PATENT DOCUMENT

Abstract:
The invention relates to a zoom lens and an imaging apparatus incorporating the same, and more particularly to a zoom lens of small format that lends itself to imaging apparatus inclusive of video cameras and digital cameras. The zoom lens comprises, in order from its object side, a first lens group G 1  of positive refracting power, a second lens group G 2  of negative refracting power and a third lens group G 3  of positive refracting power. Zooming is implemented by changing the space between the respective lens groups. The first lens group G 1  comprises one negative lens and one positive lens in order from the object side. The zoom lens satisfies conditions (1) and (2):
 
5.0 &lt;f   t   /f   w &lt;50.0  (1)
 
1.4&lt;N d1p &lt;1.7  (2)
 
where f w  is the focal length of the whole zoom lens system at a wide-angle end, f t  is the focal length of the whole zoom lens system at a telephoto end, and N d1p  is the d-line refractive index of the positive lens in the first lens group.

Full Description:
This application claims benefit of Japanese Application No. 2007-224240 filed in Japan on Aug. 30, 2007, the content of which are incorporated by this reference. 
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to a zoom lens and an imaging apparatus incorporating the same, and more particularly to a zoom lens of small format that lends itself to imaging apparatus inclusive of video cameras and digital cameras. 
     In recent years, imaging apparatus such as digital cameras designed to take images of subjects using solid-state imaging devices such as CCDs or CMOSs have became mainstream in place of silver-halide film cameras. Further, they have now a wide spectrum of categories from the commercial high-end type to the compact low-end type. 
     The present invention gives weight to the compact low-end type category in particular. Users of such low-end type digital cameras would enjoy snapping shots over a wide range of scenes at anytime in anyplace. For this reason, preference is given to small-format digital cameras, especially of the type that can be well put away in the pockets of clothing or baggage, is convenient to carry around, and is slimmed down in their thickness direction, and there is a mounting demand for size reductions of taking lens systems, too. 
     On the other hand, as the pixels of imaging devices are now on the increase, there is an increasing demand for higher optical performance keeping pace with a lot more pixels. Further, to make sure mass productivity, it is required to minimize the sensitivity of optical performance deterioration to production errors in the process, of processing and assembling lenses. From the point of view of making taking ranges wide, high zooming lenses having zoom ratios exceeding 5 or 7, too, are generally available; much higher zoom ratios are expected, and so are wider-angle arrangements. 
     To meet such demands, there are now various types of zoom lenses proposed in the art. Among prior zoom lenses having relatively high zoom ratios and compact format, there is a type comprising, in order from its object side, a first lens group of positive refracting power, a second lens group of negative refracting power, a third lens group of positive refracting power and a fourth lens group of positive refracting power, as set forth in the following patent publications 1, 2 and 3. 
     [Patent Publication 1] 
     JP(A)2006-171055 
     [Patent Publication 2] 
     JP(A)11-52244 
     [Patent Publication 3] 
     JP(A)8-271788 
     Problems with the zoom lenses put forward in Patent Publications 1, 2 and 3 are, however, that as their total lens length gets short at increased zoom ratios, the effect of surface precision to aberration properties grows too large, resulting in difficulty with which lenses are processed, and an increase in lens fabrication costs. 
     Having being accomplished in view of such problems, the present invention has for its object to provide a zoom lens the total length of which is curtailed at increased zoom ratios, thereby reducing the ensuing effect of surface precision with good enough aberration properties, and an imaging apparatus incorporating the same. 
     SUMMARY OF THE INVENTION 
     According to the invention, the aforesaid object is accomplishable by the provision of a zoom lens comprising, in order from an object side thereof, a first lens group of positive refracting power, a second lens group of negative refracting power and a third lens group of positive refracting power, wherein zooming is implemented by changing the spacing between the respective lens groups, and said first lens group consist of, in order from the object side, one negative lens and one positive lens, with the satisfaction of the following conditions:
 
5.0 &lt;f   t   /f   w &lt;50.0  (1)
 
1.4&lt;N d1p &lt;1.7  (2)
 
where f w  is the focal length of the whole zoom lens system at a wide-angle end, f t  is the focal length of the whole zoom lens system at a telephoto end, and N d1p  is the d-line refractive index of the positive lens in the aforesaid first lens group.
 
     The requirements for, and the advantages of, such arrangement are now explained. 
     In the invention, the zoom lens comprises, in order from the object side, a first lens group of positive refracting power, a second lens group of negative refracting power and a third lens group of positive refracting power, and implements zooming by changing the spacing between the respective lens groups. Such arrangement permits the zoom function to be shared between the respective lens groups, and prevents an increase in the amounts of movement of the respective lens groups while minimizing aberration fluctuations during zooming, leading to a decrease in the size of the optical system. The location of one negative lens and one positive lens in the first lens group ensures good correction of aberrations. 
     As the upper limit to condition (1) is exceeded, it renders it difficult for the inventive arrangement to make sure sufficient optical performance. As the lower limit to condition (1) is not reached, the merit of the inventive arrangement in terms of size and cost is no longer obtained, because the object of the invention is achievable even with a simpler arrangement. 
     More preferably, condition (1) should be satisfied:
 
8.0 &lt;f   t   /f   w &lt;30.0  (1)
 
     Most preferably, condition (1) should be satisfied:
 
9.5 &lt;f   t   /f   w &lt;20.0  (1)
 
     To develop a small-format, high-zooming zoom lens that is easy to manufacture, the material for the positive lens in the first lens group should be selected in such a way as to satisfy condition (2). It is then possible to minimize deterioration of the performance due to fabrication errors from the lens surface shape in the first lens group. 
     Abiding by the upper limit of condition (2) provides an arrangement preferable for fabrication because of minimizing fabrication errors from the surface shape of the positive lens in the first lens group. Abiding by the lower limit of condition (2) makes sure availability of vitreous material and so prevents cost increases and facilitates mass fabrication. 
     More preferably, condition (2) should be satisfied:
 
1.42&lt;N d1p &lt;1.65  (2)
 
     Most preferably, condition (2) should be satisfied:
 
1.45&lt;N d1p &lt;1.6  (2)
 
     Furthermore, the invention as described above should preferably satisfy any one of the following requirements. 
     Preferably, the image-side surface in the first lens group should be configured in aspheric form having positive power becoming weak with a distance from an optical axis. It is then possible to minimize spherical aberrations and coma produced at the first lens group. It is here noted that the aforesaid arrangement renders distortion at the wide-angle end likely to grow large. However, this arrangement for the first lens group makes the most of its merit of achieving compactness when used with an electronic imaging apparatus designed to store distortion correction data for each zoom position and produce images with distortion reduced by image processing. 
     It is preferable to satisfy the following condition:
 
0.8&lt;(( R   pr   +R   pf )/( R   pr   −R   pf )+1)/ N   d1p &lt;1.4  (3)
 
where R pr  is the radius of curvature of the image-side surface of the positive lens in the aforesaid first lens group, R pf  is the radius of curvature of the object-side surface of the positive lens in the aforesaid first lens group, and N d1p  is the d-line refractive index of the positive lens in the aforesaid first lens group.
 
     To, during zooming, implement well-balanced correction of field curvature at the wide-angle end and coma at the telephoto end, it is preferable for the first lens group to have a −+ construction from the object side and satisfy the aforesaid condition, because various off-axis aberrations can be held back in a well-balanced state all over the zoom range. Most preferably, the positive lens in the first lens group should be configured in double-convex form having a larger radius of curvature on the image-plane side, because various off-axis aberrations can be minimized in a well-balanced state all over the zoom range. 
     Abiding by the upper limit of condition (3) makes sure the positive lens in the first lens group has power on the image plane side and the zoom lens has a large zoom ratio. Abiding by the lower limit of condition (3) enables the image plane-side power of the positive lens in the first lens group to diminish, and holds back axial field curvature and chromatic aberrations. It is also preferable for making sure the edge thickness of the positive lens in the first lens group. 
     More preferably, condition (3) should be satisfied:
 
1.0&lt;(( R   pr   +R   pf )/( R   pr   −R   pf )+1)/ N   d1p &lt;1.3  (3)
 
     Most preferably, condition (3) should be satisfied:
 
1.1&lt;(( R   pr   +R   pf )/( R   pr   −R   pf )+1)/ N   d1p &lt;1.2  (3)
 
     The negative and positive lenses in the first lens group may be cemented together. This allows for effective correction of axial chromatic aberration apt to become a problem when the focus length grows long at the telephoto end due to an increased zoom ratio. Further, it is possible to hold back deterioration of the optical performance from lens relative decentration due to assembly errors, contributing to yield improvements and cost decreases. 
     Alternatively, the negative and positive lenses in the first lens group may comprise independent lens components. This allows for more effective correction of distortion and coma at the wide-angle end, and coma at the telephoto end. 
     To keep the whole length of the zoom lens short at a long focus length at the telephoto end, the first lens group must have strong power. To correct aberrations from positive power, the negative lens must have a relatively high power, too; however, the radius of curvature of the negative lens is likely to become small. In the first lens group having positive refracting power, the negative lens is usually located on a high dispersion side for the need of correction of chromatic aberrations. 
     As the radius of curvature of the negative lens decreases, there is the likelihood of higher-order chromatic aberration of magnification. In particular, there is higher-order chromatic aberration of magnification produced under the influences of that high dispersion to such an extent that its amount exceeds that of chromatic aberrations produced from the positive lens, giving rise to some considerable deterioration of the quality of taken images. The more off the optical axis, the more that amount is, and the wider the angle of view at the wide-angle end, the more its influences show up: it is difficult to balance axial chromatic aberrations at the telephoto end against chromatic aberration of magnification. 
     For this reason, it is of vital importance to properly select the vitreous material for the negative lens in the first lens group. Specifically, it is preferable for the vitreous material for the negative lens in the first lens group to satisfy the following conditions (4) and (5):
 
1.99&lt;N d1n &lt;2.3  (4)
 
13.0&lt;ν d1n &lt;35.0  (5)
 
0.02 &lt;d   1n   /d   1p &lt;0.35  (6)
 
where N d1n  is the d-line refractive index of the negative lens in the aforesaid first lens group, ν d1n  is the Abbe constant of the negative lens in the aforesaid first lens group, d 1n  is the axial thickness of the negative lens in the aforesaid first lens group, and d 1p  is the axial thickness of the positive lens in the aforesaid first lens group.
 
     Abiding by the upper limit of condition (4) makes sure availability of vitreous material, averts cost increases, and allows for easy mass fabrication. Abiding by the lower limit of condition (4) prevents the radius of curvature of the negative lens from getting small, and holds back the occurrence of off-axis chromatic aberration of magnification. It also makes sure the negative lens has negative power, working for correction of spherical aberrations, coma and other aberrations produced at the positive lens. 
     More preferably, condition (4) should be satisfied:
 
2.04&lt;N d1n &lt;2.25  (4)
 
     Most preferably, condition (4) should be satisfied:
 
2.08&lt;N d1n &lt;2.20  (4)
 
     Further, condition (4) may be satisfied:
 
1.92&lt;N d1n &lt;2.3  (4)
 
     Furthermore, condition (4) may be satisfied:
 
1.94&lt;N d1n &lt;2.3  (4)
 
     Abiding by the upper limit of condition (5) allows for an arrangement preferable for correction of axial chromatic aberration. Abiding by the lower limit of condition (5) is preferable for prevention of the partial dispersion ratio of the vitreous material from growing high, holding back the occurrence of chromatic aberrations on a short wavelength side, and correction of secondary spectral correction of chromatic aberrations. 
     More preferably, condition (5) should be satisfied:
 
14.0&lt;ν d1n &lt;32.0  (5)
 
     Most preferably, condition (5) should be satisfied:
 
15.0&lt;ν d1n &lt;30.0  (5)
 
     For such reasons as described above, if conditions (4) and (5) are satisfied, then it is possible to easily achieve a small-format, high-zooming optical system that has improved optical performance. 
     Condition (6) is to implement well-balanced correction of chromatic aberration of magnification and axial chromatic aberration at the telephoto end. Abiding by the upper limit of condition (6) allows for an arrangement preferable for averting overcorrection of chromatic aberration of magnification, and correction of axial chromatic aberration at the telephoto end. Abiding by the lower limit of condition (6) allows for an arrangement for averting overcorrection of axial chromatic aberration at the telephoto end, and correction of chromatic aberration of magnification as well. It prevents the negative lens from running short of strength, and facilitates lens fabrication. 
     More preferably, condition (6) should be satisfied:
 
0.03 &lt;d   1n   /d   1p &lt;0.30  (6)
 
     Most preferably, condition (6) should be satisfied:
 
0.04 &lt;d   1n   /d   1p &lt;0.25  (6)
 
     The negative lens in the first lens group may as well be configured in meniscus form convex on its object side. It is then possible to decrease the angle of incidence of off-axis rays on the lens surface, thereby minimizing the aberrations produced. 
     It is then preferable to satisfy the following condition (7):
 
−15.0&lt;( R   nr   +R   nf )/( R   nr   −R   nf )&lt;−1.0  (7)
 
where R nr  is the radius of curvature of the image plane-side of the negative lens in the aforesaid first lens group, and R nf  is the radius of curvature of the object side of the negative lens in the aforesaid first lens group.
 
     Abiding by the upper limit of condition (7) is preferable for holding back the occurrence of higher-order chromatic aberrations with no need of extremely reducing the radius of curvature of both lens surfaces to maintain the negative power. Abiding by the lower limit of condition (7) provides an arrangement for making sure the negative lens has negative power so that aberrations from the positive lens in this group can be fully canceled out. 
     More preferably, condition (7) should be satisfied:
 
−12.0&lt;( R   nr   +R   nf )/( R   nr   −R   nf )&lt;−4.0  (7)
 
     Most preferably, condition (7) should be satisfied:
 
−9.3&lt;( R   nr   +R   nf )/( R   nr   −R   nf )&lt;−7.5  (7)
 
     With the first lens group comprising two lenses, it is preferable for the first lens group to have as high a refractive index as possible and for an Abbe constant difference between the negative lens and the positive lens to be as large as possible, because monochromatic aberrations and chromatic aberrations are reduced while allowing the first lens group to have a relatively strong positive power, thereby obtaining good enough aberration performance. To this end, it is preferable to satisfy the following conditions (8) and (9) with respect to the vitreous material for the negative and positive lenses:
 
0.20 &lt;N   d1n   −N   d1p &lt;0.70  (8)
 
35&lt;ν d1p −ν d1n &lt;80  (9)
 
where N d1n  is the d-line refractive index of the negative lens in the aforesaid first lens group, ν d1n  is the Abbe constant of the negative lens in the aforesaid first lens group, N d1p  is the d-line refractive index of the positive lens in the aforesaid first lens group, and ν d1p  is the Abbe constant of the positive lens in the aforesaid first lens group.
 
     Abiding by the upper limit of condition (8) provides an arrangement preferable for keeping the refractive index of the positive lens from going down and the radius of curvature of the lens surface from getting small, thereby holding back the occurrence of coma that is likely to occur at the telephoto end in particular. Abiding by the lower limit of condition (8) provides an arrangement preferable for preventing the refractive index of the positive lens in the first lens group from growing too high, thereby making sure an Abbe constant difference between the positive lens and the negative lens and so implementing good enough correction of chromatic aberrations. 
     More preferably, condition (8) should be satisfied:
 
0.30 &lt;N   d1n   −N   d1p &lt;0.65  (8)
 
     Most preferably, condition (8) should be satisfied:
 
0.40 &lt;N   d1n   −N   d1p &lt;0.60  (8)
 
     Abiding by the upper limit of condition (9) provides an arrangement preferable for preventing the refractive index of the positive lens from going down and so preventing the radius of curvature of the lens surface from getting small, thereby holding back the occurrence of coma that is likely to occur at the telephoto end in particular. As the radius of curvature of the lens surface grows large, it gives rise to excessive coma at the telephoto end in particular. Abiding by the lower limit of condition (9) provides an arrangement preferable for preventing the refractive index of the positive lens in the first lens group from growing too high, thereby making sure an Abbe constant difference between the positive lens and the negative lens and so implementing good enough correction of chromatic aberrations. 
     More preferably, condition (9) should be satisfied:
 
37&lt;ν d1p −ν d1n &lt;75  (9)
 
     Most preferably, condition (9) should be satisfied:
 
40&lt;ν d1p −ν d1n &lt;70  (9)
 
     The inventive zoom lens should preferably satisfy the following condition with respect to the power of the first lens group:
 
0.2 &lt;f   1   /f   t &lt;1.0  (10)
 
where f 1  is the focal length of the aforesaid first lens group, and f t  is the focal length of the whole zoom lens system at the telephoto end.
 
     Abiding by the upper limit of condition (10) is preferable for keeping the power of the first lens group from getting small and shortening the total length of the whole zoom lens system, thereby reducing the size of the lens barrel. Abiding by the lower limit of condition (10) is preferable for preventing the power of the first lens group from growing too strong and holding back the occurrence of spherical aberrations and coma at the telephoto end, thereby making sure good enough optical performance. 
     More preferably, condition (10) should be satisfied:
 
0.5 &lt;f   1   /f   t &lt;0.8  (10)
 
     Most preferably, condition (10) should be satisfied:
 
0.6 &lt;f   1   /f   t &lt;0.75  (10)
 
     The inventive zoom lens may as well satisfy the following condition with respect to the focal length of the second lens group:
 
−0.5 &lt;f   2   /f   t &lt;−0.05  (11)
 
where f 2  is the focal length of the aforesaid second lens group, and f t  is the focal length of the whole zoom lens system at the telephoto end.
 
     This condition is about the balance between size reductions and aberration performance. Abiding by the upper limit of condition (11) provides an arrangement preferable for preventing the power of the second lens group from growing too strong and holding back the occurrence of various off-axis aberrations at the wide-angle end and spherical aberrations at the telephoto end. Abiding by the lower limit of condition (11) is preferable for preventing the power of the second lens group from getting too weak and reducing the size of the whole lens system. 
     More preferably, condition (11) should be satisfied:
 
−0.2 &lt;f   2   /f   t &lt;−0.10  (11)
 
     Most preferably, condition (11) should be satisfied:
 
−0.15 &lt;f   2   /f   t &lt;−0.13  (11)
 
     The inventive zoom lens system may as well be of a four-group arrangement comprising, in order from its object side, a first lens group of positive refracting power, a second lens group of negative refracting power, a third lens group of positive refracting power and a fourth lens group of positive refracting power. The location of the fourth lens group of positive refracting power on the image plane side of the third lens group makes it easy to locate an exit pupil at a far position, and can reduce a decrease in rim light due to compatibility with an imaging device. 
     Referring to the zooming operation from the wide-angle end to the telephoto end of a zoom lens optical system comprising four lens groups with an aperture stop located in place, it is preferable that the first lens group moves such that it is positioned more on the object side at the telephoto end than at the wide-angle end; the second lens group moves; the third lens group moves such that it is positioned more on the object side at the telephoto end than at the wide-angle end; the fourth lens group moves; the fourth lens group moves; and the aforesaid aperture stop moves. In this case, the first lens group may move toward the object side alone or toward the object or image side in a convex locus; the second lens group may move toward the object side alone or toward the object or image side in a convex locus; the third lens group may move toward the object side alone or toward the object side in a convex locus; and the fourth lens group may move such that it is positioned more on the object or image side at the telephoto end than at the wide-angle end, or toward the object or image side monotonously or in a convex locus. 
     Alternatively, the inventive zoom lens may just as well be of a five-group arrangement comprising, in order from the object side, a positive first lens group, a negative second lens group, a positive third lens group, a negative fourth lens group and a positive fifth lens group. Referring to the zooming operation from the wide-angle end to the telephoto end of a zoom lens optical system further comprising an aperture stop, it is preferable that the first lens group moves such that it is positioned more on the object side at the telephoto end than at the wide-angle end; the second lens group moves; the third lens group moves such that it is positioned more on the object side at the telephoto end than at the wide-angle end; the fourth lens group moves; the fifth lens group moves; and the aforesaid aperture stop moves. 
     In that case, the first lens group may move toward the object side alone or toward the object or image side in a convex locus; the second lens group may move toward the object side alone or toward the object or image side in a convex locus; the third lens group may move toward the object side alone or toward the object or image side in a convex locus; the fourth lens group may move toward the object side alone or toward the object or image side in a convex locus; and the fifth lens group may move such that it is positioned more on the object or image side at the telephoto end than at the wide-angle end, or toward the object or image side monotonously or in a convex locus. 
     Preferably, the aperture stop and a shutter unit are located between the second lens group and the third lens group, and they move in unison with the third lens group during zooming. This enables the entrance pupil to be positioned at a position near to the object side, and the exit pupil to be away from the exit plane. The position where these components are located is also where the height of off-axis rays goes down: the shutter unit is prevented from getting bulky, and there is a decrease in the dead space in moving the aperture stop and shutter unit. By moving all the lens groups in this way, the zoom function can be effectively shared between the respective lens groups, and even a wide-angle, high-zoom arrangement can perform better. By the movement of the aperture stop, not only is it possible to improve performance by effective correction of chromatic aberration of magnification and distortion, but it is also possible to gain proper control of both the entrance pupil position and the exit pupil position. More specifically, it is possible to attain a sensible balance between the heights of off-axis light beams at the wide-angle end and the telephoto end: the outer diameter of the first lens group and the outer diameter of the lens group located nearest to the image side can be kept compact in a well-balanced state. Reducing the outer diameter of the first lens group at the wide-angle end in particular would lead to a reduction in the size of the zoom lens in the thickness direction. It is also possible to control the zoom lens such that there is a decrease in fluctuations of the exit pupil position during zooming: it is possible to maintain the angle of incidence of light rays on a CCD, CMOS or the like in a suitable range, thereby getting around shading at the corners of the screen and, hence, using the zoom lens with an electronic imaging apparatus. 
     The inventive zoom lens should preferably be composed of a total of up to 9 lenses. A lot more lenses give rise to increases in the size and cost of the zoom lens system. 
     By the incorporation of an imaging device adapted to covert an image formed through the zoom lens into electric signals, it is possible to provide an electronic imaging apparatus that satisfies the requirements for size reductions, high zoom ratios and a wide-angle arrangement, and allows to the quality of taken images to be well and easily maintained. 
     The inventive zoom lens should preferably satisfy the following condition:
 
0.5 &lt;I   mw   /f   w &lt;1.0  (12)
 
where I mw  is an image height at the wide-angle end, and f w  is the focal length of the whole zoom lens system at the wide-angle end.
 
     As the upper limit of condition (12) is exceeded, it is difficult to make sure sufficient optical performance with the inventive arrangement. As the lower limit of condition (12) is not reached, the inventive arrangement can no longer make the most of its own merit of achieving size and cost reductions, because the object of the invention is accomplishable even with a simpler arrangement. 
     More preferably, condition (12) should be satisfied:
 
0.6 &lt;I   mw   /f   w &lt;0.95  (12)
 
     Most preferably, condition (12) should be satisfied:
 
0.7 &lt;I   mw   /f   w &lt;0.8  (12)
 
     The inventive zoom lens should preferably satisfy the following condition with respect to its total length.
 
5.0 &lt;L   t   /I   mw &lt;17.5  (13)
 
where L t  is the total length of the whole zoom lens system at the telephoto end, and I mw  is an image height at the wide-angle end.
 
     Abiding by the upper limit of condition (13) provides an arrangement preferable for preventing the total length of the lens system from getting long, thereby making the size of the lens barrel small upon received at a lens mount. Abiding by the lower limit of condition (13) works favorably for preventing the power of each lens group from growing too strong, thereby reducing the amount of various aberrations produced. 
     More preferably, condition (13) should be satisfied:
 
8.0 &lt;L   t   /I   mw &lt;16.8  (13)
 
     Most preferably, condition (13) should be satisfied:
 
14.0 &lt;L   t   /I   mw &lt;16.0  (13)
 
     It is also preferable to have an image transformation block wherein electric signals containing distortion from the zoom lens are transformed into image signals with distortion corrected by image processing. The toleration of the distortion from the zoom lens would work more for a decrease in the number of lenses and its size reductions. 
     Furthermore, it is preferable to have an image transformation block wherein image processing is applied to electric signals containing distortion from the zoom lens, thereby implementing distortion correction with a value changed for each color so that distortion and chromatic aberration of magnification can be corrected. The toleration of the distortion and chromatic aberration of magnification of the zoom lens would work more for a decrease in the number of lenses and its size reductions. 
     As can be appreciated from the foregoing explanation, the invention provides a zoom lens that, albeit having an increased zoom ratio, can be reduced in terms of its total length, and the ensuing surface precision is kept from showing up so that good enough aberration properties are obtainable. 
     Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification. 
     The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is illustrative in lens arrangement section of Example 1 of the inventive zoom lens at the wide-angle end (a), in an intermediate state (b) and at the telephoto end (c) upon focusing on an object point at infinity. 
         FIG. 2  is illustrative, as in  FIG. 1 , of Example 2 of the inventive zoom lens. 
         FIG. 3  is illustrative, as in  FIG. 1 , of Example 3 of the inventive zoom lens. 
         FIG. 4  is illustrative, as in  FIG. 1 , of Example 4 of the inventive zoom lens. 
         FIG. 5  is illustrative, as in  FIG. 1 , of Example 5 of the inventive zoom lens. 
         FIG. 6  is illustrative, as in  FIG. 1 , of Example 6 of the inventive zoom lens. 
         FIG. 7  is illustrative, as in  FIG. 1 , of Example 7 of the inventive zoom lens. 
         FIG. 8  is illustrative, as in  FIG. 1 , of Example 8 of the inventive zoom lens. 
         FIG. 9  is illustrative, as in  FIG. 1 , of Example 9 of the inventive zoom lens. 
         FIG. 10  is illustrative, as in  FIG. 1 , of Example 10 of the inventive zoom lens. 
         FIG. 11  is an aberration diagram for Example 1 upon focusing on an object point at infinity. 
         FIG. 12  is an aberration diagram for Example 2 upon focusing on an object point at infinity. 
         FIG. 13  is an aberration diagram for Example 3 upon focusing on an object point at infinity. 
         FIG. 14  is an aberration diagram for Example 4 upon focusing on an object point at infinity. 
         FIG. 15  is an aberration diagram for Example 5 upon focusing on an object point at infinity. 
         FIG. 16  is an aberration diagram for Example 6 upon focusing on an object point at infinity. 
         FIG. 17  is an aberration diagram for Example 7 upon focusing on an object point at infinity. 
         FIG. 18  is an aberration diagram for Example 8 upon focusing on an object point at infinity. 
         FIG. 19  is an aberration diagram for Example 9 upon focusing on an object point at infinity. 
         FIG. 20  is an aberration diagram for Example 10 upon focusing on an object point at infinity. 
         FIG. 21  is a front perspective view of the outside shape of a digital camera according to the invention. 
         FIG. 22  is a rear perspective view of the digital camera of  FIG. 21 . 
         FIG. 23  is a sectional view of the digital camera of  FIG. 21 . 
         FIG. 24  is a block diagram illustrative of the construction of internal circuits in part of the digital camera of  FIG. 21 . 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following examples that underlies the invention, there are less costly zoom lens optical system provided, which, through such tweaks as described above, meet simultaneously the requirements for a downsized arrangement and a wide-angle/higher zoom ratio arrangement for cameras that satisfy users demands for making the taking area involved wider than ever before without detrimental to the ability of cameras to be carried around, enable the quality of taken images to be well maintained, and lend themselves to electronic imaging devices such as CCDs or CMOSs. 
     The following examples are each directed to a zoom lens of the type wherein lenses are let out at the startup of an imaging apparatus as well as an imaging apparatus incorporating the same. More exactly, Examples 1 to 20 each provide a zoom lens having higher optical performance and improved in terms of compactness. Throughout Examples 1 to 20, the effective imaging area is of constant rectangular shape in all zooming states. In the respective examples, the values for the specific conditions have been found at the time of focusing on an object point at infinity. Total Length is the axial distance from the entrance surface to the exit surface of the zoom lens plus a back focus as calculated on an air basis. 
     The zoom lens of the invention is now explained with reference to Examples 1 to 10.  FIGS. 1 to 10  are illustrative in lens arrangement section of Examples 1 to 10 at the wide-angle ends (a), in the intermediate states (b) and at the telephoto ends (c) upon focusing on an object point at infinity. Throughout  FIGS. 1 to 10 , G 1  stands for the first lens group; G 2  the second lens group; S an aperture stop; G 3  the third lens group; G 4  the fourth lens group; G 5  the fifth lens group; F an optical low-pass filter; C the cover glass of a CCD that is an electronic imaging device; and I the image plane of the CCD. Note here that for a near infrared sharp cut coating, for instance, it may be coated directly on the optical low-pass filter F or, alternatively, there may be another infrared cut absorption filter located. 
     It is here noted that drawings for Examples 11 to 20 are not attached hereto because they are similar in construction to Examples 1 to 10, respectively. 
     Example 1 
     Example 1 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power, the fourth lens group G 4  of positive refracting power and the fifth lens group G 5  of negative refracting power, as shown in  FIG. 1 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. Throughout Examples 1 to 10, the intermediate state is defined as the point of change in the direction of movement of the second lens group G 2 , the third lens group G 3  or the fourth lens group G 4  from the wide-angle end to the telephoto end. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned more on the object side than at the wide-angle end, and at the telephoto end, it is positioned a little more on the image side than at the wide-angle end. 
     From the wide-angle end to the telephoto end, the aperture stop S and the third lens group G 3  move in unison toward the object side. 
     From the wide-angle end to the intermediate state, the fourth lens group G 4  moves toward the object side while the spacing between the third lens group G 3  and it grows wide and the spacing between it and the fifth lens group G 5  becomes narrow, and from the intermediate state to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide and the spacing between it and the fifth lens group G 5  becomes narrow. In the intermediate state, the fourth lens group G 4  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a double-convex positive lens and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a negative meniscus lens convex on its object side; the fourth lens group G 4  is made up of one double-convex positive lens; and the fifth lens group G 5  is made up of one negative meniscus lens convex on its image side. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side of the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , one at the image-side surface of the negative meniscus lens in the third lens group G 3 , and one at the object-side surface of the negative meniscus lens in the fifth lens group G 5 . 
     Example 2 
     Example 2 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 2 . 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side at the wide-angle end and more on the image side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a double-convex positive lens and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a positive meniscus lens convex on its image side. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , one at the image-side surface of the negative meniscus lens in the third lens group G 3 , and one at the image-side surface of the positive meniscus lens in the fourth lens group G 4 . 
     Example 3 
     Example 3 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 3 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a positive meniscus lens convex on its image side and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a cemented lens of a positive meniscus lens convex on its object side and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a double-convex positive lens. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , and two at both surfaces of the double-convex positive lens in the fourth lens group G 4 . 
     Example 4 
     Example 4 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 4 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned a little more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a positive meniscus lens convex on its image side and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a cemented lens of a positive meniscus lens convex on its object side and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a double-convex positive lens. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , and two at both surfaces of the double-convex positive lens in the fourth lens group G 4 . 
     Example 5 
     Example 5 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 5 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side than at the intermediate state and a little more on the image side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a double-convex positive lens and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a positive meniscus lens convex on its image side. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , one at the image side-surface of the negative meniscus lens in the third lens group G 3 , and one at the image-side surface of the positive meniscus lens in the fourth lens group G 4 . 
     Example 6 
     Example 6 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 6 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the image side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned a little more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a positive meniscus lens convex on its image side and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a cemented lens of a positive meniscus lens convex on its object side and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a double-convex positive lens. 
     Eight aspheric surfaces are used: one at the image-side surface of the double-convex positive lens in the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , and two at both surfaces of the double-convex positive lens in the fourth lens group G 4 . 
     Example 7 
     Example 7 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 7 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned a little more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens, a positive meniscus lens convex on its image side and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a cemented lens of a positive meniscus lens convex on its object side and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a double-convex positive lens. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens on the object side of the second lens group G 2 , one at the image-side surface of the double-concave negative lens on the image side of the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , and two at both surfaces of the double-convex positive lens in the fourth lens group G 4 . 
     Example 8 
     Example 8 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 8 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned a little more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     From the wide-angle end to the intermediate state, the aperture stop S and the third lens group G 3  move toward the object side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide, and from the intermediate state to the telephoto end, they move toward the image side while the spacing between the second lens group G 2  and them becomes narrow and the spacing between them and the fourth lens group G 4  grows wide. In the intermediate state, they are positioned more on the object side than at the wide-angle end and at the telephoto end, they are positioned more on the object side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide. In the intermediate state, the fourth lens group G 4  is positioned a little more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     In order from the object side, the first lens group G 1  is made up of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens, a positive meniscus lens convex on its image side and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a cemented lens of a positive meniscus lens convex on its object side and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of a double-convex positive lens. 
     Eight aspheric surfaces are used: one at the image-side surface of the double-convex positive lens in the first lens group G 1 , two at both surfaces of the double-concave negative lens on the object side of the second lens group G 2 , one at the image-side surface of the double-concave negative lens on the image side of the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , and two at both surfaces of the double-convex positive lens in the fourth lens group G 4 . 
     Example 9 
     Example 9 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 9 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the object side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state 
     From the wide-angle end to the telephoto end, the aperture stop S and the third lens group G 3  move in unison toward the object side. 
     From the wide-angle end to the intermediate state, fourth lens group G 4  moves toward the object side while the spacing between the third lens group G 3  and it groves wide and the spacing between it the fifth lens group G 5  grows wide, and from the intermediate state to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide and the spacing while it and the fifth lens group G 5  becomes narrow. In the intermediate state, the fourth lens group G 4  is positioned more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wise-angle end. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a double-convex positive lens and a double-concave negative lens; the third lens group G 3  is made up of a double-convex positive lens and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of one double-convex positive lens. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , one at the image side-surface of the negative meniscus lens in the third lens group G 3 , and one at the object-side surface of the double-convex positive lens in the fourth lens group G 4 . 
     Example 10 
     Example 10 is directed to a zoom lens made up of, in order from its object side, the first lens group G 1  of positive refracting power, the second lens group G 2  of negative refracting power, the aperture stop S, the third lens group G 3  of positive refracting power and the fourth lens group G 4 , as shown in  FIG. 10 . 
     Upon zooming from the wide-angle end to the telephoto end, the respective lens groups move as follows. 
     The first lens group G 1  moves toward the object side from the wide-angle end to the telephoto end. 
     From the wide-angle end to the intermediate state, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow and, from the intermediate state to the telephoto end, the second lens group G 2  moves toward the image side while the spacing between the first lens group G 1  and it grows wide and the spacing between it and the third lens group G 3  becomes narrow. In the intermediate state, the second lens group G 2  is positioned more on the image side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than in the intermediate state. 
     From the wide-angle end to the telephoto end, the aperture stop S and the third lens group G 3  move in unison toward the object side. 
     From the wide-angle end to the intermediate state, the fourth lens group G 4  moves toward the object side while the spacing between the third lens group G 3  and it grows wide and the spacing between it and the fifth lens group G 5  grows wide, and from the intermediate state to the telephoto end, the fourth lens group G 4  moves toward the image side while the spacing between the third lens group G 3  and it grows wide and the spacing between it and the fifth lens group G 5  becomes narrow. In the intermediate state, the fourth lens group G 4  is positioned more on the object side than at the wide-angle end, and at the telephoto end, it is positioned more on the image side than at the wide-angle end. 
     In order from the object side, the first lens group G 1  is made up of a cemented lens of a negative meniscus lens convex on its object side and a double-convex positive lens; the second lens group G 2  is made up of a double-concave negative lens and a cemented lens of a positive meniscus lens convex on its image side and a negative meniscus lens convex on its image side; the third lens group G 3  is made up of a double-convex positive lens and a negative meniscus lens convex on its object side; and the fourth lens group G 4  is made up of one double-convex positive lens. 
     Eight aspheric surfaces are used: one at the surface of the cemented lens located in, and nearest to the image side of, the first lens group G 1 , two at both surfaces of the double-concave negative lens in the second lens group G 2 , one at the surface of the cemented lens nearest to the image side in the second lens group G 2 , two at both surfaces of the double-convex positive lens in the third lens group G 3 , one at the image-side surface of the negative meniscus lens in the third lens group G 3 , and one at the object-side surface of the double-convex positive lens in the fourth lens group G 4 . 
     Set out below are the numerical data about the zoom lens of each example. 
     With regard to Examples 11 to 20 similar in construction to Examples 1 to 10, there are only zoom lens data shown. 
     Symbols mentioned hereinafter but not hereinbefore have the following meanings:
         r is the radius of curvature of each lens surface,   d is the space between adjoining lens surfaces,   n is the d-line refractive index of each lens,   νd is the d-line Abbe constant of each lens,   K is the conic coefficient,   A4, A6, A8, and A10 is the aspheric coefficient, and   E±n is ×10 ±n .       

     Note here that each aspheric surface is given by the following equation using each aspheric coefficient in each example.
 
 Z =( Y   2   /r )/[1+{1−( K+ 1)·( Y/r ) 2 } 1/2   ]+A 4 ×Y   4   +A 6 ×Y   6   +A 8 ×Y   8   +A 10 ×Y   10  
 
Here Z is the coordinates in the optical axis direction, and Y is the coordinates in a direction vertical to the optical axis.
 
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 1 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 18.671 
                 0.80 
                 1.94595 
                 17.98 
               
               
                  2 
                 16.177 
                 3.85 
                 1.49700 
                 81.54 
               
               
                  3 (Aspheric surface) 
                 −66.153 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −24.070 
                 0.80 
                 1.85135 
                 40.10 
               
               
                  5 (Aspheric surface) 
                 5.779 
                 2.57 
               
               
                  6 
                 59.959 
                 1.60 
                 2.00170 
                 20.64 
               
               
                  7 
                 −12.272 
                 0.60 
                 1.77250 
                 49.60 
               
               
                  8 (Aspheric surface) 
                 54.857 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 4.180 
                 2.35 
                 1.49700 
                 81.54 
               
               
                 11 (Aspheric surface) 
                 −14.626 
                 0.10 
               
               
                 12 
                 5.823 
                 0.70 
                 2.00170 
                 20.64 
               
               
                 13 (Aspheric surface) 
                 3.620 
                 Variable 
               
               
                 14 
                 62.555 
                 1.60 
                 1.76802 
                 49.24 
               
               
                 15 
                 −20.469 
                 Variable 
               
               
                 16 (Aspheric surface) 
                 −46.810 
                 0.40 
                 1.52542 
                 55.78 
               
               
                 17 
                 −75.059 
                 0.50 
               
               
                 18 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 19 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 2.04323E−05, A6 = −3.00803E−08 
               
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.18050E−03, A6 = −4.90687E−05, A8 = 9.80445E−07, 
               
               
                 A10 = −8.25305E−09 
               
               
                 5th surface 
               
               
                 K = 0.000, A4 = 1.21707E−03, A6 = 3.60823E−05, A8 = −2.55122E−06, 
               
               
                 A10 = −1.82263E−08 
               
               
                 8th surface 
               
               
                 K = 0.000, A4 = −4.99108E−04, A6 = −1.60668E−05, 
               
               
                 A8 = 4.60705E−07, A10 = −4.90352E−09 
               
               
                 10th surface 
               
               
                 K = 0.000, A4 = −1.33737E−03, A6 = −2.81594E−05, 
               
               
                 A8 = −3.78589E−06, A10 = −7.30724E−08 
               
               
                 11th surface 
               
               
                 K = 0.000, A4 = 9.13071E−04, A6 = −6.38110E−05, A8 = 2.56974E−06, 
               
               
                 A10 = −2.74414E−08 
               
               
                 13th surface 
               
               
                 K = 0.000, A4 = −2.41554E−05, A6 = 8.05573E−05 
               
               
                 16th surface 
               
               
                 K = −0.082, A4 = 3.20633E−05, A6 = 3.75035E−07 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.11 
                 14.96 
                 47.81 
               
               
                   
                 F-number 
                 3.54 
                 5.23 
                 6.00 
               
               
                   
                 Angle of view 
                 82.08 
                 28.58 
                 9.08 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 40.02 
                 50.29 
                 57.26 
               
               
                   
                 BF 
                 1.19 
                 1.16 
                 1.28 
               
               
                   
                 d3 
                 0.30 
                 8.11 
                 18.43 
               
               
                   
                 d8 
                 12.41 
                 5.40 
                 1.14 
               
               
                   
                 d13 
                 4.28 
                 13.50 
                 17.72 
               
               
                   
                 d15 
                 6.16 
                 6.44 
                 3.03 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.87 
               
               
                 2 
                 4 
                 −6.53 
               
               
                 3 
                 10 
                 11.08 
               
               
                 4 
                 14 
                 20.15 
               
               
                 5 
                 16 
                 −236.87 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 2 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 21.257 
                 0.80 
                 1.94595 
                 17.98 
               
               
                  2 
                 18.209 
                 3.85 
                 1.49700 
                 81.54 
               
               
                  3 (Aspheric surface) 
                 −66.917 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −22.219 
                 0.80 
                 1.76802 
                 49.24 
               
               
                  5 (Aspheric surface) 
                 5.481 
                 1.89 
               
               
                  6 
                 74.445 
                 1.60 
                 1.94595 
                 17.98 
               
               
                  7 
                 −23.299 
                 0.60 
                 1.76802 
                 49.24 
               
               
                  8 (Aspheric surface) 
                 215.699 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 4.226 
                 2.35 
                 1.49700 
                 81.54 
               
               
                 11 (Aspheric surface) 
                 −16.223 
                 0.10 
               
               
                 12 
                 5.044 
                 0.70 
                 2.00170 
                 20.64 
               
               
                 13 (Aspheric surface) 
                 3.439 
                 Variable 
               
               
                 14 
                 −21.102 
                 1.60 
                 1.51825 
                 64.14 
               
               
                 15 (Aspheric surface) 
                 −8.879 
                 Variable 
               
               
                 16 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 17 
                 ∞ 
                 0.50 
               
               
                 18 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 19 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 1.43757E−05, A6 = −1.36130E−08 
               
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.21703E−03, A6 = −5.46492E−05, A8 = 1.04169E−06, 
               
               
                 A10 = −7.77129E−09 
               
               
                 5th surface 
               
               
                 K = 0.000, A4 = 1.04613E−03, A6 = 3.25777E−05, A8 = −2.65926E−06, 
               
               
                 A10 = −1.84775E−08 
               
               
                 8th surface 
               
               
                 K = 0.000, A4 = −4.17728E−04, A6 = −2.92962E−05, 
               
               
                 A8 = 4.40061E−07, A10 = −4.99489E−09 
               
               
                 10th surface 
               
               
                 K = 0.000, A4 = −1.10207E−03, A6 = −2.77492E−05, 
               
               
                 A8 = −3.77816E−06, A10 = −7.30453E−08 
               
               
                 11th surface 
               
               
                 K = 0.000, A4 = 9.87282E−04, A6 = −6.65232E−05, A8 = 2.56751E−06, 
               
               
                 A10 = −2.74580E−08 
               
               
                 13th surface 
               
               
                 K = 0.000, A4 = −1.52619E−05, A6 = 8.16567E−05 
               
               
                             15           
               
               
                 K = −2.836 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.26 
               
               
                   
                 F-number 
                 3.35 
                 4.87 
                 5.00 
               
               
                   
                 Angle of view 
                 81.14 
                 27.47 
                 8.45 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 39.80 
                 48.84 
                 56.76 
               
               
                   
                 BF 
                 7.38 
                 7.17 
                 4.95 
               
               
                   
                 d3 
                 0.30 
                 9.12 
                 22.08 
               
               
                   
                 d8 
                 13.26 
                 6.10 
                 1.46 
               
               
                   
                 d13 
                 4.26 
                 11.86 
                 13.69 
               
               
                   
                 d15 
                 5.89 
                 5.69 
                 3.47 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 36.74 
               
               
                 2 
                 4 
                 −6.49 
               
               
                 3 
                 10 
                 10.09 
               
               
                 4 
                 14 
                 28.20 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 3 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 20.909 
                 0.80 
                 2.00170 
                 20.64 
               
               
                  2 
                 16.720 
                 3.62 
                 1.61881 
                 63.85 
               
               
                  3 (Aspheric surface) 
                 −99.283 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −76.528 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  5 (Aspheric surface) 
                 7.133 
                 2.58 
               
               
                  6 
                 −206.923 
                 1.63 
                 2.10225 
                 16.79 
               
               
                  7 
                 −18.640 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  8 (Aspheric surface) 
                 54.142 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 5.593 
                 2.49 
                 1.69350 
                 53.21 
               
               
                 11 (Aspheric surface) 
                 −19.473 
                 0.08 
               
               
                 12 
                 5.572 
                 1.46 
                 1.49700 
                 81.54 
               
               
                 13 
                 37.089 
                 0.71 
                 2.00330 
                 28.27 
               
               
                 14 
                 3.573 
                 Variable 
               
               
                 15 (Aspheric surface) 
                 32.825 
                 3.00 
                 1.74330 
                 49.33 
               
               
                 16 (Aspheric surface) 
                 −14.479 
                 Variable 
               
               
                 17 
                 ∞ 
                 0.40 
                 1.54771 
                 62.84 
               
               
                 18 
                 ∞ 
                 0.50 
               
               
                 19 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 20 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 1.14689E−05, A6 = 4.83606E−09, A8 = −2.02752E−10, 
               
               
                 A10 = 7.85884E−13 
               
               
                 4th surface 
               
               
                 K = 9.178, A4 = 8.86386E−05, A6 = −2.97753E−06, A8 = 4.62415E−08, 
               
               
                 A10 = −3.04205E−10 
               
               
                 5th surface 
               
               
                 K = 0.265, A4 = 1.50448E−04, A6 = 6.43712E−06, A8 = −2.33528E−07, 
               
               
                 A10 = −2.66160E−09 
               
               
                 8th surface 
               
               
                 K = −1.493, A4 = −3.07535E−04, A6 = −4.47187E−06, 
               
               
                 A8 = 2.37774E−07, A10 = −5.43727E−09 
               
               
                 10th surface 
               
               
                 K = 0.822, A4 = −1.07173E−03, A6 = −3.12892E−05, 
               
               
                 A8 = −1.48549E−06, A10 = −1.40758E−08 
               
               
                 11th surface 
               
               
                 K = −3.282, A4 = 4.48842E−04, A6 = 3.09551E−06, 
               
               
                 A8 = −8.51889E−07, A10 = 1.92356E−07 
               
               
                             15           
               
               
                 K = 0.000, A4 = 3.25911E−05, A6 = 1.49778E−07 
               
               
                 16th surface 
               
               
                 K = 0.000, A4 = 1.36486E−04, A6 = −4.26236E−06, 
               
               
                 A8 = 7.39509E−08 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.14 
                 15.85 
                 49.07 
               
               
                   
                 F-number 
                 3.22 
                 4.92 
                 6.00 
               
               
                   
                 Angle of view 
                 80.40 
                 26.86 
                 9.00 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 42.87 
                 51.96 
                 57.58 
               
               
                   
                 BF 
                 5.44 
                 5.15 
                 4.75 
               
               
                   
                 d3 
                 0.18 
                 8.37 
                 16.20 
               
               
                   
                 d8 
                 16.03 
                 8.55 
                 1.75 
               
               
                   
                 d14 
                 2.97 
                 11.62 
                 16.62 
               
               
                   
                 d16 
                 3.93 
                 3.71 
                 3.30 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.05 
               
               
                 2 
                 4 
                 −7.25 
               
               
                 3 
                 10 
                 10.94 
               
               
                 4 
                 15 
                 13.89 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 4 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 20.015 
                 0.80 
                 2.00170 
                 20.64 
               
               
                  2 
                 16.318 
                 3.62 
                 1.59201 
                 67.02 
               
               
                  3 (Aspheric surface) 
                 −95.128 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −72.309 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  5 (Aspheric surface) 
                 7.089 
                 2.58 
               
               
                  6 
                 −222.779 
                 1.64 
                 2.10225 
                 16.79 
               
               
                  7 
                 −18.442 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  8 (Aspheric surface) 
                 56.401 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 5.596 
                 2.49 
                 1.69350 
                 53.21 
               
               
                 11 (Aspheric surface) 
                 −19.119 
                 0.08 
               
               
                 12 
                 5.586 
                 1.46 
                 1.49700 
                 81.54 
               
               
                 13 
                 38.700 
                 0.71 
                 2.00330 
                 28.27 
               
               
                 14 
                 3.565 
                 Variable 
               
               
                 15 (Aspheric surface) 
                 33.330 
                 3.00 
                 1.74330 
                 49.33 
               
               
                 16 (Aspheric surface) 
                 −14.041 
                 Variable 
               
               
                 17 
                 ∞ 
                 0.40 
                 1.54771 
                 62.84 
               
               
                 18 
                 ∞ 
                 0.50 
               
               
                 19 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 20 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 1.25893E−05, A6 = 5.29224E−09, A8 = −2.09551E−10, 
               
               
                 A10 = 7.93834E−13 
               
               
                 4th surface 
               
               
                 K = 7.869, A4 = 6.69751E−05, A6 = −2.58449E−06, A8 = 6.22145E−08, 
               
               
                 A10 = −5.23773E−10 
               
               
                 5th surface 
               
               
                 K = 0.227, A4 = 1.07973E−04, A6 = 6.32093E−06, A8 = −5.41685E−07, 
               
               
                 A10 = 1.70854E−08 
               
               
                 8th surface 
               
               
                 K = −1.493, A4 = −3.10021E−04, A6 = 5.60758E−07, 
               
               
                 A8 = −8.83358E−08, A10 = −2.21573E−09 
               
               
                 10th surface 
               
               
                 K = 0.822, A4 = −1.11343E−03, A6 = −3.05892E−05, 
               
               
                 A8 = −1.85139E−06, A10 = −1.78845E−08 
               
               
                 11th surface 
               
               
                 K = −2.814, A4 = 4.08676E−04, A6 = −1.21638E−06, 
               
               
                 A8 = −7.04762E−07, A10 = 1.50032E−07 
               
               
                             15           
               
               
                 K = 0.000, A4 = 4.74683E−05, A6 = −7.77189E−07 
               
               
                 16th surface 
               
               
                 K = 0.000, A4 = 1.67236E−04, A6 = −5.05549E−06, A8 = 6.48089E−08 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.11 
                 15.78 
                 48.99 
               
               
                   
                 F-number 
                 3.24 
                 4.95 
                 6.00 
               
               
                   
                 Angle of view 
                 80.45 
                 26.99 
                 9.02 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 42.85 
                 51.98 
                 57.55 
               
               
                   
                 BF 
                 5.43 
                 5.17 
                 4.72 
               
               
                   
                 d3 
                 0.18 
                 8.37 
                 16.20 
               
               
                   
                 d8 
                 16.03 
                 8.55 
                 1.74 
               
               
                   
                 d14 
                 2.96 
                 11.63 
                 16.63 
               
               
                   
                 d16 
                 3.93 
                 3.73 
                 3.25 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.03 
               
               
                 2 
                 4 
                 −7.26 
               
               
                 3 
                 10 
                 10.97 
               
               
                 4 
                 15 
                 13.59 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 5 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 21.257 
                 0.80 
                 1.94595 
                 17.98 
               
               
                  2 
                 18.209 
                 3.85 
                 1.49700 
                 81.54 
               
               
                  3 (Aspheric surface) 
                 −66.917 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −22.219 
                 0.80 
                 1.76802 
                 49.24 
               
               
                  5 (Aspheric surface) 
                 5.481 
                 1.89 
               
               
                  6 
                 74.445 
                 1.60 
                 1.94595 
                 17.98 
               
               
                  7 
                 −23.299 
                 0.60 
                 1.76802 
                 49.24 
               
               
                  8 (Aspheric surface) 
                 215.699 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 4.226 
                 2.35 
                 1.49700 
                 81.54 
               
               
                 11 (Aspheric surface) 
                 −16.223 
                 0.10 
               
               
                 12 
                 5.044 
                 0.70 
                 2.00170 
                 20.64 
               
               
                 13 (Aspheric surface) 
                 3.439 
                 Variable 
               
               
                 14 
                 −21.102 
                 1.60 
                 1.51825 
                 64.14 
               
               
                 15 (Aspheric surface) 
                 −8.879 
                 Variable 
               
               
                 16 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 17 
                 ∞ 
                 0.50 
               
               
                 18 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 19 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 1.43757E−05, A6 = −1.36130E−08 
               
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.21703E−03, A6 = −5.46492E−05, A8 = 1.04169E−06, 
               
               
                 A10 = −7.77129E−09 
               
               
                 5th surface 
               
               
                 K = 0.000, A4 = 1.04613E−03, A6 = 3.25777E−05, A8 = −2.65926E−06, 
               
               
                 A10 = −1.84775E−08 
               
               
                 8th surface 
               
               
                 K = 0.000, A4 = −4.17728E−04, A6 = −2.92962E−05, 
               
               
                 A8 = 4.40061E−07, A10 = −4.99489E−09 
               
               
                 10th surface 
               
               
                 K = 0.000, A4 = −1.10207E−03, A6 = −2.77492E−05, 
               
               
                 A8 = −3.77816E−06, A10 = −7.30453E−08 
               
               
                 11th surface 
               
               
                 K = 0.000, A4 = 9.87282E−04, A6 = −6.65232E−05, A8 = 2.56751E−06, 
               
               
                 A10 = −2.74580E−08 
               
               
                 13th surface 
               
               
                 K = 0.000, A4 = −1.52619E−05, A6 = 8.16567E−05 
               
               
                             15           
               
               
                 K = −2.836 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.26 
               
               
                   
                 F-number 
                 3.35 
                 4.87 
                 5.00 
               
               
                   
                 Angle of view 
                 81.14 
                 27.47 
                 8.45 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 39.80 
                 48.84 
                 56.76 
               
               
                   
                 BF 
                 7.38 
                 7.17 
                 4.95 
               
               
                   
                 d3 
                 0.30 
                 9.12 
                 22.08 
               
               
                   
                 d8 
                 13.26 
                 6.10 
                 1.46 
               
               
                   
                 d13 
                 4.26 
                 11.86 
                 13.69 
               
               
                   
                 d15 
                 5.89 
                 5.69 
                 3.47 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 36.74 
               
               
                 2 
                 4 
                 −6.49 
               
               
                 3 
                 10 
                 10.09 
               
               
                 4 
                 14 
                 28.20 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 6 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 20.846 
                 0.80 
                 2.00170 
                 20.64 
               
               
                  2 
                 16.766 
                 0.10 
               
               
                  3 
                 16.944 
                 3.62 
                 1.61881 
                 63.85 
               
               
                  4 (Aspheric surface) 
                 −97.907 
                 Variable 
               
               
                  5 (Aspheric surface) 
                 −77.096 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  6 (Aspheric surface) 
                 7.139 
                 2.58 
               
               
                  7 
                 −210.704 
                 1.63 
                 2.10225 
                 16.79 
               
               
                  8 
                 −18.613 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  9 (Aspheric surface) 
                 54.391 
                 Variable 
               
               
                 10 (Stop) 
                 ∞ 
                 0.30 
               
               
                 11 (Aspheric surface) 
                 5.591 
                 2.49 
                 1.69350 
                 53.21 
               
               
                 12 (Aspheric surface) 
                 −19.444 
                 0.08 
               
               
                 13 
                 5.570 
                 1.46 
                 1.49700 
                 81.54 
               
               
                 14 
                 36.999 
                 0.71 
                 2.00330 
                 28.27 
               
               
                 15 
                 3.573 
                 Variable 
               
               
                 16 (Aspheric surface) 
                 32.909 
                 3.00 
                 1.74330 
                 49.33 
               
               
                 17 (Aspheric surface) 
                 −14.495 
                 Variable 
               
               
                 18 
                 ∞ 
                 0.40 
                 1.54771 
                 62.84 
               
               
                 19 
                 ∞ 
                 0.50 
               
               
                 20 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 21 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.11417E−05, A6 = 4.77301E−09, A8 = −1.76384E−10, 
               
               
                 A10 = 5.67505E−13 
               
               
                 5th surface 
               
               
                 K = 9.178, A4 = 8.69795E−05, A6 = −1.63148E−06, A8 = 8.03659E−09, 
               
               
                 A10 = −1.24224E−11 
               
               
                             6            
               
               
                 K = 0.265, A4 = 1.50147E−04, A6 = 7.13726E−06, A8 = −8.18039E−08, 
               
               
                 A10 = −8.56450E−09 
               
               
                             9            
               
               
                 K = −1.493, A4 = −3.05420E−04, A6 = −3.72321E−06, 
               
               
                 A8 = 1.95408E−07, A10 = −4.53534E−09 
               
               
                 11th surface 
               
               
                 K = 0.822, A4 = −1.07795E−03, A6 = −3.09591E−05, 
               
               
                 A8 = −1.21284E−06, A10 = 1.00402E−08 
               
               
                             12            
               
               
                 K = −3.118, A4 = 4.44583E−04, A6 = 4.62513E−06, 
               
               
                 A8 = −3.41403E−07, A10 = 2.10091E−07 
               
               
                 16th surface 
               
               
                 K = 0.000, A4 = 3.25824E−05, A6 = 4.25516E−07 
               
               
                             17            
               
               
                 K = 0.000, A4 = 1.37067E−04, A6 = −4.13492E−06, A8 = 7.46073E−08 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.12 
                 15.83 
                 48.93 
               
               
                   
                 F-number 
                 3.21 
                 4.92 
                 6.00 
               
               
                   
                 Angle of view 
                 79.98 
                 26.88 
                 9.04 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 42.93 
                 51.97 
                 57.60 
               
               
                   
                 BF 
                 5.40 
                 5.06 
                 4.68 
               
               
                   
                 d4 
                 0.18 
                 8.37 
                 16.20 
               
               
                   
                 d9 
                 16.03 
                 8.55 
                 1.75 
               
               
                   
                 d15 
                 2.97 
                 11.62 
                 16.62 
               
               
                   
                 d17 
                 3.90 
                 3.62 
                 3.22 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.05 
               
               
                 2 
                 5 
                 −7.27 
               
               
                 3 
                 11 
                 10.91 
               
               
                 4 
                 16 
                 13.85 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 7 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 19.302 
                 0.80 
                 2.00170 
                 20.64 
               
               
                  2 
                 15.365 
                 3.62 
                 1.58913 
                 61.14 
               
               
                  3 (Aspheric surface) 
                 −104.689 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −93.884 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  5 (Aspheric surface) 
                 6.716 
                 2.58 
               
               
                  6 
                 −700.605 
                 1.68 
                 2.10225 
                 16.79 
               
               
                  7 
                 −19.733 
                 0.10 
               
               
                  8 
                 −17.664 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  9 (Aspheric surface) 
                 95.016 
                 Variable 
               
               
                 10 (Stop) 
                 ∞ 
                 0.30 
               
               
                 11 (Aspheric surface) 
                 5.420 
                 2.49 
                 1.69350 
                 53.21 
               
               
                 12 (Aspheric surface) 
                 −19.583 
                 0.08 
               
               
                 13 
                 5.498 
                 1.46 
                 1.49700 
                 81.54 
               
               
                 14 
                 34.975 
                 0.54 
                 2.00330 
                 28.27 
               
               
                 15 
                 3.525 
                 Variable 
               
               
                 16 (Aspheric surface) 
                 39.743 
                 3.00 
                 1.74330 
                 49.33 
               
               
                 17 (Aspheric surface) 
                 −13.96 
                 Variable 
               
               
                 18 
                 ∞ 
                 0.40 
                 1.54771 
                 62.84 
               
               
                 19 
                 ∞ 
                 0.50 
               
               
                 20 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 21 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 1.23054E−05, A6 = 2.60212E−09, A8 = −3.07823E−10, 
               
               
                 A10 = 1.71458E−12 
               
               
                 4th surface 
               
               
                 K = 7.869, A4 = 3.85724E−05, A6 = −1.69314E−06, A8 = 4.09224E−08, 
               
               
                 A10 = −3.42105E−10 
               
               
                 5th surface 
               
               
                 K = 0.227, A4 = 4.89518E−05, A6 = 5.35203E−06, A8 = −5.51299E−07, 
               
               
                 A10 = 1.60553E−08 
               
               
                             9            
               
               
                 K = −1.493, A4 = −3.26017E−04, A6 = 9.90185E−07, 
               
               
                 A8 = −1.35284E−07, A10 = −1.79042E−09 
               
               
                 11th surface 
               
               
                 K = 0.781, A4 = −1.18366E−03, A6 = −2.67284E−05, 
               
               
                 A8 = −2.83249E−06, A10 = 2.20918E−08 
               
               
                             12            
               
               
                 K = −2.672, A4 = 4.44282E−04, A6 = 1.65015E−05, 
               
               
                 A8 = −3.53535E−06, A10 = 3.82848E−07 
               
               
                 16th surface 
               
               
                 K = 0.000, A4 = 5.39933E−05, A6 = −2.94851E−06 
               
               
                             17            
               
               
                 K = 0.000, A4 = 1.52333E−04, A6 = −7.37192E−06, A8 = 8.02981E−08 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.12 
                 15.83 
                 49.08 
               
               
                   
                 F-number 
                 3.26 
                 4.97 
                 6.00 
               
               
                   
                 Angle of view 
                 80.46 
                 27.07 
                 9.06 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 42.91 
                 51.75 
                 57.66 
               
               
                   
                 BF 
                 5.49 
                 5.17 
                 4.74 
               
               
                   
                 d3 
                 0.18 
                 8.28 
                 16.32 
               
               
                   
                 d9 
                 16.03 
                 8.34 
                 1.61 
               
               
                   
                 d15 
                 2.98 
                 11.72 
                 16.76 
               
               
                   
                 d17 
                 4.00 
                 3.73 
                 3.27 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.45 
               
               
                 2 
                 4 
                 −7.30 
               
               
                 3 
                 11 
                 10.95 
               
               
                 4 
                 16 
                 14.17 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 8 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 19.671 
                 0.80 
                 2.00170 
                 20.64 
               
               
                  2 
                 15.603 
                 0.10 
               
               
                  3 
                 15.450 
                 3.62 
                 1.58913 
                 61.14 
               
               
                  4 (Aspheric surface) 
                 −100.545 
                 Variable 
               
               
                  5 (Aspheric surface) 
                 −84.986 
                 0.80 
                 1.83481 
                 42.71 
               
               
                  6 (Aspheric surface) 
                 6.782 
                 2.58 
               
               
                  7 
                 20800.198 
                 1.65 
                 2.10225 
                 16.79 
               
               
                  8 
                 −20.211 
                 0.10 
               
               
                  9 
                 −17.058 
                 0.80 
                 1.83481 
                 42.71 
               
               
                 10 (Aspheric surface) 
                 114.384 
                 Variable 
               
               
                 11 (Stop) 
                 ∞ 
                 0.30 
               
               
                 12 (Aspheric surface) 
                 5.434 
                 2.49 
                 1.69350 
                 53.21 
               
               
                 13 (Aspheric surface) 
                 −19.397 
                 0.08 
               
               
                 14 
                 5.474 
                 1.46 
                 1.49700 
                 81.54 
               
               
                 15 
                 33.364 
                 0.52 
                 2.00330 
                 28.27 
               
               
                 16 
                 3.517 
                 Variable 
               
               
                 17 (Aspheric surface) 
                 40.792 
                 2.99 
                 1.74330 
                 49.33 
               
               
                 18 (Aspheric surface) 
                 −13.902 
                 Variable 
               
               
                 19 
                 ∞ 
                 0.40 
                 1.54771 
                 62.84 
               
               
                 20 
                 ∞ 
                 0.50 
               
               
                 21 
                 ∞ 
                 0.50 
                 1.51633 
                 64.14 
               
               
                 22 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.29756E−05, A6 = 6.43761E−09, A8 = −3.58863E−10, 
               
               
                 A10 = 2.03026E−12 
               
               
                 5th surface 
               
               
                 K = 7.869, A4 = 8.02051E−05, A6 = −2.23965E−06, A8 = 3.94995E−08, 
               
               
                 A10 = −3.00060E−10 
               
               
                             6            
               
               
                 K = 0.227, A4 = 7.38440E−05, A6 = 6.33121E−06, A8 = −4.73985E−07, 
               
               
                 A10 = 1.42758E−08 
               
               
                 10th surface 
               
               
                 K = −1.493, A4 = −3.07032E−04, A6 = −8.00912E−07, 
               
               
                 A8 = −8.47630E−08, A10 = −2.11918E−09 
               
               
                             12            
               
               
                 K = 0.781, A4 = −1.18705E−03, A6 = −2.86980E−05, 
               
               
                 A8 = −2.73106E−06, A10 = 5.40040E−09 
               
               
                 13th surface 
               
               
                 K = −2.671, A4 = 4.20020E−04, A6 = 1.36038E−05, 
               
               
                 A8 = −3.42454E−06, A10 = 3.29100E−07 
               
               
                             17            
               
               
                 K = 0.000, A4 = 5.57926E−05, A6 = −2.76078E−06 
               
               
                             18            
               
               
                 K = 0.000, A4 = 1.63767E−04, A6 = −7.83584E−06, A8 = 9.06245E−08 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.12 
                 15.82 
                 49.12 
               
               
                   
                 F-number 
                 3.19 
                 4.91 
                 6.00 
               
               
                   
                 Angle of view 
                 80.22 
                 27.08 
                 9.06 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 42.99 
                 51.80 
                 57.66 
               
               
                   
                 BF 
                 5.51 
                 5.18 
                 4.72 
               
               
                   
                 d4 
                 0.18 
                 8.26 
                 16.33 
               
               
                   
                 d10 
                 16.03 
                 8.33 
                 1.58 
               
               
                   
                 d16 
                 2.99 
                 11.75 
                 16.76 
               
               
                   
                 d18 
                 3.65 
                 3.37 
                 2.88 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 32.39 
               
               
                 2 
                 4 
                 −7.32 
               
               
                 3 
                 12 
                 10.96 
               
               
                 4 
                 17 
                 14.21 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 9 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 16.961 
                 0.50 
                 2.00330 
                 28.272 
               
               
                  2 
                 14.770 
                 4.00 
                 1.43875 
                 94.93 
               
               
                  3 (Aspheric surface) 
                 −53.613 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −34.831 
                 0.80 
                 1.85135 
                 40.10 
               
               
                  5 (Aspheric surface) 
                 5.706 
                 2.40 
               
               
                  6 
                 −100.668 
                 1.60 
                 2.00170 
                 20.64 
               
               
                  7 
                 −10.639 
                 0.60 
                 1.77250 
                 49.60 
               
               
                  8 (Aspheric surface) 
                 −637.390 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 4.308 
                 2.35 
                 1.49700 
                 81.54 
               
               
                 11 (Aspheric surface) 
                 −22.956 
                 0.10 
               
               
                 12 
                 4.628 
                 0.70 
                 2.11753 
                 16.79 
               
               
                 13 (Aspheric surface) 
                 3.321 
                 Variable 
               
               
                 14 (Aspheric surface) 
                 47.653 
                 1.60 
                 1.76802 
                 49.24 
               
               
                 15 
                 −47.407 
                 Variable 
               
               
                 16 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 17 
                 ∞ 
                 0.40 
               
               
                 18 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 19 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 2.35896E−05, A6 = −2.69490E−08 
               
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.11996E−03, A6 = −5.27085E−05, A8 = 1.02790E−06, 
               
               
                 A10 = −8.27781E−09 
               
               
                 5th surface 
               
               
                 K = 0.000, A4 = 1.14365E−03, A6 = 3.28026E−05, A8 = −2.56467E−06, 
               
               
                 A10 = −1.82498E−08 
               
               
                 8th surface 
               
               
                 K = 0.000, A4 = −3.36403E−04, A6 = −2.39068E−05, 
               
               
                 A8 = 4.13921E−07, A10 = −5.00834E−09 
               
               
                 10th surface 
               
               
                 K = 0.000, A4 = −8.40786E−04, A6 = −2.45662E−05, 
               
               
                 A8 = −3.78182E−06, A10 = −7.30622E−08 
               
               
                 11th surface 
               
               
                 K = 0.000, A4 = 7.01731E−04, A6 = −6.28115E−05, A8 = 2.56803E−06, 
               
               
                 A10 = −2.74507E−08 
               
               
                 13th surface 
               
               
                 K = 0.000, A4 = 1.25269E−04, A6 = 8.07357E−05 
               
               
                             14            
               
               
                 K = 0.003, A4 = −5.52596E−05, A6 = 4.86922E−06 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.28 
               
               
                   
                 F-number 
                 3.99 
                 5.41 
                 6.00 
               
               
                   
                 Angle of view 
                 80.86 
                 27.97 
                 8.59 
               
               
                   
                 Image height 
                 3.80 
                 3.80 
                 3.80 
               
               
                   
                 Total lens length 
                 42.32 
                 48.72 
                 56.76 
               
               
                   
                 BF 
                 6.72 
                 9.67 
                 4.79 
               
               
                   
                 d3 
                 0.30 
                 8.84 
                 20.09 
               
               
                   
                 d8 
                 14.68 
                 5.92 
                 1.47 
               
               
                   
                 d13 
                 5.67 
                 9.34 
                 15.46 
               
               
                   
                 d15 
                 5.39 
                 8.34 
                 3.48 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 34.37 
               
               
                 2 
                 4 
                 −6.52 
               
               
                 3 
                 10 
                 10.76 
               
               
                 4 
                 14 
                 31.02 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
             
               
             
               
             
               
               
               
               
               
             
               
             
               
               
               
             
           
               
                   
               
               
                 Numerical Example 10 
               
               
                 Unit mm 
               
               
                   
               
             
             
               
                 Surface data 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                  1 
                 16.897 
                 0.20 
                 2.00330 
                 28.27 
               
               
                  2 
                 14.779 
                 4.00 
                 1.43875 
                 94.93 
               
               
                  3 (Aspheric surface) 
                 −49.691 
                 Variable 
               
               
                  4 (Aspheric surface) 
                 −31.866 
                 0.80 
                 1.85135 
                 40.10 
               
               
                  5 (Aspheric surface) 
                 5.725 
                 2.40 
               
               
                  6 
                 −117.803 
                 1.60 
                 2.00170 
                 20.64 
               
               
                  7 
                 −10.489 
                 0.60 
                 1.77250 
                 49.60 
               
               
                  8 (Aspheric surface) 
                 −1044.801 
                 Variable 
               
               
                  9 (Stop) 
                 ∞ 
                 0.30 
               
               
                 10 (Aspheric surface) 
                 4.258 
                 2.35 
                 1.43875 
                 94.93 
               
               
                 11 (Aspheric surface) 
                 −16.042 
                 0.10 
               
               
                 12 
                 4.743 
                 0.70 
                 2.11753 
                 16.79 
               
               
                 13 (Aspheric surface) 
                 3.502 
                 Variable 
               
               
                 14 (Aspheric surface) 
                 53.061 
                 1.60 
                 1.76802 
                 49.24 
               
               
                 15 
                 −53.202 
                 Variable 
               
               
                 16 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 17 
                 ∞ 
                 0.40 
               
               
                 18 
                 ∞ 
                 0.40 
                 1.51633 
                 64.14 
               
               
                 19 
                 ∞ 
                 0.37 
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspheric surface data 
               
               
                   
               
             
          
           
               
                 3rd surface 
               
               
                 K = 0.000, A4 = 2.47118E−05, A6 = −3.04634E−08 
               
               
                 4th surface 
               
               
                 K = 0.000, A4 = 1.14452E−03, A6 = −5.29437E−05, A8 = 1.02645E−06, 
               
               
                 A10 = −8.30318E−09 
               
               
                 5th surface 
               
               
                 K = 0.000, A4 = 1.13134E−03, A6 = 3.28374E−05, A8 = −2.56480E−06, 
               
               
                 A10 = −1.82504E−08 
               
               
                 8th surface 
               
               
                 K = 0.000, A4 = −3.14067E−04, A6 = −2.40621E−05, 
               
               
                 A8 = 4.11703E−07, A10 = −5.01045E−09 
               
               
                 10th surface 
               
               
                 K = 0.000, A4 = −8.85261E−04, A6 = −2.50159E−05, 
               
               
                 A8 = −3.78209E−06, A10 = −7.30617E−08 
               
               
                 11th surface 
               
               
                 K = 0.000, A4 = 8.40012E−04, A6 = −6.26357E−05, A8 = 2.56818E−06, 
               
               
                 A10 = −2.74502E−08 
               
               
                 13th surface 
               
               
                 K = 0.000, A4 = 9.93954E−05, A6 = 8.05403E−05 
               
               
                             14           
               
               
                 K = 0.074, A4 = −9.22032E−05, A6 = 5.26721E−06 
               
               
                   
               
             
          
           
               
                 Zoom lens data 
               
               
                 Zoom ratio 9.35 
               
             
          
           
               
                   
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.29 
               
               
                   
                 F-number 
                 4.12 
                 5.47 
                 6.00 
               
               
                   
                 Angle of view 
                 82.31 
                 28.29 
                 8.71 
               
               
                   
                 Image height 
                 3.88 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 43.17 
                 49.09 
                 56.58 
               
               
                   
                 BF 
                 6.76 
                 10.23 
                 4.82 
               
               
                   
                 d3 
                 0.30 
                 8.98 
                 20.04 
               
               
                   
                 d8 
                 15.23 
                 6.15 
                 1.55 
               
               
                   
                 d13 
                 6.24 
                 9.07 
                 15.52 
               
               
                   
                 d15 
                 5.43 
                 8.89 
                 3.53 
               
               
                   
                   
               
             
          
           
               
                 Data on zoom lens groups 
               
             
          
           
               
                 Group 
                 Starting surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 33.69 
               
               
                 2 
                 4 
                 −6.52 
               
               
                 3 
                 10 
                 11.00 
               
               
                 4 
                 14 
                 34.65 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 11 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.11 
                 14.96 
                 47.81 
               
               
                   
                 F-number 
                 3.54 
                 5.23 
                 6.00 
               
               
                   
                 Angle of view 
                 78.15 
                 28.58 
                 9.08 
               
               
                   
                 Image height 
                 3.66 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 12 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.26 
               
               
                   
                 F-number 
                 3.35 
                 4.87 
                 5.00 
               
               
                   
                 Angle of view 
                 77.31 
                 27.47 
                 8.45 
               
               
                   
                 Image height 
                 3.69 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 13 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.14 
                 15.85 
                 49.07 
               
               
                   
                 F-number 
                 3.22 
                 4.92 
                 6.00 
               
               
                   
                 Angle of view 
                 77.63 
                 26.86 
                 9.00 
               
               
                   
                 Image height 
                 3.71 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 14 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.11 
                 15.78 
                 48.99 
               
               
                   
                 F-number 
                 3.24 
                 4.95 
                 6.00 
               
               
                   
                 Angle of view 
                 77.73 
                 26.99 
                 9.02 
               
               
                   
                 Image height 
                 3.71 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 15 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.26 
               
               
                   
                 F-number 
                 3.35 
                 4.87 
                 5.00 
               
               
                   
                 Angle of view 
                 80.41 
                 28.65 
                 8.84 
               
               
                   
                 Image height 
                 3.69 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 16 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.12 
                 15.83 
                 48.93 
               
               
                   
                 F-number 
                 3.21 
                 4.92 
                 6.00 
               
               
                   
                 Angle of view 
                 77.67 
                 26.88 
                 9.04 
               
               
                   
                 Image height 
                 3.74 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 17 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.12 
                 15.83 
                 49.08 
               
               
                   
                 F-number 
                 3.26 
                 4.97 
                 6.00 
               
               
                   
                 Angle of view 
                 77.63 
                 27.07 
                 9.06 
               
               
                   
                 Image height 
                 3.71 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 18 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.12 
                 15.82 
                 49.12 
               
               
                   
                 F-number 
                 3.19 
                 4.91 
                 6.00 
               
               
                   
                 Angle of view 
                 77.54 
                 27.08 
                 9.06 
               
               
                   
                 Image height 
                 3.72 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 19 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.28 
               
               
                   
                 F-number 
                 3.99 
                 5.41 
                 6.00 
               
               
                   
                 Angle of view 
                 76.72 
                 27.97 
                 8.59 
               
               
                   
                 Image height 
                 3.59 
                 3.80 
                 3.80 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Numerical Example 20 
               
               
                 Unit mm 
               
             
          
           
               
                   
                 Wide-angle 
                 Intermediate 
                 Telephoto 
               
               
                   
                   
               
             
          
           
               
                   
                 Focal length 
                 5.10 
                 14.79 
                 49.28 
               
               
                   
                 F-number 
                 3.99 
                 5.41 
                 6.00 
               
               
                   
                 Angle of view 
                 76.72 
                 27.97 
                 8.59 
               
               
                   
                 Image height 
                 3.61 
                 3.88 
                 3.88 
               
               
                   
                   
               
             
          
         
       
     
       FIGS. 11 to 20  are aberration diagrams for Examples 1 to 10 upon focusing on an object point at infinity. In these aberration diagrams, (a), (b) and (c) are indicative of spherical aberrations, astigmatism, distortion and chromatic aberration of magnification at the wide-angle end, in the intermediate state, and at the telephoto end, respectively, and FIY stands for a half angle of view. Note here that there are no aberration diagrams presented for Examples 11 to 20 attached hereto because they are similar in construction to Examples 1 to 10, respectively. 
     Set out below are the values of conditions (1) to (13) in the aforesaid Examples 1 to 10. 
     
       
         
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 Condition 
                 Example 1 
                 Example 2 
                 Example 3 
                 Example 4 
                 Example 5 
               
               
                   
               
               
                 (1) 
                 9.35 
                 9.66 
                 9.55 
                 9.58 
                 9.66 
               
               
                 (2) 
                 1.50 
                 1.50 
                 1.62 
                 1.59 
                 1.50 
               
               
                 (3) 
                 1.07 
                 1.05 
                 1.06 
                 1.07 
                 1.05 
               
               
                 (4) 
                 1.96 
                 1.96 
                 2.00 
                 2.01 
                 1.96 
               
               
                 (5) 
                 17.98 
                 17.98 
                 20.64 
                 20.64 
                 17.98 
               
               
                 (6) 
                 0.208 
                 0.208 
                 0.221 
                 0.221 
                 0.208 
               
               
                 (7) 
                 −13.98 
                 −12.95 
                 −8.98 
                 −9.83 
                 −12.95 
               
               
                 (8) 
                 0.46 
                 0.46 
                 0.38 
                 0.42 
                 0.46 
               
               
                 (9) 
                 63.56 
                 63.56 
                 43.21 
                 46.38 
                 63.56 
               
               
                 (10)  
                 0.688 
                 0.746 
                 0.653 
                 0.654 
                 0.746 
               
               
                 (11)  
                 −0.137 
                 −0.132 
                 −0.148 
                 −0.148 
                 −0.132 
               
               
                 (12)  
                 0.759 
                 0.761 
                 0.755 
                 0.759 
                 0.761 
               
               
                 (13)  
                 14.80 
                 14.71 
                 14.92 
                 14.91 
                 14.71 
               
               
                   
               
               
                 Condition 
                 Example 6 
                 Example 7 
                 Example 8 
                 Example 9 
                 Example 10 
               
               
                   
               
               
                 (1) 
                 9.55 
                 9.59 
                 9.59 
                 9.66 
                 9.67 
               
               
                 (2) 
                 1.62 
                 1.59 
                 1.59 
                 1.44 
                 1.44 
               
               
                 (3) 
                 1.05 
                 1.10 
                 1.09 
                 1.09 
                 1.07 
               
               
                 (4) 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
               
               
                 (5) 
                 20.64 
                 20.64 
                 20.64 
                 28.27 
                 28.27 
               
               
                 (6) 
                 0.221 
                 0.221 
                 0.221 
                 0.125 
                 0.050 
               
               
                 (7) 
                 −9.22 
                 −8.81 
                 −8.67 
                 −8.67 
                 −14.96 
               
               
                 (8) 
                 0.39 
                 0.42 
                 0.42 
                 0.57 
                 0.57 
               
               
                 (9) 
                 43.21 
                 40.50 
                 40.50 
                 66.66 
                 66.66 
               
               
                 (10)  
                 0.655 
                 0.661 
                 0.659 
                 0.697 
                 0.683 
               
               
                 (11)  
                 −0.149 
                 −0.149 
                 −0.149 
                 −0.132 
                 −0.132 
               
               
                 (12)  
                 0.757 
                 0.758 
                 0.758 
                 0.745 
                 0.761 
               
               
                 (13)  
                 14.93 
                 14.94 
                 14.94 
                 15.01 
                 14.65 
               
               
                   
               
               
                   
                 Example 
                 Example 
                 Example 
                 Example 
               
               
                 Condition 
                 11 
                 12 
                 13 
                 14 
                 Example 15 
               
               
                   
               
               
                 (1) 
                 9.35 
                 9.66 
                 9.55 
                 9.58 
                 9.66 
               
               
                 (2) 
                 1.50 
                 1.50 
                 1.62 
                 1.59 
                 1.50 
               
               
                 (3) 
                 1.07 
                 1.05 
                 1.06 
                 1.07 
                 1.05 
               
               
                 (4) 
                 1.96 
                 1.96 
                 2.00 
                 2.01 
                 1.96 
               
               
                 (5) 
                 17.98 
                 17.98 
                 20.64 
                 20.64 
                 17.98 
               
               
                 (6) 
                 0.208 
                 0.208 
                 0.221 
                 0.221 
                 0.208 
               
               
                 (7) 
                 −13.98 
                 −12.95 
                 −8.98 
                 −9.83 
                 −12.95 
               
               
                 (8) 
                 0.46 
                 0.46 
                 0.38 
                 0.42 
                 0.46 
               
               
                 (9) 
                 63.56 
                 63.56 
                 43.21 
                 46.38 
                 63.56 
               
               
                 (10)  
                 0.688 
                 0.746 
                 0.653 
                 0.654 
                 0.746 
               
               
                 (11)  
                 −0.137 
                 −0.132 
                 −0.148 
                 −0.148 
                 −0.132 
               
               
                 (12)  
                 0.717 
                 0.724 
                 0.723 
                 0.726 
                 0.724 
               
               
                 (13)  
                 15.70 
                 15.47 
                 15.59 
                 15.58 
                 15.47 
               
               
                   
               
               
                   
                 Example 
                 Example 
                 Example 
                 Example 
               
               
                 Condition 
                 16 
                 17 
                 18 
                 19 
                 Example 20 
               
               
                   
               
               
                 (1) 
                 9.55 
                 9.59 
                 9.59 
                 9.66 
                 9.67 
               
               
                 (2) 
                 1.62 
                 1.59 
                 1.59 
                 1.44 
                 1.44 
               
               
                 (3) 
                 1.05 
                 1.10 
                 1.09 
                 1.09 
                 1.07 
               
               
                 (4) 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
                 2.01 
               
               
                 (5) 
                 20.64 
                 20.64 
                 20.64 
                 28.27 
                 28.27 
               
               
                 (6) 
                 0.221 
                 0.221 
                 0.221 
                 0.125 
                 0.050 
               
               
                 (7) 
                 −9.22 
                 −8.81 
                 −8.67 
                 −8.67 
                 −14.96 
               
               
                 (8) 
                 0.39 
                 0.42 
                 0.42 
                 0.57 
                 0.57 
               
               
                 (9) 
                 43.21 
                 40.50 
                 40.50 
                 66.66 
                 66.66 
               
               
                 (10)  
                 0.655 
                 0.661 
                 0.659 
                 0.697 
                 0.683 
               
               
                 (11)  
                 −0.149 
                 −0.149 
                 −0.149 
                 −0.132 
                 −0.132 
               
               
                 (12)  
                 0.729 
                 0.725 
                 0.726 
                 0.703 
                 0.709 
               
               
                 (13)  
                 15.50 
                 15.63 
                 15.60 
                 15.91 
                 15.73 
               
               
                   
               
             
          
         
       
     
     Each example may further be modified as follows. 
     In the zoom lens of each example, barrel distortion is produced on the rectangular photoelectric transformation plane at the wide-angle end, while the occurrence of distortion is hold back near an intermediate focal length or at the telephoto end. For electrical correction of distortion, the effective imaging area should preferably be configured into barrel form at the wide-angle end and rectangular form near the intermediate focal length or at the telephoto end. And the predetermined effective imaging area is converted by image processing into rectangular image information with reduced distortion. The image height I mw  at the wide-angle end is lower than the image height I mt  at the telephoto end. 
     Preferably, the zoom lens has an image transformation block in which electric signals for an image taken through the zoom lens are transformed into image signals that are corrected by image processing for color shifts from chromatic aberration of magnification. Electric correction of the zoom lens for chromatic aberration of magnification is going to make sure much better images are obtained. 
     Generally speaking, an electronic still camera is designed such that the image of a subject is separated into three primary colors images: the first, the second and the third primary color image, so that the respective output signals are superposed one upon another by operation to reconstruct a color image. Suppose here that a zoom lens has chromatic aberration of magnification. Then, given an image from light of the first primary color, the positions where light of the second and the third primary color is imaged is going to be off the position where the light of the first primary color is imaged. For electronic correction of the image for chromatic aberration of magnification, the amount of shifts of the imaging positions for the second and the third primary color from that for the first primary color is previously found for each pixel of an imaging device based on aberration information about the zoom lens. Then, coordination transformation is implemented such that only the amount of the shifts from the first primary color is corrected for each pixel of the taken image. 
     Referring typically to an image made up of three primary colors output signals of red (R), green (G) and blue (B), shifts of the imaging positions R and B from G are first found for each pixel. Then, coordination transformation is applied to the taken image to eliminate any shift from G, and finally signals of R and G are produced. 
     Chromatic aberration of magnification varies with zoom, focus and f numbers; it is preferable that the amount of shifts of the second and the third primary color from the first primary color is stored as correction data in a storage device for each lens position (zoom, focus and f numbers). By referring to this correction data depending on the zoom position, it is possible to produce the second and the third primary color signals that are corrected for the shifts of the second and the third primary color from the first primary color signal. 
     To cut off unwanted light such as ghosts and flares, it is acceptable to rely on a flare stop other than the aperture stop. That flare stop may then be located somewhere on the object side of the first lens group, between the first and the second lens group, between the second and the third lens group, between the third and the fourth lens group, between the fourth and the fifth lens group, and between the group nearest to the image plane side and the image plane. A frame member or other member may also be located to cut off flare rays. For that purpose, the optical system may be directly printed, coated or sealed in any desired shape inclusive of round, oval, rectangular, polygonal shapes or a shape delimited by a function curve. Further, just only a harmful light beam but also coma flares around the screen may be cut off. 
     Each lens may be applied with an antireflection coating to reduce ghosts and flares. A multicoating is then desired because of being capable of effectively reducing ghosts and flares. Each lens, a cover glass or the like may just as well be applied with an infrared cut coating. 
     Desirously, focusing for the adjusting the focus is implemented with the lens group nearest to the image plane side. Focusing with that lens group eases off loads on a motor because the lens weight is light, and works for making the lens barrel compact because there is none of the change in the total length during zooming, and a drive motor is mounted in the lens barrel. 
     As noted just above, it is desired that focusing for adjusting the focus is implemented with the lens group nearest to the image plane side; however, it may be implemented with the first, the second, the third or the fourth lens group, or by the movement of multiple lens groups. The movement of multiple lens groups is more effectively capable of holding back deterioration of the performance in association with focusing. Furthermore, focusing may be implemented by letting out the whole lens system or letting out or in some lenses. 
     The shading of brightness at the peripheral position of an image may be reduced by shifting the mircolenses of a CCD. For instance, the CCD microlens design may be modified in conformity with the angle of incidence of light rays at each image height, or decreases in the quantity of light at the peripheral position of the image may be corrected by image processing. 
     By the way, an antireflection coating is generally applied to the air contact surface of a lens for the purpose of preventing ghosts and flares. At the cementing surface of a cemented lens, on the other hand, the refractive index of an adhesive material is much higher than that of air; in most cases, the cementing surface has a reflectivity that is on a par with or lower than that of a single layer coating, so that there is little need of applying the antireflection coating to it. However, if the antireflection coating is intentionally applied to the cementing surface too, there are then further reductions achievable in ghosts and flares, which could in turn make sure images of better quality. 
     Especially in recent years, vitreous materials having high refractive indices have gained popularity, and they have often been used with camera optical systems for the reasons of their enhanced effect on correction of aberrations. When a high-refractive-index vitreous material is used as a cemented lens, however, the reflection of light off the cementing surface would also be not negligible. In such a case, it would be particularly effective to have an antireflection coating applied on the cementing surface. 
     Effective use of cementing surface coating is disclosed in JP(A) s 2-27301, 2001-324676 and 2005-92115 and U.S. Pat. No. 7,116,482, etc. In those publications, there is the particular mention of the cementing lens surface coating in the first lens group of the zoom lens having positive power at the foremost lens group. In the invention, too, the cementing lens surface in the first lens group of positive power may just as well be coated, as set forth there. 
     Depending on the refractive index of the lens involved and the refractive index of the adhesive material used, use may be made of coating materials of relatively high refractive indices such as Ta 2 O 5 , TiO 2 , Nb 2 O 5 , ZrO 2 , HfO 2 , CeO 2 , SnO 2 , In 2 O 3 , ZnO, and Y 2 O 3  as well as coating materials of relatively low refractive indices such as MgF 2 , SiO 2 , and Al 2 O 3 . These coating materials may then have a suitable thickness selected in such a way as to meet phase conditions. As a matter of course, the cementing surface coating may just as well be multi-coating as is the case with the coating to the air contact surface of the lens. By optional combinations of two- or multi-layer coating materials with thicknesses, it is possible to achieve a further lowering of reflectivity, and control the spectral and angle properties of reflectivity, etc. On the base of a similar idea, cementing surface coating can effectively be applied to lens cementing surfaces other than those in the first lens group, too. 
       FIGS. 21 ,  22  and  23  are conceptual illustrations of a digital camera, in which such an inventive zoom lens as set forth above is incorporated in a taking optical system  41 .  FIG. 21  is a front perspective view of the appearance of a digital camera  40 ;  FIG. 22  is a rear perspective view of the same; and  FIG. 23  is a schematic sectional view of the setup of the digital camera  40 . However,  FIGS. 21 and 23  show the taking optical system  41  in operation. In the embodiment here, the digital camera  40  comprises a taking optical system  41  positioned on a taking optical path  42 , a finder optical system  43  positioned on a finder optical path  44 , a shutter button  45 , a flash  46 , a liquid crystal display monitor  47 , a focal length change button  61 , a mode select switch  62 , and so on. With the taking optical system  41  received at a lens mount, a cover  60  is slid over the taking optical system  41 , finder optical system  43  and flash  46 . And, as the cover  60  is slid open to place the camera  40  in operation, the taking optical system  41  is let out, as in  FIG. 23 . As the shutter  45  mounted on the upper portion of the camera  40  is pressed down, it causes an image to be taken through the taking optical system  41 , for instance, the zoom optical system of Example 1. An object image formed by the taking optical system  41  is formed on the imaging plane (photoelectric transformation plane) of CCD  49  via a low-pass filter F with a wavelength limiting coating applied on it and a cover glass C. An object image received at CCD  49  is shown as an electronic image on the liquid crystal display monitor  47  via processing means  51 , which monitor is mounted on the back of the camera. This processing means  51  is connected with recording means  52  in which the taken electronic image may be recorded. It is here noted that the recording means  52  may be provided separately from the processing means  51  or, alternatively, it may be constructed in such a way that images are electronically recorded and written therein by means of floppy discs, memory cards, MOs or the like. This camera could also be set up in the form of a silver-halide camera using a silver-halide film in place of CCD  49 . 
     Moreover, a finder objective optical system  53  is located on the finder optical path  44 . The finder objective optical system  53  comprises a zoom optical system which is made up of a plurality of lens groups (three in  FIGS. 21-23 ) and an erecting prism system  55  composed of erecting prisms  55   a ,  55   b  and  55   c , and whose focal length varies in association with the zoom optical system that is the taking optical system  41 . An object image formed by the finder objective optical system  53  is in turn formed on the field frame  57  of the erecting prism system  55  that is an image-erecting member. In the rear of the erecting prism system  55  there is an eyepiece optical system  59  located for guiding an erected image into the eyeball E of an observer. It is here noted that a cover member  50  is provided on the exit side of the eyepiece optical system  59 . 
       FIG. 24  is a block diagram for the internal circuits of the main part of the aforesaid digital camera  40 . In the following explanation, the aforesaid processing means  51  comprises, for instance, a CDS/ADC block  24 , a temporal storage memory block  17 , an image processor block  18  and so on, and the storage means  52  comprises, for instance, a storage medium block  19  and so on. 
     As shown in  FIG. 24 , the digital camera  40  is built up of an operating block  12 , a control block  13  connected to the operating block  12  and an imaging drive circuit  16  connected to the control signal output port of the control block  13  via buses  14  and  15  as well as a temporal storage memory block  17 , an image processor block  18 , a storage medium block  19 , a display block  20  and a preset information storage memory block  21 . 
     Data may be entered in or produced out of the aforesaid temporal storage memory block  17 , image processor block  18 , storage medium block  19 , display block  20  and preset information storage memory block  21  via a bus  22 , and the imaging drive circuit  16  is connected with CCD  49  and CDS/ADC block  24 . 
     The operating block  12  comprising various input buttons and switches is a circuit through which event information entered from outside (a camera operator) via such input buttons and switches is notified to the control block. The control block  13  is a central processor comprising a CPU as an example: it is a circuit that, according to a program loaded in a program memory (not shown) stored therein, puts the whole digital camera  40  under control in response to the instruction and order entered by the camera operator via the operating block  12 . 
     The CCD  49  receives an object image formed through the inventive taking optical system  41 . The CCD  49  is an imaging device that is driven and controlled by the imaging drive circuit  16  to convert the quantity of light of that object image for each pixel into an electric signal and produce it to the CDS/ADC block  24 . 
     The CDS/ADC block  24  is a circuit that amplifies an electric signal entered from CCD  49  and subjects it to analog/digital conversion to produce image raw data (Bayer data: hereinafter called RAW data) only subjected to such amplification and digital conversion to the temporal storage memory  17 . 
     The temporal storage memory  17  is a buffer comprising SDRAM for instance: it is a memory device that temporarily stores the aforesaid RAW data produced out of the CDS/ADC block  24 . The image processor block  18  is a circuit that reads the RAW data stored in the temporal storage memory  17  or the RAW data stored in the storage medium  19  to implement a variety of image processing including distortion correction on the basis of an image quality parameter designated from the control block  13 . 
     The recording medium block  19  is a control circuit that detachably receives a card type or stick type recording medium comprising, for instance, a flash memory or the like so that the RAW data transferred from the temporal storage memory  17  or the image data subjected to image processing at the image processor block  18  are recorded and loaded in the card type or stick type flash memory. 
     The display block  20  is a circuit that comprises a liquid crystal display monitor  47  to display images, menus or the like on that liquid crystal display monitor  47 . The preset information storage memory block  21  comprises a ROM block having various image quality parameters previously loaded in it and a RAM block in which an image quality parameter selected by input operation at the operating block  12  from the image quality parameters read out of that ROM block is stored. The preset information storage memory block  21  is a circuit that puts inputs in and outputs from those memories under control. 
     With the thus constructed digital camera  40 , it is possible to achieve high performance, size reductions and a wide-angle arrangement, because the taking optical system  41  incorporated in it has high zoom capabilities and extremely stable image-formation capabilities all over the zoom range, albeit having a sufficient wide-angle arrangement and compact construction. And faster focusing operation is achievable on the wide-angle and telephoto sides. 
     The present invention may be applied to just only the so-called compact digital camera adapted to take pictures of general subjects but also surveillance cameras required to have wide angles of view and lens interchangeable type cameras.