# Patent

## Title
Variable-magnification optical system and image-taking apparatus therewith

## Abstract

A variable-magnification optical system has, from the object side to the image side, at least a first lens group having a positive optical power, a second lens group having a negative optical power, and a third lens group having a positive optical power. The first lens group includes an optical prism that changes the optical path, and a prescribed conditional formula is fulfilled.

## Background
This application claims foreign priority is based on Japanese Patent Application No. 2005-177288 filed on Jun. 17, 2005, the contents of which are hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a variable-magnification optical system for use in a lens unit or the like, and to an image-taking apparatus incorporating such a variable-magnification optical system.
2. Description of Related Art
With the recent spread of personal computers (PCs), there has been increasing popularity in digital cameras (image-taking apparatuses), which permit easy capturing of images. In such digital cameras, as in cameras using silver-halide film (silver-halide film cameras), compactness (slimness) and high-performance (for example, high zooming and aberration-correcting capabilities) are eagerly sought for.
To meet these requirements, there have been developed image-taking apparatuses (video cameras and the like) that incorporate a variable-magnification optical system (zoom lens system) that includes a rectangular prism in the lens group (first lens group) closest to the object side. Examples of such image-taking apparatuses are disclosed in, to name a few, Japanese Patent Application Laid-open No. H8-248318, laid-open on Sep. 27, 1996 (hereinafter Patent Publication 1) and Japanese Patent Application Laid-open No. H9-146000, laid-open on Jun. 6, 1997 (hereinafter Patent Publication 2).
In these image-taking apparatuses, the rectangular prism bends the optical axis, and thereby serves to reduce the length of the first lens group, and thus the total length of the zoom lens system. This permits a zoom lens system with a so reduced total length to be arranged within the limited space inside the housing of an image-taking apparatus, and accordingly helps make the housing, and thus the image-taking apparatus itself, compact and slim.
The image-taking apparatuses of Patent Publications 1 and 2, however, have the following disadvantages. These image-taking apparatuses incorporate a variable-magnification optical system composed of a plurality of lens groups arranged in a positive-negative-positive-positive optical power arrangement. Thus, to achieve magnification variation (zooming), for example, the second lens group needs to be moved through a comparatively long distance.
Here, the distance through which the second lens group needs to be moved may make the variable-magnification optical system (zoom lens system) unduly long (make its total length unduly large). As a result, the image-taking apparatuses of Patent Publications 1 and 2 cannot be said to be made satisfactorily compact or otherwise favorably constructed.
SUMMARY OF THE INVENTION
In view of the conventionally encountered disadvantages discussed above, it is an object of the present invention to provide a variable-magnification optical system or the like in which, through appropriate setting of the optical powers (refractive powers) of a first to a third lens group (in particular, a second lens group), a proper balance is achieved among the movement distances of the individual lens groups for zooming and thereby the total length of the variable-magnification optical system is successfully reduced.
To achieve the above object, according to the present invention, a variable-magnification optical system is provided with a plurality of lens groups through which light from an object is imaged on an image sensor. Here, the plurality of lens groups include, from the object side to the image side, at least a first lens group having a positive optical power, a second lens group having a negative optical power, and a third lens group having a positive optical power. Moreover, the first lens group includes a first optical axis changing element that changes the optical axis.
In this variable-magnification optical system according to the present invention, it is preferable that conditional formula (1) below be fulfilled:

0.1<|f2/√{square root over (fw×ft)}|<0.45  (1)

where

    
    
        f2 represents the focal length of the second lens group;
        fw represents the focal length of the entire variable-magnification optical system at the wide-angle end; and
        ft represents the focal length of the entire variable-magnification optical system at the telephoto end.
    
    


Alternatively, in the variable-magnification optical system according to the present invention, it is preferable that conditional formula (2) below be fulfilled:

0.5<f1/√{square root over (fw×ft)}<1.4  (2)

where

    
    
        f1 represents the focal length of the first lens group;
        fw represents the focal length of the entire variable-magnification optical system at the wide-angle end; and
        ft represents the focal length of the entire variable-magnification optical system at the telephoto end.
    
    


Alternatively, in the variable-magnification optical system according to the present invention, it is preferable that conditional formula (3) below be fulfilled:

0.3<f3/√{square root over (fw×ft)}<1.0  (3)

where

    
    
        f3 represents the focal length of the third lens group;
        fw represents the focal length of the entire variable-magnification optical system at the wide-angle end; and
        ft represents the focal length of the entire variable-magnification optical system at the telephoto end.
    
    


Conditional formula (1), (2), or (3) relates to the optical power of a particular lens group. Moreover, conditional formula (1), (2), or (3) defines, based on the optical power of the particular lens group, a conditional range that should preferably be fulfilled to achieve a proper balance between reduction of the total length of the variable-magnification optical system (with a view to making it compact) and reduction of various aberrations.
By observing the upper limit of conditional formula (1), (2), or (3), it is possible to prevent the variable-magnification optical system from becoming unduly long (to prevent its total length from becoming unduly large). On the other hand, by observing the lower limit of conditional formula (1), (2), or (3), it is possible to prevent the various aberrations attributable to the optical powers of the individual lens groups from becoming extremely large (to prevent degradation of optical performance). Thus, according to the present invention, within the range defined by conditional formula (1), (2), or (3), it is possible to realize a variable-magnification optical system that is compact but nevertheless offers good optical performance.
The above and other objects and features of the present invention will be clear in light of the detailed description of preferred embodiments below with reference to the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 1 of the invention;
FIG. 2A is a spherical aberration diagram of the variable-magnification optical system of Example 1 at the wide-angle end (W);
FIG. 2B is a astigmatism diagram of the variable-magnification optical system of Example 1 at the wide-angle end (W);
FIG. 2C is a distortion diagram of the variable-magnification optical system of Example 1 at the wide-angle end (W);
FIG. 3A is a spherical aberration diagram of the variable-magnification optical system of Example 1 at the middle-focal-length position (M);
FIG. 3B is a astigmatism diagram of the variable-magnification optical system of Example 1 at the middle-focal-length position (M);
FIG. 3C is a distortion diagram of the variable-magnification optical system of Example 1 at the middle-focal-length position (M);
FIG. 4A is a spherical aberration diagram of the variable-magnification optical system of Example 1 at the telephoto end (T);
FIG. 4B is a astigmatism diagram of the variable-magnification optical system of Example 1 at the telephoto end (T);
FIG. 4C is a distortion diagram of the variable-magnification optical system of Example 1 at the telephoto end (T);
FIG. 5 is a diagram schematically showing the construction, as seen from the back, of a digital camera embodying the invention;
FIG. 6 is a diagram schematically showing the construction, as seen from a side, of a digital camera embodying the invention;
FIG. 7 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 2 of the invention;
FIG. 8A is a spherical aberration diagram of the variable-magnification optical system of Example 2 at the wide-angle end (W);
FIG. 8B is a astigmatism diagram of the variable-magnification optical system of Example 2 at the wide-angle end (W);
FIG. 8C is a distortion diagram of the variable-magnification optical system of Example 2 at the wide-angle end (W);
FIG. 9A is a spherical aberration diagram of the variable-magnification optical system of Example 2 at the middle-focal-length position (M);
FIG. 9B is a astigmatism diagram of the variable-magnification optical system of Example 2 at the middle-focal-length position (M);
FIG. 9C is a distortion diagram of the variable-magnification optical system of Example 2 at the middle-focal-length position (M);
FIG. 10A is a spherical aberration diagram of the variable-magnification optical system of Example 2 at the telephoto end (T);
FIG. 10B is a astigmatism diagram of the variable-magnification optical system of Example 2 at the telephoto end (T);
FIG. 10C is a distortion diagram of the variable-magnification optical system of Example 2 at the telephoto end (T);
FIG. 11 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 3 of the invention;
FIG. 12A is a spherical aberration diagram of the variable-magnification optical system of Example 3 at the wide-angle end (W);
FIG. 12B is a astigmatism diagram of the variable-magnification optical system of Example 3 at the wide-angle end (W);
FIG. 12C is a distortion diagram of the variable-magnification optical system of Example 3 at the wide-angle end (W);
FIG. 13A is a spherical aberration diagram of the variable-magnification optical system of Example 3 at the middle-focal-length position (M);
FIG. 13B is a astigmatism diagram of the variable-magnification optical system of Example 3 at the middle-focal-length position (M);
FIG. 13C is a distortion diagram of the variable-magnification optical system of Example 3 at the middle-focal-length position (M);
FIG. 14A is a spherical aberration diagram of the variable-magnification optical system of Example 3 at the telephoto end (T);
FIG. 14B is a astigmatism diagram of the variable-magnification optical system of Example 3 at the telephoto end (T);
FIG. 14C is a distortion diagram of the variable-magnification optical system of Example 3 at the telephoto end (T);
FIG. 15 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 4 of the invention;
FIG. 16A is a spherical aberration diagram of the variable-magnification optical system of Example 4 at the wide-angle end (W);
FIG. 16B is a astigmatism diagram of the variable-magnification optical system of Example 4 at the wide-angle end (W);
FIG. 16C is a distortion diagram of the variable-magnification optical system of Example 4 at the wide-angle end (W);
FIG. 17A is a spherical aberration diagram of the variable-magnification optical system of Example 4 at the middle-focal-length position (M);
FIG. 17B is a astigmatism diagram of the variable-magnification optical system of Example 4 at the middle-focal-length position (M);
FIG. 17C is a distortion diagram of the variable-magnification optical system of Example 4 at the middle-focal-length position (M);
FIG. 18A is a spherical aberration diagram of the variable-magnification optical system of Example 4 at the telephoto end (T);
FIG. 18B is a astigmatism diagram of the variable-magnification optical system of Example 4 at the telephoto end (T);
FIG. 18C is a distortion diagram of the variable-magnification optical system of Example 4 at the telephoto end (T);
FIG. 19 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 5 of the invention;
FIG. 20A is a spherical aberration diagram of the variable-magnification optical system of Example 5 at the wide-angle end (W);
FIG. 20B is a astigmatism diagram of the variable-magnification optical system of Example 5 at the wide-angle end (W);
FIG. 20C is a distortion diagram of the variable-magnification optical system of Example 5 at the wide-angle end (W);
FIG. 21A is a spherical aberration diagram of the variable-magnification optical system of Example 5 at the middle-focal-length position (M);
FIG. 21B is a astigmatism diagram of the variable-magnification optical system of Example 5 at the middle-focal-length position (M);
FIG. 21C is a distortion diagram of the variable-magnification optical system of Example 5 at the middle-focal-length position (M);
FIG. 22A is a spherical aberration diagram of the variable-magnification optical system of Example 5 at the telephoto end (T);
FIG. 22B is a astigmatism diagram of the variable-magnification optical system of Example 5 at the telephoto end (T);
FIG. 22C is a distortion diagram of the variable-magnification optical system of Example 5 at the telephoto end (T);
FIG. 23 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 6 of the invention;
FIG. 24A is a spherical aberration diagram of the variable-magnification optical system of Example 6 at the wide-angle end (W);
FIG. 24B is a astigmatism diagram of the variable-magnification optical system of Example 6 at the wide-angle end (W);
FIG. 24C is a distortion diagram of the variable-magnification optical system of Example 6 at the wide-angle end (W);
FIG. 25A is a spherical aberration diagram of the variable-magnification optical system of Example 6 at the middle-focal-length position (M);
FIG. 25B is a astigmatism diagram of the variable-magnification optical system of Example 6 at the middle-focal-length position (M);
FIG. 25C is a distortion diagram of the variable-magnification optical system of Example 6 at the middle-focal-length position (M);
FIG. 26A is a spherical aberration diagram of the variable-magnification optical system of Example 6 at the telephoto end (T);
FIG. 26B is a astigmatism diagram of the variable-magnification optical system of Example 6 at the telephoto end (T);
FIG. 26C is a distortion diagram of the variable-magnification optical system of Example 6 at the telephoto end (T);
FIG. 27 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 7 of the invention;
FIG. 28A is a spherical aberration diagram of the variable-magnification optical system of Example 7 at the wide-angle end (W);
FIG. 28B is a astigmatism diagram of the variable-magnification optical system of Example 7 at the wide-angle end (W);
FIG. 28C is a distortion diagram of the variable-magnification optical system of Example 7 at the wide-angle end (W);
FIG. 29A is a spherical aberration diagram of the variable-magnification optical system of Example 7 at the middle-focal-length position (M);
FIG. 29B is a astigmatism diagram of the variable-magnification optical system of Example 7 at the middle-focal-length position (M);
FIG. 29C is a distortion diagram of the variable-magnification optical system of Example 7 at the middle-focal-length position (M);
FIG. 30A is a spherical aberration diagram of the variable-magnification optical system of Example 7 at the telephoto end (T);
FIG. 30B is a astigmatism diagram of the variable-magnification optical system of Example 7 at the telephoto end (T);
FIG. 30C is a distortion diagram of the variable-magnification optical system of Example 7 at the telephoto end (T);
FIG. 31 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 8 of the invention;
FIG. 32A is a spherical aberration diagram of the variable-magnification optical system of Example 8 at the wide-angle end (W);
FIG. 32B is a astigmatism diagram of the variable-magnification optical system of Example 8 at the wide-angle end (W);
FIG. 32C is a distortion diagram of the variable-magnification optical system of Example 8 at the wide-angle end (W);
FIG. 33A is a spherical aberration diagram of the variable-magnification optical system of Example 8 at the middle-focal-length position (M);
FIG. 33B is a astigmatism diagram of the variable-magnification optical system of Example 8 at the middle-focal-length position (M);
FIG. 33C is a distortion diagram of the variable-magnification optical system of Example 8 at the middle-focal-length position (M);
FIG. 34A is a spherical aberration diagram of the variable-magnification optical system of Example 8 at the telephoto end (T);
FIG. 34B is a astigmatism diagram of the variable-magnification optical system of Example 8 at the telephoto end (T);
FIG. 34C is a distortion diagram of the variable-magnification optical system of Example 8 at the telephoto end (T);
FIG. 35 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 9 of the invention;
FIG. 36A is a spherical aberration diagram of the variable-magnification optical system of Example 9 at the wide-angle end (W);
FIG. 36B is a astigmatism diagram of the variable-magnification optical system of Example 9 at the wide-angle end (W);
FIG. 36C is a distortion diagram of the variable-magnification optical system of Example 9 at the wide-angle end (W);
FIG. 37A is a spherical aberration diagram of the variable-magnification optical system of Example 9 at the middle-focal-length position (M);
FIG. 37B is a astigmatism diagram of the variable-magnification optical system of Example 9 at the middle-focal-length position (M);
FIG. 37C is a distortion diagram of the variable-magnification optical system of Example 9 at the middle-focal-length position (M);
FIG. 38A is a spherical aberration diagram of the variable-magnification optical system of Example 9 at the telephoto end (T);
FIG. 38B is a astigmatism diagram of the variable-magnification optical system of Example 9 at the telephoto end (T);
FIG. 38C is a distortion diagram of the variable-magnification optical system of Example 9 at the telephoto end (T);
FIG. 39 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 10 of the invention;
FIG. 40A is a spherical aberration diagram of the variable-magnification optical system of Example 10 at the wide-angle end (W);
FIG. 40B is a astigmatism diagram of the variable-magnification optical system of Example 10 at the wide-angle end (W);
FIG. 40C is a distortion diagram of the variable-magnification optical system of Example 10 at the wide-angle end (W);
FIG. 41A is a spherical aberration diagram of the variable-magnification optical system of Example 10 at the middle-focal-length position (M);
FIG. 41B is a astigmatism diagram of the variable-magnification optical system of Example 10 at the middle-focal-length position (M);
FIG. 41C is a distortion diagram of the variable-magnification optical system of Example 10 at the middle-focal-length position (M);
FIG. 42A is a spherical aberration diagram of the variable-magnification optical system of Example 10 at the telephoto end (T);
FIG. 42B is a astigmatism diagram of the variable-magnification optical system of Example 10 at the telephoto end (T);
FIG. 42C is a distortion diagram of the variable-magnification optical system of Example 10 at the telephoto end (T);
FIG. 43 is a lens construction diagram of a lens unit incorporating the variable-magnification optical system of Example 11 of the invention;
FIG. 44A is a spherical aberration diagram of the variable-magnification optical system of Example 11 at the wide-angle end (W);
FIG. 44B is a astigmatism diagram of the variable-magnification optical system of Example 11 at the wide-angle end (W);
FIG. 44C is a distortion diagram of the variable-magnification optical system of Example 11 at the wide-angle end (W);
FIG. 45A is a spherical aberration diagram of the variable-magnification optical system of Example 11 at the middle-focal-length position (M);
FIG. 45B is a astigmatism diagram of the variable-magnification optical system of Example 11 at the middle-focal-length position (M);
FIG. 45C is a distortion diagram of the variable-magnification optical system of Example 11 at the middle-focal-length position (M);
FIG. 46A is a spherical aberration diagram of the variable-magnification optical system of Example 11 at the telephoto end (T);
FIG. 46B is a astigmatism diagram of the variable-magnification optical system of Example 11 at the telephoto end (T); and
FIG. 46C is a distortion diagram of the variable-magnification optical system of Example 11 at the telephoto end (T).



DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
Embodiment 1
An embodiment (Embodiment 1) of the present invention will be described below with reference to the drawings.
1. Digital Camera
FIGS. 5 and 6 are diagrams schematically showing the construction of a digital camera 29, as an example of an image-taking apparatus embodying the invention. FIG. 5 shows the interconnection among individual internal blocks, and also shows a lens unit 1 (including a variable-magnification optical system 11 and an image sensor SR) incorporated in the digital camera 29. On the other hand, FIG. 6 is a side view of the digital camera 29, and shows, in particular, the variable-magnification optical system 11 included in the lens unit 1.
As shown in FIG. 5, the digital camera 29 includes a variable-magnification optical system 11, an optical system driving section 13, an image sensor SR, a signal processing section 14, a display section 15, a recording section 16, a recording medium 17, an operation section 18, and a control section 19.
The variable-magnification optical system 11 directs the light from the shooting target to the image sensor SR in such a way that the light is imaged on the light-receiving surface (image-sensing surface) of the image sensor SR. Hence, the variable-magnification optical system 11 may be called an image-forming or image-taking optical system. The variable-magnification optical system 11 will be described in detail later.
The optical system driving section 13 includes several driving motors (optical system driving motors) and transmission mechanisms (optical system transmission mechanisms) for transmitting the driving force of the motors to the lens groups constituting the variable-magnification optical system 11 (the driving motors and transmission mechanisms are not illustrated). By using these driving motors and transmission mechanisms, the optical system driving section 13 sets the focal length or focal position of the variable-magnification optical system 11. Specifically, the optical system driving section 13 sets the focal length or focal position according to instructions from the control section 19.
The image sensor SR is, for example, a CCD (charge-coupled device) area sensor or a CMOS (complementary metal oxide semiconductor) sensor. The image sensor SR receives the light that has passed through the variable-magnification optical system 11, and converts it into an electrical signal (sensed data). The image sensor SR then feeds the sensed data to the signal processing section 14.
The signal processing section 14 processes the electronic data (sensed data) from the image sensor SR, and produces, based on the sensed data, sensed-image data. The signal processing section 14 starts and stops its processing according to instructions from the control section 19. Moreover, according to instructions from the control section 19, the signal processing section 14 feeds the sensed-image data to the display section 15 and to the recording section 16.
The display section 15 is built with, for example, a liquid crystal display panel. The display section 15 displays the sensed-image data from the signal processing section 14, the status of use of the digital camera 29, and other indications and information.
The recording section 16 records the sensed-image data produced by the signal processing section 14 to the recording medium 17 according to instructions from the control section 19. Moreover, according to instructions from the control section 19 based on how the operation section 18 and other parts are operated, the recording section 16 reads sensed-image data from the recording medium 17.
The recording medium 17 may be, for example, of the type that is unremovably built in the digital camera 29 or, like a flash memory, of the type that is removably loaded in the digital camera 29. The only requirement about the recording medium 17 is that it be a medium (such as an optical disk or semiconductor memory) that permits sensed-image data and other data to be recorded thereto.
The operation section 18 accepts various kinds of operation and instructions from the user or the like, and then feeds them to the control section 19. The operation section 18 includes, for example, a shutter release button and an operation dial.
The control section 19 functions as a control center that controls, among others, the operation of the digital camera 29 as a whole. Thus, the control section 19 centrally controls the operation of the digital camera 29 by controlling the driving of the individual members thereof in an organized manner.
2. Lens Unit
Now, the lens unit 1, which includes the variable-magnification optical system 11 and the image sensor SR, will be described with reference to FIGS. 1, 5 and 6. The example of the lens unit 1 shown in FIGS. 5 and 6 is housed inside the digital camera 29. The lens unit 1 is so designed as to bend the light beam that passes therethrough by the use of an optical prism PR or a reflective mirror MR.
The lens unit 1, however, does not necessarily have to be a lens system (bending optical system) that bends the light beam as described above (that is, the optical prism PR and the reflective mirror MR shown in FIGS. 5 and 6 may be omitted). In fact, for the sake of convenience, the reflective mirror MR is omitted in FIG. 1 (lens construction diagram), which shows, in a straightened form, the lens unit 1 shown in FIGS. 5 and 6. The optical axis of the lens unit 1 is represented by AX (AX1 to AX3, see FIGS. 5 and 6).
In FIG. 1, GRi represents a lens group, Li represents a lens element, and si represents a surface (such as a transmissive surface). The numerical suffix “i” with which each symbol GRi, Li, or si ends indicates the place as counted from the object side to the image side at which the element it refers to is located among all the elements of the same kind. An aspherical surface is marked with an asterisk “*”. The variable-magnification optical system 11 (and thus the lens unit 1) shown in FIG. 1 is referred to as Example 1.
2-1. Lens Unit Construction (Example 1)
The variable-magnification optical system 11 of the lens unit 1 includes, from the shooting target side (object side), a first lens group GR1, a second lens group GR2, a third lens group GR3, a fourth lens group GR4, and an image sensor unit SU. Since this image sensor unit SU takes the fifth place as counted from the object side, it is identified also by SU5 in the following description.
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. The first lens group GR1 as a whole has a “positive” optical power (refractive power). It should be understood that an optical power is defined as the reciprocal of a focal length.
The first lens element (front lens element) is a negative meniscus lens element convex on the object side.
The optical prism (a first optical axis changing member) PR is a prism (for example, a rectangular prism) that bends at right angles the light beam incoming from the object side. The optical prism PR receives the light beam at an entrance surface s3 thereof, and lets the light beam exit therefrom at an exit surface s4 thereof.
The second lens element L2 is a positive lens element convex on both sides (a biconvex lens element). The third lens element L3 is a positive lens element convex on both sides.
Second Lens Group
The second lens group GR2 includes, from the object side, a fourth lens element (the most object side lens element) L4, a fifth lens element L5, and a sixth lens element L6. The second lens group GR2 as a whole has a “negative” optical power.
The fourth lens element L4 is a negative lens element having concave surface on both sides (a biconcave lens element). The fourth lens element L4 has (as its object-side surface) an aspherical surface s9 (an aspherical surface denotes a refractive optical surface having an aspherical shape, a surface exerting a refractive effect equivalent to that exerted by an aspherical surface, or the like).
The fifth lens element L5 is a negative lens element concave on both sides. The sixth lens element L6 is a positive lens element convex on both sides. The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element. The cementing together of the lens elements is achieved, for example, by the use of adhesive (likewise, any cemented lens element mentioned later is formed by cementing together the constituent lens elements thereof, for example, with adhesive).
Third Lens Group
The third lens group GR3 includes, from the object side, an optical aperture stop ST, a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, and a tenth lens element Lb. The third lens group GR3 as a whole has a “positive” optical power.
The optical aperture stop ST is an aperture stop that permits the aperture diameter RS to be varied. The optical aperture stop ST is built integrally with the third lens group GR3. For the sake of convenience, in FIG. 1, the optical aperture stop ST itself is indicated as s15.
The seventh lens element L7 is a positive lens element convex on both sides. The seventh lens element L7 has an aspherical surface sl6. The eighth lens element L8 is a negative meniscus lens element concave on the object side. The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element.
The ninth lens element L9 is a positive lens element convex on both sides. The ninth lens element L9 has an aspherical surface s20. The tenth lens element L10 is a negative meniscus lens element concave on the object side. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.
Fourth Lens Group
The fourth lens group GR4 includes, from the object side, an eleventh lens element L11 and a twelfth lens element L12. The fourth lens group GR4 as a whole has a “positive” optical power.
The eleventh lens element L11 is a negative meniscus lens element concave on the object side. The twelfth lens element L12 is a positive lens element convex on both sides. The twelfth lens element L12 has aspherical surfaces s26 and s27.
Image Sensor Unit
The image sensor unit SU includes, from the object side, a cover glass CG, which has two surfaces s28 and s29, and an image sensor SR. These are so arranged that the surface s29 of the cover glass CG is located very close to the light-receiving surface of the image sensor SR.
In the lens unit 1 of Example 1, the image sensor SR is kept at a fixed position (that is, the image sensor unit SU is stationary). The cover glass CG may function as an optical filter (for example, an infrared cut filter) that has a predetermined cut-off frequency characteristic determined by the pixel pitch of the image sensor SR (although the cover glass CG itself has no optical power).
2-2. Construction Data of the Variable-Magnification Optical System (Example 1)
Tables 1 and 2 show the construction data of the variable-magnification optical system 11 of Example 1.
In Table 1, a symbol in the form of “ri” represents the radius of curvature (in mm) of a surface si. An aspherical surface is marked with an asterisk (*). A symbol in the form of “di” represents the axial distance (in mm) between the i-th surface si and the (i+1)-th surface si+1. For any axial distance that varies with zooming, three values are given that are, from left, the value of di at the wide-angle end (W), that at the middle-focal-length position (M), and that at the telephoto end (T).
Symbols in the forms of “Ni” and “vi” represent the refractive index Nd and the Abbe number vi, respectively, of the medium filling a given axial distance di. Here, the refractive index Nd and the Abbe number vi are those for the d-line (having a wavelength of 587.56 nm).
Shown together in Table 1 are the focal length f (in mm) and f-number FNO of the entire system as observed at each of the following different “focal length positions”: the wide-angle end (shortest-focal-length position) (W); the middle-focal-length position (M); and the telephoto end (longest-focal-length position) (T).
Here, an aspherical surface is defined by formula (i) below.

X(H)=C0·H2/(1+√{square root over (1−ε·C02·H2)}+ΣAj·Hj  (i)

where

    
    
        H represents the height in a direction perpendicular to the optical axis AX;
        X(H) represents the displacement along the optical axis (the sag) at the height h;
        C0 represents the paraxial curvature (=1/ri);
        ε represents the quadric surface parameter;
        j represents the order of the aspherical surface; and
        Aj represents the aspherical coefficient of order j.
    
    


Table 2 shows the data related to the aspherical surfaces. The coefficient of any term that does not appear in the table equals 0 (zero). For all the data shown, “E-n” represent “×10−n”.
2-3. Movement of the Individual Lens Groups in the Lens Unit
Zooming
Now, the movement of the individual lens groups (GR1 to GR4) will be described with reference to FIG. 1. In the lens unit 1, zooming (magnification variation or the like) is achieved by varying the distances between the individual lens groups along the optical axis AX.
For example, in the lens unit 1 shown in FIG. 1, zooming is achieved by moving part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side while moving the rest of the lens groups (namely, the fourth lens group GR4) toward the image side.
During this zooming, the distances (group-to-group distances) between the individual lens groups vary. Accordingly, in FIG. 1, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, dl4, d23, and d27 are shown.
In FIG. 1, arrows MMi schematically indicate the movement of the individual lens groups from the wide-angle end (W) to the middle-focal-length position (M) and further to the telephoto end (T). The numerical suffix “i” with which each symbol MMi ends indicates the place as counted from the object side to the image side at which the arrow it refers to is located, the number thus coinciding with that of the lens unit the arrow is relevant to.
FIGS. 2A to 2C, 3A to 3C, and 4A to 4C show the aberrations observed in the variable-magnification optical system 11 at different zoom positions. Specifically, FIGS. 2A to 2C show the aberrations observed at the wide-angle end (W), FIGS. 3A to 3C show the aberrations observed at the middle-focal-length position (M), and FIGS. 4A to 4C show the aberrations observed at the telephoto end (T).
FIGS. 2A, 3A, and 4A show spherical aberration (S.A.) and sine condition (S.C.). In these diagrams, a solid line d represents the spherical aberration (in mm) for the d-line, and a broken line SC represents the deviation (in mm) from the ideal sine condition. Shown together in these diagrams are the FNOs (f-numbers) at the respective focal length positions.
FIGS. 2B, 3B, and 4B show astigmatism. In these diagrams, a broken line DM represents the astigmatism (in mm) for the d-line as observed on the meridional surface, and a solid line DS represents the astigmatism (in mm) for the d-line as observed on the sagittal surface. Shown together in these diagrams are the values of Y′ (in mm), which represents the maximum image height (the distance from the optical axis AX) on the light-receiving surface of the image-sensing device SR.
FIGS. 2C, 3C, and 4C show distortion. In these diagrams, a solid line represents the distortion (%) for the d-line. Shown together in these diagrams are the values of Y′.
3. Examples of Various Features of the Present Invention
As will be understood from the foregoing, a variable-magnification optical system 11 according to the invention includes, from the object side to the image side, at least a first lens group GR1 having a positive optical power, a second lens group GR2 having a negative optical power, and a third lens group GR3 having a positive optical power. Moreover, the first lens group GR1 includes a optical prism PR that changes the optical axis.
In addition, a variable-magnification optical system 11 according to the invention fulfills at least one of conditional formula (A), (B), or (C) below. Not all of these conditional formulae need to be fulfilled simultaneously. Fulfilling any of them brings the corresponding effects and benefits in the variable-magnification optical system 11. Needless to say, the more of the conditional formulae are fulfilled, the more effects and benefits are obtained.
Conditional formula (A) (conditional formula (1)) is as shown below.

0.1<|f2/√{square root over (fw×ft)}|<0.45  (A)

where

    
    
        f2 represents the focal length of the second lens group;
        fw represents the focal length of the entire variable-magnification optical system at the wide-angle end; and
        ft represents the focal length of the entire variable-magnification optical system at the telephoto end.
    
    


Conditional formula (B) (conditional formula (2)) is as shown below.

0.5<f1/√{square root over (fw×ft)}<1.4  (B)

where

    
    
        f1 represents a focal length of the first lens group.
    
    


Conditional formula (C) (conditional formula (3)) is as shown below.

0.3<f3/√{square root over (fw×ft)}<1.0  (C)

where

    
    
        f3 represents a focal length of the third lens group.
    
    


Conditional formulae (A), (B), or (C) relates to the focal length f2, f1, or f3, and thus the optical power (refractive power), of a particular lens group GR2, GR1, or GR3. Moreover, conditional formula (A), (B), or (C) defines, based on the optical power of the particular lens group GR2, GR1, or GR3, a conditional range that should preferably be fulfilled to achieve a proper balance between reduction of the total length of the variable-magnification optical system, and thus the total length of the lens unit 1 (with a view to making them compact), and reduction of various aberrations.
With respect to the geometric mean √{square root over (fw×ft)} of the focal lengths fw and ft of the variable-magnification optical system at the wide-angle end (W) and the telephoto end (T), respectively, if the ratio thereto of the focal length f2, f1, or f3 of a particular lens group Gr2, Gr1, or Gr3 exceeds (is greater than) the upper limit of conditional formula (A), (B), or (C), this means that the focal length f2, f1, or f3 is comparatively long (that is, the corresponding optical power is comparatively weak).
Here, the weaker the optical power of the lens group Gr2, Gr1, or Gr3, the longer the distance through which the lens group Gr2, Gr1, or Gr3 needs to move for zooming (and thus the larger the variable-magnification optical system 11). On the other hand, generally, the weaker an optical power, the smaller the various aberrations (such as astigmatism) it produces.
Thus, disregarding the upper limit of conditional formula (A), (B), or (C) has the disadvantage of increasing the total length of the variable-magnification optical system 11 (making the lens unit 1 larger), but has the advantage of alleviating degradation (appearing as various aberrations) of optical performance.
By contrast, with respect to the geometric mean √{square root over (fw×ft)} (the focal length at the middle-focal-length position (M)), if the ratio thereto of the focal length f2, f1, or f3 of a particular lens group Gr2, Gr1, or Gr3 exceeds (is smaller than) the lower limit of conditional formula (A), (B), or (C), this means that the focal length f2, f1, or f3 is comparatively short (that is, the corresponding optical power is comparatively strong).
Here, the stronger the optical power of the lens group Gr2, Gr1, or Gr3, the shorter the distance through which the lens group Gr2, Gr1, or Gr3 needs to move for zooming (and thus the smaller the variable-magnification optical system 1). On the other hand, the stronger the negative optical power given to the lens group Gr2, Gr1, or Gr3, the larger the various aberrations it produces (and thus the lower the optical performance obtained).
Thus, disregarding the lower limit of conditional formula (A), (B), or (C) has the disadvantage of aggravating degradation (appearing as various aberrations) of optical performance, but has the advantage of reducing the total length of the variable-magnification optical system 11 (making it more compact).
As will be understood from the foregoing, observing the upper limit of conditional formula (A), (B), or (C) helps prevent the total length of the variable-magnification optical system 11 from becoming unduly large (and thus prevent the lens unit 1 from becoming unduly large), and observing the lower limit of conditional formula (A), (B), or (C) helps prevent the optical power of a particular lens group GR2, GR1, or GR3 from causing extreme degradation of optical performance. Thus, according to the invention, within the range defined by conditional formula (A), (B), or (C), it is possible to realize a variable-magnification optical system 11 (lens unit 1) that is compact but nevertheless suffers less from degradation of optical performance (offers good optical performance).
The values of conditional formula (A), (B), or (C) as calculated in the variable-magnification optical system 11 of Example 1 are as follows (see Table 23 described later):
In Example 1, |f2/√{square root over (fw×ft)}|=0.42
In Example 1, |f1/√{square root over (fw×ft)}|=1.29
In Example 1, |f3/√{square root over (fw×ft)}|=0.90
According to the invention, for further compactness, the third lens group GR3 may include a reflective mirror MR or the like (a second optical axis changing element; see FIGS. 5 and 6) that changes the optical axis by reflecting the light beam, though the provision of such an element is not an absolute requirement. With this construction, it is possible to build, instead of a variable-magnification optical system 11 that extends along a straight line (that is, a straight-type variable-magnification optical system 11), a bent-type variable-magnification optical system 11 (that is, a variable-magnification bending optical system).
This permits increased flexibility in the arrangement of the variable-magnification optical system 11 (lens unit 1). Specifically, the variable-magnification optical system 11 (lens unit 1) so bent and thereby made compact can be arranged in a position suitable therefor inside the housing of the digital camera 29. This helps reduce the dimensions of the digital camera 29 in, among others, the height direction U and the horizontal direction V. Incidentally, the inclusion of the optical prism PR in the first lens group GR1 helps reduce the dimension of the digital camera 29 incorporating the lens unit 1 in the depth direction Z.
In the variable-magnification optical system 11, when the first and third lens groups GR1 and GR3 are moved for zooming, the group-to-group distance between them (the first and third lens groups GR1 and GR3) may be kept constant. For example, the first and third lens groups GR1 and GR3 are built integrally via a lens frame (linking member, not illustrated) so that they are moved simultaneously.
Keeping the first and third lens groups GR1 and GR3 in a linked state as described above helps simplify the structure (arrangement structure) needed for the arrangement of those lens groups GR1 and GR3. This makes it possible, for example, to house the two lens groups GR1 and GR3 in the same lens barrel (not illustrated). This helps make the lens barrel compact.
Moreover, there is now no need to provide separate sources of driving force for moving the first and third lens groups GR1 and GR3 (this helps simplify the structure (driving structure) needed for their movement). That is, the two lens groups, namely the first and third lens groups GR1 and GR3, can now be moved with a single source of driving force.
With the features described above, it is possible to realize a variable-magnification optical system 11 that is remarkably compact but can nevertheless suppress various aberrations. For more effective suppression or correction of various aberrations, a variable-magnification optical system 11 according to the invention may be further provided with the features described below.
For example, the lens unit 1 described above incorporates a variable-magnification optical system 11 including a plurality of lens groups (GR1 to GR4) arranged in a positive-negative-positive-positive optical power arrangement. Here, the second lens group GR2 needs to make diverge the light that has just been made to converge by the positive optical power of the first lens group GR1. Thus, the second lens group GR2 needs to have a comparatively strong optical power. This comparatively strong optical power tends to cause the second lens group GR2 to produce various aberrations.
To avoid this, according to the invention, at least one of the lens elements Li included in the second lens group GR2 fulfills conditional formula (D) below (see Table 1).

N2g>1.7  (D)

where

    
    
        N2g represents the refractive index, for the d-line, of a lens element Li included in the second lens group GR2.
    
    


With this comparatively high refractive index, it is possible, for example on a lens element having a given focal length, to form a lens surface having a comparatively gentle curvature (a larger radius of curvature). This gentle curvature permits a variable-magnification optical system 11 according to the invention to suppress various aberrations.
For more effective correction of various aberrations, at least one lens element (in Example 1, the fourth lens element L4) may have an aspherical surface. With this aspherical lens surface, it is possible to effectively correct the distortion and other aberrations produced (in particular at the wide-angle end (W)) by the comparatively strong negative optical power.
To make the light incident on the image sensor SR highly telecentric, in a variable-magnification optical system 11 according to the invention, a fourth lens group GR4 having a positive optical power is disposed to follow the first to third lens groups GR1 to GR3 arranged in a positive-negative-positive optical power arrangement.
4. Other Examples
A variable-magnification optical system 11 according to the invention may be constructed in any other manner than specifically described above in connection with the variable-magnification optical system 11 of Example 1. Now, lens units 1 incorporating other variable-magnification optical systems 11 (Examples 2 and 3) that have the thus far described features and that thus offer the comparable effects and benefits will be presented.
In Examples 2 and 3 presented below, as in Example 1, the variable-magnification optical system 11 includes, from the shooting target side, a first lens group GR1, a second lens group GR2, a third lens group GR3, and a fourth lens group GR4 arranged in a positive-negative-positive-positive optical power arrangement. Moreover, on the image side of the fourth lens group GR4, an image sensor unit SU5 is disposed.
Variable-Magnification Optical System of Example 2 (see FIG. 7) First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive lens element convex on both sides.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s9 as the object-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, and a tenth lens element L10. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a positive lens element convex on both sides (and having an aspherical surface s20); and
        The tenth lens element L10 is a negative meniscus lens element concave on the object side.

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 only includes an eleventh lens element Lii. Used as this lens element is as follows:

    
    
        The eleventh lens element L11 is a positive lens element convex on both sides (and having aspherical surfaces s24 and s25).

Image Sensor Unit

    
    


The cover glass CG of the image sensor unit SU5 has two surfaces s26 and s27 for protecting the light-receiving surface of the image sensor SR.
Construction Data of the Variable-Magnification Optical System (Example 2)
Tables 3 and 4 show the construction data of the variable-magnification optical system 11 of Example 2. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 2, as shown in FIG. 7, zooming is achieved by moving part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side while moving the rest of the lens groups (namely, the fourth lens group GR4) toward the image side. Accordingly, in FIG. 7, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, dl4, d23, and d25 are shown.
FIGS. 8A to 8C, 9A to 9C, and 10A to 10C show the aberrations observed in the variable-magnification optical system 11 of Example 2 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 3 (see FIG. 11)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive lens element convex on both sides.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s9 as the object-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as s15; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a positive lens element convex on both sides (and having an aspherical surface s20);
        The tenth lens element L10 is a positive lens element convex on both sides; and
        The eleventh lens element L11 is a negative meniscus lens element concave on the object side.

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The tenth and eleventh lens elements L10 and L11 are cemented together at the surfaces s23 and s24 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 only includes a twelfth lens element L12. Used as this lens element is as follows:

    
    
        The twelfth lens element L12 is a positive meniscus lens element convex on the object side (and having an aspherical surface s26).

Image Sensor Unit

    
    


The cover glass CG of the image sensor unit SU5 has two surfaces s28 and s29 for protecting the light-receiving surface of the image sensor SR.
Construction Data of the Variable-Magnification Optical System (Example 3)
Tables 5 and 6 show the construction data of the variable-magnification optical system 11 of Example 3. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 3, as shown in FIG. 11, zooming is achieved by moving all the lens groups (namely, the first to fourth lens groups GR1 to GR4) toward the object side, except that the fourth lens group GR4 first moves toward the object side but then makes a U-turn to move back toward the image side. Accordingly, in FIG. 11, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, dl4, d25, and d27 are shown.
FIGS. 12A to 12C, 13A to 13C, and 14A to 14C show the aberrations observed in the variable-magnification optical system 11 of Example 3 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Embodiment 2
Another embodiment (Embodiment 2) of the present invention will be described below. In the following description, such members as serve the same purposes as in Embodiment 1 are identified with common reference symbols, and no overlapping explanations will be repeated.
In the lens unit 1 of Embodiment 1, it is assumed that the most object-side lens element (the fourth lens element L4) of the second lens group GR2 has an aspherical surface as the object-side surface s9 thereof. The present invention, however, may be practiced with any other construction.
For example, the most object-side lens element Li of the second lens group GR2 may have an aspherical surface as the image-side surface si thereof. The variable-magnification optical system 11 may be so constructed as to include, instead of an image sensor unit SU including an image sensor SR and a cover glass CG, a lens group GRi including a lens element Li, a cover glass CG, and an image sensor SR.
1. Constructions of Lens Units Incorporating Various Variable-Magnification Optical Systems
Hereinafter, other variable-magnification optical systems 11 (Examples 4 to 11) embodying the present invention will be presented. In Example 4, the variable-magnification optical system 11 is constructed as follows: instead of a reflective mirror MR (see FIGS. 5 and 6), an optical prism (second optical prism) PR′ is included in the third lens group GR3; moreover, the most object-side lens element (the fourth lens element L4) in the second lens group GR2 has an aspherical surface as the image-side surface s10 thereof.
In Examples 5 to 11, the variable-magnification optical system 11 constructed as follows: there is provided a fourth lens group GR4 that includes a lens element Li, a cover glass CG, and an image sensor SR; moreover, the most object-side lens element (the fourth lens element L4) in the second lens group GR2 has an aspherical surface as the image-side surface s10 thereof.
In Examples 4 to 11 presented below, as in Examples 1 to 3, the variable-magnification optical system 11 includes, from the shooting target side, a first lens group GR1, a second lens group GR2, a third lens group GR3, and a fourth lens group GR4 arranged in a positive-negative-positive-positive optical power arrangement.
Variable-Magnification Optical System of Example 4 (See FIG. 15)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism (first optical prism) PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative meniscus lens element convex on the object side (and having an aspherical surface s9 as the object-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an optical prism (second optical axis changing element) PR′, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements (including the optical prism PR′) are as follows:

    
    
        The seventh lens element L7 is a plano-convex lens element convex on the object side (and having an aspherical surface s16);
        The optical prism PR′ is, for example, an optical prism similar to the optical prism PR;
        The eighth lens element L8 is a positive lens element convex on both sides;
        The ninth lens element L9 is a negative lens element concave on both sides; and
        The tenth lens element L10 is a negative lens element concave on both sides; and
        The eleventh lens element L11 is a positive meniscus lens element convex on the object side (and having aspherical surfaces s26 and s27).

The seventh lens element L7 and the optical prism PR′ are cemented together at the surfaces s17 and s18 thereof. The eighth and ninth lens elements L8 and L9 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12 and a thirteenth lens element LI3. Used as these lens elements are as follows:

    
    
        The twelfth lens element L12 is a positive lens element convex on both sides (and having aspherical surfaces s28 and s29); and
        The thirteenth lens element L13 is a negative meniscus lens element concave on the object side.

Image Sensor Unit

    
    


The cover glass CG of the image sensor unit SU5 has two surfaces s32 and s33 for protecting the light-receiving surface of the image sensor SR. Moreover, as in Examples 1 to 3, the image sensor unit SU5 remains stationary.
Construction Data of the Variable-Magnification Optical System (Example 4)
Tables 7 and 8 show the construction data of the variable-magnification optical system 11 of Example 4. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 4, as shown in FIG. 15, zooming is achieved by moving at least part of the lens groups. Specifically, for zooming, the first to fourth lens groups GR1 to GR4 (that is, all the lens groups) move toward the object side, except that the second lens group GR2 first moves toward the object side but then makes a U-turn to move back toward the image side. Accordingly, in FIG. 15, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, d27, and d31 are shown.
FIGS. 16A to 16C, 17A to 17C, and 18A to 18C show the aberrations observed in the variable-magnification optical system 11 of Example 4 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 5 (See FIG. 19)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as si5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, an eleventh lens element L11, and a twelfth lens element L12. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive lens element convex on both sides;
        The eleventh lens element L11 is a negative meniscus lens element concave on the object side; and
        The twelfth lens element L12 is a positive lens element convex on both sides.

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a thirteenth lens element L13, a fourteenth lens element L14, and a cover glass CG (having two surfaces s32 and s33). Used as these lens elements are as follows:

    
    
        The thirteenth lens element L13 is a positive lens element convex on both sides (and having aspherical surfaces s28 and s29); and
        The fourteenth lens element L14 is a negative lens element concave on both sides.

Here, the cover glass CG included in the fourth lens group GR4 is stationary (this applies also to Examples 6 to 11 presented later).

Construction Data of the Variable-Magnification Optical System (Example 5)

    
    


Tables 9 and 10 show the construction data of the variable-magnification optical system 11 of Example 5. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 5, as shown in FIG. 19, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 19, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, and d27 are shown.
FIGS. 20A to 20C, 21A to 21C, and 22A to 22C show the aberrations observed in the variable-magnification optical system 11 of Example 5 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 6 (See FIG. 23)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative meniscus lens element convex on the object side (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as si5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, an eleventh lens element L11, and a twelfth lens element L12. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive lens element convex on both sides;
        The eleventh lens element L11 is a negative meniscus lens element concave on the object side; and
        The twelfth lens element L12 is a positive lens element convex on both sides.

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a thirteenth lens element L13, a fourteenth lens element L14, and a cover glass CG (having two surfaces s32 and s33). Used as these lens elements are as follows:

    
    
        The thirteenth lens element L13 is a positive lens element convex on both sides (and having aspherical surfaces s28 and s29); and
        The fourteenth lens element LI4 is a negative lens element concave on both sides.

Construction Data of the Variable-Magnification Optical System (Example 6)

    
    


Tables 11 and 12 show the construction data of the variable-magnification optical system 11 of Example 6. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 6, as shown in FIG. 23, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 23, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, dl4, and d27 are shown.
FIGS. 24A to 24C, 25A to 25C, and 26A to 26C show the aberrations observed in the variable-magnification optical system 11 of Example 6 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 7 (see FIG. 27)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive meniscus lens element convex on the object side; and
        The eleventh lens element L11 is a positive meniscus lens element convex on the object side (and having aspherical surfaces s24 and s25).

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12 and a cover glass CG (having two surfaces s28 and s29). Used as this lens element is as follows:

    
    
        The twelfth lens element L12 is a positive lens element convex on the object side (having aspherical surfaces s26 and s27).

Construction Data of the Variable-Magnification Optical System (Example 7)

    
    


Tables 13 and 14 show the construction data of the variable-magnification optical system 11 of Example 7. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 7, as shown in FIG. 27, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 27, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, and d25 are shown.
FIGS. 28A to 28C, 29A to 29C, and 30A to 30C show the aberrations observed in the variable-magnification optical system 11 of Example 7 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 8 (see FIG. 31)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive lens element convex on both sides.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive meniscus lens element convex on the object side; and
        The eleventh lens element L11 is a positive lens element convex on both sides (and having aspherical surfaces s24 and s25).

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12, a thirteenth lens element L13, and a cover glass CG (having two surfaces s30 and s31). Used as these lens elements are as follows:

    
    
        The twelfth lens element L12 is a positive lens element convex on both sides (having aspherical surfaces s26 and s27); and
        The thirteenth lens element L13 is a negative lens element concave on both sides.

Construction Data of the Variable-Magnification Optical System (Example 8)

    
    


Tables 15 and 16 show the construction data of the variable-magnification optical system 11 of Example 8. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 8, as shown in FIG. 31, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 31, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, and d25 are shown.
FIGS. 32A to 32C, 33A to 33C, and 34A to 34C show the aberrations observed in the variable-magnification optical system 11 of Example 8 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 9 (See FIG. 35)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive lens element convex on both sides.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive meniscus lens element convex on the object side; and
        The eleventh lens element L11 is a positive meniscus lens element convex on the object side (and having aspherical surfaces s24 and s25).

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12, a thirteenth lens element L13, and a cover glass CG (having two surfaces s30 and s31). Used as these lens elements are as follows:

    
    
        The twelfth lens element L12 is a positive lens element convex on both sides (having aspherical surfaces s26 and s27); and
        The thirteenth lens element L13 is a negative lens element concave on both sides.

Construction Data of the Variable-Magnification Optical System (Example 9)

    
    


Tables 17 and 18 show the construction data of the variable-magnification optical system 11 of Example 9. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 9, as shown in FIG. 35, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 35, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, and d25 are shown.
FIGS. 36A to 36C, 37A to 37C, and 38A to 38C show the aberrations observed in the variable-magnification optical system 11 of Example 9 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 10 (see FIG. 39)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative meniscus lens element convex on the object side (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a negative meniscus lens element convex on the object side; and
        The tenth lens element L10 is a positive meniscus lens element convex on the object side; and
        The eleventh lens element L11 is a positive meniscus lens element convex on the object side (and having aspherical surfaces s24 and s25).

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12, a thirteenth lens element L13, and a cover glass CG (having two surfaces s30 and s31). Used as these lens elements are as follows:

    
    
        The twelfth lens element L12 is a positive lens element convex on both sides (having aspherical surfaces s26 and s27); and
        The thirteenth lens element L13 is a negative meniscus lens element concave on the object side.

Construction Data of the Variable-Magnification Optical System (Example 10)

    
    


Tables 19 and 20 show the construction data of the variable-magnification optical system 11 of Example 10. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 10, as shown in FIG. 39, zooming is achieved by moving at least part of the lens groups (namely, the first to third lens groups GR1 to GR3) toward the object side. Accordingly, in FIG. 39, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, dl4, and d25 are shown.
FIGS. 40A to 40C, 41A to 41C, and 42A to 42C show the aberrations observed in the variable-magnification optical system 11 of Example 10 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
Variable-Magnification Optical System of Example 11 (See FIG. 43)
First Lens Group
The first lens group GR1 includes, from the object side, a first lens element L1, an optical prism PR, a second lens element L2, and a third lens element L3. Used as these lens elements are as follows:

    
    
        The first lens element L1 is a negative meniscus lens element convex on the object side;
        The second lens element L2 is a positive lens element convex on both sides; and
        The third lens element L3 is a positive meniscus lens element convex on the object side.

Second Lens Group

    
    


The second lens group GR2 includes, from the object side, a fourth lens element (the most object-side lens element) L4, a fifth lens element L5, and a sixth lens element L6. Used as these lens elements are as follows:

    
    
        The fourth lens element L4 is a negative lens element concave on both sides (and having an aspherical surface s10 as the image-side surface);
        The fifth lens element L5 is a negative lens element concave on both sides; and
        The sixth lens element L6 is a positive lens element convex on both sides.

The fifth and sixth lens elements L5 and L6 are cemented together at the surfaces s12 and s13 thereof to form a cemented lens element.

Third Lens Group

    
    


The third lens group GR3 includes, from the object side, an optical aperture stop ST (also indicated as sl5; built integrally with the third lens group GR3), a seventh lens element L7, an eighth lens element L8, a ninth lens element L9, a tenth lens element L10, and an eleventh lens element L11. Used as these lens elements are as follows:

    
    
        The seventh lens element L7 is a positive lens element convex on both sides (and having an aspherical surface s16);
        The eighth lens element L8 is a negative meniscus lens element concave on the object side;
        The ninth lens element L9 is a positive lens element convex on both sides; and
        The tenth lens element L10 is a negative lens element concave on both sides; and
        The eleventh lens element L11 is a negative meniscus lens element concave on the object side (and having aspherical surfaces s24 and s25).

The seventh and eighth lens elements L7 and L8 are cemented together at the surfaces s17 and s18 thereof to form a cemented lens element. The ninth and tenth lens elements L9 and L10 are cemented together at the surfaces s21 and s22 thereof to form a cemented lens element.

Fourth Lens Group

    
    


The fourth lens group GR4 includes, from the object side, a twelfth lens element L12 and a cover glass CG (having two surfaces s28 and s29). Used as this lens element is as follows:

    
    
        The twelfth lens element L12 is a positive meniscus lens element convex on the object side (having aspherical surfaces s26 and s27).

Construction Data of the Variable-Magnification Optical System (Example 11)

    
    


Tables 21 and 22 show the construction data of the variable-magnification optical system 11 of Example 11. In these tables, the same conventions apply as in Tables 1 and 2 described earlier.
Movement of the Individual Lens Groups in the Lens Unit
Zooming
In the variable-magnification optical system 11 of Example 11, as shown in FIG. 43, zooming is achieved by moving at least part of the lens groups. Specifically, for zooming, the first to third lens groups GR1 to GR3 move toward the object side, except that the second lens group GR2 first moves toward the object side but then makes a U-turn to move back toward the image side. Accordingly, in FIG. 43, only those axial distances di that vary as zooming is performed are indicated by their respective symbols; specifically, only the axial distances d8, d14, and d25 are shown.
FIGS. 44A to 44C, 45A to 45C, and 46A to 46C show the aberrations observed in the variable-magnification optical system 11 of Example 11 at different zoom positions. In these diagrams, the same conventions apply as in FIGS. 2A to 2C, 3A to 3C, and 4A to 4C.
2. Examples of Various Features of the Present Invention
A lens unit 1 incorporating the variable-magnification optical system 1 of any of Examples 4 to 11 has a construction similar to that of Example 1, the main difference being that the most object-side lens element (the fourth lens element L4) of the second lens group GR2 has an aspherical surface as the image-side surface thereof (S10). It is therefore needless to say that such a lens unit 1 offers the same effects and benefits as described in connection with Example 1.
Moreover, using an aspherical surface as the image-side surface s10 of the most object-side lens element (the fourth lens element L4) in the second lens group GR2 as in a variable-magnification optical system 11 according to the invention makes it possible to set optical powers appropriately.
For example, using an aspherical surface of which the curvature is so set as to become increasingly gentle away from the optical axis AX makes it possible to set optical powers appropriately. Thus, with a variable-magnification optical system 11 according to the invention, it is possible to more effectively reduce the distortion and other aberrations resulting from an excessive or insufficient optical power of a lens element that refracts the off-axial rays (rays passing off the optical axis AX) exiting therefrom.
Other Embodiments
The present invention may be carried out in any manner other than specifically described above as embodiments, and many variations and modifications are possible within the scope and spirit of the invention. For example, it is preferable, though not essential, that the zoom ratio (magnification variation ratio) of a variable-magnification optical system 11 according to the invention fulfill conditional formula (E) below.
Conditional formula (E) (conditional formula (4)) is as shown below.

4.7<ft/fw  (E)

where

    
    
        ft represents the focal length of the variable-magnification optical system (the entire system) at the telephoto end; and
        fw represents the focal length of the variable-magnification optical system at the wide-angle end.
    
    


Conditional formula (E) defines the room ratio of the variable-magnification optical system 11 (and thus of the lens unit 1). Fulfilling conditional formula (E) therefor achieves a high zoom ratio as compared with those (for example, about 3×) achieved by conventional digital cameras 29.
That is, according to the invention, it is possible to realize a variable-magnification optical system 11 that offers a high zoom ratio and in addition offers the effects described above. Thus, with a variable-magnification optical system 11 according to the invention, zoom performance (magnification variation performance) has a greater meaning, achieving user benefits.
In the course of the description given hereinbefore, conditional formulae (A) to (E) have been described. Table 23 shows the values of conditional formulae (A) to (C) and (E) as actually observed in each of Examples 1 to 11. For the value of conditional formula (D), reference is to be made to the tables that have been referred to in the course of the description given hereinbefore.
On the other hand, Table 24 shows the values of f2, f1, f3, √{square root over (fw×ft)}, ft, and fw, which need to be known for the calculation of the values of conditional formulae (A) to (C) and (E). As will be understood from Table 23, the variable-magnification optical system 11 of Examples 1 to 11 all fulfill conditional formulae (A) to (C) and (E).
An image-taking apparatus according to the invention is an optical apparatus that optically captures an image of a subject and that then outputs it in the form of an electrical signal. Such an image-taking apparatus is used as a main component of a camera that is used to shoot still and moving pictures of a subject.
Examples of such cameras include: digital cameras, video cameras, surveillance cameras, vehicle-mounted cameras, cameras for videophones, and cameras for intercoms. Further examples of such cameras include cameras incorporated in or externally attached to personal computers, portable information appliances (that is, compact, portable information appliance terminals such as mobile computers, cellular phones, and personal digital assistances (PDAs)), and peripheral devices therefor (such as mouses, scanners, printers, and memories).
As these examples show, not only is it possible to build cameras by the use of an image-taking apparatus, it is also possible to incorporate an image-taking apparatus in various appliances to add camera capabilities thereto. It is thereby possible to build, for example, a digital appliance equipped with an image-capturing capability, such as a cellular phone equipped with a camera.
In the past, the term “digital camera” was used to refer exclusively to cameras that are dedicated to the recording of still pictures; now that digital still cameras and home-use digital movie cameras are available that can handle both still and moving pictures, the term has come to be used with no such connotation.
Accordingly, in the present specification, the term “digital camera” is used to denote any camera, be it a digital still camera, a digital movie camera, or a web camera (a camera, either open or private, that is connected to a device connected to a network to permit exchange of pictures, irrespective of whether the camera is connected to the network directly or via a device, such as a personal computer, capable of image processing) that incorporates, as its main components, an image-taking apparatus including an image-taking lens system for forming an optical image, an image sensor for converting the optical image into an electrical image signal, and other components.
A variable-magnification optical system 11 according to the invention is used in various image-taking apparatuses (such as silver-halide-film cameras and digital still cameras) and digital input devices (such as digital appliances equipped with an image-taking apparatus). By the use of a variable-magnification optical system 11 according to the invention, it is possible to make such image-taking apparatuses and the like compact.
Moreover, in an image-taking apparatus or like, it is possible to reduce the volume occupied by the variable-magnification optical system 11 within the limited space inside the housing. This makes it possible to arrange various components (such as electrical components) within an ample space inside the housing of an image-taking apparatuses and the like (that is, it is possible to efficiently use the space inside the housing). This makes it possible to realize an image-taking apparatus incorporating various components for high performance.
A digital camera 29 as shown in FIGS. 5 and 6 may be so constructed that, while the image sensor SR is kept stationary, zooming or the like is achieved by moving the first and third lens groups GR1 and GR3, which include an optical axis changing element (a optical prism PR or a reflective mirror MR). Alternatively, a digital camera 29 may be so constructed that, while the first and third lens groups GR1 and GR3, which include an optical axis changing element, is kept stationary, zooming or the like is achieved by moving the image sensor SR.
The present invention is useful in variable-magnification optical systems and in image-taking apparatuses incorporating such optical systems, and can alternatively be expressed as follows.
For further compactness, in a variable-magnification optical system according to the invention, the third lens group may include a second optical axis changing element.
In that case, the second optical axis changing element bends the optical axis, for example, by reflection. This makes the variable-magnification optical system bent, instead of straight. Thus, according to the invention, it is possible to make a variable-magnification optical system compact in one direction (for example, in the direction of the total length thereof).
In a variable-magnification optical system according to the invention, when the first and third lens groups move for zooming, the group-to-group distance between the first and third lens groups may be kept constant. For example, the first and third lens groups are linked together with a linking member so that they move together for zooming.
In that case, the structure (arrangement structure) for the arrangement of those two lens groups is simplified. Thus, the two lens groups can be housed in the same lens barrel. This makes the lens barrel compact.
In a variable-magnification optical system according to the invention, for higher telecentricity in the light exiting therefrom, a fourth lens group having a positive optical power may be disposed on the image side of the third lens group.
Needless to say, incorporating a variable-magnification optical system as described above, an image-taking apparatus according to the invention is compact and high-performance.
The embodiments, examples, and the like specifically described above are merely intended to make the technical idea of the present invention clear. The present invention, therefore, should not be interpreted narrowly within the extent of what is specifically described above, but should be interpreted to allow many modifications and variations within the scope of the appended claims.









TABLE 1







Example 1
Focal Length Position
(W)~(M)~(T)



f[mm]
6.42~19.90~42.37



FNO
2.87~4.54~5.15

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
25.845

1
0.800
1
1.84666
23.78
L1
GR1


2
13.592

2
2.500


3
∞

3
10.500 
2
1.84666
23.78
PR


4
∞

4
0.300


5
40.234

5
1.518
3
1.62162
52.18
L2


6
−79.125

6
0.100


7
19.655

7
2.044
4
1.49393
68.98
L3


8
−37.690

8
0.600~7.401~12.233


9
−39.951
*
9
0.800
5
1.86550
30.54
L4
GR2


10
6.849

10
2.919


11
−5.372

11
0.700
6
1.48750
70.00
L5


12
26.191

12
0.010
7
1.51400
42.83


13
26.191

13
1.703
8
1.84666
23.78
L6


14
−13.441

14
12.433~5.632~0.800


15
∞

15
0.500



ST
GR3


16
10.075
*
16
2.864
9
1.68238
46.68
L7


17
−10.343

17
0.010
10
1.51400
42.83


18
−10.343

18
0.700
11
1.79879
31.79
L8


19
−1367.035

19
9.000


20
11.366
*
20
4.388
12
1.48749
70.44
L9


21
−5.803

21
0.010
13
1.51400
42.83


22
−5.803

22
0.700
14
1.87344
34.53
L10


23
−27.680

23
1.340~19.690~25.105


24
−25.520

24
0.800
15
1.86683
31.14
L11
GR4


25
−123.336

25
0.100


26
15.311
*
26
3.000
16
1.53048
55.72
L12


27
−29.644
*
27
8.521~2.600~3.114


28
∞

28
0.500
17
1.51680
64.20
CG
SU5


29
∞
















TABLE 2





Example 1




















Aspherical Surface Data

Aspherical Surface Data




of Surface 9(i = 9)

of Surface 26(i = 26)
















−9
−57.2352
ε
1.0000



A4
0.15882965E−03
A4
0.17474167E−03



A6
−0.20931606E−05
A6
0.45181466E−05



A8
0.91486827E−08
A8
−0.99350042E−07



A10
−0.61919454E−09
A10
−0.13011353E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.59577286E−04
A4
0.29000283E−03



A6
−0.17872322E−06
A6
0.42202831E−05



A8
0.99574761E−08
A8
−0.36866613E−07



A10
−0.10774847E−09
A10
−0.51991943E−08














Aspherical Surface Data




of Surface 20(i = 20)














ε
1.0000



A4
0.24168919E−04



A6
0.50164245E−05



A8
−0.50460778E−07



A10
0.10596959E−07



















TABLE 3







Example 2
Focal Length Position
(W)~(M)~(T)



f[mm]
6.42~19.89~42.36



FNO
2.74~4.30~5.24

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
25.626

1
0.800
1
1.84666
23.78
L1
GR1


2
13.501

2
2.500


3
∞

3
10.500 
2
1.84666
23.78
PR


4
∞

4
0.300


5
45.796

5
1.515
3
1.64959
50.15
L2


6
−77.773

6
0.100


7
21.317

7
2.037
4
1.49098
69.64
L3


8
−33.075

8
0.600~7.807~12.362


9
−54.932
*
9
0.800
5
1.86327
29.57
L4
GR2


10
6.826

10
2.351


11
−5.382

11
1.122
6
1.48750
70.00
L5


12
21.534

12
0.010
7
1.51400
42.83


13
21.534

13
1.748
8
1.84666
23.78
L6


14
−14.655

14
12.562~5.355~0.800


15
∞

15
0.500



ST
GR3


16
10.875
*
16
3.845
9
1.68970
47.74
L7


17
−9.571

17
0.010
10
1.51400
42.83


18
−9.571

18
0.700
11
1.81695
29.81
L8


19
−70.155

19
9.000


20
11.002
*
20
5.000
12
1.48749
70.44
L9


21
−5.356

21
0.010
13
1.51400
42.83


22
−5.356

22
0.700
14
1.87537
35.64
L10


23
−41.330

23
1.251~16.433~24.224


24
16.044
*
24
5.000
15
1.48749
70.44
L11
GR4


25
−267.212
*
25
4.899~2.629~2.200


26
∞

26
0.500
16
1.51680
64.20
CG
SU5


27
∞
















TABLE 4





Example 2




















Aspherical Surface Data

Aspherical Surface Data




of Surface 9(i = 9)

of Surface 24(i = 24)
















ε
−46.8957
ε
1.0000



A4
0.16612137E−03
A4
0.34828366E−04



A6
−0.30195691E−05
A6
0.26647497E−05



A8
0.10294541E−06
A8
−0.24037181E−06



A10
−0.58985283E−08
A10
0.31168919E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.60435282E−04
A4
0.11578483E−03



A6
−0.14662407E−06
A6
0.10989257E−04



A8
0.89430287E−08
A8
−0.11450034E−05



A10
−0.57567701E−010
A10
0.21945455E−07














Aspherical Surface Data




of Surface 20(i = 20)














ε
1.0000



A4
0.99687280E−04



A6
0.79377958E−05



A8
−0.13714060E−06



A10
0.18930633E−07



















TABLE 5







Example 3
Focal Length Position
(W)~(M)~(T)



f[mm]
6.20~19.22~40.92



FNO
2.95~3.89~5.15

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
43.945

1
1.000
1
1.84666
23.78
L1
GR1


2
14.738

2
2.500


3
∞

3
10.500 
2
1.84666
23.78
PR


4
∞

4
0.300


5
29.047

5
2.211
3
1.50361
66.96
L2


6
−23.867

6
0.100


7
19.166

7
1.792
4
1.59788
54.21
L3


8
−1103.887

8
0.618~8.058~11.141


9
−92.087
*
9
0.800
5
1.88300
40.80
L4
GR2


10
6.538

10
3.258


11
−5.464

11
0.700
6
1.48749
70.44
L5


12
21.910

12
0.010
7
1.51400
42.83


13
21.910

13
1.616
8
1.84666
23.78
L6


14
−16.381

14
11.723~4.283~1.200


15
∞

15
0.500



ST
GR3


16
9.712
*
16
2.795
9
1.51965
53.34
L7


17
−10.625

17
0.010
10
1.51400
42.83


18
−10.625

18
0.700
11
1.84849
27.07
L8


19
−21.963

19
9.000


20
18.366
*
20
1.801
12
1.48750
70.00
L9


21
−29.054

21
0.100


22
46.731

22
2.620
13
1.49700
81.61
L10


23
−5.291

23
0.010
14
1.51400
42.83


24
−5.291

24
0.700
15
1.86028
38.20
L11


25
−110.496

25
1.546~10.431~25.999


26
12.244
*
26
4.068
16
1.48749
70.44
L12
GR4


27
52.879

27
7.807~10.947~6.070


28
∞

28
0.500
17
1.51680
64.20
CG
SU5


29
∞
















TABLE 6





Example 3




















Aspherical Surface Data

Aspherical Surface Data




of Surface 9(i = 9)

of Surface 20(i = 20)
















ε
−371.38
ε
1.0000



A4
0.13198863E−03
A4
0.21611656E−03



A6
−0.16010305E−05
A6
0.95781187E−05



A8
−0.62426729E−07
A8
−0.21006691E−06



A10
0.18494727E−08
A10
0.19977665E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.11924623E−03
A4
−0.26101522E−04



A6
−0.48997232E−06
A6
0.13312555E−06



A8
0.17242597E−07
A8
−0.58207864E−08



A10
−0.48425913E−09
A10
−0.83031131E−10



















TABLE 7







Example 4
Focal Length Position
(W)~(M)~(T)



f[mm]
8.10~25.10~53.45



FNO
3.15~4.88~5.15

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
50.950

1
0.800
1
1.84666
23.82
L1
GR1


2
21.173

2
2.500


3
∞

3
14.000 
2
1.84666
23.78
PR


4
∞

4
0.300


5
58.530

5
2.142
3
1.53437
61.67
L2


6
−31.696

6
0.100


7
18.750

7
2.190
4
1.49700
81.61
L3


8
451.038

8
0.601~8.131~13.990


9
397.251

9
0.800
5
1.77250
49.77
L4
GR2


10
7.579
*
10
2.875


11
−8.879

11
0.700
6
1.48749
70.44
L5


12
13.313

12
0.010
7
1.51400
42.83


13
13.313

13
1.696
8
1.84668
23.83
L6


14
−152.442

14
14.189~6.660~0.800


15
∞

15
0.500



ST
GR3


16
8.643
*
16
2.567
9
1.69350
53.39
L7


17
∞

17
0.010
10
1.51400
42.83


18
∞

18
10.000 
11
1.84666
23.78
PR


19
∞

19
0.380


20
12.454

20
2.480
12
1.48767
70.40
L8


21
−6.038

21
0.010
13
1.51400
42.83


22
−6.038

22
0.700
14
1.85011
24.89
L9


23
216.003

23
0.453


24
−24.235

24
0.800
15
1.87594
35.98
L10


25
47.926

25
3.324


26
12.460
*
26
2.031
16
1.62017
24.01
L11


27
42.795
*
27
1.468~17.723~20.079


28
12.815
*
28
3.749
17
1.53048
55.72
L12
GR4


29
−21.925
*
29
1.000


30
−19.794

30
1.000
18
1.84666
23.82
L13


31
−235.550

31
2.229~1.565~2.704


32
∞

32
0.500
19
1.51680
64.20
CG
SU5


33
∞
















TABLE 8





Example 4




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.41219237E−04
A4
−0.38494478E−03



A6
−0.13871421E−05
A6
−0.14104688E−04



A8
0.26102532E−07
A8
0.15157903E−06



A10
0.38454974E−08
A10
−0.57939620E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 28(i = 28)
















ε
1.0000
ε
1.0000



A4
−0.99341543E−04
A4
0.24897817E−05



A6
−0.87994965E−06
A6
0.83881297E−06



A8
0.14095947E−07
A8
−0.14212718E−06



A10
−0.48483908E−09
A10
0.18928651E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 26(i = 26)

of Surface 29(i = 29)
















ε
1.0000
ε
1.0000



A4
−0.62593936E−03
A4
0.10391893E−03



A6
−0.12198423E−04
A6
−0.45223886E−05



A8
0.34700666E−07



A10
−0.78808573E−08



















TABLE 9







Example 5
Focal Length Position
(W)~(M)~(T)



f[mm]
7.98~17.55~37.74



FNO
3.31~4.13~5.20

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
43.419

1
0.800
1
1.92286
20.88
L1
GR1


2
19.667

2
2.150


3
∞

3
12.349 
2
1.88300
40.79
PR


4
∞

4
0.100


5
30.532

5
2.016
3
1.58913
61.25
L2


6
−40.926

6
0.100


7
16.808

7
1.757
4
1.49700
81.61
L3


8
99.776

8
0.745~5.910~9.810


9
−124.542

9
0.800
5
1.77250
49.77
L4
GR2


10
7.058
*
10
2.378


11
−9.524

11
1.038
6
1.72916
54.67
L5


12
12.650

12
0.010
7
1.51400
42.83


13
12.650

13
1.476
8
1.92286
20.88
L6


14
−48.404

14
10.048~4.883~0.984


15
∞

15
0.500



ST
GR3


16
11.975
*
16
4.379
9
1.69350
53.39
L7


17
−10.341

17
0.010
10
1.51400
42.83


18
−10.341

18
0.700
11
1.80518
25.46
L8


19
−43.772

19
9.841


20
18.390

20
0.700
12
1.88300
40.79
L9


21
10.262

21
0.010
13
1.51400
42.83


22
10.262

22
2.935
14
1.58144
40.89
L10


23
−23.748

23
0.903


24
−9.495

24
1.271
15
1.80610
33.27
L11


25
−55.610

25
0.432


26
26.936

26
2.227
16
1.49700
81.61
L12


27
−19.736

27
3.413~14.807~29.913


28
19.346
*
28
4.000
17
1.53048
55.72
L13
GR4


29
−16.159
*
29
0.270


30
−200.000

30
0.893
18
1.84666
23.78
L14


31
18.290

31
6.000


32
∞

32
0.500
19
1.51680
64.20
CG


33
∞
















TABLE 10





Example 5




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 28(i = 28)
















ε
1.0000
ε
1.0000



A4
−0.10197203E−03
A4
−0.15307901E−04



A6
−0.59864948E−05
A6
−0.16093656E−04



A8
0.63239314E−06
A8
0.50352433E−06



A10
−0.22955553E−07
A10
−0.11138404E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 29(i = 29)
















ε
1.0000
ε
1.0000



A4
−0.90047005E−04
A4
0.19494141E−03



A6
0.10298751E−05
A6
−0.12810081E−04



A8
−0.67772055E−07
A8
0.18629352E−06



A10
0.20176346E−08
A10
−0.38610777E−08



















TABLE 11







Example 6
Focal Length Position
(W)~(M)~(T)



f[mm]
7.83~24.24~44.26



FNO
3.32~4.59~5.50

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
41.341

1
0.800
1
1.92286
20.88
L1
GR1


2
20.309

2
2.150


3
∞

3
12.000 
2
1.88300
40.79
PR


4
∞

4
0.100


5
32.423

5
1.862
3
1.58913
61.25
L2


6
−57.490

6
0.100


7
15.686

7
1.857
4
1.49700
81.61
L3


8
122.827

8
0.608~7.691~10.573


9
105.786

9
0.800
5
1.77250
49.77
L4
GR2


10
6.480
*
10
2.162


11
−8.696

11
0.700
6
1.72916
54.67
L5


12
12.191

12
0.010
7
1.51400
42.83


13
12.191

13
1.481
8
1.92286
20.88
L6


14
−46.939

14
10.872~3.789~0.907


15
∞

15
0.500



ST
GR3


16
11.433
*
16
3.481
9
1.69350
53.39
L7


17
−10.070

17
0.010
10
1.51400
42.83


18
−10.070

18
0.700
11
1.80518
25.46
L8


19
−42.498

19
9.840


20
15.469

20
0.700
12
1.88300
40.79
L9


21
8.807

21
0.010
13
1.51400
42.83


22
8.807

22
2.839
14
1.58144
40.89
L10


23
−28.176

23
0.828


24
−9.309

24
0.700
15
1.80610
33.27
L11


25
−45.550

25
0.486


26
20.950

26
2.449
16
1.49700
81.61
L12


27
−25.746

27
1.839~17.111~28.339


28
47.082
*
28
4.000
17
1.53048
55.72
L13
GR4


29
−13.563
*
29
0.122


30
−200.000

30
1.000
18
1.84666
23.78
L14


31
22.980

31
6.000


32
∞

32
0.500
19
1.51680
64.20
CG


33
∞
















TABLE 12





Example 6




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 28(i = 28)
















ε
1.0000
ε
1.0000



A4
−0.99302225E−04
A4
−0.87972213E−04



A6
−0.70030523E−05
A6
−0.18945029E−04



A8
0.67791112E−06
A8
0.64601763E−06



A10
−0.22461986E−07
A10
−0.15667561E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 29(i = 29)
















ε
1.0000
ε
1.0000



A4
−0.94093498E−04
A4
0.21761696E−03



A6
0.90824359E−06
A6
−0.16245656E−04



A8
−0.75884840E−07
A8
0.30350491E−06



A10
0.25367720E−08
A10
−0.57410322E−08



















TABLE 13







Example 7
Focal Length Position
(W)~(M)~(T)



f[mm]
7.99~19.17~45.16



FNO
3.35~4.42~5.93

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
44.704

1
0.800
1
1.92286
20.88
L1
GR1


2
21.386

2
2.450


3
∞

3
11.400 
2
1.88300
40.79
PR


4
∞

4
0.195


5
36.489

5
1.918
3
1.58913
61.25
L2


6
−44.135

6
0.129


7
18.219

7
1.757
4
1.49700
81.61
L3


8
214.691

8
0.801~6.709~11.275


9
−48.164

9
0.800
5
1.77250
49.77
L4
GR2


10
7.688
*
10
3.181


11
−10.526

11
0.700
6
1.72916
54.67
L5


12
15.314

12
0.010
7
1.51400
42.83


13
15.314

13
1.471
8
1.92286
20.88
L6


14
−33.140

14
11.424~5.516~0.950


15
∞

15
1.000



ST
GR3


16
14.709
*
16
3.157
9
1.69350
53.39
L7


17
−11.220

17
0.010
10
1.51400
42.83


18
−11.220

18
2.948
11
1.80518
25.46
L8


19
−21.569

19
10.200 


20
16.714

20
0.700
12
1.80518
25.46
L9


21
5.882

21
0.010
13
1.51400
42.83


22
5.882

22
2.854
14
1.48749
70.44
L10


23
36.212

23
3.282


24
20.118
*
24
2.054
15
1.60700
27.00
L11


25
37.298
*
25
0.800~11.677~25.629


26
22.688
*
26
6.000
16
1.53048
55.72
L12
GR4


27
∞
*
27
3.797


28
∞

28
0.500
17
1.51680
64.20
CG


29
∞
















TABLE 14





Example 7




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.15663490E−03
A4
−0.41777597E−03



A6
−0.17225086E−05
A6
−0.19349262E−05



A8
0.13760168E−07
A8
0.15808145E−06



A10
−0.19099660E−08
A10
−0.91796432E−09
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.10403172E−03
A4
−0.85892111E−04



A6
0.29726559E−06
A6
0.42881465E−05



A8
−0.15823879E−07
A8
−0.38774715E−06



A10
0.39989178E−09
A10
0.57234103E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 24(i = 24)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.27390750E−03
A4
0.75585543E−04



A6
−0.15628240E−05
A6
0.13968653E−04



A8
0.19691831E−06
A8
−0.12010832E−05



A10
−0.74042374E−09
A10
0.19260161E−07



















TABLE 15







Example 8
Focal Length Position
(W)~(M)~(T)



f[mm]
7.99~24.73~52.67



FNO
3.19~4.69~5.78

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
39.700

1
0.800
1
1.92286
20.88
L1
GR1


2
20.903

2
2.150


3
∞

3
12.000 
2
1.88300
40.79
PR


4
∞

4
0.149


5
44.432

5
1.768
3
1.58913
61.25
L2


6
−45.713

6
0.100


7
17.910

7
1.839
4
1.49700
81.61
L3


8
−2118.420

8
0.697~7.698~11.717


9
−73.605

9
0.800
5
1.77250
49.77
L4
GR2


10
7.922
*
10
2.473


11
−10.526

11
0.700
6
1.72916
54.67
L5


12
13.422

12
0.010
7
1.51400
42.83


13
13.422

13
1.496
8
1.92286
20.88
L6


14
−47.090

14
11.820~4.819~0.800


15
∞

15
0.500



ST
GR3


16
13.501
*
16
3.007
9
1.69350
53.39
L7


17
−11.543

17
0.010
10
1.51400
42.83


18
−11.543

18
1.205
11
1.80518
25.46
L8


19
−24.338

19
9.311


20
13.513

20
0.700
12
1.80518
25.46
L9


21
6.079

21
0.010
13
1.51400
42.83


22
6.079

22
2.618
14
1.48749
70.44
L10


23
21.534

23
4.284


24
60.095
*
24
3.000
15
1.60700
27.00
L11


25
−1816.893
*
25
0.800~16.148~27.300


26
13.759
*
26
5.034
16
1.53048
55.72
L12
GR4


27
−88.521
*
27
1.000


28
−200.000

28
1.206
17
1.84666
23.78
L13


29
44.381

29
1.502


30
∞

30
0.500
18
1.51680
64.20
CG


31
∞
















TABLE 16





Example 8




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.10347630E−03
A4
−0.52970460E−03



A6
0.10571704E−07
A6
0.17563218E−06



A8
−0.10147936E−06
A8
−0.61275210E−07



A10
0.40490268E−08
A10
0.86383888E−09
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.10745558E−03
A4
0.82635382E−04



A6
0.94049800E−07
A6
−0.37172310E−05



A8
−0.72034064E−08
A8
−0.29629917E−07



A10
0.24899348E−09
A10
−0.19532084E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 24(i = 24)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.48200103E−03
A4
0.46636778E−03



A6
0.23899796E−06
A6
0.33804543E−05



A8
−0.14206418E−06
A8
−0.10852266E−05



A10
0.27280903E−08
A10
0.15300655E−07



















TABLE 17







Example 9
Focal Length Position
(W)~(M)~(T)



f[mm]
8.10~25.10~53.45



FNO
2.71~4.11~5.15

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















1
28.794

1
0.800
1
1.92286
20.88
L1
GR1


2
17.862

2
3.024


3
∞

3
13.400 
2
1.72916
54.67
PR


4
∞

4
0.200


5
66.289

5
1.652
3
1.62041
60.34
L2


6
−56.704

6
0.100


7
21.375

7
2.221
4
1.49700
81.61
L3


8
−65.593

8
0.600~7.765~11.935


9
−52.828

9
1.281
5
1.77250
49.77
L4
GR2


10
9.133
*
10
2.444


11
−9.616

11
0.700
6
1.83481
42.72
L5


12
16.877

12
0.010
7
1.51400
42.83


13
16.877

13
1.790
8
1.92286
20.88
L6


14
−21.804

14
12.135~4.970~0.800


15
∞

15
0.500



ST
GR3


16
13.775
*
16
2.868
9
1.69350
53.39
L7


17
−11.093

17
0.010
10
1.51400
42.83


18
−11.093

18
0.700
11
1.80518
25.46
L8


19
−22.342

19
10.082 


20
19.314

20
0.700
12
1.80518
25.46
L9


21
6.173

21
0.010
13
1.51400
42.83


22
6.173

22
5.801
14
1.48749
70.44
L10


23
15.109

23
1.734


24
12.411
*
24
2.092
15
1.60700
27.00
L11


25
26.761
*
25
0.800~15.919~27.300


26
12.442
*
26
3.808
16
1.53048
55.72
L12
GR4


27
−43.564
*
27
0.999


28
−200.000

28
1.090
17
1.84666
23.78
L13


29
29.288

29
1.955


30
∞

30
0.500
18
1.51680
64.20
CG


31
∞
















TABLE 18





Example 9




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.11251572E−03
A4
−0.38660182E−03



A6
0.81065978E−06
A6
−0.81368352E−05



A8
−0.20573522E−06
A8
0.28754443E−06



A10
0.89121016E−08
A10
−0.23391449E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.11389588E−03
A4
0.36504125E−03



A6
0.30155805E−06
A6
−0.74333710E−05



A8
−0.16602730E−07
A8
−0.41127534E−07



A10
0.33990965E−09
A10
−0.34151284E−08
















Aspherical Surface Data

Aspherical Surface Data




of Surface 24(i = 24)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.32855269E−03
A4
0.98907401E−03



A6
−0.61225955E−05
A6
−0.70237988E−05



A8
0.20169935E−06
A8
−0.12081571E−05



A10
−0.32385413E−09
A10
0.18264023E−07



















TABLE 19







Example 10
Focal Length Position
(W)~(M)~(T)



f[mm]
6.30~19.52~41.57



FNO
2.66~3.90~5.15

















i
ri[mm]
i
di[mm]
i
Ni
νi
Eelement



















1
48.110

1
0.800
1
1.92286
20.88
L1
GR1


2
19.270

2
2.000


3
∞

3
10.800 
2
1.88300
40.79
PR


4
∞

4
0.127


5
40.997

5
1.901
3
1.58913
61.25
L2


6
−30.751

6
0.100


7
15.739

7
1.871
4
1.49700
81.61
L3


8
170.924

8
0.600~6.966~10.150


9
140.361

9
0.800
5
1.77250
49.77
L4
GR2


10
6.442
*
10
2.185


11
−7.197

11
0.700
6
1.72916
54.67
L5


12
12.245

12
0.010
7
1.51400
42.83


13
12.245

13
1.641
8
1.92286
20.88
L6


14
−30.167

14
10.377~4.012~0.827


15
∞

15
0.500



ST
GR3


16
12.223
*
16
2.758
9
1.69350
53.39
L7


17
−10.946

17
0.010
10
1.51400
42.83


18
−10.946

18
0.988
11
1.80518
25.46
L8


19
−24.189

19
9.009


20
10.533

20
1.000
12
1.80518
25.46
L9


21
4.830

21
0.010
13
1.51400
42.83


22
4.830

22
3.677
14
1.48749
70.44
L10


23
13.721

23
1.000


24
15.633
*
24
2.433
15
1.60700
27.00
L11


25
57.853
*
25
1.704~14.872~28.205


26
13.095
*
26
3.158
16
1.53048
55.72
L12
GR4


27
−16.163
*
27
0.781


28
−11.990

28
1.000
17
1.84666
23.78
L13


29
−45.718

29
2.052


30
∞

30
0.500
18
1.51680
64.20
CG


31
∞
















TABLE 20





Example 10




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.10732497E−03
A4
−0.56438517E−03



A6
0.57313839E−06
A6
−0.13991709E−04



A8
−0.42087595E−06
A8
0.48071072E−06



A10
0.36617830E−07
A10
−0.10628856E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.14050118E−03
A4
0.94933667E−04



A6
0.15126826E−06
A6
−0.20612676E−05



A8
−0.17592819E−07
A8
−0.36313239E−06



A10
0.61027539E−09
A10
−0.18922759E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 24(i = 24)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.39055016E−03
A4
0.18297925E−03



A6
−0.83755556E−05
A6
0.19313027E−04



A8
0.34012017E−06
A8
−0.34461882E−05



A10
0.10816659E−08
A10
0.67376749E−07



















TABLE 21







Example 11
Focal Length Position
(W)~(M)~(T)



f[mm]
7.99~19.17~45.16



FNO
3.77~5.09~5.20

















i
ri[mm]
i
di[mm]
i
Ni
νi
Element



















 1
47.775

1
0.800
1
1.92286
20.88
L1
GR1


 2
20.558

2
2.450


 3
∞

3
14.000
2
1.88300
40.79
PR


 4
∞

4
0.100


 5
36.725

5
1.908
3
1.63854
55.45
L2


 6
−42.803

6
0.100


 7
21.430

7
1.657
4
1.49700
81.61
L3


 8
286.719

8
0.649~7.285~14.915


 9
−382.266

9
0.800
5
1.77250
49.77
L4
GR2


10
7.035
*
10
2.004


11
−7.645

11
0.700
6
1.51680
64.20
L5


12
12.557

12
0.010
7
1.51400
42.83


13
12.557

13
1.502
8
1.84666
23.78
L6


14
−59.208

14
11.167~6.009~0.950


15
∞

15
1.000



ST
GR3


16
7.807
*
16
2.332
9
1.58913
61.25
L7


17
−8.642

17
0.010
10
1.51400
42.83


18
−8.642

18
0.700
11
1.83500
42.98
L8


19
−24.972

19
5.765


20
9.133

20
3.437
12
1.48749
70.44
L9


21
−5.326

21
0.010
13
1.51400
42.83


22
−5.326

22
0.700
14
1.80610
33.27
L10


23
54.405

23
4.240


24
−15.211
*
24
2.803
15
1.60700
27.00
L11


25
−18.730
*
25
0.800~9.075~9.769


26
19.006
*
26
2.650
16
1.53048
55.72
L12
GR4


27
467.395
*
27
3.471


28
∞

28
0.500
17
1.51680
64.20
CG


29
∞
















TABLE 22





Example 11




















Aspherical Surface Data

Aspherical Surface Data




of Surface 10(i = 10)

of Surface 25(i = 25)
















ε
1.0000
ε
1.0000



A4
−0.67799158E−04
A4
−0.97032523E−03



A6
0.96058817E−06
A6
0.16497548E−04



A8
0.41344081E−07
A8
0.34413689E−07



A10
−0.46262692E−08
A10
0.17182245E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 16(i = 16)

of Surface 26(i = 26)
















ε
1.0000
ε
1.0000



A4
−0.12912082E−03
A4
−0.37757354E−04



A6
0.91847279E−06
A6
0.89018556E−05



A8
−0.72780971E−07
A8
−0.19277655E−05



A10
0.30673980E−08
A10
0.47192370E−07
















Aspherical Surface Data

Aspherical Surface Data




of Surface 24(i = 24)

of Surface 27(i = 27)
















ε
1.0000
ε
1.0000



A4
−0.13966519E−02
A4
0.29913138E−03



A6
0.13278370E−04
A6
0.10639857E−04



A8
0.12272916E−05
A8
−0.27271667E−05



A10
0.21670247E−07
A10
0.62761401E−07






















TABLE 23







Conditional
Conditional
Conditional
Conditional



Formula (A)
Formula (B)
Formula (C)
Formula (E)




















Example 1
0.42
1.29
0.90
6.60


Example 2
0.44
1.33
0.84
6.60


Example 3
0.40
1.13
0.91
6.60


Example 4
0.38
1.17
0.69
6.60


Example 5
0.35
1.26
0.91
4.73


Example 6
0.33
1.22
0.79
5.65


Example 7
0.35
1.24
0.77
5.65


Example 8
0.33
1.14
0.69
6.59


Example 9
0.35
1.14
0.66
6.60


Example 10
0.36
1.29
0.76
6.60


Example 11
0.38
1.26
0.62
5.65























TABLE 24







f2
f1
f3
{square root over ((fw × ft))}
ft
fw






















Example 1
6.927
21.276
14.844
16.493
42.37
6.42


Example 2
7.256
21.933
13.852
16.491
42.36
6.42


Example 3
6.371
17.999
14.495
15.928
40.92
6.20


Example 4
7.907
24.345
14.357
20.807
53.45
8.10


Example 5
6.074
21.866
15.792
17.354
37.74
7.98


Example 6
6.143
22.712
14.707
18.616
44.26
7.83


Example 7
6.648
23.554
14.627
18.995
45.16
7.99


Example 8
6.770
23.386
14.155
20.514
52.67
7.99


Example 9
7.283
23.720
13.733
20.807
53.45
8.10


Example 10
5.826
20.876
12.299
16.183
41.57
6.30


Example 11
7.218
23.934
11.777
18.995
45.16
7.99

## Claims

1. A variable-magnification optical system comprising a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (1) below is fulfilled:


0.1<|f2/√{square root over (fw×ft)}|<0.45  (1)



where
f2 represents a focal length of the second lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
ft represents a focal length of the entire variable-magnification optical system at a telephoto end.

2. A variable-magnification optical system comprising a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (2) below is fulfilled:


0.5<f1/√{square root over (fw×ft)}<1.4  (2)



where
f1 represents a focal length of the first lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
ft represents a focal length of the entire variable-magnification optical system at a telephoto end.

3. A variable-magnification optical system comprising a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (3) below is fulfilled:


0.3<f3/√{square root over (fw×ft)}<1.0  (3)



where
f3 represents a focal length of the third lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
ft represents a focal length of the entire variable-magnification optical system at a telephoto end.

4. The variable-magnification optical system of claim 1,
wherein the third lens group includes a second optical axis changing element.

5. The variable-magnification optical system of claim 2,
wherein the third lens group includes a second optical axis changing element.

6. The variable-magnification optical system of claim 3,
wherein the third lens group includes a second optical axis changing element.

7. The variable-magnification optical system of claim 1,
wherein, when the first and third lens groups move for zooming, a group-to-group distance between the first and third lens groups remains constant.

8. The variable-magnification optical system of claim 2,
wherein, when the first and third lens groups move for zooming, a group-to-group distance between the first and third lens groups remains constant.

9. The variable-magnification optical system of claim 3,
wherein, when the first and third lens groups move for zooming, a group-to-group distance between the first and third lens groups remains constant.

10. The variable-magnification optical system of claim 1,
wherein the first and third lens groups are linked together.

11. The variable-magnification optical system of claim 2,
wherein the first and third lens groups are linked together.

12. The variable-magnification optical system of claim 3,
wherein the first and third lens groups are linked together.

13. The variable-magnification optical system of claim 1,
wherein a fourth lens group having a positive optical power is disposed on an image side of the third lens group.

14. The variable-magnification optical system of claim 2,
wherein a fourth lens group having a positive optical power is disposed on an image side of the third lens group.

15. The variable-magnification optical system of claim 3,
wherein a fourth lens group having a positive optical power is disposed on an image side of the third lens group.

16. The variable-magnification optical system of claim 1,
wherein conditional formula (4) below is fulfilled:


4.7<ft/fw.

17. The variable-magnification optical system of claim 2,
wherein conditional formula (4) below is fulfilled:


4.7<ft/fw.

18. The variable-magnification optical system of claim 3,
wherein conditional formula (4) below is fulfilled:


4.7<ft/fw.

19. An image-taking apparatus comprising a variable-magnification optical system,
wherein the variable-magnification optical system comprises a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (1) below is fulfilled:


0.1<|f2/√{square root over (fw×ft)}|<0.45  (1)



where
f2 represents a focal length of the second lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
fit represents a focal length of the entire variable-magnification optical system at a telephoto end.

20. An image-taking apparatus comprising a variable-magnification optical system,
wherein the variable-magnification optical system comprises a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (2) below is fulfilled:


0.5<f1/√{square root over (fw×ft)}<1.4  (2)



where
f1 represents a focal length of the first lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
ft represents a focal length of the entire variable-magnification optical system at a telephoto end.

21. An image-taking apparatus comprising a variable-magnification optical system,
wherein the variable-magnification optical system comprises a plurality of lens groups through which light from an object is imaged on an image sensor, the plurality of lens groups including, from an object side to an image side, at least:
a first lens group having a positive optical power;
a second lens group having a negative optical power; and
a third lens group having a positive optical power,
wherein the first lens group includes a first optical axis changing element that changes an optical axis, and
wherein conditional formula (3) below is fulfilled:


0.3<f3/√{square root over (fw×ft)}<1.0  (3)



where
f3 represents a focal length of the third lens group;
fw represents a focal length of the entire variable-magnification optical system at a wide-angle end; and
ft represents a focal length of the entire variable-magnification optical system at a telephoto end.