Abstract:
There is provided a zoom lens of an inner focusing system which is capable of an auto-focusing operation and a manual focusing operation with a high precision. 
     A zoom lens system in which a movement locus of a focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam is arranged such that a ratio of an amount of rotation for focusing from infinity to closest to an amount of rotation for zooming from wide angle to telephoto in the focus cam is set within a predetermined range so that, when the sensitivity of a movement of an imaging point with respect to a movement of the focusing lens unit in the direction of the optical axis in the closest in-focus state is larger than that in the infinity in-focus state, the sensitivity of the movement of the imaging point with respect to the movement of the focusing lens unit in the rotational direction satisfies specific conditions.

Description:
The entire disclosure of Japanese Patent Application Nos. 8-27182 and 8-35994 including specifications, claims, drawings and summaries is incorporated herein by reference in their entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a zoom lens and, more particularly, to a zoom lens attached to a so-called auto-focusing camera, video camera, or the like, which has a focus detection device, and moves a focusing lens unit in a photographing optical system in accordance with the detected defocus amount. 
     2. Related Background Art 
     In recent years, along with the wide spread use of auto-focusing cameras, various focusing systems such as a so-called inner focusing system, rear focusing system, and the like have been examined to make a focusing lens of a zoom lens compact. 
     However, in general, when a focusing system other than a so-called front focusing system is adopted, the lens driving amount for focusing changes upon a change in focal length. To solve this problem, Japanese Patent Application Laid-Open Nos. 4-293008 and 5-142475 assigned to the same assignee as the present invention proposed a method of realizing a so-called manual focusing operation in a zoom lens having a plurality of lens units including a focusing lens unit having both zooming and focusing functions. In this method, when a predetermined movement locus for zooming is expressed by the amount of movement of the lens units in the direction of the optical axis and the angle of rotation of a rotatable lens barrel, the movement locus of the focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam. With this arrangement, even when the amount of movement for focusing along the optical axis changes depending on the zooming state, the angle of rotation of the rotatable lens barrel for focusing is left unchanged, thus achieving a manual focusing operation. 
     However, when the above-mentioned zoom lens is applied to an auto-focusing camera system, which comprises focus detection means, storage means for storing the conversion coefficient γ and the correction coefficient ε used for calculating the lens driving amount Δx for focusing the focusing lens unit on the basis of the detected defocus amount ΔBf of a photographing optical system, and calculation means for calculating the lens driving amount Δx for focusing using the defocus amount ΔBf, the conversion coefficient γ, and the correction coefficient ε, problems associated with the storage capacity, calculation error, and the like are posed. 
     As in Japanese Patent Application Laid-Open Nos. 4-293008 and 5-142475 above, in a zoom lens disclosed in Japanese Patent Application Laid-Open Nos. 57-37307, 57-37308, 63-49715, 63-314511, 3-144411, 3-235908, 3-249717, 4-184402, 4-184403, 4-184404, 4-184405, 4-184406, 4-186207, 4-186208, 7-110446, and the like, in each of which the movement locus of the focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam, the above-mentioned problems concerning the storage capacity, calculation error, and the like have not been examined, either. 
     Furthermore, in a zoom lens disclosed in Japanese Patent Application Laid-Open Nos. 57-4018, 58-137812, 58-137814, 58-144808, 58-149014, 58-150925, and the like, each of which utilizes only a focus cam, the problems of the storage capacity, calculation error, and the like have not been examined, either. 
     On the other hand, as in Japanese Patent Application Laid-Open Nos. 63-163808, 1-154014, and the like, in a zoom lens disclosed in Japanese Patent Application Laid-Open Nos. 64-35515, 64-35516, 4-140704, and the like, each of which commonly uses a single cam as both a focus cam and a zoom cam, the above-mentioned problems of the storage capacity, calculation error, and the like have not been examined, either. In addition, the zoom lens disclosed in these references has a basic structure different from that of the present invention since it does not require any zoom compensation cam, and does not take a so-called flexible manual focusing operation into account, which has been examined in Japanese Patent Application Laid-Open Nos. 4-293008, 5-142475, and the like. 
     A zoom lens disclosed in Japanese Patent Application Laid-open Nos. 2-256011 and 3-101707 which have been assigned to the same assignee as the present invention, and Japanese Patent Application Laid-Open No. 7-120662 which discloses a technical content similar to those disclosed in the above Japanese Patent Application Laid-Open Nos. 2-256011 and 3-101707, has a basic structure different from that of the present invention since it realizes zooming by a relative movement, in the direction of rotation of a lens barrel, between a focus cam and a zoom cam, and focusing by a relative movement in the direction of the optical axis, and does not examine an auto-focusing operation at all. 
     Similarly, in Japanese Patent Application Laid-Open No. 7-5362, a zoom lens disclosed therein has a basic structure different from that of the present invention since the amount of movement for focusing is to be defined by synthesizing two kinds of cams without using a focus cam directly, and the above-mentioned problems concerning the storage capacity, calculation error, and the like have not been examined. 
     Furthermore, Japanese Patent Application Laid-Open Nos. 61-77027, 1-232313, and the like disclose a lens system having a focus cam so as to realize an accurate auto-focusing operation with a small calculation error. However, these references relate to a single-focus lens having no zooming function, and cannot be applied to a focus cam required to achieve a so-called manual focusing operation in a zoom lens in which the amount of movement in the direction of the optical axis for focusing changes depending on the zooming state. 
     The principle of the auto-focus operation will be briefly described below. 
     An auto-focusing system disclosed in Japanese Patent Application Laid-Open Nos. 62-78519, 62-170924, 1-131507, 1-131508, 1-131509, 3-228006, and the like, comprises focus detection means, calculation means for calculating the lens driving amount for focusing, and storage means for storing specific constants used in calculations. In this system, the focus detection means detects the defocus amount ΔBf between the imaging position of an actual object by the photographing optical system and a predetermined imaging point position, and the calculation means for calculating the lens driving amount for focusing calculates the lens driving amount Δx for focusing on the basis of the detected defocus amount ΔBf of the photographing optical system, thus achieving an auto-focusing operation. 
     If the relationship between the lens driving amount Δx for focusing and the defocus amount ΔBf is expressed using a conversion coefficient K associated with focusing as follows: 
     
         Δx=ΔBf/K 
    
     then, the lens driving amount Δx can be calculated by setting the conversion coefficient K. 
     However, as described in Japanese Patent Application Laid-Open No. 62-170924, the conversion coefficient K changes in correspondence not only with the focal length but also with the object position and lens arrangement. 
     Therefore, as described in Japanese Patent Application Laid-Open Nos. 62-78519, 62-170924, and the like, using the conversion coefficient γ defined as the ratio (sensitivity) of the amount of infinitesimal movement of the imaging plane with respect to the amount of infinitesimal movement of the focusing lens unit in the vicinity of a predetermined in-focus point, and the correction coefficient ε for correcting the conversion coefficient in accordance with the defocus amount ΔBf, the conversion coefficient K is calculated by the following formulas: 
     
         K=γ+ε·f(ΔBf) 
    
     
         K=γ+ε·ΔBf.sup.2 in Japanese Patent Application Laid-Open No. 62-78519 
    
     
         K=γ(1+ε·ΔBf) in Japanese Patent Application Laid-Open No. 62-170924 
    
     and thereafter, the lens driving amount Δx is calculated based on the conversion coefficient K. (Of course, the lens driving amount Δx for focusing may be directly calculated from the defocus amount ΔBf using the conversion coefficient γ and the correction coefficient ε.) 
     Furthermore, in a photographing system having a zooming optical system, since the values of the conversion coefficient γ and the correction coefficient ε change depending on the lens arrangement, a plurality of pairs of data of the conversion coefficient γ and the correction coefficient ε are stored in the storage means in units of a plurality of divided zoom ranges and focus ranges, as described in Japanese Patent Application Laid-Open No. 3-228006. 
     In other words, in the photographing system having the zooming optical system, the focus detection means detects the defocus amount ΔBf caused by the zooming optical system, and values of the conversion coefficient γ and the correction coefficient ε corresponding to the zoom and focus positions respectively detected by zoom and focus position detection means are read out from the storage means. The calculation means for calculating the lens driving amount for focusing calculates the lens driving amount Δx for focusing using the defocus amount ΔBf, the conversion coefficient γ, and the correction coefficient ε, and driving means drives a lens by the calculated lens driving amount Δx for focusing, thus achieving a focusing operation. 
     However, in a normal focusing mechanism using a helicoid mechanism or a cam mechanism, the lens driving amount for focusing must be described not as a lens driving amount Δx in the direction of the optical axis but as a lens driving amount Δa in the direction of rotation. 
     Therefore, when the relationship between the lens driving amount Δx and the defocus amount ΔBf in the direction of the optical axis is converted into the relationship between the lens driving amount Δa and the defocus amount ΔBf in the direction of rotation using a conversion coefficient K a  associated with the direction of rotation, we have: 
     
         Δa=ΔBf/K.sub.a 
    
     If conversion coefficient K associated with the direction of the optical axis is newly defined as K x , the conversion coefficient K a  associated with the direction of rotation is expressed using a conversion coefficient Φ between the lens driving amount Δx in the direction of the optical axis and the lens driving amount Δa in the direction of rotation as follows: 
     
         K.sub.a =K.sub.x ·Φ 
    
     Thus, the formula in Japanese Patent Application Laid-Open No. 62-170924 is modified to a formula associated with the conversion coefficient K a  in the direction of rotation as follows: 
     
         K.sub.a =Φγ(1+ε·ΔBf) 
    
     If Δx and Δa have a linear relationship therebetween like in a helicoid mechanism, Φ becomes a constant. However, when a cam mechanism is used, the conversion coefficient Φ changes depending on the cam shape. The conversion coefficient Φ can be replaced by a slope (dx/da) defined by the cam shape as follows: 
     
         K.sub.a =γ·(dx/da)(1+ε·ΔBf) 
    
     The conversion coefficient γ and the correction coefficient ε in an inner focusing type zoom lens disclosed in Japanese Patent Application Laid-Open Nos. 4-293008, 5-142475, and the like will be examined below. 
     When a zoom lens system is constituted by n lens units, and its k-th lens unit is used as the focusing lens unit, if the ratio of the amount dBf of infinitesimal movement of the imaging plane to the amount dx of infinitesimal movement, in the direction of the optical axis, of the focusing lens unit, i.e., the conversion coefficient γ (dBf/dx: the sensitivity associated with movement in the direction of the optical axis) is defined as a new conversion coefficient γ x  associated with the amount x of movement in the direction of the optical axis, the conversion coefficient γ x  can be expressed using the imaging magnifications β of the respective lens units as follows: 
     
         γ.sub.x =(1-β.sub.k.sup.2)β.sub.k+1.sup.2 β.sub.k+2.sup.2 . . . β.sub.n.sup.2 
    
     Therefore, the rate of change, from the infinity in-focus value (γ xO ) to the closest in-focus value (γ xR ), of the conversion coefficient γ x  associated with the amount x of movement in the direction of the optical axis can be expressed using the imaging magnifications β Ok  and β Rk  of the focusing lens unit at the infinity and closest in-focus points as follows: 
     
         γ.sub.xR /γ.sub.xO =(1-β.sub.Rk.sup.2)/(1-β.sub.Ok.sup.2) 
    
     Furthermore, if the ratio of the amount dBf of infinitesimal movement of the imaging plane to the angle da of infinitesimal rotation of the focusing lens unit (dBf/da: the sensitivity associated with movement in the direction of rotation) is defined as a new conversion coefficient γ a  associated with the angle a of rotation of a rotatable lens barrel, the conversion coefficient γ a  associated with the angle a of rotation of the rotatable lens barrel can be expressed by: 
     
         γ.sub.a =γ.sub.x ·(dx/da) 
    
     where dx/da is the slope of the focus cam. 
     Therefore, the rate of change, from the infinity in-focus value (γ aO ) to the closest in-focus value (γ aR ), of the conversion coefficient γ a  associated with the angle a of rotation of the rotatable lens barrel can be expressed using slopes (dx/da) O  and (dx/da) R  at the infinity and closest corresponding positions on the focus cam as follows: 
     
         γ.sub.aR /γ.sub.aO =(γ.sub.xR /γ.sub.xO)·((dx/da).sub.R /(dx/da).sub.O) 
    
     The rate of change of the conversion coefficient γ x  with respect to the amount x of movement in the direction of the optical axis and the rate of change of the conversion coefficient γ a  with respect to the angle a of rotation of the rotatable lens barrel will be examined below in association with a case in which the amount of rotation corresponding to the zooming from the wide-angle end to the telephoto end and the ratio of amounts of rotation (a F  /a Z ) with respect to the focusing from the infinity in-focus state to the closest in-focus state are set to be 1.0 in the first embodiment of the present invention, like in an embodiment of Japanese Patent Application Laid-Open No. 5-142475 mentioned above. Note that the amount of rotation for zooming from the wide-angle end to the telephoto end and the amount of rotation for focusing are respectively re-set to be 10.0 for the purpose of a comparison with an embodiment of the present invention. 
     Table 1 below summarizes various paraxial data of an optical system and data for defining the shape of the focus cam in a case in which the ratio of the amounts of rotation (a F  /a Z ) is to set to be 1.0 in the first embodiment of the present invention, like in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. (Said case will be hereinafter called the comparative example I). 
     The upper table in Table 1 summarizes the focal length data and principal point interval data of the respective lens units of the optical system corresponding to the comparative example I. In this table, F1, F2, F3, and F4 are respectively the focal lengths of first, second, third and fourth lens units, and D1, D2, D3, and D4 are respectively the principal point interval between the first and second lens units, the principal point interval between the second and third lens units, the principal point interval between the third and fourth lens units, and the principal point interval between the fourth lens unit and a predetermined imaging plane in six zooming states (focal lengths F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 85.0 (4-POS), 135.0 (5-POS), and 194.0 mm (6-POS)). 
     The middle table in Table 1 summarizes spline sample point data when the shape of the focus cam in the second lens unit which is used for focusing is expressed by a spline function associated with the angle a of rotation of the rotatable lens barrel and the amount x of movement in the direction of the optical axis (complying with &#34;Numerical Analysis and FORTRAN&#34;, MARUZEN, &#34;Spline Function and Its Applications&#34;, Kyoiku Shuppan, and the like). In this middle table, (1), (2), (3), and (4) correspond to the first, second, third, and fourth lens units, respectively. 
     Furthermore, the lower table in Table 1 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=28.8, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) using the focus cam. Since both the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=194.0) and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.95 m) are 10.0, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming is 1.0. 
     
                                           TABLE 1__________________________________________________________________________F = 28.0-194.0 (Rotation Amount Ratio: a.sub.F /a.sub.z__________________________________________________________________________= 1.0)Focal lengths and Principal Point Intervals of Lens Units of ComparativeExample I    1-POS        2-POS            3-POS                4-POS                     5-POS                          6-POS__________________________________________________________________________  F 28.8000        35.0000            50.0000                85.0000                     135.0000                          194.0000F1  85.0000  D1    11.5063        15.6399            23.6055                35.1974                     44.4737                          50.4202F2  -14.7000  D2    25.8069        23.2088            19.3898                14.8844                     11.1724                          7.8560F3  43.5000  D3    8.0000        7.3138            5.7748                3.8464                     2.8540                          2.0039F4  61.0000  D4    59.7035        64.5166            73.5311                86.9840                     97.2356                          104.6041__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) ofComparative Example I   ANGLE    (1)          (2)       (3)                       (4)__________________________________________________________________________1  .0000    .0000          .0000     .0000                       .00002  4.8070   .0000          .0973     .0000                       .00003  6.1968   .0000          .1633     .0000                       .00004  7.4292   .0000          .2472     .0000                       .00005  8.3658   .0000          .3325     .0000                       .00006  9.1510   .0000          .4194     .0000                       .00007  10.0000  .0000          .5362     .0000                       .00008  14.8070  .0000          1.9234    .0000                       .00009  16.1968  .0000          2.6178    .0000                       .000010 17.4292  .0000          3.3494    .0000                       .000011 18.3658  .0000          3.9814    .0000                       .000012 19.1510  .0000          4.5444    .0000                       .000013 20.0000  .0000          5.2095    .0000                       .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofComparative Example IRotation Amount Ratio: a.sub.F /a.sub.Z = 1.0)__________________________________________________________________________          Infinity        Amount of          Correspond-                Photograph-                          Rotation forFocal Length   ing Position                ing Distance                          Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m   4.80735.0 mm        .5467  3.00 m   6.19750.0 mm        1.7264                 2.00 m   7.42985.0 mm        4.0063                 1.50 m   8.366135.0 mm       6.8742                 1.20 m   9.151194.0 mm       10.0000                 0.95 m   10.000Condition Corresponding Value (1)                 1.81Condition Corresponding Value (2)                 8.72Condition Corresponding Value (3)                 1.00Condition Corresponding Value (4)                14.32 (wide-angle end)                 9.37 (telephoto end)Condition Corresponding Value (5)                 5.05 (wide-angte end)                 9.49 (telephoto end)Condition Corresponding Value (6)                 0.33 (wide-angle end)                 0.30 (telephoto end)__________________________________________________________________________ 
    
     Table 2 below summarizes the numerical value data of the cams of the focusing lens unit in the comparative example I, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 1. In this table, (ANGLE) is the angle of rotation of the rotatable lens barrel, (2) is the amount (mm) of movement, in the direction of the optical axis, of the second lens unit, and (F) is the focal length (mm) of the entire system in an infinity in-focus state corresponding to the amount (ANGLE) of rotation. 
     
                       TABLE 2______________________________________Cam Numerical Value Data of Focusing Lens Unit in ComparativeExample I            Zoom Compensation Cam NumericalFocus Cam Numerical Value Data            Value DataANGLE (2)       F        ANGLE  (2)   F______________________________________.0000 .0000     28.8000  .0000  .0000 28.8000.5000 .0056     34.4507  .5000  1.3899                                 34.45071.0000 .0114     40.4957  1.0000 2.8644                                 40.49571.5000 .0179     46.9366  1.5000 4.4323                                 46.93662.0000 .0252     53.8335  2.0000 6.0605                                 53.83352.5000 .0338     61.1687  2.5000 7.6964                                 61.16873.0000 .0438     68.8474  3.0000 9.2783                                 68.84743.5000 .0557     76.7811  3.5000 10.7612                                 76.78114.0000 .0696     84.8965  4.0000 12.1183                                 84.89654.5000 .0860     93.1568  4.5000 13.3400                                 93.15685.0000 .1050     101.6074 5.0000 14.4342                                 101.60745.5000 .1271     110.2708 5.5000 15.4096                                 110.27086.0000 .1524     119.1222 6.0000 16.2732                                 119.12226.5000 .1814     128.1362 6.5000 17.0347                                 128.13627.0000 .2146     137.3353 7.0000 17.7078                                 137.33537.5000 .2529     146.7582 7.5000 18.3072                                 146.75828.0000 .2969     156.3343 8.0000 18.8416                                 156.33438.5000 .3462     165.8058 8.5000 19.3089                                 165.80589.0000 .4013     175.1330 9.0000 19.7185                                 175.13309.5000 .4641     184.6090 9.5000 20.0905                                 184.609010.0000 .5362     194.0000 10.0000                           20.4174                                 194.000010.5000 .6194     .000011.0000 .7146     .000011.5000 .8227     .000012.0000 .9446     .000012.5000 1.0810    .000013.0000 1.2328    .000013.5000 1.4009    .000014.0000 1.5861    .000014.5000 1.7894    .000015.0000 2.0114    .000015.5000 2.2523    .000016.0000 2.5112    .000016.5000 2.7872    .000017.0000 3.0811    .000017.5000 3.3952    .000018.0000 3.7290    .000018.5000 4.0750    .000019.0000 4.4323    .000019.5000 4.8124    .000020.0000 5.2095    .0000______________________________________ 
    
     The left table in Table 2 summarizes the numerical value data of the focus cam in the comparative example I, and the right table in Table 2 summarizes the numerical value data of the zoom compensation cam of the comparative example I. A value obtained by synthesizing the amount (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the amount (2) of movement in the direction of the optical axis in the numerical value data of the zoom compensation cam in a range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) agrees with the movement locus of the second lens unit calculated using the paraxial data in the upper table in Table 1. 
     Tables 3, 4, and 5 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β k  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=85.0), and the telephoto end (F=194.0), respectively. In these tables, (R) on the left side is the photographing distance (m), (ANG) is the amount of rotation on the focus cam upon focusing to the respective photographing distances, and 1), 2), 3), and 4) on the right side respectively represent the first, second, third, and fourth lens units. Also, in these tables, the first table summarizes the amount DX (mm) of movement for focusing in the direction of the optical axis upon focusing to the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) (note that movement toward the object side is positive). The second table summarizes the imaging magnifications β k  of the respective lens units in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). The third table summarizes the conversion coefficient γ x  associated with the direction of the optical axis of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). Furthermore, the fourth table summarizes the slope (dx/da) of the focus cam at the positions, on the focus cam, corresponding to an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m), and the fifth table summarizes the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). 
     
                                           TABLE 3__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End (28.8 mm) in Comparative Example 1R .000 ANG    .000        1)          .000              2)                .000                    3)                      .000 4)                             .000R 10.000 ANG    3.203        1)          .000              2)                .048                    3)                      .000 4)                             .000R 5.000 ANG    4.807        1)          .000              2)                .097                    3)                      .000 4)                             .000R 3.000 ANG    6.197        1)          .000              2)                .163                    3)                      .000 4)                             .000R 2.000 ANG    7.429        1)          .000              2)                .247                    3)                      .000 4)                             .000R 1.500 ANG    8.366        1)          .000              2)                .332                    3)                      .000 4)                             .000R 1.200 ANG    9.151        1)          .000              2)                .419                    3)                      .000 4)                             .000R .950 ANG    10.000        1)          .000              2)                .536                    3)                      .000 4)                             .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) inComparative Example IR .000 ANG    .000        1)          .000              2)                -.250                    3)                      -63.758                           4)                             .021R 10.000 ANG    3.203        1)          -.009              2)                -.247                    3)                      -63.758                           4)                             .021R 5.000 ANG    4.807        1)          -.018              2)                -.243                    3)                      -63.758                           4)                             .021R 3.000 ANG    6.197        1)          -.030              2)                -.239                    3)                      -63.758                           4)                             .021R 2.000 ANG    7.429        1)          -.047              2)                -.233                    3)                      -63.758                           4)                             .021R 1.500 ANG    8.366        1)          -.065              2)                -.227                    3)                      -63.758                           4)                             .021R 1.200 ANG    9.151        1)          -.084              2)                -.221                    3)                      -63.758                           4)                             .021R .950 ANG    10.000        1)          -.112              2)                -.214                    3)                      -63.758                           4)                             .021Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angleEnd (28.8 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                1.722                    3)                      .000 4)                             .000R 10.000 ANG    3.203        1)          .000              2)                1.725                    3)                      .000 4)                             .000R 5.000 ANG    4.807        1)          .000              2)                1.728                    3)                      .000 4)                             .000R 3.000 ANG    6.197        1)          .000              2)                1.732                    3)                      .000 4)                             .000R 2.000 ANG    7.429        1)          .000              2)                1.737                    3)                      .000 4)                             .000R 1.500 ANG    8.366        1)          .000              2)                1.741                    3)                      .000 4)                             .000R 1.200 ANG    9.151        1)          .000              2)                1.746                    3)                      .000 4)                             .000R .950 ANG    10.000        1)          .000              2)                1.753                    3)                      .000 4)                             .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in ComparativeExample IR .000 ANG    .000        1)          .000              2)                .011                    3)                      .000 4)                             .000R 10.000 ANG    3.203        1)          .000              2)                .023                    3)                      .000 4)                             .000R 5.000 ANG    4.807        1)          .000              2)                .039                    3)                      .000 4)                             .000R 3.000 ANG    6.197        1)          .000              2)                .057                    3)                      .000 4)                             .000R 2.000 ANG    7.429        1)          .000              2)                .081                    3)                      .000 4)                             .000R 1.500 ANG    8.366        1)          .000              2)                .101                    3)                      .000 4)                             .000R 1.200 ANG    9.151        1)          .000              2)                .122                    3)                      .000 4)                             .000R .950 ANG    10.000        1)          .000              2)                .155                    3)                      .000 4)                             .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End(28.8 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                .019                    3)                      .000 4)                             .000R 10.000 ANG    3.203        1)          .000              2)                .040                    3)                      .000 4)                             .000R 5.000 ANG    4.807        1)          .000              2)                .067                    3)                      .000 4)                             .000R 3.000 ANG    6.197        1)          .000              2)                .099                    3)                      .000 4)                             .000R 2.000 ANG    7.429        1)          .000              2)                .140                    3)                      .000 4)                             .000R 1.500 ANG    8.366        1)          .000              2)                .176                    3)                      .000 4)                             .000R 1.200 ANG    9.151        1)          .000              2)                .213                    3)                      .000 4)                             .000R .950 ANG    10.000        1)          .000              2)                .272                    3)                      .000 4)                             .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.02, γ.sub.aR /γ.sub.a0 = 14.32 
    
     
                                           TABLE 4__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (85.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    3.101        1)          .000              2)                .152                    3)                      .000                          4)                            .000R 5.000 ANG    4.741        1)          .000              2)                .303                    3)                      .000                          4)                            .000R 3.000 ANG    6.206        1)          .000              2)                .500                    3)                      .000                          4)                            .000R 2.000 ANG    7.448        1)          .000              2)                .743                    3)                      .000                          4)                            .000R 1.500 ANG    8.387        1)          .000              2)                .981                    3)                      .000                          4)                            .000R 1.200 ANG    9.154        1)          .000              2)                1.215                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                1.519                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Middle Position (85.0mm) inComparative Example IR .000 ANG    .000        1)          .000              2)                -.419                    3)                      5.606                          4)                            -.426R 10.000 ANG    3.101        1)          -.009              2)                -.408                    3)                      5.606                          4)                            -.426R 5.000 ANG    4.741        1)          -.018              2)                -.398                    3)                      5.606                          4)                            -.426R 3.000 ANG    6.206        1)          -.031              2)                -.385                    3)                      5.606                          4)                            -.426R 2.000 ANG    7.448        1)          -.048              2)                -.368                    3)                      5.606                          4)                            -.426R 1.500 ANG    8.387        1)          -.067              2)                -.352                    3)                      5.606                          4)                            -.426R 1.200 ANG    9.154        1)          -.087              2)                -.336                    3)                      5.606                          4)                            -.426R .950 ANG    10.000        1)          -.117              2)                -.315                    3)                      5.606                          4)                            -.426Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at MiddlePosition (85.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                4.702                    3)                      .000                          4)                            .000R 10.000 ANG    3.101        1)          .000              2)                4.751                    3)                      .000                          4)                            .000R 5.000 ANG    4.741        1)          .000              2)                4.798                    3)                      .000                          4)                            .000R 3.000 ANG    6.206        1)          .000              2)                4.858                    3)                      .000                          4)                            .000R 2.000 ANG    7.448        1)          .000              2)                4.929                    3)                      .000                          4)                            .000R 1.500 ANG    8.387        1)          .000              2)                4.995                    3)                      .000                          4)                            .000R 1.200 ANG    9.154        1)          .000              2)                5.058                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                5.135                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Middle Position (85.0 mm) in ComparativeExample IR .000 ANG    .000        1)          .000              2)                .030                    3)                      .000                          4)                            .000R 10.000 ANG    3.101        1)          .000              2)                .073                    3)                      .000                          4)                            .000R 5.000 ANG    4.741        1)          .000              2)                .110                    3)                      .000                          4)                            .000R 3.000 ANG    6.206        1)          .000              2)                .165                    3)                      .000                          4)                            .000R 2.000 ANG    7.448        1)          .000              2)                .227                    3)                      .000                          4)                            .000R 1.500 ANG    8.387        1)          .000              2)                .281                    3)                      .000                          4)                            .000R 1.200 ANG    9.154        1)          .000              2)                .330                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                .389                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at MiddlePosition (85.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                .142                    3)                      .000                          4)                            .000R 10.000 ANG    3.101        1)          .000              2)                .349                    3)                      .000                          4)                            .000R 5.000 ANG    4.741        1)          .000              2)                .528                    3)                      .000                          4)                            .000R 3.000 ANG    6.206        1)          .000              2)                .799                    3)                      .000                          4)                            .000R 2.000 ANG    7.448        1)          .000              2)                1.120                    3)                      .000                          4)                            .000R 1.500 ANG    8.387        1)          .000              2)                1.406                    3)                      .000                          4)                            .000R 1.200 ANG    9.154        1)          .000              2)                1.670                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                1.996                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.09, γ.sub.aR /γ.sub.a0 = 14.06 
    
     
                                           TABLE 5__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End (194.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    3.212        1)          .000              2)                .766                    3)                      .000                          4)                            .000R 5.000 ANG    4.807        1)          .000              2)                1.387                    3)                      .000                          4)                            .000R 3.000 ANG    6.197        1)          .000              2)                2.082                    3)                      .000                          4)                            .000R 2.000 ANG    7.429        1)          .000              2)                2.813                    3)                      .000                          4)                            .000R 1.500 ANG    8.366        1)          .000              2)                3.445                    3)                      .000                          4)                            .000R 1.200 ANG    9.151        1)          .000              2)                4.008                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                4.673                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (194.0mm) inComparative Example IR .000 ANG    .000        1)          .000              2)                -.739                    3)                      4.318                          4)                            -.715R 10.000 ANG    3.212        1)          -.009              2)                -.687                    3)                      4.318                          4)                            -.715R 5.000 ANG    4.807        1)          -.018              2)                -.645                    3)                      4.318                          4)                            -.715R 3.000 ANG    6.197        1)          -.031              2)                -.598                    3)                      4.318                          4)                            -.715R 2.000 ANG    7.429        1)          -.049              2)                -.548                    3)                      4.318                          4)                            -.715R 1.500 ANG    8.366        1)          -.068              2)                -.505                    3)                      4.318                          4)                            -.715R 1.200 ANG    9.151        1)          -.089              2)                -.467                    3)                      4.318                          4)                            -.715R .950 ANG    10.000        1)          -.121              2)                -.422                    3)                      4.318                          4)                            -.715Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at TelephotoEnd (194.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                4.318                    3)                      .000                          4)                            .000R 10.000 ANG    3.212        1)          .000              2)                5.026                    3)                      .000                          4)                            .000R 5.000 ANG    4.807        1)          .000              2)                5.563                    3)                      .000                          4)                            .000R 3.000 ANG    6.197        1)          .000              2)                6.122                    3)                      .000                          4)                            .000R 2.000 ANG    7.429        1)          .000              2)                6.665                    3)                      .000                          4)                            .000R 1.500 ANG    8.366        1)          .000              2)                7.097                    3)                      .000                          4)                            .000R 1.200 ANG    9.151        1)          .000              2)                7.451                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                7.834                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Telephoto End (194.0 mm) in ComparativeExample IR .000 ANG    .000        1)          .000              2)                .155                    3)                      .000                          4)                            .000R 10.000 ANG    3.212        1)          .000              2)                .334                    3)                      .000                          4)                            .000R 5.000 ANG    4.807        1)          .000              2)                .448                    3)                      .000                          4)                            .000R 3.000 ANG    6.197        1)          .000              2)                .548                    3)                      .000                          4)                            .000R 2.000 ANG    7.429        1)          .000              2)                .644                    3)                      .000                          4)                            .000R 1.500 ANG    8.366        1)          .000              2)                .696                    3)                      .000                          4)                            .000R 1.200 ANG    9.151        1)          .000              2)                .750                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                .800                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(194.0 mm) in Comparative Example IR .000 ANG    .000        1)          .000              2)                .669                    3)                      .000                          4)                            .000R 10.000 ANG    3.212        1)          .000              2)                1.677                    3)                      .000                          4)                            .000R 5.000 ANG    4.807        1)          .000              2)                2.495                    3)                      .000                          4)                            .000R 3.000 ANG    6.197        1)          .000              2)                3.356                    3)                      .000                          4)                            .000R 2.000 ANG    7.429        1)          .000              2)                4.290                    3)                      .000                          4)                            .000R 1.500 ANG    8.366        1)          .000              2)                4.938                    3)                      .000                          4)                            .000R 1.200 ANG    9.151        1)          .006              2)                5.592                    3)                      .000                          4)                            .000R .950 ANG    10.000        1)          .000              2)                6.267                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.81, γ.sub.aR /γ.sub.a0 = 9.37 
    
     As can be seen from Tables 3, 4, and 5, the conversion coefficient γ x  associated with the direction of the optical axis and the slope (dx/da) of the focus cam at the respective focal lengths increase as the photographing distance becomes closer to the closest distance. Especially, the slope (dx/da) of the focus cam changes largely. Therefore, as can be seen from these tables, the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of γ x  and (dx/da), further increases. 
     More specifically, in a zoom lens in which the conversion coefficient γ x  associated with the amount x of movement, in the direction of the optical axis, of the focusing lens unit in a closest in-focus state is larger than that in an infinity in-focus state, i.e., which satisfies: 
     
         1.0&lt;γ.sub.xR /γ.sub.xO 
    
     when the focus cam which satisfies the following inequality, i.e., the focus cam has a shape having a larger slope (dx/da) at the closest corresponding position than that at the infinity corresponding position: 
     
         1.0&lt;&lt;(dx/da).sub.R /(dx/da).sub.O 
    
     the following inequality is satisfied: 
     
         1.0&lt;γ.sub.xR /γ.sub.xO &lt;&lt;γ.sub.aR /γ.sub.aO 
    
     The rate of change, from the infinity in-focus value (γ aO ) to the closest in-focus value (γ aR ), of the conversion coefficient γ a  associated with the angle a of rotation of the rotatable lens barrel undesirably becomes larger than the rate of change, from the infinity in-focus value (γ xO ) to the closest in-focus value (γ xR ), of the conversion coefficient γ x  associated with the amount x of movement in the direction of the optical axis. 
     From Tables 3, 4, and 5 above, the rate of change of γ a  is ×14.32 at the wide-angle end (F=28.8), ×14.06 at the middle position (F=85.0), and ×9.37 at the telephoto end (F=194.0). 
     As described above, when the conversion coefficient γ changes in correspondence with the lens arrangement (e.g., focusing), as described in Japanese Patent Application Laid-Open No. 3-228006, a plurality of pairs of data of the conversion coefficient γ and the correction coefficient ε must be stored in the storage means in units of a plurality of divided focus ranges. Therefore, when the rate of change of γ a  is large (γ aR  /γ aO  &gt;&gt;1.0), the number of divisions increases, and the storage capacity inevitably becomes large, resulting in an increase in cost. For example, when a change in γ a  in a single focus range is divided under the condition defined by the following inequality: 
     
         γ.sub.max /γ.sub.min &lt;1.2 
    
     the number N of divisions is expressed by inequality (a) below: 
     
         N&gt;log (γ.sub.MAX /γ.sub.MIN)/log (1.2)         (a) 
    
     Therefore, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end have large values as follows: 
     
         N.sub.W &gt;14.6N.sub.M &gt;14.5N.sub.T &gt;12.3 
    
     The formula K=γ(1+ε·ΔBf) presented by Japanese Patent Application Laid-Open No. 62-170924 is rewritten to the conversion coefficient K a  associated with the angle a of rotation of the rotatable lens barrel: 
     
         K.sub.a =γ.sub.a (1+ε·ΔBf) 
    
     Then, the following formula is defined by using a correction coefficient μ (ε=-1/μ): 
     
         K.sub.a =γ.sub.a (1-ΔBf/μ) 
    
     Tables 6, 7, and 8 below summarize the calculation results of the values of the conversion coefficient K a  and the correction coefficient μ according to the comparative example I at the wide-angle end (F=28.8), middle position (F=85.0), and telephoto end (F=194.0) using the above formula. 
     In these tables, (R) is the object distance (m), (ANG) is the amount of rotation for focusing from the infinity corresponding position on the focus cam, (r) is the conversion coefficient γ a  in the direction of rotation, (rs) is the conversion coefficient K a , (bf) is the defocus amount (mm), and (l) is the correction coefficient μ. Each table has a matrix structure, and eight rows in the vertical direction indicated by (POS) represent the object positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 mm), and four pairs (R, ANGLE) in the horizontal direction represent the lens arrangements of the focusing lens unit. 
     More specifically, the position of the focusing lens in the first pair in the upper two tables in each of Tables 6, 7, and 8, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Therefore, the third column (r) in the first table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on an infinity object, and the fourth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. Furthermore, the third column (bf) in the second table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the infinity corresponding position, and the object is located at an object distance in the second column, and the fourth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. 
     Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 6, 7, and 8, i.e., in the ninth and 10th columns is (R, ANGLE)=(0.95, 10.0), and it indicates that this position corresponds to the closest in-focus (R=0.95 m) corresponding position. Therefore, the ninth column (r) in the third table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on a closest distance (R=0.95 m) object, and the 10th column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.95 m) object to an in-focus state at the object distance in the second column. Furthermore, the ninth column (bf) in the fourth table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the closest corresponding position, and the object is located at an object distance in the second column, and the 10th column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.95 m) object to an in-focus state at the object distance in the second column. 
     From the above formulas, since the conversion coefficient in the direction of rotation is calculated by K a  =ΔBf/Δa (where Δa: the amount of rotation for focusing), and the correction coefficient μ is calculated by μ=ΔBf/(1-K a  /γ a ), the value of the conversion coefficient K a  (eighth row, fourth column in first table: 0.096) when the focusing lens unit is moved from an in-focus state on the infinity object to an in-focus state at the object distance (R=0.95 m) in Table 6 is calculated by K a  =0.96/10.0=0.096 using ΔBf=0.96 and Δa=10.0. On the other hand, the value of the correction coefficient μ (eighth row, fourth column in second table: -0.24) is calculated as μ=-0.24 using ΔBf=0.96, K a  =0.096, and Y a  =0.019. 
     
                                           TABLE 6__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation andCorrection Coefficient μ: (l) at Wide-angle End (28.8 mm) inComparative Example IF = 28.8 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              3.203                  5.000                      4.807                          3.000                              6.197POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .019      .000    .026    .035    .0452  10.000  .026          .040              .000    .052    .0663  5.000   .035    .053                  .067                      .000    .0824  3.000   .046    .067    .082                          .099                              .0005  2.000   .058    .082    .100    .1196  1.500   .070    .097    .116    .1377  1.200   .082    .111    .131    .1538  .950    .096    .129    .151    .175__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              -.24                  -.17                      -.35                          -.28                              -.512  10.000  .08 -.22          .00 .00 -.08                      -.39                          -.20                              -.593  5.000  .17 -.20          .08 -.27                  .00 .00 -.11                              -.664  3.000  .28 -.20          .20 -.30                  .11 -.49                          .00 .005  2.000  .43 -.21          .35 -.33                  .26 -.53                          .15 -.736  1.500  .59 -.22          .50 -.35                  .41 -.56                          .30 -.777  1.200  .75 -.23          .66 -.38                  .57 -.59                          .45 -.828  .950  .96 -.24          .87 -.40                  .79 -.62                          .67 -.86__________________________________________________________________________(R, ANGLE) =  2.000      7.429          1.500              8.366                  1.200                      9.151                          .950                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    .057    .067    .077    .0902  10.000  .080    .094    .106    .1213  5.000   .098    .113    .126    .1434  3.000   .117    .134    .148    .1675  2.000  .140      .000    .158    .172    .1936  1.500   .159          .176              .000    .192    .2157  1.200   .176    .194                  .213                      .000    .2398  .950    .200    .221    .242                          .272                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.42      -.71          -.56              -.91                  -.71                      -1.11                          -.90                              -1.352  10.000  -.34      -.80          -.48              -1.03                  -.63                      -1.25                          -.82                              -1.483  5.000  -.26      -.86          -.40              -1.12                  -.55                      -1.35                          -.74                              -1.574  3.000  -.14      -.89          -.29              -1.22                  -.44                      -1.45                          -.63                              -1.655  2.000  .00 .00 -.15              -1.40                  -.30                      -1.56                          -.50                              -1.706  1.500  .15 -1.09          .00 .00 -.15                      -1.53                          -.35                              -1.697  1.200  .30 -1.18          .15 -1.49                  .00 .00 -.20                              -1.698  .950  .51 -1.21          .36 -1.43                  .21 -1.48                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 5.05, K.sub.aR /γ.sub.aR = 0.33 
    
     
                                           TABLE 7__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (85.0 mm) in Comparative ExampleF = 85.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              3.101                  5.000                      4.741                          3.000                              6.206POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .142      .000    .229    .294    .3662  10.000  .236          .349              .000    .431    .5193  5.000   .313    .444                  .527                      .000    .6384  3.000   .406    .558    .664                          .800                              .0005  2.000   .520    .700    .828    .9796  1.500   .631    .835    .979    1.1427  1.200   .741    .967    1.125   1.2988  .950    .886    1.140   1.314   1.499__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.71              -2.06                  -1.39                      -3.16                          -2.27                              -4.202  10.000  .73 -1.11          .00 .00 -.71                      -3.86                          -1.61                              -4.603  5.000  1.49      -1.24          .73 -2.67                  .00 .00 -.93                              -4.614  3.000  2.52      -1.36          1.73              -2.90                  .97 -3.75                          .00 .005  2.000  3.87      -1.46          3.04              -3.03                  2.24                      -3.94                          1.22                              -5.446  1.500  5.29      -1.54          4.41              -3.17                  3.57                      -4.17                          2.49                              -5.827  1.200  6.78      -1.61          5.86              -3.31                  4.96                      -4.38                          3.83                              -6.148  .950  8.86      -1.69          7.87              -3.47                  6.91                      -4.63                          5.69                              -6.51__________________________________________________________________________(R, ANGLE) =  2.000      7.448          1.500              8.387                  1.200                      9.154                          .950                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    .446    .515    .576    .6462  10.000  .619    .704    .776    .8593  5.000   .756    .851    .931    1.0214  3.000   .931    1.034   1.120   1.2145  2.000  1.120      .000    1.229   1.319   1.4186  1.500   1.291          1.407              .000    1.499   1.6017  1.200   1.454   1.574                  1.669                      .000    1.7748  .950    1.664   1.789   1.889                          1.994                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -3.32      -5.52          -4.32              -6.82                  -5.27                      -8.05                          -6.46                              -9.572  10.000  -2.69      -6.02          -3.72              -7.44                  -4.70                      -8.78                          -5.92                              -10.403  5.000  -2.05      -6.28          -3.10              -7.85                  -4.11                      -9.30                          -5.37                              -11.004  3.000  -1.16      -6.84          -2.26              -8.51                  -3.30                      -10.03                          -4.61                              -11.785  2.000  .00 .00 -1.15              -9.14                  -2.25                      -10.73                          -3.62                              -12.516  1.500  1.21      -7.96          .00 .00 -1.15                      -11.31                          -2.58                              -13.097  1.200  2.48      -8.32          1.21              -10.17                  .00 .00 -1.50                              -13.608  .950  4.25      -8.75          2.89              -10.62                  1.60                      -12.13                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 6.24, K.sub.aR /γ.sub.aR = 0.32 
    
     
                                           TABLE 8__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (#) at Telephoto End (194.0 mm) in Comparative ExampleF = 194.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              3.212                  5.000                      4.807                          3.000                              6.197POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .669      .000    1.031   1.244   1.4362  10.000  1.215          1.676              .000    1.930   2.1443  5.000   1.686   2.218                  2.493                      .000    2.7044  3.000   2.298   2.897   3.175                          3.354                              .0005  2.000   3.084   3.736   4.002   4.1606  1.500   3.937   4.623   4.862   4.9797  1.200   4.881   5.567   5.752   5.7938  .950    6.351   6.992   7.074   6.992__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -3.31              -8.60                  -5.98                      -11.93                          -8.90                              -15.572  10.000  3.90      -4.79          .00 .00 -3.08                      -13.65                          -6.40                              -17.743  5.000  8.11      -5.34          3.54              -10.95                  .00 .00 -3.76                              -19.404  3.000  14.24      -5.85          8.65              -11.88                  4.41                      -16.11                          .00 .005  2.000  22.91      -6.35          15.76              -12.82                  10.49                      -17.33                          5.13                              -21.346  1.500  32.94      -6.75          23.83              -13.55                  17.30                      -18.20                          10.80                              -22.297  1.200  44.67      -7.10          33.06              -14.25                  24.99                      -19.11                          17.11                              -23.548  .950  63.51      -7.48          47.46              -14.97                  36.73                      -19.99                          26.59                              -24.52__________________________________________________________________________(R, ANGLE) =  2.000      7.429          1.500              8.366                  1.200                      9.151                          .950                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    1.600   1.718   1.804   1.8932  10.000  2.310   2.424   2.498   2.5743  5.000   2.856   2.958   3.013   3.0714  3.000   3.493   3.577   3.601   3.6335  2.000  4.289      .000    4.313   4.277   4.2756  1.500   5.033          4.934              .000    4.876   4.8697  1.200   5.748   5.608                  5.589                      .000    5.2278  .950    6.830   6.633   6.536                          6.260                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -11.89      -18.96          -14.37              -22.05                  -16.51                      -24.38                          -18.93                              -27.142  10.000  -9.74      -21.12          -12.49              -24.56                  -14.83                      -26.83                          -17.47                              -29.663  5.000  -7.49      -22.43          -10.53              -26.29                  -13.09                      -28.40                          -15.95                              -31.304  3.000  -4.31      -23.22          -7.76              -28.21                  -10.64                      -29.91                          -13.82                              -32.935  2.000  .00 .00 -4.04              -32.10                  -7.36                      -31.37                          -10.99                              -34.666  1.500  4.71      -27.17          .00 .00 -3.83                      -30.02                          -7.96                              -35.797  1.200  9.90      -29.09          4.40              -32.20                  .00 .00 -4.69                              -40.038  .950  17.56      -29.64          10.84              -31.46                  5.55                      -32.72                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 9.49, K.sub.aR /γ.sub.aR = 0.30 
    
     As can be seen from Tables 6, 7, and 8 above, when a change in conversion coefficient K a  : (rs) (e.g., the fourth column in the first table) and a change in correction coefficient μ: (l) (e.g., the fourth column in the second table) at a given lens arrangement (e.g., at the infinity in-focus arrangement) are considered, the conversion coefficient K a  and the correction coefficient μ considerably change depending on the object positions. In particular, the conversion coefficient K a  has a larger value at the closest object side than that at the infinity object side. Since the conversion coefficient K a  in the direction of rotation is defined by K a  =ΔBf/Δa, the amount Δa of rotation for focusing at the infinity object side becomes larger than that at the closest object side relative to the defocus amount ΔBf. 
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end (F=28.8), middle position (F=85.0), and telephoto end (F=194.0) in the comparative example I are as follows. 
     
         ______________________________________Comparative Example I    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      5.05           0.33(F = 28.8)Middle Position      6.24           0.32(F = 85.0)Telephoto End      9.49           0.30(F = 194.0)______________________________________ 
    
     As described above, in the comparative example I, since the change in conversion coefficient K a  is large, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) becomes large, and the value of the correction coefficient μ becomes close to that of the defocus amount ΔBf. In addition, the value of the correction coefficient μ largely changes depending on the object positions. 
     Therefore, as described in Japanese Patent Application Laid-Open No. 3-228006, under the condition that only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range (e.g., an infinity in-focus arrangement range), if the correction coefficient μ which changes largely is represented by only one value, a large error is included in the value of the conversion coefficient K a  which is calculated from the conversion coefficient γ a  and the correction coefficient μ. Therefore, when the lens driving amount Δa for focusing is finally calculated from the defocus amount ΔBf using the conversion coefficient K a , the lens driving amount includes an error, and an auto-focus operation cannot be accurately performed. 
     For example, upon calculation of the lens driving amount Δa for focusing with respect to a closest distance (R=0.95 m) object when the correction coefficient μ (which changes from -4.79 to -7.48 depending on the object distances) at the infinity in-focus arrangement at the telephoto end (F=194.0) is represented by the value (μ=-6.35) at the middle object distance (R=2.0 m), the lens driving amount Δa for focusing is calculated as Δa=8.63 by substituting ΔBf=63.51, γ a  =0.669, and μ=-6.35. The actual lens driving amount for focusing from the state of the infinity in-focus arrangement at the telephoto end (F=194.0) to the closest distance (R=0.95 m) object is Δa=10.0 from (R, ANGLE)=(0.95, 10.0) in the upper right portion of the third table in Table 8. Therefore, an error as large as -13.7% is produced between the actual value and the calculated value Δa=8.74 of the lens driving amount for focusing. 
     Similarly, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following large values are obtained. 
     
         ______________________________________Comparative Example I    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -9.3%         -27.2%(F = 28.8)Middle Position      -11.7%         -28.3%(F = 85.0)Telephoto End      -13.7%         -28.9%(F = 194.0)______________________________________ 
    
     Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (R=2.0 m), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (R=3.0 m). 
     Finally, Table 9 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 1) of the comparative example I, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and a displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     The upper table in Table 9 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and the photographing distances. In the lower table, (F) is the focal length (mm) of the entire system, (R) is the photographing distance (m), and (DX) is the amount (mm) of movement, in the direction of the optical axis, of each of the first, second, third, and fourth lens units in turn from the right side (movement toward the object side is represented by a positive value). 
     
                                           TABLE 9__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Comparative Example I__________________________________________________________________________    0.95 m        1.20 m             1.50 m                 2.00 m                      3.00 m                          5.00 m__________________________________________________________________________F 28.800 Bf    .000        .000 .000                 .000 .000                          .000F 35.000 Bf    .000        .004 .003                 -.002                      -.001                          -.001F 50.000 Bf    .000        .014 .023                 .007 -.007                          -.009F 85.000 Bf    .000        .005 .029                 .021 .007                          -.035F 135.000 Bf    .000        -.068             -.044                 -.067                      -.072                          -.069F 194.000 Bf    .000        .000 .000                 .000 .000                          .000__________________________________________________________________________   ANGLE DA    10.000         9.151             8.366                 7.429 6.197                           4.807__________________________________________________________________________F  28.800 DX    .000 .536             .000                 .000                    R  0.95 mF  35.000 DX    .000 .622             .000                 .000                    R  0.95 mF  50.000 DX    .000 .855             .000                 .000                    R  0.95 mF  85.000 DX    .000 1.519             .000                 .000                    R  0.95 mF  135.000 DX    .000 2.800             .000                 .000                    R  0.95 mF  194.000 DX    .000 4.673             .000                 .000                    R  0.95 mF  28.800 DX    .000 .419             .000                 .000                    R  1.20 mF  35.000 DX    .000 .485             .000                 .000                    R  1.20 mF  50.000 DX    .000 .669             .000                 .000                    R  1.20 mF  85.000 DX    .000 1.214             .000                 .000                    R  1.20 mF  135.000 DX    .000 2.319             .000                 .000                    R  1.20 mF  194.000 DX    .000 4.008             .000                 .000                    R  1.20 mF  28.800 DX    .000 .332             .000                 .000                    R  1.50 mF  35.000 DX    .000 .385             .000                 .000                    R  1.50 mF  50.000 DX    .000 .530             .000                 .000                    R  1.50 mF  85.000 DX    .000 .975             .000                 .000                    R  1.50 mF  135.000 DX    .000 1.919             .000                 .000                    R  1.50 mF  194.000 DX    .000 3.445             .000                 .000                    R  1.50 mF  28.800 DX    .000 .247             .000                 .000                    R  2.00 mF  35.000 DX    .000 .289             .000                 .000                    R  2.00 mF  85.000 DX    .000 .738             .000                 .000                    R  2.00 mF  135.000 DX    .000 1.501             .000                 .000                    R  2.00 mF  194.000 DX    .000 2.813             .000                 .000                    R  2.00 mF  28.800 DX    .000 .163             .000                 .000                    R  3.00 mF  35.000 DX    .000 .191             .000                 .000                    R  3.00 mF  50.000 DX    .000 .269             .000                 .000                    R  3.00 mF  85.000 DX    .000 .499             .000                 .000                    R  3.00 mF  135.000 DX    .000 1.050             .000                 .000                    R  3.00 mF  194.000 DX    .000 2.082             .000                 .000                    R  3.00 mF  28.800 DX    .000 .097             .000                 .000                    R  5.00 mF  35.000 DX    .000 .114             .000                 .000                    R  5.00 mF  50.000 DX    .000 .162             .000                 .000                    R  5.00 mF  85.000 DX    .000 .310             .000                 .000                    R  5.00 mF  135.000 DX    .000 .659             .000                 .000                    R  5.00 mF  194.000 DX    .000 1.387             .000                 .000                    R  5.00 m__________________________________________________________________________ 
    
     The rate of change of the conversion coefficient γ x  with respect to the amount x of movement in the direction of the optical axis and the rate of change of the conversion coefficient γ a  with respect to the angle a of rotation of the rotatable lens barrel will be examined below in association with a case in which the amount of rotation corresponding to the zooming from the wide-angle end to the telephoto end and the ratio of amounts of rotation (a F  /a Z ) with respect to the focusing from the infinity in-focus state to the closest in-focus state are set to be 1.0 in the fifth embodiment of the present invention, like in an embodiment of Japanese Patent Application Laid-open No. 5-142475 mentioned above. Note that the amount of rotation for zooming from the wide-angle end to the telephoto end and the amount of rotation for focusing are respectively re-set to be 10.0 for the purpose of a comparison with an embodiment of the present invention. 
     Table 10 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam in a case in which the ratio of the amounts of rotation (a F  /a Z ) is set to be 1.0 in the fifth embodiment of the present invention, like in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 (said case will be hereinafter called the comparative example II). 
     The upper table in Table 10 summarizes the focal length data and principal point interval data of the respective lens units of the optical system corresponding to the comparative example II. In this table, F1, F2, F3, F4 and F5 are respectively the focal lengths of first, second, third and fourth lens units, and D1, D2, D3, and D4 are respectively the principal point interval between the first and second lens units, the principal point interval between the second and third lens units, the principal point interval between the third and fourth lens units, the principal point interval between the fourth and fifth lens units, and the principal point interval between the fourth lens unit and a predetermined imaging plane in six zooming states (focal lengths F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0 (4-POS), 95.0 (5-POS), and 126.0 mm (6-POS)). 
     The middle table in Table 10 summarizes spline sample point data when the shape of the focus cam in the fourth lens unit which is used for focusing is expressed by a spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), (4) and (5) correspond to the first, second, third, fourth, and fifth lens units, respectively. 
     Furthermore, the lower table in Table 10 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=28.8, 35.0, 50.0, 70.0, 95.0, and 126.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) using the focus cam. Since both the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=126.0) and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.80 m) are 10.0, the rotation amount ratio (a F  /a z ) of the amount of rotation for focusing to the amount of rotation for zooming is 1.0. 
     
                                           TABLE 10__________________________________________________________________________F = 28.8-126.0 Rotation Amount Ratio: a.sub.F /a.sub.Z = 1.00)__________________________________________________________________________Focal Lengths and Principal Point Intervals of Lens Units of ComparativeExample II    1-POS        2-POS             3-POS                 4-POS                      5-POS                          6-POS__________________________________________________________________________  F 28.8000        35.0000             50.0000                 70.0000                      95.0000                          126.0000F1  98.0000  D1    9.3696        15.5678             26.0774                 35.1343                      42.9607                          49.3378F2  -20.2000  D2    34.5121        30.5093             24.1872                 19.0594                      14.7856                          10.6994F3  21.3000  D3    8.9319        9.5307             10.6727                 11.7442                      12.4611                          13.1911F4  -19.6000  D4    14.4820        13.8832             12.7412                 11.6697                      10.9528                          10.2228F5  35.5000  D5    49.8013        51.5975             55.0237                 58.2383                      61.1451                          63.0195__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) of ComparativeExampleII    ANGLE   (1)    (2)             (3)    (4)  (5)__________________________________________________________________________1   .0000   .0000  .0000             .0000  .0000                         .00002   4.2963   .0000  .0000             .0000  -.0524                         .00003   5.6678   .0000  .0000             .0000  -.0886                         .00004   6.8749   .0000  .0000             .0000  -.1351                         .00005   7.8043   .0000  .0000             .0000  -.1832                         .00006   9.1848   .0000  .0000             .0000  -.2845                         .00007   10.0000   .0000  .0000             .0000  -.3653                         .00008   14.2963   .0000  .0000             .0000  -1.2787                         .00009   15.6678   .0000  .0000             .0000  -1.9076                         .000010  16.8749   .0000  .0000             .0000  -2.7174                         .000011  17.8043   .0000  .0000             .0000  -3.5551                         .000012  19.1848   .0000  .0000             .0000  -5.3209                         .000013  20.0000   .0000  .0000             .0000  -6.7318                         .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofComparative Example IIRotation Amount Ratio: a.sub.F /a.sub.Z = 1.00)__________________________________________________________________________          Infinity        Amount of          Correspond-                Photograph-                          Rotation forFocal Length   ing Position                ing Distance                          Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m   4.29635.0 mm        1.3838                 3.00 m   5.66850.0 mm        3.7931                 2.00 m   6.87570.0 mm        6.0270                 1.50 m   7.80495.0 mm        8.0868                 1.00 m   9.185126.0 mm       10.0000                 0.80 m   10.000Condition Corresponding Value (1)                 1.31Condition Corresponding Value (2)                17.44Condition Corresponding Value (3)                 1.00Condition Corresponding Value (4)                14.24 (wide-angle end)                21.70 (telephoto end)Condition Corresponding Value (5)                 4.76 (wide-angle end)                6.58 (telephoto end)Condition Corresponding Value (6)                 0.34 (wide-angle end)                 0.28 (telephoto end)__________________________________________________________________________ 
    
     Table 11 below summarizes the numerical value data of the cams of the focusing lens unit in the comparative example II, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 10. In this table, (ANGLE) is the angle of rotation of the rotatable lens barrel, (4) is the amount (mm) of movement, in the direction of the optical axis, of the second lens unit, and (F) is the focal length (mm) of the entire system in an infinity in-focus state corresponding to the amount (ANGLE) of rotation. 
     
                       TABLE 11______________________________________Cam Numerical Value Data of Focusing Lens Units in ComparativeExample II            Zoom Comparative CamFocus Cam numerical Value Data            Numerical Value DataANGLE (4)       F        ANGLE   (4)   F______________________________________.0000 .0000     28.8000  .0000   .0000 28.8000.5000 -.0039    30.8977  .5000   .4276 30.89771.0000 -.0079    33.1447  1.0000  .8636 33.14471.5000 -.0124    35.5868  1.5000  1.3155                                  35.58682.0000 -.0173    38.2569  2.0000  1.7855                                  38.25692.5000 -.0231    41.1789  2.5000  2.2688                                  41.17893.0000 -.0297    44.3685  3.0000  2.7579                                  44.36853.5000 -.0374    47.8358  3.5000  3.2440                                  47.83584.0000 -.0464    51.5859  4.0000  3.7188                                  51.58594.5000 -.0569    55.6175  4.5000  4.1839                                  55.61755.0000 -.0691    59.9543  5.0000  4.6556                                  59.95435.5000 -.0833    64.6457  5.5000  5.1530                                  64.64576.0000 -.0998    69.7157  6.0000  5.6946                                  69.71576.5000 -.1189    75.1502  6.5000  6.2879                                  75.15027.0000 -.1408    80.9450  7.0000  6.8895                                  80.94507.5000 -.1660    87.1351  7.5000  7.4492                                  87.13518.0000 -.1951    93.7913  8.0000  7.9384                                  93.79138.5000 -.2291    101.0094 8.5000  8.3526                                  101.00949.0000 -.2684    108.8867 9.0000  8.7143                                  108.88679.5000 -.3139    117.4149 9.5000  9.0402                                  117.414910.0000 -.3653    126.0000 10.0000 9.3243                                  126.000010.5000 -.4227    .000011.0000 -.4879    .000011.5000 -.5633    .000012.0000 -.6511    .000012.5000 -.7536    .000013.0000 -.8731    .000013.5000 -1.0119   .000014.0000 -1.1724   .000014.5000 -1.3569   .000015.0000 -1.5693   .000015.5000 -1.8160   .000016.0000 -2.1031   .000016.5000 -2.4356   .000017.0000 -2.8180   .000017.5000 -3.2565   .000018.0000 -3.7613   .000018.5000 -4.3476   .000019.0000 -5.0362   .000019.5000 -5.8441   .000020.0000 -6.7318   .0000______________________________________ 
    
     The left table in Table 11 summarizes the numerical value data of the focus cam in the comparative example II, and the right table in Table 11 summarizes the numerical value data of the zoom compensation cam of the comparative example II. A value obtained by synthesizing the amount (4) of movement in the direction of the optical axis in the numerical value data of the focus cam and the amount (4) of movement in the direction of the optical axis in the numerical value data of the zoom compensation cam in a range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) agrees with the movement locus of the fourth lens unit calculated using the paraxial data in the upper table in Table 10. 
     Tables 12, 13, and 14 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β k  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=70.0), and the telephoto end (F=126.0), respectively. In these tables, (R) on the left side is the photographing distance (m), (ANG) is the amount of rotation on the focus cam upon focusing to the respective photographing distances, and 1), 2), 3), 4), and 5) on the right side respectively represent the first, second, third, fourth, and fifth lens units. Also, in these tables, the first table summarizes the amount DX (mm) of movement for focusing in the direction of the optical axis upon focusing to the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.8 m) (note that movement toward the object side is positive). The second table summarizes the imaging magnifications β k  of the respective lens units in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m). The third table summarizes the conversion coefficient γ x  associated with the direction of the optical axis of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m). Furthermore, the fourth table summarizes the slope (dx/da) of the focus cam at the positions, on the focus cam, corresponding to an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m), and the fifth table summarizes the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m). 
     
                                           TABLE 12__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End(28.8 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    2.729        1)          .000              2)                .000                    3)                      .000                          4)                            -.026                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -.052                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -.089                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -.135                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -.183                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -.284                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -.365                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                -.295                    3)                      -.541                          4)                            -4.568                                5)                                  -.403R 10.000 ANG    2.729        1)          -.010              2)                -.291                    3)                      -.542                          4)                            -4.570                                5)                                  -.403R 5.000 ANG    4.296        1)          -.020              2)                -.287                    3)                      -.543                          4)                            -4.571                                5)                                  -.403R 3.000 ANG    5.668        1)          -.035              2)                -.281                    3)                      -.545                          4)                            -4.573                                5)                                  -.403R 2.000 ANG    6.875        1)          -.055              2)                -.274                    3)                      -.547                          4)                            -4.575                                5)                                  -.403R 1.500 ANG    7.804        1)          -.076              2)                -.266                    3)                      -.549                          4)                            -4.578                                5)                                  -.403R 1.000 ANG    9.185        1)          -.125              2)                -.250                    3)                      -.554                          4)                            -4.583                                5)                                  -.403R .800 ANG    10.000        1)          -.168              2)                -.238                    3)                      -.557                          4)                            -4.587                                5)                                  -.403Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angle End (28.8mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.225                                5)                                  .000R 10.000 ANG    2.729        1)          .000              2)                .000                    3)                      .000                          4)                            -3.227                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -3.229                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -3.231                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -3.235                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -3.239                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -3.246                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.252                                5)                                  .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in ComparativeExample IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -.008                                5)                                  .000R 10.000 ANG    2.729        1)          .000              2)                .000                    3)                      .000                          4)                            -.013                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -.021                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -.032                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -.045                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -.059                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -.089                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -.109                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End (28.8mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .025                                5)                                  .000R 10.000 ANG    2.729        1)          .000              2)                .000                    3)                      .000                          4)                            .042                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            .069                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            .104                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            .146                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            .192                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            .290                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            .353                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = γ.sub.aR /γ.sub.a0 = 14.24 
    
     
                                           TABLE 13__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddle Position(70.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    2.704        1)          .000              2)                .000                    3)                      .000                          4)                            -.146                                5)                                  .000R 5.000 ANG    4.237        1)          .000              2)                .000                    3)                      .000                          4)                            -.294                                5)                                  .000R 3.000 ANG    5.671        1)          .000              2)                .000                    3)                      .000                          4)                            -.496                                5)                                  .000R 2.000 ANG    6.903        1)          .000              2)                .000                    3)                      .000                          4)                            -.754                                5)                                  .000R 1.500 ANG    7.822        1)          .000              2)                .000                    3)                      .000                          4)                            -1.021                                5)                                  .000R 1.000 ANG    9.204        1)          .000              2)                .000                    3)                      .000                          4)                            -1.578                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -2.019                                5)                                  .000Imaging Magnification β.sub.K of Lens Lens Units at Middle Position(70.0 mm) in ComparativeExample IIR .000 ANG    .000        1)          .000              2)                -.473                    3)                      -.774                          4)                            -3.044                                5)                                  -.641R 10.000 ANG    2.704        1)          -.010              2)                -.463                    3)                      -.780                          4)                            -3.051                                5)                                  -.641R 5.000 ANG    4.237        1)          -.021              2)                -.452                    3)                      -.786                          4)                            -3.059                                5)                                  -.641R 3.000 ANG    5.671        1)          -.035              2)                -.438                    3)                      -.795                          4)                            -3.069                                5)                                  -.641R 2.000 ANG    6.903        1)          -.055              2)                -.420                    3)                      -.806                          4)                            -3.082                                5)                                  -.641R 1.500 ANG    7.822        1)          -.077              2)                -.402                    3)                      -.817                          4)                            -3.096                                5)                                  -.641R 1.000 ANG    9.204        1)          -.128              2)                -.366                    3)                      -.840                          4)                            -3.124                                5)                                  -.641R .800 ANG    10.000        1)          -.173              2)                -.339                    3)                      -.859                          4)                            -3.147                                5)                                  -.641Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Middle Position(70.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.390                                5)                                  .000R 10.000 ANG    2.704        1)          .000              2)                .000                    3)                      .000                          4)                            -3.409                                5)                                  .000R 5.000 ANG    4.237        1)          .000              2)                .000                    3)                      .000                          4)                            -3.428                                5)                                  .000R 3.000 ANG    5.671        1)          .000              2)                .000                    3)                      .000                          4)                            -3.454                                5)                                  .000R 2.000 ANG    6.903        1)          .000              2)                .000                    3)                      .000                          4)                            -3.487                                5)                                  .000R 1.500 ANG    7.822        1)          .000              2)                .000                    3)                      .000                          4)                            -3.521                                5)                                  .000R 1.000 ANG    9.204        1)          .000              2)                .000                    3)                      .000                          4)                            -3.594                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.652                                5)                                  .000Slope dx/da of Focus Cam at Middle Position (70.0 mm) in ComparativeExample IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -.036                                5)                                  .000R 10.000 ANG    2.704        1)          .000              2)                .000                    3)                      .000                          4)                            -.078                                5)                                  .000R 5.000 ANG    4.237        1)          .000              2)                .000                    3)                      .000                          4)                            -.115                                5)                                  .000R 3.000 ANG    5.671        1)          .000              2)                .000                    3)                      .000                          4)                            -.173                                5)                                  .000R 2.000 ANG    6.903        1)          .000              2)                .000                    3)                      .000                          4)                            -.252                                5)                                  .000R 1.500 ANG    7.822        1)          .000              2)                .000                    3)                      .000                          4)                            -.330                                5)                                  .000R 1.000 ANG    9.204        1)          .000              2)                .000                    3)                      .000                          4)                            -.490                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -.623                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Middle Position(70.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .122                                5)                                  .000R 10.000 ANG    2.704        1)          .000              2)                .000                    3)                      .000                          4)                            .267                                5)                                  .000R 5.000 ANG    4.237        1)          .000              2)                .000                    3)                      .000                          4)                            .394                                5)                                  .000R 3.000 ANG    5.671        1)          .000              2)                .000                    3)                      .000                          4)                            .596                                5)                                  .000R 2.000 ANG    6.903        1)          .000              2)                .000                    3)                      .000                          4)                            .879                                5)                                  .000R 1.500 ANG    7.822        1)          .000              2)                .000                    3)                      .000                          4)                            1.162                                5)                                  .000R 1.000 ANG    9.204        1)          .000              2)                .000                    3)                      .000                          4)                            1.761                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            2.275                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.08, γ.sub.aR /γ.sub.a0 = 18.73 
    
     
                                           TABLE 14__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End(126.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    2.777        1)          .000              2)                .000                    3)                      .000                          4)                            -.452                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -.913                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -1.542                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -2.352                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -3.190                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -4.956                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -6.366                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (126.0mm) in ComparativeExample IIR .000 ANG    .000        1)          -.000              2)                -.710                    3)                      -.890                          4)                            -2.626                                5)                                  -.775R 10.000 ANG    2.777        1)          -.010              2)                -.686                    3)                      -.908                          4)                            -2.649                                5)                                  -.775R 5.000 ANG    4.296        1)          -.021              2)                -.663                    3)                      -.927                          4)                            -2.673                                5)                                  -.775R 3.000 ANG    5.668        1)          -.036              2)                -.632                    3)                      -.952                          4)                            -2.705                                5)                                  -.775R 2.000 ANG    6.875        1)          -.056              2)                -.595                    3)                      -.985                          4)                            -2.746                                5)                                  -.775R 1.500 ANG    7.804        1)          -.078              2)                -.559                    3)                      -1.019                          4)                            -2.789                                5)                                  -.775R 1.000 ANG    9.185        1)          -.130              2)                -.491                    3)                      -1.092                          4)                            -2.879                                5)                                  -.775R .800 ANG    10.000        1)          -.176              2)                -.442                    3)                      -1.150                          4)                            -2.951                                5)                                  -.775Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Telephoto End(126.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.543                                5)                                  .000R 10.000 ANG    2.777        1)          .000              2)                .000                    3)                      .000                          4)                            -3.617                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -3.692                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -3.795                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -3.931                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -4.073                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -4.380                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -4.632                                5)                                  .000Slope dx/da of Focus Cam at Telephoto End (126.0 mm) in ComparativeExample IIR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -.109                                5)                                  .000R 10.000 ANG    2.777        1)          .000              2)                .000                    3)                      .000                          4)                            -.241                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            -.373                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            -.560                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            -.791                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            -1.024                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            -1.588                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            -1.802                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(126.0 mm) in Comparative Example IIR .000 ANG    .000        1)          .090              2)                .000                    3)                      .000                          4)                            .385                                5)                                  .000R 10.000 ANG    2.777        1)          .000              2)                .000                    3)                      .000                          4)                            .871                                5)                                  .000R 5.000 ANG    4.296        1)          .000              2)                .000                    3)                      .000                          4)                            1.378                                5)                                  .000R 3.000 ANG    5.668        1)          .000              2)                .000                    3)                      .000                          4)                            2.124                                5)                                  .000R 2.000 ANG    6.875        1)          .000              2)                .000                    3)                      .000                          4)                            3.107                                5)                                  .000R 1.500 ANG    7.804        1)          .000              2)                .000                    3)                      .000                          4)                            4.172                                5)                                  .000R 1.000 ANG    9.185        1)          .000              2)                .000                    3)                      .000                          4)                            6.955                                5)                                  .000R .800 ANG    10.000        1)          .000              2)                .000                    3)                      .000                          4)                            8.348                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.31, γ.sub.aR /γ.sub.a0 = 21.70 
    
     As can be seen from Tables 12, 13, and 14, the conversion coefficient γ x  associated with the direction of the optical axis and the slope (dx/da) of the focus cam at the respective focal lengths increase as the photographing distance becomes closer to the closest distance. Especially, the slope (dx/da) of the focus cam changes largely. Therefore, as can be seen from these tables, the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of γ x  and (dx/da), further increases. 
     More specifically, in a zoom lens in which the conversion coefficient γ x  associated with the amount x of movement, in the direction of the optical axis, of the focusing lens unit in a closest in-focus state is larger than that in an infinity in-focus state, i.e., which satisfies: 
     
         1.0&lt;γ.sub.xR /γ.sub.xO 
    
     when the focus cam which satisfies the following inequality, i.e., the focus cam has a shape having a larger slope (dx/da) at the closest corresponding position than that at the infinity corresponding position: 
     
         1.0&lt;&lt;(dx/da).sub.R /(dx/da).sub.O 
    
     the following inequality is satisfied: 
     
         1.0&lt;γ.sub.xR /γ.sub.xO &lt;&lt;γ.sub.aR /γ.sub.aO 
    
     The rate of change, from the infinity in-focus value (γ aO ) to the closest in-focus value (γ aR ), of the conversion coefficient γ a  associated with the angle a of rotation of the rotatable lens barrel undesirably becomes larger than the rate of change, from the infinity in-focus value (γ xO ) to the closest in-focus value (γ xR ), of the conversion coefficient γ x  associated with the amount x of movement in the direction of the optical axis. 
     From Tables 12, 13, and 14 above, the rate of change of γ a  is ×14.24 at the wide-angle end (F=28.8), ×18.73 at the middle position (F=70.0), and ×21.70 at the telephoto end (F=126.0). 
     As described above, when the conversion coefficient γ changes in correspondence with the lens arrangement (e.g., focusing), as described in Japanese Patent Application Laid-Open No. 3-228006, a plurality of pairs of data of the conversion coefficient γ and the correction coefficient ε must be stored in the storage means in units of a plurality of divided focus ranges. Therefore, when the rate of change of γ a  is large (γ aR  /γ aO  &gt;&gt;1.0), the number of divisions increases, and the storage capacity inevitably becomes large, resulting in an increase in cost. For example, when a change in γ a  in a single focus range is divided under the condition defined by the following inequality: 
     
         γ.sub.max /γ.sub.min &lt;1.2 
    
     the number N of divisions is expressed by inequality (a) below: 
     
         N&gt;log (γ.sub.MAX /γ.sub.MIN) /log (1.2) 
    
     Therefore, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end have large values as follows: 
     
         N.sub.W &gt;14.6 N.sub.M &gt;16.1 N.sub.T &gt;16.9 
    
     The formula K=γ(1+ε·ΔBf) presented by Japanese Patent Application Laid-Open No. 62-170924 is rewritten to the conversion coefficient K a  associated with the angle a of rotation of the rotatable lens barrel: 
     
         K.sub.a =γ.sub.a (1+ε·ΔBf) 
    
     Then, the following formula is defined by using a correction coefficient μ (ε=-1/μ): 
     
         K.sub.a =γ.sub.a (1-ΔBf/μ) 
    
     Tables 15, 16, and 17 below summarize the calculation results of the values of the conversion coefficient K a  and the correction coefficient μ according to the comparative example II at the wide-angle end (F=28.8), middle position (F=70.0), and telephoto end (F=126.0) using the above formula. 
     In these tables, (R) is the object distance (m), (ANG) is the amount of rotation for focusing from the infinity corresponding position on the focus cam, (r) is the conversion coefficient γ a  in the direction of rotation, (rs) is the conversion coefficient K a , (bf) is the defocus amount (mm), and (l) is the correction coefficient μ. Each table has a matrix structure, and eight rows in the vertical direction indicated by (POS) represent the object positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 mm), and four pairs (R, ANGLE) in the horizontal direction represent the lens arrangements of the focusing lens unit. 
     More specifically, the position of the focusing lens in the first pair in the upper two tables in each of Tables 15, 16, and 17, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Therefore, the third column (r) in the first table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on an infinity object, and the fourth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. Furthermore, the third column (bf) in the second table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the infinity corresponding position, and an object is located at an object distance in the second column, and the fourth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. 
     Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 15, 16, and 17, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.80, 10.0), and it indicates that this position corresponds to the closest in-focus (R=0.80 m) corresponding position. Therefore, the ninth column (r) in the third table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on a closest distance (R=0.80 m) object, and the tenth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.80 m) object to an in-focus state at the object distance in the second column. Furthermore, the ninth column (bf) in the fourth table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the closest corresponding position, and the object is located at an object distance in the second column, and the tenth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.80 m) object to an in-focus state at the object distance in the second column. 
     From the above formulas, since the conversion coefficient in the direction of rotation is calculated by K a  =ΔBf/Δa (where Δa: the amount of rotation for focusing), and the correction coefficient μ is calculated by μ=ΔBf/(1-K a  /γ a ), the value of the conversion coefficient K a  (eighth row, fourth column in first table: 0.118) when the focusing lens unit is moved from an in-focus state on the infinity object to an in-focus state at the object distance (R=0.80 m) in Table 15 is calculated by K a  =1.18/10.0=0.118 using ΔBf=1.18 and Δa=10.0. On the other hand, the value of the correction coefficient μ (eighth row, fourth column in second table: -0.31) is calculated as μ=-0.31 using ΔBf=1.18, K a  =0.118, and γ a  =0.025. 
     
                                           TABLE 15__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation andCorrection Coefficient μ; (l) at Wide-angle End (28.8 mm) inComparative Example IIF = 28.8 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              2.729                  5.000                      4.296                          3.000                              5.668POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .025      .000    .031    .039    .0502  10.000  .031          .042              .000    .055    .0693  5.000   .039    .055                  .069                      .000    .0854  3.000   .050    .069    .085                          .104                              .0005  2.000   .063    .085    .104    .1256  1.500   .076    .100    .120    .1437  1.000   .100    .129    .153    .1808  .800    .118    .151    .177    .207__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              -.30                  -.17                      -.40                          -.29                              -.562  10.000  .08 -.35          .00 .00 -.09                      -.42                          -.20                              -.603  5.000  .17 -.29          .09 -.30                  .00 .00 -.12                              -.644  3.000  .29 -.28          .20 -.33                  .12 -.48                          .00 .005  2.000  .44 -.28          .35 -.35                  .27 -.52                          .15 -.776  1.500  .59 -.29          .51 -.37                  .42 -.56                          .31 -.827  1.000  .92 -.30          .84 -.41                  .75 -.61                          .63 -.878  .800  1.18      31  1.10              -.43                  1.01                      -.64                          .90 -.91__________________________________________________________________________(R, ANGLE) =  2.000      6.875          1.500              7.804                  1.000                      9.185                          .800                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    .064    .076    .100    .1192  10.000  .085    .100    .130    .1523  5.000   .104    .121    .154    .1784  3.000   .125    .143    .181    .2075  2.000  .146      .000    .168    .210    .2396  1.500   .167          .192              .000    .238    .2697  1.000   .209    .238                  .290                      .000    .3228  .800    .239    .269    .322                          .353                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.44      -.77          -.59              -.98                  -.92                      -1.41                          -1.19                              -1.792  10.000  -.35      -.84          -.51              -1.07                  -.84                      -1.52                          -1.10                              -1.933  5.000  -.27      -.91          -.42              -1.14                  -.75                      -1.61                          -1.02                              -2.054  3.000  -.15      -1.01          -.31              -1.21                  -.64                      -1.69                          -.90                              -2.185  2.000  .00 .00 -.16              -1.24                  -.48                      -1.76                          -.75                              -2.326  1.500  .16 -1.08          .00 .00 -.33                      -1.85                          -.59                              -2.507  1.000  .48 -1.13          .33 -1.37                  .00 .00 -.26                              -3.028  .800  .75 -1.19          .59 -1.47                  .26 -2.35                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 4.76, K.sub.aR /γ.sub.aR = 0.34 
    
     
                                           TABLE 16__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation andCorrection Coefficient μ; (l) at Wide-angle End (70.0 mm) inComparative Example IIF = 70.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              2.704                  5.000                      4.237                          3.000                              5.671POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .122      .000    .183    .237    .3002  10.000  .183          .267              .000    .331    .4053  5.000   .236    .330                  .394                      .000    .4844  3.000   .298    .404    .483                          .596                              .0005  2.000   .374    .498    .596    .7286  1.500   .448    .589    .702    .8497  1.000   .593    .765    .902    1.0748  .800    .702    .897    1.050   1.242__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.50              -1.58                  -1.00                      -2.52                          -1.70                              -3.422  10.000  .50 -.98          .00 .00 -.51                      -3.16                          -1.20                              -3.763  5.000  1.00      -1.06          .51 -2.13                  .00 .00 -.69                              -3.704  3.000  1.69      -1.16          1.20              -2.34                  .69 -3.06                          .00 .005  2.000  2.58      -1.24          2.09              -2.41                  1.59                      -3.10                          .90 -4.056  1.500  3.51      -1.30          3.02              -2.50                  2.52                      -3.22                          1.83                              -4.307  1.000  5.46      -1.41          4.97              -2.66                  4.48                      -3.48                          3.80                              -4.738  .800  7.02      -1.47          6.54              -2.77                  6.05                      -3.64                          5.37                              -4.96__________________________________________________________________________(R, ANGLE) =  2.000      6.875          1.500              7.804                  1.000                      9.185                          .800                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    .377    .452    .600    .7112  10.000  .501    .594    .773    .9073  5.000   .598    .706    .909    1.0604  3.000   .730    .853    1.081.  1.2515  2.000  .879      .000    1.016   1.269   1.4586  1.500   1.014          1.162              .000    1.435   1.6447  1.000   1.263   1.432                  1.762                      .000    2.0088  .800    1.450   1.639   2.007                          2.275                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -2.60      -4.55          -3.54              -5.79                  -5.52                      -8.38                          -7.11                              -10.352  10.00.0  -2.10      -4.89          -3.04              -6.22                  -5.03                      -8.96                          -6.62                              -11.003  5.000  -1.59      -4.99          -2.53              -6.45                  -4.52                      -9.33                          -6.11                              -11.444  3.000  -.90      -5.29          -1.83              -6.89                  -3.82                      -9.89                          -5.41                              -12.025  2.000  .00 .00 -.93              -7.43                  -2.92                      -10.42                          +4.51                              -12.576  1.500  .93 -6.07          .00 .00 -1.98                      -10.70                          -3.58                              -12.917  1.000  2.91      -6.66          1.98              -8.54                  .00 .00 -1.60                              -13.618  .800  4.49      -6.91          3.57              -8.70                  1.60                      -11.50                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 5.78, K.sub.aR /γ.sub.aR = 0.31 
    
     
                                           TABLE 17__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation andCorrection Coefficient μ; (l) at Wide-angle End (126.0 mm) inComparative Example IIF = 126.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              2.704                  5.000                      4.237                          3.000                              5.671POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  .385      .000    .584    .771    .9992  10.000  .582          .871              .000    1.110   1.3983  5.000   .765    1.107                  1.379                      .000    1.7174  3.000   .991    1.392   1.714                          2.125                              .0005  2.000   1.264   1.738   2.121   2.5926  1.500   1.533   2.075   2.509   3.0357  1.000   2.090   2.772   3.317   3.9768  .800    2.531   3.322   3.953   4.715__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -1.62              -4.93                  -3.31                      -7.51                          -5.66                              -10.692  10.000  1.62      -3.16          .00 .00 -1.69                      -8.66                          -4.04                              -11.813  5.000  3.29      -3.33          1.68              -6.19                  .00 .00 -2.35                              -12.254  3.000  5.62      -3.57          4.02              -6.72                  2.35                      -9.66                          .00 .005  2.000  8.69      -3.81          7.12              -7.15                  5.47                      -10.16                          3.13                              -14.246  1.500  11.96      -4.01          10.43              -7.54                  8.80                      -10.74                          6.48                              -15.157  1.000  19.19      -4.33          17.76              -8.13                  16.22                      -11.53                          13.98                              -16.068  .800  25.31      -4.54          23.99              -8.52                  22.55                      -12.08                          20.43                              -16.76__________________________________________________________________________(R, ANGLE) =  2.000      6.875          1.500              7.804                  1.000                      9.185                          .800                              10.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    1.272   1.533   2.034   2.3792  10.000  1.742   2.066   2.683   3.1033  5.000   2.119   2.491   3.200   3.6764  3.000   2.587   3.008   3.825   4.3675  2.000  3.107      .000    3.590   4.551   5.1726  1.500   3.616          4.178              .000    5.298   5.9897  1.000   4.726   5.467                  6.953                      .000    7.6168  .800    5.586   6.435   7.943                          8.360                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -8.75      -14.81          -11.97              -18.90                  -18.68                      -26.40                          -23.79                              -33.262  10.000  -7.14      -16.25          -10.39              -20.55                  -17.19                      -28.00                          -22.41                              -35.643  5.000  -5.46      -17.19          -8.74              -21.64                  -15.64                      -28.97                          -20.96                              -37.424  3.000  -3.12      -18.64          -6.43              -22.95                  -13.45                      -29.91                          -18.92                              -39.625  2.000  .00 .00 -3.34              -23.74                  -10.51                      -30.43                          -16.16                              -42.386  1.500  3.36      -20.51          .00 .00 -7.31                      -30.73                          -13.15                              -46.377  1.000  10.92      -20.95          7.55              -24.46                  .00 .00 -6.21                              -69.718  .800  17.46      -21.88          14.13              -26.15                  6.48                      -45.45                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 6.58, K.sub.aR /γ.sub.aR = 0.28 
    
     As can be seen from Tables 15, 16, and 17 above, when a change in conversion coefficient K a  : (rs) (e.g., the fourth column in the first table) and a change in correction coefficient μ: (l) (e.g., the fourth column in the second table) at a given lens arrangement (e.g., at the infinity in-focus arrangement) are considered, the conversion coefficient K a  and the correction coefficient μ considerably change depending on the object positions. In particular, the conversion coefficient K a  has a larger value at the closest object side than that at the infinity object side. Since the conversion coefficient K a  in the direction of rotation is defined by K a  =ΔBf/Δa, the amount Δa of rotation for focusing at the infinity object side becomes larger than that at the closest object side relative to the defocus amount ΔBf. 
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end (F=28.8), middle position (F=70.0), and telephoto end (F=126.0) in the comparative example II are as follows. 
     
         ______________________________________Comparative Example II    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      4.76           0.34(F = 28.8)Middle Position      5.78           0.31(F = 70.0)Telephoto End      6.58           0.28(F = 126.0)______________________________________ 
    
     As described above, in the comparative example II, since the change in conversion coefficient K a  is large, the contribution of the correction term (Δf/μ) in K a  =γ a  (1-ΔBf/μ) becomes larger, and the value of the correction coefficient μ becomes close to that of the defocus amount ΔBf. In addition, the value of the correction coefficient μ largely changes depending on the object positions. 
     Therefore, as described in Japanese Patent Application Laid-Open No. 3-228006, under the condition that only a pair of a conversion coefficient γ a  value and a correction coefficient γ value are set for a given lens arrangement range (e.g., an infinity in-focus arrangement range), if the correction coefficient γ which changes largely is represented by only one value, a large error is included in the value of the conversion coefficient K a  which is calculated from the conversion coefficient γ a  and the correction coefficient γ. Therefore, when the lens driving amount γa for focusing is finally calculated from the defocus amount ΔBf using the conversion coefficient K a , the lens driving amount includes an error, and an auto-focus operation cannot be accurately performed. 
     For example, upon calculation of the lens driving amount Δa for focusing with respect to a closest distance (R=0.80 m) object when the correction coefficient μ (which changes from -3.16 to -4.54 depending on the object distances) at the infinity in-focus arrangement at the telephoto end (F=126.0) is represented by the value (μ=-3.81) at the middle object distance (R=2.0 m), the lens driving amount Δa for focusing is calculated as Δa=8.59 by substituting ΔBf=25.31, γ a  =0.385, and μ=-3.81. The actual lens driving amount for focusing from the state of the infinity in-focus arrangement at the telephoto end (F=126.0) to the closest distance (R=0.80 m) object is Δa=10.0 from (R, ANGLE)=(0.80, 10.0) in the upper right portion of the third table in Table 17. Therefore, an error as large as -14.1% is produced between the actual value and the calculated value Δa=8.59 of the lens driving amount for focusing. 
     Similarly, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following large values are obtained. 
     
         ______________________________________Comparative Example II    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -8.7%         -26.3%(F = 28.8)Middle Position      -13.2%         -23.4%(F = 70.0)Telephoto End      -14.1%         -28.7%(F = 126.0)______________________________________ 
    
     Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (R=2.0 m), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (R=3.0 m). 
     Finally Table 18 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 10) of the comparative example II, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     The upper table in Table 18 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 70.0, 95.0, and 126.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and the photographing distances. In the lower table, (F) is the focal length (mm) of the entire system, (R) is the photographing distance (m), and (DX) is the amount (mm) of movement, in the direction of the optical axis, of each of the first, second, third, fourth, and fifth lens units in turn from the right side (movement toward the object side is represented by a positive value). 
     
                                           TABLE 18__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Comparative Example II__________________________________________________________________________   0.80 m        1.00 m            1.50 m                 2.00 m                     3.00 m                           5.00 m__________________________________________________________________________F 28.800 Bf   .000 .000            .000 .000                     .000  .000F 35.000 Bf   .000 -.013            -.017                 -.009                     -.007 -.003F 50.000 Bf   .000 .012            -.006                 -.020                     -.027 -.015F 70.000 Bf   .000 .035            .021 .024                     .002  -.023F 95.000 Bf   .000 .034            .041 .050                     .023  .015F 126.000 Bf   .000 .000            .000 .000                     .000  .000__________________________________________________________________________  ANGLE DA   10.000        9.185            7.804                 6.875                     5.668 4.296__________________________________________________________________________F 28.800 DX   .000 .000            .000 -.365                     .000                         R 0.80 mF 35.000 DX   .000 .000            .000 -.533                     .000                         R 0.80 mF 50.000 DX   .000 .000            .000 -1.061                     .000                         R 0.80 mF 70.000 DX   .000 .000            .000 -2.019                     .000                         R 0.80 mF 95.000 DX   .000 .000            .000 -3.656                     .000                         R 0.80 mF 126.000 DX   .000 .000            .000 -6.366                     .000                         R 0.80 mF 28.000 DX   .000 .000            .000 -.284                     .000                         R 1.00 mF 35.000 DX   .000 .000            .000 -.420                     .000                         R 1.00 mF 50.000 DX   .000 .000            .000 -.825                     .000                         R 1.00 mF 70.000 DX   .000 .000            .000 -1.568                     .000                         R 1.00 mF 95.000 DX   .000 .000            .000 -2.848                     .000                         R 1.00 mF 126.000 DX   .000 .000            .000 -4.956                     .000                         R 1.00 mF 28.800 DX   .000 .000            .000 -.183                     .000                         R 1.50 mF 35.000 DX   .000 .000            .000 -.273                     .000                         R 1.50 mF 50.000 DX   .000 .000            .000 -.537                     .000                         R 1.50 mF 70.000 DX   .000 .000            .000 -1.015                     .000                         R 1.50 mF 95.000 DX   .000 .000            .000 -1.836                     .000                         R 1.50 mF 126.000 DX   .000 .000            .000 -3.190                     .000                         R 1.50 mF 28.800 DX   .000 .000            .000 -.135                     .000                         R 2.00 mF 35.000 DX   .000 .000            .000 -.201                     .000                         R 2.00 mF 50.000 DX   .000 .000            .000 -.401                     .000                         R 2.00 mF 70.000 DX   .000 .000            .000 -.747                     .000                         R 2.00 mF 95.000 DX   .000 .000            .000 -1.351                     .000                         R 2.00 mF 126.000 DX   .000 .000            .000 -2.352                     .000                         R 2.00 mF 28.800 DX   .000 .000            .000 -.089                     .000                         R 3.00 mF 35.000 DX   .000 .000            .000 -.132                     .000                         R 3.00 mF 50.000 DX   .000 .000            .000 -.268                     .000                         R 3.00 mF 70.000 DX   .000 .000            .000 -.495                     .000                         R 3.00 mF 95.000 DX   .000 .000            .000 -.890                     .000                         R 3.00 mF 126.000 DX   .000 .000            .000 -1.542                     .000                         R 3.00 mF 28.800 DX   .000 .000            .000 -.052                     .000                         R 5.00 mF 35.000 DX   .000 .000            .000 -.078                     .000                         R 5.00 mF 50.000 DX   .000 .000            .000 -.158                     .000                         R 5.00 mF 70.000 DX   .000 .000            .000 -.301                     .000                         R 5.00 mF 95.000 DX   .000 .000            .000 -.528                     .000                         R 5.00 mF 126.000 DX   .000 .000            .000 -.913                     .000                         R 5.00 m__________________________________________________________________________ 
    
     SUMMARY OF THE INVENTION 
     It is, therefore, an object of the present invention to provide a zoom lens which can suppress changes in conversion coefficient γ a  and correction coefficient μ above even when the focus cam is used for achieving manual focusing, can suppress the storage capacity by reducing the number of data of the conversion coefficient γ a  and correction coefficient μ to be stored in the storage means, can eliminate an error upon calculation of the lens driving amount Δa for focusing from the defocus amount ΔBf using the conversion coefficient K a , and can achieve accurate auto-focusing, without increasing the size of a barrel mechanism. 
     According to the present invention, in a zoom lens system in which the movement locus of a focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam so as to achieve an in-focus state by a substantially constant amount of rotation for an identical object distance independently of a zooming state upon expression of a predetermined movement locus for zooming by the amount of movement, in the direction of the optical axis, of lens units, and the angle of rotation of a rotatable lens barrel, when the ratios (dBf/dx) of the amount dBf of infinitesimal movement of the imaging plane to the amount dx of infinitesimal movement, in the direction of the optical axis, of the focusing lens unit at the infinity and closest in-focus points are respectively represented by γ xO  and γ xR , the amounts of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end are respectively represented by Δx WR  and Δx TR , and the amount of rotation of the focusing lens unit on the focus cam corresponding to zooming from the wide-angle end to the telephoto end and the amount of rotation corresponding to focusing from the infinity in-focus state to the closest in-focus state are respectively represented by a Z  and a F , the zoom lens satisfies conditional formulas (1), (2), and (3) below at least at the telephoto end: 
     
         1.00&lt;γ.sub.xR /γ.sub.xO                        ( 1) 
    
     
         4.50&lt;Δx.sub.TR /Δx.sub.WR &lt;10.00               (2) 
    
     
         -1.00&lt;a.sub.F /a.sub.z &lt;-0.60                              (3) 
    
     On the other hand, when the ratios (dBf/da) of the amount dBf of infinitesimal movement of the imaging plane with respect to the angle da of infinitesimal rotation of the focusing lens unit on the focus cam at the infinity and closest in-focus points are respectively represented by γ aO  and γ aR , the zoom lens satisfies the following formula at least at the wide-angle end and the telephoto end: 
     
         0.13 &lt;γ.sub.aR /γ.sub.aO &lt;0.80 
    
     Furthermore, when the conversion coefficients K a , which are used when the focusing lens unit are located at the lens arrangements corresponding to the infinity and closest in-focus states and are expressed by K a  =ΔBf/Δa, are respectively represented by K aO  and K aR , the zoom lens satisfies the following formulas at least at the wide-angle end and the telephoto end: 
     
         0.50&lt;K.sub.aO /γ.sub.aO &lt;1.30 
    
     
         0.80&lt;K.sub.aR /γ.sub.aR &lt;1.80 
    
     where 
     ΔBf: the defocus amount between the imaging position of an object at an arbitrary position and a predetermined imaging point position 
     Δa: the angle of rotation of the focusing lens unit on the focus cam required for attaining an in-focus state on the object 
     As in the above-mentioned first aspect of the present invention, in the third aspect of the present invention, since the above-mentioned conditional formulas are satisfied, even when the focus cam is used to achieve so-called manual focusing, changes in conversion coefficient γ a  and correction coefficient μ required for realizing accurate auto-focusing can be reduced, without a barrel mechanism in an increased size. For this reason, the number of data of the conversion coefficient γ a  and correction coefficient μ to be stored in the storage means can be reduced. Furthermore, since the change in correction coefficient μ is small, an error upon calculation of the lens driving amount Δa for focusing from the defocus amount ΔBf using the conversion coefficient K a  is small, and accurate auto-focusing can be realized. 
     As described above, when the zoom lens system is constituted by n lens units, and its k-th lens unit is used as a focusing lens unit, the conversion coefficient γ x  associated with the direction of the optical axis of the focusing lens unit (the ratio dBf/dx of the amount dBf of infinitesimal movement of the imaging plane to the amount dx of infinitesimal movement in the direction of the optical axis) is expressed using the imaging magnifications β of the respective lens units as follows: 
     
         γ.sub.x =(1-β.sub.k.sup.2)β.sub.k+1.sup.2 β.sub.k+2.sup.2. . . β.sub.n.sup.2 
    
     Therefore, the rate of change, from the infinity in-focus value (γ xO ) to the closest in-focus value (γ xR ), of the conversion coefficient γ x  associated with the direction of the optical axis can be expressed using the imaging magnifications β Ok  and β Rk  of the focusing lens unit at the infinity and closest in-focus points as follows: 
     
         γ.sub.xR /γ.sub.xO =(1-β.sub.Rk.sup.2)/(1-β.sub.Ok.sup.2) 
    
     On the other hand, the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit (the ratio dBf/da of the amount dBf of infinitesimal movement of the imaging plane to the angle da of infinitesimal rotation) can be expressed by: 
     
         γ.sub.a =γ.sub.x ·(dx/da) 
    
     where dx/da is the slope of the focus cam. For this reason, the rate of change, from the infinity in-focus value (y aO ) to the closest in-focus value (γ aR ), of the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit can be expressed using slopes (dx/da) O  and (dx/da) R  at the infinity and closest corresponding positions on the focus cam as follows: 
     
         γ.sub.aR /γ.sub.aO =(γ.sub.xR /γ.sub.xO)·((dx/da).sub.R /(dx/da).sub.O) 
    
     Therefore, like in the present invention, in the zoom lens system in which the value of the conversion coefficient γ x  associated with the amount x of movement, in the direction of the optical axis, of the focusing lens unit in the closest in-focus state becomes larger than that in the infinity in-focus state (1.0&lt;γ xR  /γ xO ), the ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state and the amount a z  of rotation corresponding to zooming from the wide-angle end to the telephoto end is set to be negative (a F  /a Z  &lt;0), so that the focus cam can have a shape in which the slope (dx/da) at the closest corresponding position becomes smaller than that at the infinity corresponding position (0&lt;(dx/da) R  /(dx/da) O  &lt;1.0), thereby reducing the change in conversion coefficient γ a  associated with the direction of rotation. 
     More specifically, since the rate of change (γ aR  /γ aO ), from the infinity in-focus value (γ aO ) to the closest in-focus value (γ aR ), of the conversion coefficient γ a  associated with the direction of rotation is expressed as a product of the rate of change (γ xR  /γ xO ) of the conversion ratio γ x  associated with the direction of the optical axis and the slope ratio (dx/da) R  /(dx/da) O  of the focus cam, as described above, the final rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  associated with the direction of rotation can be compressed by adopting an arrangement in which the two changes cancel out each other. 
     According to the present invention, in a zoom lens in which the conversion coefficients γ xO , γ xR  associated with the amount x of movement, in the direction of the optical axis, of the focusing lens unit at the infinity and closest in-focus points at the telephoto end satisfies conditional formula (1): 
     
         1.00&lt;γ.sub.xR /γ.sub.xO                        ( 1) 
    
     and the amounts Δx WR  and Δx TR  of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end satisfies conditional formula (2): 
     
         4.50&lt;Δx.sub.TR /Δx.sub.WR &lt;10.00               (2) 
    
     the ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a Z  of rotation corresponding to zooming from the wide-angle end to the telephoto end is set to satisfy conditional formula (3): 
     
         -1.00&lt;a.sub.F /a.sub.Z &lt;-0.60                              (3) 
    
     Under these conditions, the final rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  associated with the direction of rotation can be set to be a small value which satisfies conditional formula (4) below: 
     
         0.13&lt;γ.sub.aR /γ.sub.aO &lt;0.80                  (4) 
    
     As described above, since the change in conversion coefficient γ a  can be reduced as compared to that in the conventional system, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. 
     For example, upon division of the focus range like in formula (a) (N&gt;log(γ MAX  /γ MIN )/log(1.2)) above, the following relation is satisfied: 
     
         1.2&lt;log (γ.sub.MAX /γ.sub.MIN)/log (1.2)&lt;11.2 
    
     and the number of divisions can be smaller than in the conventional system. Therefore, cost can be reduced in terms of the storage capacity. Furthermore, as will be described later in the following description of the embodiments, since the changes in conversion coefficient K a  and correction coefficient μ are smaller than those in the conventional system, an error obtained upon calculation of the lens driving amount Δa for focusing from the defocus amount ΔBf using the conversion coefficient K a  is small, and an accurate auto-focusing operation can be realized. 
     The conditional formulas of the present invention will be explained below. 
     Conditional formula (1) is associated with the focusing lens unit in the zoom lens according to the present invention. When γ xR  /γ xO  is smaller than the lower limit of conditional formula (1) (γ xR  /γ xO  &lt;1.0), the conversion coefficient γ x  associated with the direction of the optical axis in the closest in-focus state becomes smaller than that in the infinity in-focus state. For this reason, when the focus cam (0&lt;(dx/da) R  /(dx/da) O  &lt;1.0) according to the present invention is used, the rate of change of the conversion coefficient γ a  associated with the direction of rotation, which rate is expressed as a product of the rate of change (γ xR  /γ xO ) of the conversion coefficient γ x  associated with the direction of the optical axis and the slope ratio ((dx/da) R  /(dx/da) O ) of the focus cam, becomes excessively smaller than 1.0 (γ aR  /γ aO  &lt;&lt;1.0), and changes in γ a  become large. As a result, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases. In addition, since the changes in conversion coefficient K a  and correction coefficient μ become large, the error obtained upon calculation of the lens driving amount Δa from the defocus amount ΔBf is large, and an accurate auto-focusing operation cannot be performed. 
     Conditional formula (2) is associated with the ratio between the amounts of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end. As will be described later in the description of the embodiments, this ratio is an amount which is associated with the ratio of the slope (dx/da) R  at the closest corresponding position to the slope (dx/da) O  at the infinity corresponding position on the focus cam. As the ratio between the two amounts of movement becomes smaller, changes in slope on the focus cam become smaller. On the contrary, as the ratio between the two amounts of movement becomes larger, changes in slope on the focus cam become larger. Therefore, when the ratio is smaller than the lower limit of conditional formula (2), changes in conversion coefficient γ a  associated with the direction of rotation become small. However, in the zoom lens of the present invention, which satisfies conditional formula (1), the optimal ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a z  of rotation corresponding to zooming from the wide-angle end to the telephoto end falls outside a range defined by conditional formula (3). On the other hand, when the ratio exceeds the upper limit of conditional formula (2), and if said ratio of the amount of rotation is set in the conditional formula (3), since changes in slope on the focus cam become too large as compared to those in conversion coefficient γ x  associated with the direction of the optical axis, changes in conversion coefficient γ a  associated with the direction of rotation become large, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases. In addition, an accurate auto-focusing operation cannot be performed. 
     Conditional formula (3) defines an appropriate ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a z  of rotation corresponding to zooming from the wide-angle end to the telephoto end. When the ratio is smaller than the lower limit of conditional formula (3), the slope (dx/da) of the focus cam considerably decreases at the closest corresponding position as compared to the slope at the infinity corresponding position, and they have a ratio: 
     
         0&lt;(dx/da).sub.R /(dx/da).sub.O &lt;&lt;1.0 
    
     For this reason, the rate of change of the conversion coefficient γ a  associated with the direction of rotation, which rate is expressed as a product of the rate of change (γ xR  /γ xO ) of the conversion coefficient γ x  associated with the direction of the optical axis and the slope ratio ((dx/da) R  /(dx/da) O ) of the focus cam, becomes excessively smaller than 1.0 (γ aR  /γ aO  &lt;&lt;1.0), and changes in γ a  become large. As a result, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases. In addition, since changes in μ are large, an error obtained upon calculation of the lens driving amount Δa from the defocus amount ΔBf is large, and an accurate auto-focusing operation cannot be performed. 
     On the contrary, when the ratio exceeds the upper limit of conditional formula (3), since the rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  becomes closer to 1.0, changes in γ a  become small, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. However, the slope (dx/da) O  of the focus cam at the infinity corresponding position at the telephoto end becomes large. Therefore, it is required to increase the diameter of a cam barrel corresponding to the focus cam in order to effect a smooth focusing operation by reducing the slope angle of the cam in the barrel mechanism. Thus, it becomes impossible to maintain the barrel to be small. 
     Conditional formula (4) is a condition associated with the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means, i.e., the number of divisions of the focus range. When γ aR  /γ aO  is smaller than the lower limit of conditional formula (4), the rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  becomes excessively smaller than 1.0, and changes in γ a  become large. As a result, since the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases, a storage means with a large storage capacity is required, resulting in an increase in cost. 
     On the contrary, when γ aR  /γ aO  exceeds the upper limit of conditional formula (4), since the rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  becomes closer to 1.0, changes in γ a  become small, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. However, since the conversion coefficient γ a  must have a considerably large value, the sensitivity (dBf/da) associated with the movement in the direction of rotation becomes strict, and a change in imaging point caused by a slight error factor in the direction of rotation becomes large, thus disturbing accurate auto-focusing. 
     Furthermore, in order to attain accurate auto-focusing while lowering the sensitivity (dBf/da) associated with the movement in the direction of rotation, the upper and lower limits of conditional formula (4) are preferably set as follows: 
     
         0.16&lt;γ.sub.aR /γ.sub.aO &lt;0.70 
    
     In order to obtain a zoom lens which can perform auto-focusing more accurately, when the conversion coefficients K a  (=ΔBf/Δa) used when the focusing lens unit is located at the lens arrangements corresponding to the infinity in-focus state and the closest in-focus state are respectively represented by K aO  and K aR , the zoom lens preferably satisfies conditional formulas (5) and (6) below at least at the wide-angle end and the telephoto end: 
     
         0.50&lt;K.sub.aO /γ.sub.aO &lt;1.30                        (5) 
    
     
         0.80&lt;K.sub.aR /γ.sub.aR &lt;1.80                        (6) 
    
     Conditional formula (5) defines the rate of change of the conversion coefficient K a  in the direction of rotation upon a change in object position when the focusing lens unit corresponds to an arrangement in the infinity in-focus state. When the rate is smaller than the lower limit of conditional formula (5), the change in conversion coefficient K aO  upon a change in object position becomes too small as compared to the conversion coefficient γ aO  as the sensitivity associated with the movement in the direction of rotation of the focusing lens unit at the infinity in-focus point. Therefore, for example, when the conversion coefficient K aO  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value on the basis of the relationship K aO  =γ aO  (1-ΔBf/μ aO ), a large error is produced in the value of the conversion coefficient K a0  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO , thus disturbing accurate auto-focusing. 
     On the contrary, when the rate exceeds the upper limit of conditional formula (5), the change in conversion coefficient K aO  in the direction of rotation upon a change in object position becomes large as compared to the conversion coefficient γ aO  in the direction of rotation of the focusing lens unit at the infinity in-focus point. For this reason, when the conversion coefficient K aO  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value, a large error is produced in the value of the conversion coefficient K aO  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO . 
     In order to achieve auto-focusing more accurately, the upper and lower limits of conditional formula (5) are preferably set as follows: 
     
         0.60&lt;K.sub.aO /γ.sub.aO &lt;1.15 
    
     Similarly, when the conversion coefficient K aO  changes from (K aO  /γ aO  &lt;1) to (K aO  /γ aO  &gt;1) upon a change in object position when the focusing lens unit corresponds to an arrangement in the infinity in-focus state, the sign of the correction coefficient μ aO  changes before and after (K aO  /γ aO  =1). As a result, when the conversion coefficient K aO  is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value, a large error is produced in the value of the conversion coefficient K aO  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO . Therefore, the conversion coefficient K aO  does not preferably change too much after it exceeds (K aO  /γ aO  =1). 
     Therefore, even when the conversion coefficient K aO  changes from (K aO  /γ aO  &lt;1) to (K aO  /γ aO  &gt;1), the zoom lens preferably satisfies the following conditional formula: 
     
         0.60&lt;K.sub.aO /γ.sub.aO &lt;1.15 
    
     Conditional formula (6) defines the rate of change of the conversion coefficient K a  in the direction of rotation upon a change in object position when the focusing lens unit corresponds to an arrangement in the closest in-focus position. When the rate exceeds the upper limit of conditional formula (6), the change in conversion coefficient K aR  in the direction of rotation upon a change in object position becomes too large as compared to the conversion coefficient γ aR  as the sensitivity associated with the movement in the direction of rotation of the focusing lens unit at the closest in-focus point. Therefore, for example, when the conversion coefficient K aR  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aR  value and a correction coefficient μ aR  value on the basis of the relationship K aR  =γ aR  (1-ΔBf/μ aR ), a large error is produced in the value of the conversion coefficient K aR  calculated from the conversion coefficient γ aR  R and the correction coefficient μ aR , thus disturbing accurate auto-focusing. 
     On the contrary, when the rate is smaller than the lower limit of conditional formula (6), the change in conversion coefficient K aR  in the direction of rotation upon a change in object position becomes small as compared to the conversion coefficient γ aR  in the direction of rotation of the focusing lens unit at the closest in-focus point. For this reason, when the conversion coefficient K aR  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aR  value and a correction coefficient μ aR  value, a large error is produced in the value of the conversion coefficient K aR  calculated from the conversion coefficient γ aR  and the correction coefficient μ aR . 
     In order to achieve auto-focusing more accurately, the upper and lower limits of conditional formula (6) are preferably set as follows: 
     
         0.90&lt;K.sub.aR /γ.sub.aR &lt;1.70 
    
     Similarly, when the conversion coefficient K aR  changes from (K aR  /γ aR  &lt;1) to (K aR  /γ aR  &gt;1) upon a change in object position when the focusing lens unit corresponds to an arrangement in the closest in-focus state, the sign of the correction coefficient μ aR  changes before and after (K aR  /γ aR  =1). As a result, when the conversion coefficient K aR  is expressed by a pair of a conversion coefficient γ aR  value and a correction coefficient μ aR  value, a large error is produced in the value of the conversion coefficient K aR  calculated from the conversion coefficient γ aR  and the correction coefficient μ aR . Therefore, the conversion coefficient K aR  preferably does not change too much after it exceeds (K aR  /γ aR  =1). 
     Therefore, even when the conversion coefficient K aR  changes from (K aR  /γ aR  &lt;1) to (K aR  /γ aR  &gt;1), the zoom lens preferably satisfies the following conditional formula: 
     
         0.90&lt;K.sub.aR /γ.sub.aR &lt;1.70 
    
     According to the present invention, in a zoom lens system in which the movement locus of a focusing lens unit is defined by synthesizing a focus cam and a zoom compensation cam so as to achieve an in-focus state by a substantially constant amount of rotation for an identical object distance independently of a zooming state upon expression of a predetermined movement locus for zooming by the amount of movement, in the direction of the optical axis, of lens units, and the angle of rotation of a rotatable lens barrel, when the ratios (dBf/dx) of the amount dBf of infinitesimal movement of the imaging plane to the amount dx of infinitesimal movement, in the direction of the optical axis, of the focusing lens unit at the infinity and closest in-focus points are respectively represented by γ xO  and γ xR , the amounts of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end are respectively represented by Δx WR  and Δx TR , and the amount of rotation of the focusing lens unit on the focus cam corresponding to zooming from the wide-angle end to the telephoto end and the amount of rotation corresponding to focusing from the infinity in-focus state to the closest in-focus state are respectively represented by a Z  and a F , the zoom lens satisfies conditional formulas (7), (8), and (9) below at least at the telephoto end: 
     
         1.00&lt;γ.sub.xR /γ.sub.xO                        ( 7) 
    
     
         10.00&lt;Δx.sub.TR /Δx.sub.WR &lt;30.00              (8) 
    
     
         -1.00&lt;a.sub.F /a.sub.Z &lt;-0.50                              (9) 
    
     On the other hand, when the ratios (dBf/da) of the amount dBf of infinitesimal movement of the imaging plane with respect to the angle da of infinitesimal rotation of the focusing lens unit on the focus cam at the infinity and closest in-focus points are respectively represented by γ aO  and γ aR , the zoom lens satisfies the following formula at least at the wide-angle end and the telephoto end: 
     
         0.08&lt;γ.sub.aR /γ.sub.aO &lt;0.70 
    
     Furthermore, when the conversion coefficients K a  which are used when the focusing lens unit are located at the lens arrangements corresponding to the infinity and closest in-focus states and are expressed by K a  =ΔBf/Δa, are respectively represented by K aO  and K aR , the zoom lens satisfies the following formulas at least at the wide-angle end and the telephoto end: 
     
         0.35&lt;K.sub.aO /γ.sub.aO &lt;1.00 
    
     
         1.00&lt;K.sub.aR /γ.sub.aR &lt;3.00 
    
     where 
     ΔBf: the defocus amount between the imaging position of an object at an arbitrary position and a predetermined imaging point position 
     Δa: the angle of rotation of the focusing lens unit on the focus cam required for attaining an in-focus state on the object 
     According to the present invention, in a zoom lens in which the conversion coefficients γ xO , γ xR  associated with the amount x of movement, in the direction of the optical axis, of the focusing lens unit at the infinity and closest in-focus points at the telephoto end satisfies conditional formula (7): 
     
         1.00&lt;γ.sub.xR /γ.sub.xO                        ( 7) 
    
     and the amounts Δx WR  and Δx TR  of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end satisfies conditional formula (8): 
     
         10.00&lt;Δx.sub.TR /Δx.sub.WR &lt;30.00              (8) 
    
     the ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a Z  of rotation corresponding to zooming from the wide-angle end to the telephoto end is set to satisfy conditional formula (9): 
     
         -1.00&lt;a.sub.F /a.sub.Z &lt;-0.50                              (9) 
    
     Under these conditions, the final rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  associated with the direction of rotation can be set to be a small value which satisfies conditional formula (10) below: 
     
         0.08&lt;γ.sub.aR /γ.sub.aO &lt;0.70                  (10) 
    
     As described above, since the change in conversion coefficient γ a  can be reduced as compared to that in the conventional system, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. 
     For example, upon division of the focus range like in formula (a) (N&gt;log(γ MAX  /γ MIN )/log(1.2)) above, the following relation is satisfied: 
     
         2.0&lt;log (γ.sub.MAX /γ.sub.MIN)/log (1.2)&lt;13.9 
    
     and the number of divisions can be smaller than in the conventional system. Therefore, cost can be reduced in terms of the storage capacity. Furthermore, as will be described later in the following description of the embodiments, since the changes in conversion coefficient K a  and correction coefficient μ are smaller than those in the conventional system, an error obtained upon calculation of the lens driving amount Δa for focusing from the defocus amount ΔBf using the conversion coefficient K a  is small, and an accurate auto-focusing operation can be realized. 
     The conditional formulas of the present invention will be explained below. 
     Conditional formula (7) is associated with the focusing lens unit in the zoom lens according to the present invention. When γ xR  /γ xO  is smaller than the lower limit of conditional formula (1) (γ xR  /γ xO  &lt;1.0), the conversion coefficient γ x  associated with the direction of the optical axis in the closest in-focus state becomes smaller than that in the infinity in-focus state. For this reason, when the focus cam (0&lt;(dx/da) R  /(dx/da) O  &lt;1.0) according to the present invention is used, the rate of change of the conversion coefficient γ a  associated with the direction of rotation, which rate is expressed as a product of the rate of change (γ xR  /γ xO ) of the conversion coefficient γ x  associated with the direction of the optical axis and the slope ratio ((dx/da) R  /(dx/da) O ) of the focus cam, becomes excessively smaller than 1.0 (γ aR  /γ aO  &lt;&lt;1.0), and changes in γ a  become large. As a result, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases. In addition, since the changes in conversion coefficient K a  and correction coefficient μ become large, the error obtained upon calculation of the lens driving amount Δa from the defocus amount ΔBf is large, and an accurate auto-focusing operation cannot be performed. 
     Conditional formula (8) is associated with the ratio between the amounts of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end and the telephoto end. As will be described later in the description of the embodiments, this ratio is an amount which is associated with the ratio of the slope (dx/da) R  at the closest corresponding position to the slope (dx/da) O  at the infinity corresponding position on the focus cam. As the ratio between the two amounts of movement becomes smaller, changes in slope on the focus cam become smaller. On the contrary, as the ratio between the two amounts of movement becomes larger, changes in slope on the focus cam become larger. Therefore, when the ratio is smaller than the lower limit of conditional formula (8), changes in conversion coefficient γ a  associated with the direction of rotation become small. However, in the zoom lens of the present invention, which satisfies conditional formula (7), the optimal ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a Z  of rotation corresponding to zooming from the wide-angle end to the telephoto end falls outside a range defined by conditional formula (9). On the other hand, when the ratio exceeds the upper limit of conditional formula (8), and if said ratio of the amount of rotation is set in the conditional formula (9), since changes in slope on the focus cam become too large as compared to those in conversion coefficient γ x  associated with the direction of the optical axis, changes in conversion coefficient γ a  associated with the direction of rotation become very large, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases largely. In addition, an accurate auto-focusing operation cannot be performed. Therefore, it is more preferable to set the upper limit of the conditional formula (9) to be 20.0. 
     Conditional formula (9) defines an appropriate ratio of the amount a F  of rotation of the focusing lens unit on the focus cam corresponding to focusing from the infinity in-focus state to the closest in-focus state to the amount a Z  of rotation corresponding to zooming from the wide-angle end to the telephoto end. When the ratio is smaller than the lower limit of conditional formula (9), the slope (dx/da) of the focus cam considerably decreases at the closest corresponding position as compared to the slope at the infinity corresponding position, and they have a ratio: 
     
         0&lt;(dx/da).sub.R /(dx/da).sub.O &lt;&lt;1.0 
    
     For this reason, the rate of change of the conversion coefficient γ a  associated with the direction of rotation, which rate is expressed as a product of the rate of change (γ xR  /γ xO ) of the conversion coefficient γ x  associated with the direction of the optical axis and the slope ratio ((dx/da) R  /(dx/da) O ) of the focus cam, becomes excessively smaller than 1.0 (γ aR  /γ aO  &lt;&lt;1.0), and changes in γ a  become large. As a result, the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases. In addition, since changes in μ are large, an error obtained upon calculation of the lens driving amount Δa from the defocus amount ΔBf is large, and an accurate auto-focusing operation cannot be performed. Therefore, it is more preferable to set the lower limit of conditional formula (9) to -0.90. 
     On the contrary, when the ratio exceeds the upper limit of conditional formula (9), since the rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  becomes closer to 1.0, changes in γ a  become small, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. However, the slope (dx/da) O  of the focus cam at the infinity corresponding position at the telephoto end becomes large. Therefore, it is required to largely increase the diameter of a cam barrel corresponding to the focus cam in order to effect a smooth focusing operation by reducing the slope angle of the cam in the barrel mechanism. Thus, it becomes impossible to maintain the barrel to be small. 
     Conditional formula (10) is a condition associated with the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means, i.e., the number of divisions of the focus range. When γ aR  /γ aO  is smaller than the lower limit of conditional formula (10), the rate of change (γ aR  R/γ aO ) of the conversion coefficient γ a  becomes excessively smaller than 1.0, and changes in γ a  become large. As a result, since the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means increases, a storage means with a very large storage capacity is required, resulting in a large increase in cost. 
     On the contrary, when γ aR  /γ aO  exceeds the upper limit of conditional formula (10), since the rate of change (γ aR  /γ aO ) of the conversion coefficient γ a  becomes closer to 1.0, changes in γ a  become small, and the number of data of the conversion coefficient γ a  and the correction coefficient μ to be stored in the storage means can be reduced. However, since the conversion coefficient γ a  must have an extremely large value, the sensitivity (dBf/da) associated with the movement in the direction of rotation becomes very strict, and a change in imaging point caused by a slight error factor in the direction of rotation becomes large, thus disturbing accurate auto-focusing. 
     Furthermore, in order to attain accurate auto-focusing while lowering the sensitivity (dBf/da) associated with the movement in the direction of rotation, the upper and lower limits of conditional formula (10) are preferably set as follows: 
     
         0.10&lt;γ.sub.aR /γ.sub.aO &lt;0.50 
    
     In order to obtain a zoom lens which can perform auto-focusing more accurately, when the conversion coefficients K a  (=ΔBf/Δa) used when the focusing lens unit is located at the lens arrangements corresponding to the infinity in-focus state and the closest in-focus state are respectively represented by K aO  and K aR , the zoom lens preferably satisfies conditional formulas (11) and (12) below at least at the wide-angle end and the telephoto end: 
     
         0.35&lt;K.sub.aO /γ.sub.aO &lt;1.00                        (11) 
    
     
         1.00&lt;K.sub.aR /γ.sub.aR &lt;3.00                        (12) 
    
     Conditional formula (11) defines the rate of change of the conversion coefficient K a  in the direction of rotation upon a change in object position when the focusing lens unit corresponds to an arrangement in the infinity in-focus state. When the rate is smaller than the lower limit of conditional formula (11), the change in conversion coefficient K aO  upon a change in object position becomes too small as compared to the conversion coefficient y aO  as the sensitivity associated with the movement in the direction of rotation of the focusing lens unit at the infinity in-focus point. Therefore, for example, when the conversion coefficient K aO  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value on the basis of the relationship K aO  =γ aO  (1-ΔBf/μ aO ), a large error is produced in the value of the conversion coefficient K aO  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO , thus disturbing accurate auto-focusing. Therefore, it is more preferable to set the lower limit of conditional formula (11) to be 0.45. 
     On the contrary, when the rate exceeds the upper limit of conditional formula (11), the conversion coefficient K aO  changes from (K aO  /γ aO  &lt;1) to (K aO  /γ aO  &gt;1) upon a change in object position and, the sign of the correction coefficient μ aO  changes before and after (K aO  /γ aO  =1). As a result, when the conversion coefficient K aO  is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value, a large error is produced in the value of the conversion coefficient K aO  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO . 
     Conditional formula (12) defines the rate of change of the conversion coefficient K a  in the direction of rotation upon a change in object position when the focusing lens unit corresponds to an arrangement in the closest in-focus position. When the rate exceeds the upper limit of conditional formula (12), the change in conversion coefficient K aR  in the direction of rotation upon a change in object position becomes too large as compared to the conversion coefficient γ aR  as the sensitivity associated with the movement in the direction of rotation of the focusing lens unit at the closest in-focus point. Therefore, for example, when the conversion coefficient K aR  which changes upon a change in object position is expressed by a pair of a conversion coefficient γ aR  value and a correction coefficient μ aR  value on the basis of the relationship K aR  =γ aR  (1-ΔBf/μ aR ), a large error is produced in the value of the conversion coefficient K aR  calculated from the conversion coefficient γ aR  and the correction coefficient μ aR , thus disturbing accurate auto-focusing. Therefore, it is further preferable to set the upper limit of conditional formula (12) to be 2.50. 
     On the contrary, when the rate is smaller than the lower limit of conditional formula (12), the conversion coefficient K aO  changes from (K aO  /γ aO  &lt;1) to (K aO  /γ aO  &gt;1) upon a change in object position, and the sign of the correction coefficient μ aR  changes before and after (K aO  /γ aO  =1). As a result, when the conversion coefficient K aO  is expressed by a pair of a conversion coefficient γ aO  value and a correction coefficient μ aO  value, a large error is produced in the value of the conversion coefficient K aO  calculated from the conversion coefficient γ aO  and the correction coefficient μ aO . 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a view showing the movement loci for zooming of a zoom lens, the shapes of a focus cam and a zoom compensation cam of a second lens unit in the zoom lens according to the first embodiment of the present invention; 
     FIG. 2 is a view for explaining the shape of the focus cam in the zoom lens according to the first embodiment of the present invention. 
     FIG. 3 is a view showing the movement loci for zooming of a zoom lens, the shapes of a focus cam and a zoom compensation cam of a second lens unit in the zoom lens according to the fifth embodiment of the present invention; and 
     FIG. 4 is a view for explaining the shape of the focus cam in the zoom lens according to the fifth embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention will be described in detail hereinafter with reference to its embodiments. 
      First Embodiment! 
     A zoom lens of the first embodiment is a zoom lens which has a four-unit arrangement, i.e., positive, negative, positive, and positive lens units, and attains focusing by a negative second lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.95 m) to the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=194.0) is set to be -0.65. 
     Table 19 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the first embodiment. 
     The upper table in Table 19 summarizes the focal length data, and the principal point interval data of the respective lens units of the optical system corresponding to the first embodiment. 
     In this table, F1, F2, F3 and F4 are respectively the focal lengths of first, second, third and fourth lens units, and D1, D2, D3, and D4 are respectively the principal point interval between the first and second lens units, the principal point interval between the second and third lens units, the principal point interval between the third and fourth lens units, and the principal point interval between the fourth lens unit and a predetermined imaging plane in six zooming states (F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 85.0 (4-POS), 135.0 (5-POS), and 194.0 mm (6-POS)). 
     The middle table in Table 19 summarizes spline sample data when the shape (a curve g 2F  in FIG. 1B) of the focus cam in the second lens unit of the first embodiment, which is used for focusing, is expressed by the above-mentioned spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), and (4) correspond to the first, second, third, and fourth lens units, respectively. 
     Furthermore, the lower table in Table 19 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=28.8, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) using the focus cam of the first embodiment. In the lower table in Table 19, since the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=194.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.95 m) is set to be -6.5, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the first embodiment is -0.65. 
     
                                           TABLE 19__________________________________________________________________________First Embodiment F = 28.8-194.0 (Rotation Amount Ratio:a.sub.F /a.sub.Z = -0.65)__________________________________________________________________________Focal lengths and Principal Point Intervals of Lens Units of FirstEmbodiment    1-POS        2-POS            3-POS                4-POS                     5-POS                          6-POS__________________________________________________________________________  F 28.8000        35.0000            50.0000                85.0000                     135.0000                          194.0000F1  85.0000  D1    11.5063        15.6399            23.6055                35.1974                     44.4737                          50.4202F2  -14.7000  D2    25.8069        23.2088            19.3898                14.8844                     11.1724                          7.8560F3  43.5000  D3    8.0000        7.3138            5.7748                3.8464                     2.8540                          2.0039F4  61.0000  D4    59.7035        64.5166            73.5311                86.9840                     97.2356                          104.6041__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Correspondingto First Embodiment   ANGLE     (1)           (2)      (3)                       (4)__________________________________________________________________________1  -10.0000  .0000           .6790    .0000                       .00002  -6.5000   .0000           .5362    .0000                       .00003  -4.4106   .0000           .4194    .0000                       .00004  -3.2026   .0000           .3325    .0000                       .00005  -2.2078   .0000           .2472    .0000                       .00006  -1.3640   .0000           .1633    .0000                       .00007  -.7750    .0000           .0973    .0000                       .00008  .0000     .0000           .0000    .0000                       .00009  3.5000    .0000           -.6351   .0000                       .000010 5.5894    .0000           -1.3003  .0000                       .000011 6.7974    .0000           -1.8632  .0000                       .000012 7.7922    .0000           -2.4953  .0000                       .000013 8.6360    .0000           -3.2268  .0000                       .000014 9.2250    .0000           -3.9212  .0000                       .000015 10.0000   .0000           -5.3084  .0000                       .000016 10.5000   .0000           -6.7600  .0000                       .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofFirst EmbodimentRotation Amount Ratio: a.sub.F /a.sub.Z = -0.65)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal Length   ing Position                ing Distance                           Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m    -.77535.0 mm        .9456  3.00 m    -1.36450.0 mm        2.8915                 2.00 m    -2.20885.0 mm        5.9442                 1.50 m    -3.203135.0 mm       8.5249                 1.20 m    -4.411194.0 mm       10.0000                 0.95 m    -6.500Condition Corresponding Value (1)                 1.81Condition Corresponding Value (2)                 8.72Condition Corresponding Value (3)                -0.65Condition Corresponding Value (4)                 0.37 (wide-angle end)                 0.18 (telephoto end)Condition Corresponding Value (5)                 0.65 (wide-angle end)                 0.91 (telephoto end)Condition Corresponding Value (6)                 1.65 (wide-angle end)                 1.48 (telepboto end)__________________________________________________________________________ 
    
     Table 20 below summarizes the numerical value data of the cams of the focusing lens unit in the first embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 19. In this table, (ANGLE) is the angle of rotation of the rotatable lens barrel, (2) is the amount (mm) of movement, in the direction of the optical axis, of the second lens unit, and (F) is the focal length (mm) of the entire system in an infinity in-focus state corresponding to the amount (ANGLE) of rotation. 
     
                       TABLE 20______________________________________Cam Numerical Value Data of Focusing Lens Unit in FirstEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (2)       F        ANGLE  (2)   F______________________________________-6.5000  .5362     .0000-6.0000  .5114     .0000-5.5000  .4848     .0000-5.0000  .4561     .0000-4.5000  .4252     .0000-4.0000  .3917     .0000-3.5000  .3555     .0000-3.0000  .3162     .0000-2.5000  .2736     .0000-2.0000  .2276     .0000-1.5000  .1777     .0000-1.0000  .1234     .0000-.5000 .0641     .0000.0000  .0000     28.8000  .0000  .0000 28.8000.5000  -.0685    32.0242  .5000  .8742 32.02421.0000 -.1423    35.3710  1.0000 1.7614                                  35.37101.5000 -.2226    38.8814  1.5000 2.7015                                  38.88142.0000 -.3108    42.6132  2.0000 3.7069                                  42.61322.5000 -.4081    46.6255  2.5000 4.7830                                  46.62553.0000 -.5158    50.9755  3.0000 5.9325                                  50.97553.5000 -.6351    55.7062  3.5000 7.1512                                  55.70624.0000 -.7675    60.8343  4.0000 8.4253                                  60.83434.5000 -.9151    66.3964  4.5000 9.7444                                  66.39645.0000 -1.0802   72.4133  5.0000 11.0933                                  72.41335.5000 -1.2650   78.8805  5.5000 12.4518                                  78.88056.0000 -1.4722   85.7983  6.0000 13.8029                                  85.79836.5000 -1.7073   93.3264  6.5000 15.1571                                  93.32647.0000 -1.9772   101.7016 7.0000 16.5280                                  101.70167.5000 -2.2895   111.1184 7.5000 17.9167                                  111.11848.0000 -2.6536   121.7895 8.0000 19.3243                                  121.78958.5000 -3.0906   134.3107 8.5000 20.7909                                  134.31079.0000 -3.6350   149.5900 9.0000 22.3728                                  149.59009.5000 -4.3168   168.0630 9.5000 24.0881                                  168.063010.0000  -5.3084   194.0000 10.0000                            26.2620                                  194.0000______________________________________ 
    
     The left table in Table 20 summarizes the numerical value data of the focus cam of the first embodiment, and the right table in Table 20 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE =10.0) coincides with the movement locus (a curve g 2  in FIG. 1) of the second lens unit calculated using the paraxial data in the upper table in Table 19. 
     Therefore, the zoom compensation cam (a curve g 2H  in FIG. 1) is determined by subtracting the focus cam (the curve g 2  in FIG. 1) from the movement locus (the curve g 2  in FIG. 1) upon zooming of the second lens unit determined by the paraxial data in the upper table in Table 19. 
     FIG. 1 and FIG. 2 will be briefly described below. 
     FIG. 1 shows the paraxial arrangement and the movement loci upon zooming of the zoom lens according to the first embodiment, and FIG. 1 shows the shapes of the focus cam and the zoom compensation cam of the second lens unit of this embodiment. Referring to FIG. 1, G1, G2, G3, and G4 respectively represent the first, second, third, and fourth lens units, and g 1 , g 2 , g 3 , and g 4  respectively represent the movement loci upon zooming of the first, second, third, and fourth lens units. In addition, g 2F  and g 2H  respectively represent the shapes of the focus cam and the zoom compensation cam of the second lens unit. As described above, a shape obtained by synthesizing the focus cam g 2F  and the zoom compensation cam g 2H  of the second lens unit coincides with the movement locus g 2  of the second lens unit. 
     FIG. 2 is a view for explaining the shape of the focus cam  2F  of the first embodiment. Referring to FIG. 2, (F=28.8; R=un) and (F=28.8; R=0.95) respectively represent the in-focus positions at the infinity and the closest distance (R=0.95 m) at the wide-angle end, and coordinate positions (x; a) on the focus cam are respectively (x; a)=(0; 0) and (x; a)=(0.536; -6.5). On the other hand, (F=194; R=un) and (F=194; R=0.95) respectively represent the in-focus positions at the infinity and the closest distance (R=0.95 m) at the telephoto end, and coordinate positions (x; a) on the focus cam are respectively (x; a)=(-5.308; 10) and (x; a)=(-0.635; 3.5). 
     Upon zooming from the wide-angle end to the telephoto end, the second lens unit moves on the focus cam g 2F  from the coordinate position (0; 0) to the coordinate position (-5.308; 10) for an infinity object, and from the coordinate position (0.536; -6.5) to the coordinate position (-0.635; 3.5) for a closest distance object. Therefore, the second lens unit moves by 10.0 in the direction of rotation (the direction of an axis a) in both the cases. On the other hand, upon focusing from the infinity arrangement to the closest distance object, the second lens unit moves on the focus cam g 2F  from the coordinate position (0; 0) to the coordinate position (0.536, -6.5) at the wide-angle end, and from the coordinate position (-5.308; 10) to the coordinate position (-0.635; 3.5) at the telephoto end. Therefore, the second lens unit moves by -6.5 in the direction of rotation (the direction of the axis a) at these ends. In contrast to this, in the direction of the optical axis (the direction of an axis x), the second lens unit moves by 0.536 at the wide-angle end, and by 4.673 at the telephoto end. 
     Since the shape of the focus cam g 2F  is determined by interpolating the coordinates (F=28.8; R=0.95), (F=28.8; R=un), (F=194; R=0.95), and (F=194; R=un) by the spline function, the change in slope (dx/da) of the focus cam g 2F  becomes larger as the absolute value of the x-coordinate of (F=28.8; R=0.95) is smaller or as the absolute value of the x-coordinate of (F=194; R=un) is larger. More specifically, as the ratio (Δx TR  /Δx WR ) between the amounts ΔX XR  and ΔX WR  of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end or telephoto end is larger, the change in slope (dx/da) of the focus cam becomes larger. 
     Tables 21, 22, and 23 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=85.0), and the telephoto end (F=194.0) according to the first embodiment, respectively. In these tables, (R) on the left side is the photographing distance (m), (ANG) is the amount of rotation on the focus cam upon focusing to the respective photographing distances, and 1), 2), 3), and 4) on the right side respectively represent the first, second, third, and fourth lens units. Also, in these tables, the first table summarizes the amount DX (mm) of movement for focusing in the direction of the optical axis upon focusing to the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) (note that movement toward the object side is positive). The second table summarizes the imaging magnifications β K  of the respective lens units in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). The third table summarizes the conversion coefficient γ x  associated with the direction of the optical axis of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). Furthermore, the fourth table summarizes the slope (dx/da) of the focus cam at the positions, on the focus cam, corresponding to an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m), and the fifth table summarizes the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). 
     
                                           TABLE 21__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End (28.8 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000 4)                             .000R 10.000 ANG    -.374        1)          .000              2)                .048                    3)                      .000 4)                             .000R 5.000 ANG    -.775        1)          .000              2)                .097                    3)                      .000 4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                .163                    3)                      .000 4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                .247                    3)                      .000 4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                .332                    3)                      .000 4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                .419                    3)                      .000 4)                             .000R .950 ANG    -6.500        1)          .000              2)                .536                    3)                      .000 4)                             .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) in FirstEmbodimentR .000 ANG    .000        1)          .000              2)                -.250                    3)                      -63.758                           4)                             .021R 10.000 ANG    -.374        1)          -.009              2)                -.247                    3)                      -63.758                           4)                             .021R 5.000 ANG    -.775        1)          -.018              2)                -.243                    3)                      -63.758                           4)                             .021R 3.000 ANG    -1.364        1)          -.030              2)                -.239                    3)                      -63.758                           4)                             .021R 2.000 ANG    -2.208        1)          -.047              2)                -.233                    3)                      -63.758                           4)                             .021R 1.500 ANG    -3.203        1)          -.065              2)                -.227                    3)                      -63.758                           4)                             .021R 1.200 ANG    -4.411        1)          -.084              2)                -.221                    3)                      -63.758                           4)                             .021R .950 ANG    -6.500        1)          -.112              2)                -.214                    3)                      -63.758                           4)                             .021Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angleEnd (28.8 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                1.722                    3)                      .000 4)                             .000R 10.000 ANG    -.374        1)          .000              2)                1.725                    3)                      .000 4)                             .000R 5.000 ANG    -.775        1)          .000              2)                1.728                    3)                      .000 4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                1.732                    3)                      .000 4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                1.737                    3)                      .000 4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                1.741                    3)                      .000 4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                1.746                    3)                      .000 4)                             .000R .950 ANG    -6.500        1)          .000              2)                1.753                    3)                      .000 4)                             .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -.132                    3)                      .000 4)                             .000R 10.000 ANG    -.374        1)          .000              2)                -.126                    3)                      .000 4)                             .000R 5.000 ANG    -.775        1)          .000              2)                -.118                    3)                      .000 4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                -.106                    3)                      .000 4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                -.093                    3)                      .000 4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                -.079                    3)                      .000 4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                -.065                    3)                      .000 4)                             .000R .950 ANG    -6.500        1)          .0u0              2)                -.048                    3)                      .000 4)                             .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End(28.8 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -.228                    3)                      .000 4)                             .000R 10.000 ANG    -.374        1)          .000              2)                -.217                    3)                      .000 4)                             .000R 5.000 ANG    -.775        1)          .000              2)                -.204                    3)                      .000 4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                -.184                    3)                      .000 4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                -.161                    3)                      .000 4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                -.138                    3)                      .000 4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                -.114                    3)                      .000 4)                             .000R .950 ANG    -6.500        1)          .000              2)                -.084                    3)                      .000 4)                             .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.02, γ.sub.aR /γ.sub.a0 = 0.37 
    
     
                                           TABLE 22__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (85.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.367        1)          .000              2)                .152                    3)                      .000                          4)                            .000R 5.000 ANG    -.762        1)          .000              2)                .303                    3)                      .000                          4)                            .000R 3.000 ANG    -1.341        1)          .000              2)                .500                    3)                      .000                          4)                            .000R 2.000 ANG    -2.173        1)          .000              2)                .743                    3)                      .000                          4)                            .000R 1.500 ANG    -3.164        1)          .000              2)                .981                    3)                      .000                          4)                            .000R 1.200 ANG    -4.384        1)          .000              2)                1.215                    3)                      .000                          4)                            .000R .950 ANG    -6.500        1)          .000              2)                1.519                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Middle Position(85.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -.419                    3)                      5.606                          4)                            -.426R 10.000 ANG    -.367        1)          -.009              2)                -.408                    3)                      5.606                          4)                            -.426R 5.000 ANG    -.762        1)          -.018              2)                -.398                    3)                      5.606                          4)                            -.426R 3.000 ANG    -1.341        1)          -.031              2)                -.385                    3)                      5.606                          4)                            -.426R 2.000 ANG    -2.173        1)          -.048              2)                -.368                    3)                      5.606                          4)                            -.426R 1.500 ANG    -3.164        1)          -.067              2)                -.352                    3)                      5.606                          4)                            -.426R 1.200 ANG    -4.384        1)          -.087              2)                -.336                    3)                      5.606                          4)                            -.426R .950 ANG    -6.500        1)          -.117              2)                -.315                    3)                      5.606                          4)                            -.426Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at MiddlePosition (85.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                4.702                    3)                      .000                          4)                            .000R 10.000 ANG    -.367        1)          .000              2)                4.751                    3)                      .000                          4)                            .000R 5.000 ANG    -.762        1)          .000              2)                4.798                    3)                      .000                          4)                            .000R 3.000 ANG    -1.341        1)          .000              2)                4.858                    3)                      .000                          4)                            .000R 2.000 ANG    -2.173        1)          .000              2)                4.929                    3)                      .000                          4)                            .000R 1.500 ANG    -3.164        1)          .000              2)                4.995                    3)                      .000                          4)                            .000R 1.200 ANG    -4.384        1)          .000              2)                5.058                    3)                      .000                          4)                            .000R .950 ANG    -6.500        1)          .000              2)                5.135                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Middle Position (85.0 mm) in FirstEmbodimentR .000 ANG    .000        1)          .000              2)                -.434                    3)                      .000                          4)                            .000R 10.000 ANG    -.367        1)          .000              2)                -.398                    3)                      .000                          4)                            .000R 5.000 ANG    -.762        1)          .000              2)                -.364                    3)                      .000                          4)                            .000R 3.000 ANG    -1.341        1)          .000              2)                -.319                    3)                      .000                          4)                            .000R 2.000 ANG    -2.173        1)          .000              2)                -.266                    3)                      .000                          4)                            .000R 1.500 ANG    -3.164        1)          .000              2)                -.217                    3)                      .000                          4)                            .000R 1.200 ANG    -4.384        1)          .000              2)                -.170                    3)                      .000                          4)                            .000R .950 ANG    -6.500        1)          .000              2)                -.123                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Middle Position(85.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -2.040                    3)                      .000                          4)                            .000R 10.000 ANG    -.367        1)          .000              2)                -1.889                    3)                      .000                          4)                            .000R 5.000 ANG    -.762        1)          .000              2)                -1.745                    3)                      .000                          4)                            .000R 3.000 ANG    -1.341        1)          .000              2)                -1.551                    3)                      .000                          4)                            .000R 2.000 ANG    -2.173        1)          .000              2)                -1.310                    3)                      .000                          4)                            .000R 1.500 ANG    -3.164        1)          .000              2)                -1.082                    3)                      .000                          4)R 1.200 ANG    -4.384        1)          .000              2)                -.860                    3)                      .000                          4)                            .000R .950 ANG    -6.500        1)          .000              2)                -.629                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.09, γ.sub.aR /γ.sub.a0 = 0.31 
    
     
                                           TABLE 23__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End (194.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                .000 3)                       .000                           4)                             .000R 10.000 ANG    -.364        1)          .000              2)                .766 3)                       .000                           4)                             .000R 5.000 ANG    -.775        1)          .000              2)                1.387                     3)                       .000                           4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                2.082                     3)                       .000                           4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                2.813                     3)                       .000                           4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                3.445                     3)                       .000                           4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                4.008                     3)                       .000                           4)                             .000R .950 ANG    -6.500        1)          .000              2)                4.673                     3)                       .000                           4)                             .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (194.0mm) in FirstEmbodimentR .000 ANG    .000        1)          .000              2)                -.739                     3)                       4.318                           4)                             -.715R 10.000 ANG    -.364        1)          -.009              2)                -.687                     3)                       4.318                           4)                             -.715R 5.000 ANG    -.775        1)          -.018              2)                -.645                     3)                       4.318                           4)                             -.715R 3.000 ANG    -1.364        1)          -.031              2)                -.598                     3)                       4.318                           4)                             -.715R 2.000 ANG    -2.208        1)          -.049              2)                -.548                     3)                       4.318                           4)                             -.715R 1.500 ANG    -3.203        1)          -.068              2)                -.505                     3)                       4.318                           4)                             -.715R 1.200 ANG    -4.411        1)          -.089              2)                -.467                     3)                       4.318                           4)                             -.715R .950 ANG    -6.500        1)          -.121              2)                -.422                     3)                       4.318                           4)                             -.715Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at TelephotoEnd (194.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                4.318                     3)                       .000                           4)                             .000R 10.000 ANG    -.364        1)          .000              2)                5.026                     3)                       .000                           4)                             .000R 5.000 ANG    -.775        1)          .000              2)                5.563                     3)                       .000                           4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                6.122                     3)                       .000                           4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                6.665                     3)                       .000                           4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                7.097                     3)                       .000                           4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                7.451                     3)                       .000                           4)                             .000R .950 ANG    -6.500        1)          .000              2)                7.834                     3)                       .000                           4)                             .000Slope dx/da of Focus Cam at Telephoto End (194.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -2.494                     3)                       .000                           4)                             .000R 10.000 ANG    -.364        1)          .000              2)                -1.763                     3)                       .000                           4)                             .000R 5.000 ANG    -.775        1)          .000              2)                -1.332                     3)                       .000                           4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                -1.032                     3)                       .000                           4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                -.736                     3)                       .000                           4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                -.546                     3)                       .000                           4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                -.399                     3)                       .000                           4)                             .000R .950 ANG    -6.500        1)          .000              2)                -.251                     3)                       .000                           4)                             .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(194.0 mm) in First EmbodimentR .000 ANG    .000        1)          .000              2)                -10.769                     3)                       .000                           4)                             .000R 10.000 ANG    -.364        1)          .000              2)                -8.863                     3)                       .000                           4)                             .000R 5.000 ANG    -.775        1)          .000              2)                -7.412                     3)                       .000                           4)                             .000R 3.000 ANG    -1.364        1)          .000              2)                -6.321                     3)                       .000                           4)                             .000R 2.000 ANG    -2.208        1)          .000              2)                -4.908                     3)                       .000                           4)                             .000R 1.500 ANG    -3.203        1)          .000              2)                -3.877                     3)                       .000                           4)                             .000R 1.200 ANG    -4.411        1)          .000              2)                -2.971                     3)                       .000                           4)                             .000R .950 ANG    -6.500        1)          .000              2)                -1.968                     3)                       .000                           4)                             .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.81, γ.sub.aR /γ.sub.a0 = 0.18 
    
     As can be seen from Tables 21, 22, and 23, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to a case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-open No. 5-142475. 
     From Tables 21, 22, and 23, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.37 at the wide-angle end (F=28.8), ×0.31 at the middle position (F=85.0), and ×0.18 at the telephoto end (F=194.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the first embodiment is calculated using formula (a), and is compared with that a case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: when the rotation amount ratio (a F  /a Z ) is set to be 1.0. 
     
         N.sub.W &gt;14.6 N.sub.M &gt;14. 5 N.sub.T &gt;12.3 
    
     First Embodiment 
     
         N.sub.W &gt;5.5 N.sub.M &gt;6.5 N.sub.T &gt;9.3 
    
     Therefore, as can be understood from a comparison with the case in which the ratio of amounts of rotation (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N of divisions become small. 
     As described above, in the zoom lens of the first embodiment, since the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation becomes much smaller than that in a case in which the ratio (a F  /a Z ) of amounts of rotation is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open NO. 5-142475, the number of data of the conversion coefficient μ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 24, 25, and 26 summarize the calculation results of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=28.8), middle position (F=85.0), and telephoto end (F=194.0) according to the first embodiment. In these tables, (R) is the object distance (m), (ANG) is the amount of rotation for focusing from the infinity corresponding position on the focus cam, (r) is the conversion coefficient γ a  in the direction of rotation, (rs) is the conversion coefficient K a , (bf) is the defocus amount (mm), and (l) is the correction coefficient μ. Each table has a matrix structure, and eight rows in the vertical direction indicated by (POS) represent the object positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 mm), and four pairs (R, ANGLE) in the horizontal direction represent the lens arrangements of the focusing lens unit. 
     More specifically, the position of the focusing lens in the first pair in the upper two tables in each of Tables 24, 25, and 26, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Therefore, the third column (r) in the first table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on an infinity object, and the fourth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. Furthermore, the third column (bf) in the second table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the infinity corresponding position, and an object is located at an object distance in the second column, and the fourth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. 
     Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 15, 16, and 17, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.95, -6.5), and it indicates that this position corresponds to the closest in-focus (R=0.95 m) corresponding position. Therefore, the ninth column (r) in the third table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on a closest distance (R=0.95 m) object, and the tenth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.95 m) object to an in-focus state at the object distance in the second column. Furthermore, the ninth column (bf) in the fourth table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the closest corresponding position, and the object is located at an object distance in the second column, and the tenth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.95 m) object to an in-focus state at the object distance in the second column. 
     As described above, since the conversion coefficient in the direction of rotation is calculated by K a  =ΔBf/Δa (where Δa: the amount of rotation for focusing), and the correction coefficient μ is calculated by μ=ΔBf/(1-K a  /γ a ), the value of the conversion coefficient K a  (eight row, fourth column in first table: (-0.148) when the focusing lens unit is moved from an in-focus state on the infinity object to an in-focus state at the object distance (R=0.95 m) in Table 24 is calculated by K a  =0.96/-6.5=-0.148 using ΔBf=0.96 and Δa =-6.5. On the other hand, the value of the correction coefficient μ (eight row, fourth column in second table: 2.75) is calculated as μ=2.75 using ΔBf=0.96, K a  =-0.148, and γ a  =-0.228. 
     
                                           TABLE 24__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (28.8 mm) of First EmbodimentF = 28.8 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.374                  5.000                      -.775                          3.000                              -1.364POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.228      .000    -.222   -.215   -.2052  10.000  -.224          -.217              .000    -.210   -.1993  5.000   -.218   -.211                  -.204                      .000    -.1934  3.000   -.209   -.202   -.195                          -.184                              .0005  2.000   -.197   -.190   -.183   -.1736  1.500   -.184   -.177   -.171   -.1617  1.200   -.169   -.163   -.157   -.1498  .950    -.148   -.143   -.137   -.129__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              3.72                  -.17                      2.99                          -.28                              2.522  10.000  .08 4.18          .00 .00 -.08                      2.76                          -.20                              2.423  5.000  .17 3.79          .08 3.12                  .00 .00 -.11                              2.384  3.000  .28 3.39          .20 2.87                  .11 2.53                          .00 .005  2.000  .43 3.15          .35 2.77                  .26 2.54                          .15 2.426  1.500  .59 3.01          .50 2.72                  .41 2.53                          .30 2.407  1.200  .75 2.90          .66 2.65                  .57 2.48                          .45 2.338  .950  .96 2.75          .87 2.55                  .79 2.40                          .67 2.24__________________________________________________________________________(R, ANGLE) =  2.000      -2.208          1.500              -3.203                  1.200                      -4.411                          .950                              -6.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.191   -.176   -.161   -.1392  10.000  -.185   -.171   -.156   -.1343  5.000   -.179   -.166   -.151   -.1304  3.000   -.171   -.158   -.144   -.1245  2.000  -.161      .000    -.148   -.135   -.1156  1.500   -.150          -.138              .000    -.125   -.1077  1.200   -.138   -.126                  -.114                      .000    -.0978  .950    -.120   -.109   -.099                          -.084                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.42      2.28          -.56              2.02                  -.71                      1.72                          -.90                              1.392  10.000  -.34      2.25          -.48              2.00                  -.63                      1.70                          -.82                              1.383  5.000  -.26      2.24          -.40              1.99                  -.55                      1.69                          -.74                              1.374  3.000  -.14      2.24          -.29              1.97                  -.44                      1.66                          -.63                              1.365  2.000  .00 .00 -.15              1.91                  -.30                      1.62                          -.50                              1.346  1.500  .15 2.18          .00 .00 -.15                      1.57                          -.35                              1.327  1.200  .30 2.09          .15 1.81                  .00 .00 -.20                              1.328  .950  .51 2.00          .36 1.75                  .21 1.53                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.65, K.sub.aR /γ.sub.aR = 1.65 
    
     
                                           TABLE 25__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (85.0 mm) of First EmbodimentF = 85.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.367                  5.000                      -.762                          3.000                              -1.341POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -2.040      .000    -1.932  -1.830  -1.6952  10.000  -1.994          -1.888              .000    -1.789  -1.6563  5.000   -1.948  -1.845                  -1.745                      .000    -1.6134  3.000   -1.880  -1.779  -1.681                          -1.551                              .0005  2.000   -1.783  -1.685  -1.589  -1.4636  1.500   -1.673  -1.579  -1.487  -1.3677  1.200   -1.547  -1.458  -1.371  -1.2588  .950    -1.364  -1.283  -1.204  -1.103__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.71              30.55                  -1.39                      28.77                          -2.27                              24.402  10.000  .73 32.17          .00 .00 -.71                      28.19                          -1.61                              23.813  5.000  1.49      32.70          .73 32.06                  .00 .00 -.93                              23.154  3.000  2.52      32.07          1.73              30.01                  .97 26.33                          .00 .005  2.000  3.87      30.69          3.04              28.23                  2.24                      25.02                          1.22                              21.516  1.500  5.29      29.39          4.41              26.93                  3.57                      24.11                          2.49                              21.017  1.209  6.78      28.07          5.86              25.69                  4.96                      23.15                          3.83                              20.268  .950  8.86      26.72          7.87              24.52                  6.91                      22.28                          5.69                              19.69__________________________________________________________________________(R, ANGLE) =  2.000      -2.173          1.500              -3.164                  1.200                      -4.384                          .950                              -6.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -1.529  -1.365  -1.203  -.9952  10.000  -1.491  -1.330  -1.170  -.9663  5.000   -1.451  -1.292  -1.135  -.9364  3.000   -1.392  -1.238  -1.085  -.8935  2.000  -1.310      .000    -1.164  -1.017  -.8366  1.500   -1.222          -1.082              .000    -.943   -.7747  1.200   -1.122  -.989                  -.860                      .000    -.7098  .950    -.981   -.865   -.755                          -.629                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -3.32      19.86          -4.32              16.47                  -5.27                      13.23                          -6.46                              11.132  10.000  -2.69      19.45          -3.72              16.21                  -4.70                      13.04                          -5.92                              11.063  5.000  -2.05      19.03          -3.10              15.96                  -4.11                      12.86                          -5.37                              11.014  3.000  -1.16      18.54          -2.26              15.65                  -3.30                      12.62                          -4.61                              10.985  2.000  .00 .00 -1.15              15.21                  -2.25                      12.29                          -3.62                              11.006  1.500  1.21      18.15          .00 .00 -1.15                      11.96                          -2.58                              11.207  1.200  2.48      17.28          1.21              14.14                  .00 .00 -1.50                              11.768  .950  4.25      16.93          2.89              14.41                  1.60                      13.13                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.67, K.sub.aR /γ.sub.aR = 1.58 
    
     
                                           TABLE 26__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (194.0 mm) of First EmbodimentF = 194.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.364                  5.000                      -.775                          3.000                              -1.364POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -10.773      .000    -9.087  -7.713  -6.5252  10.000  -10.709          -8.864              .000    -7.498  -6.4023  5.000   -10.460 -8.614                  -7.414                      .000    -6.3824  3.000   -10.442 -8.650  -7.494                          -6.325                              .0005  2.000   -10.378 -8.548  -7.324  -6.0756  1.500   -10.286 -8.395  -7.128  -5.8747  1.200   -10.127 -8.171  -6.873  -5.6178  .950    -9.771  -7.736  -6.416  -5.177__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -3.31              131.41                  -5.98                      148.50                          -8.90                              281.642  10.000  3.90      656.67          .00 .00 -3.08                      273.04                          -6.40                              526.443  5.000  8.11      278.71          3.54              125.86                  .00 .00 -3.76                              419.924  3.000  14.24      463.41          8.65              358.25                  4.41                      -412.24                          .00 .005  2.000  22.91      625.46          15.76              442.35                  10.49                      858.42                          5.13                              129.636  1.500  32.94      727.96          23.83              450.74                  17.30                      448.54                          10.80                              151.327  1.200  44.67      745.50          33.06              423.26                  24.99                      342.21                          17.11                              152.808  .950  63.51      683.20          47.46              373.00                  36.73                      272.88                          26.59                              146.51__________________________________________________________________________(R, ANGLE) =  2.000      -2.208          1.500              -3.203                  1.200                      -4.411                          .950                              -6.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -5.384  -4.488  -3.743  -2.9132  10.000  -5.285  -4.402  -3.666  -2.8473  5.000   -5.228  -4.336  -3.600  -2.7854  3.000   -5.102  -4.219  -3.491  -2.6905  2.000  -4.907      .000    -4.060  -3.343  -2.5616  1.500   -4.738          -3.876              .000    -3.169  -2.4137  1.200   -4.493  -3.645                  -2.969                      .000    -2.2468  .950    -4.091  -3.288  -2.656                          -1.967                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -11.89      122.19          -14.37              90.97                  -16.51                      63.35                          -18.93                              39.372  10.000  -9.74      126.26          -12.49              92.01                  -14.83                      63.20                          -17.47                              39.043  5.000  -7.49      114.37          -10.53              88.60                  -13.09                      61.65                          -15.95                              38.324  3.000  -4.31      107.94          -7.76              87.53                  -10.64                      60.51                          -13.82                              37.565  2.000  .00 .00 -4.04              84.82                  -7.36                      58.59                          -10.99                              36.4l6  1.500  4.71      137.55          .00 .00 -3.83                      56.96                          -7.96                              35.097  1.200  9.90      117.35          4.40              73.94                  .00 .00 -4.69                              33.108  .950  17.56      105.60          10.84              71.42                  5.55                      52.59                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.91 K.sub.aR /γ.sub.aR = 1.48 
    
     As can be seen from Tables 24, 25, and 26 above, when a change in conversion coefficient K a  : (rs) (e.g., the fourth column in the first table) at a given lens arrangement (e.g., at the infinity in-focus arrangement) is considered, the rate of change becomes small as compared to the change in K a  (Tables 6, 7, and 8) in a case in which the ratio (a F  /a Z ) of amounts of rotation is set to be 1.0, as in the previously-discussed embodiment of Japanese Patent Application Laid-Open No. 5-142475 examined previously. 
     More specifically, the amount Δa of rotation for focusing in the first embodiment at the infinity object side becomes relatively smaller than that at the closest object side, as compared to a case in which the ratio (a F  /a Z ) of amounts of rotation is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. In fact, when the ratio between the amount of rotation for focusing upon focusing to the closest distance and the amount of rotation for focusing upon focusing to the object distance (R=5.0 m) is calculated in Tables 1 and 19, 4.807/10.0=0.481 when the ratio (a F  /a Z ) of amounts of rotation is set to be 1.0, while -0.775/-6.5=0.119 in the first embodiment. As described above, when the focus cam with the arrangement of the present invention is used, since the amount Δa of rotation for focusing becomes relatively smaller at the infinity object side, the conversion coefficient K a  becomes relatively large at the infinity object side, and consequently, the change in conversion coefficient K a  in the direction of rotation can be reduced as compared to the conventional system. 
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end (F=28.8), middle position (F=85.0), and telephoto end (F=194.0) in the case in which the ratio (a F  /a Z ) of amounts of rotation is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the first embodiment of the present invention is which said ratio (a F  /a Z ) is set to be -0.65 are as follows. 
     
         ______________________________________When the ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      5.05           0.33(F = 28.8)Middle Position      6.24           0.32(F = 85.0)Telephoto End      9.49           0.30(F = 194.0)First EmbodimentWide-angle End      0.65           1.65(F = 28.8)Middle Position      0.67           1.58(F = 85.0)Telephoto End      0.91           1.48(F = 194.0)______________________________________ 
    
     As described above, according to the present invention, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, and the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced, the value of the correction coefficient μ can be set to be large as compared to the defocus amount ΔBf, and at the same time, the change in correction coefficient μ can be decreased. 
     Therefore, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement large, an error in the conversion coefficient K a  calculated using γ a  and μ or in the actual lens driving amount Δa for focusing can be eliminated. 
     Next, in the case in which the ratio (a F  /a Z ) of amounts of rotation is set to 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the first embodiment of the present invention in which the ratio (a F  /a Z ) is set to -0.65, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end (F=28.8), middle position (F=85.0), and telephoto end (F=194.0) are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the ratio (a.sub.F /a.sub.Z) of amounts of rotation is set to 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -9.3%         -27.2%(F = 28.8)Middle Position      -11.7%         -28.3%(F = 85.0)Telephoto End      -13.7%         -28.9%(F = 194.0)First EmbodimentWide-angle End       -6.8%         -0.8%(F = 28.8)Middle Position      -6.1%          -0.5%(F = 85.0)Telephoto End      1.0%           -1.6%(F = 194.0)______________________________________ 
    
     As described above, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Next, an examination will be made as to whether not only accurate auto-focusing but also so-called manual focusing can be attained in the zoom lens of the first embodiment. 
     Table 27 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 19) of the first embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     The upper table in Table 27 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m). Note that the amounts of rotation for focusing, which have values for eliminating any displacement of the imaging point at the wide-angle end and the telephoto end, are selected. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) in the respective zooming states with the focal lengths (F=28.8, 35.0, 50.0, 85.0, 135.0, and 194.0 mm). In the lower table, (F) is the focal length (mm) of the entire system, (R) is the photographing distance (m), and (DX) is the amount (mm) of movement, in the direction of the optical axis, of each of the first, second, third, and fourth lens units in turn from the right side. Note that the amount of movement in the direction of the optical axis toward the object side is represented by a positive value. 
     
                                           TABLE 27__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and AmountDX (mm) of movement for focusing in First Embodiment__________________________________________________________________________   0.95 m       1.20 m             1.50 m                 2.00 m                       3.00 m                           5.00 m__________________________________________________________________________F 28.800 Bf   .000       .000  .000                 .000  .000                           .000F 35.000 Bf   .000       .001  .002                 .003  .006                           .006F 50.000 Bf   .000       .007  .016                 .015  .007                           .002F 85.000 Bf   .000       -.023 -.042                 -.046 -.035                           -.022F 135.000 Bf   .000       -.043 -.038                 -.042 -.027                           -.019F 194.000 Bf   .000       .000  .000                 .000  .000                           .000__________________________________________________________________________  ANGLE DA   -6.500        -4.411            -3.203                 -2.208 -1.364                            -.775__________________________________________________________________________F 28.800 DX   .000 .536            .000 .000                     R  0.95 mF 35.000 DX   .000 .622            .000 .000                     R  0.95 mF 50.000 DX   .000 .855            .000 .000                     R  0.95 mF 85.000 DX   .000 1.519            .000 .000                     R  0.95 mF 135.000 DX   .000 2.800            .000 .000                     R  0.95 mF 194.000 DX   .000 4.673            .000 .000                     R  0.95 mF 28.800 DX   .000 .419            .000 .000                     R  1.20 mF 35.000 DX   .000 .487            .000 .000                     R  1.20 mF 50.000 DX   .000 .671            .000 .000                     R  1.20 mF 85.000 DX   .000 1.220            .000 .000                     R  1.20 mF 135.000 DX   .000 2.315            .000 .000                     R  1.20 mF 194.000 DX   .000 4.008            .000 .000                     R  1.20 mF 28.800 DX   .000 .332            .000 .000                     R  1.50 mF 35.000 DX   .000 .386            .000 .000                     R  1.50 mF 50.000 DX   .000 .532            .000 .000                     R  1.50 mF 85.000 DX   .000 .989            .000 .000                     R  1.50 mF 135.000 DX   .000 1.918            .000 .000                     R  1.50 mF 194.000 DX   .000 3.445            .000 .000                     R  1.50 mF 28.800 DX   .000 .247            .000 .000                     R  2.00 mF 35.000 DX   .000 .286            .000 .000                     R  2.00 mF 50.000 DX   .000 .397            .000 .000                     R  2.00 mF 85.000 DX   .000 .752            .000 .000                     R  2.00 mF 135.000 DX   .000 1.497            .000 .000                     R  2.00 mF 194.000 DX   .000 2.813            .000 .000                     R  2.00 mF 28.800 DX   .000 .163            .000 .000                     R  3.00 mF 35.000 DX   .000 .188            .000 .000                     R  3.00 mF 50.000 DX   .000 .264            .000 .000                     R  3.00 mF 85.000 DX   .000 .507            .000 .000                     R  3.00 mF 135.000 DX   .000 1.042            .000 .000                     R  3.00 mF 194.000 DX   .000 2.082            .000 .000                     R  3.00 mF 28.800 DX   .000 .097            .000 .000                     R  5.00 mF 35.000 DX   .000 .111            .000 .000                     R  5.00 mF 50.000 DX   .000 .159            .000 .000                     R  5.00 mF 85.000 DX   .000 .307            .000 .000                     R  5.00 mF 135.000 DX   .000 .651            .000 .000                     R  5.00 mF 194.000 DX   .000 1.387            .000 .000                     R  5.00 m__________________________________________________________________________ 
    
     As can be seen from Table 27, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
      Second Embodiment! 
     The second embodiment is directed to a zoom lens which has a five-unit arrangement, i.e., positive, negative, positive, and positive lens units, and attains focusing by a negative second lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.8 m) to the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=131.0) is set to be -0.75. 
     Table 28 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the second embodiment. 
     The upper table in Table 28 summarizes the focal lengths and principal point interval data of the respective lens units of the optical system corresponding to the second embodiment in association with six zooming states (focal length F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0 (4-POS), 105.0 (5-POS) and 131.0 mm (6-POS)). 
     The middle table in Table 28 summarizes spline sample data when the shape of the focus cam in the second lens unit of the second embodiment, which is used for focusing, is expressed by a spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), (4), and (5) correspond to the first, second, third, fourth, and fifth lens units, respectively. 
     Furthermore, the lower table in Table 28 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=28.8, 35.0, 50.0, 70.0, 105.0, and 131.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) using the focus cam of the second embodiment. In this table, since the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=131.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.8 m) is set to be -7.5, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the second embodiment is -0.75. 
     
                                           TABLE 28__________________________________________________________________________Second Embodiment F = 28.8 to 131.0 (Rotation Amount Ratio: a.sub.F/a.sub.Z = -0.75)__________________________________________________________________________Focal lengths and Principal Point Intervals of Lens Units of SecondEmbodiment    1-POS        2-POS             3-POS                 4-POS                      5-POS                           6-POS__________________________________________________________________________  F 28.8000        35.0000             50.0000                 70.0000                      105.0000                           131.0000F1  77.2000  D1    10.3313        15.1893             23.5104                 30.7072                      38.5116                           42.3545F2  -14.7000  D2    27.6049        24.9667             20.7775                 17.3207                      13.3359                           11.0136F3  21.3000  D3    6.0146        7.0237             8.9018                 10.6018                      12.3379                           13.0291F4  -37.0000  D4    9.0353        8.0262             6.1481                 4.4481                      2.7120                           2.0208F5  60.0000  D5    50.6898        52.5061             55.8867                 58.9468                      62.0719                           63.3160__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Corresponding toSecondEmbodimentANGLE     (1)    (2) (3)    (4)                          (5)__________________________________________________________________________1    -10.0000     .0000  .8070                .0000  .0000                          .00002    -7.5000     .0000  .6835                .0000  .0000                          .00003    -5.1843     .0000  .5397                .0000  .0000                          .00004    -2.9523     .0000  .3538                .0000  .0000                          .00005    -2.0697     .0000  .2632                .0000  .0000                          .00006    -1.2981     .0000  .1740                .0000  .0000                          .00007    -.7436     .0000  .1038                .0000  .0000                          .00008    -.0000     .0000  .0000                .0000  .0000                          .00009    2.5000     .0000  -.4452                .0000  .0000                          .000010   4.8157     .0000  -1.0711                .0000  .0000                          .000011   7.0477     .0000  -2.0300                .0000  .0000                          .000012   7.9303     .0000  -2.5880                .0000  .0000                          .000013   8.7019     .0000  -3.2255                .0000  .0000                          .000014   9.2564     .0000  -3.8190                .0000  .0000                          .000015   10.0000     .0000  -4.9504                .0000  .0000                          .000016   11.0000     .0000  -7.4500                .0000  .0000                          .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofSecond EmbodimentRotation Amount Ratio: a.sub.F /a.sub.Z = -0.75)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal length   ing Position                ing Distance                           Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m    -.74435.0 mm        1.4190                 3.00 m    -1.29850.0 mm        3.9887                 2.00 m    -2.07070.0 mm        6.3656                 1.50 m    -2.952105.0 mm       8.9103                 1.00 m    -5.184131.0 mm       10.0000                 0.80 m    -7.500Condition Corresponding Value (1)                 1.76Condition Corresponding Value (2)                 6.59Condition Corresponding Value (3)                -0.75Condition Corresponding Value (4)                 0.38 (wide-angle end)                 0.19 (telephoto end)Condition Corresponding Value (5)                 0.65 (wide-angle end)                 0.79 (telephoto end)Condition Corresponding Value (6)                 1.59 (wide-angle end)                 1.52 (telephoto end)__________________________________________________________________________ 
    
     Table 29 below summarizes the numerical value data of the cams of the focusing lens unit in the second embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 28. Note that the meanings of the reference symbols in Table 29 are the same as those in the first embodiment. 
     
                       TABLE 29______________________________________Cam Numerical Value Data of Focusing Lens Unit in SecondEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (2)       F        ANGLE  (2)    F______________________________________-7.5000  .6835     .0000-7.0000  .6557     .0000-6.5000  .6263     .0000-6.0000  .5951     .0000-5.5000  .5618     .0000-5.0000  .5264     .0000-4.5000  .4885     .0000-4.0000  .4480     .0000-3.5000  .4047     .0000-3.0000  .3584     .0000-2.5000  .3088     .0000-2.0000  .2555     .0000-1.5000  .1983     .0000-1.0000  .1370     .0000-.5000 .0710     .0000.0000  .0000     28.8000  .0000  .0000  28.8000.5000  -.0759    30.8560  .5000  .2539  30.85601.0000 -.1573    33.0458  1.0000 -.4569 33.04581.5000 -.2454    35.3916  1.5000 -.6163 35.39162.0000 -.3410    37.9133  2.0000 -.7276 37.91332.5000 -.4452    40.6272  2.5000 -.8018 40.62723.0000 -.5589    43.5482  3.0000 -.8388 43.54823.5000 -.6834    46.6939  3.5000 -.8415 46.69394.0000 -.8198    50.0790  4.0000 -.8129 50.07904.5000 -.9694    53.7142  4.5000 -.7562 53.71425.0000 -1.1334   57.6059  5.0000 -.6746 57.60595.5000 -1.3144   61.7941  5.5000 -.5712 61.79416.0000 -1.5167   66.3669  6.0000 -.4479 66.36696.5000 -1.7450   71.4029  6.5000 -.3068 71.40297.0000 -2.0036   76.9473  7.0000 -.1503 76.94737.5000 -2.2981   83.0582  7.5000 .0186  83.05828.0000 -2.6387   89.9025  8.0000 .1978  89.90258.5000 -3.0406   97.6869  8.5000 .3859  97.68699.0000 -3.5275   106.7265 9.0000 .5812  106.72659.5000 -4.1299   117.3403 9.5000 .7803  117.340310.0000  -4.9504   131.0000 10.0000                            .9852  131.0000______________________________________ 
    
     The left table in Table 29 summarizes the numerical value data of the focus cam of the second embodiment, and the right table in Table 29 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincides with the movement locus of the second lens unit calculated using the paraxial data in the upper table in Table 28. 
     Tables 30, 31, and 32 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=70.0), and the telephoto end (F=131.0) according to the second embodiment, respectively. The arrangements of the respective tables and the meanings of the reference symbols are the same as those in the first embodiment. 
     
                                           TABLE 30__________________________________________________________________________Amount DX (min) of Movement for Focusing in Direction of Optical Axis atWide-angleEnd (28.8 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.360        1)          .000              2)                .052                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                .104                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                .174                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                .263                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                .354                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                .540                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                .684                    3)                      .000                          4)                            .000                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) in SecondEmbodimentR .000 ANG    .000        1)          .000              2)                -.282                    3)                      -.847                          4)                            10.073                                5)                                  .155R 10.000 ANG    -.360        1)          -.008              2)                -.278                    3)                      -.847                          4)                            10.073                                5)                                  .155R 5.000 ANG    -.744        1)          -.016              2)                -.275                    3)                      -.847                          4)                            10.073                                5)                                  .155R 3.000 ANG    -1.298        1)          -.027              2)                -.270                    3)                      -.847                          4)                            10.073                                5)                                  .155R 2.000 ANG    -2.070        1)          -.042              2)                -.264                    3)                      -.847                          4)                            10.073                                5)                                  .155R 1.500 ANG    -2.952        1)          -.059              2)                -.258                    3)                      -.847                          4)                            10.073                                5)                                  .155R 1.000 ANG    -5.184        1)          -.094              2)                -.245                    3)                      -.847                          4)                            10.073                                5)                                  .155R .800 ANG    -7.500        1)          -.125              2)                -.235                    3)                      -.847                          4)                            10.073                                5)                                  .155Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angle End(28.8 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                1.614                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.360        1)          .000              2)                1.617                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                1.621                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                1.625                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                1.631                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                1.636                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                1.648                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                1.656                    3)                      .000                          4)                            .000                                5)                                  .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in SecondEmbodimentR .000 ANG    .000        1)          .000              2)                -.147                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.360        1)          .000              2)                -.140                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                -.132                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                -.122                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                -.109                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                -.096                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                -.071                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.054                    3)                      .000                          4)                            .000                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End(28.8 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                -.237                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.360        1)          .000              2)                -.226                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                -.214                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                -.198                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                -.178                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                -.158                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                -.118                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.090                    3)                      .000                          4)                            .000                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.03, γ.sub.aR /γ.sub.a0 = 0.38 
    
     
                                           TABLE 31__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (70.0 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.357        1)          .000              2)                .160                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.740        1)          .000              2)                .318                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.295        1)          .000              2)                .523                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.068        1)          .000              2)                .774                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.945        1)          .000              2)                1.018                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.176        1)          .000              2)                1.491                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                1.835                    3)                      .000                          4)                            .000                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Middle Position (70.0mm) in SecondEmbodimentR .000 ANG    .000        1)          .000              2)                -.462                    3)                      1.216                          4)                            91.883                                5)                                  .018R 10.000 ANG    -.357        1)          -.008              2)                -.451                    3)                      1.216                          4)                            91.883                                5)                                  .018R 5.000 ANG    -.740        1)          -.016              2)                -.441                    3)                      1.216                          4)                            91.883                                5)                                  .018R 3.000 ANG    -1.295        1)          -.028              2)                -.427                    3)                      1.216                          4)                            91.883                                5)                                  .018R 2.000 ANG    -2.068        1)          -.043              2)                -.410                    3)                      1.216                          4)                            91.883                                5)                                  .018R 1.500 ANG    -2.945        1)          -.059              2)                -.393                    3)                      1.216                          4)                            91.883                                5)                                  .018R 1.000 ANG    -5.176        1)          -.096              2)                -.361                    3)                      1.216                          4)                            91.883                                5)                                  .018R .800 ANG    -7.500        1)          -.129              2)                -.338                    3)                      1.216                          4)                            91.883                                5)                                  .018Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Middle Position(70.0 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                3.024                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.357        1)          .000              2)                3.062                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.740        1)          .000              2)                3.099                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.295        1)          .000              2)                3.145                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.068        1)          .000              2)                3.200                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.945        1)          .000              2)                3.251                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.176        1)          .000              2)                3.345                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                3.408                    3)                      .000                          4)                            .000                                5)                                  .000Slope dx/da of Focus Cam at Middle Position (70.0 mm) in SecondEmbodimentR .000 ANG    .000        1)          .000              2)                -.469                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.357        1)          .000              2)                -.430                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.740        1)          .000              2)                -.393                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.295        1)          .000              2)                -.348                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.068        1)          .000              2)                -.302                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.945        1)          .000              2)                -.257                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.176        1)          .000              2)                -.174                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.125                    3)                      .000                          4)                            .000                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Middle Position (70.0mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                -1.419                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.357        1)          .000              2)                -1.317                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.740        1)          .000              2)                -1.217                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.295        1)          .000              2)                -1.096                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.068        1)          .000              2)                -.966                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.945        1)          .000              2)                -.835                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.176        1)          .000              2)                -.583                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.424                    3)                      .000                          4)                            .000                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.13, γ.sub.aR /γ.sub.a0 = 0.30 
    
     
                                           TABLE 32__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End(131.0 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.356        1)          .000              2)                .614                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                1.131                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                1.725                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                2.362                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                2.920                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                3.879                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                4.505                    3)                      .000                          4)                            .000                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Telepboto End (131.0mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                -.730                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 10.000 ANG    -.356        1)          -.008              2)                -.688                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 5.000 ANG    -.744        1)          -.016              2)                -.653                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 3.000 ANG    -1.298        1)          -.028              2)                -.612                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 2.000 ANG    -2.070        1)          -.043              2)                -.569                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 1.500 ANG    -2.952        1)          -.060              2)                -.531                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R 1.000 ANG    -5.184        1)          -.098              2)                -.466                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055R .800 ANG    -7.500        1)          -.131              2)                -.423                    3)                      -1.407                          4)                            -29.909                                5)                                  -.055Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Telephoto End(131.0 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                2.528                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.356        1)          .000              2)                2.848                    3)                      .000                          4)                            .000                                .5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                3.104                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                3.380                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                3.657                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                3.883                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                4.235                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                4.439                    3)                      .000                          4)                            .000                                5)                                  .000Slope dx/da of Focus Cam at Telephoto End (131.0 mm) in SecondEmbodimentR .000 ANG    .000        1)          .000              2)                -1.975                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.356        1)          .000              2)                -1.505                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                -1.200                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                -.953                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                -.719                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                -.557                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                -.332                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.218                    3)                      .000                          4)                            .000                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(131.0 mm) in Second EmbodimentR .000 ANG    .000        1)          .000              2)                -4.993                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.356        1)          .000              2)                -4.288                    3)                      .000                          4)                            .000                                5)                                  .000R 5.000 ANG    -.744        1)          .000              2)                -3.724                    3)                      .000                          4)                            .000                                5)                                  .000R 3.000 ANG    -1.298        1)          .000              2)                -3.221                    3)                      .000                          4)                            .000                                5)                                  .000R 2.000 ANG    -2.070        1)          .000              2)                -2.631                    3)                      .000                          4)                            .000                                5)                                  .000R 1.500 ANG    -2.952        1)          .000              2)                -2.164                    3)                      .000                          4)                            .000                                5)                                  .000R 1.000 ANG    -5.184        1)          .000              2)                -1.405                    3)                      .000                          4)                            .000                                5)                                  .000R .800 ANG    -7.500        1)          .000              2)                -.966                    3)                      .000                          4)                            .000                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.76, γ.sub.aR /γ.sub.a0 = 0.19 
    
     As can be seen from Tables 30, 31, and 32, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     From Tables 30, 31, and 32, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.38 at the wide-angle end (F=28.8), ×0.30 at the middle position (F=70.0), and ×0.19 at the telephoto end (F=131.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the second embodiment is calculated using formula (a), and is compared with that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: When the rotation amount ratio (a F  /a Z ) is set to be 1.0 
     
         N.sub.W &gt;13.0N.sub.M &gt;12. 6N.sub.T &gt;10.7 
    
     Second Embodiment 
     
         N.sub.W &gt;5.3N.sub.M &gt;6.6N.sub.T &gt;9.0 
    
     Therefore, it can be seen that the values of the numbers N of divisions become small, compared to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     As described above, in the second embodiment as well, since the rate of change of the conversion coefficient γ a  associated with the direction of rotation is smaller than that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient γ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 33, 34, and 35 summarize the calculation results of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=28.8), middle position (F=70.0), and telephoto end (F=131.0) according to the second embodiment. 
     The arrangements of the tables and reference symbols are the same as those in the first embodiment. The position of the focusing lens in the first pair in the upper two tables in each of Tables 33, 34, and 35, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 33, 34, and 35, i.e., in the ninth and 10th columns is (R, ANGLE)=(0.8, -7.5), and it indicates that this position corresponds to the closest in-focus (R=0.8 m) corresponding position. 
     
                                           TABLE 33__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (28.8 mm) of Second EmbodimentF = 28.8 mm__________________________________________________________________________(R, ANGLE ) =  .000      .000          10.000              -.360                  5.000                      -.744                          3.000                              -1.298POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.237      .000    -.231   -.224   -.2152  10.000  -.232          -.226              .000    -.219   -.2103  5.000   -.227   -.221                  -.214                      .000    -.2054  3.000   -.219   -.213   -.207                          -.198                              .0005  2.000   -.210   -.204   -.197   -.1896  1.500   -.199   -.193   -.187   -.1797  1.000   -.176   -.170   -.165   -.1578  .800    -.155   -.151   -.146   -.139__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              4.03                  -.17                      3.50                          -.28                              3.262  10.000  .08 4.39          .00 .00 -.08                      3.31                          -.20                              3.223  5.000  .17 4.15          .08 3.66                  .00 .00 -.11                              3.264  3.000  .28 3.91          .20 3.50                  .11 3.29                          .00 .005  2.000  .43 3.80          .35 3.50                  .26 3.36                          .15 3.276  1.500  .59 3.69          .50 3.44                  .41 3.30                          .30 3.137  1.000  .91 3.52          .82 3.32                  .73 3.18                          .61 3.008  .800  1.17      3.40          1.08              3.22                  .98 3.09                          .86 2.90__________________________________________________________________________(R, ANGLE) =  2.000      -2.070          1.500              -2.952                  1.000                      -5.184                          .800                              -7.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.203   .191    -.164   -.1432  10.000  -.198   .186    -.160   -.1393  5.000   -.193   .182    -.156   -.1364  3.000   -.187   .175    -.151   -.1315  2.000  -.178      .000    .167    -.143   -.1246  1.500   -.169          -.158              .000    -.135   -.1177  1.000   -.148   .138                  -.118                      .000    -.1028  .800    -.131   .122    -.103                          -.090                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.42      3.01          -.56              2.71                  -.85                      2.16                          -1.07                              1.802  10.000  -.34      2.99          -.48              2.69                  -.77                      2.14                          -1.00                              1.793  5.000  -.26      2.98          -.40              2.67                  -.69                      2.13                          -.92                              1.784  3.000  -.14      2.90          -.29              2.62                  -.59                      2.11                          -.81                              1.775  2.000  .00 .00 -.15              2.59                  -.45                      2.08                          -.67                              1.756  1.500  .15 2.79          .00 .00 -.30                      2.04                          -.53                              1.747  1.000  .46 2.73          .31 2.50                  .00 .00 -.24                              1.758  .800  .71 2.65          .55 2.43                  .24 1.97                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.65, K.sub.aR /γ.sub.aR = 1.59 
    
     
                                           TABLE 34__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (70.0 mm) of Second EmbodimentF = 70.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.357                  5.000                      -.740                          3.000                              -1.295POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -1.419      .000    -1.347  -1.277  -1.1892  10.000  -1.388          -1.317              .000    -1.248  -1.1613  5.000   -1.354  -1.285                  -1.217                      .000    -1.1334  3.000   -1.309  -1.241  -1.177                          -1.096                              .0005  2.000   -1.254  -1.190  -1.129  -1.0536  1.500   -1.197  -1.136  -1.078  -1.0057  1.000   -1.064  -1.008  -.955   -.8888  .800    -.947   .896    -.849   -.788__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.48              20.92                  -.95                      19.20                          -1.54                              18.172  10.000  .50 22.58          .00 .00 -.48                      19.08                          -1.09                              18.293  5.000  1.00      22.11          .49 20.04                  .00 .00 -.63                              18.594  3.000  1.70      21.91          1.16              20.27                  .65 19.45                          .00 .005  2.000  2.59      22.31          2.03              21.04                  1.50                      20.52                          .81 20.856  1.500  3.52      22.57          2.94              21.39                  2.38                      20.72                          1.66                              20.057  1.000  5.50      21.99          4.86              20.72                  4.24                      19.68                          3.45                              18.228  .800  7.10      21.34          6.40              20.06                  5.74                      18.93                          4.89                              17.38__________________________________________________________________________(R, ANGLE) =  2.000      -2.068          1.500              -2.945                  1.000                      -5.176                          .800                              -7.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -1.087  -.992   -.808   -.6752  10.000  -1.063  -.970   -.789   -.6583  5.000   -1.038  -.948   -.770   -.6424  3.000   -1.006  -.918   -.744   -.6195  2.000  -.966      .000    -.879   -.709   -.5886  1.500   -.919          -.834              .000    -.670   -.5567  1.000   -.809   -.731                  -.583                      .000    -.4848  .800    -.715   -.645   -.516                          -.424                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -2.25      17.89          -2.92              15.43                  -4.18                      10.86                          -5.06                              8.592  10.000  -1.82      18.16          -2.51              15.44                  -3.80                      10.78                          -4.70                              8.543  5.000  -1.38      18.52          -2.09              15.40                  -3.41                      10.68                          -4.34                              8.484  3.000  -.78      18.86          -1.51              15.14                  -2.89                      10.49                          -3.84                              8.395  2.000  .00 .00 -.77              14.43                  -2.20                      10.24                          -3.20                              8.286  1.500  .81 16.70          .00 .00 -1.50                      10.03                          -2.53                              8.197  1.000  2.51      15.43          1.63              13.16                  .00 .00 -1.13                              8.008  .800  3.88      14.96          2.94              12.98                  1.20                      10.34                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.67, K.sub.aR /γ.sub.aR = 1.59 
    
     
                                           TABLE 35__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (131.0 mm) of Second EmbodimentF = 131.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.356                  5.000                      -.744                          3.000                              -1.298__________________________________________________________________________POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -4.996      .000    -4.383  -3.869  -3.3742  10.000  -4.934          -4.290              .000    -3.78l  -3.3123  5.000   -4.829  -4.189                  -3.722                      .000    -3.2754  3.000   -4.757  -4.140  -3.694                          -3.222                              .0005  2.000   -4.660  -4.050  -3.597  -3.1136  1.500   -4.544  -3.936  -3.482  -3.0027  1.000   -4.248  -3.648  -3.201  -2.7398  .800    -3.951  -3.365  -2.934  -2.494__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -1.56              72.38                  -2.88                      72.51                          -4.38                              93.082  10.000  1.75      139.72          .00 .00 -1.47                      92.40                          -3.12                              112.403  5.000  3.59      107.18          1.63              68.79                  .00 .00 -1.82                              110.374  3.000  6.17      128.81          3.90              111.67                  2.05                      272.56                          .00 .005  2.000  9.65      143.36          6.94              123.86                  4.77                      142.31                          2.40                              71.106  1.500  13.42      148.20          10.22              123.71                  7.69                      119.21                          4.97                              72.577  1.000  22.02      147.09          17.61              117.64                  14.22                      101.69                          10.64                              70.938  .800  29.63      141.55          24.04              111.52                  19.82                      93.70                          15.47                              68.41__________________________________________________________________________(R, ANGLE) =  2.000      -2.070          1.500              -2.952                  1.000                      -5.184                          .800                              -7.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -2.885  -2.485  -1.854  -1.4722  10.000  -2.833  -2.439  -1.817  -1.4403  5.000   -2.793  -2.399  -1.781  -1.4104  3.000   -2.729  -2.338  -1.729  -1.3655  2.000  -2.631      .000    -2.252  -1.659  -1.3066  1.500   -2.533          -2.163              .000    -1.583  -1.2427  1.000   -2.294  -1.944                  -1.405                      .000    -1.0988  .800    -2.076  -1.749  -1.258                          -.966                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -5.97      61.81          -7.34              49.17                  -9.61                      30.11                          -11.04                              21.072  10.000  -4.86      63.05          -6.33              49.46                  -8.77                      29.96                          -10.29                              20.943  5.000  -3.70      59.96          -5.30              48.38                  -7.91                      29.57                          -9.52                              20.734  3.000  -2.11      56.51          -3.87              47.66                  -6.72                      29.14                          -8.47                              20.475  2.000  .00 .00 -1.99              47.94                  -5.17                      28.63                          -7.09                              20.146  1.500  2.24      59.82          .00 .00 -3.53                      27.94                          -5.65                              19.757  1.000  7.14      55.80          4.34              42.89                  .00 .00 -2.54                              18.548  .800  11.27      53.40          7.96              41.63                  2.91                      27.69                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.79, K.sub.aR /γ.sub.aR = 1.52 
    
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end, middle position, and telephoto end in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the second embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.75 are as follows. 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      4.18           0.36(F = 28.8)Middle Position      5.00           0.36(F = 70.0)Telephoto End      6.51           0.35(F = 131.0)Second EmbodimentWide-angle End      0.65           1.59(F = 28.8)Middle Position      0.67           1.59(F = 70.0)Telephoto End      0.79           1.52(F = 131.0)______________________________________ 
    
     As described above, in the third embodiment as well, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced. For this reason, an error of the conversion coefficient K a  calculated based on γ a  and μ or an error from the actual lens driving amount Δa obtained when only one pair of a conversion coefficient γ a  value and a correction coefficient μ value are set can be reduced. 
     Next, in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the second embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.75, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -8.1%         -21.4%(F = 28.8)Middle Position      -13.3%         -21.9%(F = 70.0)Telephoto End      -15.8%         -22.7%(F = 131.0)Second EmbodimentWide-angle End       -4.9%         -1.2%(F = 28.8)Middle Position      -2.1%          -0.7%(F = 70.0)Telephoto End      -0.3%          -1.0%(F = 131.0)______________________________________ 
    
     As described above, in the second embodiment as well, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Table 36 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 28) of the second embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     Note that the arrangement of the table and reference symbols are the same as those in the first embodiment. The upper table in Table 36 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 70.0, 105.0, and 131.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and photographing distances. 
     
                                           TABLE 36__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Second Embodiment__________________________________________________________________________   0.80 m       1.00 m             1.50 m                 2.00 m                       3.00 m                           5.00 m__________________________________________________________________________F 28.800 Bf   .000       .000  .000                 .000  .000                           ta .000F 35.000 Bf   .000       .000  .002                 .003  .003                           .002F 50.000 Bf   .000       .001  .001                 -.002 -.004                           -.003F 70.000 Bf   .000       -.005 -.006                 -.002 -.003                           -.005F 105.000 Bf   .000       -.011 -.020                 -.017 -.018                           -.016F 131.000 Bf   .000       .000  .000                 .000  .000                           .000__________________________________________________________________________ANGLE DA   -7.500       -5.184           -2.952                -2.070                    -1.298 -.744__________________________________________________________________________F 28.800 DX   .000       .684           .000 .000                    .000 R 0.80 mF 35.000 DX   .000       .831           .000 .000                    .000 R 0.80 mF 50.000 DX   .000       1.222           .000 .000                    .000 R 0.80 mF 70.000 DX   .000       1.835           .000 .000                    .000 R 0.80 mF 105.000 DX   .000       3.204           .000 .000                    .000 R 0.80 mF 131.000 DX   .000       4.505           .000 .000                    .000 r 0.80 mF 28.800 DX   .000       .540           .000 .000                    .000 R 1.00 mF 35.000 DX   .000       .659           .000 .000                    .000 R 1.00 mF 50.000 DX   .000       .978           .000 .000                    .000 R 1.00 mF 70.000 DX   .000       1.492           .000 .000                    .000 R 1.00 mF 105.000 DX   .000       2.689           .000 .000                    .000 R 1.00 mF 131.000 DX   .000       3.879           .000 .000                    .000 R 1.00 mF 28.800 DX   .000       .354           .000 .000                    .000 R 1.50 mF 35.000 DX   .000       .433           .000 .000                    .000 R 1.50 mF 50.000 DX   .000       .653           .000 .000                    .000 R 1.50 mF 70.000 DX   .000       1.020           .000 .000                    .000 R 1.50 mF 105.000 DX   .000       1.934           .000 .000                    .000 R 1.50 mF 131.000 DX   .000       2.920           .000 .000                    .000 R 1.50 mF 28.800 DX   .000       .263           .000 .000                    .000 R 2.00 mF 35.000 DX   .000       .322           .000 .000                    .000 R 2.00 mF 50.000 DX   .000       .492           .000 .000                    .000 R 2.00 mF 70.000 DX   .000       .774           .000 .000                    .000 R 2.00 mF 105.000 DX   .000       1.515           .000 .000                    .000 R 2.00 mF 131.000 DX   .000       2.362           .000 .000                    .000 R 2.00 mF 28.800 DX   .000       .174           .000 .000                    .000 R 3.00 mF 35.000 DX   .000       .213           .000 .000                    .000 R 3.00 mF 50.000 DX   .000       .329           .000 .000                    .000 R 3.00 mF 70.000 DX   .000       .524           .000 .000                    .000 R 3.00 mF 105.000 DX   .000       1.063           .000 .000                    .000 R 3.00 mF 131.000 DX   .000       1.725           .000 .000                    .000 R 3.00 mF 28.800 DX   .000       .104           .000 .000                    .000 R 5.00 mF 35.000 DX   .000       .127           .000 .000                    .000 R 5.00 mF 50.000 DX   .000       .198           .000 .000                    .000 R 5.00 mF 70.000 DX   .000       .319           .000 .000                    .000 R 5.00 mF 105.000 DX   .000       .668           .000 .000                    .000 R 5.00 mF 131.000 DX   .000       1.131           .000 .000                    .000 R 5.00 m__________________________________________________________________________ 
    
     As can be seen from Table 36, in the zoom lens of the second embodiment, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
      Third Embodiment! 
     The third embodiment is directed to a zoom lens which has a four-unit arrangement, i.e., positive, negative, positive, and positive lens units, and attains focusing by a negative second lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.8 m) to the amount of rotation for zooming from the wide-angle end (F=36.0) to the telephoto end (F=131.0) is set to be -0.85. 
     Table 37 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the third embodiment. 
     The upper table in Table 37 summarizes the focal lengths and principal point interval data of the respective lens units of the optical system corresponding to the third embodiment in association with six zooming states (focal length F=36.0 (1-POS), 50.0 (2-POS), 70.0 (3-POS), 85.0 (4-POS), 105.0 (5-POS), and 131.0 mm (6-POS)). 
     The middle table in Table 37 summarizes spline sample data when the shape of the focus cam in the second lens unit of the third embodiment, which is used for focusing, is expressed by a spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), and (4) correspond to the first, second, third, and fourth lens units, respectively. 
     Furthermore, the lower table in Table 37 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=36.0, 50.0, 70.0, 85.0, 105.0, and 131.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) using the focus cam of the third embodiment. In this table, since the amount of rotation for zooming from the wide-angle end (F=36.0) to the telephoto end (F=131.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.8 m) is set to be -8.5, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the third embodiment is -0.85. 
     
                                           TABLE 37__________________________________________________________________________Third Embodiment F = 36.0 to 131.0 (Rotation Amount Ratio:a.sub.F /a.sub.Z = -0.85)__________________________________________________________________________Focal lengths and Principal Point Intervals of Lens Units of ThirdEmbodiment    1-POS        2-POS             3-POS                 4-POS                      5-POS                           6-POS__________________________________________________________________________  F 36.0000        50.0000             70.0000                 85.0000                      105.0000                           131.0000F1  73.0000  D1    10.4075        17.8050             24.9191                 28.6662                      32.4300                           36.0004F2  -16.6000  D2    25.6151        21.3295             17.3824                 15.1421                      12.6290                           9.7969F3  42.0000  D3    10.0000        9.2923             8.2560                 7.6919                      7.2951                           7.2634F4  80.0000  D4    63.8473        70.6899             77.4519                 81.1930                      85.0439                           88.8003__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Correspondingto Third Embodiment   ANGLE     (1)           (2)       (3)                        (4)__________________________________________________________________________1  -10.0000  .0000           1.1480    .0000                        .00002  -8.5000   .0000           1.0414    .0000                        .00003  -5.9359   .0000           .8252     .0000                        .00004  -3.4109   .0000           .5436     .0000                        .00005  -2.3987   .0000           .4054     .0000                        .00006  -1.5068   .0000           .2688     .0000                        .00007  -.8645    .0000           .1606     .0000                        .00008  .0000     .0000           .0000     .0000                        .00009  1.5000    .0000           -.3253    .0000                        .000010 4.0641    .0000           -1.0736   .0000                        .000011 6.5891    .0000           -2.2211   .0000                        .000012 7.6013    .0000           -2.8951   .0000                        .000013 8.4932    .0000           -3.6785   .0000                        .000014 9.1355    .0000           -4.4302   .0000                        .000015 10.0000   .0000           -6.0011   .0000                        .000016 11.0000   .0000           -9.5000   .0000                        .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofThird EmbodimentRotation Amount Ratio: a.sub.F /a.sub.Z = -0.85)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal Length   ing Position                ing Distance                           Focusing__________________________________________________________________________36.0 mm        .0000  5.00 m    .86550.0 mm        2.9527                 3.00 m    -1.50770.0 mm        5.9439                 2.00 m    -2.39985.0 mm        7.4823                 1.50 m    -3.411105.0 mm       8.9096                 1.00 m    -5.936131.0 mm       10.0000                 0.80 m    -8.500Condition Corresponding Value (1)                 2.30Condition Corresponding Value (2)                 5.45Condition Corresponding Value (3)                -0.85Condition Corresponding Value (4)                 0.40 (wide-angle end)                 0.21 (telephoto end)Condition Corresponding Value (5)                 0.68 (wide-angle end)                 0.80 (telephoto end)Condition Corresponding Value (6)                 1.52 (wide-angle end)                 1.43 (telephoto end)__________________________________________________________________________ 
    
     Table 38 below summarizes the numerical value data of the cams of the focusing lens unit in the third embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 37. Note that the meanings of the reference symbols in Table 38 are the same as those in the first embodiment. 
     
                       TABLE 38______________________________________Cam Numerical Value Data of Focusing Lens Unit in ThirdEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (2)       F        ANGLE  (2)    F______________________________________-8.5000  1.0414    .0000-8.0000  1.0035    .0000-7.5000  .9637     .0000-7.0000  .9219     .0000-6.5000  .8779     .0000-6.0000  .8314     .0000-5.5000  .7823     .0000-5.0000  .7303     .0000-4.5000  .6752     .0000-4.0000  .6168     .0000-3.5000  .5550     .0000-3.0000  .4895     .0000-2.5000  .4200     .0000-2.0000  .3462     .0000-1.5000  .2677     .0000-1.0000  .1842     .0000-.5000 .0951     .0000.0000  .0000     36.0000  .0000  .0000  36.0000.5000  -.1013    38.1000  .5000  .4231  38.10001.0000 -.2095    40.2980  1.0000 .8495  40.29801.5000 -.3253    42.6028  1.5000 1.2799 42.60282.0000 -.4495    45.0229  2.0000 1.7151 45.02292.5000 -.5832    47.5713  2.5000 2.1565 47.57133.0000 -.7273    50.2608  3.0000 2.6053 50.26083.5000 -.8829    53.1017  3.5000 3.0625 53.10174.0000 -1.0511   56.1044  4.0000 3.5285 56.10444.5000 -1.2331   59.2847  4.5000 4.0048 59.28475.0000 -1.4322   62.6993  5.0000 4.4979 62.69935.5000 -1.6521   66.4118  5.5000 5.0141 66.41186.0000 -1.8965   70.4744  6.0000 5.5582 70.47446.5000 -2.1693   74.9275  6.5000 6.1332 74.92757.0000 -2.4745   79.8072  7.0000 6.7425 79.80727.5000 -2.8196   85.2003  7.5000 7.3952 85.20038.0000 -3.2152   91.2332  8.0000 8.1044 91.23328.5000 -3.6854   98.2632  8.5000 8.9050 98.26329.0000 -4.2566   106.6077 9.0000 9.8265 106.60779.5000 -4.9586   116.5539 9.5000 10.8970                                   116.553910.0000  -6.0011   131.0000 10.0000                            12.3994                                   131.0000______________________________________ 
    
     The left table in Table 38 summarizes the numerical value data of the focus cam of the third embodiment, and the right table in Table 38 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincides with the movement locus of the second lens unit calculated using the paraxial data in the upper table in Table 37. 
     Tables 39, 40, and 41 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=36.0), the middle position (F=70.0), and the telephoto end (F=131.0) according to the third embodiment, respectively. The arrangements of the respective tables and the meanings of the reference symbols are the same as those in the first embodiment. 
     
                                           TABLE 39__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End (36.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.419        1)          .000              2)                .080                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                .161                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                .269                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                .405                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                .544                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                .825                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                1.041                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (36.0mm) in ThirdEmbodimentR .000 ANG    .000        1)          .000              2)                -.361                    3)                      -6.767                          4)                            .202R 10.000 ANG    -.419        1)          -.007              2)                -.356                    3)                      -6.767                          4)                            .202R 5.000 ANG    -.865        1)          -.015              2)                -.351                    3)                      -6.767                          4)                            .202R 3.000 ANG    -1.507        1)          -.026              2)                -.345                    3)                      -6.767                          4)                            .202R 2.000 ANG    -2.399        1)          -.040              2)                -.337                    3)                      -6.767                          4)                            .202R 1.500 ANG    -3.411        1)          -.055              2)                -.328                    3)                      -6.767                          4)                            .202R 1.000 ANG    -5.936        1)          -.089              2)                -.311                    3)                      -6.767                          4)                            .202R .800 ANG    -8.500        1)          -.118              2)                -.298                    3)                      -6.767                          4)                            .202Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis atWide-angle End (36.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                1.624                    3)                      .000                          4)                            .000R 10.000 ANG    -.419        1)          .000              2)                1.630                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                1.637                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                1.645                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                1.655                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                1.666                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                1.686                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                1.701                    3)                      .000                          4)                            .000Slope dx/da of Focus Cain at Wide-angle End (36.0 mm) in ThirdEmbodimentR .000 ANG    .000        1)          .000              2)                -.196                    3)                      .000                          4)                            .000R 10.000 ANG    -.419        1)          .000              2)                -.186                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                -.176                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                -.162                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                -.145                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                -.129                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                -.096                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.074                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angleEnd (36.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                -.319                    3)                      .090                          4)                            .000R 10.000 ANG    -.419        1)          .000              2)                -.303                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                -.287                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                -.266                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                -.240                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                -.214                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                -.162                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.126                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.05, γ.sub.aR /γ.sub.a0 = 0.40 
    
     
                                           TABLE 40__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddle Position (70.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.416        1)          .000              2)                .203                    3)                      .000                          4)                            .000R 5.000 ANG    -.862        1)          .000              2)                .401                    3)                      .000                          4)                            .000R 3.000 ANG    -1.508        1)          .000              2)                .659                    3)                      .000                          4)                            .000R 2.000 ANG    -2.406        1)          .000              2)                .972                    3)                      .000                          4)                            .000R 1.500 ANG    -3.419        1)          .000              2)                1.278                    3)                      .000                          4)                            .000R 1.000 ANG    -5.942        1)          .000              2)                1.867                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                2.296                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Middle Position (70.0mm) in ThirdEmbodimentR .000 ANG    .000        1)          .000              2)                -.527                    3)                      -57.094                          4)                            .032R 10.000 ANG    -.416        1)          -.007              2)                -.515                    3)                      -57.094                          4)                            .032R 5.000 ANG    -.862        1)          -.015              2)                -.503                    3)                      -57.094                          4)                            .032R 3.000 ANG    -1.508        1)          -.026              2)                -.488                    3)                      -57.094                          4)                            .032R 2.000 ANG    -2.406        1)          -.041              2)                -.469                    3)                      -57.094                          4)                            .032R 1.500 ANG    -3.419        1)          -.056              2)                -.450                    3)                      -57.094                          4)                            .032R 1.000 ANG    -5.942        1)          -.091              2)                -.415                    3)                      -57.094                          4)                            .032R .800 ANG    -8.500        1)          -.122              2)                -.389                    3)                      -57.094                          4)                            .032Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at MiddlePosition (70.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                2.387                    3)                      .000                          4)                            .000R 10.000 ANG    -.416        1)          .000              2)                2.430                    3)                      .000                          4)                            .000R 5.000 ANG    -.862        1)          .000              2)                2.470                    3)                      .000                          4)                            .000R 3.000 ANG    -1.508        1)          .000              2)                2.521                    3)                      .000                          4)                            .000R 2.000 ANG    -2.406        1)          .000              2)                2.580                    3)                      .000                          4)                            .000R 1.500 ANG    -3.419        1)          .000              2)                2.636                    3)                      .000                          4)                            .000R 1.000 ANG    -5.942        1)          .000              2)                2.738                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                2.807                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Middle Position (70.0 mm) in ThirdEmbodimentR .000 ANG    .000        1)          .000              2)                -.510                    3)                      .000                          4)                            .000R 10.000 ANG    -.416        1)          .000              2)                -.466                    3)                      .000                          4)                            .000R 5.000 ANG    -.862        1)          .000              2)                -.425                    3)                      .000                          4)                            .000R 3.000 ANG    -1.508        1)          .000              2)                -.376                    3)                      .000                          4)                            .000R 2.000 ANG    -2.406        1)          .000              2)                -.325                    3)                      .000                          4)                            .000R 1.500 ANG    -3.419        1)          .000              2)                -.278                    3)                      .000                          4)                            .000R 1.000 ANG    -5.942        1)          .000              2)                -.196                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.142                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at MiddlePosition (70.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                -1.217                    3)                      .000                          4)                            .000R 10.000 ANG    -.416        1)          .000              2)                -1.132                    3)                      .000                          4)                            .000R 5.000 ANG    -.862        1)          .000              2)                -1.049                    3)                      .000                          4)                            .000R 3.000 ANG    -1.508        1)          .000              2)                -.947                    3)                      .000                          4)                            .000R 2.000 ANG    -2.406        1)          .000              2)                -.840                    3)                      .000                          4)                            .000R 1.500 ANG    -3.419        1)          .000              2)                -.734                    3)                      .000                          4)                            .000R 1.000 ANG    -5.942        1)          .000              2)                -.537                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.399                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.18, γ.sub.aR /γ.sub.a0 = 0.33 
    
     
                                           TABLE 41__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End (131.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.407        1)          .000              2)                .884                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                1.571                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                2.323                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                3.106                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                3.780                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                4.928                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                5.676                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (131.0mm) in ThirdEmbodimentR .000 ANG    .000        1)          .000              2)                -.814                    3)                      20.047                          4)                            -.110R 10.000 ANG    -.407        1)          -.007              2)                -.760                    3)                      20.047                          4)                            -.110R 5.000 ANG    -.865        1)          -.015              2)                -.719                    3)                      20.047                          4)                            -.110R 3.000 ANG    -1.507        1)          -.026              2)                -.674                    3)                      20.047                          4)                            -.110R 2.000 ANG    -2.399        1)          -.041              2)                -.627                    3)                      20.047                          4)                            -.110R 1.500 ANG    -3.411        1)          -.057              2)                -.586                    3)                      20.047                          4)                            -.110R 1.000 ANG    -5.936        1)          -.093              2)                -.517                    3)                      20.047                          4)                            -.110R .800 ANG    -8.500        1)          -.125              2)                -.472                    3)                      20.047                          4)                            -.110Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis atTelephoto End (131.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                1.643                    3)                      .000                          4)                            .000R 10.000 ANG    -.407        1)          .000              2)                2.051                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                2.348                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                2.655                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                2.954                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                3.193                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                3.564                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                3.781                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Telephoto End (131.0 mm) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                -2.632                    3)                      .000                          4)                            .000R 10.000 ANG    -.407        1)          .000              2)                -1.779                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                -1.312                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                -1.033                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                -.756                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                -.588                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                -.353                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.240                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at TelephotoEnd (131.0 nnn) in Third EmbodimentR .000 ANG    .000        1)          .000              2)                -4.324                    3)                      .000                          4)                            .000R 10.000 ANG    -.407        1)          .000              2)                -3.647                    3)                      .000                          4)                            .000R 5.000 ANG    -.865        1)          .000              2)                -3.081                    3)                      .000                          4)                            .000R 3.000 ANG    -1.507        1)          .000              2)                -2.742                    3)                      .000                          4)                            .000R 2.000 ANG    -2.399        1)          .000              2)                -2.233                    3)                      .000                          4)                            .000R 1.500 ANG    -3.411        1)          .000              2)                -1.877                    3)                      .000                          4)                            .000R 1.000 ANG    -5.936        1)          .000              2)                -1.258                    3)                      .000                          4)                            .000R .800 ANG    -8.500        1)          .000              2)                -.906                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 2.30, γ.sub.aR /γ.sub.a0 = 0.21 
    
     As can be seen from Tables 39, 40, and 41, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. From Tables 39, 40, and 41, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.40 at the wide-angle end (F=36.0), ×0.33 at the middle position (F=70.0), and ×0.21 at the telephoto end (F=131.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the fourth embodiment is calculated using formula (a), and is compared with that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: 
     When the rotation amount ratio (a F  /a Z ) is set to be 1.0 
     
         N.sub.W &gt;12.4 N.sub.M &gt;12.6 N.sub.T &gt;10.8 
    
     Third Embodiment 
     
         N.sub.W &gt;5.1 N.sub.M &gt;6.1 N.sub.T &gt;8.6 
    
     Therefore, it can be seen that the numbers of divisions become small, compared to those in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     As described above, in the third embodiment as well, since the rate of change of the conversion coefficient γ a  associated with the direction of rotation is smaller than that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, like in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient γ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 42, 43, and 44 summarize the calculation results of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=36.0), middle position (F=70.0), and telephoto end (F=131.0) according to the third embodiment. The arrangements of the tables and reference symbols are the same as those in the first embodiment. The position of the focusing lens in the first pair in the upper two tables in each of Tables 42, 43, and 44, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 42, 43, and 44, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.8, -8.5), and it indicates that this position corresponds to the closest in-focus (R=0.8 m) corresponding position. 
     
                                           TABLE 42__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (36.0 mm) of Third EmbodimentF = 36.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.419                  5.000                      -.865                          3.000                              -1.507POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.319      .000    -.309   -.300   -.2872  10.000  -.312          -.303              .000    -.294   -.2813  5.000   -.306   -.297                  -.287                      .000    -.2754  3.000   -.296   -.287   -.278                          -.266                              .0005  2.000   -.284   -.275   -.267   -.2556  1.500   -.271   -.263   -.254   -.2437  1.000   -.242   -.235   -.227   -.2178  .800    -.217   -.210   -.203   -.194__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.13              6.41                  -.26                      5.91                          -.43                              5.512  10.000  .13 6.83          .00 .00 -.13                      5.75                          -.31                              5.453  5.000  .26 6.65          .13 6.16                  .00 .00 -.18                              5.444  3.000  .45 6.45          .31 6.01                  .18 5.69                          .00 .005  2.000  .68 6.32          .55 5.95                  .41 5.69                          .23 5.426  1.500  .92 6.22          .79 5.89                  .65 5.64                          .46 5.347  1.000  1.44      6.00          1.29              5.71                  1.15                      5.47                          .96 5.168  .800  1.85      5.82          1.70              5.55                  1.55                      5.31                          1.36                              5.00__________________________________________________________________________(R, ANGLE) =  2.000      -2.399          1.500              -3.411                  1.000                      -5.936                          800 -8.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.270   -.254   -.219   -.1922  10.000  -.265   -.248   -.214   -.1873  5.000   -.259   -.243   -.209   -.1834  3.000   -.251   -.235   -.202   -.1775  2.000  -.240      .000    -.225   -.193   -.1696  1.500   -.229          -.214              .000    -.184   -.1607  1.000   -.203   -.190                  -.162                      .000    -.1418  .800    -.182   -.170   -.145                          -.126                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.65      5.11          -.87              4.69                  -1.30                      3.72                          -1.63                              3.162  10.000  -.52      5.07          -.74              4.67                  -1.18                      3.69                          -1.51                              3.143  5.000  -.40      5.05          -.62              4.65                  -4.06                      3.67                          -1.40                              3.134  3.000  -.22      5.01          -.45              4.61                  -.90                      3.63                          -1.24                              3.115  2.000  .00 .00 -.23              4.58                  -.68                      3.57                          -1.03                              3.096  1.500  .23 4.92          .00 .00 -.46                      3.51                          -.51                              3.077  1.000  .72 4.73          .48 4.27                  .00 .00 -.36                              3.148  .800  1.11      4.59          .86 4.16                  .37 3.41                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.68, K.sub.aR /γ.sub.aR = 1.52 
    
     
                                           TABLE 43__________________________________________________________________________Converison Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (70.0 mm) of Third EmbodimentF = 70.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.416                  5.000                      -.862                          3.000                              -1.508POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -1.217      .000    -1.156  -1.097  -1.0212  10.000  -1.192          -1.131              .000    -1.073  -.9993  5.000   -1.166  -1.106                  -1.049                      .000    -.9774  3.000   -1.129  -1.071  -1.016                          -.947                              .0005  2.000   -1.085  -1.030  -.978   -.9136  1.500   -1.041  -.988   -.938   -.8777  1.000   -.940   -.892   -.847   -.7908  .800    -.851   -.807   -.766   -.713__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.48              22.24                  -.95                      20.78                          -1.54                              19.682  10.000  .50 24.26          .00 .00 -.48                      20.47                          -1.09                              19.783  5.000  1.00      23.94          .49 22.26                  .00 .00 -.63                              20.214  3.000  1.70      23.67          1.17              22.08                  .66 20.89                          .00 .005  2.000  2.61      24.13          2.05              22.88                  1.51                      22.21                          .82 22.796  1.500  3.56      24.62          2.97              23.47                  2.40                      22.79                          1.67                              22.477  1.000  5.59      24.59          4.93              23.35                  4.30                      22.35                          3.50                              21.088  .800  7.24      24.10          6.53              22.81                  5.85                      21.66                          4.98                              20.16__________________________________________________________________________(R, ANGLE) =  2.000      -2.406          1.500              -3.419                  1.000                      -5.942                          .800                              -8.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.935   -.856   -.707   -.5992  10.000  -.916   -.839   -.692   -.5863  5.000   -.896   -.821   -.677   -.5734  3.000   -.870   -.798   -.657   -.5555  2.000  -.840      .000    -.768   -.630   -.5326  1.500   -.804          -.734              .000    -.601   -.5067  1.000   -.722   -.658                  -.537                      .000    -.4508  .800    -.651   -.591   -.480                          -.399                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -2.25      19.72          -2.93              17.58                  -4.20                      13.32                          -5.09                              10.172  10.000  -1.82      20.08          -2.52              17.68                  -3.82                      13.29                          -4.74                              10.113  5.000  -1.38      20.62          -2.10              17.76                  -3.44                      13.23                          -4.38                              10.044  3.000  -.78      21.31          -1.52              17.62                  -2.91                      13.10                          -3.88                              9.925  2.000  .00 .00 -.78              16.93                  -2.23                      12.88                          -3.24                              9.756  1.500  .81 19.42          .00 .00 -1.52                      12.75                          -2.57                              9.577  1.000  2.55      18.30          1.66              15.95                  .00 .00 -1.15                              9.088  .800  3.97      17.62          3.00              15.44                  1.23                      11.49                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.70, K.sub.aR /γ.sub.aR = 1.50 
    
     
                                           TABLE 44__________________________________________________________________________Converison Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (131.0 mm) of Third EmbodimentF = 131.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.407                  5.000                      -.865                          3.000                              -1.507POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -4.321      .000    -3.765  -3.255  -2.8392  10.000  -4.308          -3.649              .000    -3.138  -2.7733  5.000   -4.152  -3.496                  -3.080                      .000    -2.7644  3.000   -4.096  -3.491  -3.121                          -2.741                              .0005  2.000   4.018   -3.428  -3.043  -2.6356  1.500   -3.929  -3.346  -2.956  -2.5537  1.000   -3.703  -3.132  -2.745  -2.3568  .800    -3.477  -2.919  -2.544  -2.171__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -1.53              48.23                  -2.81                      49.46                          -4.28                              119.602  10.000  1.75      572.58          .00 .00 -1.43                      77.03                          3.05                              257.363  5.000  3.59      91.70          1.60              38.08                  .00 .00 -1.77                              212.104  3.000  6.17      118.29          3.84              88.33                  2.00                      -152.43                          .00 .005  2.000  9.64      137.16          6.83              112.61                  4.67                      386.10                          2.35                              61.086  1.500  13.40      147.45          10.05              120.80                  7.53                      187.07                          4.86                              71.087  1.000  21.98      153.73          17.31              122.07                  13.92                      128.09                          10.44                              74.428  .800  29.56      151.27          23.63              118.12                  19.42                      111.54                          15.19                              73.11__________________________________________________________________________(R, ANGLE) =  2.000      -2.399          1.500              -3.411                  1.000                      -5.936                          .800                              -8.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -2.436  -2.113  -1.606  -1.2982  10.000  -2.388  -2.073  -1.576  -1.2733  5.000   -2.366  -2.048  -1.551  -1.2504  3.000   -2.315  -2.001  -1.511  -1.2165  2.000  -2.232      .000    -1.938  -1.458  -1.1706  1.500   -2.171          -1.877              .000    -1.400  -1.1207  1.000   -1.991  -1.704                  -1.258                      .000    -1.0078  .800    -1.825  -1.555  -1.146                          -.906                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -5.84      63.88          -7.21              57.34                  -9.53                      34.47                          -11.03                              25.552  10.000  -4.76      67.97          -6.23              59.58                  -8.71                      34.51                          -10.30                              25.493  5.000  -3.63      60.51          -5.21              57.33                  -7.86                      33.81                          -9.54                              25.184  3.000  -2.06      55.43          -3.81              57.76                  -6.69                      33.28                          -8.50                              24.925  2.000  .00 .00 -1.96              60.83                  -5.16                      32.47                          -7.14                              24.566  1.500  2.20      80.09          .00 .00 -3.53                      31.39                          -5.70                              24.187  1.000  7.04      65.19          4.30              46.70                  .00 .00 -2.58                              23.328  .800  11.13      61.04          7.91              46.13                  2.94                      33.11                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.80, K.sub.aR /γ.sub.aR = 1.43 
    
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end, middle position, and telephoto end in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the third embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.85 are as follows. 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      3.94           0.36(F = 28.8)Middle Position      5.21           0.37(F = 70.0)Telephoto End      6.78           0.35(F = 131.0)Third EmbodimentWide-angle End      0.68           1.52(F = 28.8)Middle Position      0.70           1.50(F = 70.0)Telephoto End      0.80           1.43(F = 131.0)______________________________________ 
    
     As described above, in the third embodiment as well, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced. For this reason, an error of the conversion coefficient K a  calculated based on γ a  and μ or an error from the actual lens driving amount Δa obtained when only one pair of a conversion coefficient γ a  value and a correction coefficient μ value are set can be reduced. 
     Next, in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the third embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.85, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -8.5%         -20.9%(F = 36.0)Middle Position      -14.1%         -23.8%(F = 70.0)Telephoto End      -17.8%         -23.3%(F = 131.0)Third EmbodimentWide-angle End       -3.5%         -0.1%(F = 36.0)Middle Position      -0.0%          -0.8%(F = 70.0)Telephoto End      2.6%           -0.7%(F = 131.0)______________________________________ 
    
     As described above, in the third embodiment as well, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Table 45 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 37) of the third embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     Note that the arrangement of the table and reference symbols are the same as those in the first embodiment. The upper table in Table 45 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) in the respective zooming states of the focal lengths (F=36.0, 50.0, 70.0, 85.0, 105.0, and 131.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and photographing distances. 
     
                       TABLE 45______________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Third Embodiment______________________________________    0.80 m  1.00 m  1.50 m                          2.00 m                                3.00 m                                      5.00 m______________________________________36.000 Bf    .000    .000    .000  .000  .000  .00050.000 Bf    .000    -.001   .000  .001  .001  .00170.000 Bf    .000    .003    .006  .006  .001  -.00385.000 Bf    .000    .002    -.001 -.011 -.010 -.004105.000 Bf    .000    -.001   -.018 -.012 -.012 -.019131.000 Bf    .000    .000    .000  .000  .000  .000______________________________________    ANGLE DA  -8.500  -5.936                       -3.411                             -2.399                                   -1.507                                         -.865______________________________________F   36.000 DX .000    1.041 .000  .000 R                                   0.80 mF   50.000 DX .000    1.500 .000  .000 R                                   0.80 mF   70.000 DX .000    2.296 .000  .000 R                                   0.80 mF   85.000 DX .000    2.994 .000  .000 R                                   0.80 mF   105.000 DX         .000    4.063 .000  .000 R                                   0.80 mF   131.000 DX         .000    5.676 .000  .000 R                                   0.80 mF   36.000 DX .000    .825  .000  .000 R                                   1.00 mF   50.000 DX .000    1.200 .000  .000 R                                   1.00 mF   70.000 DX .000    1.866 .000  .000 R                                   1.00 mF   85.000 DX .000    2.470 .000  .000 R                                   1.00 mF   105.000 DX         .000    3.426 .000  .000 R                                   1.00 mF   131.000 DX         .000    4.928 .000  .000 R                                   1.00 mF   36.000 DX .000    .544  .000  .000 R                                   1.50 mF   50.000 DX .000    .801  .000  .000 R                                   1.50 mF   70.000 DX .000    1.275 .000  .000 R                                   1.50 mF   85.000 DX .000    1.730 .000  .000 R                                   1.50 mF   105.000 DX         .000    2.494 .000  .000 R                                   1.50 mF   131.000 DX         .000    3.780 .000  .000 R                                   1.50 mF   36.000 DX .000    .405  .000  .000 R                                   2.00 mF   50.000 DX .000    .601  .000  .000 R                                   2.00 mF   70.000 DX .000    .970  .000  .000 R                                   2.00 mF   85.000 DX .000    1.339 .000  .000 R                                   2.00 mF   105.000 DX         .000    1.970 .000  .000 R                                   2.00 mF   131.000 DX         .000    3.106 .000  .000 R                                   2.00 mF   36.000 DX .000    .269  .000  .000 R                                   3.00 mF   50.000 DX .000    .401  .000  .000 R                                   3.00 mF   70.000 DX .000    .658  .000  .000 R                                   3.00 mF   85.000 DX .000    .923  .000  .000 R                                   3.00 mF   105.000 DX         .000    1.396 .000  .000 R                                   3.00 mF   131.000 DX         .000    2.323 .000  .000 R                                   3.00 mF   36.000 DX .000    .161  .000  .000 R                                   5.00 mF   50.000 DX .000    .241  .000  .000 R                                   5.00 mF   70.000 DX .000    .402  .000  .000 R                                   5.00 mF   85.000 DX .000    .569  .000  .000 R                                   5.00 mF   105.000 DX         .000    .891  .000  .000 R                                   5.00 mF   131.000 DX         .000    1.571 .000  .000 R                                   5.00 m______________________________________ 
    
     As can be seen from Table 45, in the zoom lens of the third embodiment, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
      Fourth Embodiment! 
     The fourth embodiment is directed to a zoom lens which has a five-unit arrangement, i.e., positive, negative, positive, negative and positive lens units, and attains focusing by a negative second lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.5 m) to the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=103.0) is set to be -0.90. 
     Table 46 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the fourth embodiment. 
     The upper table in Table 46 summarizes the focal lengths and principal point interval data of the respective lens units of the optical system corresponding to the fourth embodiment in association with six zooming states (focal length F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0 (4-POS), 85.0 (5-POS), and 103.0 mm (6-POS)). 
     The middle table in Table 46 summarizes spline sample data when the shape of the focus cam in the second lens unit of the fourth embodiment, which is used for focusing, is expressed by the above-mentioned spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), and (4) correspond to the first, second, third, and fourth lens units, respectively. 
     Furthermore, the lower table in Table 46 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (focal length F=28.8, 35.0, 50.0, 70.0, 85.0, and 103.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7, and 0.5 m) using the focus cam of the fourth embodiment. In this table, since the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=103.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.5 m) is set to be -9.0, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the fourth embodiment is -0.90. 
     
                                           TABLE 46__________________________________________________________________________Fourth Embodiment F = 28.8 to 103.0 (Rotation Amount Ratio: a.sub.F/a.sub.Z = -0.90)Focal lengths and Principal Point Intervals of Lens Units of FourthEmbodiment     1-POS         2-POS              3-POS                  4-POS                       5-POS                           6-POS__________________________________________________________________________  F  28.8000         35.0000              50.0000                  70.0000                       85.0000                           103.0000F1  70.5000  D1 9.3252         13.0113              20.5346                  28.4581                       32.6851                           36.5544F2  -13.4000  D2 18.3082         16.1329              13.0216                  10.6580                       9.2279                           7.6539F3  32.9000  D3 14.6453         13.3678              10.4573                  8.4188                       7.8210                           7.5173F4  56.4000  D4 49.9916         54.4242              61.6013                  65.7605                       67.3873                           68.3296__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Correspondingto Fourth Embodiment   ANGLE     (1)           (2)       (3)                        (4)__________________________________________________________________________1  -10.0000  .0000           .9890     .0000                        .00002  -9.0000   .0000           .9281     .0000                        .00003  -5.2174   .0000           .6450     .0000                        .00004  -3.2226   .0000           .4427     .0000                        .00005  -1.4215   .0000           .2166     .0000                        .00006  -.9122    .0000           .1434     .0000                        .00007  -.5316    .0000           .0856     .0000                        .00008  .0000     .0000           .0000     .0000                        .00009  1.0000    .0000           -.1755    .0000                        .000010 4.7826    .0000           -1.1178   .0000                        .000011 6.7774    .0000           -1.9212   .0000                        .000012 8.5785    .0000           -3.0359   .0000                        .000013 9.0878    .0000           -3.4750   .0000                        .000014 9.4684    .0000           -3.8631   .0000                        .000015 10.0000   .0000           -4.5317   .0000                        .000016 11.0000   .0000           -6.2650   .0000                        .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofFourth EmbodimentRotation Amount Ratio: a.sub.F /a.sub.Z = -0.90)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal Length   ing Position                ing Distance                           Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m    -.53235.0 mm        1.3907                 3.00 m    -.91250.0 mm        4.2613                 2.00 m    -1.42170.0 mm        7.2647                 1.00 m    -3.22385.0 mm        8.7737                 0.70 m    -5.217103.0 mm       10.0000                 0.50 m    -9.000Condition Corresponding Value (1)                 1.55Condition Corresponding Value (2)                 4.69Condition Corresponding Value (3)                -0.90Condition Corresponding Value (4)                 0.39 (wide-angle end)                 0.20 (telephoto end)Condition Corresponding Value (5)                 0.68 (wide-angle end)                 0.82 (telephoto end)Condition Corresponding Value (6)                 1.51 (wide-angle end)                 1.48 (telephoto end)__________________________________________________________________________ 
    
     Table 47 below summarizes the numerical value data of the cams of the focusing lens unit in the fourth embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 46. Note that the meanings of the reference symbols in Table 47 are the same as those in the first embodiment. 
     
                       TABLE 47______________________________________Cam Numerical Value Data of Focusing Lens Unit in FourthEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (2)       F        ANGLE  (2)    F______________________________________-9.0000  .9281     .0000-8.5000  .8963     .0000-8.0000  .8630     .0000-7.5000  .8282     .0000-7.0000  .7917     .0000-6.5000  .7533     .0000-6.0000  .7219     .0000-5.5000  .6702     .0000-5.0000  .6250     .0000-4.5000  .5773     .0000-4.000 .5269     .0000-3.5000  .4736     .0000-3.0000  .4173     .0000-2.5000  .3577     .0000-2.0000  .2945     .0000-1.5000  .2275     .0000-1.0000  .1564     .0000-.5000 .0806     .0000.0000  .0000     28.8000  .0000  .0000  28.8000.5000  -.0853    30.9500  .5000  .4528  30.95001.0000 -.1755    33.1892  1.0000 .8955  33.18921.5000 -.2715    35.5168  1.5000 1.3212 35.51682.0000 -.3742    37.9389  2.0000 1.7245 37.93892.5000 -.4847    40.4555  2.5000 2.0975 40.45553.0000 -.6040    43.0624  3.0000 2.4333 43.06243.5000 -.7333    45.7538  3.5000 2.7268 45.75384.0000 -.8736    48.5235  4.0000 2.9752 48.52354.5000 -1.0260   51.3658  4.5000 3.1782 51.36585.0000 -1.1915   54.2940  5.0000 3.3456 54.29405.5000 -1.3722   57.3528  5.5000 3.4940 57.35286.0000 -1.5706   60.6006  6.0000 3.6376 60.60066.5000 -1.7897   64.0869  6.5000 3.7892 64.08697.0000 -2.0324   67.8574  7.0000 3.9608 67.85747.5000 -2.3045   72.0128  7.5000 4.1657 72.01288.0000 -2.6153   76.6717  8.0000 4.3908 76.67178.5000 -2.9745   81.8893  8.5000 4.5944 81.88939.0000 -3.3935   87.7449  9.0000 4.7514 87.74499.5000 -3.8981   94.5847  9.5000 4.8913 94.584710.0000  -4.5317   103.0000 10.0000                            5.0874 103.0000______________________________________ 
    
     The left table in Table 47 summarizes the numerical value data of the focus cam of the fourth embodiment, and the right table in Table 47 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincides with the movement locus of the second lens unit calculated using the paraxial data in the upper table in Table 46. 
     Tables 48, 49, and 50 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=50.0), and the telephoto end (F=103.0) according to the second embodiment, respectively. The arrangements of the respective tables and the meanings of the reference symbols are the same as those in the first embodiment. 
     
                                           TABLE 48__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End (28.8 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                .043                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                .086                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                .143                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                .217                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                .443                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                .645                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                .928                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -.280                    3)                      -12.818                          4)                            .114R 10.000 ANG    -.260        1)          -.007              2)                -.277                    3)                      -12.818                          4)                            .114R 5.000 ANG    -.532        1)          -.015              2)                -.274                    3)                      -12.818                          4)                            .114R 3.000 ANG    -.912        1)          -.025              2)                -.270                    3)                      -12.818                          4)                            .114R 2.000 ANG    -1.421        1)          -.038              2)                -.264                    3)                      -12.818                          4)                            .114R 1.000 ANG    -3.223        1)          -.084              2)                -.247                    3)                      -12.818                          4)                            .114R .700 ANG    -5.217        1)          -.131              2)                -.232                    3)                      -12.818                          4)                            .114R .500 ANG    -9.000        1)          -.209              2)                -.211                    3)                      -12.818                          4)                            .114Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angleEnd (28.8 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                1.954                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                1.958                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                1.962                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                1.967                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                1.973                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                1.991                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                2.007                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                2.027                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -.166                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                -.161                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                -.156                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                -.148                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                -.139                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                -.113                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                -.091                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.062                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Asociated With Direction of Rotationat Wide-angle End(28.8 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                -.324                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                -.316                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                -.306                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                -.292                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                -.275                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                -.225                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                -.182                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.127                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.04, γ.sub.aR /γ.sub.a0 = 0.39 
    
     
                                           TABLE 49__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (50.0 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.258        1)          .000              2)                .077                    3)                      .000                          4)                            .000R 5.000 ANG    -.527        1)          .000              2)                .154                    3)                      .000                          4)                            .000R 3.000 ANG    -.905        1)          .000              2)                .257                    3)                      .000                          4)                            .000R 2.000 ANG    -1.413        1)          .000              2)                .385                    3)                      .000                          4)                            .000R 1.000 ANG    -3.230        1)          .000              2)                .770                    3)                      .000                          4)                            .000R .700 ANG    -5.226        1)          .000              2)                1.103                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                1.552                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Middle Position (50.0mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -.366                    3)                      20.985                          4)                            -.092R 10.000 ANG    -.258        1)          -.007              2)                -.361                    3)                      20.985                          4)                            -.092R 5.000 ANG    -.527        1)          -.015              2)                -.355                    3)                      20.985                          4)                            -.092R 3.000 ANG    -.905        1)          -.025              2)                -.347                    3)                      20.985                          4)                            -.092R 2.000 ANG    -1.413        1)          -.039              2)                -.338                    3)                      20.985                          4)                            -.092R 1.000 ANG    -3.230        1)          -.086              2)                -.309                    3)                      20.985                          4)                            -.092R .700 ANG    -5.226        1)          -.135              2)                -.284                    3)                      20.985                          4)                            -.092R .500 ANG    -9.000        1)          -.218              2)                -.251                    3)                      20.985                          4)                            -.092Conversion Coefficient γ.sub.x Asociated With Direction of OpticalAxis at MiddlePosition (50.0 mm) in Fourth EmbodimentR .000 ANG    -.000        1)          .000              2)                3.242                    3)                      .000                          4)                            .000R 10.000 ANG    -.258        1)          .000              2)                3.258                    3)                      .000                          4)                            .000R 5.000 ANG    -.527        1)          .000              2)                3.273                    3)                      .000                          4)                            .000R 3.000 ANG    -.905        1)          .000              2)                3.294                    3)                      .000                          4)                            .000R 2.000 ANG    -1.413        1)          .000              2)                3.318                    3)                      .000                          4)                            .000R 1.000 ANG    -3.230        1)          .000              2)                3.388                    3)                      .000                          4)                            .000R .700 ANG    -5.226        1)          .000              2)                3.443                    3)                      .000                          4)                            .000R.  .500 ANG    -9.000        1)          .000              2)                3.510                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Middle Position (50.0 mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -.305                    3)                      .000                          4)                            .000R 10.000 ANG    -.258        1)          .000              2)                -.292                    3)                      .000                          4)                            .000R 5.000 ANG    -.527        1)          .000              2)                -.280                    3)                      .000                          4)                            .000R 3.000 ANG    -.905        1)          .000              2)                -.263                    3)                      .000                          4)                            .000R 2.000 ANG    -1.413        1)          .000              2)                -.242                    3)                      .000                          4)                            .000R 1.000 ANG    -3.230        1)          .000              2)                -.187                    3)                      .000                          4)                            .000R .700 ANG    -5.226        1)          .000              2)                -.147                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.095                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Asociated With Direction of Rotationat Middle Position(50.0 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                -.990                    3)                      .000                          4)                            .000R 10.000 ANG    -.258        1)          .000              2)                -.953                    3)                      .000                          4)                            .000R 5.000 ANG    -.527        1)          .000              2)                -.916                    3)                      .000                          4)                            .000R 3.000 ANG    -.905        1)          .000              2)                -.866                    3)                      .000                          4)                            .000R 2.000 ANG    -1.413        1)          .000              2)                -.804                    3)                      .000                          4)                            .000R 1.000 ANG    -3.230        1)          .000              2)                -.632                    3)                      .000                          4)                            .000R .700 ANG    -5.226        1)          .000              2)                -.507                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.335                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.08, γ.sub.aR /γ.sub.a0 = 0.34 
    
     
                                           TABLE 50__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End (103.0 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                .350                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                .669                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                1.057                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                1.496                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                2.611                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                3.414                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                4.356                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (103.0mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -.652                    3)                      10.590                          4)                            -.212R 10.000 ANG    -.260        1)          -.007              2)                -.626                    3)                      10.590                          4)                            -.212R 5.000 ANG    -.532        1)          -.015              2)                -.602                    3)                      10.590                          4)                            -.212R 3.000 ANG    -.912        1)          -.025              2)                -.573                    3)                      10.590                          4)                            -.212R 2.000 ANG    -1.421        1)          -.039              2)                -.541                    3)                      10.590                          4)                            -.212R 1.000 ANG    -3.223        1)          -.087              2)                -.457                    3)                      10.590                          4)                            -.212R .700 ANG    -5.217        1)          -.138              2)                -.397                    3)                      10.590                          4)                            -.212R .500 ANG    -9.000        1)          -.228              2)                -.327                    3)                      10.590                          4)                            -.212Conversion Coefficient γ.sub.x Asociated With Direction of OpticalAxis at Telephoto End(103.0 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                2.883                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                3.051                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                3.198                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                3.368                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                3.552                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                3.968                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                4.225                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                4.481                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Telephoto End (103.0 mm) in FourthEmbodimentR .000 ANG    .000        1)          .000              2)                -1.449                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                -1.253                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                -1.101                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                -.944                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000              2)                -.791                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                -.488                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                -.333                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.186                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Asociated With Direction of Rotationat Telephoto End(103.0 mm) in Fourth EmbodimentR .000 ANG    .000        1)          .000              2)                -4.179                    3)                      .000                          4)                            .000R 10.000 ANG    -.260        1)          .000              2)                -3.823                    3)                      .000                          4)                            .000R 5.000 ANG    -.532        1)          .000              2)                -3.520                    3)                      .000                          4)                            .000R 3.000 ANG    -.912        1)          .000              2)                -3.180                    3)                      .000                          4)                            .000R 2.000 ANG    -1.421        1)          .000)              2)                -2.810                    3)                      .000                          4)                            .000R 1.000 ANG    -3.223        1)          .000              2)                -1.935                    3)                      .000                          4)                            .000R .700 ANG    -5.217        1)          .000              2)                -1.406                    3)                      .000                          4)                            .000R .500 ANG    -9.000        1)          .000              2)                -.833                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.55, γ.sub.aR /γ.sub.a0 = 0.20 
    
     As can be seen from Tables 48, 49, and 50, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     From Tables 48, 49, and 50, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.39 at the wide-angle end (F=28.8), ×0.34 at the middle position (F=50.0), and ×0.20 at the telephoto end (F=103.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the fourth embodiment is calculated using formula (a), and is compared with that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: 
     When the rotation amount ratio (a F  /a Z ) is set to be 1.0 
     
         N.sub.W &gt;11.2 N.sub.M &gt;11.2 N.sub.T &gt;8.3 
    
     Fourth Embodiment 
     
         N.sub.W &gt;5.1 N.sub.M &gt;5.9 N.sub.T &gt;8.9 
    
     Therefore, it can be seen that the numbers of divisions become small, compared to those in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     As described above, in the fourth embodiment as well, since the rate of change of the conversion coefficient γ a  associated with the direction of rotation is smaller than that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient γ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 51, 52, and 53 summarize the calculation results of the values of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=28.8), middle position (F=50.0), and telephoto end (F=103.0) according to the fourth embodiment. 
     The arrangements of the tables and reference symbols are the same as those in the first embodiment. The position of the focusing lens in the first pair in the upper two tables in each of Tables 51, 52, and 53, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 42, 43, and 44, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.5, -9.0), and it indicates that this position corresponds to the closest in-focus (R=0.5 m) corresponding position. 
     
                                           TABLE 51__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (28.8 mm) in Fourth EmbodimentF = 28.8 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.260                  5.000                      -.532                          3.000                              -.912POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.324      .000    -.319   -.313   -.3052  10.000  -.321          -.316              .000    -.310   -.3013  5.000   -.317   -.312                  -.306                      .000    -.2974  3.000   -.312   -.306   -.300                          -.292                              .0005  2.000   -.304   -.298   -.293   -.2856  1.000   -.280   -.275   -.269   -.2627  .700    -.257   -.252   -.247   -.2408  .500    -.220   -.216   -.211   -.206__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              7.61                  -.17                      6.62                          -.28                              6.112  10.000  .08 8.40          .00 .00 -.08                      6.25                          -.20                              5.983  5.000  .17 7.80          .08 6.82                  .00 .00 -.11                              5.994  3.000  .28 7.26          .20 6.48                  .11 6.05                          .00 .005  2.000  .43 6.98          .35 6.41                  .26 6.15                          .15 6.116  1.000  .90 6.66          .81 6.33                  .73 6.15                          .61 6.007  .700  1.34      6.48          1.25              6.22                  1.16                      6.05                          1.03                              5.888  .500  1.98      6.18          1.89              5.98                  1.79                      5.82                          1.66                              5.63__________________________________________________________________________(R, ANGLE) =  2.000      -1.421          1.000              -3.223                  .700                      -5.217                          .500                              -9.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.295   -.262   -.234   -.1922  10.000  -.291   -.259   -.231   -.1903  5.000   -.287   -.256   -.228   -.1874  3.000   -.282   -.251   -.223   -.1835  2.000  -.275      .000    -.245   -.218   -.1796  1.000   -.253          -.225              .000    -.200   -.1637  .700    -.232   -.206                  -.182                      .000    -.1488  .500    -.198   -.175   -.154                          -.127                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.42      5.88          -.85              5.09                  -1.22                      4.27                          -1.73                              3.332  10.000  -.34      5.83          -.77              5.08                  -1.14                      4.25                          -1.66                              3.333  5.000  -.26      5.85          -.69              5.07                  -1.07                      4.24                          -1.58                              3.324  3.000  -.14      5.84          -.58              5.05                  -.96                      4.22                          -1.48                              3.315  2.000  .00 .00 -.44              5.03                  -.83                      4.19                          -1.35                              3.306  1.000  .46 5.74          .00 .00 -.40                      4.05                          -.94                              3.277  .700  .88 5.62          .41 4.77                  .00 .00 -.56                              3.318  .500  1.50      5.37          1.01              4.54                  .58 3.83                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.68, K.sub.aR /γ.sub.aR = 1.51 
    
     
                                           TABLE 52__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (50.0 mm) in Fourth EmbodimentF = 50.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.258                  5.000                      -.527                          3.000                              -.905POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.989      .000    -.964   -.938   -.9042  10.000  -.979          -.953              .000    -.927   -.8933  5.000   -.967   -.941                  -.915                      .000    -.8824  3.000   -.950   -.925   -.900                          -.866                              .0005  2.000   -.929   -.903   -.878   -.8456  1.000   -.855   -.832   -.808   -.7777  .700    -.791   -.769   -.747   -.7198  .500    -.686   -.667   -.648   -.623__________________________________________________________________________PQS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.25              21.45                  -.49                      20.06                          -.82                              18.892  10.000  .25 23.31          .00 .00 -.25                      19.46                          -.58                              18.673  5.000  .51 22.59          .25 20.95                  .00 .00 -.33                              18.534  3.000  .86 21.97          .60 20.56                  .34 19.74                          .00 .005  2.000  1.31      21.37          1.04              20.12                  .78 19.19                          .43 17.696  1.000  2.76      20.39          2.47              19.42                  2.18                      18.63                          1.81                              17.587  .700  4.13      20.60          3.82              19.80                  3.51                      19.13                          3.11                              18.298  .500  6.17      20.14          5.83              19.41                  5.49                      18.77                          5.04                              17.95__________________________________________________________________________(R, ANGLE) =  2.000      -1.413          1.000              -3.230                  .700                      -5.226                          .500                              -9.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.861   -.735   -.637   -.5062  10.000  -.850   -.726   -.629   -.5003  5.000   -.839   -.716   -.621   -.4934  3.000   -.824   -.703   -.609   -.4845  2.000  -.804      .000    -.685   -.595   -.4726  1.000   -.739          -.632              .000    -.551   -.4357  .700    -.684   -.588                  -.507                      .000    -.3978  .500    -.592   -.506   -.433                          -.335                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -1.22      17.17          -2.37              14.61                  -3.33                      13.01                          -4.56                              8.912  10.000  -.98      16.98          -2.16              14.60                  -3.13                      13.02                          -4.37                              8.883  5.000  -.74      16.81          -1.94              14.62                  -2.92                      13.04                          -4.18                              8.854  3.000  -.42      16.58          -1.63              14.68                  -2.63                      13.07                          -3.92                              8.815  2.000  .00 .00 -1.25              14.86                  -2.27                      13.12                          -3.58                              8.756  1.000  1.34      16.67          .00 .00 -1.11                      12.70                          -2.51                              8.437  .700  2.61      17.58          1.17              16.71                  .00 .00 -1.50                              8.128  .500  4.49      17.09          2.92              14.54                  1.63                      11.09                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.69, K.sub.aR /γ.sub.aR = 1.51 
    
     
                                           TABLE 53__________________________________________________________________________Conversion Coefficient K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (103.0 mm) in Fourth EmbodimentF = 103.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.260                  5.000                      -.532                          3.000                              -.912POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -4.180      .000    -3.855  -3.573  -3.2592  10.000  -4.152          -3.8l9              .000    -3.543  -3.2333  5.000   -4.121  -3.794                  -3.520                      .000    -3.2134  3.000   -4.091  -3.767  -3.495                          -3.180                              .0005  2.000   -4.050  -3.726  -3.451  -3.1356  1.000   -3.907  -3.578  -3.301  -2.9867  .700    -3.747  -3.416  -3.139  -2.8278  .500    -3.440  -3.112  -2.841  -2.540__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -1.02              106.64                  -1.90                      127.23                          -2.97                              120.342  10.000  1.08      164.84          .00 .00 -.96                      151.92                          -2.11                              126.783  5.000  2.19      156.83          1.03              152.81                  .00 .00 -1.22                              119.674  3.000  3.73      176.52          2.46              179.24                  1.33                      184.76                          .00 .005  2.000  5.76      186.20          4.33              176.43                  3.07                      156.05                          1.60                              113.276  1.000  12.59      192.95          10.60              168.02                  8.88                      142.43                          6.90                              113.067  .700  19.55      189.03          16.94              160.55                  14.71                      135.70                          12.17                              109.628  .500  30.96      175.08          27.20              146.97                  24.06                      124.62                          20.54                              102.06__________________________________________________________________________(R, ANGLE) =  2.000      -1.421          1.000              -3.223                  .700                      -5.217                          .500                              -9.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -2.926  -2.181  -1.718  -1.2322  10.000  -2.902  -2.160  -1.700  -1.2183  5.000   -2.880  -2.140  -1.682  -1.2034  3.000   -2.847  -2.111  -1.657  -1.1835  2.000  -2.810      .000    -2.073  -1.624  -1.1576  1.000   -2.659          -1.934              .000    -1.514  -1.0697  .700    -2.506  -1.815                  -1.406                      .000    -.9818  .500    -2.234  -1.590  -1.214                          -.833                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -4.16      100.97          -7.03              55.12                  -8.96                      40.47                          -11.09                              23.172  10.000  -3.37      103.32          -6.40              54.80                  -8.43                      40.38                          -10.65                              23.073  5.000  -2.56      103.11          -5.76              54.22                  -7.88                      40.24                          -10.19                              22.964  3.000  -1.45      109.95          -4.88              53.47                  -7.13                      40.09                          -9.57                              22.805  2.000  .00 .00 -3.73              52.11                  -6.16                      39.89                          -8.77                              22.606  1.000  4.79      89.05          .00 .00 -3.02                      39.55                          -6.18                              21.857  .700  9.51      87.85          3.62              58.52                  .00 .00 -3.71                              20.988  .500  16.93      82.65          9.19              51.65                  4.59                      33.50                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.82, K.sub.aR /γ.sub.aR = 1.48 
    
     As calculation results of the rate of change of K a  with respect to .sub.γ av at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end, middle position, and telephoto end in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the fourth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.90 are as follows. 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      3.47           0.40(F = 28.8)Middle Position      4.09           0.39(F = 50.0)Telephoto End      4.98           0.39(F = 103.0)Fourth EmbodimentWide-angle End      0.68           1.51(F = 28.8)Middle Position      0.69           1.51(F = 50.0)Telephoto End      0.82           1.48(F = 103.0)______________________________________ 
    
     As described above, in the fourth embodiment as well, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced. For this reason, an error of the conversion coefficient K a  calculated based on γ a  and μ or an error from the actual lens driving amount Δa obtained when only one pair of a conversion coefficient γ a  value and a correction coefficient μ value are set can be reduced. 
     Next, in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the fourth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.90, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -7.4%         -12.2%(F = 28.8)Middle Position      -18.4%         -12.1%(F = 50.0)Telephoto End      -20.2%         -13.4%(F = 103.0)Fourth EmbodimentWide-angle End       -5.2%         -0.6%(F = 28.8)Middle Position      -2.5%          -0.3%(F = 50.0)Telephoto End      -1.3%          -0.5%(F = 103.0)______________________________________ 
    
     As described above, in the fourth embodiment as well, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Table 54 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 46) of the fourth embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     Note that the arrangement of the table and reference symbols are the same as those in the first embodiment. The upper table in Table 54 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.0, 0.7, and 0.5 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 70.0, 85.0, and 103.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and photographing distances. 
     
                                           TABLE 54__________________________________________________________________________Displament Amount Bf (mm) of Imaging Point and Amount DX(mm) of Movement for Focusing in Fourth Embodiment__________________________________________________________________________   0.50 m       0.70 m             1.00 m                 2.00 m                       3.00 m                           5.00 m__________________________________________________________________________F 28.800 Bf   .000       .000  .000                 .000  .000                           .000F 3S.000 Bf   .000       -.001 .001                 .005  .005                           .003F 50.000 Bf   .000       .004  .005                 -.006 -.006                           -.004F 70.000 Bf   .000       -.005 -.011                 -.001 .002                           .003F 85.000 Bf   .000       -.015 -.009                 -.014 -.013                           -.007F 103.000 Bf   .000       .000  .000                 .000  .000                           .000__________________________________________________________________________ANGLE DA   -9.000        -5.217            -3.223                  -1.421                       -.912                           -.532__________________________________________________________________________F 28.800 DX   .000 .928            .000  .000                     R .0.50 mF 35.000 DX   .000 1.086            .000  .000                     R 0.50 mF 50.000 DX   .000 1.552            .000  .000                     R 0.50 mF 70.000 DX   .000 2.432            .000  .000                     R 0.50 mF 85.000 DX   .000 3.232            .000  .000                     R 0.50 mF 103.000 DX   .000 4.356            .000  .000                     R 0.50 mF 28.800 DX   .000 .645            .000  .000                     R 0.70 mF 35.000 DX   .000 .759            .000  .000                     R 0.70 mF 50.000 DX   .000 1.102            .000  .000                     R 0.70 mF 70.000 DX   .000 1.788            .000  .000                     R 0.70 mF 85.000 DX   .000 2.447            .000  .000                     R 0.70 mF 103.000 DX   .000 3.414            .000  .000                     R 0.70 mF 28.800 DX   .000 .443            .000  .000                     R 1.00 mF 35.000 DX   .000 .522            .000  .000                     R 1.00 mF 50.000 DX   .000 .769            .000  .000                     R 1.00 mF 70.000 DX   .000 1.286            .000  .000                     R 1.00 mF 85.000 DX   .000 1.804            .000  .000                     R 1.00 mF 103.000 DX   .000 2.611            .000  .000                     R 1.00 mF 28.800 DX   .000 .217            .000  .000                     R 2.00 mF 35.000 DX   .000 .255            .000  .000                     R 2.00 mF 50.000 DX   .000 .387            .000  .000                     R 2.00 mF 70.000 DX   .000 .666            .000  .000                     R 2.00 mF 85.000 DX   .000 .975            .000  .000                     R 2.00 mF 103.000 DX   .000 1.496            .000  .000                     R 2.00 mF 28.800 DX   .000 .143            .000  .000                     R 3.00 mF 35.000 DX   .000 .169            .000  .000                     R 3.00 mF 5 0.000 DX   .000 .258            .000  .000                     R 3.00 mF 70.000 DX   .000 .449            .000  .000                     R 3.00 mF 85.000 DX   .000 .670            .000  .000                     R 3.00 mF 103.000 DX   .000 1.057            .000  .000                     R 3.00 mF 28.800 DX   .000 .086            .000  .000                     R 5.00 mF 35.000 DX   .000 .100            .000  .000                     R 5.00 mF 50.000 DX   .000 .155            .000  .000                     R 5.00 mF 70.000 DX   .000 .272            .000  .000                     R 5.00 mF 85.000 DX   .000 .412            .000  .000                     R 5.00 mF 103.000 DX   .000 .669            .000  .000                     R 5.00 m__________________________________________________________________________ 
    
     As can be seen from Table 54, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
      Fifth Embodiment! 
     A zoom lens of the fifth embodiment is a zoom lens which has a five-unit arrangement, i.e., positive, negative, positive, negative and positive lens units, and attains focusing by a negative fourth lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.80 m) to the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=126.0) is set to be -0.55. 
     Table 55 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the fifth embodiment. 
     The upper table in Table 55 summarizes the focal lengths data, and principal point interval data of the respective lens units of the optical system corresponding to the fifth embodiment. 
     In this table, F1, F2, F3, F4 and F5 are respectively the focal lengths of first, second, third, fourth, and fifth lens units, and D1, D2, D3, D4, and D5 are respectively the principal point interval between the first and second lens units, the principal point interval between the second and third lens units, the principal point interval between the third and fourth lens units, and the principal point interval between the fourth and fifth lens unit, and the principal point interval between the fifth lens unit and a predetermined imaging plane in six zooming states (F=28.8 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 70.0 (4-POS), 95.0 mm (5-POS), and 126.0 mm (6-POS)). 
     The middle table in Table 55 summarizes spline sample data when the shape (a curve g 2F  in FIG. 3) of the focus cam in the fourth lens unit of the fifth embodiment, which is used for focusing, is expressed by the above-mentioned spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), (4), and (5) correspond to the first, second, third, fourth, and fifth lens units, respectively. 
     Furthermore, the lower table in Table 55 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=28.8, 35.0, 50.0, 70.0, 95.0, and 126.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) using the focus cam of the fifth embodiment. In the lower table in Table 55, since the amount of rotation for zooming from the wide-angle end (F=28.8) to the telephoto end (F=126.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.80 m) is set to be -5.5, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the first embodiment is -0.55. 
     
                                           TABLE 55__________________________________________________________________________Fifth Embodiment F = 28.8 to 126.0 (Rotation Amount Ratio: a.sub.F/a.sub.Z = -0.55)__________________________________________________________________________Focal lengths and Principal Point Intervals of Lens Units of FifthEmbodiment     1-POS         2-POS              3-POS                  4-POS                       5-POS                           6-POS__________________________________________________________________________  F  28.8000         35.0000              50.0000                  70.0000                       95.0000                           126.0000F1  98.0000  D1 9.3696         15.5678              26.0774                  35.1343                       42.9607                           49.3378F2  -20.2000  D2 34.5121         30.5093              24.1872                  19.0594                       14.7856                           10.6994F3  21.3000  D3 8.9319         9.5307              10.6727                  11.7442                       12.4611                           13.1911F4  -19.6000  D4 14.4820         13.8832              12.7412                  11.6697                       10.9528                           10.2228F5  35.5000  D5 49.8013         51.5975              55.0237                  58.2383                       61.1451                           63.0195__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Corresponding toFifthEmbodimentANGLE     (1)    (2)               (3)    (4) (5)__________________________________________________________________________1    -10.0000     .0000  .0000               .0000  -.4328                          .00002    -5.5000     .0000  .0000               .0000  -.3653                          .00003    -3.3884     .0000  .0000               .0000  -.2845                          .00004    -1.7882     .0000  .0000               .0000  -.1832                          .00006    .7550     .0000  .0000               .0000  -.0886                          .00007    .4267     .0000  .0000               .0000  -.0524                          .00008    .0000     .0000  .0000               .0000  .0000                          .00009    .5000     .0000  .0000               .0000  .0720                          .000010   4.5000     .0000  .0000               .0000  1.1810                          .000011   6.0000     .0000  .0000               .0000  2.0800                          .000012   6.6116     .0000  .0000               .0000  2.5920                          .000013   8.2118     .0000  .0000               .0000  4.3577                          .000014   8.7719     .0000  .0000               .0000  5.1954                          .000015   9.2450     .0000  .0000               .0000  6.0053                          .000016   9.5733     .0000  .0000               .0000  6.6341                          .000017   10.0000     .0000  .0000               .0000  7.5475                          .000018   11.0000     .0000  .0000               .0000  10.1892                          .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofFifth Embodiment(Rotation Amount Ratio: a.sub.F /a.sub.Z = -0.55)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal Length   ing Position                ing Distance                           Focusing__________________________________________________________________________28.8 mm        .0000  5.00 m    -.42735.0 mm        1.3439                 3.00 m    -.75550.0 mm        3.8037                 2.00 m    -1.22870.0 mm        6.0180                 1.50 m    -1.78895.0 mm        8.0481                 1.00 m    -3.388126.0 mm       10.0000                 0.80 m    -5.500Condition Corresponding Value (1)                 1.31Condition Corresponding Value (2)                 17.44Condition Corresponding Value (3)                -0.55Condition Corresponding Value (4)                 0.21 (wide-angle end)                 0.26 (telephoto end)Condition Corresponding Value (5)                 0.50 (wide-angle end)                 0.56 (telephoto end)Condition Corresponding Value (6)                 2.39 (wide-angle end)                 2.00 (telephoto end)__________________________________________________________________________ 
    
     Table 56 below summarizes the numerical value data of the cams of the focusing lens unit in the fifth embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 55. In this table (ANGLE) is the angle of rotation of the rotatable lens barrel, (2) is the amount (mm) of movement, in the direction of the optical axis, of the second lens unit, and (F) is the focal length (mm) of the entire system in an infinity in-focus state corresponding to the amount (ANGLE) of rotation. 
     
                       TABLE 56______________________________________Cam Numerical Value Data of Focusing Lens Unit in FifthEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (4)       F        ANGLE  (4)    F______________________________________-5.5000  -.3653    .0000-5.0000  -.3503    .0000-4.5000  -.3329    .0000-4.0000  -.3129    .0000-3.5000  -.2900    .0000-3.0000  -.2640    .0000-2.5000  -.2341    .0000-2.0000  -.1995    .0000-1.5000  -.1593    .0000-1.0000  -.1134    .0000-.5000 -.0608    .0000.0000  .0000     28.8000  .0000  .0000  28.8000.5000  .0720     31.0285  .5000  .3775  31.02851.0000 .1527     33.3443  1.0000 .7403  33.34431.5000 .2437     35.7763  1.5000 1.0933 35.77632.0000 .3482     38.3954  2.0000 1.4434 38.39542.5000 .4691     41.2540  2.5000 1.7885 41.25403.0000 .6098     44.3801  3.0000 2.1201 44.38013.5000 .7732     47.7884  3.5000 2.4272 47.78844.0000 .9626     51.4883  4.0000 2.6982 51.48834.5000 1.1810    55.4931  4.5000 2.9324 55.49315.0000 1.4331    59.8203  5.0000 3.1395 59.82035.5000 1.7289    64.5708  5.5000 3.3332 64.57086.0000 2.0800    69.8013  6.0000 3.5238 69.80136.5000 2.4927    75.5383  6.5000 3.7167 75.53837.0000 2.9552    81.4767  7.0000 3.8432 81.47677.5000 3.4759    87.6730  7.5000 3.8489 87.67308.0000 4.0752    94.3296  8.0000 3.7003 94.32968.5000 4.7727    101.5681 8.5000 3.3763 101.56819.0000 5.5729    109.2585 9.0000 2.8865 109.25859.5000 6.4888    117.3718 9.5000 2.2362 117.371810.0000  7.5475    126.0000 10.0000                            1.4115 126.0000______________________________________ 
    
     The left table in Table 56 summarizes the numerical value data of the focus cam of the fifth embodiment, and the right table in Table 56 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (4) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincides with the movement locus (a curve g 4  in FIG. 3) of the fourth lens unit calculated using the paraxial data in the upper table in Table 55. 
     Therefore, the zoom compensation cam (a curve g 4H  in FIG. 3) is determined by subtracting the focus cam (the curve g 4F  in FIG. 3) from the movement locus (the curve g 4  in FIG. 3) upon zooming of the fourth lens unit determined by the paraxial data in the upper table in Table 55. 
     FIG. 3 and FIG. 4 will be briefly described below. 
     FIG. 3 shows the paraxial arrangement and the movement loci upon zooming of the zoom lens according to the fifth embodiment, and FIG. 3 shows the shapes of the focus cam and the zoom compensation cam of the fourth lens unit of this embodiment. Referring to FIG. 1, G1, G2, G3, G4, and G5 respectively represent the first, second, third, fourth, and fifth lens units, and g 1 , g 2 , g 3 , g 4  and g 5  respectively represent the movement loci upon zooming of the first, second, third, fourth, and fifth lens units. In addition, g 4F  and g 4H  respectively represent the shapes of the focus cam and the zoom compensation cam of the fourth lens unit. As described above, a shape obtained by synthesizing the focus cam g 4F  and the zoom compensation cam g 4H  of the fourth lens unit coincides with the movement locus g 4  of the fourth lens unit. 
     FIG. 4 is a view for explaining the shape of the focus cam g 4  F of the fifth embodiment. Referring to FIG. 4, (F=28.8; R=un) and (F=28.8; R=0.80) respectively represent the in-focus positions at the infinity and the closest distance (R=0.80 m) at the wide-angle end, and coordinate positions (x; a) on the focus cam are respectively (x; a)=(0; 0) and (x; a)=(-0.363; -5.5). On the other hand, (F=126; R=un) and (F=126; R=0.80) respectively represent the in-focus positions at the infinity and the closest distance (R=0.80 m) at the telephoto end, and coordinate positions (x; a) on the focus cam are respectively (x; a)=(7.548; 10) and (x; a)=(1.181; 4.5). 
     Upon zooming from the wide-angle end to the telephoto end, the fourth lens unit moves on the focus cam g 4F  from the coordinate position (0; 0) to the coordinate position (7.548; 10) for an infinity object, and from the coordinate position (-0.365; -5.5) to the coordinate position (1.181; 4.5) for a closest distance object. Therefore, the fourth lens unit moves by 10.0 in the direction of rotation (the direction of an axis a) in both the cases. On the other hand, upon focusing from the infinity arrangement to the closest distance object, the fourth lens unit moves on the focus cam g 4F  from the coordinate position (0; 0) to the coordinate position (-0.365; -5.5) at the wide-angle end, and from the coordinate position (7.548; 10) to the coordinate position (1.181; 4.5) at the telephoto end. Therefore, the fourth lens unit moves by -5.5 in the direction of rotation (the direction of the axis a) at these ends. In contrast to this, in the direction of the optical axis (the direction of an axis x), the fourth lens unit moves by -0.365 at the wide-angle end, and by -6.367 at the telephoto end. 
     Since the shape of the focus cam g 4F  is determined by interpolating the coordinates (F=28.8; R=0.80), (F=28.8; R=un), (F=126; R=0.80), and (F=126; R=un) by the spline function, the change in slope (dx/da) of the focus cam g 4F  becomes larger as the absolute value of the x-coordinate of (F=28.8; R=0.80) is smaller or as the absolute value of the x-coordinate of (F=126; R=un) is larger. More specifically, as the ratio (Δx TR  /Δx WR ) between the amounts Δx TR  and Δx WR  of movement, in the direction of the optical axis, of the focusing lens unit required for focusing from the infinity position to the closest distance position at the wide-angle end or telephoto end is larger, the change in slope (dx/da) of the focus cam becomes larger. 
     Tables 57, 58, and 59 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=28.8), the middle position (F=70.0), and the telephoto end (F=126.0) according to the first embodiment, respectively. In these tables, (R) on the left side is the photographing distance (m), (ANG) is the amount of rotation on the focus cam upon focusing to the respective photographing distances, and 1), 2), 3), 4), and 5) on the right side respectively represent the first, second, third, fourth, and fifth lens units. Also, in these tables, the first table summarizes the amount DX (mm) of movement for focusing in the direction of the optical axis upon focusing to the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m) (note that movement toward the object side is positive). The second table summarizes the imaging magnifications β K  of the respective lens units in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m). The third table summarizes the conversion coefficient γ x  associated with the direction of the optical axis of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m). Furthermore, the fourth table summarizes the slope (dx/da) of the focus cam at the positions, on the focus cam, corresponding to an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m), and the fifth table summarizes the conversion coefficient γ a  associated with the direction of rotation of the focusing lens unit in an in-focus state at the respective photographing distances (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.80 m). 
     
                                           TABLE 57__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angleEnd (28.8 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.204        1)          .000              2)                .000                    3)                      .000                          4)                            -.026                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -.052                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -.089                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -.135                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -.183                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            -.284                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -.365                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (28.8mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                -.295                    3)                      -.541                          4)                            -4.568                                5)                                  -.403R 10.000 ANG    -.204        1)          -.010              2)                -.291                    3)                      -.542                          4)                            -4.570                                5).                                  -.403R 5.000 ANG    -.427        1)          -.020              2)                -.287                    3)                      -.543                          4)                            -4.571                                5)                                  -.403R 3.000 ANG    -.755        1)          -.035              2)                -.281                    3)                      -.545                          4)                            -4.573                                5)                                  -.403R 2.000 ANG    -1.228        1)          -.055              2)                -.274                    3)                      -.547                          4)                            -4.575                                5)                                  -.403R 1.500 ANG    -1.788        1)          -.076              2)                -.266                    3)                      -.549                          4)                            -4.578                                5)                                  -.403R 1.000 ANG    -3.388        1)          -.125              2)                -.250                    3)                      -.554                          4)                            -4.583                                5)                                  -.403R .800 ANG    -5.500        1)          -.168              2)                -.238                    3)                      -.557                          4)                            -4.587                                5)                                  -.403Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angle End(28.8 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.225                                5)                                  .000R 10.000 ANG    -.204        1)          .000              2)                .000                    3)                      .000                          4)                            -3.227                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -3.229                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -3.231                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -3.235                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -3.239                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            -3.246                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -3.252                                5)                                  .000Slope dx/da of Focus Cam at Wide-angle End (28.8 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .133                                5)                                  .000R 10.000 ANG    -.204        1)          .000              2)                .000                    3)                      .000                          4)                            .123                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            .115                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            .105                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            .092                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            .079                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            .050                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            .028                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End(28.8 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -.428                                5)                                  .000R 10.000 ANG    -.204        1)          .000              2)                .000                    3)                      .000                          4)                            -.397                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -.371                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -.339                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -.299                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -.257                                5)                                  .000R 1.000 ANG    -3.388        1)          .900              2)                .000                    3)                      .000                          4)                            -.163                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -.090                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.01, γ.sub.aR /γ.sub.a0 = 0.21 
    
     
                                           TABLE 58__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (70.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.196        1)          .000              2)                .000                    3)                      .000                          4)                            -.146                                5)                                  .000R 5.000 ANG    -.410        1)          .000              2)                .000                    3)                      .000                          4)                            -.294                                5)                                  .000R 3.000 ANG    -.729        1)          .000              2)                .000                    3)                      .000                          4)                            -.496                                5)                                  .000R 2.000 ANG    -1.195        1)          .000              2)                .000                    3)                      .000                          4)                            -.754                                5)                                  .000R 1.500 ANG    -1.756        1)          .000              2)                .000                    3)                      .000                          4)                            -1.021                                5)                                  .000R 1.000 ANG    -3.344        1)          .000              2)                .000                    3)                      .000                          4)                            -1.578                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -2.019                                5)                                  .000Imaging Magnification β.sub.K of Lens Units at Middle Position (70.0mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                -.473                    3)                      -.774                          4)                            -3.044                                5)                                  -.641R 10.000 ANG    -.196        1)          -.010              2)                -.463                    3)                      -.780                          4)                            -3.051                                5)                                  -.641R 5.000 ANG    -.410        1)          -.021              2)                -.452                    3)                      -.786                          4)                            -3.059                                5)                                  -.641R 3.000 ANG    -.729        1)          -.035              2)                -.438                    3)                      -.795                          4)                            -3.069                                5)                                  -.641R 2.000 ANG    -1.195        1)          -.055              2)                -.420                    3)                      -.806                          4)                            -3.082                                5)                                  -.641R 1.500 ANG    -1.756        1)          -.077              2)                -.402                    3)                      -.817                          4)                            -3.096                                5)                                  -.641R 1.000 ANG    -3.344        1)          -.128              2)                -.366                    3)                      -.840                          4)                            -3.124                                5)                                  -.641R .800 ANG    -5.500        1)          -.173              2)                -.339                    3)                      -.859                          4)                            -3.147                                5)                                  -.641Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Middle Position(70.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.390                                5)                                  .000R 10.000 ANG    -.196        1)          .000              2)                .000                    3)                      .000                          4)                            -3.409                                5)                                  .000R 5.000 ANG    -.410        1)          .000              2)                .000                    3)                      .000                          4)                            -3.428                                5)                                  .000R 3.000 ANG    -.729        1)          .000              2)                .000                    3)                      .000                          4)                            -3.454                                5)                                  .000R 2.000 ANG    -1.195        1)          .000              2)                .000                    3)                      .000                          4)                            -3.487                                5)                                  .000R 1.500 ANG    -1.756        1)          .000              2)                .000                    3)                      .000                          4)                            -3.521                                5)                                  .000R 1.000 ANG    -3.344        1)          .000              2)                .000                    3)                      .000                          4)                            -3.594                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -3.652                                5)                                  .000Slope dx/da of Focus Cam at Middle Position (70.0 m) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .770                                5)                                  .000R 10.000 ANG    -.196        1)          .000              2)                .000                    3)                      .000                          4)                            .719                                5)                                  .000R 5.000 ANG    -.410        1)          .000              2)                .000                    3)                      .000                          4)                            .668                                5)                                  .000R 3.000 ANG    -.729        1)          .000              2)                .000                    3)                      .000                          4)                            .599                                5)                                  .000R 2.000 ANG    -1.195        1)          .000              2)                .000                    3)                      .000                          4)                            .514                                5)                                  .000R 1.500 ANG    -1.756        1)          .000              2)                .000                    3)                      .000                          4)                            .438                                5)                                  .000R 1.000 ANG    -3.344        1)          .000              2)                .000                    3)                      .000                          4)                            .275                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            .154                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Middle Position(70.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -2.611                                5)                                  .000R 10.000 ANG    -.196        1)          .000              2)                .000                    3)                      .000                          4)                            -2.452                                5)                                  .000R 5.000 ANG    -.410        1)          .000              2)                .000                    3)                      .000                          4)                            -2.288                                5)                                  .000R 3.000 ANG    -.729        1)          .000              2)                .000                    3)                      .000                          4)                            -2.067                                5)                                  .000R 2.000 ANG    -1.195        1)          .000              2)                .000                    3)                      .000                          4)                            -1.794                                5)                                  .000R 1.500 ANG    -1.756        1)          .000              2)                .000                    3)                      .000                          4)                            -1.542                                5)                                  .000R 1.000 ANG    -3.344        1)          .000              2)                .000                    3)                      .000                          4)                            -.987                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -.562                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.08, γ.sub.aR /γ.sub.a0 = 0.22 
    
     
                                           TABLE 59__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End(126.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000                                5)                                  .000R 10.000 ANG    -.203        1)          .000              2)                .000                    3)                      .000                          4)                            -.452                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -.913                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -1.542                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -2.352                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -3.190                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            -4.956                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -6.367                                5)                                  .000Imaging Magnification β.sub.x of Lens Units at Telephoto End (126.0mm) in Fifth EmbodimentR .000 ANG    .000        1)          -.000              2)                -.710                    3)                      -.890                          4)                            -2.626                                5)                                  -.775R 10.000 ANG    -.203        1)          -.010              2)                -.686                    3)                      -.908                          4)                            -2.649                                5)                                  -.775R 5.000 ANG    -.427        1)          -.021              2)                -.663                    3)                      -.927                          4)                            -2.673                                5)                                  -.775R 3.000 ANG    -.755        1)          -.036              2)                -.632                    3)                      -.952                          4)                            -2.705                                5)                                  -.775R 2.000 ANG    -1.228        1)          -.056              2)                -.595                    3)                      -.985                          4)                            -2.746                                5)                                  -.775R 1.500 ANG    -1.788        1)          -.078              2)                -.559                    3)                      -1.019                          4)                            -2.789                                5)                                  -.775R 1.000 ANG    -3.388        1)          -.130              2)                -.491                    3)                      -1.092                          4)                            -2.879                                5)                                  -.775R .800 ANG    -5.500        1)          -.176              2)                -.442                    3)                      -1.150                          4)                            -2.951                                5)                                  -.775Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Telephot End(126.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -3.543                                5)                                  .000R 10.000 ANG    -.203        1)          .000              2)                .000                    3)                      .000                          4)                            -3.617                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -3.692                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -3.795                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -3.931                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -4.073                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .Q00                    3)                      .000                          4)                            -4.380                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -4.632                                5)                                  .000Slope dx/da of Focus Cam at Telephoto End (126.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            2.316                                5)                                  .000R 10.000 ANG    -.203        1)          .000              2)                .000                    3)                      .000                          4)                            2.140                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            2.000                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            1.828                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            1.608                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            1.379                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            .899                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            .468                                5)                                  .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(126.0 mm) in Fifth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            -8.205                                5)                                  .000R 10.000 ANG    -.203        1)          .000              2)                .000                    3)                      .000                          4)                            -7.738                                5)                                  .000R 5.000 ANG    -.427        1)          .000              2)                .000                    3)                      .000                          4)                            -7.383                                5)                                  .000R 3.000 ANG    -.755        1)          .000              2)                .000                    3)                      .000                          4)                            -6.939                                5)                                  .000R 2.000 ANG    -1.228        1)          .000              2)                .000                    3)                      .000                          4)                            -6.321                                5)                                  .000R 1.500 ANG    -1.788        1)          .000              2)                .000                    3)                      .000                          4)                            -5.615                                5)                                  .000R 1.000 ANG    -3.388        1)          .000              2)                .000                    3)                      .000                          4)                            -3.936                                5)                                  .000R .800 ANG    -5.500        1)          .000              2)                .000                    3)                      .000                          4)                            -2.168                                5)                                  .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.31, γ.sub.aR /γ.sub.a0 = 0.26 
    
     As can be seen from Tables 57, 58, and 59, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     From Tables 57, 58, and 59, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.21 at the wide-angle end (F=28.8), ×0.22 at the middle position (F=70.0), and ×0.26 at the telephoto end (F=126.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the fifth embodiment is calculated using formula (a), and is compared with that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: 
     When the rotation amount ratio (a F  /a Z ) is set to be 1.0 
     
         N.sub.W &gt;14.6N.sub.M &gt;16.1N.sub.T &gt;16.9 
    
     Fifth Embodiment 
     
         N.sub.W &gt;8.5N.sub.M &gt;8.4N.sub.T &gt;7.3 
    
     Therefore, it can be seen that the numbers of divisions become small, compared to those in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     As described above, in the zoom lens of the fifth embodiment, since the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation becomes much smaller than that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient γ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 60, 61, and 62 summarize the calculation results of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=28.8), middle position (F=70.0), and telephoto end (F=126.0) according to the first embodiment. In these tables, (R) is the object distance (m), (ANG) is the amount of rotation for focusing from the infinity corresponding position on the focus cam, (r) is the conversion coefficient γ a  in the direction of rotation, (rs) is the conversion coefficient K a , (bf) is the defocus amount (mm), and (l) is the correction coefficient μ. Each table has a matrix structure, and eight rows in the vertical direction indicated by (POS) represent the object positions (R=10.0, 5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 mm), and four pairs (R, ANGLE) in the horizontal direction represent the lens arrangements of the focusing lens unit. 
     More specifically, the position of the focusing lens in the first pair in the upper two tables in each of Tables 60, 61, and 62, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Therefore, the third column (r) in the first table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on an infinity object, and the fourth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. Furthermore, the third column (bf) in the second table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the infinity corresponding position, and an object is located at an object distance in the second column, and the fourth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on an infinity object to an in-focus state at the object distance in the second column. 
     Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 60, 61, and 62, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.80, -5.5), and it indicates that this position corresponds to the closest in-focus (R=0.80 m) corresponding position. Therefore, the ninth column (r) in the third table represents the value of the conversion coefficient γ a  in the direction of rotation when the focusing lens unit is focused on a closest distance (R=0.80 m) object, and the tenth column (rs) represents the value of the conversion coefficient K a  when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.80 m) object to an in-focus state at the object distance in the second column. Furthermore, the ninth column (bf) in the fourth table represents the defocus amount ΔBf from a predetermined imaging position when the position of the focusing lens unit corresponds to the closest corresponding position, and the object is located at an object distance in the second column, and the tenth column (l) represents the value of the correction coefficient μ when the focusing lens unit is moved from an in-focus state on the closest distance (R=0.80 m) object to an in-focus state at the object distance in the second column. 
     As described above, since the conversion coefficient in the direction of rotation is calculated by K a  =ΔBf/Δa (where Δa: the amount of rotation for focusing), and the correction coefficient μ is calculated by μ=ΔBf/(1-K a  /γ a ), the value of the conversion coefficient K a  (eight row, fourth column in first table: -0.214) when the focusing lens unit is moved from an in-focus state on the infinity object to an in-focus state at the object distance (R=0.80 m) in Table 60 is calculated by K a  =1.18/-5.5 =-0.214 using ΔBf=1.18 and Δa=-5.5. On the other hand, the value of the correction coefficient μ (eight row, fourth column in second table: 2.37) is calculated as μ=2.37 using ΔBf=1.18, K a  =-0.214, and γ a  =-0.428. 
     
                                           TABLE 60__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (28.8 mm) of Fifth EmbodimentF = 28.8 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.204                  5.000                      -.427                          3.000                              -.755POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.428      .000    -.412   -.397   -.3792  10.000  -.411          -.397              .000    -.383   -.3673  5.000   -.396   -.383                  -.371                      .000    -.3554  3.000   -.378   -.366   -.355                          -.339                              .0005  2.000   -.355   -.344   -.333   -.3186  1.500   -.331   -.320   -.310   -.2967  1.000   -.271   -.262   -.253   -.2418  .800    -.214   -.207   -.199   -.189__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.08              2.20                  -.17                      2.43                          -.29                              2.452  10.000  .08 2.20          .00 .00 -.09                      2.62                          -.20                              2.503  5.000  .17 2.32          .09 2.50                  .00 .00 -.12                              2.464  3.000  .29 2.48          .20 2.65                  .12 2.74                          .00 .005  2.000  .44 2.56          .35 2.65                  .27 2.61                          .15 2.376  1.500  .59 2.60          .51 2.64                  .42 2.58                          .31 2.407  1.000  .92 2.51          .84 2.46                  .75 2.36                          .63 2.188  .800  1.18      2.37          1.10              2.29                  1.01                      2.19                          .90 2.02__________________________________________________________________________(R, ANGLE) =  2.000      -1.228          1.000              -1.788                  1.000                      -3.388                          .800                              -5.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.356   -.331   -.272   -.2162  10.000  -.344   -.321   -.263   -.2083  5.000   -.333   -.311   -.254   -.2004  3.000   -.318   -.296   -.241   -.1895  2.000  -.299      .000    -.278   -.224   -.1756  1.500   -.278          -.257              .000    -.205   -.1597  1.000   -.224   -.205                  -.163                      .000    -.1248  .800    -.175   -.159   -.124                          -.090                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.44      2.29          -.59              2.04                  -.92                      1.37                          -1.19                              .862  10.000  -.35      2.31          -.51              2.04                  -.84                      1.36                          -1.10                              .853  5.000  -.27      2.30          -.42              2.02                  -.75                      1.34                          -1.02                              .844  3.000  -.15      2.32          -.31              1.99                  -.64                      1.32                          -.90                              .825  2.000  .00 .00 -.16              1.89                  -.48                      1.28                          -.75                              .806  1.500  .16 2.23          .00 .00 -.33                      1.26                          -.59                              .787  1.000  .48 1.93          .33 1.63                  .00 .00 -.26                              .708  .800  .75 1.79          .59 1.55                  .26 1.11                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.50, K.sub.aR /γ.sub.aR = 2.39 
    
     
                                           TABLE 61__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (70.0 mm) of Fifth EmbodimentF = 70.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.196                  5.000                      -.410                          3.000                              -.729POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -2.610      .000    -2.533  -2.450  -2.3332  10.000  -2.528          -2.450              .000    -2.371  -2.2573  5.000   -2.442  -2.367                  -2.290                      .000    -2.1784  3.000   -2.321  -2.249  -2.173                          -2.066                              .0005  2.000   -2.161  -2.093  -2.022  -1.9236  1.500   -1.996  -1.933  -1.868  -1.7787  1.000   -1.632  -1.580  -1.526  -1.4518  .800    -1.277  -1.234  -1.189  -1.126__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.50              14.70                  -1.00                      14.34                          -1.70                              13.152  10.000  .50 15.81          .00 .00 -.51                      14.33                          -1.20                              13.023  5.000  1.00      15.51          .51 14.93                  .00 .00 -.69                              12.874  3.000  1.69      15.25          1.20              14.58                  .69 13.60                          .00 .005  2.000  2.58      15.00          2.09              14.35                  1.59                      13.58                          .90 12.956  1.500  3.51      14.90          3.02              14.30                  2.52                      13.66                          1.83                              13.087  1.000  5.46      14.57          4.97              14.01                  4.48                      13.43                          3.80                              12.758  .800  7.02      13.75          6.54              13.18                  6.05                      12.59                          5.37                              11.82__________________________________________________________________________(R, ANGLE) =  2.000      -1.195          1.500              -1.756                  1.000                      -3.344                          .800                              -5.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -2.177  -2.015  -1.652  -1.2932  10.000  -2.105  -1.948  -1.597  -1.2473  5.000   -2.031  -1.879  -1.539  -1.2004  3.000   -1.927  -1.785  -1.461  -1.1355  2.000  -1.793      .000    -1.664  -1.359  -1.0496  1.500   -1.661          -1.543              .000    -1.250  -.9567  1.000   -1.353  -1.247                  -.987                      .000    -.7418  .800    -1.044  -.954   -.740                          -.561                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -2.60      12.16          -3.54              11.58                  -5.52                      8.21                          -7.11                              5.462  10.000  -2.10      12.10          -3.04              11.59                  -5.03                      8.15                          -6.62                              5.423  5.000  -1.59      12.06          -2.53              11.62                  -4.52                      8.08                          -6.11                              5.374  3.000  -.90      12.05          -1.83              11.72                  -3.82                      7.97                          -5.41                              5.305  2.000  .00 .00 -.93              11.93                  -2.92                      7.76                          -4.51                              5.206  1.500  .93 12.62          .00 .00 -1.98                      7.46                          -3.58                              5.097  1.000  2.91      11.83          1.98              10.31                  .00 .00 -1.60                              5.008  .800  4.49      10.74          3.57              9.34                  1.60                      6.39                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.49, K.sub.aR /γ.sub.aR = 2.30 
    
     
                                           TABLE 62__________________________________________________________________________Conversion Coefficient K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (126.0 mm) of Fifth EmbodimentF = 126.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          -.203              2.777                  5.000                      -.427                          3.000                              -.755POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -8.209      .000    -7.975  -7.761  -7.5002  10.000  -7.943          -7.742              .000    -7.554  -7.3253  5.000   -7.708  -7.534                  -7.387                      .000    -7.1704  3.000   -7.437  -7.294  -7.160                          -6.930                              .0005  2.000   -7.075  -6.951  -6.823  -6.6146  1.500   -6.689  -6.581  -6.464  -6.2767  1.000   -5.664  -5.576  -5.475  -5.3108  .800    -4.602  -4.530  -4.444  -4.305__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -1.62              53.88                  -3.31                      65.46                          -5.66                              68.892  10.000  1.62      49.82          .00 .00 -1.69                      74.73                          -4.04                              70.943  5.000  3.29      53.95          1.68              62.63                  .00 .00 -2.35                              67.914  3.000  5.62      59.75          4.02              69.57                  2.35                      76.44                          .00 .005  2.000  8.69      62.90          7.12              69.69                  5.47                      71.55                          3.13                              68.606  1.500  11.96      64.62          10.43              69.54                  8.80                      70.43                          6.48                              68.737  1.000  19.19      61.91          17.76              63.48                  16.22                      62.65                          13.98                              59.848  .800  25.31      57.61          23.99              57.82                  22.55                      56.60                          20.43                              53.93__________________________________________________________________________(R, ANGLE) =  2.000      -1.228          1.500              -1.788                  1.000                      -3.388                          .800                              -5.500POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -7.122  -6.691  -5.513  -4.3262  10.000  -6.967  -6.553  -5.399  -4.2323  5.000   -6.819  -6.417  -5.281  -4.1324  3.000   -6.600  -6.220  -5.109  -3.9885  2.000  -6.322      .000    -5.958  -4.866  -3.7836  1.500   -6.000          -5.618              .000    -4.571  -3.5437  1.000   -5.053  -4.716                  -3.938                      .000    -2.9408  .800    -4.086  -3.807  -3.066                          -2.167                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -8.75      69.13          -11.97              62.65                  -18.68                      46.70                          -23.79                              23.872  10.000  -7.14      69.99          -10.39              62.40                  -17.19                      46.35                          -22.41                              23.523  5.000  -5.46      69.51          -8.74              61.42                  -15.64                      45.85                          -20.96                              23.114  3.000  -3.12      70.92          -6.43              59.98                  -13.45                      45.24                          -18.92                              22.515  2.000  .00 .00 -3.34              55.23                  -10.51                      44.59                          -16.16                              21.666  1.500  3.36      65.93          .00 .00 -7.31                      45.49                          -13.15                              20.707  1.000  10.92      54.38          7.55              47.00                  .00 .00 -6.21                              17.398  .800  17.46      49.36          14.13              43.83                  6.48                      29.27                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.56, K.sub.aR /γ.sub.aR = 2.00 
    
     As can be seen from Tables 60, 61, and 62 above, when a change in conversion coefficient K a  : (rs) (e.g., the fourth column in the first table) at a given lens arrangement (e.g., at the infinity in-focus arrangement) is considered, the rate of change becomes small as compared to the change in K a  (Tables 15, 16, and 17) in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 examined previously. 
     More specifically, the amount Δa of rotation for focusing in the first embodiment at the infinity object side becomes relatively smaller than that at the closest object side, as compared to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as the embodiment of Japanese Patent Application Laid-Open No. 5-142475. In fact, when the ratio between the amount of rotation for focusing upon focusing to the closest distance and the amount of rotation for focusing upon focusing to the object distance (R=5.0 m) is calculated in Tables 10 and 55, 4.296/10.0=0.430 in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, while -0.427/-5.5=0.078 in the fifth embodiment. As described above, when the focus cam with the arrangement of the present invention is used, since the amount Δa of rotation for focusing becomes relatively smaller at the infinity object side, the conversion coefficient K a  becomes relatively large at the infinity object side, and consequently, the change in conversion coefficient K a  in the direction of rotation can be reduced as compared to the conventional system. 
     The calculation results of the rate of change of K a  with respect to γ a  at the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end, middle position, and telephoto end in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the fifth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.55 are as follows. 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      4.76           0.34(F = 28.8)Middle Position      5.78           0.31(F = 70.0)Telephoto End      6.58           0.28(F = 126.0)Fifth EmbodimentWide-angle End      0.50           2.39(F = 28.8)Middle Position      0.49           2.30(F = 70.0)Telephoto End      0.56           2.00(F = 126.0)______________________________________ 
    
     As described above, according to the present invention, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced, the value of the correction coefficient μ can be set to be large as compared to the defocus amount ΔBf, and at the same time, the change in correction coefficient μ can be decreased. 
     Therefore, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error in the conversion coefficient K a  calculated using γ a  and μ or in the actual lens driving amount Δa for focusing can be eliminated. 
     Next, in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the fifth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.55, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end (F=28.8), middle position (F=70.0), and telephoto end (F=126.0) are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -8.7%         -26.3%(F = 28.8)Middle Position      -13.2%         -23.4%(F = 70.0)Telephoto End      -14.1%         -28.7%(F = 126.0)Fifth EmbodimentWide-angle End       -6.9%         -2.4%(F = 28.8)Middle Position      -8.0%          -1.6%(F = 70.0)Telephoto End      -6.2%          -2.9%(F = 126.0)______________________________________ 
    
     As described above, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Next, an examination will be made as to whether not only accurate auto-focusing but also so-called manual focusing can be attained in the zoom lens of the fifth embodiment. 
     Table 63 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 55) of the fifth embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     The upper table in Table 63 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) in the respective zooming states of the focal lengths (F=28.8, 35.0, 50.0, 70.0, 95.0, and 126.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.80 m). Note that the amounts of rotation for focusing, which have values for eliminating any displacement of the imaging point at the wide-angle end and the telephoto end, are selected. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.0, and 0.8 m) in the respective zooming states with the focal lengths (F=28.8, 35.0, 50.0, 70.0, 95.0, and 126.0 mm). In the lower table, (F) is the focal length (mm) of the entire system, (R) is the photographing distance (m), and (DX) is the amount (mm) of movement, in the direction of the optical axis, of each of the first, second, third, fourth, and fifth lens units in turn from the right side. Note that the amount of movement in the direction of the optical axis toward the object side is represented by a positive value. 
     
                                           TABLE 63__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Fifth Embodiment__________________________________________________________________________  0.80 m      1.00 m            1.50 m                2.00 m                      3.00 m                          5.00 m__________________________________________________________________________28.800 Bf  .000      .000  .000                .000  .000                          .00035.000 Bf  .000      .003  -.001                -.002 .005                          .00550.000 Bf  .000      .008  .006                -.002 -.003                          -.00170.000 Bf  .000      .044  .049                -.059 -.054                          -.03995.000 Bf  .000      -.092 -.012                .037  .039                          .027126.000 Bf  .000      .000  .000                .000  .000                          .000__________________________________________________________________________ANGLE DA   -5.500        -3.388            -1.788                 -1.228                     -.755 -.427__________________________________________________________________________F 28.800 DX   .000 .000            .000 -.365                     .000                         R 0.80 mF 35.000 DX   .000 .000            .000 -.533                     .000                         R 0.80 mF 50.000 DX   .000 .000            .000 -1.061                     .000                         R 0.80 mF 70.000 DX   .000 .000            .000 -2.019                     .000                         R 0.80 mF 95.000 DX   .000 .000            .000 -3.656                     .000                         R 0.80 mF 126.000 DX   .000 .000            .000 -6.367                     .000                         R 0.80 mF 28.800 DX   .000 .000            .000 -.284                     .000                         R 1.00 mF 35.000 DX   .000 .000            .000 -.417                     .000                         R 1.00 mF 50.000 DX   .000 .000            .000 -.826                     .000                         R 1.00 mF 70.000 DX   .000 .000            .000 -1.590                     .000                         R 1.00 mF 95.000 DX   .000 .000            .000 -2.880                     .000                         R 1.00 mF 126.000 DX   .000 .000            .000 -4.956                     .000                         R 1.00 mF 28.800 DX   .000 .000            .000 -.183                     .000                         R 1.50 mF 35.000 DX   .000 .000            .000 -.268                     .000                         R 1.50 mF 50.000 DX   .000 .000            .000 -.533                     .000                         R 1.50 mF 70.000 DX   .000 .000            .000 -1.035                     .000                         R 1.50 mF 126.000 DX   .000 .000            .000 -3.190                     .000                         R 1.50 mF 28.800 DX   .000 .000            .000 -.135                     .000                         R 2.00 mF 35.000 DX   .000 .000            .000 -.198                     .000                         R 2.00 mF 50.000 DX   .000 .000            .000 -.396                     .000                         R 2.00 mF 70.000 DX   .000 .000            .000 -.771                     .000                         R 2.00 mF 95.000 DX   .000 .000            .000 -1.355                     .000                         R 2.00 mF 126.000 DX   .000 .000            .000 -2.352                     .000                         R 2.00 mF 28.800 DX   .000 .000            .000 -.089                     .000                         R 3.00 mF 35.000 DX   .000 .000            .000 -.128                     .000                         R 3.00 mF 50.000 DX   .000 .000            .000 -.260                     .000                         R 3.00 mF 70.000 DX   .000 .000            .000 -.511                     .000                         R 3.00 mF 95.000 DX   .000 .000            .000 -.886                     .000                         R 3.00 mF 126.000 DX   .000 .000            .000 -1.542                     .000                         R 3.00 mF 28.800 DX   .000 .000            .000 -.052                     .000                         R 5.00 mF 35.000 DX   .000 .000            .000 -.075                     .000                         R 5.00 mF 50.000 DX   .000 .000            .000 -.154                     .000                         R 5.00 mF 70.000 DX   .000 .000            .000 -.305                     .000                         R 5.00 mF 95.000 DX   .000 .000            .000 -.524                     .000                         R 5.00 mF 126.000 DX   .000 .000            .000 -.913                     .000                         R 5.00 m__________________________________________________________________________ 
    
     As can be seen from Table 63, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
      Sixth Embodiment! 
     The sixth embodiment is directed to a zoom lens which has a five-unit arrangement, i.e., positive, negative, positive, and positive lens units, and attains focusing by a negative second lens unit. In this zoom lens, the rotation amount ratio (a F  /a Z ) of the rotation amount for focusing from the infinity in-focus position to the closest in-focus position (R=0.95 m) to the amount of rotation for zooming from the wide-angle end (F=24.7) to the telephoto end (F=194.0) is set to be -0.80. 
     Table 64 below summarizes various paraxial data of an optical system and data for defining the shape of a focus cam according to the sixth embodiment. 
     The upper table in Table 64 summarizes the focal lengths and principal point interval data of the respective lens units of the optical system corresponding to the sixth embodiment in association with six zooming states (focal length F=24.7 (1-POS), 35.0 (2-POS), 50.0 (3-POS), 85.0 (4-POS), 135.0 (5-POS), and 194.0 mm (6-POS)). 
     The middle table in Table 64 summarizes spline sample data when the shape of the focus cam in the second lens unit of the sixth embodiment, which is used for focusing, is expressed by the above-mentioned spline function associated with the angle a of rotation of a rotatable lens barrel and the amount x of movement in the direction of the optical axis. In this middle table, (1), (2), (3), and (4) correspond to the first, second, third, and fourth lens units, respectively. 
     Furthermore, the lower table in Table 64 summarizes the infinity focusing positions (infinity corresponding positions) at the respective focal lengths (F=24.7, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the amounts of rotation (amounts of rotation for focusing) upon focusing to respective photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) using the focus cam of the sixth embodiment. In this table, since the amount of rotation for zooming from the wide-angle end (F=24.7) to the telephoto end (F=194.0) is set to be 10.0, and the amount of rotation for focusing from the infinity in-focus position to the closest in-focus position (R=0.95 m) is set to be -8.0, the rotation amount ratio (a F  /a Z ) of the amount of rotation for focusing to the amount of rotation for zooming in the fourth embodiment is -0.80. 
     
                                           TABLE 64__________________________________________________________________________Second Embodiment F = 24.7 to 194.0 (RotationAmount Ratio: a.sub.F /a.sub.Z = -0.80)__________________________________________________________________________Focal lengths and Principal Point Intervals of Lens Units of SixthEmbodiment    1-POS        2-POS             3-POS                 4-POS                      5-POS                           6-POS__________________________________________________________________________  F 24.7000        35.0000             50.0000                 85.0000                      135.0000                           194.0000F1  83.0000  D1    8.4075        15.4045             23.5767                 34.4070                      43.3980                           49.1234F2  -15.0000  D2    28.3223        23.1584             19.2184                 14.3263                      10.2768                           6.6130F3  44.0000  D3    8.1372        7.7418             7.2728                 5.5880                      5.1884                           4.7906F4  60.0000  D4    55.0055        63.1527             71.4749                 84.9444                      94.8409                           101.9854__________________________________________________________________________Focus Cam Shape (Spline Interpolation Sample Point) Correspondingto Sixth Embodiment   ANGLE     (1)           (2)       (3)                        (4)__________________________________________________________________________1  -10.0000  .0000           .5780     .0000                        .00002  -8.0000   .0000           .5191     .0000                        .00003  -5.1006   .0000           .4059     .0000                        .00004  -3.6046   .0000           .3218     .0000                        .00005  -2.4342   .0000           .2392     .0000                        .00006  -1.4844   .0000           .1580     .0000                        .00007  -.8361    .0000           .0942     .0000                        .00008  .0000     .0000           .0000     .0000                        .00009  .5000     .0000           -.0640    .0000                        .000010 2.0000    .0000           -.2910    .0000                        .000011 4.8994    .0000           -.9968    .0000                        .000012 6.3953    .0000           -1.5990   .0000                        .000013 7.5658    .0000           -2.2827   .0000                        .000014 8.5156    .000           -3.0883   .0000                        .000015 9.1639    .000           -3.8748   .0000                        .000016 10.0000   .000           -5.5825   .0000                        .000017 11.0000   .0000           -9.9000   .0000                        .0000__________________________________________________________________________Amount of Rotation for Zooming and Amount of Rotation for Focusing ofSixth Embodiment(Rotation Amount Ratio: a.sub.F /a.sub.Z = -0.80)__________________________________________________________________________          Infinity         Amount of          Correspond-                Photograph-                           Rotation forFocal Length   ing Position                ing Distance                           Focusing__________________________________________________________________________24.7 mm        .0000  5.00 m    -.83635.0 mm        1.4533                 3.00 m    -1.48450.0 mm        3.3444                 2.00 m    -2.43485.0 mm        6.1312                 1.50 m    -3.605135.0 mm       8.6279                 1.20 m    -5.101194.0 mm       10.0000                 0.95 m    -8.000Condition Corresponding Value (1)                 2.18Condition Corresponding Value (2)                 10.19Condition Corresponding Value (3)                -0.80Condition Corresponding Value (4)                 0.26 (wide-angle end)                 0.12 (telephoto end)Condition Corresponding Value (5)                 0.55 (wide-angle end)                 0.80 (telephoto end)Condition Corresponding Value (6)                 1.98 (wide-angle end)                 1.85 (telephoto end)__________________________________________________________________________ 
    
     Table 65 below summarizes the numerical value data of the cams of the focusing lens unit in the sixth embodiment, which data are calculated by interpolation based on a spline function on the basis of the sample data of the focus cam summarized in the middle table in Table 64. Note that the meanings of the reference symbols in Table 65 are the same as those in the fifth embodiment. 
     
                       TABLE 65______________________________________Cam Numerical Value Data of Focusing Lens Unit in SixthEmbodiment             Zoom Compensation CamFocus Cam Numerical Value Data             Numerical Value DataANGLE  (2)       F        ANGLE  (2)    F______________________________________-8.0000  .5191     .0000-7.5000  .5029     .0000-7.0000  .4856     .0000-6.5000  .4670     .0000-6.0000  .4468     .0000-5.5000  .4249     .0000-5.0000  .4009     .0000-4.5000  .3747     .0000-4.0000  .3462     .0000-3.5000  .3151     .0000-3.0000  .2812     .0000-2.5000  .2443     .0000-2.0000  .2038     .0000-1.5000  .1595     .0000-1.0000  .1110     .0000-.5000 .0581     .0000.0000  .0000     24.7000  .0000  .0000  24.7000.5000  -.0640    28.1820  .5000  .9557  28.18201.0000 -.1332    31.7391  1.0000 1.9059 31.73911.5000 -.2084    35.3374  1.5000 2.8823 35.33742.0000 -.2910    38.9843  2.0000 3.9161 38.98432.5000 -.3824    42.7873  2.5000 5.0190 42.78733.0000 -.4844    46.8974  3.0000 6.2000 46.89743.5000 -.5985    51.4940  3.5000 7.4659 51.49404.0000 -.7264    56.7072  4.0000 8.8121 56.70724.5000 -.8699    62.5219  4.5000 10.2142                                   62.52195.0000 -1.0306   68.8723  5.0000 11.6417                                   68.87235.5000 -1.2111   75.6992  5.5000 13.0715                                   75.69926.0000 -1.4162   83.0056  6.0000 14.4965                                   83.00566.5000 -1.6509   90.7764  6.5000 15.9065                                   90.77647.0000 -1.9215   99.1459  7.0000 17.3051                                   99.14597.5000 -2.2373   108.3906 7.5000 18.7079                                   108.39068.0000 -2.6106   118.8434 8.0000 20.1317                                   118.84348.5000 -3.0721   131.3527 8.5000 21.6429                                   131.35279.0000 -3.6548   146.7241 9.0000 23.2762                                   146.72419.5000 -4.3955   165.4668 9.5000 25.0563                                   165.466810.0000  -5.5825   194.0000 10.0000                            27.5064                                   194.0000______________________________________ 
    
     The left table in Table 65 summarizes the numerical value data of the focus cam of the sixth embodiment, and the right table in Table 65 summarizes the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesizing the amounts (2) of movement in the direction of the optical axis in the numerical value data of the focus cam and the zoom compensation cam in the range from the amount of rotation (ANGLE=0.0) to the amount of rotation (ANGLE=10.0) coincides with the movement locus of the second lens unit calculated using the paraxial data in the upper table in Table 64. 
     Tables 66, 67, and 68 below summarize the amount DX (mm) of movement for focusing, in the direction of the optical axis, of the focusing lens unit, the imaging magnifications β K  of the respective lens units, the conversion coefficient γ x  associated with the direction of the optical axis, the slope (dx/da) of the focus cam, and the conversion coefficient γ a  associated with the direction of rotation at the wide-angle end (F=24.7), the middle position (F=85.0), and the telephoto end (F=194.0) according to the sixth embodiment, respectively. The arrangements of the respective tables and the meanings of the reference symbols are the same as those in the sixth embodiment. 
     
                                           TABLE 66__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atWide-angle End (24.7 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000 4)                             .000R 10.000 ANG    -.399        1)          .000              2)                .047                    3)                      .000 4)                             .000R 5.000 ANG    -.836        1)          .000              2)                .094                    3)                      .000 4)                             .000R 3.000 ANG    -1.484        1)          .000              2)                .158                    3)                      .000 4)                             .000R 2.000 ANG    -2.434        1)          .000              2)                .239                    3)                      .000 4)                             .000R 1.500 ANG    -3.605        1)          .000              2)                .322                    3)                      .000 4)                             .000R 1.200 ANG    -5.101        1)          .000              2)                .406                    3)                      .000 4)                             .000R .950 ANG    -8.000        1)          .000              2)                .519                    3)                      .000 4)                             .000Imaging Magnification β.sub.K of Lens Units at Wide-angle End (24.7mm) in SixthEmbodimentR .000 ANG    .000        1)          .000              2)                -.252                    3)                      -14.203                           4)                             .083R 10.000 ANG    -.399        1)          -.008              2)                -.249                    3)                      -14.202                           4)                             .083R 5.000 ANG    -.836        1)          -.017              2)                -.245                    3)                      -14.203                           4)                             .083R 3.000 ANG    -1.484        1)          -.029              2)                -.241                    3)                      -14.203                           4)                             .083R 2.000 ANG    -2.434        1)          -.046              2)                -.236                    3)                      -14.203                           4)                             .083R 1.500 ANG    -3.605        1)          -.063              2)                -.230                    3)                      -14.203                           4)                             .083R 1.200 ANG    -5.101        i)          -.082              2)                -.225                    3)                      -14.203                           4)                             .083R .950 ANG    -8.000        1)          -.108              2)                -.217                    3)                      -14.203                           4)                             .083Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at Wide-angleEnd (24.7 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                1.309                    3)                      .000 4)                             .000R 10.000 ANG    -.399        1)          .000              2)                1.311                    3)                      .000 4)                             .000R 5.000 ANG    -.836        1)          .000              2)                1.314                    3)                      .000 4)                             .000R 3.000 ANG    -1.484        1)          .000              2)                1.316                    3)                      .000 4)                             .000R 2.000 ANG    -2.434        1)          .000              2)                1.320                    3)                      .000 4)                             .000R 1.500 ANG    -3.605        1)          .000              2)                1.324                    3)                      .000 4)                             .000R 1.200 ANG    -5.101        1)          .000              2)                1.327                    3)                      .000 4)                             .000R .950 ANG    -8.000        1)          .000              2)                1.332                    3)                      .000 4)                             .000Slope dx/da of Focus Cam at Wide-angle End (24.7 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                -.122                    3)                      .000 4)                             .000R 10.000 ANG    -.399        1)          .000              2)                -.113                    3)                      .000 4)                             .000R 5.000 ANG    -.836        1)          .000              2)                -.104                    3)                      .000 4)                             .000R 3.000 ANG    -1.484        1)          .000              2)                -.093                    3)                      .000 4)                             .000R 2.000 ANG    -2.434        1)          .000              2)                -.078                    3)                      .000 4)                             .000R 1.500 ANG    -3.605        1)          .000              2)                -.064                    3)                      .000 4)                             .000R 1.200 ANG    -5.101        1)          .000              2)                -.049                    3)                      .000 4)                             .000R .950 ANG    -8.000        1)          .000              2)                -.032                    3)                      .000 4)                             .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Wide-angle End(24.7 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                -.160                    3)                      .000 4)                             .000R 10.000 ANG    -.399        1)          .000              2)                -.148                    3)                      .000 4)                             .000R 5.000 ANG    -.836        1)          .000              2)                -.137                    3)                      .000 4)                             .000R 3.000 ANG    -1.484        1)          .000              2)                -.122                    3)                      .000 4)                             .000R 2.000 ANG    -3.434        1)          .000              2)                -.103                    3)                      .000 4)                             .000R 1.500 ANG    -3.605        1)          .000              2)                -.084                    3)                      .000 4)                             .000R 1.200 ANG    -5.101        1)          .000              2)                -.065                    3)                      .000 4)                             .000R .950 ANG    -8.000        1)          .000              2)                -.042                    3)                      .000 4)                             .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.02, γ.sub.aR /γ.sub.a0 = 0.26 
    
     
                                           TABLE 67__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atMiddlePosition (85.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.395        1)          .000              2)                .170                    3)                      .000                          4)                            .000R 5.000 ANG    -.827        1)          .000              2)                .337                    3)                      .000                          4)                            .000R 3.000 ANG    -1.470        1)          .000              2)                .555                    3)                      .000                          4)                            .000R 2.000 ANG    -2.411        1)          .000              2)                .822                    3)                      .000                          4)                            .000R 1.500 ANG    -3.579        1)          .000              2)                1.082                    3)                      .000                          4)                            .000R 1.200 ANG    -5.105        1)          .000              2)                1.338                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                1.667                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Unit at Middle Position (85.0mm) in SixthEmbodimentR .000 ANG    .000        1)          .000              2)                -.447                    3)                      5.517                          4)                            -.416R 10.000 ANG    -.395        1)          -.008              2)                -.435                    3)                      5.517                          4)                            -.416R 5.000 ANG    -.827        1)          -.017              2)                -.424                    3)                      5.517                          4)                            -.416R 3.000 ANG    -1.470        1)          -.030              2)                -.410                    3)                      5.517                          4)                            -.416R 2.000 ANG    -2.411        1)          -.047              2)                -.392                    3)                      5.517                          4)                            -.416R 1.500 ANG    -3.579        1)          -.065              2)                -.374                    3)                      5.517                          4)                            -.416R 1.200 ANG    -5.105        1)          -.085              2)                -.357                    3)                      5.517                          4)                            -.416R .950 ANG    -8.000        1)          -.114              2)                -.335                    3)                      5.517                          4)                            -.416Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at MiddlePosition (85.0 mm) in Sixth EmbodimentR .000 ANG    -.000        1)          .000              2)                4.211                    3)                      .000                          4)                            .000R 10.000 ANG    -.395        1)          .000              2)                4.264                    3)                      .000                          4)                            .000R 5.000 ANG    -.827        1)          .000              2)                4.314                    3)                      .000                          4)                            .000R 3.000 ANG    -1.470        1)          .000              2)                4.378                    3)                      .000                          4)                            .000R 2.000 ANG    -2.411        1)          .000              2)                4.453                    3)                      .000                          4)                            .000R 1.500 ANG    -3.579        1)          .000              2)                4.523                    3)                      .000                          4)                            .000R 1.200 ANG    -5.105        1)          .000              2)                4.588                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                4.668                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Middle Position (85.0 mm) in SixthEmbodimentR .000 ANG    .000        1)          .000              2)                -.454                    3)                      .000                          4)                            .000R 10.000 ANG    -.395        1)          .000              2)                -.408                    3)                      .000                          4)                            .000R 5.000 ANG    -.827        1)          .000              2)                -.365                    3)                      .000                          4)                            .000R 3.000 ANG    -1.470        1)          .000              2)                -.315                    3)                      .000                          4)                            .000R 2.000 ANG    -2.411        1)          .000              2)                -.254                    3)                      .000                          4)                            .000R 1.500 ANG    -3.579        1)          .000              2)                -.195                    3)                      .000                          4)                            .000R 1.200 ANG    -5.105        1)          .000              2)                -.145                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                -.087                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Middle Position(85.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                -1.912                    3)                      .000                          4)                            .000R 10.000 ANG    -.395        1)          .000              2)                -1.741                    3)                      .000                          4)                            .000R 5.000 ANG    -.827        1)          .000              2)                -1.577                    3)                      .000                          4)                            .000R 3.000 ANG    -1.470        1)          .000              2)                -1.378                    3)                      .000                          4)                            .000R 2.000 ANG    -2.411        1)          .000              2)                -1.131                    3)                      .000                          4)                            .000R 1.500 ANG    -3.579        1)          .000              2)                -.882                    3)                      .000                          4)                            .000R 1.200 ANG    -5.105        1)          .000              2)                -.663                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                -.405                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 1.11, γ.sub.aR /γ.sub.a0 = 0.21 
    
     
                                           TABLE 68__________________________________________________________________________Amount DX (mm) of Movement for Focusing in Direction of Optical Axis atTelephoto End (194.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                .000                    3)                      .000                          4)                            .000R 10.000 ANG    -.387        1)          .000              2)                .975                    3)                      .000                          4)                            .000R 5.000 ANG    -.836        1)          .000              2)                1.708                    3)                      .000                          4)                            .000R 3.000 ANG    -1.484        1)          .000              2)                2.494                    3)                      .000                          4)                            .000R 2.000 ANG    -2.434        1)          .000              2)                3.300                    3)                      .000                          4)                            .000R 1.500 ANG    -3.605        1)          .000              2)                3.983                    3)                      .000                          4)                            .000R 1.200 ANG    -5.101        1)          .000              2)                4.586                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                5.291                    3)                      .000                          4)                            .000Imaging Magnification β.sub.K of Lens Units at Telephoto End (194.0mm) in SixthEmbodimentR .000 ANG    .000        1)          .000              2)                -.795                    3)                      4.203                          4)                            -.700R 10.000 ANG    -.387        1)          -.009              2)                -.730                    3)                      4.203                          4)                            -.700R 5.000 ANG    -.836        1)          -.017              2)                -.681                    3)                      4.203                          4)                            -.700R 3.000 ANG    -1.484        1)          -.030              2)                -.628                    3)                      4.203                          4)                            -.700R 2.000 ANG    -2.434        1)          -.047              2)                -.575                    3)                      4.203                          4)                            -.700R 1.500 ANG    -3.605        1)          -.066              2)                -.529                    3)                      4.203                          4)                            -.700R 1.200 ANG    -5.101        1)          -.087              2)                -.489                    3)                      4.203                          4)                            -.700R .950 ANG    -8.000        1)          -.118              2)                -.442                    3)                      4.203                          4)                            -.700Conversion Coefficient γ.sub.x Associated With Direction of OpticalAxis at TelephotoEnd (194.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                3.189                    3)                      .000                          4)                            .000R 10.000 ANG    -.387        1)          .000              2)                4.046                    3)                      .000                          4)                            .000R 5.000 ANG    -.836        1)          .000              2)                4.642                    3)                      .000                          4)                            .000R 3.000 ANG    -1.484        1)          .000              2)                5.236                    3)                      .000                          4)                            .000R 2.000 ANG    -2.434        1)          .000              2)                5.795                    3)                      .000                          4)                            .000R 1.500 ANG    -3.605        1)          .000              2)                6.230                    3)                      .000                          4)                            .000R 1.200 ANG    -5.101        1)          .000              2)                6.584                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                6.963                    3)                      .000                          4)                            .000Slope dx/da of Focus Cam at Telephot End (194.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                -3.120                    3)                      .000                          4)                            .000R 10.000 ANG    -.387        1)          .000              2)                -2.002                    3)                      .000                          4)                            .000R 5.000 ANG    -.836        1)          .000              2)                -1.388                    3)                      .000                          4)                            .000R 3.000 ANG    -1.484        1)          .000              2)                -1.044                    3)                      .000                          4)                            .000R 2.000 ANG    -2.434        1)          .000              2)                -.697                    3)                      .000                          4)                            .000R 1.500 ANG    -3.605        1)          .000              2)                -.488                    3)                      .000                          4)                            .000R 1.200 ANG    -5.101        1)          .000              2)                -.332                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                -.174                    3)                      .000                          4)                            .000Conversion Coefficient γ.sub.a Associated With Direction ofRotation at Telephoto End(194.0 mm) in Sixth EmbodimentR .000 ANG    .000        1)          .000              2)                -9.950                    3)                      .000                          4)                            .000R 10.000 ANG    -.387        1)          .000              2)                -8.098                    3)                      .000                          4)                            .000R 5.000 ANG    -.836        1)          .000              2)                -6.441                    3)                      .000                          4)                            .000R 3.000 ANG    -1.484        1)          .000              2)                -5.466                    3)                      .000                          4)                            .000R 2.000 ANG    -2.434        1)          .000              2)                -4.041                    3)                      .000                          4)                            .000R 1.500 ANG    -3.605        1)          .000              2)                -3.041                    3)                      .000                          4)                            .000R 1.200 ANG    -5.101        1)          .000              2)                -2.187                    3)                      .000                          4)                            .000R .950 ANG    -8.000        1)          .000              2)                -1.208                    3)                      .000                          4)                            .000__________________________________________________________________________ Condition Corresponding Values: γ.sub.xR /γ.sub.x0 = 2.18, γ.sub.aR /γ.sub.a0 = 0.12 
    
     As can be seen from Tables 66, 67, and 68, at each focal length, the conversion coefficient γ x  associated with the direction of the optical axis increases but the value of the slope (dx/da) of the focus cam decreases as the photographing distance becomes closer to the closest distance. Therefore, as can be seen from these tables, the value of the conversion coefficient γ a  associated with the direction of rotation, which is defined as the product of the conversion coefficient γ x  and the slope (dx/da) of the focus cam, decreases as the photographing distance becomes closer to the closest distance by the influence of the slope (dx/da) of the focus cam, contrary to the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     From Tables 66, 67, and 68, the rate of change, from the infinity in-focus position to the closest in-focus position, of the conversion coefficient γ a  associated with the direction of rotation is ×0.26 at the wide-angle end (F=24.7), ×0.21 at the middle position (F=85.0), and ×0.12 at the telephoto end (F=194.0). When the number N of divisions of the focus range upon a change in conversion coefficient γ a  in the second embodiment is calculated using formula (a), and is compared with that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the numbers N W , N M , and N T  of divisions at the wide-angle end, middle position, and telephoto end respectively have the following values: 
     When the rotation amount ratio (a F  /a Z ) is set to be 1.0 
     
         N.sub.W &gt;16.1N.sub.M &gt;15.8N.sub.T &gt;13.7 
    
     Sixth Embodiment 
     
         N.sub.W &gt;7.3N.sub.M &gt;8.5N.sub.T &gt;11.6 
    
     Therefore, it can be seen that the numbers of divisions become small, compared to those in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475. 
     As described above, in the sixth embodiment as well, since the rate of change of the conversion coefficient γ a  associated with the direction of rotation is smaller than that in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient γ a  and the correction coefficient μ can be reduced, and the storage capacity can be suppressed. 
     Tables 69, 70, and 71 summarize the calculation results of the conversion coefficient K a  and the correction coefficient μ at the wide-angle end (F=24.7), middle position (F=85.0), and telephoto end (F=194.0) according to the sixth embodiment. The arrangements of the tables and reference symbols are the same as those in the fifth embodiment. The position of the focusing lens in the first pair in the upper two tables in each of Tables 69, 70, and 71, i.e., in the third and fourth columns is (R, ANGLE)=(0.0, 0.0), and it indicates that this position corresponds to the infinity corresponding position. Similarly, the position of the focusing lens in the fourth pair in the lower two tables in each of Tables 69, 70, and 71, i.e., in the ninth and tenth columns is (R, ANGLE)=(0.95, -8.0), and it indicates that this position corresponds to the closest in-focus (R=0.95 m) corresponding position. 
     
                                           TABLE 69__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Wide-angle End (24.7 mm) in Sixth EmbodimentF = 24.7 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.399                  5.000                      -.836                          3.000                              -1.484POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -.160      .000    -.153   -.147   -.1392  10.000  -.154          -.148              .000    -.142   -.1343  5.000   -.148   -.143                  -.137                      .000    -.1294  3.000   -.141   -.135   -.130                          -.122                              .0005  2.000   -.131   -.126   -.120   -.1136  1.500   -.120   -.115   -.110   -.1037  1.200   -.107   -.103   -.098   -.0928  .950    -.088   -.084   -.080   -.075__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.06              1.65                  -.12                      1.66                          -.21                              1.562  10.000  .06 1.70          .00 .00 -.06                      1.71                          -.15                              1.563  5.000  .12 1.73          .06 1.73                  .00 .00 -.08                              1.534  3.000  .21 1.77          .15 1.76                  .08 1.71                          .00 .005  2.000  .32 1.76          .26 1.71                  .19 1.61                          .11 1.426  1.500  .43 1.71          .37 1.65                  .30 1.54                          .22 1.377  1.200  .55 1.67          .48 1.59                  .42 1.49                          .33 1.338  .950  .71 1.58          .64 1.49                  .58 1.40                          .49 1.26__________________________________________________________________________(R, ANGLE) =  2.000      -2.434          1.500              -3.605                  1.200                      -5.101                          .950                              -8.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -.127   -.115   -.103   -.0832  10.000  -.123   -.111   -.099   -.0803  5.000   -.119   -.107   -.095   -.0774  3.000   -.112   -.101   -.089   -.0725  2.000  -.103      .000    -.093   -.082   -.0666  1.500   -.094          -.084              .000    -.074   -.0597  1.200   -.084   -.075                  -.065                      .000    -.0528  .950    -.068   -.060   -.052                          -.042                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -.31      1.32          -.42              1.13                  -.52                      .92 -.67                              .682  10.000  -.25      1.31          -.36              1.12                  -.46                      .91 -.61                              .673  5.000  -.19      1.28          -.30              1.10                  -.40                      .89 -.55                              .674  3.000  -.11      1.24          -.21              1.08                  -.32                      .88 -.47                              .665  2.000  .00 .00 -.11              1.07                  -.22                      .86 -.37                              .656  1.500  .11 1.19          .00 .00 -.11                      .82 -.26                              .657  1.200  .22 1.17          .11 1.00                  .00 .00 -.15                              .668  .950  .38 1.10          .26 .93 .15 .76 .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.55, K.sub.aR /γ.sub.aR = 1.98 
    
     
                                           TABLE 70__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Middle Position (85.0 mm) in Sixth EmbodimentF = 85.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.395                  5.000                      -.827                          3.000                              -1.470POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -1.912      .000    -1.795  -1.681  -1.5382  10.000  -1.856          -1.741              .000    -1.630  -1.4913  5.000   -1.796  -1.684                  -1.576                      .000    -1.4434  3.000   -1.715  -1.608  -1.506                          -1.378                              .0005  2.000   -1.607  -1.505  -1.409  -1.2856  1.500   -1.478  -1.383  -1.291  -1.1737  1.200   -1.329  -1.240  -1.156  -1.0468  .950    -1.108  -1.032  -.959   -.865__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -.71              22.83                  -1.39                      20.87                          -2.26                              19.582  10.000  .73 24.85          .00 .00 -.70                      20.65                          -1.60                              19.713  5.000  1.48      24.54          .73 22.39                  .00 .00 -.93                              19.974  3.000  2.52      24.47          1.73              22.64                  .97 21.68                          .00 .005  2.000  3.87      24.25          3.04              22.45                  2.23                      21.01                          1.21                              17.896  1.500  5.29      23.33          4.40              21.43                  3.56                      19.68                          2.48                              16.647  1.200  6.78      22.22          5.84              20.32                  4.94                      18.53                          3.80                              15.788  .950  8.86      21.06          7.85              19.27                  6.88                      17.56                          5.65                              15.19__________________________________________________________________________(R, ANGLE) =  2.000      -2.411          1.500              -3.579                  1.200                      -5.105                          .950                              -8.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -1.366  -1.194  -1.020  -.7962  10.000  -1.324  -1.155  -.985   -.7673  5.000   -1.280  -1.115  -.948   -.7374  3.000   -1.220  -1.058  -.897   -.6955  2.000  -1.131      .000    -.976   -.824   -.6376  1.500   -1.027          -.882              .000    -.744   -.5757  1.200   -.913   -.783                  -.663                      .000    -.5108  .950    -.753   -.645   -.545                          -.405                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -3.29      15.85          -4.27              12.08                  -5.21                      9.68                          -6.37                              6.592  10.000  -2.67      15.66          -3.68              11.88                  -4.64                      9.56                          -5.84                              6.523  5.000  -2.03      15.38          -3.07              11.62                  -4.06                      9.43                          -5.29                              6.454  3.000  -1.15      14.71          -2.23              11.20                  -3.26                      9.26                          -4.54                              6.345  2.000  .00 .00 -1.14              10.72                  -2.22                      9.14                          -3.56                              6.216  1.500  1.20      13.05          .00 .00 -1.14                      9.27                          -2.54                              6.057  1.200  2.46      12.71          1.19              10.61                  .00 .00 -1.48                              5.688  .950  4.21      12.58          2.85              10.64                  1.58                      8.81                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.58, K.sub.aR /γ.sub.aR = 1.97 
    
     
                                           TABLE 71__________________________________________________________________________Conversion Coefficients K.sub.a : (rs), γ.sub.a : (r) Associatedwith Direction of Rotation and CorrectionCoefficient μ: (l) at Telephoto End (194.0 mm) in Sixth EmbodimentF = 194.0 mm__________________________________________________________________________(R, ANGLE) =  .000      .000          10.000              -.387                  5.000                      -.836                          3.000                              -.484POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000  -9.949      .000    -8.337  -6.891  -5.7302  10.000  -10.079          -8.097              .000    -6.609  -5.5713  5.000   -9.704  -7.682                  -6.441                      .000    -5.5344  3.000   -9.609  -7.677  -6.548                          -5.466                              .0005  2.000   -9.436  -7.493  -6.308  -5.1406  1.500   -9.170  -7.203  -5.997  -4.8447  1.200   -8.799  -6.817  -5.614  -4.4938  .950    -7.993  -6.050  -4.901  -3.865__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  .00 .00 -3.23              108.94                  -5.76                      82.57                          -8.51                              175.822  10.000  3.90      -300.11          .00 .00 -2.97                      114.03                          -6.11                              316.753  5.000  8.11      328.89          3.45              67.21                  .00 .00 -3.59                              290.184  3.000  14.26      417.01          8.42              162.09                  4.24                      -256.10                          .00 .005  2.000  22.97      445.08          15.34              205.66                  10.08                      488.95                          4.88                              81.866  1.500  33.05      422.06          23.17              209.83                  16.60                      240.82                          10.27                              90.197  1.200  44.88      388.16          32.13              203.11                  23.94                      186.33                          16.25                              91.238  .950  63.94      325.16          46.05              182.14                  35.11                      146.87                          25.18                              85.98__________________________________________________________________________(R, ANGLE) =  2.000      -2.434          1.500              -3.605                  1.200                      -5.101                          .950                              -8.000POS   R   r   rs  r   rs  r   rs  r   rs__________________________________________________________________________1  .000    -4.642  -3.779  -3.063  -2.2372  10.000  -4.521  -3.678  -2.977  -2.1683  5.000   -4.449  -3.599  -2.901  -2.1024  3.000   -4.299  -3.461  -2.778  -2.0025  2.000  -4.041      .000    -3.260  -2.606  -1.8626  1.500   -3.809          -3.041              .000    -2.412  -1.7057  1.200   -3.505  -2.773                  -2.187                      .000    -1.5238  .950    -2.973  -2.319  -1.799                          -1.209                              .000__________________________________________________________________________POS   R   bf  l   bf  l   bf  l   bf  l__________________________________________________________________________1  .000  -11.30      76.03          -13.62              56.13                  -15.62                      39.02                          -17.90                              21.032  10.000  -9.25      77.85          -11.83              56.48                  -14.03                      38.86                          -16.51                              20.793  5.000  -7.11      70.37          -9.96              54.30                  -12.37                      37.91                          -15.06                              20.374  3.000  -4.08      63.91          -7.34              53.20                  -10.05                      37.18                          -13.04                              19.885  2.000  .00 .00 -3.82              52.99                  -6.95                      36.33                          -10.36                              19.176  1.500  4.46      77.72          .00 .00 -3.61                      35.12                          -7.50                              18.247  1.200  9.35      70.51          4.15              47.13                  .00 .00 &#34;4.42                              16.988  .950  16.54      62.58          10.19              42.94                  5.21                      29.35                          .00 .00__________________________________________________________________________ Condition Corresponding Values: K.sub.a0 /γ.sub.a0 = 0.80, K.sub.aR /γ.sub.aR = 1.85 
    
     The calculation results of the rate of change of K a  with respect to γ a  the infinity in-focus arrangement and the closest in-focus arrangement at the wide-angle end, middle position, and telephoto end in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and in the sixth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.80 are as follows. 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity     Closest    Arrangement K.sub.a0 /γ.sub.a0                 Arrangement K.sub.aR /γ.sub.aR______________________________________Wide-angle End      6.14           0.31(F = 24.7)Middle Position      7.63           0.31(F = 85.0)Telephoto End      12.40          0.29(F = 194.0)Sixth EmbodimentWide-angle End      0.55           1.98(F = 24.7)Middle Position      0.58           1.97(F = 85.0)Telephoto End      0.80           1.85(F = 194.0)______________________________________ 
    
     As described above, in the sixth embodiment as well, since the rate of change of K a  with respect to γ a  is small as compared to the conventional system, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced. For this reason, an error of the conversion coefficient K a  calculated based on γ a  and μ or an error from the actual lens driving amount Δa obtained when only one pair of a conversion coefficient γ a  value and a correction coefficient μ value are set can be reduced. 
     Next, in the case in which the rotation amount ratio (a F  /a Z ) is set to be 1.0, as in the embodiment of Japanese Patent Application Laid-Open No. 5-142475 and the sixth embodiment of the present invention in which said ratio (a F  /a Z ) is set to be -0.80, when the lens driving amounts upon focusing from the infinity in-focus lens arrangement to the closest distance object and upon focusing from the closest in-focus lens arrangement to the infinity object at the wide-angle end, middle position, and telephoto end are calculated from Δa=ΔBf/ γ a  (1-ΔBf/μ)!, and errors from the actual lens driving amounts are then calculated, the following values are obtained. Note that the value of the correction coefficient μ upon focusing from the infinity in-focus lens arrangement to the closest distance object adopts a value at the object distance (POS-5), and the value of the correction coefficient μ upon focusing from the closest in-focus lens arrangement to the infinity object adopts a value at the object distance (POS-4). 
     
         ______________________________________When the rotation amount ratio (a.sub.F /a.sub.Z) is set to be 1.0    Infinity Arrangement →                 Closest Arrangement →    Closest In-focus State                 Infinity In-focus State______________________________________Wide-angle End       -11.4%        -29.7%(F = 24.7)Middle Position      -12.3%         -34.8%(F = 85.0)Telephoto End      -15.1%         -32.9%(F = 194.0)Sixth EmbodimentWide-angle End       -7.8%         -1.5%(F = 24.7)Middle Position      -8.7%          -2.0%(F = 85.0)Telephoto End      -6.2%          -2.6%(F = 194.0)______________________________________ 
    
     As described above, in the sixth embodiment as well, even when only a pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a given lens arrangement range, an error between the conversion coefficient K a  calculated from γ a  and μ and the lens driving amount Δa for focusing becomes small as compared to the conventional system, and focusing can be realized with higher accuracy. 
     Table 72 summarizes the amount (ANGLE DA) of rotation for focusing upon manual focusing using the focus cam (the middle table in Table 64) of the sixth embodiment, the amount DX (mm) of movement, in the direction of the optical axis, of the focusing lens unit corresponding to the amount of rotation for focusing, and the displacement amount Bf (mm) of the imaging point when the amount (DX) of movement in the direction of the optical axis is given. 
     Note that the arrangement of the table and reference symbols are the same as those in the fifth embodiment. The upper table in Table 72 summarizes the displacement amount (Bf) of the imaging point corresponding to the photographing distances (R=5.0, 3.0, 2.0, 1.5, 1.2, and 0.95 m) in the respective zooming states of the focal lengths (F=24.7, 35.0, 50.0, 85.0, 135.0, and 194.0 mm), and the middle table summarizes the values of the amount (ANGLE DA) of rotation for focusing required for attaining an optimal in-focus state with respect to the respective photographing distances. The lower table summarizes the amounts (DX) of movement, in the direction of the optical axis, of the respective lens units corresponding to the amount (ANGLE DA) of rotation for focusing in association with the focal lengths and photographing distances. 
     
                                           TABLE 72__________________________________________________________________________Displacement Amount Bf (mm) of Imaging Point and Amount DX(mm) of movement for focusing in Sixth Embodiment__________________________________________________________________________   0.95 m       1.20 m             1.50 m                 2.00 m                       3.00 m                           5.00 m__________________________________________________________________________F 24.700 Bf   .000       .000  .000                 .000  .000                           .000F 35.000 Bf   .000       .000  .000                 .002  .002                           .003F 50.000 Bf   .000       .003  .007                 .012  .005                           .000F 85.000 Bf   .000       .003  -.022                 -.026 -.020                           -.015F 135.000 Bf   .000       -.049 -.048                 -.047 -.053                           -.063F 194.000 Bf   .000       .000  .000                 .000  .000                           .000__________________________________________________________________________ANGLE DA   -8.000        -5.101            -3.605                 -2.434                       -1.484                           -.836__________________________________________________________________________F 24.700 DX   .000 .519            .000 .000                    R  0.95 mF 35.000 DX   .000 .670            .000 .000                    R  0.95 mF 50.000 DX   .000 .945            .000 .000                    R  0.95 mF 85.000 DX   .000 1.667            .000 .000                    R  0.85 mF 135.000 DX   .000 3.128            .000 .000                    R  0.95 mF 194.000 DX   .000 5.291            .000 .000                    R  0.95 mF 24.700 DX   .000 .406            .000 .000                    R  1.20 mF 35.000 DX   .000 .526            .000 .000                    R  1.20 mF 50.000 DX   .000 .744            .000 .000                    R  1.20 mF 85.000 DX   .000 1.337            .000 .000                    R  1.20 mF 135.000 DX   .000 2.604            .000 .000                    R  1.20 mF 194.000 DX   .000 4.586            .000 .000                    R  1.20 mF 24.700 DX   .000 .322            .000 .000                    R  1.50 mF 35.000 DX   .000 .418            .000 .000                    R  1.50 mF 50.000 DX   .000 .593            .000 .000                    R  1.50 mF 85.000 DX   .000 1.087            .000 .000                    R  1.50 mF 135.000 DX   .000 2.170            .000 .000                    R  1.50 mF 194.000 DX   .000 3.983            .000 .000                    R  1.50 mF 24.700 DX   .000 .239            .000 .000                    R  2.00 mF 35.000 DX   .000 .310            .000 .000                    R  2.00 mF 50.000 DX   .000 .441            .000 .000                    R  2.00 mF 85.000 DX   .000 .828            .000 .000                    R  2.00 mF 135.000 DX   .000 1.705            .000 .000                    R  2.00 mF 194.000 DX   .000 3.300            .000 .000                    R  2.00 mF 24.700 DX   .000 .158            .000 .000                    R  3.00 mF 35.000 DX   .000 .205            .000 .000                    R  3.00 mF 50.000 DX   .000 .295            .000 .000                    R  3.00 mF 85.000 DX   .000 .559            .000 .000                    R  3.00 mF 135.000 DX   .000 1.202            .000 .000                    R  3.00 mF 194.000 DX   .000 2.494            .000 .000                    R  3.00 mF 24.700 DX   .000 .094            .000 .000                    R  5.00 mF 35.000 DX   .000 .121            .000 .000                    R  5.00 mF 50.000 DX   .000 .178            .000 .000                    R  5.00 mF 85.000 DX   .000 .340            .000 .000                    R  5.00 mF 135.000 DX   .000 .762            .000 .000                    R  5.00 mF 194.000 DX   .000 1.708            .000 .000                    R  5.00 m__________________________________________________________________________ 
    
     As can be seen from Table 72, in the zoom lens of the sixth embodiment, so-called manual focusing can be attained since the displacement amounts of the imaging point at the respective focal lengths and photographing distances are very small, and fall within the depth of focus independently of the zooming state and photographing distance. 
     As described above, in the embodiments, the present invention can be applied to zoom lens systems based on various lens unit arrangements or focusing lens units. 
     As described above, according to the present invention, in an inner focusing type zoom lens which is attached to, e.g., an auto-focusing camera which has focus detection means, storage means, calculation means, and the like, the number of data of specific coefficients (e.g., the conversion coefficient γ a  and the correction coefficient μ) required for auto-focusing can be reduced as compared to the conventional system, without making the barrel mechanism larger. Furthermore, an error upon calculation of the lens driving amount of the focusing lens unit using the stored specific coefficients in correspondence with the detected defocus amount can be reduced as compared to the conventional system. 
     In other words, when the arrangement of the present invention is adopted, since the rate of change of the conversion coefficient γ a  is reduced as compared to the conventional system, the number of data of the conversion coefficient γ a , the correction coefficient μ, and the like which are stored for calculating the lens driving amount for focusing can be reduced, and a cost reduction can be realized in terms of the storage capacity. 
     Furthermore, since the change in conversion coefficient K a  to the conversion coefficient γ a  becomes small, the contribution of the correction term (ΔBf/μ) in K a  =γ a  (1-ΔBf/μ) can be reduced. 
     Therefore, an error of the conversion coefficient K a  calculated based on γ a  and μ or an error from the actual lens driving amount Δa obtained when only one pair of a conversion coefficient γ a  value and a correction coefficient μ value are set for a certain lens arrangement range can be reduced. 
     In the present invention, the conversion coefficient γ a  at an in-focus point and the conversion coefficient μ which is defined by formula K a  =γ a  (1-ΔBf/μ) are set to be specific coefficients. Alternatively, a correction coefficient defined by a formula different from the above-mentioned formula may be set. Furthermore, the conversion coefficient γ a  need not always be set in correspondence with the sensitivity (dBf/da) associated with the direction of rotation at an in-focus point. As long as focusing accuracy can be improved, the sensitivity at a point other than the in-focus point and the corresponding correction coefficient may be set to be specific coefficients. 
     Note that the present invention can be applied to various other zoom lens systems based on lens unit arrangements or focusing lens units other than those in the above-mentioned embodiments, as a matter of course.