Abstract:
A zoom lens achieves a high zoom ratio and high optical performance in an entire zoom range. The zoom lens includes, in order from an object side to an image side, a first lens unit having a positive refractive power, a second lens unit having a negative refractive power, and a rear unit which includes at least one lens unit. At least the second lens unit is moved during zooming such that a distance between the first and second lens units is larger at a telephoto end than at a wide-angle end. The first lens unit includes at least a first lens element made of a material which satisfies Nd 1   a &gt;2.3−0.01·νd 1   a  and 1.65&lt;Nd 1   a &lt;2.70. The first and second lens units satisfy 2.5&lt;|f 1 /f 2 |&lt;12.0.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to a zoom lens and an image-pickup apparatus, and more particularly to an image-pickup apparatus, such as a video camera, an electronic still camera, a broadcasting camera, or a monitoring camera, which uses a solid-state image-pickup element. 
         [0002]    A high function has been achieved for the image-pickup apparatus, such as a video camera, a digital still camera, a broadcasting camera, a monitoring camera, or a silver-haloid film, which uses the solid-state image-pickup element to miniaturize the entire apparatus. 
         [0003]    The image-pickup apparatus requires, as an image-pickup optical system to be used, a zoom lens short in total length and compact, and having a high zoom ratio (large magnification) and a high resolving power. 
         [0004]    To meet such a requirement, a zoom lens has been developed which includes, in order from an object side to an image side, a first lens unit having a positive refractive power, a second lens unit having a negative refractive power, and a rear unit including at least one lens unit disposed further on the image side than the second lens unit (Japanese Patent Laid-Open No. [U.S. Pat. No. 5,0963,378], Japanese Patent Laid-Open No. 2000-347102 [U.S. Pat. No. 6,867,925], Japanese Patent Laid-Open No. 2003-315676 [U.S. Pat. No. 6,975,461], and Japanese Patent Laid-Open No. 6-148523). 
         [0005]    Lens configurations of the rear unit have been known which include a configuration formed by one lens unit of a positive refraction power, a configuration formed by plural lens units of positive refractive powers, and a configuration formed by at least one lens unit of a positive refractive power and one lens unit of a negative refractive power. 
         [0006]    The zoom lenses of such types perform zooming by moving the second lens unit and after to enlarge or reduce an image formed by the first lens unit. 
         [0007]    A zoom lens of a positive-lead type in which a first lens unit has a positive refractive power enables easier acquisition of a higher zoom ratio as compared with a negative-lead type in which a first lens unit has a negative refractive power. 
         [0008]    Transparent (transmissive) ceramics has recently been developed, resulting in an image-pickup optical system which uses the transparent ceramics as an optical material. The transparent ceramics has a refractive index, hardness, and strength higher than those of optical glasses. An image-pickup apparatus that uses these characteristics to thin the entire lens system has been developed (Japanese Patent Laid-Open No. 2006-84887 [U.S. Publication No. 2006/0062569]). 
         [0009]    The zoom lens used for the image-pickup apparatus is strongly required to be high in zoom ratio and compact in entire lens system. 
         [0010]    Generally, to miniaturize the zoom lens, the number of lenses only has to be reduced while a refractive power of each lens unit constituting the zoom lens is increased. 
         [0011]    However, once the zoom lens is configured this way, a lens thickness increases to make inadequate a reduction effect of the lens system and simultaneously difficult correction of various aberrations. 
         [0012]    Thus, to achieve a high zoom ratio and compactness of the entire lens system, a zoom type, a refractive power of each lens unit, and a configuration of each lens unit have to be appropriately set. 
         [0013]    A material used for the lens has to be selected, in view of a refractive index and an Abbe number, such that various aberrations including a chromatic aberration can be reduced at each zoom position. 
         [0014]    For example, to achieve a high zoom ratio while miniaturizing the entire zoom lens system of the positive-lead type, an appropriate material has to be selected for a lens element(s) in the first lens unit in view of the refractive index and Abbe number. 
         [0015]    The image-pickup apparatus disclosed in Japanese Patent Laid-Open No. 2006-84887 [U.S. Publication No. 2006/0062569]) uses the transparent ceramic for a material of a negative lens element in a cemented lens element in which a positive lens element and the negative lens element are cemented to reduce a lens thickness, thereby miniaturizing the entire lens system. 
         [0016]    The image-pickup apparatus disclosed in Japanese Patent Laid-Open No. 2006-84887 [U.S. Publication No. 2006/0062569] is designed based on recognition that ceramics has a refractive index, hardness, and flexural strength higher than those of optical glasses, which enables miniaturization by an amount equal to one thinned negative lens. 
         [0017]    In the optical glasses, generally, when the refractive indexes and Abbe numbers thereof are mapped on a graph (hereinafter referred to as “nd-νd diagram”) respectively to be larger in value upward on a vertical axis and larger in value leftward on a horizontal axis, the refractive indexes and the Abbe numbers are distributed almost along several straight lines. 
         [0018]    Generally, the optical glasses have characteristics in which a larger refractive index provides a smaller Abbe number, resulting in increase of dispersion. 
         [0019]    On the other hand, some ceramics of high transmittance in a visible light wavelength region and some oxide monocrystals or polycrystals are present in a region where the relationship between the refractive index and the Abbe number is different from that of a normal optical glass in the nd-νd diagram. 
         [0020]    In other words, materials have been known which have refractive indexes higher than that of the optical glass having an Abbe number equal to the materials. 
         [0021]    Use of materials having such a relationship between the refractive index and the Abbe number different from that of the normal optical glass, such as ceramics and oxide monocrystals or polycrystals, is advantageous for aberration correction and miniaturization of the entire optical system. 
         [0022]    However, simple use of lens elements made of such materials in zoom lenses does not warrant easy acquisition of high optical performance in the entire zoom range. 
         [0023]    To achieve a high zoom ratio and miniaturization of the entire lens system through use of the lens elements made of the above materials, a zoom type, a refractive power of each lens unit, and a configuration of each lens unit have to be appropriately set. 
       BRIEF SUMMARY OF THE INVENTION 
       [0024]    The present invention provides a compact zoom lens and an image-pickup apparatus including the same, which can achieve a high zoom ratio and high optical performance in the entire zoom range by appropriately using lens elements made of materials such as transparent ceramics and oxide monocrystals or polycrystals where a relationship between a refractive index and an Abbe number is different from that of a normal optical glass. 
         [0025]    The present invention provides as an aspect thereof a zoom lens including, in order from an object side to an image side, a first lens unit having a positive refractive power, a second lens unit having a negative refractive power, and a rear unit which includes at least one lens unit. At least the second lens unit is moved during zooming such that a distance between the first and second lens units is larger at a telephoto end than at a wide-angle end. The first lens unit includes at least a first lens element made of a material which satisfies the following conditions: 
         [0000]        Nd 1 a&gt; 2.3−0.01 ·νd 1 a    
         [0000]      1.65&lt;Nd1a&lt;2.70 
         [0026]    where Nd 1   a  denotes a refractive index for a d-line, and νd 1   a  denotes an Abbe number for the d-line. The first and second lens units satisfy the following condition: 
         [0000]      2.5 &lt;|f 1 /f 2|&lt;12.0 
         [0027]    where f 1  denotes a focal length of the first lens unit, and f 2  denotes a focal length of the second lens unit. 
         [0028]    The present invention provides as another aspect thereof an image-pickup element including the above-described zoom lens, and a solid-state image-pickup element which receives an image formed by the zoom lens. 
         [0029]    Other aspects of the present invention will become apparent from the following description and the attached drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]      FIG. 1  is a sectional view of a zoom lens that is a first embodiment (Embodiment 1) of the present invention at a wide-angle end. 
           [0031]      FIG. 2  is an aberration diagram of a numerical example of Embodiment 1 at the wide-angle end. 
           [0032]      FIG. 3  is an aberration diagram of the numerical example of Embodiment 1 at a middle zoom position. 
           [0033]      FIG. 4  is an aberration diagram of the numerical example of Embodiment 1 at a telephoto end. 
           [0034]      FIG. 5  is a sectional view of a zoom lens that is a second embodiment (Embodiment 2) of the present invention at a wide-angle end. 
           [0035]      FIG. 6  is an aberration diagram of a numerical example of Embodiment 2 at the wide-angle end. 
           [0036]      FIG. 7  is an aberration diagram of the numerical example of Embodiment 2 at a middle zoom position. 
           [0037]      FIG. 8  is an aberration diagram of the numerical example of Embodiment 2 at a telephoto end. 
           [0038]      FIG. 9  is a sectional view of a zoom lens that is a third embodiment (Embodiment 3) of the present invention at a wide-angle end. 
           [0039]      FIG. 10  is an aberration diagram of a numerical example of Embodiment 3 at the wide-angle end. 
           [0040]      FIG. 11  is an aberration diagram of the numerical example of Embodiment 3 at a middle zoom position. 
           [0041]      FIG. 12  is an aberration diagram of the numerical example of Embodiment 3 at a telephoto end. 
           [0042]      FIG. 13  is a sectional view of a zoom lens that is a fourth embodiment (Embodiment 4) of the present invention at a wide-angle end. 
           [0043]      FIG. 14  is an aberration diagram of a numerical example of Embodiment 4 at the wide-angle end. 
           [0044]      FIG. 15  is an aberration diagram of the numerical example of Embodiment 4 at a middle zoom position. 
           [0045]      FIG. 16  is an aberration diagram of the numerical example of Embodiment 4 at a telephoto end. 
           [0046]      FIG. 17  is a sectional view of a zoom lens that is a fifth embodiment (Embodiment 5) of the present invention at a wide-angle end. 
           [0047]      FIG. 18  is an aberration diagram of a numerical example of Embodiment 5 at the wide-angle end. 
           [0048]      FIG. 19  is an aberration diagram of the numerical example of Embodiment 5 at a middle zoom position. 
           [0049]      FIG. 20  is an aberration diagram of the numerical example of Embodiment 5 at a telephoto end. 
           [0050]      FIG. 21  is a sectional of a zoom lens of a sixth embodiment (Embodiment 6) of the present invention at a wide-angle end. 
           [0051]      FIG. 22  is an aberration diagram of a numerical example of Embodiment 6 at the wide-angle end. 
           [0052]      FIG. 23  is an aberration diagram of the numerical example of Embodiment 6 at a middle zoom position. 
           [0053]      FIG. 24  is an aberration diagram of the numerical example of Embodiment 6 at a telephoto end. 
           [0054]      FIG. 25  is a sectional view of a zoom lens that is a seventh embodiment (Embodiment 7) of the present invention at a wide-angle end. 
           [0055]      FIG. 26  is an aberration diagram of a numerical example of Embodiment 7 at the wide-angle end. 
           [0056]      FIG. 27  is an aberration diagram of the numerical example of Embodiment 7 at a middle zoom position. 
           [0057]      FIG. 28  is an aberration diagram of the numerical example of Embodiment 7 at a telephoto end. 
           [0058]      FIG. 29  is a view schematically showing a digital camera that includes the zoom lens of any one of Embodiment 1 to 7. 
           [0059]      FIG. 30  is a view schematically showing a video camera that includes the zoom lens of any one of Embodiment 1 to 7. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0060]    Exemplary embodiments of the present invention will hereinafter be described with reference to the accompanying drawings. 
         [0061]    Embodiments of zoom lenses and image-pickup apparatuses including the same will be described below. 
         [0062]    The zoom lens of each embodiment includes, in order from an object side to an image side, a first lens unit having a positive refractive power, a second lens unit having a negative refractive power, and a rear unit including at least one lens unit. 
         [0063]    During zooming, at least the second lens unit is moved such that a distance between the first and second lens units is larger at a telephoto end than at a wide-angle end. 
         [0064]    The rear unit includes, in order from the object side to the image side, a third lens unit having a positive refractive power and a fourth lens unit having a positive refractive power. 
         [0065]    Alternatively, the rear unit includes, in order from the object side to the image side, a third lens unit having a positive refractive power, a fourth lens unit having a negative refractive power, and a fifth lens unit having a positive refractive power. 
         [0066]      FIG. 1  is a main-portion sectional view (lens sectional view) of the zoom lens of a first embodiment (Embodiment 1) at a wide-angle end (short focal length end).  FIGS. 2 to 4  are aberration diagrams respectively at the wide-angle end, a middle zoom position (middle focal length position), and a telephoto end (long focal length end) of the zoom lens of a numerical example corresponding to Embodiment 1. 
         [0067]      FIG. 5  is a main-portion sectional view of a zoom lens of a second embodiment (Embodiment 2) at a wide-angle end.  FIGS. 6 to 8  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 2. 
         [0068]      FIG. 9  is a main-portion sectional view of a zoom lens of a third embodiment (Embodiment 3) at a wide-angle end.  FIGS. 10 to 12  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 3. 
         [0069]      FIG. 13  is a main-portion sectional view of a zoom lens of a fourth embodiment (Embodiment 4) at a wide-angle end.  FIGS. 14 to 16  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 4. 
         [0070]      FIG. 17  is a main-portion sectional view of a zoom lens of a fifth embodiment (Embodiment 5) at a wide-angle end.  FIGS. 18 to 20  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 5. 
         [0071]      FIG. 21  is a main-portion sectional view of a zoom lens of a sixth embodiment (Embodiment 6) at a wide-angle end.  FIGS. 22 to 24  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 6. 
         [0072]      FIG. 25  is a main-portion sectional view of a zoom lens of a seventh embodiment (Embodiment 7) at a wide-angle end.  FIGS. 26 to 28  are aberration diagrams respectively at the wide-angle end, a middle zoom position, and a telephoto end of the zoom lens of a numerical example corresponding to Embodiment 7. 
         [0073]    The zoom lens of each embodiment is an image-pickup lens system used for an image-pickup apparatus such as a video camera and a digital camera. In the lens sectional view, a left side is an object side (front), and a right side is an image side (rear). 
         [0074]    When the zoom lens of each embodiment is used as a projection lens of a projector, the left side is a screen side, and the right side is an image projection side. 
         [0075]    In the lens sectional view, reference character i denotes the order of lens units from the object side, and reference character Li denotes a first lens unit. Reference character LR denotes a rear unit which includes at least one lens unit. 
         [0076]    Reference character SP denotes an aperture stop. In each of the zoom lenses of Embodiments 2, 3, and 5 to 7 shown in  FIGS. 5 ,  9 ,  17 ,  21  and  25 , the aperture stop SP is disposed closer to an object than a third lens unit L 3 . 
         [0077]    In each of the zoom lenses of Embodiments 1 and 4 shown in  FIGS. 1 and 13 , the aperture stop SP is disposed in the third lens unit L 3 . 
         [0078]    In  FIGS. 9 and 17 , reference character FP denotes a flare-cutting stop disposed closer to an image than the third lens unit L 3 . 
         [0079]    Reference character G denotes an optical block including an optical filter, a face plate, a crystal low-pass filter, or an infrared-cutting filter. 
         [0080]    Reference character IP denotes an image plane (image surface). In use as an image-pickup system of a video camera or a digital still camera, an image-pickup plane of a solid-state image-pickup element (photoelectric conversion element) such as a CCD sensor or a CMOS sensor is placed at the image plane. In use as an image-pickup optical system of a camera for a silver-haloid film, a film plane is placed at the image plane. 
         [0081]    In the aberration diagram, d-LINE and g-LINE respectively represent a d-line and g-line. ΔM and ΔS respectively represent a meridional image surface and a sagittal image surface. Chromatic aberration of magnification is represented by the g-line. Reference characters ω and Fno respectively denote a half-field angle and an F-number. 
         [0082]    In each embodiment below, the wide-angle end and the telephoto end mean zoom positions where a magnification-varying lens unit(s) mechanically reaches both ends of its movable range on an optical axis of the zoom lens. 
         [0083]    Arrows indicate movement tracks of respective lens units in zooming from the wide-angle end to the telephoto end. 
         [0084]    The zoom lens of each embodiment includes, in order from the object side to the image side, a first lens unti L 1  having a positive refractive power, a second lens unit L 2  having a negative refractive power, and a rear unit LR which is closer to the image than the second lens unit L 2  and includes at least one lens unit. 
         [0085]    During zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved such that a distance between the first and second lens unti L 1  and L 2  is larger at the telephoto end than at the wide-angle end. 
         [0086]    In each of the zoom lenses of Embodiments 1 to 6, the rear unit LR includes the third lens unit L 3  having a positive refractive power and a fourth lens unit L 4  having a positive refractive power. 
         [0087]    In each of the zoom lenses of Embodiments 1, 2, 4, and 6, in zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved to the image side to mainly perform variation of magnification. The fourth lens unit L 4  is moved to correct variation of the image plane accompanying the variation of magnification, and to perform focusing. 
         [0088]    The movement track of the fourth lens unit L 4  during zooming is convexed toward the object to make effective use of a space between the third and fourth lens units L 3  and L 4 , thereby effectively reducing the entire lens length. 
         [0089]    A solid curved line  4   a  and a dotted curved line  4   b  regarding the fourth lens unit L 4  indicate movement tracks to correct variation of the image plane accompanying the variation of magnification when the zoom lens is focused on an infinite object and a near object. 
         [0090]    To perform focusing from the infinite object to the near object at the telephoto end, the fourth lens unit L 4  is moved forward as indicated by an arrow  4   c.    
         [0091]    The first and third lens units L 1  and L 3  and the aperture stop SP are not moved in an optical axis direction for zooming or focusing. However, they may be moved when necessary for aberration correction. 
         [0092]    In the zoom lenses of Embodiments 3 and 5, each lens unit is moved to perform zooming. During zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved so as to draw a movement track convex toward the image. The first and third lens unit L 1  and L 3  are moved to be located closer to the object at the telephoto end than at the wide-angle end. 
         [0093]    The fourth lens unit L 4  is moved so as to draw a movement track convex toward the object during zooming. 
         [0094]    During zooming, the first lens unti L 1  is moved closer to the object at the telephoto end than at the wide-angle end, thereby obtaining a high zoom ratio while reducing the total lens length at the wide-angle end. 
         [0095]    During zooming, the third lens unit L 3  is moved to be located closer to the object at the telephoto end than at the wide-angle end, whereby the third lens unit L 3  provides a larger magnification varying effect. 
         [0096]    During zooming from the wide-angle end to the telephoto end, the first lens unti L 1  having a positive refractive power is moved closer to the object, thereby providing a magnification varying effect to the second lens unit L 2 . Thus, a high zoom ratio is obtained without increasing refractive powers of the first and second lens units L 1  and L 2 . 
         [0097]    The zoom lenses of Embodiments 3 and 5 employ a rear-focus system which performs focusing by moving the fourth lens unit L 4  on the optical axis. 
         [0098]    The movement track of the fourth lens unit L 4  for focusing is similar to that of each in Embodiments 1, 2, 4, and 6. 
         [0099]    The aperture stop SP is moved integrally with the third lens unit L 3  during zooming. However, the aperture stop SP may be moved separately from the third lens unit L 3 , or fixed. The integral movement simplifies a mechanical structure of the zoom lens. 
         [0100]    The movement of the aperture stop SP separately from the third lens unit L 3  is advantageous for miniaturizing the first lens unti L 1 . 
         [0101]    On the other hand, fixing of the aperture stop SP is advantageous for saving power because driving torque of an actuator driving the third lens unit L 3  during zooming can be set small. 
         [0102]    The flare-cutting stop FP is moved integrally with the third lens unit L 3  during zooming. 
         [0103]    In the zoom lens of Embodiment 7, the rear unit LR includes a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative refractive power, and a fifth lens unit L 5  having a positive refractive power. 
         [0104]    During zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved to the object side to mainly perform variation of magnification. The fourth lens unit L 4  is moved to correct variation of the image plane accompanying the variation of magnification. 
         [0105]    The movement track of the fourth lens unit L 4  is convexed toward the image to make effective use of a space between the fourth and fifth lens units L 4  and L 5 , thereby effectively reducing the entire lens length. 
         [0106]    To perform focusing from the infinite object to the near object at the telephoto end, the fourth lens unit L 4  is moved rearward (to the image side) as indicated by an arrow  4   c.    
         [0107]    A solid curved line  4   a  and a dotted curved line  4   b  regarding the fourth lens unit L 4  indicate movement tracks to correct variation of the image plane accompanying the variation of magnification from the wide-angle end to the telephoto end when the zoom lens is focused on an infinite object and a near object. 
         [0108]    Focusing from the infinite object to the near object may be performed by moving the fifth lens unit L 5  toward the object. 
         [0109]    The movement track of the fifth lens unit L 5  for focusing is similar to that of the fourth lens unit L 4  in Embodiments 1 to 6. 
         [0110]    The first and third lens units L 1  and L 3  and the aperture stop SP are not moved on the optical axis direction for zooming or focusing. However, they may be moved when necessary for aberration correction. 
         [0111]    Each embodiment shows the zoom lens which includes four or five lens units. However, the zoom lens may include a lens unit or converter lens unit having a refractive power on the object side of the first lens unti L 1  as occasion demands. 
         [0112]    The zoom lens may include the lens unit or converter lens unit having a refractive power on the image side of the fourth lens unit L 4  of each of Embodiments 1 to 4 or on the image side of the fifth lens unit L 5  of Embodiment 7. 
         [0113]    In each embodiment, Nd 1   a  denotes a refractive index for the d-line, and νd 1   a  denotes an Abbe number for the d-line. 
         [0114]    In this case, the first lens unti L 1  includes at least one lens element (first lens element) G 1   a  made of a material which satisfies the following conditions: 
         [0000]        Nd 1 a&gt; 2.3−0.01 ·νd 1 a    (1) 
         [0000]      1.65&lt;Nd1a&lt;2.70   (2) 
         [0115]    Technical meanings of the conditional expressions (1) and (2) will be described below. 
         [0116]    The conditional expressions (1) and (2) define a relationship between the refractive index Nd 1   a  and the Abbe number νd 1   a  of the material of the one lens element G 1   a  constituting the first lens unti L 1 . 
         [0117]    The conditional expression (1) indicate that, when the Abbe number νd 1   a  of the material of the lens element G 1   a  is decided, the refractive index Nd 1   a  of the material should be larger than a value calculated by the right side of the conditional expression (1). 
         [0118]    The conditional expression (1) means that, to reduce the Abbe number νd 1   a  of the material of the lens element G 1   a,  in other words, to increase dispersion thereof, the refractive index Nd 1   a  of the material should be larger. 
         [0119]    When the refractive index Nd 1   a  is lower than the lower limit of the conditional expression (1) calculated from the Abbe number, a curvature of each surface of the lens element G 1   a  is increased. As a result, spherical and longitudinal chromatic aberrations generated in the lens element G 1   a  become too large, so that residual spherical and longitudinal chromatic aberrations become large in the first lens unti L 1 . 
         [0120]    The amount of aberration generated in the first lens unti L 1  becomes an aberration value obtained by multiplying a product of lateral magnifications of the second lens unit L 2  and others closer to the image than the second lens unit L 2  in the entire lens system. 
         [0121]    In the zoom lens, a product of the lateral magnifications of the second lens unit L 2  and others closer to the image than the second lens unit L 2  becomes maximum at the telephoto end. 
         [0122]    Thus, when the residual spherical and longitudinal chromatic aberrations of the first lens unit Li are large, particularly in the zoom lens of a high zoom ratio, the amount of the aberrations are large at the telephoto end in the entire lens system. Consequently, flare is increased, resolution is reduced, and color blur is increased, thereby deteriorating image quality. 
         [0123]    When the refractive index Nd 1   a  of the material of the lens element G 1   a  is lower than the lower limit of the conditional expression (2), a curvature of the lens element G 1   a  is increased. As a result, spherical aberration generated in the lens element G 1   a  becomes too large, and therefore flare is increased and resolution is reduced particularly at the telephoto end. 
         [0124]    Further, when the refractive index Nd 1   a  of the material of the lens element G 1   a  is higher than the upper limit of the conditional expression (2), the refractive index Nd 1   a  is too large. This makes correction of Petzval sum of the entire lens system difficult and generates field curvature. 
         [0125]    In each embodiment, satisfying the conditional expressions (1) and (2) can provide a compact zoom lens having a high zoom ratio and high optical performance. 
         [0126]    In each embodiment, it is more preferable that at least one of the following conditions be satisfied in addition to the conditional expressions (1) and (2). Thus, effects corresponding to the conditions can be obtained. 
         [0127]    When the lens element G 1   a  has a positive refractive power, the lens element G 1   a  is referred to as a positive lens element G 1   pa.  In this case, νd 1   pa  denotes an Abbe number of a material of the positive lens element G 1   pa,  R 1   p  denotes a curvature radius of an object side surface thereof, and R 2   p  denotes a curvature radius of an image side surface thereof. 
         [0128]    f 1   pa  denotes a focal length of the positive lens element G 1   pa  and f 1  denotes a focal length of the first lens unit. 
         [0129]    When the lens element G 1   a  has a negative refractive power, the lens element G 1   a  is referred to as a negative lens element G 1   na.  In this case, νd 1   na  denotes an Abbe number of a material of the negative lens element G 1   na,  R 1   n  denotes a curvature radius of an object side surface thereof, and R 2   n  denotes a curvature radius of an image side surface thereof. 
         [0130]    f 1   na  denotes a focal length of the negative lens element G 1   na,  and f 2  denotes a focal length of the second lens unit. 
         [0131]    In this case, it is preferable that at least one of the following conditions be satisfied. Especially, it is more preferable that the conditional expression (9) be satisfied. 
         [0000]      νd1pa&gt;45   (3) 
         [0000]      0.5&lt;( R 1 p+R 2 p )/( R 2 p−R 1 p )&lt;10.0   (4) 
         [0000]      0.3 &lt;f 1 pa/f 1&lt;3.0   (5) 
         [0000]      νd1na&lt;45   (6) 
         [0000]      −10.0&lt;( R 1 n+R 2 n )/( R 2 n−R 1 n )&lt;−1.5   (7) 
         [0000]      1.0 &lt;|f 1 na/f 1|&lt;3.0   (8) 
         [0000]      2.5 &lt;|f 1/ f 2|&lt;12.0   (9) 
         [0132]    Technical meanings of the conditional expressions (3) to (9) will be described below. 
         [0133]    The conditional expressions (3) and (4) define the Abbe number of the material of the lens element G 1   a  and a lens shape thereof when the lens element G 1   a  is a positive lens element G 1   pa  having a positive refractive power. 
         [0134]    When the Abbe number νd 1   a  is lower than the lower limit of the conditional expression (3), longitudinal chromatic aberration generated in the positive lens element G 1   pa  becomes excessively large. Even if achromatizing is carried out by a combination with the negative lens element in the first lens unti L 1 , correction of a secondary spectrum of the longitudinal chromatic aberration is difficult at the telephoto end. 
         [0135]    The conditional expression (4) relates to a shape factor (lens shape) of the positive lens element G 1   pa.    
         [0136]    When the value of the conditional expression (4) is lower than the lower limit thereof because, in the positive lens element G 1   pa  which is a biconvex lens element, a curvature of its image side surface is too large, an emergent angle of off-axis rays from the image side surface of the positive lens element G 1   pa  becomes excessively large at the wide-angle end, disadvantageously generating a large chromatic aberration of magnification and a large astigmatism at the wide-angle end. 
         [0137]    When the value of the conditional expression (4) is higher than the upper limit thereof because a difference between the curvature radiuses R 1   p  and R 2   p  of the positive lens element G 1   pa  is too small, the refractive power of the positive lens element G 1   pa  is reduced, resulting in a difficulty of providing an adequate aberration correction capability to the positive lens element G 1   pa.    
         [0138]    Thus, characteristics of the material of the positive lens element G 1   pa,  in other words, a lower dispersion and a higher refractive index than those of general glass materials cannot be effectively used, resulting in a difficulty of achieving increase of the magnification (zoom) ratio and miniaturization of the entire lens system. 
         [0139]    From another viewpoint, when the value of the conditional expression (4) is higher than the upper limit thereof because the difference between the curvature radiuses R 1   p  and R 2   p  of the positive lens element G 1   pa  is too small, providing an adequate refractive power to the positive lens element G 1   pa  excessively reduces the curvature radius R 1   p  of the positive lens element G 1   pa.    
         [0140]    In this case, a refractive power of the convex object side surface becomes too large, and therefore an incident angle of axial rays whose height is large at the telephoto end in the first lens unti L 1  is increased. This generates a large spherical aberration, deteriorating optical performance at the telephoto end. 
         [0141]    The conditional expression (5) defines a refractive power distribution of the positive lens element G 1   pa  in the first lens unti L 1 . 
         [0142]    When the value of the conditional expression (5) is lower than the lower limit thereof because the focal length of the positive lens element G 1   pa  is too small, in other words, the refractive power thereof is too large, spherical and longitudinal chromatic aberrations generated in the positive lens element G 1   pa  at the telephoto end are too large. This makes correction of the aberrations by another lens element(s) of the first lens unti L 1  difficult. 
         [0143]    When the value of the conditional expression (5) is higher than the upper limit thereof because the refractive power of the positive lens element G 1   pa  is excessively reduced, the characteristics of the material of the positive lens element G 1   pa  in which the dispersion is lower and the refractive index is higher as compared with those of general glass materials cannot be effectively used, resulting in a difficulty of achieving increase of the zoom ratio and miniaturization of the entire lens system. 
         [0144]    The conditional expressions (6) to (8) is employed when the lens element G 1   a  is a negative lens element G 1   na  having a negative refractive power. 
         [0145]    The conditional expressions (6) to (8) define the Abbe number of the material and a lens shape of the negative lens element G 1   na.    
         [0146]    In the first lens unti L 1  having a positive refractive power, a combination of the negative lens element G 1   na  with the positive lens element provides an achromatizing effect. 
         [0147]    When the Abbe number νd 1   na  is larger than the upper limit of the conditional expression (6), a difference of the Abbe number of the negative lens element G 1   na  from that of the positive lens element is small, and therefore sufficient achromatizing cannot be performed. This causes a correction shortage of the longitudinal chromatic aberration at the telephoto end. 
         [0148]    The conditional expression (7) relates to a shape factor of the negative lens element G 1   na.    
         [0149]    Within the range of the conditional expression (7), the negative lens element G 1   na  has a meniscus shape where its image side surface is a concave surface having a strong curvature. 
         [0150]    When the value of the conditional expression (7) is lower than the lower limit thereof because the curvature radius R 2   n  of the image side surface of the negative lens element G 1   na  is too small, in other words, the curvature thereof is too strong, an incident angle of axial rays whose height is large at the telephoto end in the first lens unti L 1  is too large. 
         [0151]    Consequently, at the telephoto end, a large spherical aberration is generated on the image side surface of the negative lens element G 1   na.  Such a large spherical aberration cannot be sufficiently corrected by the positive lens element of the first lens unit, causing deterioration of optical performance at the telephoto end. 
         [0152]    When the value of the conditional expression (7) is higher than the upper limit thereof because a difference between the curvature radiuses R 1   n  and R 2   n  of the negative lens element G 1   na  is too small, the refractive power of the negative lens element G 1   na  is reduced, causing a difficulty of providing an adequate aberration correction capability to the negative lens element G 1   na.    
         [0153]    Consequently, characteristics of the material of the negative lens element G 1   na,  in other words, a lower dispersion and a higher refractive index than those of general glass materials cannot be effectively used, resulting in a difficulty of achieving increase of the zoom ratio and miniaturization of the entire lens system. 
         [0154]    The conditional expression (8) defines an appropriate refractive power of the negative lens element G 1   na  for the purpose of performing achromatizing in combination with the positive lens element in the first lens unti L 1  having a positive refractive power. 
         [0155]    When the value of the conditional expression (8) is lower than the lower limit thereof because the focal length f 1   na  of the negative lens element G 1   na  is too small, in other words, the refractive power of the negative lens element G 1   na  is too large, the correction amount for longitudinal chromatic aberration generated in the negative lens element G 1   na  is too large, causing a difficulty of performing good achromatizing. 
         [0156]    On the other hand, when the value of the conditional expression (8) is higher than the upper limit thereof because the focal length f 1   na  of the negative lens element G 1   na  is too large, in other words, the refractive power of the negative lens element G 1   na  is too small, the correction amount for the longitudinal chromatic aberration generated in the negative lens element G 1   na  is short, causing a difficulty of performing good achromatizing. 
         [0157]    The conditional expression (9) defines a ratio of refractive powers between the first and second lens units L 1  and L 2 . 
         [0158]    When the value of the conditional expression (9) is lower than the lower limit thereof because the focal length f 1  of the first lens unti L 1  is too small, sufficient correction of spherical and longitudinal chromatic aberrations generated in the first lens unti L 1  is difficult. Even when a material which satisfies at least one of the conditional expressions (1) to (8) is used, aberration correction is difficult. 
         [0159]    When the value of the conditional expression (9) is higher than the upper limit thereof because the focal length f 1  of the first lens unti L 1  is too large, an image-forming position of the first lens unti L 1  is far away from the first lens unti L 1  toward the image. 
         [0160]    This is not good, because the movement amount of the second lens unit L 2  or the rear unit LR has to be increased to obtain a high zoom ratio, consequently enlarging the entire lens system. 
         [0161]    In each embodiment, more preferably, the numerical ranges of the conditional expressions (2) to (9) are set as follows: 
         [0000]      1.7&lt;Nd1a&lt;2.65   (2a) 
         [0000]      νd1pa&gt;48   (3a) 
         [0000]      0.6&lt;( R 1 p+R 2 p )/( R 2 p−R 1 p )&lt;7.0   (4a) 
         [0000]      0.4 &lt;f 1 pa/f 1&lt;2.4   (5a) 
         [0000]      νd1na&lt;42   (6a) 
         [0000]      −8.0&lt;( R 1 n+R 2 n )/( R 2 n−R 1 n )&lt;−2.0   (7a) 
         [0000]      1.1 &lt;|f 1 na/f 1|&lt;2.5   (8a) 
         [0000]      3.0 &lt;|f 1 /f 2|&lt;10.0   (9a) 
         [0162]    Still more preferably, the numerical ranges of the conditional expressions (2a) to (9a) are set as follows: 
         [0000]      1.7&lt;Nd1a&lt;2.6   (2b) 
         [0000]      ν d 1 pa&lt;f 1 pa/f 1&lt;1.8   (3b) 
         [0000]      0.7&lt;( R 1 p+R 2 p )/( R 2 n−R 1 p )&lt;5.0   (4b) 
         [0000]      0.45 &lt;f 1 pa/f 1&lt;1.8   (5b) 
         [0000]      νd1na&lt;40   (6b) 
         [0000]      −6.5&lt;( R 1 n+R 2 n )/( R 2 n−R 1 n )&lt;−2.5   (7b) 
         [0000]      1.2 &lt;|f 1 na/f 1|&lt;2.0   (8b) 
         [0000]      3.5 &lt;|f 1 /f 2|&lt;9.0   (9b) 
         [0163]    Satisfying each of the conditional expressions (2b) to (9b) can obtain the maximal effect described above. 
         [0164]    It is preferable that the second lens unit L 2  include at least one positive lens element and at least one negative lens element. 
         [0165]    This configuration of the second lens unit L 2  moved during zooming facilitates suppression of variation of chromatic aberration of magnification accompanying the zooming. 
         [0166]    Among the lens units constituting the rear unit LR closer to the image than the second lens unit L 2 , the lens unit closest to the object preferably has a positive refractive power. 
         [0167]    At the wide-angle end, axial rays are dispersed after passage through the second lens unit L 2  having a negative refractive power. However, the positive refractive power of the lens unit closest to the object constituting the rear unit closer to the image than the second lens unit L 2  provides a converging effect to the axial rays, thereby reducing a lens effective diameter of the rear unit. 
         [0168]    Thus, the above configuration of the second lens unit L 2  is advantageous for miniaturizing the zoom lens. 
         [0169]    Further, the number of the positive lens element(s) included in the first lens unti L 1  is preferably two or less for the purpose of miniaturizing the entire lens system. 
         [0170]    Thus, according to each embodiment, effective use of the material different in optical characteristics from general optical glasses for the first lens unit can realize a compact zoom lens having a high zoom ratio and being capable of obtaining high optical performance over the entire zoom range. 
         [0171]    Next, a specific lens configuration of each embodiment will be described. Hereinafter, the lens units or the lens elements are disposed in order from the object side to the image side unless otherwise noted. 
         [0172]    The zoom lens of Embodiment 1 shown in  FIG. 1  includes a first lens unti L 1  having a positive refractive power, a second lens unit L 2  having a negative refractive power, a third lens unit L 3  having a positive refractive power, and a fourth lens unit L 4  having a positive refractive power. 
         [0173]    During zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved toward the image to mainly perform variation of magnification, and the fourth lens unit L 4  is moved along a movement track convex toward the object to mainly correct variation of an image plane accompanying the variation of magnification. 
         [0174]    The first lens unti L 1  includes a cemented lens element formed by cementing a negative lens element G 11  having a meniscus shape and a convex object side surface with a positive lens element G 12 , and a positive lens element G 13  having a meniscus shape and a convex object side surface. 
         [0175]    The three-lens element configuration of the first lens unit can perform good correction of spherical aberration and good correction of longitudinal chromatic aberration and chromatic aberration of magnification in each color even in the zoom lens having a high zoom ratio. 
         [0176]    The positive lens element G 12  corresponds to the positive lens element G 1   pa.  The positive lens element G 12  uses a material where a refractive index and an Abbe number satisfy the conditional expressions (1) and (2), such as yttrium aluminum garnet ceramics. 
         [0177]    The yttrium aluminum garnet is called “YAG”, which is a transparent oxide in a visible light area and represented by Y3Al5O12. 
         [0178]    The material has optical characteristics that its refractive index is 1.83 and its Abbe number is 59, and is characterized by being present within a region where no general optical glass materials are present in the nd-νd diagram, the region being located on the left above a region where the general optical glass materials are present in that diagram. 
         [0179]    In other words, the material has a lower dispersion than that of an optical glass material having a refractive index equal to that of the material. 
         [0180]    In the zoom lens of the embodiment which includes the first lens unti L 1  having a positive refractive power and being fixed during zooming and the second lens unit L 2  having a negative refractive power and being moved for variation of magnification, providing a high refractive power to the first lens unti L 1  is effective for miniaturizing the entire lens system. 
         [0181]    To provide a high refractive power to the first lens unti L 1 , the curvature of a surface of the positive lens element in the first lens unti L 1  has to be set strong or the refractive index of the material thereof has to be increased. 
         [0182]    When the curvature of the surface of the positive lens element is increased, large spherical and longitudinal chromatic aberrations are generated in the positive lens element. Especially, at the telephoto end where the height of the axial rays is large in the first lens unti L 1 , the spherical and longitudinal chromatic aberration are large, causing a difficulty of achieving a high zoom ratio while maintaining high optical performance. 
         [0183]    On the other hand, use of a material having a high refractive index for the positive lens element reduces the curvature of its image side surface, enabling suppression of the occurrence of spherical aberration. 
         [0184]    However, in the general optical glass materials, the Abbe number reduces, in other words, the dispersion increases as the refractive index increases. Accordingly, chromatic aberration generated in the positive lens element increases, and thereby longitudinal chromatic aberration generated at the telephoto end increases. 
         [0185]    Thus, in the general optical glass materials, there is a limit to simultaneous achievement of a high zoom ratio and miniaturization of the entire lens system while maintaining high optical performance. 
         [0186]    On the other hand, use of a material having a higher refractive index and a larger Abbe number than those of the general optical glass materials for the positive lens element of the first lens unti L 1  facilitates correction of both of spherical and longitudinal chromatic aberrations at the telephoto end. Thus, miniaturization of the entire lens system and a high zoom ratio can simultaneously be realized easily. 
         [0187]    According to the embodiment, the YAG ceramics having optical characteristics different from those of the general optical glass materials is used as the material for the positive lens element G 12  of the first lens unti L 1 . Thus, spherical and longitudinal chromatic aberrations are corrected well at the telephoto end to simultaneously achieve a high zoom ratio of about 10 and miniaturization of the entire lens system. 
         [0188]    The YAG has optical characteristics similar to those of ceramics even in a monocrystal, and use of the monocrystal in place of the ceramics as the material for the positive lens element G 12  provides similar effects. Manufacturing conditions of the ceramics may necessitate slight variations in refractive index and Abbe number. Such variations, however, poses no practical problems. 
         [0189]    The use of the material of a high refractive index for the positive lens element G 12  of the first lens unti L 1  causes a change in Petzval sum of the entire lens system in a negative direction. 
         [0190]    The change in Petzval sum can be corrected easily by providing a higher refractive index to the material of the negative lens element included in the first lens unti L 1  or the lens units closer to the image than the second lens unit L 2 , or by providing a lower refractive index to the material of the positive lens element included therein. 
         [0191]    The second lens unit L 2  includes three lens elements, i.e., a negative lens element G 21  having a meniscus shape and a concave image side surface, a biconcave negative lens element G 22 , and a positive lens element G 23  having a meniscus shape and a convex object side surface. The second lens unit L 2  suppresses aberration variation accompanying zooming. 
         [0192]    The third lens unit L 3  includes three lens elements, i.e., a positive lens element G 31  having a convex object side surface, a negative lens element G 32  having a concave image side surface, and a biconvex positive lens element G 33 . 
         [0193]    The positive lens element G 31  corrects spherical aberration well by its object side surface formed as an aspheric surface. The positive lens element G 33  mainly corrects spherical aberration and astigmatism well by its object side surface formed as an aspheric surface. 
         [0194]    The aperture stop SP is disposed in the third lens element L 3  to shorten a distance between the second and third lens units L 2  and L 3  at the telephoto end. Thus, the entire lens length is reduced. 
         [0195]    The fourth lens unit L 4  is constituted by a cemented lens element formed by cementing a biconvex positive lens element G 41  with a negative lens element G 42  having a meniscus shape and a convex image side surface. The cemented lens element of the positive and negative lens elements suppresses aberration variation accompanying the movement of the fourth lens unit L 4  during zooming and focusing. 
         [0196]    Next, the zoom lens of Embodiment 2 shown in  FIG. 5  will be described. The basic lens configuration of this embodiment including the sign of the refractive power of each lens unit and the movement conditions of the lens units during zooming are identical to those of Embodiment 1 shown in  FIG. 1 . 
         [0197]    Embodiment 2 is different from Embodiment 1 in that a second lens unit L 2  is constituted by four lens elements including one additional negative lens element. As a result, the refractive power and aberration correction capability of the second lens unit L 2  which is a magnification-varying lens unit are enhanced, thereby realizing a higher zoom ratio of 34. 
         [0198]    Further, Embodiment 2 is different from Embodiment 1 in that a third lens unit L 3  includes two lens elements, i.e., a positive lens element and a negative lens element, and an aperture stop SP is disposed closer to the object side than (on the object side of) the third lens unit L 3 . 
         [0199]    The disposition of the aperture stop SP on the object side of the third lens unit L 3  enables an entrance pupil to be located closer to the object, thereby reducing the diameter of the first lens unti L 1 . 
         [0200]    A positive lens element G 13  of the first lens unti L 1  corresponds to the positive lens element G 1   pa.    
         [0201]    As the material for the positive lens element G 13  of the first lens unti L 1 , YAG identical to that of the lens element G 12  of Embodiment 1 is used. 
         [0202]    The YAG has a higher refractive index than that of a normal optical glass material having an almost equal level of dispersion. Thus, a large refractive power can be easily provided to the positive lens element G 13  without increasing spherical and achromatic aberrations. As a result, an effect of reducing a lens thickness is added to facilitate the miniaturization of the entire lens system. 
         [0203]    Next, the zoom lens of Embodiment 3 shown in  FIG. 9  will be described. The basic lens configuration of this embodiment including the number of the lens units and the refractive power arrangement are identical to those of Embodiment 1. The zoom lens of Embodiment 3 performs zooming by moving all four lens units. 
         [0204]    A first lens unti L 1  includes one positive lens element G 11  having a convex object side surface. The positive lens element G 11  corresponds to the positive lens element G 1   pa.    
         [0205]    As the material for the positive lens element G 11 , YAG whose refractive index and Abbe number satisfy the conditional expressions (1) and (2) is used. 
         [0206]    A larger refractive power is provided to the positive lens element G 11 , i.e., the first lens unti L 1  by utilizing characteristics of the YGA in which its refractive index is higher and its dispersion is lower than those of normal optical glass materials while suppressing the occurrence of spherical and chromatic aberrations in the first lens unti L 1 . As a result, a zoom ratio of the second lens unit L 2  is increased to miniaturize the entire lens system. 
         [0207]    The second lens unit L 2  includes three lens elements, i.e., a negative lens element G 21  having a meniscus shape and a concave image side surface, a biconcave negative lens element G 22 , and a positive lens element G 23  having a convex object side surface. 
         [0208]    The third lens unit L 3  includes two lens elements, i.e., a biconvex positive lens element G 31 , and a cemented lens element formed by cementing a positive lens element G 32  having a meniscus shape and a convex object side surface with a negative lens element G 33  having a meniscus shape and a concave image side surface. The cemented lens element has a negative combined refractive power. 
         [0209]    The positive lens element G 31  corrects spherical aberration well by its object side surface formed as an aspheric surface. 
         [0210]    The fourth lens unit L 4  is constituted by one positive lens element G 41  whose object side surface has a stronger curvature than that of its image side surface. 
         [0211]    Next, the zoom lens of Embodiment 4 shown in  FIG. 13  will be described. The basic lens configuration of this embodiment including the sign of the refractive power of each lens unit and the movement conditions of the lens units during zooming are identical to those of Embodiment 1 shown in  FIG. 1 . 
         [0212]    In Embodiment 4, a negative lens element G 11  of a first lens unti L 1  corresponds to the negative lens element G 1   na.  As the material for the negative lens element G 11 , transparent ceramics “LUMI-CERA” (registered trademark) made by Murata Manufacturing Company. Ltd., is used whose refractive index and Abbe number satisfy the conditional expressions (1) and (2). 
         [0213]    The “LUMI-CERA” has characteristics that its refractive index nd for the d-line is 2.095 which is high, and its Abbe number νd for the d-line is 29.4, and is characterized by being present within a region where no general optical glass materials are present in an nd-νd diagram and by having a refractive index higher than that of the general optical glass materials having an almost equal level of dispersion. 
         [0214]    The use of the material having a high refractive index for the negative lens element G 11  of the first lens unti L 1  enables further reduction of the curvature of a first lens surface (object side surface of the negative lens element G 11 ). As a result, at the telephoto end where axial rays pass through the negative lens element G 11  at a high ray height, an incident angle of the axial rays can be reduced, thereby suppressing the occurrence of spherical aberration at the telephoto end. 
         [0215]    Thus, a high zoom ratio can be easily achieved. 
         [0216]    Further, a difference in refractive index between the negative and positive lens elements G 11  and G 12  can be increased. Thus, the capability of correcting various aberrations in a cemented lens surface can be enhanced, and variation of spherical aberration during variation of magnification can be suppressed. 
         [0217]    In the zoom lens of this embodiment which performs variation of magnification mainly by the second lens unit L 2  having a negative refractive power, to achieve miniaturization of the entire lens system and a high zoom ratio, it is necessary that a negative refractive power of the second lens unit L 2  be increased to reduce its movement amount during the variation of magnification. 
         [0218]    When increasing the zoom ratio and the negative refractive power of the second lens unit L 2 , Petzval sum tends to take a negative value. 
         [0219]    Increasing a refractive index of a material of a negative lens unit included in the second lens unit L 2  enables correction of Petzval sum to a certain extent. However, dispersion of the material of the negative lens element is increased, thereby causing incomplete correction of chromatic aberration at the second lens unit L 2 . Consequently, variation of chromatic aberration of magnification during variation of magnification is increased. 
         [0220]    Reducing a refractive index of a material of a positive lens element enables correction of Petzval sum to a certain extent in a plus direction. However, a curvature of a surface of the positive lens is increased to cause a difficulty of correcting spherical aberration and an increase of the thickness of the positive lens element, which increases the size of the entire lens system. 
         [0221]    Thus, in this embodiment, a material of a high refractive index is used for the negative lens element G 11  of the first lens unti L 1  to correct Petzval sum in the plus direction, which is changed in the minus direction by increasing the zoom ratio. Thereby, a high zoom ratio is achieved while correcting field curvature. 
         [0222]    Next, the zoom lens of Embodiment 5 shown in  FIG. 17  will be described. The basic lens configuration of this embodiment including the sign of the refractive power of each lens unit and the movement conditions of the lens units during zooming are identical to those of Embodiment 3 shown in  FIG. 9 . 
         [0223]    Embodiment 5 is different from Embodiment 3 in that a first lens unti L 1  is constituted by a cemented lens element formed by cementing a negative lens unit G 11  with a positive lens unit G 12 , thereby increasing a refractive power and aberration correction capability of the first lens unti L 1  to realize a higher zoom ratio. In Embodiment 5, the negative lens element G 11  corresponds to the negative lens element G 1   na,  and the positive lens element G 12  corresponds to the positive lens element G 1   pa.    
         [0224]    In Embodiment 5, as the material for the negative lens element G 11 , transparent ceramics “LUMI-CERA” (registered trademark) made by Murata Manufacturing Company Ltd., is used whose refractive index and Abbe number satisfy the conditional expressions (1) and (2). 
         [0225]    As the material for the positive lens element G 12 , YAG whose refractive index and Abbe number satisfy the conditional expressions (1) and (2) is used. 
         [0226]    As described above, the materials that satisfy the conditional expressions (1) and (2) are used for the positive and negative lens elements of the first lens unti L 1 . Thus, the combination of the above-described effects of using such a material for the positive lens element with the above-described effects of using such a material for the negative lens element reduces spherical and longitudinal chromatic aberrations at the telephoto end and realizes miniaturization of the entire lens system and a high zoom ratio. 
         [0227]    Next, the zoom lens of Embodiment 6 shown in  FIG. 21  will be described. The basic lens configuration of this embodiment including the sign of the refractive power of each lens unit and the movement conditions of the lens units during zooming are identical to those of Embodiment 2 shown in  FIG. 5 . 
         [0228]    A negative lens element G 11  corresponds to the negative lens element G 1   na,  and each of positive lens elements G 12  and G 13  corresponds to the positive lens element G 1   pa.    
         [0229]    In Embodiment 6, a material whose refractive index and Abbe number satisfy the conditional expressions (1) and (2) is used for the negative lens element G 11  of the first lens unti L 1 , and YAG whose refractive index and Abbe number satisfy the conditional expressions (1) and (2) is used for the positive lens elements G 12  and G 13 . 
         [0230]    Use of the materials whose refractive indexes and the Abbe numbers satisfy the conditional expressions (1) and (2) for all the three lenses of the first lens unti L 1  increases the refractive power of the first lens unti L 1  while suppressing spherical and longitudinal chromatic aberrations at the telephoto end. Thus, a high zoom ratio higher than 37 and miniaturization of the entire lens system can be achieved. 
         [0231]    In Embodiment 6, the negative lens element G 11  and the positive lens elements G 12  and G 13  are formed to have a meniscus shape having a convex object side surface. 
         [0232]    In the first lens unti L 1 , light rays passing through a peripheral portion which is a high portion from the optical axis of the zoom lens include marginal rays which are axial rays at the telephoto end, and off-axis rays at the middle zoom position slightly closer to the telephoto end from the wide-angle end. 
         [0233]    The amount of aberrations generated in the lens is larger for light rays at a high position from the optical axis. Thus, the lens is preferably formed to have a shape advantageous for the marginal rays and the off-axis rays in view of aberration correction. 
         [0234]    The axial rays at the telephoto end are substantially parallel to the optical axis. Thus, in view of spherical aberration correction at the telephoto end, curvatures of lens surfaces of the first lens unit Li are preferably weak. 
         [0235]    On the other hand, the off-axis rays at the middle zoom position enter the first lens unti L 1  at a large incident angle with respect to the optical axis. Thus, forming each lens element of the first lens unti L 1  into a meniscus shape can reduce the incident angle of the off-axis rays to the first lens unti L 1 . This lens configuration is advantages for correcting aberrations for the off-axis rays, especially astigmatism. 
         [0236]    Thus, the meniscus shape of the lens elements of the first lens unti L 1  whose curvatures are as weak as possible is advantageous for correcting aberrations in the entire zoom range. However, the meniscus shape reduces the refractive power of the first lens unti L 1 , which prevents miniaturization of the entire lens system. 
         [0237]    On the other hand, use of materials having a high refractive index and low dispersion which satisfy the conditional expressions (1) and (2) for the negative and positive lens elements of the first lens unti L 1  can form a meniscus shape having curvatures weaker as compared with a case where the normal glass materials are used, while maintaining a positive refractive power of the first lens unti L 1 . 
         [0238]    Thus, a high zoom ratio of the zoom lens and miniaturization of the entire lens system which cannot be achieved by using the normal glass materials are easily achieved, and therefore realizing a compact zoom lens having a zoom ratio higher than 37. 
         [0239]    Next, the zoom lens of Embodiment 7 shown in  FIG. 25  will be described. 
         [0240]    The zoom lens of Embodiment 7 includes a first lens unti L 1  having a positive refractive power, a second lens unit L 2  having a negative refractive power, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative refractive power, and a fifth lens unit L 5  having a positive refractive power. 
         [0241]    During zooming from the wide-angle end to the telephoto end, the second lens unit L 2  is moved toward the image to mainly perform variation of magnification, and the fourth lens unit L 4  is moved along a movement track convex toward the image to mainly correct variation of an image plane accompanying the variation of magnification. 
         [0242]    The first lens unti L 1  includes a negative lens element G 11  having a meniscus shape and a convex object side surface, a positive lens element G 12  having a meniscus shape similar to a planoconvex shape and a convex object side surface, and a positive lens element G 13  having a meniscus shape and a convex object side surface. 
         [0243]    The three-lens configuration of the first lens unti L 1  enables good correction of spherical aberration and good correction of longitudinal chromatic aberration and chromatic aberration of magnification of each color while having a high zoom ratio. The negative and positive lens elements G 11  and G 12  are separated from each other with an air space therebetween, thereby increasing a freedom degree of aberration correction. 
         [0244]    The positive lens element G 12  corresponds to the positive lens element G 1   pa.    
         [0245]    As the material for the positive lens unit G 12 , YAG whose refractive index and Abbe number satisfy the conditional expressions (1) and (2) is used. 
         [0246]    Thus, at the telephoto end, chromatic and spherical aberrations are corrected well, realizing a compact zoom lens having a zoom ratio higher than 20. 
         [0247]    The configuration of the second lens unit L 2  is similar to that of Embodiment 1. 
         [0248]    The third lens unit L 3  includes, in order from the object side to the image side, a positive lens element G 31  having a biconvex shape, and a cemented lens element formed by cementing a positive lens element G 32  having a biconvex shape with a negative lens element G 33  having a meniscus shape and a convex image side surface. The cemented lens element has a positive combined refractive power. 
         [0249]    The fourth lens unit L 4  includes a cemented lens element formed by cementing a positive lens element G 41  having a meniscus shape and a convex image side surface with a biconcave lens element G 42 . The fourth lens unit L 4  corrects variation of chromatic aberration accompanying zooming and focusing well. 
         [0250]    The fifth lens unit L 5  includes a cemented lens element formed by cementing a negative lens element G 51  having a meniscus shape and a convex object side surface with a biconvex lens element G 52 . The positive lens element G 52  has an aspheric image side surface, and thereby field curvature and astigmatism are corrected well. 
         [0251]    In the zoom lens of Embodiment 7, variation of distortion accompanying zooming is large. However, in a case where the zoom lens is used for an electronic image-pickup apparatus having a solid-state image-pickup element, the distortion may be electrically corrected when digital processing of a captured image is performed. 
         [0252]    Next, numerical examples 1 to 7 corresponding to Embodiments 1 to 7 of the present invention will be described. 
         [0253]    In each numerical example, a surface number i denotes an order of optical surfaces from the object side. Reference character ri denotes a curvature radius of an i-th optical surface. Reference character di denotes a distance between the i-th surface and an i+1-th surface. Reference characters ndi and νdi respectively denote a refractive index and an Abbe number of a material of an i-th optical member for the d-line. 
         [0254]    A back focus (BF) is an air-equivalent value of a distance from a most-image side surface of the zoom lens to a paraxial image plane. A total lens length is represented by a value obtained by adding the back focus (BF) to the distance from a most-object side surface to the most-image side surface. A length is expressed by mm. 
         [0255]    An aspheric shape is represented by the following expression, where K denotes an eccentricity, A 4  to A 13  denote aspheric coefficients, and x denotes a displacement in the optical axis direction at a height position H from the optical axis with reference to an apex of the surface. R denotes a curvature radius. 
         [0000]    
       
         
           
             X 
             = 
             
               
                 
                   
                     ( 
                     
                       1 
                       / 
                       R 
                     
                     ) 
                   
                    
                   
                     H 
                     2 
                   
                 
                 
                   1 
                   + 
                   
                     
                       1 
                       - 
                       
                         
                           ( 
                           
                             1 
                             + 
                             K 
                           
                           ) 
                         
                          
                         
                           
                             ( 
                             
                               H 
                               / 
                               R 
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 4 
                  
                 
                     
                 
                  
                 
                   H 
                   4 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 6 
                  
                 
                     
                 
                  
                 
                   H 
                   6 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 8 
                  
                 
                     
                 
                  
                 
                   H 
                   8 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 10 
                  
                 
                     
                 
                  
                 
                   H 
                   10 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 12 
                  
                 
                     
                 
                  
                 
                   H 
                   12 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 5 
                  
                 
                     
                 
                  
                 
                   H 
                   5 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 7 
                  
                 
                     
                 
                  
                 
                   H 
                   7 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 9 
                  
                 
                     
                 
                  
                 
                   H 
                   9 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 11 
                  
                 
                     
                 
                  
                 
                   H 
                   11 
                 
               
               + 
               
                 A 
                  
                 
                     
                 
                  
                 13 
                  
                 
                     
                 
                  
                 
                   H 
                   13 
                 
               
             
           
         
       
     
         [0256]    In aspheric surface data, “E-Z” means “x10-z”. Table 1 shows the values of the above-described conditional expressions in each numerical example. 
         [0257]    f denotes a focal length, Fno denotes an F-number, and ω denotes a half-field angle. 
       NUMERICAL EXAMPLE 1 
       [0258]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 44.94323 
                 1.10000 
                 1.922860 
                 20.9 
               
               
                  2 
                 24.87922 
                 3.40000 
                 1.830000 
                 59.0 
               
               
                  3 
                 −311.66846 
                 0.17000 
               
               
                  4 
                 16.91453 
                 2.10000 
                 1.651597 
                 58.6 
               
               
                  5 
                 29.24701 
                 variable 
               
               
                  6 
                 63.67081 
                 0.70000 
                 1.882997 
                 40.8 
               
               
                  7 
                 5.89294 
                 2.25000 
               
               
                  8 
                 −21.44479 
                 0.60000 
                 1.603112 
                 60.6 
               
               
                  9 
                 11.64233 
                 0.75000 
               
               
                 10 
                 10.52093 
                 1.30000 
                 1.922860 
                 18.9 
               
               
                 11 
                 28.99573 
                 variable 
               
               
                  12* 
                 8.44269 
                 2.20000 
                 1.693500 
                 53.2 
               
               
                 13 
                 45.79602 
                 1.30000 
               
               
                 14 (aperture stop) 
                 ∞ 
                 2.20000 
               
               
                 15 
                 97.99307 
                 0.60000 
                 1.761821 
                 26.5 
               
               
                 16 
                 8.37410 
                 0.30000 
               
               
                  17* 
                 12.47224 
                 1.75000 
                 1.583126 
                 59.4 
               
               
                 18 
                 −27.34674 
                 variable 
               
               
                 19 
                 12.29636 
                 2.70000 
                 1.772499 
                 49.6 
               
               
                 20 
                 −12.20927 
                 0.60000 
                 1.846660 
                 23.9 
               
               
                 21 
                 −60.76956 
                 variable 
               
               
                 22 
                 ∞ 
                 2.00000 
                 1.516330 
                 64.1 
               
               
                 23 
                 ∞ 
                 1.71844 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 12 
               
               
                   
                 K = 2.74483E−01, A4 = −1.79594E−04, A6 = −2.82547E−06 
               
               
                   
                 surface 17 
               
               
                   
                 K = −2.26672, A4 = 1.00000E−05 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 9.6600 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 5.0000 
                 20.3823 
                 48.2999 
               
               
                 F-number 
                 1.85 
                 2.70 
                 3.01 
               
               
                 field angle 
                 27.83° 
                 7.38° 
                 3.13° 
               
               
                 image height 
                 2.64 
                 2.64 
                 2.64 
               
               
                 total lens length 
                 58.8035 
                 58.8035 
                 58.8035 
               
               
                 BF 
                 8.2944 
                 10.2099 
                 5.3366 
               
               
                 d5 
                 0.70000 
                 12.12237 
                 16.13564 
               
               
                 d11 
                 16.47378 
                 5.05141 
                 1.03814 
               
               
                 d18 
                 4.31536 
                 2.39985 
                 7.27320 
               
               
                 d21 
                 5.25699 
                 7.17251 
                 2.29916 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 27.41611 
                 0 
                 0 
               
               
                 2 
                 6 
                 −6.31700 
                 −0.3798 
                 −5.2872 
               
               
                 3 
                 12 
                 17.27190 
                 −1.5598 
                 −0.6484 
               
               
                 4 
                 19 
                 14.35338 
                 0.3078 
                 0.5139 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 2 
       [0259]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 49.68739 
                 1.55000 
                 1.846660 
                 23.9 
               
               
                  2 
                 25.12842 
                 6.50000 
                 1.696797 
                 55.5 
               
               
                  3 
                 −1729.79837 
                 0.15000 
               
               
                  4 
                 22.95080 
                 3.00000 
                 1.830000 
                 55.5 
               
               
                  5 
                 46.68457 
                 variable 
               
               
                  6 
                 30.14527 
                 0.70000 
                 2.003300 
                 28.3 
               
               
                  7 
                 4.83006 
                 2.65000 
               
               
                  8 
                 −18.55234 
                 0.55000 
                 1.882997 
                 40.8 
               
               
                  9 
                 31.55988 
                 0.47000 
               
               
                 10 
                 9.84009 
                 2.40000 
                 1.922860 
                 18.9 
               
               
                 11 
                 −27.02062 
                 0.19158 
               
               
                 12 
                 −16.28005 
                 0.50000 
                 1.772499 
                 49.6 
               
               
                 13 
                 18.04116 
                 variable 
               
               
                 14 (aperture stop) 
                 ∞ 
                 0.60000 
               
               
                  15* 
                 11.32193 
                 5.50000 
                 1.693500 
                 53.2 
               
               
                  16* 
                 −18.18735 
                 0.15000 
               
               
                 17 
                 71.04026 
                 0.80000 
                 1.846660 
                 23.9 
               
               
                 18 
                 11.99239 
                 variable 
               
               
                 19 
                 14.22355 
                 3.00000 
                 1.517417 
                 52.4 
               
               
                 20 
                 −7.53774 
                 0.50000 
                 1.846660 
                 23.9 
               
               
                 21 
                 −12.54537 
                 variable 
               
               
                 22 
                 ∞ 
                 2.50000 
                 1.516330 
                 64.1 
               
               
                 23 
                 ∞ 
                 2.59916 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 15 
               
               
                   
                 K = −7.89114E−01, A5 = −1.23901E−06, A7 = −7.85814E−08, 
               
               
                   
                 A9 = 4.32890E−09, 
               
               
                   
                 A11 = −4.74759E−11, A13 = −9.62495E−15 
               
               
                   
                 surface 16 
               
               
                   
                 K = −1.11433E+01, A5 = −4.76449E−06, A7 = 2.83204E−07, 
               
               
                   
                 A9 = −3.15298E−09, 
               
               
                   
                 A11 = −1.25945E−12 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 33.9934 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 3.5301 
                 13.5231 
                 120.0000 
               
               
                 F-number 
                 1.44 
                 2.14 
                 4.47 
               
               
                 field angle 
                 32.51° 
                 9.45° 
                 1.07° 
               
               
                 image height 
                 2.25 
                 2.25 
                 2.25 
               
               
                 total lens length 
                 78.7449 
                 78.7449 
                 78.7449 
               
               
                 BF 
                 10.1989 
                 16.0116 
                 6.9572 
               
               
                 d5 
                 0.88000 
                 14.23147 
                 22.76765 
               
               
                 d13 
                 24.80688 
                 11.45541 
                 2.91923 
               
               
                 d18 
                 12.74753 
                 6.93479 
                 15.98924 
               
               
                 d21 
                 5.95102 
                 11.76375 
                 2.70930 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 33.14114 
                 0 
                 0 
               
               
                 2 
                 6 
                 −4.29030 
                 −0.1912 
                 −7.7263 
               
               
                 3 
                 15 
                 20.53690 
                 −1.7653 
                 −0.9303 
               
               
                 4 
                 19 
                 17.23578 
                 0.3156 
                 0.5037 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 3 
       [0260]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 29.03236 
                 1.95000 
                 1.830000 
                 59.0 
               
               
                  2 
                 361.46208 
                 variable 
               
               
                  3 
                 43.30611 
                 0.75000 
                 1.882997 
                 40.8 
               
               
                  4 
                 7.43068 
                 3.20000 
               
               
                  5 
                 −44.95277 
                 0.70000 
                 1.834807 
                 42.7 
               
               
                  6 
                 23.04121 
                 0.65000 
               
               
                  7 
                 14.66845 
                 2.00000 
                 1.846660 
                 23.9 
               
               
                  8 
                 306.51010 
                 variable 
               
               
                  9 (aperture stop) 
                 ∞ 
                 0.80000 
               
               
                  10* 
                 7.77952 
                 2.00000 
                 1.693500 
                 53.2 
               
               
                 11 
                 −73.84500 
                 0.20000 
               
               
                 12 
                 10.01787 
                 2.44000 
                 1.696797 
                 55.5 
               
               
                 13 
                 26.22635 
                 0.60000 
                 1.846660 
                 23.9 
               
               
                 14 
                 4.95903 
                 1.00000 
               
               
                 15 (flare-cutting stop) 
                 ∞ 
                 variable 
               
               
                  16* 
                 14.29660 
                 2.40000 
                 1.740130 
                 49.3 
               
               
                 17 
                 2942.84542 
                 variable 
               
               
                 18 
                 ∞ 
                 1.34000 
                 1.516330 
                 64.1 
               
               
                 19 
                 ∞ 
                 1.05653 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 10 
               
               
                   
                 K = −1.77968, A4 = 2.34400E−04, A6 = −8.25752E−07, 
               
               
                   
                 A8 = −3.09637E−08 
               
               
                   
                 surface 16 
               
               
                   
                 K = −2.06255, A4 = 6.52119E−05, A6 = −7.88598E−08, 
               
               
                   
                 A8 = 1.46548E−09 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 3.9829 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 7.5277 
                 13.4557 
                 28.9817 
               
               
                 F-number 
                 2.88 
                 3.42 
                 4.24 
               
               
                 field angle 
                 30.94° 
                 18.54° 
                 8.85° 
               
               
                 image height 
                 4.512 
                 4.512 
                 4.512 
               
               
                 total lens length 
                 51.6564 
                 51.1266 
                 62.1662 
               
               
                 BF 
                 8.2402 
                 10.3825 
                 11.3115 
               
               
                 d2 
                 0.40000 
                 4.73517 
                 12.32247 
               
               
                 d8 
                 18.26571 
                 8.64734 
                 1.89877 
               
               
                 d15 
                 4.66050 
                 7.27162 
                 16.54343 
               
               
                 d17 
                 5.50000 
                 7.64222 
                 8.57123 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 37.93266 
                 0 
                 0 
               
               
                 2 
                 3 
                 −11.04148 
                 −0.4351 
                 −0.8207 
               
               
                 3 
                 10 
                 16.50600 
                 −0.9050 
                 −2.6932 
               
               
                 4 
                 16 
                 19.40387 
                 0.5039 
                 0.3456 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 4 
       [0261]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 35.34824 
                 1.15000 
                 2.095000 
                 29.4 
               
               
                  2 
                 18.89327 
                 4.60000 
                 1.592400 
                 68.3 
               
               
                  3 
                 −462.33550 
                 0.17000 
               
               
                  4 
                 18.19543 
                 3.25000 
                 1.696797 
                 55.5 
               
               
                  5 
                 100.74837 
                 variable 
               
               
                  6 
                 57.14802 
                 0.70000 
                 1.882997 
                 40.8 
               
               
                  7 
                 5.44873 
                 2.30000 
               
               
                  8 
                 −21.33697 
                 0.60000 
                 1.589130 
                 61.1 
               
               
                  9 
                 12.29605 
                 0.68000 
               
               
                 10 
                 9.96332 
                 1.30000 
                 1.922860 
                 18.9 
               
               
                 11 
                 25.22782 
                 variable 
               
               
                  12* 
                 8.21640 
                 2.20000 
                 1.693500 
                 53.2 
               
               
                 13 
                 39.96669 
                 1.30000 
               
               
                 14 (aperture stop) 
                 ∞ 
                 2.20000 
               
               
                 15 
                 17.98871 
                 0.60000 
                 1.808095 
                 22.8 
               
               
                 16 
                 7.32207 
                 0.30000 
               
               
                  17* 
                 16.39284 
                 1.70000 
                 1.583126 
                 59.4 
               
               
                 18 
                 −125.78137 
                 variable 
               
               
                 19 
                 10.73560 
                 2.75000 
                 1.772499 
                 49.6 
               
               
                 20 
                 −11.53581 
                 0.60000 
                 1.846660 
                 23.9 
               
               
                 21 
                 −61.29131 
                 variable 
               
               
                 22 
                 ∞ 
                 2.00000 
                 1.516330 
                 64.1 
               
               
                 23 
                 ∞ 
                 0.50000 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 12 
               
               
                   
                 K = −2.39110E−01, A4 = −6.38329E−05, A6 = −2.20313E−06, 
               
               
                   
                 A8 = 3.96290E−08 
               
               
                   
                 surface 17 
               
               
                   
                 K = 1.08967, A4 = −1.77316E−04 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 12.3703 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 4.8502 
                 21.6739 
                 59.9984 
               
               
                 F-number 
                 1.85 
                 2.70 
                 3.01 
               
               
                 field angle 
                 28.56° 
                 6.94° 
                 2.52° 
               
               
                 image height 
                 2.64 
                 2.64 
                 2.64 
               
               
                 total lens length 
                 56.5775 
                 56.5775 
                 56.5775 
               
               
                 BF 
                 8.4535 
                 10.4579 
                 3.6112 
               
               
                 d5 
                 0.70000 
                 12.44849 
                 16.57634 
               
               
                 d11 
                 16.58036 
                 4.83187 
                 0.70402 
               
               
                 d18 
                 4.44365 
                 2.43920 
                 9.28589 
               
               
                 d21 
                 6.63450 
                 8.63895 
                 1.79226 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 27.01512 
                 0 
                 0 
               
               
                 2 
                 6 
                 −6.09464 
                 −0.3670 
                 −8.3333 
               
               
                 3 
                 12 
                 18.43591 
                 −2.3795 
                 −0.4561 
               
               
                 4 
                 19 
                 12.78447 
                 0.2056 
                 0.5844 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 5 
       [0262]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 29.35857 
                 1.15000 
                 2.095000 
                 29.4 
               
               
                  2 
                 20.80064 
                 4.10000 
                 1.83000 
                 59.0 
               
               
                  3 
                 158.16504 
                 variable 
               
               
                  4 
                 32.93325 
                 0.90000 
                 1.882997 
                 40.8 
               
               
                  5 
                 8.00027 
                 4.75000 
               
               
                  6 
                 −24.37164 
                 0.75000 
                 1.658441 
                 50.9 
               
               
                  7 
                 38.21908 
                 0.70000 
               
               
                  8 
                 18.43647 
                 1.60000 
                 1.922860 
                 18.9 
               
               
                  9 
                 65.59441 
                 variable 
               
               
                 10 (aperture stop) 
                 ∞ 
                 0.80000 
               
               
                  11* 
                 11.14242 
                 2.90000 
                 1.583126 
                 59.4 
               
               
                  12* 
                 −22.17583 
                 0.20000 
               
               
                 13 
                 6.15396 
                 2.44000 
                 1.487490 
                 70.2 
               
               
                 14 
                 14.25292 
                 0.85000 
                 1.805181 
                 25.4 
               
               
                 15 
                 4.86983 
                 1.00000 
               
               
                 16 (flare-cutting stop) 
                 ∞ 
                 variable 
               
               
                 17 
                 12.26968 
                 2.50000 
                 1.487490 
                 70.2 
               
               
                 18 
                 268.50377 
                 variable 
               
               
                 19 
                 ∞ 
                 1.28000 
                 1.516330 
                 64.1 
               
               
                 20 
                 ∞ 
                 0.49976 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 11 
               
               
                   
                 K = −8.44270E−01, A4 = −7.50417E−05, A6 = −3.15793E−07, 
               
               
                   
                 A8 = −5.26465E−08, 
               
               
                   
                 A10 = −2.90595E−09 
               
               
                   
                 surface 12 
               
               
                   
                 K = −1.37996, A4 = −4.94528E−07, A6 = 1.84265E−07, 
               
               
                   
                 A8 = −1.31698E−07, 
               
               
                   
                 A10 = −6.15376E−10 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 5.7319 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 7.5941 
                 19.8449 
                 43.5285 
               
               
                 F-number 
                 2.88 
                 3.61 
                 4.87 
               
               
                 field angle 
                 31.36° 
                 13.13° 
                 6.07° 
               
               
                 image height 
                 4.629 
                 4.629 
                 4.629 
               
               
                 total lens length 
                 60.4644 
                 62.4548 
                 74.5041 
               
               
                 BF 
                 5.0003 
                 9.2602 
                 6.2429 
               
               
                 d3 
                 0.30000 
                 11.20167 
                 19.32764 
               
               
                 d9 
                 22.31348 
                 6.93307 
                 2.32569 
               
               
                 d16 
                 8.25059 
                 10.45985 
                 22.00786 
               
               
                 d18 
                 3.65645 
                 7.91633 
                 4.89900 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 50.07550 
                 0 
                 0 
               
               
                 2 
                 4 
                 −11.15245 
                 −0.3273 
                 −0.7411 
               
               
                 3 
                 11 
                 15.21537 
                 −0.6236 
                 −1.6858 
               
               
                 4 
                 17 
                 26.29025 
                 0.7430 
                 0.6958 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 6 
       [0263]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 46.17511 
                 1.45000 
                 2.180000 
                 30.0 
               
               
                  2 
                 24.00867 
                 5.80000 
                 1.830000 
                 59.0 
               
               
                  3 
                 237.51436 
                 0.15000 
               
               
                  4 
                 24.05337 
                 3.50000 
                 1.830000 
                 55.5 
               
               
                  5 
                 68.08192 
                 variable 
               
               
                  6 
                 24.47196 
                 0.70000 
                 2.003300 
                 28.3 
               
               
                  7 
                 4.62238 
                 2.65000 
               
               
                  8 
                 −16.14275 
                 0.55000 
                 1.882997 
                 40.8 
               
               
                  9 
                 36.29418 
                 0.45000 
               
               
                 10 
                 9.84248 
                 2.30000 
                 1.922860 
                 18.9 
               
               
                 11 
                 −31.05346 
                 0.19625 
               
               
                 12 
                 −17.37440 
                 0.50000 
                 1.772499 
                 49.6 
               
               
                 13 
                 18.85440 
                 variable 
               
               
                 14 (aperture stop) 
                 ∞ 
                 0.60000 
               
               
                  15* 
                 11.58017 
                 5.50000 
                 1.693500 
                 53.2 
               
               
                  16* 
                 −18.33363 
                 0.15000 
               
               
                 17 
                 67.16966 
                 0.80000 
                 1.846660 
                 23.9 
               
               
                 18 
                 12.28976 
                 variable 
               
               
                 19 
                 14.60839 
                 3.85000 
                 1.517417 
                 52.4 
               
               
                 20 
                 −7.46088 
                 0.50000 
                 1.846660 
                 23.9 
               
               
                 21 
                 −12.39644 
                 variable 
               
               
                 22 
                 ∞ 
                 2.50000 
                 1.516330 
                 64.1 
               
               
                 23 
                 ∞ 
                 2.59528 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                   
               
             
          
           
               
                   
                 surface 15 
               
               
                   
                 K = −8.75470E−01, A5 = −1.50137E−07, A7 = −9.41021E−08, 
               
               
                   
                 A9 = 4.38545E−09, A11 = −4.74233E−11, A13 = 4.76488E−14 
               
               
                   
                 surface 16 
               
               
                   
                 K = −1.06523E+01, A5 = −4.77242E−06, A7 = 2.58060E−07, 
               
               
                   
                 A9 = −2.61728E−09, A11 = −6.15950E−13 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 37.1395 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 3.5003 
                 13.6219 
                 129.9995 
               
               
                 F-number 
                 1.44 
                 2.18 
                 4.45 
               
               
                 field angle 
                 32.51° 
                 9.38° 
                 1.07° 
               
               
                 image height 
                 2.25 
                 2.25 
                 2.25 
               
               
                 total lens length 
                 79.1489 
                 79.1489 
                 79.1489 
               
               
                 BF 
                 10.2501 
                 16.7025 
                 6.9435 
               
               
                 d5 
                 0.65000 
                 14.36067 
                 23.12650 
               
               
                 d13 
                 24.65644 
                 10.94577 
                 2.17994 
               
               
                 d18 
                 13.94613 
                 7.49367 
                 17.25271 
               
               
                 d21 
                 6.00607 
                 12.45854 
                 2.69950 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 33.36071 
                 0 
                 0 
               
               
                 2 
                 6 
                 −4.19566 
                 −0.1823 
                 −7.8405 
               
               
                 3 
                 15 
                 20.50245 
                 −1.7872 
                 −0.9705 
               
               
                 4 
                 19 
                 17.39000 
                 0.3220 
                 0.5121 
               
               
                   
               
             
          
         
       
     
       NUMERICAL EXAMPLE 7 
       [0264]      
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 SURFACE DATA 
               
             
          
           
               
                 surface no. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 object 
                 ∞ 
                 ∞ 
               
               
                  1 
                 49.38630 
                 1.20000 
                 1.846660 
                 29.4 
               
               
                  2 
                 28.39763 
                 0.12827 
               
               
                  3 
                 29.34852 
                 3.50000 
                 1.830000 
                 59.0 
               
               
                  4 
                 734.29207 
                 0.15000 
               
               
                  5 
                 25.76807 
                 2.20000 
                 1.487490 
                 70.2 
               
               
                  6 
                 65.14833 
                 variable 
               
               
                  7 
                 30.53921 
                 0.60000 
                 1.882997 
                 40.8 
               
               
                  8 
                 6.67815 
                 2.15000 
               
               
                  9 
                 −9.34365 
                 0.60000 
                 1.804000 
                 46.6 
               
               
                 10 
                 16.16627 
                 0.85000 
               
               
                 11 
                 18.17120 
                 1.80000 
                 1.808095 
                 22.8 
               
               
                 12 
                 −33.66452 
                 variable 
               
               
                 13 (aperture stop) 
                 ∞ 
                 1.30000 
               
               
                 14 
                 59.09637 
                 2.40000 
                 1.719995 
                 50.2 
               
               
                 15 
                 −20.71318 
                 0.20000 
               
               
                 16 
                 25.37819 
                 4.40000 
                 1.696797 
                 55.5 
               
               
                 17 
                 −9.45301 
                 0.70000 
                 1.846660 
                 23.9 
               
               
                 18 
                 −33.54028 
                 variable 
               
               
                 19 
                 −12.36401 
                 1.80000 
                 1.846660 
                 23.9 
               
               
                 20 
                 −7.36880 
                 0.60000 
                 1.603112 
                 60.6 
               
               
                 21 
                 19.13063 
                 variable 
               
               
                 22 
                 15.19297 
                 0.60000 
                 1.846660 
                 23.9 
               
               
                 23 
                 7.54403 
                 6.80000 
                 1.583126 
                 59.4 
               
               
                  24* 
                 −9.23242 
                 5.00000 
               
               
                 25 
                 ∞ 
                 2.00000 
                 1.516330 
                 64.1 
               
               
                 26 
                 ∞ 
                 2.60076 
               
               
                 image plane 
                 ∞ 
               
               
                   
               
             
          
           
               
                 ASPHERIC SURFACE DATA 
               
               
                 surface 24 
               
               
                   
               
             
          
           
               
                   
                 K = −1.26921, A4 = 1.85516E−04, A6 = −7.25684E−07, 
               
               
                   
                 A8 = −7.90180E−08, A10 = 1.01940E−09 
               
               
                   
                   
               
             
          
           
               
                 ZOOM LENS DATA 
               
               
                   
               
             
          
           
               
                   
                 zoom ratio 
                 20.4487 
               
               
                   
                   
               
             
          
           
               
                   
                 wide-angle end 
                 middle 
                 telephoto end 
               
               
                   
               
               
                 focal length 
                 3.9122 
                 17.8500 
                 79.9994 
               
               
                 F-number 
                 1.83 
                 2.33 
                 3.69 
               
               
                 field angle 
                 32.06° 
                 7.82° 
                 1.75° 
               
               
                 image height 
                 2.45 
                 2.45 
                 2.45 
               
               
                 total lens length 
                 82.4471 
                 82.4471 
                 82.4471 
               
               
                 BF 
                 8.9197 
                 8.9197 
                 8.9197 
               
               
                 d6 
                 0.50000 
                 17.21963 
                 27.03909 
               
               
                 d12 
                 27.76047 
                 11.04084 
                 1.22138 
               
               
                 d18 
                 2.36314 
                 7.42124 
                 2.14799 
               
               
                 d21 
                 10.92557 
                 5.86747 
                 11.14072 
               
               
                   
               
             
          
           
               
                 LENS UNIT DATA 
               
             
          
           
               
                   
                   
                   
                 magnification 
                 magnification 
               
               
                 Lens 
                 most-object 
                 focal 
                 ratio 
                 ratio 
               
               
                 unit 
                 side surface 
                 length 
                 (wide-angle end) 
                 (telephoto end) 
               
               
                   
               
               
                 1 
                 1 
                 38.60000 
                 0 
                 0 
               
               
                 2 
                 7 
                 −6.18383 
                 −0.2220 
                 −4.7181 
               
               
                 3 
                 14 
                 12.52021 
                 −0.4143 
                 −0.3977 
               
               
                 4 
                 19 
                 −14.87151 
                 5.5809 
                 5.5954 
               
               
                 5 
                 22 
                 12.88148 
                 0.1974 
                 0.1974 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Conditional 
                 numerical 
                 numerical 
                 numerical 
                 numerical 
                 numerical 
                 numerical 
                 numerical 
               
               
                 expression 
                 example 1 
                 example 2 
                 example 3 
                 example 4 
                 example 5 
                 example 6 
                 example 7 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 (1) left side, (2) 
                 1.830 
                 1.830 
                 1.830 
                 2.095 
                 2.095/1.830 
                 2.180/1.830 
                 1.830 
               
               
                 (1) right side 
                 1.710 
                 1.710 
                 1.710 
                 2.006 
                 2.006/1.710 
                 2.000/1.710 
                 1.710 
               
               
                 (3) 
                 59.0 
                 59.0 
                 59.0 
                 — 
                 59.0 
                 59.0 
                 59.0 
               
               
                 (4) 
                 0.852 
                 2.934 
                 1.175 
                 — 
                 1.303 
                 1.225/2.093 
                 1.083 
               
               
                 (5) 
                 1.017 
                 1.552 
                 1.000 
                 — 
                 0.569 
                 0.953/1.297 
                 0.952 
               
               
                 (6) 
                 — 
                 — 
                 — 
                 29.4 
                 29.4 
                 30.0 
                 — 
               
               
                 (7) 
                 — 
                 — 
                 — 
                 −3.296 
                 −5.861 
                 −3.166 
                 — 
               
               
                 (8) 
                 — 
                 — 
                 — 
                 1.424 
                 1.400 
                 1.317 
                 — 
               
               
                 (9) 
                 4.340 
                 7.725 
                 3.436 
                 4.432 
                 4.490 
                 7.951 
                 6.242 
               
               
                   
               
             
          
         
       
     
         [0265]    Each embodiment achieves a high-performance compact zoom lens having a high zoom ratio and being capable of correcting spherical aberration, comatic aberration, longitudinal chromatic aberration, chromatic aberration of magnification and field curvature well, which is applicable to a high-pixel digital camera and a high-pixel video camera. 
         [0266]    Further, each embodiment provides a compact zoom lens which has excellent optical performance within the entire zoom range from the wide-angle end to the telephoto end and a high zoom ratio. 
         [0267]    Next, referring to  FIG. 29 , an embodiment of a digital still camera which uses the zoom lens of each embodiment as an image-pickup optical system will be described. 
         [0268]    In  FIG. 29 , reference numeral  20  denotes a camera body, and reference numeral  21  denotes an image-pickup optical system which is constituted by the zoom lens of any one of Embodiments 1 to 7. 
         [0269]    Reference numeral  22  denotes a solid-state image-pickup element (photoelectric conversion element) such as a CCD sensor or a CMOS sensor which receives an object image formed by the image-pickup optical system  21 . Reference numeral  23  denotes a memory which records image information corresponding to the object image photoelectrically converted by the solid-state image-pickup element  22 . 
         [0270]    Reference numeral  24  denotes a viewfinder which is formed by a liquid crystal display panel. A user can observe the object image formed on the solid-state image-pickup element  22 . 
         [0271]    Next, referring to  FIG. 30 , an embodiment of a video camera (optical apparatus) which uses the zoom lens of each embodiment as an image-pickup optical system will be described. 
         [0272]    In  FIG. 30 , reference numeral  10  denotes a video camera body, and reference numeral  11  denotes an image-pickup optical system which is constituted by the zoom lens of any one of Embodiments 1 to 7. 
         [0273]    Reference numeral  12  denotes a solid-state image-pickup element (photoelectric conversion element) such as a CCD sensor or a CMOS sensor which receives an object image formed by the image-pickup optical system  11 . Reference numeral  13  denotes a recording medium for recording image information corresponding to the object image photoelectrically converted by the solid-state image-pickup element  12 . 
         [0274]    Reference numeral  14  denotes a viewfinder for observing the object image displayed in a display device (not shown). 
         [0275]    The display device is constituted by a liquid crystal panel or the like, and displays the object image formed on the image-pickup element  12 . 
         [0276]    Thus, applying the zoom lens of each embodiment to the image-pickup apparatus such as a digital still camera and a video camera can realize a compact image-pickup apparatus having high optical performance. 
         [0277]    Furthermore, the present invention is not limited to these embodiments and various variations and modifications may be made without departing from the scope of the present invention. 
         [0278]    This application claims the benefit of Japanese Patent Application No. 2007-280207, filed on Oct. 29, 2007, which is hereby incorporated by reference herein in its entirety.