Abstract:
A zoom lens of the rear-focus type includes, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power. The variation of magnification from a wide-angle end to a telephoto end is effected by moving the second lens unit toward the image side. Shifting of an image plane caused by the variation of magnification is compensated for by moving the fourth lens unit. Focusing is effected by moving the fourth lens unit. The second lens unit consists of, in order from the object side to the image side, a negative lens, a negative lens, a positive lens and a negative lens, the third lens unit comprises a plurality of positive lenses and a negative lens, and the fourth lens unit consists of a negative lens and a positive lens, and wherein the following condition is satisfied: 
     
       
           0.25 &lt;(Fm−Fw)/(Ft−Fw)&lt; 0.45   
       
     
     where Fm is a focal length of the entire zoom lens in a position where the fourth lens unit has moved a maximum distance during the variation of magnification with focusing on an infinitely distant object, Fw is a focal length of the entire zoom lens at the wide-angle end, and Ft is a focal length of the entire zoom lens at the telephoto end.

Description:
This application is a division of application Ser. No. 09/389,454 filed Sep. 3, 1999, now U.S. Pat. No. 6,118,593. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to zoom lenses and, more particularly, to a zoom lens of the rear focus type having a long back-focal distance for use in film cameras or image pickup apparatus, such as video cameras or broadcasting cameras, while still permitting the relative aperture to be made as large as 1.6 in F-number in the wide-angle end and the range to be extended to as high as 30. 
     2. Description of Related Art 
     Recently, home video cameras and the like have reduced their sizes and weights. Along with this there is seen a remarkable advance even in the improvements of the compact form of the zoom lens for the image pickup apparatus. In particular, efforts are being devoted to shortening of the total length of the complete lens, to a reduction of the diameter of the front lens members and to simplification of the configuration. 
     As one means for achieving these ends, there is known the so-called rear-focus type of zoom lens in which a lens unit other than the front or first one is moved for focusing purposes. 
     In general, the zoom lenses of the rear focus type have features, as compared with the zoom lens of a type in which the first lens unit is moved to effect focusing, that the first lens unit becomes smaller in effective diameter, making it easier to improve the compact form of the entire lens system, and also that closeup photography, particularly, super-short focusing, becomes easier to do. Further, because the focusing lens unit is relatively small in size and light in weight, a much weaker torque suffices for driving the focusing lens unit. Accordingly, rapid focus adjustment can be performed. 
     Such a zoom lens of the rear focus type, as disclosed in, for example, Japanese Laid-Open Patent Applications No. Sho 62-215225 (corresponding to U.S. Pat. No. 4,859,042), No. Sho 62-206516, No. Sho 62-24213 (corresponding to U.S. Pat. No. 4,859,042), No. Sho 62-247316, and No. Hei 4-43311, comprises, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, totaling four lens units, wherein the second lens unit axially moves to vary the focal length, while simultaneously moving the fourth lens unit to compensate for the image shift resulting from the variation of magnification and to effect focusing. 
     Also, in Japanese Laid-Open Patent Applications No. Hei 4-43311, No. Hei 4-153615, No. Hei 5-19165, No. Hei 5-27167 and No. Hei 5-60973, the fourth lens unit is constructed with one or two positive lenses, so that a zoom lens of short total length is proposed. In Japanese Laid-Open Patent Application No. Hei 5-60974, there is proposed a zoom lens in which the fourth lens unit is constructed with a positive lens and a negative lens, totaling two lenses. 
     In Japanese Laid-Open Patent Applications No. Sho 55-62419, No. Sho 62-24213, No. Sho 62-215225, No. Sho 56-114920, No. Hei 3-200113, No. Hei 4-242707, No. Hei 4-343313 and No. Hei 5-297275, there are disclosed, in the embodiments thereof, zoom lenses whose third and fourth lens units each are comprised of a positive lens and a negative lens, totaling two lenses. 
     Further, in Japanese Laid-Open Patent Application No. Hei 3-158813, similarly, there is disclosed a zoom lens comprising, in order from an object side to an image side, a positive first lens unit, a negative second lens unit, a positive third lens unit and a positive fourth lens unit, in which the second and third lens units are axially moved, while varying the air separation therebetween, to vary the focal length continuously, and a stop is positioned in the space either between the second and third lens units or between the third and fourth lens units and is made movable in unison with the third lens unit. 
     According to the specification of the above Japanese Laid-Open Patent Application No. Hei 3-158813, it is suggested that, during zooming from the wide-angle end to the telephoto end, the air separation between the second and third lens units decreases. Also, in the embodiments thereof, the third lens unit having the aperture stop takes, in the wide-angle end, a position closest to the image side. Thus, at the wide-angle end or a slightly zoomed position therefrom, where the front lens members admit of a light beam of largest diameter, that neighborhood of the third lens unit which contains the stop is located closest to the image side. The entrance pupil is, therefore, brought to a deep position. 
     As a result, the zoom lens disclosed in the above Japanese Laid-Open Patent Application No. Hei 3-158813 is disadvantageous at reducing the diameter of the front lens members. Also, the distortion for the wide-angle end becomes large. Accordingly, there is a drawback that it is difficult to extend the range to an ultra high value in good performance while removing the large distortion. 
     In view of the above examples, there have been proposed a variety of zoom lenses. For example, in Japanese Laid-Open Patent Application No. 3-215810, a zoom lens of the rear-focus type is proposed, comprising, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a stop, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, totaling four lens units, in which, during zooming from the wide-angle end to the telephoto end, the second lens unit moves toward the image side, while simultaneously moving the stop and the third and fourth lens units in differential relation with their respective loci each being convex toward the object side, and the fourth lens unit is made movable for focusing. 
     Further, in Japanese Laid-Open Patent Application No. Hei 8-82743, a zoom lens of the rear-focus type having a high range as much as 20 is proposed, comprising, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power having a stop and a fourth lens unit of positive refractive power, totaling four lens units. During zooming from the wide-angle end to the telephoto end, the second lens unit moves toward the image side, while simultaneously moving the stop and the third lens unit in fixed relation with their locus being convex toward the object side and moving the fourth lens unit in a locus convex toward the object side. Focusing is performed by moving the fourth lens unit. 
     Further, in Japanese Laid-Open Patent Applications No. Hei 8-5913 (corresponding to U.S. Pat. No. 5,847,882) and No. Hei 8-190051 (corresponding to U.S. Pat. No. 5,847,882), five-unit zoom lenses of the rear focus type whose range is about 20 are proposed, comprising, in order from an object side to an image side, a first lens unit of positive refractive power stationary during zooming, a second lens unit of negative refractive power, a third lens unit of positive refractive power, a fourth lens unit of negative refractive power and a fifth lens unit of positive refractive power stationary during zooming. At least the second and fourth lens units move to effect zooming. The fourth lens unit moves to effect focusing. 
     Further, in Japanese Laid-Open Patent Applications No. Hei 8-201695 (corresponding to U.S. Pat. No. 5,712,733) and No. Hei 9-21954, four-unit zoom lenses of the rear-focus type are proposed, comprising, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, totaling four lens units. The second lens unit moves toward the image side to vary the focal length from the wide-angle end to the telephoto end. The shift of the image plane with zooming is compensated for by moving the fourth lens unit in a locus convex toward the object side. Focusing is performed by moving the fourth lens unit. The third lens unit has a positive lens and a negative lens of meniscus form convex toward the image side in this order from the object side. The fourth lens unit is comprised of a negative lens of meniscus form convex toward the object side and a positive lens in this order from the object side. 
     In general, when employing the rear-focus type, a zoom lens is made to have such advantages that the entirety of the lens system is improved in compact form, rapid focusing becomes possible and the minimum object distance is easy to shorten. 
     However, with the back-focal distance secured so long as to accommodate the optical low-pass filter, color filter and others, on the other hand, if it is intended to minimize the variation of aberrations with focusing or to maintain a high optical performance stable throughout the entire focusing range, the appropriate construction and arrangement of constituent lenses of the zoom lens become very difficult to find. 
     Particularly, for a zoom lens which has secured a large relative aperture and a high range at once, it becomes very difficult to obtain a high optical performance through the entire zooming range and throughout the entire focusing range. 
     BRIEF SUMMARY OF THE INVENTION 
     It is, therefore, an object of the present invention to provide a zoom lens of the rear-focus type which has the large relative aperture and a high range as much as 30 and which maintains good stability of optical performance at a high level throughout the entire zooming range from the wide-angle end to the telephoto end and throughout the entire focusing range from an infinitely distant object to a super close object. 
     To attain the above object, in accordance with an aspect of the invention, there is provided a zoom lens, comprising, in order from an object side to an image side, a first lens unit of positive refractive power, a second lens unit of negative refractive power, a third lens unit of positive refractive power and a fourth lens unit of positive refractive power, a variation of magnification from a wide-angle end to a telephoto end being effected by moving the second lens unit toward the image side, the shift of an image plane caused by the variation of magnification being compensated for by moving the fourth lens unit, and focusing being effected by moving the fourth lens unit, wherein the second lens unit consists of, in order from the object side to the image side, a negative lens, a negative lens, a positive lens and a negative lens, the third lens unit comprises a plurality of positive lenses and a negative lens, and the fourth lens unit consists of a negative lens and a positive lens, and wherein the following condition is satisfied: 
     
       
         0.25&lt;(Fm−Fw)/(Ft−Fw)&lt;0.45  (1) 
       
     
     where Fm is a focal length of the entire zoom lens in a position where the fourth lens unit has moved a maximum distance during the variation of magnification with focusing on an infinitely distant object, Fw is a focal length of the entire zoom lens at the wide-angle end, and Ft is a focal length of the entire zoom lens at the telephoto end. 
     The above and further objects and features of the invention will become apparent from the following detailed description of preferred embodiments thereof taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     FIG. 1 is a longitudinal section view of a zoom lens according to a numerical example 1. 
     FIGS. 2A to  2 C are graphic representations of the aberrations in the wide-angle end of the zoom lens according to the numerical example 1. 
     FIGS. 3A to  3 C are graphic representations of the aberrations in the telephoto end of the zoom lens according to the numerical example 1. 
     FIG. 4 is a longitudinal section view of a zoom lens according to a numerical example 2. 
     FIGS. 5A to  5 C are graphic representations of the aberrations in the wide-angle end of the zoom lens according to the numerical example 2. 
     FIGS. 6A to  6 C are graphic representations of the aberrations in the telephoto end of the zoom lens according to the numerical example 2. 
     FIG. 7 is a longitudinal section view of a zoom lens according to a numerical example 3. 
     FIGS. 8A to  8 C are graphic representations of the aberrations in the wide-angle end of the zoom lens according to the numerical example 3. 
     FIGS. 9A to  9 C are graphic representations of the aberrations in the telephoto end of the zoom lens according to the numerical example 3. 
     FIG. 10 is a longitudinal section view of a zoom lens according to a numerical example 4. 
     FIGS. 11A to  11 C are graphic representations of the aberrations in the wide-angle end of the zoom lens according to the numerical example 4. 
     FIGS. 12A to  12 C are graphic representations of the aberrations in the telephoto end of the zoom lens according to the numerical example 4. 
     FIG. 13 is a schematic diagram of the main parts of an image pickup apparatus using the zoom lens of any of the numerical examples 1 to 4 as the photographic optical system. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Hereinafter, preferred embodiments of the invention will be described in detail with reference to the drawings. 
     FIG. 1, FIG. 4, FIG.  7  and FIG. 10 in block diagrams show four numerical examples 1 to 4 of the rear-focus type zoom lens according to the invention. FIGS. 2A to  2 C and FIGS. 3A to  3 C graphically show the aberrations at the wide-angle end and the telephoto end, respectively, of the zoom lens of the numerical example  1 . FIGS. 5A to  5 C and FIGS. 6A to  6 C show the aberrations at the wide-angle end and the telephoto end, respectively, of the zoom lens of the numerical example  2 . FIGS. 8A to  8 C and FIGS. 9A to  9 C show the aberrations at the wide-angle end and the telephoto end, respectively, of the zoom lens of the numerical example  3 . FIGS. 11A to  11 C and FIGS. 12A to  12 C show the aberrations in the wide-angle end and the telephoto end, respectively, of the zoom lens of the numerical example  4 . 
     Referring to FIGS. 1,  4 ,  7  and  10 , the zoom lens comprises, in order from an object side to an image side, a first lens unit L 1  of positive refractive power, a second lens unit L 2  of negative refractive power, a third lens unit L 3  of positive refractive power and a fourth lens unit L 4  of positive refractive power. An aperture stop SP is disposed in front of the third lens unit L 3 . 
     A face plate, filters and others in a glass block G are, if necessary, provided in front of an image plane IP, in which an image pickup element, such as a CCD, is located. 
     In the present embodiments, during zooming from the wide-angle end to the telephoto end, the second lens unit axially moves toward the image side as indicated by the arrow. The shift of the image plane caused by the zooming is compensated for by moving a part or the whole of the fourth lens unit (in the present embodiments, the whole) in a locus convex toward the object side. 
     Also, for focusing purposes, a part or the whole of the fourth lens unit axially moves (in the present embodiments, the whole). That is, the rear-focus type lens is employed. With an object at infinity or at the minimum object distance, during zooming from the wide-angle end to the telephoto end, the fourth lens unit moves in the locus indicated by a solid line curve  4   a  or a dashed line curve  4   b , respectively, in FIGS. 1,  4 ,  7  and  10 . Incidentally, the first and third lens units remain stationary during zooming and during focusing. 
     In the present embodiments, the compensating provision for the image shift and the focusing provision are both made in a common lens unit, say, the fourth lens unit. 
     In particular, as shown by the curves  4   a  and  4   b  in FIGS. 1,  4 ,  7  and  10 , the locus of movement of the fourth lens unit is made convex toward the object side, thereby assuring efficient utilization of the space between the third and fourth lens units. A shortening of the total length of the complete zoom lens is thus advantageously achieved. 
     In the present embodiments, at the setting in, for example, the telephoto end, during focusing from an infinitely distant object to an object at the minimum distance, the fourth lens unit moves forward as indicated by a straight line  4   c  in FIGS. 1,  4 ,  7  and  10 . 
     In the present embodiments, the second lens unit L 2  is composed of, in order from the object side to the image side, a negative lens of meniscus form convex toward the object side, a negative lens of bi-concave form, a positive lens of bi-convex form and a negative lens having a concave surface facing the object side. This arrangement brings the front principal point of the second lens unit toward the first lens unit, thereby reducing the interval between the principal points of the first and second lens units. Improvements of the compact form of the entire lens system are thus assured. Another advantage is to minimize the range of variation of chromatic aberrations with zooming. 
     Further, the third lens unit L 3  is composed of two positive lenses of bi-convex form and a negative lens having a concave surface facing the object side. Also, the fourth lens unit L 4  is constructed with a cemented lens composed of a negative lens of meniscus form convex toward the object side and a positive lens of bi-convex form. 
     In addition, where Fm is a focal length of the entire zoom lens in a position where the fourth lens unit has moved a maximum distance during zooming with focusing on an infinitely distant object, Fw is a focal length of the entire zoom lens at the wide-angle end, and Ft is a focal length of the entire zoom lens at the telephoto end, and the zoom lens is made to satisfy the above-described condition (1). 
     According to the above arrangement, a zoom lens of the rear-focus type having a high range as much as 30 is obtained without causing the size of the entire lens system from unduly increasing, while still permitting good optical performance to be maintained stable throughout the entire zooming range from the wide-angle end to the telephoto end and throughout the entire focusing range. 
     The technical significance of the above-described condition (1) is next explained. The condition (1) is concerned with the zooming movement of the fourth lens unit and has an aim to improve the compact form of the entire lens system, while still maintaining an increase of the performance to be achieved. When the lower limit of the condition (1) is exceeded, as this implies that the focal length Fm is too short, the required total movement for the adequate zoom ratio of the second lens unit becomes large, causing the size of the entire lens system to increase greatly. 
     On the other hand, when the upper limit of the condition (1) is exceeded, i.e., when the focal length Fm is too long, the amount of movement of the fourth lens unit becomes too large in the neighborhood of the telephoto end, so that the movement of the fourth lens unit becomes difficult to control, giving rise to a problem of increasing the variation of aberrations with zooming. 
     In the present embodiments, the form and the construction and arrangement of the constituent lenses of the zoom lens are determined as described above. Thereby, despite as high a zoom ratio as 30, a high optical performance is obtained throughout the entire zooming range and throughout the entire focusing range. 
     Further, in the rear-focus type zoom lens according to the invention, there is room for further improvements of the optical performance. So, it is preferable to satisfy at least one of the following features or conditions. 
     (a) The third lens unit and/or the fourth lens unit each have at least one aspheric surface. 
     In the present embodiments, by providing the aspheric surface to the third and/or fourth lens unit through which the on-axial light beam passes at a high position at the wide-angle end, the variation with zooming of spherical aberration, coma flare of higher orders and comatic aberrations is corrected well regardless of reducing the number of lens elements. 
     (b) Where fi is a focal length of the i-th lens unit, and D 34 t is a separation between the third lens unit and the fourth lens unit at the telephoto end with focusing on an infinitely distant object, the following conditions are satisfied: 
     
       
         −8.5&lt;f 1 /f 2 &lt;−7.0  (2) 
       
     
     
       
         0.1&lt;D 34 t/Ft&lt;0.2  (3) 
       
     
     The condition (2) is concerned with the ratio of the focal lengths of the first and second lens units and has an aim to simultaneously fulfill the requirements of, despite the high range, achieving improvements of the compact form and of elongating the back-focal distance, while still maintaining good optical performance. When the lower limit of the condition (2) is exceeded, as this means that the focal length f 2  of the second lens unit is too long and the focal length f 1  of the first lens unit is too short, the total zooming movement of the second lens unit is increased so greatly that the total length of the complete lens and the diameter of the front lens members become difficult to minimize. 
     Such a violation also causes an increase of the movement of the fourth lens unit in the telephoto region. So, another problem even arises in that the aberrations vary to a larger extent with zooming. Conversely, when the upper limit of the condition (2) is exceeded, distortion and other aberrations become difficult to correct well. 
     The condition (3) is concerned with the axial separation between the third and fourth lens units in the telephoto end with an object at infinity. When the separation between the third and fourth lens units is wider than the upper limit, the height of incidence of the off-axial light beam on the fourth lens unit becomes higher, causing an increase in the difficulty of correcting aberrations. Moreover, the effective diameter of the fourth lens unit is caused to increase greatly, thus giving rise to another problem. 
     Conversely, when the lower limit of the condition (3) is exceeded, as this means that the separation between the third and fourth lens units is too narrow, a problem arises in that the required forward movement for close-up focusing of the fourth lens unit becomes difficult to secure. 
     (c) As described above, the conditions (1), (2) and (3) suffice for maintaining good stability of optical performance over the high range and for satisfactory improvements of the compact form. For more desired results, it is preferred that the numerical ranges of the conditions (1) to (3) are made even narrower as follows: 
     
       
         0.32&lt;(Fm-Fw)/(Ft-Fw)&lt;0.41 
       
     
     
       
         −8.0&lt;f 1 /f 2 &lt;−7.2 
       
     
     
       
         0.12&lt;D 34 t/Ft&lt;0.16 
       
     
     (d) In order to minimize the diameter of the front lens members advantageously, the stop is preferably positioned in the most front of the third lens unit. Such an arrangement puts the entrance pupil in a place nearest to (shallowest from) the first lens unit, thus facilitating reduction of the diameter of the first lens unit to a minimum. 
     (e) In order to minimize the bulk and size of the whole lens system, where fi is a focal length of the i-th lens unit, Fw is a focal length of the entire zoom lens at the wide-angle end, Ft is a focal length of the entire zoom lens at the telephoto end, and N 2 A is an average refractive index of materials of the negative lenses included in the second lens unit, it is preferred to satisfy at least one of the following conditions: 
     
       
         −0.45&lt;f 2 /(Fw×Ft) 0.5 &lt;−0.25  (4) 
       
     
     
       
         12.0&lt;f 1 /Fw&lt;16.0  (5) 
       
     
     
       
         4.0&lt;f 4 /Fw&lt;6.0  (6) 
       
     
     
       
         1.75&lt;N 2 A  (7) 
       
     
     The condition (4) is concerned with the focal length of the second lens unit. When the lower limit of the condition (4) is exceeded, as this means that the focal length of the second lens unit is too short, the Petzval sum becomes large in the under, so that the declination of the field and other aberrations become difficult to correct. Conversely, when the upper limit of the condition (4) is exceeded, the movement of the second lens unit is increased greatly, giving rise to a problem that the diameter of the front lens members becomes too much large. 
     The factor in the condition (5) represents the object point for the second lens unit, that is, the magnification. To assure minimization of the size of the entire lens system, it is preferred that the second lens unit takes unity of magnification in the middle of zooming. 
     If the second lens unit takes unity of magnification in the middle of zooming, the fourth lens unit, during zooming, depicts a locus of motion like an almost complete reciprocation, thus making it possible to obtain the high range with a highest space efficiency. Concretely speaking, when the upper limit of the condition (5) is exceeded, the object point for the second lens unit stands afar off, lowering the image magnification of the second lens unit. Therefore, it becomes difficult to improve the compact form advantageously. 
     Further, the separation between the first and second lens units is caused to increase. The size of the zoom lens becomes difficult to minimize. When the lower limit of the condition (5) is exceeded, as this means that the magnification of the second lens unit is too large, the increase of the range becomes difficult to achieve, so that the object of the invention cannot be accomplished. 
     The condition (6) is concerned with the focal length of the fourth lens unit. When the upper limit of the condition (6) is exceeded, the movement of the fourth lens unit is caused to increase, which in turn causes an increase in the range of variation of aberrations with zooming and with focusing. Conversely, when the lower limit of the condition (6) is exceeded, the fourth lens unit gets a higher degree of sensitivity and, therefore, becomes difficult to control. It becomes also difficult to correct aberrations, too, and it becomes difficult to obtain a sufficient back-focal distance. 
     The condition (7) is concerned with the choice of the materials for the negative lenses in the second lens unit for varying the focal length. To minimize the size, there is need to limit the total zooming movement of the second lens unit to a minimum. For this purpose, the refractive power of the second lens unit must be strengthened. If so, there is a possibility of increasing the negative Petzval sum so greatly as to damage the flatness of the field. 
     With such a background in mind, the condition (7) is set forth for strengthening the refractive power of the second lens unit, while still keeping good characteristics of the image surface. Therefore, the negative lenses in the second lens unit are made up from materials of appropriate refractive indices to prevent the Petzval sum from increasing. 
     When the condition (7) is violated, it becomes difficult to correct well the variation of field curvature with zooming. 
     (f) It will be appreciated from the foregoing that the rules of lens design described above can achieve further improvements of the compact form. However, to facilitate the simultaneous fulfillment of the requirements of, despite the high range, obtaining an improved compact form and of correcting all aberrations well, it is preferred that the factors in the conditions (4) to (7) lie within the following ranges: 
     
       
         −0.36&lt;f 2 /(Fw×Ft) 0.5 &lt;−0.30 
       
     
     
       
         13.2&lt;f 1 /Fw&lt;14.5 
       
     
     
       
         5.0&lt;f 4 /Fw&lt;5.5 
       
     
     
       
         1.77&lt;N 2 A 
       
     
     Next, four numerical examples 1 to 4 of the invention are shown. In the numerical data for the examples 1 to 4, Ri is the radius of curvature of the i-th surface, when counted from the object side, Di is the i-th optical element thickness or air separation and Ni and vi are respectively the refractive index and Abbe number of the material of the i-th optical element. 
     In the numerical examples 1 to 4, the last two surfaces define a glass block such as a face plate and filters. The values of the factors in the above-described conditions (1) to (7) for the numerical examples 1 to 4 are listed in Table-1. 
     The shape of an aspheric surface is expressed in the coordinates with an X axis in the axial direction and an H axis in the direction perpendicular to an optical axis, the direction in which light advances being taken as positive, by the following equation:        X   =           (     1   /   R     )          H   2         1   +       1   -       (     1   +   K     )            (     H   /   R     )     2               +     BH   4     +     CH   6     +     DH   8     +     EH   10                              
     where R is the radius of the osculating sphere, and K, B, C, D and E are the aspheric coefficients. Also, it is to be noted that the notation “e−0X” means “10 −X ”. 
     NUMERICAL EXAMPLE 1 
     
       
         
               
             
               
               
               
               
             
           
               
                   
               
               
                 f = 1˜31.95   Fno = 1.65˜3.96   2ω = 63.0°˜2.2°  
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 30.575 
                 D1 = 0.44 
                 N1 = 1.846660 
                 ν1 = 23.8 
               
               
                 R2 = 9.247 
                 D2 = 0.06 
               
               
                 R3 = 9.301 
                 D3 = 1.50 
                 N2 = 1.603112 
                 ν2 = 60.6 
               
               
                 R4 = −78.480 
                 D4 = 0.05 
               
               
                 R5 = 9.944 
                 D5 = 0.82 
                 N3 = 1.834000 
                 ν3 = 37.2 
               
               
                 R6 = 36.274 
                 D6 = Variable 
               
               
                 R7 = 4.670 
                 D7 = 0.20 
                 N4 = 1.772499 
                 ν4 = 49.6 
               
               
                 R8 = 1.519 
                 D8 = 1.02 
               
               
                 R9 = −5.229 
                 D9 = 0.17 
                 N5 = 1.772499 
                 ν5 = 49.6 
               
               
                 R10 = 4.735 
                 D10 = 0.05 
               
               
                 R11 = 3.086 
                 D11 = 0.65 
                 N6 = 1.846660 
                 ν6 = 23.8 
               
               
                 R12 = −26.842 
                 D12 = 0 08 
               
               
                 R13 = −7.296 
                 D13 = 0.17 
                 N7 = 1.882997 
                 ν7 = 40.8 
               
               
                 R14 = 348.989 
                 D14 = Variable 
               
               
                 R15 = Stop 
                 D15 = 0.35 
               
               
                 R16 = 9.665 
                 D16 = 0.80 
                 N8 = 1.583126 
                 ν8 = 59.4 
               
               
                 R17 = −6.913 
                 D17 = 0.05 
               
               
                 R18 = 8.764 
                 D18 = 0.62 
                 N9 = 1.603112 
                 ν9 = 60.6 
               
               
                 R19 = −9.686 
                 D19 = 0.16 
               
               
                 R20 = −4.597 
                 D20 = 0.20 
                 N10 = 1.834807 
                 ν10 = 42.7 
               
               
                 R21 = 78.140 
                 D21 = Variable 
               
               
                 R22 = 3.922 
                 D22 = 0.17 
                 N11 = 1.805181 
                 ν11 = 25.4 
               
               
                 R23 = 2.273 
                 D23 = 0.90 
                 N12 = 1.583126 
                 ν12 = 59.4 
               
               
                 R24 = −6.595 
                 D24 = 1.15 
               
               
                 R25 = ∞ 
                 D25 = 0.87 
                 N13 = 1.516330 
                 ν13 = 64.2 
               
               
                 R26 = ∞  
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Variable 
                 Focal Length 
               
             
          
           
               
                   
                 Separation 
                 1.00 
                 10.07 
                 31.95  
               
               
                   
                   
               
             
          
           
               
                   
                 D6 
                 0.27 
                 8.88 
                 10.77 
               
               
                   
                 D14 
                 10.82 
                 2.21 
                 0.32 
               
               
                   
                 D21 
                 4.60 
                 2.44 
                 4.80  
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients: 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R16: 
                 K =   2.43687e+00 
                 B =   1.06494e−03 
                 C =   1.61941e−04 
               
               
                   
                 D = −2.06750e−05 
                 E =   5.70981e−06 
               
               
                 R24: 
                 K = −6.52187e+00 
                 B = −2.46310e−04 
                 C = −1.12363e−04 
               
               
                   
                 D =   1.29821e−04 
                 E = −6.82885e−05  
               
               
                   
               
             
          
         
       
     
     NUMERICAL EXAMPLE 2 
     
       
         
               
             
               
               
               
               
             
           
               
                   
               
               
                 f = 1˜31.35   Fno = 1.65˜3.70   2ω = 63.0°˜2.2°  
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 22.935 
                 D1 = 0.44 
                 N1 = 1.846660 
                 ν1 = 23.8 
               
               
                 R2 = 9.291 
                 D2 = 1.50 
                 N2 = 1.622992 
                 ν2 = 58.2 
               
               
                 R3 = −273.258 
                 D3 = 0.05 
               
               
                 R4 = 9.603 
                 D4 = 0.82 
                 N3 = 1.834807 
                 ν3 = 42.7 
               
               
                 R5 = 26.112 
                 D5 = Variable 
               
               
                 R6 = 4.740 
                 D6 = 0.20 
                 N4 = 1.804000 
                 ν4 = 46.6 
               
               
                 R7 = 1.527 
                 D7 = 1.00 
               
               
                 R8 = −5.294 
                 D8 = 0.17 
                 N5 = 1.772499 
                 ν5 = 49.6 
               
               
                 R9 = 4.724 
                 D9 = 0.05 
               
               
                 R10 = 3.071 
                 D10 = 0.65 
                 N6 = 1.846660 
                 ν6 = 23.8 
               
               
                 R11 = −19.602 
                 D11 = 0.11 
               
               
                 R12 = −6.087 
                 D12 = 0.17 
                 N7 = 1.834000 
                 ν7 = 37.2 
               
               
                 R13 = 91.367 
                 D13 = Variable 
               
               
                 R14 = Stop 
                 D14 = 0.35 
               
               
                 R15 = 9.408 
                 D15 = 0.80 
                 N8 = 1 583126 
                 ν8 = 59.4 
               
               
                 R16 = −6.767 
                 D16 = 0.05 
               
               
                 R17 = 8.654 
                 D17 = 0.62 
                 N9 = 1.603112 
                 ν9 = 60.6 
               
               
                 R18 = −9.191 
                 D18 = 0.16 
               
               
                 R19 = −4.580 
                 D19 = 0.20 
                 N10 = 1.834807 
                 ν10 = 42.7 
               
               
                 R20 = 67.415 
                 D20 = Variable 
               
               
                 R21 = 3.920 
                 D21 = 0.17 
                 N11 = 1.805181 
                 ν11 = 25.4 
               
               
                 R22 = 2.284 
                 D22 = 0.90 
                 N12 = 1.583126 
                 ν12 = 59.4 
               
               
                 R23 = −6.947 
                 D23 = 1.15 
               
               
                 R24 = ∞ 
                 D24 = 0.87 
                 N13 = 1.516330 
                 ν13 = 64.2 
               
               
                 R25 = ∞  
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Variable 
                 Focal Length 
               
             
          
           
               
                   
                 Separation 
                 1.00 
                 11.56 
                 31.35  
               
               
                   
                   
               
             
          
           
               
                   
                 D5 
                 0.28 
                 8.90 
                 10.54 
               
               
                   
                 D13 
                 10.59 
                 1.97 
                 0.32 
               
               
                   
                 D20 
                 4.52 
                 2.05 
                 4.28  
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients: 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R15: 
                 K =   2.53535e+00 
                 B =   1.02195e−03 
                 C =   1.50257e−04 
               
               
                   
                 D = −7.45575e−06 
                 E =   2.88428e−06 
               
               
                 R23: 
                 K = −6.32967e+00 
                 B =   1.83073e−05 
                 C = −6.82268e−05 
               
               
                   
                 D =   1.20294e−04 
                 E = −7.19961e−05  
               
               
                   
               
             
          
         
       
     
     NUMERICAL EXAMPLE 3 
     
       
         
               
             
               
               
               
               
             
           
               
                   
               
               
                 f = 1˜30.04   Fno = 1.65˜3.90   2ω = 63.0°˜2.3°  
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 22.113 
                 D1 = 0.44 
                 N1 = 1.846660 
                 ν1 = 23.8 
               
               
                 R2 = 8.814 
                 D2 = 1.50 
                 N2 = 1.622992 
                 ν2 = 58.2 
               
               
                 R3 = −189.638 
                 D3 = 0.05 
               
               
                 R4 = 9.019 
                 D4 = 0.82 
                 N3 = 1.834807 
                 ν3 = 42.7 
               
               
                 R5 = 24.538 
                 D5 = Variable 
               
               
                 R6 = 4.772 
                 D6 = 0.20 
                 N4 = 1.804000 
                 ν4 = 46.6 
               
               
                 R7 = 1.530 
                 D7 = 1.03 
               
               
                 R8 = −4.660 
                 D8 = 0.17 
                 N5 = 1.696797 
                 ν5 = 55.5 
               
               
                 R9 = 4.385 
                 D9 = 0.05 
               
               
                 R10 = 3.011 
                 D10 = 0.65 
                 N6 = 1.846660 
                 ν6 = 23.8 
               
               
                 R11 = −29.069 
                 D11 = 0.14 
               
               
                 R12 = −6.157 
                 D12 = 0.17 
                 N7 = 1.834000 
                 ν7 = 37.2 
               
               
                 R13 = 41.871 
                 D13 = Variable 
               
               
                 R14 = Stop 
                 D14 = 0.35 
               
               
                 R15 = 9.782 
                 D15 = 0.80 
                 N8 = 1.583126 
                 ν8 = 59.4 
               
               
                 R16 = −6.742 
                 D16 = 0.05 
               
               
                 R17 = 8.908 
                 D17 = 0.62 
                 N9 = 1.603112 
                 ν9 = 60.6 
               
               
                 R18 = −9.210 
                 D18 = 0.15 
               
               
                 R19 = −4.595 
                 D19 = 0.20 
                 N10 = 1.834807 
                 ν10 = 42.7 
               
               
                 R20 = 139.182 
                 D20 = Variable 
               
               
                 R21 = 4.025 
                 D21 = 0.17 
                 N11 = 1.805181 
                 ν11 = 25.4 
               
               
                 R22 = 2.322 
                 D22 = 1.00 
                 N12 = 1.583126 
                 ν12 = 59.4 
               
               
                 R23 = −6.391 
                 D23 = 1.15 
               
               
                 R24 = ∞ 
                 D24 = 0.88 
                 N13 = 1.516330 
                 ν13 = 64.2 
               
               
                 R25 = ∞  
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Variable 
                 Focal Length 
               
             
          
           
               
                   
                 Separation 
                 1.00 
                 11.56 
                 30.04  
               
               
                   
                   
               
             
          
           
               
                   
                 D5 
                 0.27 
                 8.21 
                 9.73 
               
               
                   
                 D13 
                 9.78 
                 1.84 
                 0.32 
               
               
                   
                 D20 
                 4.21 
                 1.75 
                 4.00  
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients: 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R15: 
                 K =   2.44598e+00 
                 B =   8.69023e−04 
                 C =   1.68820e−04 
               
               
                   
                 D = −8.16971e−06 
                 E =   2.13455e−06 
               
               
                 R23: 
                 K = −6.46142e+00 
                 B = −5.42052e−04 
                 C =   2.63913e−05 
               
               
                   
                 D =   8.71904e−05 
                 E = −6.81494e−05  
               
               
                   
               
             
          
         
       
     
     NUMERICAL EXAMPLE 4 
     
       
         
               
             
               
               
               
               
             
           
               
                   
               
               
                 f = 1˜30.33   Fno = 1.65˜3.92  2ω = 63.0°˜2.3°  
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 R1 = 22.442 
                 D1 = 0.44 
                 N1 = 1.846660 
                 ν1 = 23.8 
               
               
                 R2 = 8.771 
                 D2 = 1.50 
                 N2 = 1.622992 
                 ν2 = 58.2 
               
               
                 R3 = −294.493 
                 D3 = 0.05 
               
               
                 R4 = 9.353 
                 D4 = 0.82 
                 N3 = 1˜882997 
                 ν3 = 40.8 
               
               
                 R5 = 25.754 
                 D5 = Variable 
               
               
                 R6 = 4.404 
                 D6 = 0.20 
                 N4 = 1.882997 
                 ν4 = 40.8 
               
               
                 R7 = 1.611 
                 D7 = 0.97 
               
               
                 R8 = −4.790 
                 D8 = 0.17 
                 N5 = 1.693501 
                 ν5 = 53.2 
               
               
                 R9 = 4.417 
                 D9 = 0.20 
               
               
                 R10 = 3.184 
                 D10 = 0.65 
                 N6 = 1 846660 
                 ν6 = 23.8 
               
               
                 R11 = −9.528 
                 D11 = 0.09 
               
               
                 R12 = −6.009 
                 D12 = 0.17 
                 N7 = 1.834000 
                 ν7 = 37.2 
               
               
                 R13 = 9.338 
                 D13 = Variable 
               
               
                 R14 = Stop 
                 D14 = 0.35 
               
               
                 R15 = 9.821 
                 D15 = 0.80 
                 N8 = 1.583126 
                 ν8 = 59.4 
               
               
                 R16 = −6.586 
                 D16 = 0 05 
               
               
                 R17 = 9.002 
                 D17 = 0.62 
                 N9 = 1.603112 
                 ν9 = 60.6 
               
               
                 R18 = −8.607 
                 D18 = 0.14 
               
               
                 R19 = −4.676 
                 D19 = 0.20 
                 N10 = 1.834807 
                 ν10 = 42.7 
               
               
                 R20 = 58.562 
                 D20 = Variable 
               
               
                 R21 = 4.099 
                 D21 = 0.17 
                 N11 = 1.805181 
                 ν11 = 25.4 
               
               
                 R22 = 2.343 
                 D22 = 1.00 
                 N12 = 1.583126 
                 ν12 = 59.4 
               
               
                 R23 = −6.259 
                 D23 = 1.15 
               
               
                 R24 = ∞ 
                 D24 = 0.87 
                 N13 = 1.516330 
                 ν13 = 64.2 
               
               
                 R25 = ∞  
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Variable 
                 Focal Length 
               
             
          
           
               
                   
                 Separation 
                 1.00 
                 11.38 
                 30.33   
               
               
                   
                   
               
               
                   
                 D5 
                 0.27 
                 8.28 
                 9.80 
               
               
                   
                 D13 
                 9.82 
                 1.82 
                 0.30 
               
               
                   
                 D20 
                 4.43 
                 1.97 
                 4.20  
               
               
                   
                   
               
             
          
         
       
     
     Aspheric Coefficients: 
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R15: 
                 K =   2.04144e+00 
                 B =   6.86749e−04 
                 C = 1.57910e−04 
               
               
                   
                 D = −9.88649e−06 
                 E =   2.44554e−06 
               
               
                 R23: 
                 K = −6.24623e+00 
                 B = −7.61255e−04 
                 C = 2.48918e−05 
               
               
                   
                 D =   8.22867e−05 
                 E = −6.94856e−05  
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 R15: 
                 K =   2.04144e+00 
                 B =   6.86749e−04 
                 C = 1.57910e−04 
               
               
                   
                 D = −9.88649e−06 
                 E =   2.44554e−06 
               
               
                 R23: 
                 K = −6.24623e+00 
                 B = −7.61255e−04 
                 C = 2.48918e−05 
               
               
                   
                 D =   8.22867e−05 
                 E = −6.94856e−05  
               
               
                   
               
             
          
         
       
     
     In view of the employment of the rear-focus type, the rules of design of the zoom lens are set forth as described above. Accordingly, when making the relative aperture as large as 1.6 in F-number and extending the range to as high as 30 in zoom ratio, it is made possible to improve the compact form of the entire zoom lens, while still permitting good optical performance to be maintained stable throughout the entire zooming range from the wide-angle end to the telephoto end and throughout the entire focusing range from an infinitely distance object to a super close object. 
     Another embodiment of the invention is described as applied to an image pickup apparatus (video camera) using one of the zoom lenses of the numerical examples 1 to 4 as the photographic optical system, with reference to FIG.  13 . 
     In FIG. 13, reference numeral  10  denotes a body of the image pickup apparatus, reference numeral  11  denotes a photographic optical system formed as the zoom lens of one of the numerical examples 1 to 4, reference numeral  12  denotes an image pickup element such as a CCD arranged to receive an object image formed by the photographic optical system  11 , reference numeral  13  denotes recording means for recording the object image received by the image pickup element  12 , and reference numeral  14  denotes a viewfinder used for observing the object image. As the viewfinder  14 , not only the optical one, but also an electronic type of observing the object image as displayed on the liquid crystal panel can be considered. 
     In such a manner, the zoom lenses of the numerical examples 1 to 4 are applied to the video camera or like image pickup apparatus. A compact, high-performance image pickup apparatus can thus be realized