D =   0.314620E−03   F =   0.490785E−06           k =   0   E =   0.206307E−04   G =   0.569552E−07                Surface S 6 :                                                C =   −0.11505867   D =   0.210325E−03   F =   −0.864282E−06           k =   0   E =   0.170648E−04   G =   0.394302E−07                Focal   Back   Front   Best   Lens   Exit Pupil   Relative           Length   Focus   Focus   Focus   Length   Diameter   Aperture                                                            Wide angle   28.81   27.27   22.06   0.372   9.9153   3.13   10       Telephoto   46.52   43.56   41.41   −0.147   9.9153   4.35   11                    
         [0055]    In wide angle, Example 6 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 35.87°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  28  has a focal length of 65.496 mm.  
         [0056]    In telephoto, Example 6 has a cylindrically curved image plane with a radius=−120.0; a semi-field of 24.70°; and a semi-diagonal of 21.63 (Illum.), 20.58 (Image). The first lens element  26  has a focal length of 40.000 mm, and the second lens element  32  has a focal length of −1060.655 mm.  
         [0057]    Referring to FIGS.  12 A- 12 B, MTF performance plots are measured at best focus using weighted wavelengths (440 nanometers at 15%, 546.1 nanometers at 50%, and 650 nanometers at 35%) at a frequency of 4.45 cycles per millimeter with full field (100%) being 20.58 mm. FIG. 12A shows MTF plots for Example 6 in wide angle format. FIG. 12B shows MTF plots for Example 6 in telephoto format. MTF plots are centered along the diagonal of the film cylinder (long dimension of 24×36 mm image format is measured along cylinder radius of curvature in all examples).  
         [0058]    FIGS.  14 A- 14 B describe additional performance characteristics of the variable focal length lens  20  of Example 6. FIG. 14A shows lateral color correction for Example 6 in wide angle format. FIG. 14B shows lateral color correction for Example 6 in telephoto format.  
         [0059]    The common lens element  26  of the two position variable focal length lens  20  has an image side surface S 2  that preferably satisfies the condition (1/−20.8)≦c≦(1/5), where c is the curvature of the image side surface. More preferably, the common lens element  26  satisfies the condition (1/−76)≦c≦(1/18.7), where c is the curvature of the image side surface S 2 . Still more preferably, the common lens element  26  satisfies the condition: (1/−100)≦c≦(1/25.5), where c is the curvature of the image side surface S 2 , and more preferably, the common lens element  26  satisfies the condition: c=0, where c is the curvature of the image side surface S 2  of the common lens element  26 .  
         [0060]    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 scope of the invention.