FR2724023A1 - ZOOM LENS SYSTEM - Google Patents

Abstract

A zoom lens system is disclosed. It relates to a system in which a place of displacement of a set of focusing lenses is defined by a focusing cam and a zoom compensation cam, said lenses fulfill a particular condition at least at the telephoto end in function of a ratio (dBf / dx) of an amplitude dBf of infinitesimal displacement of an image plane and of the amplitude dx of infinitesimal displacement in a direction of an optical axis for a point focused at infinity and for the closest focused point. Application to photographic devices and cameras.

Description

The present invention relates to a variable focal length lens

  called "zoom", and more precisely it coneoe mL Cb] eCtlfzoom oî St zoom lens to an extogrhig auto focus, a video camera or the like, having a focusing detection device and moving a set of lenses focusing in a photographic optical system according to the detected fault

of focus.

  Recently, in view of the significant development of autofocus cameras, various focusing systems, such as a so-called "internal focusing" system, a rear focus system and the like, have been examined for achieving an objective.

  of a compact photographic camera with zoom.

  However, in general, when adopting a focusing system other than the so-called focusing system before,

  the training range of the lenses

  sation varies with the change in focal length. Japanese Patent Application Laid-Open Nos. 4-293008 and 5-142475 assigned to the Applicant have proposed, for the solution of this problem, a method of performing a so-called "manual focusing" operation in an objective zoom lens having a plurality of lens assemblies comprising a lens assembly having both focus and zoom or zoom function. In this method, if the predetermined location of zoom displacement is represented by the displacement amplitude of the lens assemblies in the direction of the optical axis and by the rotation angle of a rotating lens barrel, the location of the focusing lens assembly is defined by the synthetic association of a focusing cam and a cam of

  compensation for variation of focal length or zoom.

  In this arrangement, even when the amplitude of the displacement of focus along the optical axis varies with the state of the zoom, the angle of rotation of the rotating focusing cylinder remains unchanged, so that an operation of

  Manual focus is achieved.

  However, when the aforesaid zoom lens is used in an autofocus camera system which includes a focus detecting device, a y conversion coefficient storage device and a correction coefficient E used for the calculation of objective drive amplitude Ax for focusing the set of focusing lenses according to the detected defocus amplitude ABf of a photographic optical system, and a device for calculating the amplitude Ax focusing drive as a function of focus defocus amplitude ABf, conversion coefficient y and correction coefficient E, problems with storage capacity, calculation errors, etc. arise. As indicated in the aforementioned Japanese Patent Application Laid-Open Nos. 4-293008 and 5-142475, in the zoom lenses described in Japanese Patent Application Laid-open No. 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 and the like, in each of which the locus of displacement of the set of focusing lenses is defined by synthesis of a focusing cam and a compensation cam of variation of focal length or zoom, the aforementioned problems concerning the storage capacity, the calculation error and the like have not been

examined.

  In addition, 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, using each a focusing cam, the problems of storage capacity, calculation error and the like have not been examined either. On the other hand, as set forth in Japanese Patent Application Laid-Open No. 63-163808, 1-154014 and the like assigned to the assignee of the present application, in a zoom lens disclosed in the Japanese Patent Application Laid-Open. No. 64-35515, 64-35516, 4-140704 and the like, all of which disclose the use of a single cam as both a focus cam and a focal length variation cam, the aforementioned problems of storage capacity, calculation error and the like have not been considered either. In addition, the zoom lens described in these documents has a fundamental structure that differs from that of the invention because it does not require a zoom compensation cam and does not take into account a so-called flexible "manual" focusing operation which has has been reviewed in Japanese Patent Application Laid-open No. 4-293008, 5-142475

and the like.

  A zoom lens disclosed in Japanese Patent Application Laid-open Nos. 2-256011, 3-101707 and the like assigned to the assignee of the present invention has a different fundamental structure from that of the invention as it ensures the variation. of focal length by a relative displacement, in the direction of rotation of the barrel of the lens, between a focusing cam and a cam of variation of focal length or zoom, and the focusing by a relative displacement in the direction of the optical axis, and does not examine at all an operation of

automatic focus.

  In addition, Japanese Laid-Open Patent Applications Nos. 61-77027, 1-232313 and the like disclose a lens assembly having a focus cam for performing a precise autofocus operation with a small error. Calculation. However, these documents only refer to a single focusing lens having no focal length variation function and they can not be applied to a focusing cam necessary to obtain the focussing operation. so-called "manual" in a zoom lens in which the amplitude of displacement in the direction of the optical axis for focusing

  changes with the variation of the focal length.

  We now describe quickly in the following the

  principle of the automatic focusing operation.

  An autofocusing system disclosed in Japanese Laid-open Patent Applications Nos. 62-78519, 62-170924, 1-131507, 1-131508, 1-131509, 3-228006 and the like comprises a device for detecting focusing, a device for calculating the lens driving amplitude for focusing and a device for storing particular constants used in the calculations. In such a system, the focus detection device detects the focus defect amplitude ABf between the training position

  image of a real object by the optical system

  graph and a predetermined image-forming point position, and the lens-shift amount calculator for focusing calculates the lens-driving amplitude Ax for focusing according to the detected amplitude of focusing defect ABf of the photographic optical system, although

  that an automatic focusing operation is performed.

  If the relation between the lens drive amplitude Ax for focussing and the focus defocus amplitude ABf is plotted against a conversion factor K associated with focusing in the form: Ax = ABf / K l The lens drive amplitude Ax can be calculated by adjusting the conversion coefficient K. However, as disclosed in Japanese Laid-Open Patent Application No. 62-170924, the conversion coefficient K changes not only with focal length but also with the relative layout of

  the purpose and position of the object.

  Accordingly, as disclosed in Japanese Laid-Open Patent Applications No. 62-78519, 62-170924 and the like, the use of the conversion coefficient y defined as the ratio (sensitivity) of the magnitude of the displacement. infinitesimal of the image plane and the amplitude of the infinitesimal displacement of the set of focusing lenses in the vicinity of a predetermined point of focusing, and the coefficient ú of correction of the conversion coefficient according to the AFf defocus amplitude, the conversion coefficient K is calculated using the following formulas: K = y + -f (ABf) K = y + E.ABf2 according to the Japanese patent application placed under inspection No. 62-78519 K = y (1 + c.ABf) according to Japanese Patent Application Laid-open No. 62-170924 and accordingly the lens drive amplitude Ax is calculated from the coefficient K. (Obviously, the amplitude Ax of Lens drive for focusing can be calculated directly from the focusing defocus amplitude ABf using the conversion factor y and the correction coefficient ú). Furthermore, in a photographic system having an optical system with zooming or zooming, as the values of the conversion coefficient y and the correction coefficient c change with the arrangement of the lenses, several pairs of data of the conversion coefficient y and of the correction coefficient E are kept in the storage device in the form of several divided zoom effect ranges and of several divided focusing ranges, as described in Japanese Patent Application Laid-Open.

3-228006.

  In other words, in the photographic system having the optical system with focal length variation, the focusing detecting device detects the focusing defocus amplitude ABf due to the zoom optical system, and the values of the conversion coefficient y and the correction coefficient E corresponding to the focusing and zooming positions respectively detected by the focusing position detection and zooming devices are read in the storage device. The device for calculating the driving amplitude of

  focussing lenses then calculates the ampli-

  Axis drive study Ax for focusing using focus defocus amplitude ABf, conversion coefficient y and correction coefficient E, and the driving device moves a lens of the calculated amplitude Ax for focusing so much that a

  focusing operation is performed.

  However, in a normal focusing mechanism employing a helical mechanism or a cam mechanism, the lens driving amplitude for focusing should be described not as a lens drive amplitude Ax in the direction of the lens. optical axis, but as a drive Aa amplitude of

rotating lenses.

  Accordingly, when the relationship between the lens drive amplitude Ax and the focus defocus amplitude ABf in the direction of the optical axis is transformed into a relationship between the lens drive amplitude Aa and the ABf amplitude of rotational focusing defect using the conversion coefficient Ka associated with the direction of rotation, we obtain:

Aa = ABf / Ka.

  If the associated conversion coefficient K in the

  direction of the optical axis is then called Kx, the coeffi-

  The conversion coefficient Ka associated with the rotation is expressed by means of a conversion coefficient Δ between the driving amplitude Ax of the lenses in the direction of the optical axis and the driving amplitude Aa of the lenses. the direction of rotation, as follows:

Ka = Kx.

  Thus, the formula given in Japanese Patent Application Laid-Open No. 62-170924 is

  modified into a formula associated with the conversion coefficient

  Ka direction in the direction of rotation in the form Ka = Iy (1 + E. ABf) If Ax and Aa have a linear relation as in a helical mechanism, D becomes constant. However, when using a cam mechanism, the conversion coefficient ci varies with the shape of the cam. The conversion coefficient (> can be replaced by a slope (dx / da) defined by the configuration of the cam in the form Ka = y. (Dx / da) (1 + E.ABf) The conversion coefficient y and the correction coefficient g, in a zoom lens of the in-focus type disclosed in Japanese Patent Application Laid-open No. 4-293008, 5-142475 and the like are

examined in the following.

  When a zoom lens system consists of n sets of lenses and the ke set of lenses is used as a set of focusing lenses, if the ratio of the amplitude dBf of the infinitesimal displacement of the image plane to the amplitude dx of the displacement infinitesimal in the direction of the optical axis of the set of focusing lenses, i.e.

  y conversion (dBf / dx is the sensitivity associated with moving

  in the direction of the optical axis), is defined by a new conversion coefficient yx associated with the amplitude x of displacement in the direction of the optical axis, the conversion coefficient Yx can be expressed using the magnifications P of the respective sets of lenses in the form YX = (1 - Pk2) Pk + l2Pk + 22 .. n2 Accordingly, the rate of variation, from the value focused to infinity (yx,) to the value focussed at the nearest point (yxR) of the conversion coefficient yx, associated with the amplitude x of displacement in the direction of the optical axis can be expressed from the magnitudes P0k and PRk of the set of lenses of focusing at points of focus to infinity and the closest, in the form: YXR / YXO = (1 - Rk2) / (1 POk2)

  In addition, if the ratio of the amplitude dBf of the displacement

  infinitesimal infinitesimal rotation of the lens plane (dBf / da is the sensitivity associated with the rotational displacement) is defined as the new conversion coefficient Ya associated with the angle of rotation of the rotary barrel of the lens, the conversion coefficient Ya associated with the angle of rotation of the barrel can be expressed in the form: Ya = Yx. (Dx / da)

  dx / da being the slope of the focusing cam.

  Consequently, the rate of variation, from the value focused to infinity (Yao) to the closest focused value (YaR), of the conversion coefficient Ya associated with the rotation angle a of the cylinder can be expressed in FIG. using slopes (dx / da) 0 and (dx / da) R at infinity and at the closest corresponding location on the focusing cam, in the form: YaR / Yao = (yXR / yxo) ( (dx / da) R / (dx / da) 0) The rate of change of the conversion coefficient yx with respect to the displacement amplitude x in the direction of the optical axis and the rate of change of the conversion coefficient relative to rotational barrel angle a are discussed below in the case of an embodiment of Japanese Patent Application Laid-Open No. 5-142475. It should be noted that the rotation amplitude for the focal length variation of the wide-angle end at the telephoto end and the focus rotation amplitude are respectively set at 10.0 for ease of comparison.

  with an embodiment of the present invention.

  Table 1 which follows summarizes various paraxial data of an optical system and data for determining the configuration of the focusing cam corresponding to the embodiment of the patent application.

  Japanese Opened to Public Inspection No. 5-142475.

  The upper portion of Table 1 indicates focal length data and key point interval data of the respective lens units of the optical system corresponding to the embodiment of the request.

  Japanese Patent Laid-Open No. 5-142475.

  In this table, F1, F2, F3 and F4 are respectively the focal distances of the first, second, third and fourth sets of lenses, and D1, D2, D3 and D4 are respectively the interval of the main points between the first and second sets of lenses. and the second set of lenses, between the second and third set of lenses, between the third and fourth set of lenses, and between the fourth set of lenses and a predetermined imaging plane in six states of variation of distance focal length (focal lengths F = 36.0, 50.0, 60.0, 70.0, 85.0 and

103.0 mm).

  The middle part of Table 1 shows the data of the spline interpolation sample points when the focus cam configuration of the second set of lenses used for focusing is expressed by a spline function associated with the angle α of the spline. rotation of the rotating barrel and amplitude x of

  displacement in the direction of the optical axis (corre-

  in the "Numerical Analysis and FORTRAN" paper, Maruzen, "Spline Function and Its Applications", Kyoiku

Shuppan and the like).

  In addition, the lower part of Table 1 indicates the infinite focusing positions (position corresponding to infinity) for the respective focal lengths (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm), and the rotational amplitudes (rotation amplitudes for focusing) when focusing at respective photographing distances (R = 5.0, 3.0, 2.0, 1, 5, 1.0 and 0.85 m) using the focusing cam. As the rotation amplitude for the focal length variation from the wide-angle end (F = 36.0 mm) to the telephoto end (F = 103.0 mm) and the rotation amplitude for focusing from the infinitely focused position to the closest focused position (R = 0.85 m) are equal to 10.0, the ratio (aF / az) of the rotation amplitude for focus and the amplitude of rotation for the

  Focal length variation is 1.0.

Table 1

  Japanese Patent Application Laid-Open Example No. 5-142475 (Rotational Amplitude Ratio: aF / az = 1.0) Focal distances and target point intervals of the example of Japanese Patent Application Laid-open No. 5-142475

1-POS 2-POS 3-POS 4-POS 5-POS 6-POS

  F 36,0000 50,0000 60.0000 70.0000 85.0000 103.0000

  F1 71.3528 D1 10.0000 16.9506 20.8432 24.0040 27.6859 31, 0684

  F2 -16.8076 D2 18.0119 13.8825 11.8221 10.1086 7.9077 5, 6236

  F3 37.3219 D3 13.2200 12.3744 11.9702 11.6986 11.3811 11, 3103

  F4 61.7098 D4 53.2211 59.4228 62.5744 65.172 68.2854 71, 2371

  Focusing cam shape (spline interpolated point) corresponding to the example of Japanese Patent Application Laid-Open No. 5-142475

ANGLE (1) (2) (3) (4)

  1 0.0000 0.0000 0.0000 0.0000 0.0000

  2 3.3787 0.0000 0.171 0.0000 0.0000

  3 4.8214 0.0000 0.2847 0.0000 0.0000

  4 6,2247 0.0000 0.4295 0.0000 0.0000

7.3653 0.0000 0.5760 0.0000 0.0000

  6 9.1918 0.0000 0.8749 0.0000 0.0000

  7 10.0000 0.0000 1.0365 0.0000 0.0000

  8 13.3787 0.0000 1.9870 0.0000 0.0000

  9 14.8214 0.0000 2.5248 0.0000 0.0000

16.2247 0.0000 3.1200 0.0000 0.0000

  11 17.3653 0.0000 3.6722 0.0000 0.0000

  12 19.1918 0.0000 4.6460 0.0000 0.0000

  13 20,0000 0.0000 5,1165 0.0000 0.0000

  Rotational amplitude for focal length change and focusing amplitude of the example of Japanese Patent Application Laid-open No. 5-142475 (rotational amplitude ratio: aF / az = 1.0) Focal distance Corresponding position Distance of amplitude of rotation to infinity photography for focusing 36.0 mm 0.0000 5, 00 m 3,379, 0 mm 2,1079 3,00 m 4,821, 0 mm 3,5742 2,00 m 6,225 , 0 mm 5.0485 1.50 m 7.365 85.0 mm 7.2321 1.00 m 9.192 103.0 mm 10.00.00 0.85 m 10,000 The following table 2 summarizes the numerical values of the cams in the assembly. of focusing lenses of the Japanese Patent Application Laid-open No. 5-142475, the results being calculated by interpolation from the spline function with the summarized focus cam sample data. in the middle table of Table 1. In this table (ANGLE) designates the angle of rotation of the rotary drum, (2) is the mplitude (mm) of displacement in the direction of the optical axis of the second set of lenses, and (F) is the focal length (mm) of the entire system in the state of focus at infinity corresponding to

the amplitude of rotation (ANGLE).

Table 2

  Digital cam values for focusing objective of Japanese Patent Application Laid-Open No. 5-142475 Focus Cam Digital Values Focal Distance Variation Compensation Cam Numerals

ANGLE (2) F ANGLE (2) F

  0.0000 0.0000 36.0000 0.0000 0.0000 36.0000

  0.5000 0.2889 39.1417 0.5000 0.0208 39.1417

  1.0000 0.0423 42.4381 1.0000 0.5684 42.4381

  1.5000 0.0649 45.8280 1.5000 0.8335 45, 8280

  2.0000 0.0892 49.2589 2.0000 1.0810 49.2589

  2.5000 0.1558 52.6890 2.5000 1.3090 52.6890

  3.0000 0.1454 56.1033 3.0000 1.5167 56.1033

  3.5000 0.1785 59.4978 3.5000 1.7038 59.4978

  4.0000 0.2154 62.8763 4.0000 1.8710 62, 8763

  4.5000 0.2563 66.2597 4.5000 2.0204 66.2597

  , 0000 0.3012 69.6675 5.0000 2.1534 69.6675

  , 5000 0.3503 73.1066 5.5000 2.2712 73.1066

  6,0000 0,4039 76,5591 6,0000 2,3738 76,5591

  6.5000 0.4623 80.0055 6.5000 2.4616 80, 0055

  7.0000 0.5260 83.4263 7.0000 2.5347 83.4263

  7.5000 0.5953 86.8023 7.5000 2.5931 86.8023

  8.0000 0.6705 90.1274 8.0000 2.6372 90.1274

  8.5000 0.7518 93.4109 8.5000 2.6680 93.4109

  9.0000 0.8395 96.6628 9.0000 2.6860 96, 6628

  9.5000 0.9340 99.8856 9.5000 2.6916 99.8856

  , 0000 1,0365 103,0000 10,0000 2,6814 103,0000

, 5000 1,1489 0,0000

11.0000 1.2714 0.0000

11.5000 1.4038 0.0000

12.0000 1.5460 0.0000

12,5000 1,6977 0,0000

13.0000 1.8588 0.0000

13,5000 2.0292 0.0000

14.0000 2.2088 0.0000

14.5000 2.3980 0.0000

, 0000 2.5971 0.0000

, 5000 2.8062 0.0000

16.0000 3.0252 0.0000

16,5000 3.2540 0.0000

17.0000 3.4924 0.0000

17,5000 3,7397 0.0000

18.0000 3.9959 0.0000

18,5000 4,2617 0,0000

19.0000 4.5374 0.0000

19,5000 4,8236 0,0000

, 0000 5,1165 0.0000

  The left-hand portion of Table 2 summarizes the numerical values of the focusing cam in the embodiment of Japanese Patent Application Laid-Open No. 5-142475, and the right-hand portion of Table 2 summarizes the numerical values of the FIG. zoom compensation cam of this embodiment. A value obtained by synthesis of the amplitude (2) of displacement in the direction of the optical axis of the numerical values of the focusing cam and the numerical values of the zoom compensation cam in a range starting from the amplitude of rotation (ANGLE = 0.0) to the amplitude of rotation (ANGLE = 10.0) corresponds to the displacement location of the second set of lenses, calculated with the paraxial data

  from the top of Table 1.

  The following tables 3, 4 and 5 summarize the amplitude DX (mm) of displacement for the focusing, in the direction of the optical axis, of the set of focusing lenses, the training magnifications PK

  images of the respective sets of lenses, the coeffi-

  yx conversion coefficient associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation for the wide-angle end (F = 36.0 mm), the center position (F = 50.0 mm) and the telephoto end (F = 103.0 mm) respectively. In these tables, (R) on the left represents the distance of photography (in meters), (ANG) designates the rotation amplitude of the focusing cam during focusing at the respective photography distances, and 1), 2), 3) and 4) to the right respectively represent the first, second, third and fourth sets of lenses. In addition, in these tables, the first part indicates the displacement amplitude DX (mm) for focusing in the direction of the optical axis when focusing at the respective photographing distances (R = 10.0, 5.0 , 3.0, 2.0, 1, 5, 1.0 and 0.85 m) (note that moving to the side of the object is positive). The second part indicates the PK magnifications of the respective sets of lenses in the focused state at the respective photographing distances (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m). The third part indicates the conversion coefficient Yx associated with the direction of the optical axis of the set of focusing lenses in the focused state at the respective distances of

  photograph (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m).

  In addition, the fourth part indicates the slope (dx / da) of the focusing cam for the positions on the focusing cam, which correspond to the focused state at the respective photographing distances (R = 10.0, 5, 0, 3.0, 2.0, 1.5, 1.0 and 0.85 m) and the fifth table summarizes the conversion coefficient Ya associated with the direction of rotation of the set of focusing lenses in the state. focused at the respective photography distances (R = 10, 0, 5.0,

3.0, 2.0, 1.5, 1.0 and 0.85 m).

Table 3

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (36.0 mm) according to Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG 1,912 1) 0,000 2) 0,085 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,170 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,285 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 0.429 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 0,576 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 1.037 3) 0.000 4) 0.000

  Pk magnification of lenses at the wide-angle end (36.0 mm) in Japanese Patent Application Laid-open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) -0,377 3) -9,721 4) 0,138

  R, 000, AN 1,912 1) -0.007 2) -0.372 3) -9.721 4) 0.138

  R 5,000 ANG 3,379 1) -0,015 2) -0,367 3) -9,721 4) 0,138

  R 3,000 ANG 4,821 1) -0,025 2) -0,360 3) -9,721 4) 0,138

  R 2,000 ANG 6.225 1) -0.039 2) -0.352 3) -9.721 4) 0.138

  R 1.500 ANG 7.365 1) -0.054 2) -0.343 3) -9.7214) 0.138

  R 1,000 ANG 9,192 1) -0,088 2) -0,325 3) -9,7214) 0,138

  R 0.850 ANG 10,000 1) -0.107 2) -0.316 3) -9.721 4) 0.138

  Yx conversion coefficient associated with the direction of the optical axis at the wide-angle end (36.0 mm) in Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 1,533 3) 0,000 4) 0,000

  R 10,000 ANG 1,912 1) 0,000 2) 1,540 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 1,547 3) 0,000 4) 0,000 R 3,000 ANG 4,821 1) 0,000 2) 1,556 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 1.567 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 1,578 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 1,599 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 1.610 3) 0.000 4) 0.000

  Slope dx / da of focusing cam at the wide-angle end (36.0 mm) in Japanese Patent Application Laid-open No. 5142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,041 3) 0,000 4) 0,000

  R 10,000 ANG 1,912 1) 0,000 2) 0,050 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,068 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,091 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 0.116 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 0,141 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 0,187 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 0.215 3) 0.000 4) 0.000

  Conversion coefficient y associated with the direction of rotation at the wide-angle end (36.0 mm) in Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,064 3) 0,000 4) 0,000

  R 10,000 ANG 1,912 1) 0,000 2) 0,077 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,105 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,141 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 0.182 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 0,223 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 0,299 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 0.346 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.05, YaR / Yao = 5.43

Table 4

  Amplitude DX (mm) of focusing displacement in the optical axis direction at the center position (50.0 mm) according to Japanese Patent Application Laid-open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG 1,972 1) 0,000 2) 0,127 3) 0,000 4) 0,000

  R 5,000 ANG 3,373 1) 0,000 2) 0,254 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,422 3) 0,000 4) 0,000

  R 2,000 ANG 6,241 1) 0,000 2) 0,632 3) 0,000 4) 0,000

  R 1,500 ANG 7,403 1) 0,000 2) 0,841 3) 0,000 4) 0,000

  R 1,000 ANG 9,213 1) 0,000 2) 1,261 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 1.483 3) 0.000 4) 0.000

  Magnification Pk of objective image at the median position (50.0 mm) in Japanese Patent Application Laid-open No. 5- 142475

  R 0,000 ANG 0.000 1) 0.000 2) -0.447 3) -42.292 4) 0.037

  R 10,000 ANG 1,972 1) -0,007 2) -0,440 3) -42,292 4) 0,037

  R 5,000 ANG 3,373 1) -0,015 2) -0,432 3) -42,292 4) 0,037

  R 3,000 ANG 4,821 1) -0,025 2) -0,422 3) -42,292 4) 0,037

  R 2,000 ANG 6,241 1) -0,040 2) -0,409 3) -42,292 4) 0,037

  R 1.500 ANG 7.440 1) -0.055 2) -0.397 3) -42.292 4) 0.037

  R 1,000 ANG 9,213 1) -0,089 2) -0,372 3) -42,292 4) 0,037

  R 0.850 ANG 10,000 1) -0.109 2) -0.359 3) -42.292 4) 0.037

  Conversion coefficient yx associated with the direction of the optical axis at the median position (50.0 mm) in Japanese Patent Application Laid-open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 1,966 3) 0,000 4) 0,000

  R 10,000 ANG 1,972 1) 0,000 2) 1,982 3) 0,000 4) 0,000

  R 5,000 ANG 3,373 1) 0,000 2) 1,998 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 2,019 3) 0,000 4) 0,000

  R 2,000 ANG 6,241 1) 0,000 2) 2,045 3) 0,000 4) 0,000

  R 1,500 ANG 7,403 1) 0,000 2) 2,069 3) 0,000 4) 0,000

  R 1,000 ANG 9,213 1) 0,000 2) 2,117 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 2.140 3) 0.000 4) 0.000

  Slope dx / da of focus cam at center position (50.0 mm) in Japanese Patent Application Laid-open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,052 3) 0,000 4) 0,000

  R 10,000 ANG 1,972 1) 0,000 2) 0,079 3) 0,000 4) 0,000

  R 5,000 ANG 3,373 1) 0,000 2) 0,102 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,131 3) 0,000 4) 0,000

  R 2,000 ANG 6,241 1) 0,000 2) 0,165 3) 0,000 4) 0,000

  R 1,500 ANG 7,403 1) 0,000 2) 0,197 3) 0,000 4) 0,000

  R 1,000 ANG 9,213 1) 0,000 2) 0,268 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 0.298 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the middle position (50.0 mm) in Japanese Patent Application Laid-open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,102 3) 0,000 4) 0,000

  R 10,000 ANG 1,972 1) 0,000 2) 0,157 3) 0,000 4) 0,000

  R 5,000 ANG 3,373 1) 0,000 2) 0,204 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,265 3) 0,000 4) 0,000

  R 2,000 ANG 6,241 1) 0,000 2) 0,338 3) 0,000 4) 0,000

  R 1,500 ANG 7,403 1) 0,000 2) 0,407 3) 0,000 4) 0,000

  R 1,000 ANG 9,213 1) 0,000 2) 0,566 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 0.638 3) 0.000 4) 0.000

  Condition corresponding to the values: yxR / YxO = 1.09, yaR / yao = 6.26

* Table 5

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at 1 15 the telephoto end (103.0 mm) according to Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG 1,975 1) 0,000 2) 0,502 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,951 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 1,488 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 2.090 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 2,636 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 3,609 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 4.080 3) 0.000 4) 0.000

  3k lens magnification at the telephoto end (103.0 mm) in Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) -0,716 3) 13,060 4) - 0,154

  R, 000, FR 1,975 1) -0,007 2) -0,686 3) 13,060 4) - 0,154

  R 5,000 ANG 3,379 1) -0,015 2) -0,659 3) 13,060 4) - 0,154

  R 3,000 ANG 4,821 1) -0,026 2) -0,627 3) 13,060 4) -0,154

  R 2,000 ANG 6.225 1) -0.040 2) -0.592 3) 13.060 4) - 0.154

  R 1,500 ANG 7,365 1) -0,055 2) -0,559 3) 13,060 4) - 0,154

  R 1,000 ANG 9,192 1) -0,090 2) -0,501 3) 13,060 4) - 0,154

  R 0.850 ANG 10,000 1) -0.112 2) -0.473 3) 13.060 4) - 0.154

  Conversion coefficient yx associated with the direction of the optical axis at the telephoto end (103.0 mm) in Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 1,982 3) 0,000 4) 0,000

  R 10,000 ANG 1,975 1) 0,000 2) 2,152 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 2,298 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 2,465 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 2.643 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 2,795 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 3,044 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 3.155 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (103.0 mm) in Japanese Patent Application Laid-Open No. 5142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,215 3) 0,000 4) 0,000

  R 10,000 ANG 1,975 1) 0,000 2) 0,293 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,345 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,401 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 0.457 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 0,499 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 0,570 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 0.588 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (103.0 mm) in Japanese Patent Application Laid-Open No. 5-142475

  R 0,000 ANG 0,000 1) 0,000 2) 0,425 3) 0,000 4) 0,000

  R 10,000 ANG 1,975 1) 0,000 2) 0,630 3) 0,000 4) 0,000

  R 5,000 ANG 3,379 1) 0,000 2) 0,794 3) 0,000 4) 0,000

  R 3,000 ANG 4,821 1) 0,000 2) 0,989 3) 0,000 4) 0,000

  R 2,000 ANG 6.225 1) 0.000 2) 1.207 3) 0.000 4) 0.000

  R 1,500 ANG 7,365 1) 0,000 2) 1,394 3) 0,000 4) 0,000

  R 1,000 ANG 9,192 1) 0,000 2) 1,736 3) 0,000 4) 0,000

  R 0.850 ANG 10,000 1) 0.000 2) 1.855 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / YxO = 1.59, YaR / YaO = 4.36 As indicated in Tables 3, 4 and 5, the conversion coefficient yx associated with the direction of the optical axis and the slope ( dx / da) of the focus cam for the respective focal lengths increase as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the direction of rotation,

  defined by the product of yx and (dx / da), increases further.

  More specifically, in a zoom lens in which the conversion coefficient yx associated with the amplitude x of displacement, in the direction of the optical axis, of the set of focusing lenses to the closest focused state is greater to that which is obtained in the state focused at infinity, that is to say which corresponds to the relation: 1.0 <YxR / YxO when the focusing cam which corresponds to the following inequality, c ' that is, the focusing cam having a relatively large slope pattern (dx / da) at the position corresponding to the shortest distance from the position corresponding to infinity is such that: 1.0 <(dx / da) R / (dx / da) 0 the following inequality is obtained: 1.0 <YxR / Yxo <YaR / Yao The rate of variation, from the value focused at infinity (Yao) to the focused value la closer (YaR) of the conversion coefficient Ya associated with the angle of rotation of the cylinder then takes a value which, undesirably, is greater than the rate of change, from the value focused to infinity (yxo) to the nearest focused value (yxR), of the conversion coefficient yx associated with the amplitude x of displacement in the direction of the axis

optical.

  According to Tables 3, 4 and 5 above, the

  velocity of variation of Ya is x5.43 at the far end

  angle (F = 36.0 mm), is x6.26 in the middle position (F = 50.0 mm), and is x4.36 at the telephoto end

(F = 103.0 mm).

  As previously described, when the conversion coefficient y varies in a manner which corresponds to the arrangement of the lenses (for example by focusing) as disclosed in Japanese Patent Application Laid-Open No. 3-228006, several pairs of Data of the conversion coefficient γ and the correction coefficient e must be stored in the storage device in sets of several separate focusing ranges. Consequently, when the rate of variation of Ya is large (YaR / Yao >> 1.0), the number of divisions increases and the storage capacity necessarily becomes high, so that the cost increases. For example, when the variation of ya in a single focusing range is divided under the conditions defined by the following inequality: Ymax / Ymin <1.2 the number N of divisions is given by the inequality (a) which follows: N> 1og (YMAX / YMIN) / log (1,2) (a) Accordingly, the numbers Nw, NM and NT of divisions at the wide-angle end, in the middle position and at the telephoto end, have important values which are: Nw> 9, 3, NM> 10.1, NT> 8.1 The formula K = y (1 + E.ABf) presented in Japanese Patent Application laid open to the public n 62-170924 is rewritten in the form of the conversion coefficient Ka associated with the rotation angle a of the rotary barrel: Ka = YaU (1 + Ec.ABf) The following formula is then defined using the correction coefficient i (E = -1 / H) Ka = yYa (1 - ABf / u) Tables 6, 7 and 8 give the results of the calculation of the values of the conversion coefficient Ka and the correction coefficient y in s the embodiment of Japanese Patent Application Laid-Open No. 5-142475 at the wide-angle end (F = 36.0 mm), in the middle position (F = 50.0 mm) and at the telephoto end

  (F = 103.0 mm) using the previous formula.

  In these tables, (R) denotes the object distance (in meters), (ANG) designates the amplitude of rotation for the focusing of the position corresponding to infinity on the focusing cam, (r) denotes the correction coefficient Ya in the direction of rotation, (rs) denotes the conversion coefficient Ka, (bf) denotes the defocusing amplitude (mm), and (I) represents the correction coefficient y. Each table has a matrix structure, and eight lines in the vertical direction, indicated by (POS) represent the positions of the object (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1 , 0 and 0.85 m), and four pairs (R, ANGLE) in the horizontal direction represent the sets of

  lenses of the set of focusing lenses.

  More precisely, the position of the focusing lens of the first pair in the two upper parts of each of the tables 6, 7 and 8, that is to say in the third and fourth columns, is (R, ANGLE) = (0,0; 0,0) and indicates that this position corresponds to infinity. Consequently, the third column (r) of the first part represents the value of the conversion coefficient Ya in rotation when the set of focusing lenses is focused on the object at infinity, and the fourth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is moved from the focused state to an object at infinity to the focused state at the distance of the object indicated in the second column. Further, the third column (bf) of the second part of each array represents the focus defocus amplitude ABf with respect to a predetermined imaging position when the position of the focus lens assembly corresponds to the infinity, and the object is at the object distance indicated in the second column, and the fourth column (1) represents the value of the correction coefficient y when the set of focusing lenses is shifted from a focused state to an object at infinity to a focused state at the distance from the object indicated in the

second column.

  Similarly, the position of the focus lens assembly of the fourth pair in the last two parts of Tables 6, 7 and 8, i.e. in the ninth and tenth columns, is (R, ANGLE ) = (0, 85; 10.0), and indicates that this position corresponds to the focus at the nearest point (R = 0.85 m). Accordingly, the ninth column (r) of the third part of the table represents the value of the conversion coefficient Ya in rotation when the set of focusing lenses is focused on the object at the closest distance (R = 0, 85 m), and the tenth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is shifted from the focused state to the nearest object (R = 0.85 m) to the focused state at the distance of the object indicated in the second column. In addition, the ninth column (bf) of the fourth part of the tables represents the focus defocus amplitude ABf for a predetermined image-forming position when the position of the focus lens assembly corresponds to the highest position. close and the object is at the object distance indicated in the second column, while the tenth column (Q) represents the value of the correction coefficient g when the set of focusing lenses is moved from a focused state to the closest object (A = 85 m) in the focused state on

  the object at the distance indicated in the second column.

  According to the formulas above and as the conversion coefficient in rotation is calculated by the relation Ka = ABf / Aa (Aa being the rotation amplitude for the focusing), and the correction coefficient y is calculated by the relation g = Abf / (1-Ka / Ya), the value of the conversion coefficient Ka (eighth row, fourth column of the first table 0.175), when the set of focusing lenses is shifted from the focused state to the object to infinity in the object-focused state at distance (R = 0.85 m) in Table 6, is calculated as Ka = 1.75 / 10.0 = 0.175 using the ABf = values 1.75 and Aa = 10.0. On the other hand, the value of the correction coefficient p (eighth row, fourth column of the second table part -1.00) is calculated as g = -1.00 using the values ABf = 1, 75

Ka = 0.175 and Ya = 0.064.

Table 6

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the wide-angle end (36.0 mm) of the example of the patent application Japanese placed in the public inspection n 5-142475 f = 36.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 1,912 5,000 3,379 3,000 4,821

POS R rs r rs r rs

  1 0,000 0.064 0.000 0.068 0.077 0, 090

  2 10,000 0.069 0.077 0.000 0.089 0, 105

  3 5,000 0.078 0.090 0.105 0.000 0, 122

  4 3,000 0.093 0.108 0.124 0.142 0.000

2,000 0,110 0,127 0,144 0,163

6 1,500 0,126 0,145 0,163 0, 183

7 1,000 0.158 0.180 0.200 0, 221

8 0.850 0.175 0.197 0.219 0, 241

  POS R bf I bf e bf I bf i 0.000 0.00 0.00 -0.13 -1.08 -0.26 -0.95 -0.43 -1.18

  2 10,000 0.13 -1.71 0.00 0.00 -0.13 -0.86 -0.31 - 1.19

  3 5,000 0.26 -1.14 0.13 -0.77 0.00 0.00 -0.18 - 1.30

  4 3,000 0.45 -0.97 0.31 -0.78 0.18 -1.00 0.00 0.00

  2,000 0.68 -0.94 0.55 -0.84 0.41 -1.11 0.23 -1.53

  6 1,500 0.93 -0.94 0.79 -0.90 0.65 -1.18 0.47 - 1.59

  7 1,000 1.45 -0.98 1.31 -0.98 1.16 -1.29 0.97 - 1.71

  8 0.850 1.75 -1.00 1.60 -1.02 1.45 -1.34 1.25 - 1.77

  (R, ANGLE) = 2,000 6,225 1,500 7,365 1,000 9,192 0,850 10,000

POS R rs r rs r rs

1 0.000 0.104 0.117 0.141 0.15

2 10,000 0.121 0.136 0.162 0, 175

3 5,000 0.140 0.155 0.182 0, 196

4 3,000 0.160 0.176 0.205 0, 219

2,000 0,182 0,000 0,200 0,231 0,246

  6 1,500 0,204 0,223 0,000 0,255 0, 271

  7 1,000 0.245 0.265 0.299 0.000 0, 318

  8 0.850 0.266 0.287 0.324 0.346 0.000

3 5 POS R bf a bf t bf a bf

  1 0.000 -0.65 -1.51 -0.86 -1.82 -1.30 -2.46 -1.53 - 2.74

  2 10,000 -0.52 -1.57 -0.74 -1.91 -1.18 -2.58 -1.41 - 2.86

  3 5,000 -0.40 -1.69 -0.62 -2.03 -1.06 -2.72 -1.30 - 2.99

  4 3,000 -0.22 -1.79 -0.45 -2.14 -0.90 -2.85 -1.14 - 3.11

  4 0.00 0.00 0.00 -0.23 -2.24 -0.69 -3.00 -0.93 -3.22

  6 1,500 0.23 -1.97 0.00 0.00 -0.47 -3.15 -0.71 - 3.29

  7 1,000 0.73 -2.13 0.48 -2.55 0.00 0.00 -0.26 - 3.16

  8 0.850 1.00 -2.19 0.76 -2.62 0.26 -3.15 0.00 0.00

  Condition corresponding to the values: Kao / YaO = 2.75, KaR / YaR = 0.44 a) 0 Ln t-. ## EQU1 ## ## STR1 ##

n (N ----- - -o -

  ## EQU1 ## where ## EQU1 ## where ## EQU1 ## % 6662co N0 8I 111 oea> OC) o 01 01 0 0 0 -N N_- o cN, r oO, OO ci a)) O OO. N. so oo oo oCoO (- EO the _Co << NeO (o (C-_ V qmCDC) CD Cl0 N mU - CD - - N 0oo o .... - o C, _ "xs NC) 0 tz > 0 aaa C) CD - Nttt 00 0N E 0 0 a N the 8NtN C); o9Ov "<the aCD C CD rC oo)> o0 o <08 oo qc Nr o0n to 0 u E) o Lo or 0NOo - U0 N <-E <N <C (n (n> (- 6 n 0 to 8 9 9 _CN 0 CtU D sgN J lD (0, gNq Ct Os00 N0tI D 0o O 0 Oo U 0 0a) (CD m ") L 0CD12ç0 C '0I this ClMl M0C I

(n U) a) i o o o ..

-CI << 0c << E

MC 0'.0.0 6C

  CD) o NCDm o C4 00 COr-CMCD <o o 6666666 x 2.9C) <N C0 (n -r-CD- <o i CONr-oD

ci.6CD c000 - '<N iCD -99900, -

  0 0 0 CC C0i0 000000 I 00 0 0an 0 00 cu) - c 00 00000 00000000 a> OOOOL 0 C DaQjam 0 O0 0000 a O oooooooooooooooooo M = L ME 0 d j6oI 16 06 (4 - o-JcSOLOmC'i ## STR5 ## ## STR1 ##

O 8E0 E

  z 0 0 0 Oo zf z Llo << <a. at. 0- 0 0 O CD m - t c '00_u0 ---_- _ N the Ln) n q -N O81 cNL Dto Um U) 0 N o

  CIa) O NU - CL) D OOj 0 0g 00 0 r0 g g i s-

  00D004 m n00 OO9r, V) mI'mOle JCDS..C; na O> D0 00 N

N 0 <00 <0 '0C0 Co-

  P <n N) 0 - O_ toE C- m oLO r- <Dc) C0 CD o

  a) nCoCDM ') -l_ooo mo oCoe <0 f r0' - LO '-rrcc'r- ov-

  ## EQU1 ## where ## EQU1 ## where ## EQU1 ## where ## EQU1 ## o, o oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ## EQU1 ## where ## STR1 ## is a compound of the formula ## STR1 ## wherein C) Cf) o <0col lo Li- om o

CCo C-

  Cu = 30 m m (7 I m i a 0CD. <05 N-CD - 0 CD - rC <) f a

O CDr0r '- 0 -a) .n --- -

  ## EQU1 ## ## EQU1 ## ## ## ## ## ## ## ## ################################################################################## 0 CD00l ilO OaOOaLCDOaOOO <N <aOaa CDq.o lDC o wckioOOOaeOg

  = oE o o oooo L6 (V oooo o: qooooM Not66I: r-E-

  M As indicated in Tables 6, 7 and 8 above, if we consider the change in the conversion coefficient Ka (rs) (for example the fourth column of the first part of the table) and the change in the correction coefficient y (t) (for example the fourth column of the second table part) for a given set of lenses (for example for the set focusing at infinity), the conversion coefficient Ka and the correction coefficient y vary considerably. with the positions of the object. In particular, the conversion coefficient Ka has a larger value on the side of the nearest object than on the side of the object at infinity. Since the conversion coefficient Ka in rotation is given by Ka = ABf / Aa, the amplitude Aa of rotation for the focusing of the object side at infinity becomes larger than on the side of the nearest object for the amplitude of defect of

ABf focus.

  The results of calculating the rate of variation of Ka as a function of ya for the set placed at infinite focusing and the closest focusing at the wide-angle end (F = 36.0 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the embodiment of the Japanese patent application

  Public Inspection No. 5-142475 are as follows.

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity KaoIyao Nearest KaR / YaR Wide-angle (F = 36, 0) 2.75 0.44 Median position (F = 50.0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 As previously described, in the embodiment of Japanese Patent Application Laid-open No. 5-142475, such as the change of conversion coefficient Ka is important, the contribution of the correction term (ABf / z) in Ka = Ya (1 - ABf /) becomes high, and the value of the correction coefficient becomes close to that of the defect amplitude of ABf focus. In addition, the value of the correction coefficient y varies

  a lot with the position of the object.

  Accordingly, as disclosed in Japanese Patent Application Laid-open No. 3-228006, when a single pair of values of the conversion coefficient Ya and the value of the correction coefficient j are used for a given range of positions. of lenses (for example a focusing range to infinity), if the correction coefficient y which varies greatly is represented by a single value, a high error is incorporated in the value of the conversion coefficient Ka which is calculated according to the conversion coefficient Ya and the correction coefficient y. Accordingly, when the lens driving amplitude Aa for focusing is finally calculated from the focusing defect amplitude ABf using the conversion coefficient Ka, the lens driving amplitude includes a error, and an autofocus operation can not be performed accurately.

  For example, after calculating the amplitude Aa of

  focus for the object at the shortest distance (R = 0.85 m) when the correction coefficient A (which varies from -3.76 to -5.77 depending on the distance of the object) in the set infinitely focussed at the telephoto end (F = 103.0 mm) is represented by the value (g = -4.82) at the median distance of the object (R = 2.0 m),

  the lens drive amplitude Aa for focusing

  is calculated as Aa = 0.74 using ABf = 16.18, Ya = 0.85 and u = -4.82. The actual lens drive amplitude for focussing the infinitely focused state at the telephoto end (F = 103.0 mm) to the object at the shortest distance (R = 0.85 m) is Aa = 10.0 from (R, ANGLE) = (0.85, 10.0) at the top right of the third part of Table 8. Thus, an error of -12.6% is created

  between the actual and calculated values Aa = 0.74 for the ampli-

  lens training study for focusing.

  Similarly, when the lens drive amplitudes for focusing the infinite focused set toward focusing on the object at the shortest distance and for focusing the focused assembly at the shortest distance to the object at infinity on the wide-angle side, in the middle position and at the telephoto end are calculated from the relation Aa = ABf / Ya (l-ABf / I), and the errors with respect to the real amplitudes of lens training are then calculated, we get

the following important values.

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest Near-state Focused at Infinity Wide-angle (F = 36.0) 4.4% - 13.0% Median Position (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% It should be noted that the value of the correction coefficient y during focusing with the set focused to infinity on the object at the shortest distance takes the value corresponding to the object distance (R = 2.0 m) and the value of the correction coefficient y when focusing the set focused to the nearest location on the object to infinity takes the value

  corresponding to the object distance (R = 3.0 m).

  Finally, Table 9 summarizes the focus rotation amplitude (ANGLE DA) during manual focusing with the focusing cam (middle portion of Table 1) in the embodiment of the Japanese patent application being inspected. No. 5-142475, the displacement amplitude DX (mm) in the direction of the optical axis of the focusing lens assembly corresponding to the focusing rotation amplitude, and the displacement amplitude Bf (mm) ) of the image point when the amplitude (DX) of displacement in the direction of the optical axis is

determined.

  The upper part of Table 9 gives the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m ) in the respective states of variation of focal lengths (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm), and the middle portion gives the values of the amplitude (ANGLE DA) focusing rotation necessary to obtain an optimal focused state for the respective photography distances. The lower part of the table gives the amplitudes (DX) of displacement, in the direction of the optical axis, of the respective sets of lenses corresponding to the amplitude (ANGLE DA) of rotation for focusing.

  with focal lengths and photography distances. In the lower part of the table, (F) is the focal length (mm)

  of the entire system, (R) the distance of photography (m) and (DX) the displacement amplitude (m) in the direction of the optical axis of each of the first, second, third and fourth sets of lenses from the right side (moving the side of

  the object is represented by a positive value).

Table 9

  Displacement amplitude Bf (mm) of image point and displacement amplitude DX (mm) for focus of Japanese Patent Application Laid-open No. 5-142475 0.85m 1.00m 1.50m 2 , 00m 3.00m 5.00 m 36.000 Bf 0.000 0.000 0, 000 0.000 0.000 0.000, 000 Bf 0.000 0.012 0.015 0.005 0.000 -0.001, 000 Bf 0.000 0.005 0.022 0.017 -0.001 -0.007, 000 Bf 0.000 -0.006 0.001 0.010 0.008 - 0.007 85,000 Bf 0,000 0,015 -0,024 -0,024 -0,010 0.005 103,000 Bf 0,000 0,000 0,000 0,000 0,000 0,000

  ANGLE DA 10,000 9,192 7,365 6,225 4,821 3,379

  F 36,000 DX 0,000 1,037 0,000 0,000 R 0,85 m F 50,000 DX 0,000 1,483 0,000 0,000 R 0,85 m F 60,000 DX 0,000 1,872 0,000 0,000 R 0.85 m F 70,000 DX 0,000 2,311 0,000 0,000 R 0.85 m F 85,000 DX 0,000 3,049 0,000 0,000 R 0,85 m F 103,000 DX 0,000 4,080 0,000 0,000 R 0.85 m F 36,000 DX 0,000 0,875 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,255 0,000 0,000 R 1,00 m F 60,000 DX 0,000 1,599 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,993 0,000 0,000 R 1,00 m F 85,000 DX 0,000 2,000 2,661 0,000 0,000 R 1,00 m F 103,000 DX 0,000 3,609 0,000 0,000 R 1 00 m F 36,000 DX 0,000 0,576 0,000 0,000 R 1,50 m F 50,000 DX 0,000 0,834 0,000 0,000 R 1,50 m F 60,000 DX 0,000 1,072 0,000 0,000 R 1, 50 m F 70,000 DX 0,000 1,365 0,000 0,000 R 1, 50m F 85,000 DX 0,000 1,879 0,000 0,000 R 1,50m F 103,000 DX 0,000 2,636 0,000 0,000 R 1,50m F 36,000 DX 0,000 0,429 0,000 0,000 R 2.00m F 50,000 DX 0,000 0,629 0,000 0,000 R 2,00 m F 60,000 DX 0,000 0,810 0,000 0,000 R 2,00 m F 70,000 DX 0,000 1,037 0,000 0,000 R 2,00 m F 85,000 DX 0,000 1,457 0,000 0,000 R 2,00 m F 103,000 DX 0,000 2,090 0,000 0,000 R 2,00 m F 36,000 DX 0,000 0,285 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,422 0,000 0,000 R 3,00 m F 60,000 DX 0.000 0.551 0.000 0.000 R 3.00 m F 70,000 DX 0.000 0.703 0.000 0.000 R 3.00 m F 85,000 DX 0.000 1.004 0.000 000 3.00 m F 103.000 DX 0.000 1.488 0.000 0.000 R 3.00 m F 36,000 DX 0.000 0.170 0.000 0.000 R 5.00 m F 50.000 DX 0.000 0.254 0.000 0.000 R 5.00 m F 60.000 DX 0.000 0.336 0.000 0.000 R 5.00 m F 70.000 DX 0.000 0.434 0.000 0.000 R 5.00 m F 85.000 DX 0 , 000 0,618 0,000 0,000 R 5,00 m F 103,000 DX 0,000 0,951 0,000 0,000 R 5,00 m The invention therefore relates to the realization of a zoom lens that allows the removal of changes in the conversion coefficient ya and the correction coefficient

  g, indicated above, even when the focus cam

  is used to perform a manual focusing, which allows the reduction of the storage capacity by reducing the number of data of the conversion coefficient Ya and the correction coefficient g which must be kept in the storage device, which allows the elimination of an error in calculating the lens driving amplitude Aa for focusing from the focusing defect amplitude ABf by means of the conversion coefficient Ka, and which makes it possible to obtain a

automatic focus accurate.

  In the first aspect of the invention, in a zoom lens in which the locus of displacement of a set of focusing lenses is defined by synthesis of a focusing cam and a zoom compensation cam so that a focused state is obtained with a substantially constant rotation amplitude for the same distance from the object, independently of the focal length variation state by expression of a predetermined displacement location for the focal length variation by the amplitude in the optical axis direction of the lens assemblies, and the rotational angle of a lens support rotary barrel, when the ratio (dBf / dx, sensitivity associated with the direction of the lens assembly) optical axis) of the amplitude dBf of an infinitesimal displacement of the image plane and the amplitude dx of the infinitesimal displacement, in the direction of the optical axis, of the set of focusing lenses, and the ratio (dBf / da, sensitivity associated with the rotation) of the amplitude dBf of the infinitesimal displacement of the image plane and the angle of infinitesimal rotation of the set of focusing lenses, obtained with the focusing cam, are represented by Yxo respectively. and Yao at the point focused at infinity and are respectively represented by yxR and YaR at the nearest focused point, the zoom lens fulfills condition (1) at least at the telephoto end:

1.0 <YXR / YXO

  Simultaneously, the ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam, this amplitude corresponding to the focusing of the focused state to infinity to the closest focused state and of the az amplitude of rotation corresponding to the variation in focal length from the wide-angle end to the telephoto end fulfills the condition (2): - 1.0 <aF / az <-0.7 (2) In these conditions, the zoom lens fulfills the condition (3) at least at the wide-angle end and at the telephoto end: 0.3 <YaR / Yao <0.7 (3) In the objective in which the locating point of the focusing lens assembly is defined by synthesis of a focusing cam and a zoom compensation cam so that a focused state is obtained for a substantially constant rotation amplitude for an identical distance of the object regardless of the state of variation of focal length, when the values The values of the conversion coefficient Ka, used when the set of focusing lenses corresponds to focusing arrangements at infinity and the nearest position and which are expressed by Ka = ABf / Aa, are respectively represented by Kao and KaR, the zoom lens fulfills the following conditions at least at the wide-angle end and at the telephoto end: 0.6 <Kao / Yao <1.2 0.8 <KaR / YaR <1.7 ABf being the focus defocus amplitude between the image position of an object at an arbitrary position and a predetermined image point position, and Aa being the angle of rotation of the focus lens assembly on the focusing cam required to obtain

the state focused on the object.

  In the first aspect of the invention, if the aforesaid conditions are fulfilled, even when the focusing cam is used to perform the so-called manual focusing, the changes in the conversion coefficient Ya and the correction coefficient y necessary for the precise automatic focusing can be reduced. For this reason, the number of data of the conversion coefficient ta and the correction coefficient y which must be kept in the storage device can be reduced. In addition, since the change in the correction coefficient is small, an error obtained by calculating the lens drive amplitude Aa for focusing from the focusing defect amplitude ABf by using the conversion coefficient Ka is weak, and auto focusing can be accurate. As described above, when the zoom lens is formed of n sets of lenses and the ke lens set is used as a set of focusing lenses, the conversion coefficient yx associated with the direction of the optical axis of the lens unit focusing lenses (dBf / dx ratio of the amplitude dBf of the infinitesimal displacement of the image plane to the amplitude dx of the infinitesimal displacement in the direction of the optical axis) is expressed using the magnifications X of image formation respective sets of lenses in the form: Yx = (1 - k2) k + l213k + 22 ... n2 Accordingly, the rate of change, from the value focused to infinity (yxo) to the most focused value near (yxR), the conversion coefficient yx associated with the direction of the optical axis can be expressed with the magnitudes 0Ok and PRk of imaging of the set of focusing lenses at the points focused at infinity and the closer, in the form e: YXR / YXO = (1 - PRk) / (1 - Pok2) On the other hand, the conversion coefficient associated with the rotation of the set of focusing lenses (dBf / da ratio of the amplitude dBf of the displacement infinitesimal of the image plane at the angle of infinitesimal rotation da) can be expressed as: Ya = Yx- (dx / da) where dx / da is the slope of the focusing cam. For this reason, the rate of change, from the focus value to infinity (Ya0o) to the closest focus value (YaR), to the conversion coefficient Ya associated with the rotation of the set of focusing lenses can be expressed in the following manner using the slopes (dx / da) 0 and (dx / da) R at the positions corresponding to infinity and the closest point on the focusing cam: YaR / YaC = ( YxR / yxo) ((dx / da) R / (dx / da) 0) Accordingly, according to the invention, in the zoom lens which fulfills the condition (1): 1.0 <YxR / x (1) that is to say in the zoom lens in which the value of the conversion coefficient yx associated with the amplitude x of displacement in the direction of the optical axis of the set of focusing lenses in the focused state the closest becomes greater than the value obtained in the state focused to infinity, the ratio of the amplitude aF of rotation of the set of focusing lenses of the focusing cam corresponding to the focusing of the state focused to infinity in the focused state at the nearest point and the amplitude az of rotation corresponding to the variation in focal length of the wide-angle end at the end of telephoto is set so that it fulfills the following condition (2): -1.0 <aF / az <-0.7 (2) Under these conditions, as described in detail about the various embodiments, the cam of may have a shape in which the slope (dx / da) at the nearest position becomes less than that which is obtained at the position which corresponds to infinity, that is to say can have a configuration which corresponds to the following formula: O <(dx / da) R / (dx / da) O <1.0 The rate of change (YaR / YaO) of the infinite focus value (Yao) to the focus value at the nearest point (YaR) of the conversion coefficient associated with the rotation is expressed by the product of the speed of variation (yxR / yx0) of the conversion coefficient yx associated with the direction of the optical axis and the ratio of the slopes (dx / da) R / (dx / da) o of the focusing cam in the form: TaR / YaO = (yxR / yxo) ( (dx / da) R / (dx / da)) For this reason, the two changes compensate each other, and the final speed of variation (YaR / Yao) of the conversion coefficient ga associated with the rotation can be set to a low value. which corresponds to the following condition (3): 0.3 <YaR / YaO <0.7 (3) As previously described, since the variation of the conversion coefficient γ can be reduced compared to that of the conventional system, the number of Data of the conversion coefficient γ and the correction coefficient γ to be stored in the storage device can be reduced. For example, when dividing the focusing range in the same way as with formula (a) (N> 10g (YMAX / MIN) / log (1,2)), the number of divisions becomes: 2, 0 <1Og (yMX / YMIN) / log (1,2) <6,6 and the number of divisions may be smaller than in the case of the classical system. As a result, the cost can be reduced from the point of view of the storage capacity. Moreover, as described hereinafter with regard to the various embodiments, since the variations of the conversion coefficient Ka and of the correction coefficient y are smaller than those of the conventional system, an error obtained by calculating the amplitude Aa of lens drive for focusing according to the focus defocus amplitude ABf, obtained using the conversion coefficient Ka, is low, and a precise operation of

  automatic focusing can be achieved.

  The various formulas representing

the conditions according to the invention.

  Condition (1) is associated with the lens set

  focusing in the zoom lens according to the invention.

  When the range given by condition (1) is exceeded (yxR / x0 <1.0), the conversion coefficient yx associated with the direction of the optical axis becomes smaller in the focused state at the nearest point than 'in the focused state to infinity. For this reason, when the focusing cam (0 <(dx / da) R / (dx / da) 0 <1.0) according to the invention is used, the speed of variation of the conversion coefficient Ya associated with the rotation , expressed by the product of the rate of change (yxR / yxo) of the conversion coefficient yx associated with the direction of the optical axis and the ratio of the slopes ((dx / da) R / (dx / da) o) of the focusing cam, becomes much less than 1.0 (YaR / Yao "<1.0), and the variations of Ya become large, therefore the number of data of the conversion coefficient Ya and the correction coefficient g In addition, since the changes in the conversion coefficient Ka and in the correction coefficient g become significant, an error obtained by calculating the driving amplitude Aa of the lenses according to FIG. ABf amplitude of focusing defect is high, and an accurate focusing operation has UTOMATIC

can not be achieved.

  The condition of formula (2) defines a suitable ratio of the rotation amplitude aF of the focus lens assembly on the focusing cam corresponding to the focusing of the focused state to infinity in the focused state. at the nearest point, and the az amplitude of rotation corresponding to the focal length variation of the wide-angle end at the telephoto end. When the ratio is lower than the lower limit of condition (2), the slope (dx / da) of the focusing cam decreases considerably at the position corresponding to the nearest object with respect to the slope corresponding to the object to infinity and we obtain the ratio: 0 <(dx / da) R / (dx / da) o <"1.0 For this reason, the rate of variation YaR / Yao of the conversion coefficient Ya associated with the rotation, expressed as the product of the rate of change (yxR / yxo) of the conversion coefficient yx associated with the direction of the optical axis and the slope ratio ((dx / dx) R / (dx / da) 0) of the focusing cam, becomes much too weak with respect to 1.0 (YaR / Yao << 1.0), and the variations of ya become important.Therefore, the number of data of the conversion coefficient Ya and the coefficient g must be stored in the storage device, so that since the variations of g are large, an error obtained by calculating the lens drive amplitude Aa from the focus defocus amplitude ABf is high, and a precise autofocus operation can not be

performed.

  For a precise autofocusing operation to be obtained by further reducing the variations of ya, by reducing the number of data of the conversion coefficient γ and the correction coefficient g to be retained in the storage device and by reducing the variations in , the lower limit of the condition (2) is preferably such that: -0.95 aF / az <-0.7 On the contrary, when the ratio exceeds the upper line of the condition (2), as the speed of variation (TaR / Tao) of the conversion coefficient Ya becomes closer to 1.0, the variations of Ya become small, and the number of data of the conversion coefficient Ya and the correction coefficient g to be stored in the storage device can be reduced. However, since the amplitude aF of rotation for focusing becomes small relative to the amplitude az of rotation corresponding to the variation of focal length from the wide-angle end to the telephoto end, the necessary amplitude of rotation at the so-called manual focus becomes low, and it becomes difficult to manually obtain a precise focus. In addition, the upper limit value is preferably set to -0.75 so that the

  Manual focus possibilities are good.

  Condition (3) is associated with the number of data of the conversion coefficient γ and the correction coefficient g to be stored in the storage device, i.e. the number of divisions in the focus range. When YaR / yaO is less than the lower limit of condition (3), the rate of change (YaR / Yao) of the conversion coefficient Ya becomes excessively less than 1.0 and the variations of Ya become large. Consequently, since the number of data of the conversion coefficient Ya and the correction coefficient y to be stored in the storage device increases, the storage device must have a

  large capacity and the cost is increased.

  On the contrary, when the YaR / yao ratio exceeds the upper limit of the condition (3), as the rate of variation (YaR / Yao) of the conversion coefficient Ya becomes closer to 1.0, the variations of ya become small, and the number of data of the conversion coefficient Ya and the correction coefficient y to be stored in the storage device can be reduced. However, as described hereinafter with regard to the various embodiments, since the conversion coefficient Ya must have a very high value, the sensitivity (dBf / da) associated with the rotational displacement becomes large, and a change in the image point due a small error factor in rotation becomes important, so that the precise automatic focus

is disturbed.

  In addition, in order for the autofocus to be accurate with reduction of the sensitivity (dBf / da) associated with the rotational movement, the upper limit of the condition (3) is preferably: 0.3 <YaR / Yao <0 , 6 So that the zoom lens can realize a more precise automatic focusing, when the conversion coefficients Ka = (ABf / Aa) used when the set of focusing lenses has the provisions corresponding to the focus at infinity and at the focal point at the nearest point are respectively represented by Kao and KaR, the zoom lens preferably fulfills at least one of the following conditions (4) and (5), at least at the wide-angle end and at the telephoto end: 0.6 <Ka0 / yao <1.2 (4) 0.8 <KaR / YaR <1.7 (5) Condition (4) defines the rate of change of the conversion coefficient Ka in rotation when changing the position of the object when the lens set of

  focus corresponds to the state focused to infinity.

  When the speed is lower than the lower limit of condition (4), the variation of the conversion coefficient Kao during the change of position of the object becomes too small compared to the conversion coefficient Yao because of the sensitivity associated with the displacement in rotation of the set of focusing lenses in the infinitely focused position. Consequently, for example, when the conversion coefficient Kao which varies during a change in the position of the object is expressed by a pair comprising a value of the conversion coefficient Yao and a value of the correction coefficient 1a0 according to the Kao = Yao (1 - ABf / Lao) relationship, a significant error is produced on the value of the conversion coefficient Kao calculated from the conversion coefficient Δθ and the correction coefficient Ma0 so that the focusing

  precise automatic is disturbed.

  On the contrary, when the speed exceeds the upper limit of the condition (4), the change of the conversion coefficient Kao in rotation during the change of the position of the object becomes significant compared to the conversion coefficient y0 in rotation of the set of focusing lenses at the infinity focused location. For this reason, when the conversion coefficient Kao, which varies during a change in the position of the object, is represented by a pair of values including the conversion coefficient Yao and the correction coefficient pao, an important error is produced on the value of the Kao conversion coefficient calculated from the conversion coefficient YaO and the correction coefficient a0- In order for the automatic focusing to be performed more precisely, the upper and lower limits of the condition (4) are preferably the following ones: 0.7 <Kao / Yao <1.1 Similarly, when the conversion coefficient Kao varies from (KaO / Yao <1) to (Ka0 / yao> 1) during a change of the position of the object when the set of focusing lenses corresponds to a disposition focused at infinity, the sign of the correction coefficient ga0 changes before and after (Kao / Yao = 1). Consequently, when the conversion coefficient Kao is expressed by the pair of values of the conversion coefficient Yao and the correction coefficient jaO, a significant error is produced on the value of the conversion coefficient Kao calculated from the conversion coefficient Yao and Therefore, the Kao conversion coefficient does not vary too much preference after it has exceeded the value of

corresponding to (Ka0 / Yao = 1) -

  As a result, even when the Kao conversion coefficient changes from (Kao / yao <1) to (Kao / Yao> 1) the zoom lens fulfills the following condition: 0, 7 <KaO / ao <1.1 The condition ( 5) defines the rate of change of the conversion coefficient Ka in rotation upon a change of position of the object when the set of focusing lenses corresponds to a focused disposition at the shortest distance. When the speed exceeds the upper limit of the condition (5), the change of the conversion coefficient KaR in rotation during a change of the position of the object becomes too high compared to the conversion coefficient YaR in the form of the sensitivity associated with the rotational displacement of the set of

  focusing lenses at the closest focused point.

  Consequently, for example, when the conversion coefficient KaR which changes during a change of the position of the object is expressed by a pair comprising a value of the conversion coefficient YaR and a value of the correction coefficient gaR according to the relation KaR = YaR (1 ABf / IaR), a significant error is produced on the value of the conversion coefficient KaR calculated from the conversion coefficient YaR and the correction coefficient AaR, so that the precise automatic focusing is disturbed. On the other hand, when the speed is lower than the lower limit of the condition (5), the change of the conversion coefficient KaR in rotation during the change of the position of the object becomes small compared to the conversion coefficient YaR in rotation of all

  focusing lenses at the closest focused point.

  For this reason, when the conversion coefficient KaR which varies during a change in the position of the object is expressed by a pair of values comprising the conversion coefficient YaR and the correction coefficient gaR, a significant error is produced on the value of the KaR conversion coefficient calculated from the coefficient of

  YaR conversion and gaR- correction coefficient

  In order for the autofocus to be more accurately obtained, the upper and lower limits of the condition (5) are preferably: 0.9 <KaR / YaR <1.5 Similarly, when the KaR conversion coefficient changes from (KaR / YaR <1) to (KaR / YaR)> 1) when changing the position of the object when the focus lens assembly corresponds to the focused state at the nearest point, the signal of the correction coefficient AaR changes before and after (KaR / yaR = 1). Consequently, when the conversion coefficient KaR is expressed by a pair of values of the conversion coefficient YaR and the correction coefficient IaR, a significant error is produced on the value of the conversion coefficient KaR calculated from the conversion coefficient YaR and the correction coefficient IaR. As a result, the conversion coefficient KaR does not change too much preferably after it has exceeded

(KaR / YaR = 1) -

  Accordingly, even when the conversion coefficient KaR changes from (KaR / YaR <1) a (KaR / YaR> 1) the zoom lens preferably fulfills the following condition: 0.9 <KaR / YaR <1.5 In the second aspect of the invention, in a zoom lens in which the locus of displacement of the set of focusing lenses is defined by synthesis of a focusing cam and a zoom compensation cam so that a focused state is obtained with a substantially constant rotation amplitude for the same object distance regardless of the focal length variation state, by expression of the predetermined displacement location used for the focal length variation by the displacement amplitude, in the direction of the optical axis, lens assemblies, and the rotation angle of a lens-supporting rotating barrel, when the ratios (dBf / dx) of the amplitude dBf of the infinitesimal displacement of the image plane to the amplitude dx of displacement In the direction of the optical axis, the set of focusing lenses at the point focused at infinity and at the nearest point are respectively represented by Yxo and yxR, when the amplitudes of displacement, in the direction of the optical axis, the set of focusing lenses needed to focus the position to infinity at the nearest position at the wide-angle end and at the telephoto end are represented by AxwR respectively and AXTR, and when the rotation amplitude of the focus lens assembly on the focus cam corresponding to the focal length variation of the wide-angle end at the telephoto end and the corresponding rotational amplitude the focusing of the focused state to infinity in the focused state at the nearest point are respectively represented by az and aF, the zoom lens fulfills the following conditions (6), (7) and (8) at least at the telephoto end: 1.00 <YxR / YxO <1.80 (6)

3.20 <AXTR / AXWR <4.50 (7)

  -0.90 <aF / az <-0.70 (8) In a variant, the zoom lens fulfills the following conditions (9), (10) and (11): 1.00 <YXR / YxO <1, 80 (9) 2.00 <AxTR / AxwR <3.20 (10) -1.0 <aF / az <-0.80 (11) On the other hand, when the ratios (dBf / da) of the amplitude dBf of the infinitesimal displacement of the image plane and the infinitesimal rotation angle da of the set of focusing lenses on the focusing cam at the point of focus at infinity and at the nearest point are respectively represented by YaO and YaR , zoom lens

  fulfills the following condition at least at the

  angle and at the telephoto end: 0.25 <YaR / Yao <0.70 In addition, when the conversion coefficients Ka, used when the set of focussing lenses correspond to the focus at infinity and the point the which are expressed by Ka = DBf / Aa, are respectively represented by KaO and KaR, the zoom lens fulfills the following conditions, at least at the wide-angle end and at the telephoto end: 0.60 < Kao / yao <1.20 0.80 <KaR / YaR <1.70 ABf being the amount of focus defect between the image forming position of an object in an arbitrary position and a predetermined position of the image point, and Aa being the angle of rotation of the set of focusing lenses on the focusing cam, necessary for

  obtaining the focused state of the object.

  As in the first aspect of the invention, in this second aspect, as the above conditions are met, even when the focusing cam is used to achieve the so-called manual focusing, the variations of the conversion coefficient Ya and the correction coefficient y needed for precise auto focus can be reduced. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y which must be kept in the storage device can be reduced. In addition, since the change in the correction coefficient is small, the error after calculation of the lens drive amplitude Aa for focusing the amplitude corresponding to the focusing defect ABf with the conversion coefficient Ka is small. , and automatic focusing can

  be done accurately.

  As described above, when the zoom lens consists of n sets of lenses and the ke lens set is used as a set of focusing lenses, the conversion coefficient yx associated with the direction of the optical axis of the set of lenses focus lenses (the dBf / dx ratio of the amplitude dBf of the infinitesimal displacement of the image plane to the amplitude dx of the infinitesimal displacement in the direction of the optical axis) is expressed using the X formation magnitudes images of the respective sets of lenses in the following form: Yx = (1 - Pk2) Pk + 12Pk + 22 ... n2 Accordingly, the rate of change, from the value focused to infinity (yx0) to the focused value at the nearest point (yxR), the conversion coefficient yx associated with the direction of the optical axis can be expressed from the image formation magnitudes o0k and PRk of the set of focusing lenses at the point focused at infinity and at the nearest point in the form: YxR / YxO = (1 - PRk2) / (1 - POk2) On the other hand, the conversion coefficient Ya associated with the rotation of the set of focusing lenses (dBf ratio / da of the amplitude dBf of the infinitesimal displacement of the image plane at the angle da of infinitesimal rotation) can be expressed by: Ya = yx. (dx / da) dx / da being the slope of the focusing cam. For this reason, the rate of change, from the value focused at infinity (Yao) to the value focused at the nearest point (yaR), of the conversion coefficient Ya associated with the rotation of the set of focusing lenses can be expressed using the slopes (dx / da) 0 and (dx / da) R at the positions corresponding to the infinity and the closest point of the focusing cam, in the form: YaR / Yao = ( YxR / YxO) ((dX / da) R / (dx / da) 0)) Consequently, according to the invention, in the zoom lens in which the value of the conversion coefficient yx associated with the displacement amplitude x in the direction of the optical axis of the focus lens assembly in the focused state at the nearest point becomes greater than the infinite focus state (1.0 <yxR / yxO), the ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam corresponding to the focusing of the focused state to infinity in the focused state at the nearest point and the az amplitude of rotation corresponding to the focal length variation of the wide-angle end at the telephoto end is set to a negative value (aF / az <0), so that the focusing cam may have a configuration in which the slope (dx / da) at the position focused at the nearest point becomes less than that of the position corresponding to infinity (0c (dx / da) R / (dx / da) 0 <1.0), so that the coefficient of

  Ya conversion associated with rotation is reduced.

  More precisely, as the rate of variation (YaR / Yao) of the value focused at infinity (Yao) to the value focussed at the nearest point (YaR) of the conversion coefficient Ya associated with the rotation is expressed by the product the rate of variation (yxR / yxo) of the conversion ratio yx associated with the direction of the optical axis and the ratio of the slopes (dx / da) R / (dx / da) o of the focusing cam as previously described , the final speed of variation (YaR / YaO) of the conversion coefficient Ya associated with the rotation can be reduced by adopting a set

  in which the two changes compensate each other.

  According to the invention, in a zoom lens in which the conversion coefficient yx associated with the amplitude x of displacement in the direction of the optical axis of the set of focusing lenses, at the point focused at infinity and at closest point, at the telephoto end, satisfies condition (6): 1,00 <yxR / xo <1,80 (6) when the ratio of the AxwR and AXTR amplitudes of displacement, in the direction of the optical axis, the set of focusing lenses required to focus the position at infinity at the position at the nearest point at the wide-angle end and at the telephoto end, fulfills the condition (7). ): 3.20 <AxTR / AxwR <4.50 (7) the ratio of the amplitude aF of rotation of the set of focusing lenses to the focusing cam, corresponding to the focusing of the focused state to the infinity in the focused state at the nearest point, and the amplitude az of rotation corresponding to the variati the focal length of the wide-angle end at the telephoto end, is adjusted so that it corresponds to the following condition (8): -0.90 <aF / az <-0.70 (8) In these conditions, the final speed of variation (YaR / Yao0) of the conversion coefficient Ya associated with the rotation can be set to a low value which corresponds to the

  condition (12) described below.

  In a variant, according to the invention, in a zoom lens in which the conversion coefficient yx associated with the amplitude x of displacement, in the direction of the optical axis, of the set of focusing lenses at the point focused at infinity and at the nearest point at the telephoto end, fulfills the condition (9): 1,00 <yxR / yxo <1,80 (9) when the ratio between the displacement amplitudes AxwR and AXTR, in the direction of the optical axis, the set of focusing lenses necessary to focus the infinite position to the position at the smallest distance at the wide-angle end and the telephoto end corresponds to the condition next (10): 2.00 <AxTR / AxWR <3.20 (10) the ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam corresponding to the focusing of the focused state to infinity in the focused state at the nearest point and the amplitude az d e rotation corresponding to the change in focal length from the wide-angle end to the telephoto end, is set to correspond to the following condition (11): -1.00 <aF / az <-0, 80 (11) Under these conditions, the final rate of variation (YaR / YaO) of the conversion coefficient Ya associated with the rotation can be set to a low value which fulfills the following condition (12): 0.25 <YaR / Yao <0.70 (12) As previously described, since the change in the conversion coefficient la can be reduced compared to that of the conventional system, the number of data of the conversion coefficient la and the correction coefficient y to be kept in the device memorisation can be reduced. For example, when dividing the focusing range according to the formula (a) (N> 1og (YMAX / YMIN) / log (1,2)), the following condition is fulfilled: 2.0 <log (YMAX / YMIN) / log (1,2) <7.6 and the number of divisions may be smaller than in the classical system. As a result, the cost can be reduced by reducing the storage capacity. Furthermore, as described hereinafter with respect to the embodiments, since the changes in the conversion coefficient Ka and in the correction coefficient γ are smaller than those of the conventional system, the error obtained by calculating the amplitude of Aa lens drive for focusing from the focusing defect amplitude ABf using the conversion coefficient Ka is low, and a precise autofocus operation

can be realized.

  The following conditions are described in the following

present invention.

  Condition (6) is associated with the lens set

  focusing of the zoom lens according to the invention.

* When YXR / YxO is less than the lower limit of condition (6) (yxR / Yxo <1.0), the yx conversion coefficient associated with the direction of the optical axis in the focused state at the highest point near becomes less than the value obtained for the state focused to infinity. For this reason, when the focusing cam (0 <(dx / da) R / (dx / da) 0 <1.0) according to the invention is used, the speed of variation of the conversion coefficient is associated with the rotation , this velocity being expressed by the product of the rate of variation (yxR / yxo) of the conversion coefficient yx associated with the direction of the optical axis and the ratio of the slopes ((dx / da) R / (dx / da) 0) of the focusing cam, becomes excessively less than 1.0 (YaR / Yao "<1.0), and the changes of Ya become important, therefore the number of data of the conversion coefficient γ and the coefficient of In addition, since the changes in the conversion coefficient Ka and in the correction coefficient become significant, the error obtained by calculating the amplitude Aa of driving lenses from the focus defect amplitude ABf is high, and a precise focus operation automatic operation can not

to be realized.

  On the contrary, when the YaR / Ya0 ratio exceeds the upper limit of the condition (6), as the rate of change (YaR / YaO) of the conversion coefficient Ya becomes

  closer to 1.0, the variations of Ya become small.

  However, in the zoom lens according to the invention, which corresponds to the condition (7), the optimum ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam corresponding to the focusing of the lens. state focused at infinity in the focused state at the nearest point and the rotation amplitude az corresponding to the focal length variation of the wide-angle end at the telephoto end is

  found outside the range defined by condition (8).

  Condition (7) is associated with the ratio of the magnitudes of displacement, in the optical axis direction, of the set of focusing lenses necessary to focus the position at infinity at the nearest point position. at the wide-angle end and at the telephoto end. As described hereinafter with respect to the embodiments, this ratio is an amplitude associated with the ratio of the slope (dx / da) R to the position closest to the slope (dx / da) 0 at the position corresponding to the infinity of the focusing cam. As the ratio between the two displacement amplitudes decreases,

  the slope variation at the focus becomes lower.

  On the contrary, when the ratio of the two amplitudes of displacement increases, the variation of the slope of the focusing cam increases. Consequently, when the ratio is lower than the lower limit of the condition (7), the variations of the conversion coefficient associated with the rotation become low. However, in the zoom lens according to the invention which corresponds to the condition (6), the optimum ratio of the amplitude aF of rotation of the set of focusing lenses of the focusing cam corresponding to the focusing at the infinity in the state corresponding to the nearest point and the amplitude az of rotation corresponding to the variation of focal length from the wide-angle end to the telephoto end

  found outside the range defined by condition (8).

  On the other hand, when the ratio exceeds the upper limit of the condition (7), as the slope variations on the focusing cam become too large compared to those of the conversion coefficient yx, associated with the direction of the axis Optically, the variations of the conversion coefficient Ya associated with the rotation become large and the number of data of the conversion coefficient Ya and the coefficient and correction y which must be stored increases. In addition, a specific operation of

  automatic focus can not be achieved.

  For an automatic focusing operation to be accurate by further reducing the variations of Ya, reducing the number of data of the conversion coefficient Ya and the correction coefficient y to be stored, and by reducing the changes of A, the upper limit of the condition (7) is preferably such that: 3, 20 <AxTR / AxWR <4.20 The condition (8) defines a suitable ratio of the rotation amplitude aF of the focus lens assembly on the cam of focusing corresponding to the focusing of the state to infinity in the state at the nearest point, and the amplitude az of rotation corresponding to the variation of focal length of the wide-angle end at the end of telephoto. When the ratio is lower than the lower limit of condition (8), the slope (dx / da) of the focusing cam decreases considerably at the nearest position relative to the slope at the position corresponding to infinity, and the values have the following ratio: 0 <(dx / da) R / (dx / da) 0 << 1.0 For this reason, the speed of variation of the conversion coefficient associated with the rotation, this speed being represented by the product of the rate of variation (yxR / yxo) of the conversion coefficient yx associated with the direction of the optical axis and the ratio of the slopes ((dx / da) R / (dx / da) 0) of the cam focus, becomes excessively less than 1.0 (YaR / Yao << 1.0), and the variations of Ya become large. As a result, the number of data of the conversion coefficient Ya and the correction coefficient y to be stored increases. Moreover, since the variations of y are large, an error obtained by calculating the amplitude Aa of driving the lenses from the focus defect amplitude ABf is large, a precise automatic focusing operation does not occur.

can not be executed.

  So that the autofocusing operation can be accurate with further reduction of the Ya variations, reducing the number of data of the conversion coefficient Ya and the correction coefficient y to be stored, and reducing the variations of λ, the lower limit of the condition (8) is preferably such that: -0.85 <aF / az <-0.70 On the contrary, when the ratio exceeds the upper limit of condition (8), as the rate of variation (YaR / Yao) the conversion coefficient Ya approaches 1.0, the variations of Ya become small, and the number of data of the conversion coefficient Ya and the

  correction coefficient y to be stored can be reduced.

  However, since the focusing rotation amplitude aF becomes small relative to the rotation amplitude az corresponding to the focal length variation of the wide-angle end at the telephoto end, the focusing rotation amplitude said manual becomes weak, and it becomes difficult to achieve

  manually a precise focus.

  The condition (9) is the same as the condition (6) described above, and is associated with the set of focusing lenses of the zoom lens according to the invention. When the ratio yxR / yxO is less than the lower limit of condition (9) (yxR / yx0 <1.0), the conversion coefficient yx associated with the direction of the optical axis in the focused state at point closer becomes less than that which is obtained in the focused state at infinity. For this reason, when the focusing cam (0 <(dx / da) R / (dx / da) 0 <1.0) according to the invention is used, the speed of variation of the conversion coefficient Ya associated with the rotation , this speed being expressed by the product of the rate of variation (yxR / yx0) of the conversion coefficient yx associated with the direction of the optical axis and the slope ratio ((dx / da) R / (dx / da) 0) of the focusing cam, becomes excessively small compared to 1.0

  (YaR / Yao) << 1,0), and the variations of Ya become large.

  As a result, the number of data of the conversion coefficient Ya and the correction coefficient y to be stored increases. In addition, since the variations of the conversion coefficient Ka and the correction coefficient become important thereto, an error obtained by calculating the amplitude Aa of the lens drive from the focus defocus amplitude ABf is large, and a precise autofocus operation can not be performed. On the contrary, when the ratio YaR / yao exceeds the upper limit of the condition (9), as the rate of variation (YaR / YaO) of the conversion coefficient Ya becomes

  closer to 1.0, the variations of Ya become small.

  However, in the zoom lens according to the invention, which corresponds to the condition (10), the optimum ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam corresponding to the focusing of the lens. state focused at infinity in the focused state at the nearest point, and the rotation amplitude az corresponding to the focal length variation of the wide-angle end at the telephoto end,

  found outside the range defined by condition (11).

  Condition (10) is associated with the ratio of the magnitudes of displacement, in the direction of the optical axis, of the set of focusing lenses necessary to focus the position at infinity at the nearest position to the wide-angle end and at the telephoto end as shown in condition (7). As described hereinafter with respect to the various embodiments, this ratio has an amplitude related to the ratio of the slope (dx / da) R to the position of the nearest location and the slope (dx / da) 0 at the position corresponding to infinity on the focusing cam. When the ratio of the two displacement amplitudes decreases, the slope variations of the focusing cam decrease. On the contrary, when the ratio of the two amplitudes of displacement increases, the variations of slope on the focusing cam increase. Consequently, when the ratio is lower than the lower limit of the condition (10), the variations of the conversion coefficient Ya associated with the rotation become small. However, in the zoom lens according to the invention, which corresponds to the condition (9), the optimum ratio of the amplitude aF of rotation of the set of focusing lenses on the focusing cam corresponding to the focusing of the lens. infinitely focused state in the focused state at the nearest point and the rotation az amplitude corresponding to the focal length variation of the wide-angle end at the telephoto end, lies outside the range defined by condition (11). On the other hand, when the ratio exceeds the upper limit of the condition (10), as the slope changes of the focusing cam become too large compared to those of the conversion coefficient yx associated with the direction of the optical axis , the changes in the conversion coefficient associated with the rotation become important, and the number of data of the conversion coefficient y and the correction coefficient y to be stored increases. In addition, a

  Accurate automatic focusing can not be achieved.

  Condition (11) defines a suitable ratio of the rotation amplitude aF of the focus lens assembly on the focusing cam corresponding to the focusing of the focus state to infinity in the focused state at the point on which closer and the amplitude az of rotation corresponding to the variation of focal length from the wide-angle end to the telephoto end, which corresponds to the condition (8) which precedes. When the ratio is lower than the lower limit of the condition (11), the slope (dx / da) of the focusing cam decreases considerably at the position corresponding to the nearest point with respect to the slope at the position corresponding to the 'infinite, and the ratio becomes: 0 <(dx / da) R / (dx / da) 0 << 1.0 For this reason, the rate of variation (YaR / YaO) of the coefficient Ya associated with rotation, expressed as the product of the rate of change (yxR / yxo) of the conversion coefficient yx associated with the direction of the optical axis and the ratio of the slopes ((dx / da) R / (dx / da) 0) of the focusing cam, becomes much too small compared to 1.0 (YaR / Yao << 1.0), and the variations of Ya become important. As a result, the number of data of the conversion coefficient γ and the correction coefficient γ to be stored increases. In addition, since the variations of y are large, a calculation error of the driving amplitude Aa of the lens from the focusing defect amplitude ABf is high, and an operation of

  Accurate automatic focusing can not be achieved.

  On the contrary, when the ratio exceeds the upper limit of the condition (11), as the rate of change (YaR / Yao) of the conversion coefficient Ya becomes closer to 1.0, the variations of Ya become small, and the number of the conversion coefficient Ya and the

  correction coefficient y to be stored can be reduced.

  However, since the amplitude aF of rotation for focusing becomes small relative to the amplitude az of rotation corresponding to the variation of focal length from the wide-angle end to the telephoto end, the necessary amplitude of rotation at so-called manual focus becomes weak, and it becomes difficult to ensure

  manually a precise focus.

  Condition (12) is associated with the number of data of the conversion coefficient γ and the correction coefficient γ to be stored, i.e. the number of divisions of the focusing range. When the YaR / Yao ratio is lower than the lower limit of the condition (12), the rate of change (YaR / YaO) of the conversion coefficient Ya becomes excessively less than 1.0 and the variations of Ya become large. Consequently, since the number of data of the conversion coefficient γ and the correction coefficient p to be stored increases, a large capacity memory device is required, so that the cost

increases.

  On the contrary, when the YaR / Yao ratio exceeds the upper limit of the condition (12), as the rate of variation (YaR / Yao) of the conversion coefficient Ya approaches 1.0, the variations of Ya become small and the number of data of the conversion coefficient Ya and the

  correction coefficient y to be stored can be reduced.

  However, since the conversion coefficient γ must have a very high value, the sensitivity (dBf / da) associated with the rotational displacement becomes strict and the variation of the image point caused by a slight error in rotation becomes large, although that focus

  precise automatic is disturbed.

  In addition, for the autofocus to be accurate with reduction of the sensitivity (dBf / da) associated with the rotation, the upper and lower limits of the condition (12) are preferably as follows: 0.30 <YaR / YaO <0.60 For achieving a zoom lens allowing more precise automatic focusing, when the conversion coefficients Ka (= ABf / Aa) used when the set of focusing lenses is at the positions corresponding to the focused state at infinity and in the focused state at the nearest point are respectively represented by Kao and KaR, the zoom lens preferably fills the conditions (13) and (14) which follow at least at the wide-angle end and at the telephoto end: 0.60 <Kao / Yao <1.20 (13) 0.81 <KaR / YaR <1.70 (14) Condition (13) determines the rate of change of the conversion coefficient Ka rotating when changing the position of the object when the seems of lenses of

  focus corresponds to the state focused to infinity.

  When the speed is below the lower limit of

  condition (13), the change in the conversion coefficient

  Kao when changing the position of the object becomes too weak compared to the Yao conversion coefficient and reduces the sensitivity associated with the rotational displacement of

  the set of focusing lenses focused to infinity.

  Accordingly, for example, when the conversion coefficient Kao which changes upon a change in the position of the object is represented by a pair comprising a value of the conversion coefficient Yao and a value of the correction coefficient uaO as a function of the Kao = Yao (1-ABf / ilao) relationship, a significant error is produced on the value of the conversion coefficient KaO calculated from the conversion coefficient Yao and the correction coefficient PaO, so that the automatic focusing can

difficult to be precise.

  On the contrary, when the speed exceeds the upper limit of the condition (13), the speed of the conversion coefficient Kao rotates during a change of the

  position of the object becomes large relative to the coeffi-

  Yao conversion during the rotation of the focus lens assembly focused to infinity. For this reason, when the conversion coefficient KaO which changes upon a change in the position of the object is represented by a pair comprising a value of the conversion coefficient Yao and a value of the correction coefficient Pao, a large error is produced on the value of the conversion coefficient K0ao calculated from the conversion coefficient YaO and the correction coefficient

1a0o -

  For automatic focusing to be more accurate, the upper and lower limits of condition (13) are preferably: 0.65 <Kao / Yao <1.0 Similarly, when the conversion coefficient KaO changes ( Kao / Yao <1) to (Ka0 / Yao> 1) when changing the position of the object when the set of focusing lenses corresponds to a state focused to infinity, the sign of the correction coefficient GaO changes before and after (Kao / Tao = 1). Consequently, when the conversion coefficient Kao is represented by a pair comprising a value of the conversion coefficient YaO and a value of the correction coefficient Mao, a large error is produced on the value of the conversion coefficient Kao, calculated from the coefficient of Yao conversion and correction coefficient a0ao As a result, the Kao conversion coefficient does not vary too much preference after exceeding

(KaO / Yao = 1).

  As a result, even when the Kao conversion coefficient changes from (Kao / Yao <1) to (Kao / Yao> 1) the zoom lens preferably fulfills the following condition: 0.65 <KaO / Yao <1.10 La condition (14) defines the rate of change of the conversion coefficient Ka in rotation of a change in the position of the object when the set of focusing lenses corresponds to the focused position at the nearest point. When the speed exceeds the upper limit of the condition (14), the variation of the conversion coefficient KaR in rotation during a change of the position of the object becomes too great compared to the conversion coefficient YaR which represents the associated sensitivity to the rotational displacement of the set of

  focusing lenses at the closest focused point.

  Accordingly, for example, when the conversion coefficient KaR which changes upon a change in the position of the object is expressed by a pair comprising a value of the conversion coefficient YaR and a value of the correction coefficient MaR, after the relation KaR = YaR (1 ABf / IaR), a large error is produced on the value of the conversion coefficient KaR calculated from the conversion coefficient YaR and the correction coefficient UaR, although

  that a precise automatic focusing is disturbed.

  On the contrary, when the speed is lower than the lower limit of the condition (14), the change of the conversion coefficient KaR in rotation during a change of the position of the object becomes small compared to the conversion coefficient YaR in rotation for the set of focusing lenses that is at the closest focused point. For this reason, when the conversion coefficient KaR which varies during a change in the position of the object is expressed by a pair comprising a value of the conversion coefficient YaR and a value of the correction coefficient MaR, a large error is produced on the value of the conversion coefficient KaR which is calculated from the conversion coefficient YaR and

the correction coefficient PaR-

  In order for the autofocus to be more precise, the upper and lower limits of the condition (14) are preferably: 0.90 <KaR / YaR <1.55 Similarly, when the conversion coefficient KaR changes (KaR / YaR <1) to (KaR / YaR> 1) when changing the position of the object when the set of focusing lenses corresponds to the focused state at the nearest point, the sign of the coefficient of correction gaR changes before and after (KaR / YaR = 1). Consequently, when the conversion coefficient KaR is expressed by a pair comprising a value of the conversion coefficient YaR and a value of the correction coefficient gaR, a significant error is produced on the value of the conversion coefficient KaR calculated from the coefficient of Thus, the conversion coefficient KaR does not vary too much in preference.

  after passing (KaR / YaR = 1).

  Accordingly, even when the KaR conversion coefficient changes from (KaR / YaR <1) to (KaR / YaR> 1), the zoom lens preferably fulfills the following condition: 0.90 <KaR / YaR <1.55 The foregoing and other objects, properties and advantages of the invention are described hereinafter and may be better understood with reference to the drawings and

description which follows.

  Fig. 1A shows the places of displacement when varying the focal length of a zoom lens in the first embodiment of the present invention; Fig. 1B shows the configurations of a focus cam and a zoom compensation cam of a second set of lenses of the zoom lens of the first embodiment of the present invention;

  FIG. 2 is a useful view for the description of

  the zoom lens focusing cam configuration of the first embodiment of the present invention; Fig. 3A is a view showing places of displacement during zooming of a zoom lens in the ninth embodiment of the present invention; Fig. 3B is a view showing the configurations of a focus cam and a zoom compensation cam of a second set of lenses of the zoom lens of the ninth embodiment of the present invention;

  FIG. 4 is a useful view for the description of

  the focusing cam configuration of the zoom lens of the ninth embodiment of the present invention; Fig. 5A is a view showing places of displacement during zooming of the zoom lens of the thirteenth embodiment of the present invention; Figure 5B is a view showing the configurations of a focusing cam and a zoom compensation cam of a second set of lenses of the zoom lens of the thirteenth embodiment of the present invention; and

  FIG. 6 is a useful view for the description of

  the configuration of the focusing cam of the zoom lens of the thirteenth embodiment of the present invention. The present invention is now described in detail

  with reference to embodiments.

  First Embodiment A zoom lens of the first embodiment or first example is a zoom lens which comprises a group of four sets, i.e. sets of lenses that are positive, negative, positive and positive, and which provide focus with a second set of negative type lenses, as in the embodiment of Japanese Patent Application Laid-open No. 5-142475, described in detail previously under the art earlier. In this zoom lens, the ratio (aF / az) of the amplitude of rotation for the focusing of the position focused at infinity to the position focused at the nearest location (R = 0.85 m) and of the focal length variation rotation amplitude of the wide-angle end (F = 36.0 mm) at the telephoto end (F = 103.0 mm) is set to a

value equal to -0.75.

  Table 10 which follows summarizes various paraxial data of an optical system and data to define the configuration of a cam of

  focusing in the first embodiment.

  The upper portion of Table 10 indicates the focal length data and the interval data between the main points of the respective lens assemblies of the optical system corresponding to the first embodiment. In this table, F1, F2, F3 and F4 are the respective focal lengths of the first, second, third and fourth sets of lenses, and D1, D2, D3 and D4 are respectively the main points interval between the first and second sets of lenses. and the second set of lenses, between the second and third set of lenses, between the third and fourth set of lenses, and between the fourth set of lenses and a predetermined image plane for six states of focal length variation (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm). As a result, the data are the same as the various paraxial data (upper part of Table 1) of the embodiment of the patent application.

  Japanese Opened to Public Inspection No. 5-142475.

  The middle portion of Table 10 shows the spline sample data when the configuration (a curve g2F of FIG. 1B) of the focusing cam of the second set of lenses of the first embodiment, used for focusing, is represented by a spline function associated with the angle of rotation of a rotating barrel and the amplitude x of displacement in the direction of the optical axis (see the book "Numerical Analysis and FORTRAN", Maruzen, "Spline Function and Its

  Applications ", Kyoiku Shuppan, and the like).

  In addition, the lower part of Table 10 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 36.0, 50, 0, 60.0, 70.0, 85, 0 and 103.0 mm), and the magnitudes of rotation (rotation amplitudes for focusing) when focusing at respective photographing distances (R = 5.0, 3.0, 2.0, 1, 5, 1.0 and 0.85 m) using the focusing cam of the first embodiment. In the lower part of Table 10, as the amplitude of rotation for the focal length variation of the wide-angle end (F = 36.0 mm) at the telephoto end (F = 103.0 mm) is set to a value of 10.0, and the rotation amplitude for focusing from the infinitely focused position to the focused position at the nearest point (R = 0.85 m) is -7, 5, the ratio (aF / az) of the amplitude of rotation for focusing and the amplitude of rotation for the variation of focal length in the first mode of

achievement is equal to -0.75.

Table 10

  First example f = 36.0 to 103.0 (ratio of rotation amplitudes: aF / az = -0.75) Focal distances and intervals of the main points of the objectives of the first example

  F 36,0000 50,0000 60.0000 70.0000 85.0000 103.0000

  F1 71.3528 D1 10.0000 16.9506 20.8432 24.0040 27.6859 31.0684

  F2 -16,8076 D2 18,0119 13.8825 11.8221 10,1086 7,9077 5,6236

  F3 37.3219 D3 13.2200 12.3744 11.9702 11.6986 11.3811 11.3103

  F4 61.7098 D4 53.2211 59.4228 62.5744 65.172 68.2854 71.2371

  Focusing cam shape (spline interpolated point) corresponding to the first example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.3230 0.0000 0.0000

  2 -10,0000 0.0000 1.2489 0.0000 0.0000

  3 -7.5000 0.0000 1.0365 0.0000 0.0000

  4 -5.9106 0.0000 0.8749 0.0000 0.0000

-3,4773 0.0000 0.5760 0.0000 0.0000

  6 -2.4665 0.0000 0.4295 0.0000 0.0000

  7 -1.5604 0.0000 0.2847 0.0000 0.0000

  8 -0.8999 0.0000 0.171 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,5000 0.0000 -0.5740 0.0000 0.0000

  1 1 4.0894 0.0000 -1.0445 0.0000 0.0000

  12 6.5227 0.0000 -2.0183 0.0000 0.0000

  13 7.5335 0.0000 -2.5636 0.0000 0.0000

  14 8.4396 0.0000-3.156 0.0000 0.0000

9,1001 0.0000 -3,7034 0.0000 0.0000

  16 10.0000 0.0000 -4.6540 0.0000 0.0000

  17 11.0000 0.0000 -6.0900 0.0000 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focusing of the first example (ratio of rotation amplitudes: aF / az = -0.75) Focal distance Corresponding position Distance of amplitude of rotation to infinity photography for focusing 36.0 mm 0.0000 5.00 m -0.900, 0 mm 3.3747 3.00 m -1.560, 0 mm 5.3126 2.00 m -2.466, 0 mm 6.8602 1.50 m-3.477, 0 mm 8.5875 1.00 m -5.911 103.0 mm 10.00.00 0.85 m -7.500 Table 11 which follows gives the numerical value data of the cams of the lens assembly of the first embodiment. , the data being calculated by interpolation using a spline function from the sample data of the cam of

  focus summarized in the middle part of Table 10.

  In this table (ANGLE) designates the rotation angle of the rotary barrel, (2) the displacement amplitude (in millimeters) in the direction of the optical axis of the second set of lenses, and (F) the focal length in millimeters of the entire system in the focused state to

  infinity, corresponding to the amplitude of rotation (ANGLE).

Table 1 1

  Digital Cam Values for Focusing Lens of the First Example Digital Focusing Cam Values Digital Focal Length Compensation Cam Values

ANGLE (2) F ANGLE (2) F

-7.5000 1.0365 0.0000

-7.0000 0.9882 0.0000

-6.5000 0.9376 0.0000

-6.0000 0.8846 0.0000

-5.5000 0.8292 0.0000

-5.0000 0.7711 0.0000

-4.5000 0.7102 0.0000

-4.0000 0.6463 0.0000

-3,5000 0.5792 0.0000

-3.0000 0.5087 0.0000

-2.5000 0.4346 0.0000

-2.0000 0.3567 0.0000

-1.5000 0.2746 0.0000

-1.0000 0.1880 0.0000

-0.5000 0.0965 0.0000

  0.0000 0.0000 36.0000 0.0000 0.0000 36.0000

  0.5000 -0.1018 37.8527 0.5000 0.2874 37.8527

  1.0000 -0.2095 39.7739 1.0000 0.5787 39.7739

  1.5000 -0.3236 41.7710 1.5000 0.8752 41.7710

  2.0000 -0.4449 43.8494 2.0000 1.1779 43.8494

  2.5000 -0.5740 46.0113 2.5000 1.4874 46.0113

  3,0000 -0,7115 48,2581 3,0000 1,8042 48,2581

  3,5000 -0,8583 50,5936 3,5000 2,1295 50,5936

  4.0000 -1.0153 53.0235 4.0000 2.4641 53.0235

  4.5000 -1.1834 55.5614 4.5000 2.8089 55.5614

  , 0000 -1,3645 58,2390 5,0000 3,1669 58,2390

  , 5000 -1,5607 61,0923 5,5000 3,5411 61,0923

  6,0000 -1,7743 64,1537 6,0000 3,9342 64,1537

  6,5000 -2,0072 67,4546 6,5000 4,3478 67,4546

  7,0000 -2,2622 71,0314 7,0000 4,7845 71,0314

  7.5000 -2.5437 74.9521 7.5000 5.2500 74.9521

  8.0000 -2.8572 79.2786 8.0000 5.7510 79.2786

  8,5000 -3,2109 84,0989 8,5000 6,2975 84,0989

  9.0000 -3.6152 89.5118 9.0000 6.9013 89.5118

  4 0 9.5000 -4.0860 95.6899 9.5000 7.5804 95.6899

  , 0000 -4,6540 103,0000 10,0000 8,3719 103,0000

  The left-hand side of Table 11 shows the numerical value data of the focus cam of the first embodiment, and the right-hand portion of Table 11 shows the numerical value data of the zoom compensation cam in this embodiment. A value obtained by synthesizing the amplitudes (2) of displacement in the direction of the optical axis for the numerical value data of the focusing cam and the cam of

  zoom compensation, in the range between the ampli-

  rotation study (ANGLE = 0.0) and rotation amplitude (ANGLE = 10.0), coincides with the displacement location (curve g2 of Figure 1A) of the second set of lenses, calculated with paraxial data from the top

of Table 10.

  Accordingly, the zoom compensation cam (curve g2H of Fig. 1B) is determined by subtracting the focusing cam (curve g2F of Fig. 1B) from the moving place (curve g2 of Fig. 1A) during the variation. of the focal length of the second set of lenses determined by the paraxial data of the part

Table 10.

  Figures 1A and 1B and Figure 2 are now

described quickly.

  FIG. 1A shows the paraxial arrangement and the places of displacement during the zooming of the zoom lens of the first embodiment, and FIG. 1B shows the configurations of the focusing cam and the zoom compensation cam. of the second set of lenses of this embodiment. In FIGS. 1A and 1B, G1, G2, G3 and G4 respectively represent the first, the second, the third and the fourth set of lenses, and g1, g2, g3 and g4 respectively represent the places of displacement, during the variation. focal length, first, second, third and fourth lenses. Further, g2F and g2H respectively represent the configurations of the focusing cam and the zoom compensating cam of the second set of lenses. As previously described, a configuration obtained by synthesis of the focusing cam g2F and the zoom compensation cam g2H of the second set of lenses coincides with the

  displacement place g2 of the second set of lenses.

  Figure 2 is a useful view for the description of

  the configuration of the focusing cam g2F in the first embodiment. In Figure 2,

  (f = 36, R = one) and (f = 36, R = 0.85) represent respectively

  position at infinity and at the smallest distance (R = 0.85 m) at the wide-angle end, and

  coordinate positions (x; a) on the focus cam

  are (x; a) = (0; 0) and (x; a) = (1,035; -7,5) respec-

  tively. On the other hand, (f = 103, R = one) and (f = 103, R = 0.85) represent respectively the focusing positions at infinity and at the shortest distance (R = 0.85 m) at the telephoto end, and the coordinate positions (x; a) on the focus cam are respectively

  (x; a) = (-4.654; 10) and (x; a) = (-0.574; 2.5).

  When varying the focal length from the wide-angle end to the telephoto end, the second set of lenses moves on the focusing cam g2F from the coordinate position (0; 0) to the coordinate position ( -4.654; 10) for an object at infinity, and the coordinate position (1.037; -7.5) at the coordinate position (0.574; 2.5) for an object at the shortest distance. As a result, the second set of lenses moves 10.0 in rotation (direction of the axis a) in both cases. On the other hand, when focusing the set to infinity at the object at the shortest distance, the second set of lenses moves on the focusing cam g2F of the coordinate position (0; 0) to the

  coordinate position (1.037; -7.5) at the large end

  angle and coordinate position (-4.654; 10) at the coordinate position (-0.574; 2.5) at the telephoto end. As a result, the second set of lenses moves -7.5 in rotation (direction of the axis a) at these ends. In contrast, in the direction of the optical axis (x-axis direction), the second set of lenses moves from 1.037 to the wide-angle end and

  from 4.08 to the telephoto end.

  The following tables 12, 13 and 14 indicate the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Px of image formation of the sets. of the lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient associated therewith with the rotation at the wide-angle end ( F = 36.0 mm), at the middle position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the first embodiment. In these tables, (R) on the left indicates the distance of photography (m), (ANG) designates the rotation amplitude of the focusing cam during focusing at the respective photography distances, and 1), 2), 3) and 4) on the right represent respectively the first, second, third and fourth sets of lenses. In addition, in these tables, the first part indicates the displacement amplitude DX (mm) for focusing in the direction of the optical axis when focusing at the respective photographing distances (R = 10.0, 5.0 , 3.0, 2.0, 1.5, 1.0 and 0.85 m) (note that moving to the side of the object is positive). The second part indicates the PK magnifications of the respective sets of lenses in the focused state at the respective photographing distances (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m). The third part shows the conversion coefficient yx associated with the direction of the optical axis of the focusing lens group in the focused state at the respective distances of

  photograph (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m).

  In addition, the fourth part indicates the slope (dx / da) of the focusing cam at the positions on the focusing cam, which correspond to the focused state at the respective photographing distances (R = 10.0, 5.0 , 3.0, 2.0, 1.5, 1.0 and 0.85 m), and the fifth part indicates the conversion coefficient y associated with the rotation of the focusing lens assembly in the focused state. at the respective photography distances (R = 10.0, 5.0,

3.0, 2.0, 1.5, 1.0 and 0.85 m).

  Table 12 Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (36.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 0.085 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 0,170 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 0,285 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 0,430 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 0,576 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.037 3) 0.000 4) 0.000

  Objective image magnification Pk at the wide-angle end (36.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -0,377 3) -9,721 4) 0,138

  R 10,000 ANG -0.438 1) -0.007 2) -0.372 3) -9.721 4) 0, 138

  R 5,000 ANG -0,900 1) -0,015 2) -0,367 3) -9,721 4) 0, 138

  R 3,000 ANG -1,560 1) -0,025 2) -0,360 3) -9,721 4) 0,138

  R 2,000 ANG -2,466 1) -0,039 2) -0,352 3) -9,721 4) 0, 138

  R 1.500 ANG -3.477 1) -0.054 2) -0.343 3) -9.721 4) 0, 138

  R 1,000 ANG -5,911 1) -0,088 2) -0,325 3) -9,721 4) 0, 138

  R 0.850 ANG -7.500 1) -0.107 2) -0.316 3) -9.721 4) 0, 138

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (36.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 1,533 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 1.540 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 1,547 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 1,556 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 1,567 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 1,578 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 1,599 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.610 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide-angle end (36.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -0,198 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.189 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,180 3) 0,000 4) 0, 000

  R 3,000 ANG -1,560 1) 0,000 2) -0,167 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,152 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,138 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,109 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.095 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (36.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -0,304 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.291 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,278 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -0,261 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,239 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,217 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,175 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.152 3) 0.000 4) 0.000

  Condition corresponding to the values: yxR / Yxo = 1.05, YaR / YaO = 0.50

Table 13

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the center position (50.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 0.127 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) 0,254 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) 0,422 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) 0,632 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) 0,841 3) 0,000 4) 0,000

* R 1,000 ANG -5,910 1) 0,000 2) 1,261 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.483 3) 0.000 4) 0.000

  Objective image magnification Pk at the median position (50.0 mm) of the first example

  2 R 0.000 ANG 0.000 1) 0.000 2) -0.447 3) -42, 292 4) 0.037

  R 10,000 ANG -0.438 1) -0.007 2) -0.440 3) -42.292 4) 0.037

  R 5,000 ANG -0,901 1) -0,015 2) -0,432 3) -42,292 4) 0,037

  R 3,000 ANG -1,562 1) -0,025 2) -0,422 3) -42,292 4) 0,037

  R 2,000 ANG -2,469 1) -0,040 2) -0,409 3) -42,292 4) 0,037

  R 1.500 ANG -3.480 1) -0.055 2) -0.397 3) -42.292 4) 0.037

  R 1,000 ANG -5.910 1) -0.089 2) -0.372 3) -42.292 4) 0.037

  R 0.850 ANG -7.500 1) -0.109 2) -0.359 3) -42.292 4) 0.037

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 1,966 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 1.982 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) 1,998 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) 2,019 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) 2,045 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) 2,069 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) 2,117 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 2.140 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -0,298 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.282 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) -0,265 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) -0,244 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) -0,219 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) -0,196 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) -0,151 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.129 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the center position (50.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -0,587 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.558 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) -0,530 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) -0,494 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) -0,448 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) -0,406 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) -0,320 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.277 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / Yxo = 1.09, YaR / Yao = 0, 47

Table 14

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (103.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) 0.502 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 0,951 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 1,488 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 2,090 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 2,636 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 3,609 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 4.080 3) 0.000 4) 0.000

  Lens magnification Pk at the telephoto end (103, 0 mm) of the first

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,716 3) 13,060 4) - 0,154

  R 10,000 ANG -0.437 1) -0.007 2) -0.686 3) 13.060 4) -0.154

  R 5,000 ANG -0,900 1) -0,015 2) -0,659 3) 13,060 4) -0,154

  R 3,000 ANG -1,560 1) -0,026 2) -0,627 3) 13,060 4) -0,154

  R 2,000 ANG -2,466 1) -0,040 2) -0,592 3) 13,060 4) -0,154

  R 1,500 ANG -3,477 1) -0,055 2) -0,559 3) 13,060 4) - 0,154 R 1,000 ANG -5,911 1) -0,090 2) -0,501 3) 13,060 4) -0,154

  R 0.850 ANG -7.500 1) -0.112 2) -0.473 3) 13.060 4) -0.154

  Conversion coefficient Yx associated with the direction of the optical axis at the telephoto end (103.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) 1,982 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) 2.152 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 2,298 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 2,465 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 2,643 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 2,795 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 3,044 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 3.155 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (103.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -1,257 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) -1.052 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,895 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -0,742 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,597 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,489 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,329 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.266 3) 0.000 4) 0.000

  2 0 Conversion coefficient Ya associated with the direction of rotation at the telephoto end (103.0 mm) of the first example

  R 0,000 ANG 0,000 1) 0,000 2) -2,492 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) -2.263 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -2,056 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -1,829 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -1,578 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -1,366 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -1,0013) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.840 3) 0.000 4) 0.000

  3 0 Condition corresponding to the values: YxR / Yxo = 1.59, YaR / YaO = 0, 34 As indicated in Tables 12, 13 and 14, for each focal length, the conversion coefficient yx associated with the direction of the The optical axis increases but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. As a result, as these tables indicate, the conversion coefficient y. associated with the rotation, defined as the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the smallest distance under the action of the influence the slope (dx / da) of the focusing cam, in contrast to the embodiment of Japanese Patent Application Laid-Open No. 5-142754. According to Tables 12, 13 and 14, the rate of change from the infinitely focused position to the closest focused position of the conversion coefficient Ya associated with the rotation is x0.50 at the large end. -angle (F = 36.0 mm), x0.47 at the middle position (F = 50.0 mm) and x0.34 at the telephoto end (F = 103.0 mm). When the number N of divisions of the focusing range when changing the conversion coefficient Ya of the first embodiment is calculated with the formula (a) and is compared with that of the embodiment of the Japanese patent application set forth 5-142475, it is noted that the numbers Nw, NM and NT of divisions at the wide-angle end, in the median position and at the telephoto end, respectively, have the following values: embodiment of the request Japanese Patent Application Laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 first embodiment of the invention Nw> 3.8 NM> 4.1 NT> 5, Thus, as indicated by the comparison with the calculated values of the example of Japanese Patent Application Laid-open No. 5-142475, the values are

  remarkably weak in this first embodiment.

  As described above, in the zoom lens of the first embodiment, as the speed of variation, from the position focused to infinity to the closest focused position, the conversion coefficient Ya associated with the rotation becomes lower than that of the example of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient Ya and the correction coefficient y can be

  reduced and the storage capacity can be deleted.

  Tables 15, 16 and 17 show the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 36.0 mm), in

  median position (F = 50.0 mm) and at the telephoto end

  jective (F = 103.0 mm) in the first embodiment.

  In these tables (R) denotes the distance of the object (m), (ANG) designates the amplitude of rotation for the focusing of the position corresponding to infinity on the focusing cam, (r) denotes the coefficient of conversion Ya into rotation, (rs) denotes the conversion coefficient Ka, (bf) denotes the focusing defect amplitude (mm), and (D) denotes the correction coefficient y. Each panel portion has a matrix structure and eight lines in the vertical direction indicated by (POS) represent the positions of the object (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m) and four pairs (R, ANGLE) in a horizontal direction represent the lens arrangements of the set of

focusing lenses.

  More specifically, the position of the focus lens assembly of the first pair in the two upper portions of each of Tables 15, 16 and 17, i.e. in the third and fourth columns, is

  (R, ANGLE) = (0,0; 0,0) and indicates that this position corresponds to

  pond to infinity. Accordingly, the third column (r) of the first table portion represents the value of the conversion coefficient ya rotating when the set of focusing lenses is focused on an object at infinity, and the fourth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is shifted from the focused state to an object at infinity in the focused state on an object at the distance indicated in the second column. Further, the third column (bf) of the second portion represents the focus defocus amplitude ABf with respect to a predetermined image position when the position of the focus lens assembly is infinite, and the object is at the distance indicated in the second column, and the second column (f) the value of the correction coefficient y when the set of focusing lenses is shifted from the focused state to an object at infinity to the focused state on an object at a distance

indicated in the second column.

  Similarly, the position of the focus lens assembly of the fourth pair of the two lower portions of Tables 15, 16 and 17, i.e. the ninth and tenth columns, is (R, ANGLE) = ( 0.85, -7.5) and indicates that this position corresponds to the closest focusing position (R = 0.85 m). As a result, the ninth column (r) of the third part of the table represents the value of the conversion coefficient Ya in rotation when the set of focusing lenses is focused on an object at the smallest distance (R = 0.85 m ), and the tenth column (rs) represents the value of the conversion coefficient Ka when the set of

  focusing lenses is moved from the focus state

  on the object at the smallest distance (R = 0.85 m) in the focused state at the distance indicated on the second column. In addition, the ninth column (bf) of the fourth part of the table represents the focus defocus amplitude ABf with respect to a predetermined image position when the position of the focus lens assembly corresponds to the shortest distance. , and the object is at the distance given by the second column, while the tenth column (P) represents the value of the correction coefficient y when the set of focusing lenses is moved from a focused state to the object at the shortest distance (R = 0.85 m) to a focused state on an object placed at the distance indicated in the

second column.

  As indicated previously, since the rotational conversion coefficient is calculated by Ka = ABf / Aa (where Aa is the rotation amplitude for focusing), and the correction coefficient j is calculated by the relation y = ABf / (1 - Ka / Ya), the value of the conversion coefficient Ka (eighth line, fourth column of the first part of the table: -0.233), when the set of focusing lenses is moved from the focused state to the object to the object. infinity in the object-focused state at the distance (R = 0.85 m) from Table 15 is calculated as Ka = 1.75 / -7.5 = -0.233 by using ABf = 1 , 75 and Aa = - 7.5. On the other hand, the value of the correction coefficient y (eighth row, fourth column of the second table: 7.46) is calculated as g = 7.46 using

  ABf = 1.75, Ka = -0.233 and ya = -0.304.

Table 15

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient IJ: (i) at the wide-angle end (36.0 mm) of the first example f = 36.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,438 5,000 -0,900 3,000 -1,560

POS R rs r rs r rs

  I 0.000 -0.304 0.000 -0.296 -0.288 -0, 277

  2 10,000 -0.299 -0.291 0.000 -0.283 -0, 272

  3 5,000 -0,294 -0,286 -0,278 0,000 -0, 267

  4 3,000 -0,287 -0,279 -0,271 -0,261 0, 000

2,000 -0,278 -0,270 -0,262 -0,252

  6 1,500 -0,268 -0,260 -0,253 -0, 243

  7 1,000 -0,246 -0,239 -0,232 -0, 222

  8 0.850 -0.233 -0.226 -0.219 -0, 211

POS R bf t bf i bf g bf g

  1 0.000 0.00 0.00 -0.13 8.13 -0.26 7.46 -0.43 6.94

  2 10,000 0.13 8.61 0.00 0.00 -0.13 7.23 -0.31 6, 85

  3 5,000 0.26 8.37 0.13 7.72 0.00 0.00 -0.18 6, 84

  4 3,000 0.45 8.09 0.31 7.52 0.18 7.10 0.00 0.00

  5 2,000 0.68 7.91 0.55 7.44 0.41 7.12 0.23 6.85

  6 1,500 0.93 7.80 0.79 7.39 0.65 7.09 0.47 6, 79

  7 1,000 1.45 7.58 1.31 7.23 1.16 6.96 0.97 6, 62

  8 0.850 1.75 7.46 1.60 7.13 1.45 6.86 1.25 6, 52

  (R, ANGLE) = 2,000 -2,466 1,500 -3,477 1,000 -5,911 0,850 -7,500

  POS R rs r rs r rs r rs i 0,000 -0,263 -0,248 -0,219 -0,204

  2 10,000 -0.258 -0.244 -0.216 -0, 200

  3 5,000 -0,254 -0,240 -0,212 -0,196

  4 3,000 -0.247 -2.234 -0.206 -0, 191

  5 2,000 -0,239 0,000 -0,226 -0,199 - 0,184

  6 1,500 -0,230 -0,217 0,000 -0,191 -0,177

  7 1,000 -0,211 -0,199 -0,175 0,000 -0,161

  8,850 -0,119 -0,188 -0,165 -0,152,0,000

POS R bf g bf g bf g bf i

  3 5 1 0.000 -0.65 6.51 -0.86 6.05 -1.30 5.05 -1.53 4.52

  2 10,000 -0.52 6.47 -0.74 6.03 -1.18 5.02 -1.41 4, 50

  3 5,000 -0.40 6,46 -0.62 6.01 -1.06 5.00 -1.30 4, 48

  4 3,000 -0.22 6.43 -0.45 5.98 -0.90 4.96 -1.14 4, 44

  2,000 0.00 0.00 -0.23 5.92 -0.69 4.91 -0.93 4.40

  6 1,500 0.23 6.35 0.00 0.00 -0.47 4.85 -0.71 4.35

  7 1,000 0.73 6.17 0.48 5.68 0.00 0.00 -0.26 4, 23

  8 0.850 1.00 6.06 0.76 5.59 0.26 4.68 0.00 0.00

  Condition corresponding to the values: Ka / yao = 0.77, KaR / YaR = 1.34

Table 16

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient pi: (i) at the median position (50.0 mm) of the first example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,438 5,000 -0,901 3,000 -1,562

POS R rs r rs r rs

  1 0.000 -0.587 0.000 -0.567 -0.548 -0, 522

  2 10,000 -0,578 -0,558 0,000 -0,539 -0,514

  3 5,000 -0,569 -0,549 -0,530 0,000 -0,505

  4 3,000 -0,556 -0,537 -0,518 -0,493 0,000

2,000 -0,538 -0,520 -0,502 -0,478

  6 1,500 -0,520 -0,502 -0,485 -0,461

  7 1,000 -0,480 -0,463 -0,447 -0,425

  8 0.850 -0.456 -0.440 -0.424 -0, 403

POS R bf t bf t bf a bf a

  1 0.000 0.00 0.00 -0.25 15.94 -0.49 15.15 -0.82 14.06

  2 10,000 0.25 16.72 0.00 0.00 -0.25 15.02 -0.58 13.94

  3 5,000 0.51 16.57 0.25 15.74 0.00 0.00 -0.33 13.77

  4 3,000 0.87 16.40 0.60 15.59 0.34 14.82 0.00 0.00

  5 2,000 1.33 16.14 1.06 15.33 0.79 14.55 0.43 13.53

  6 1,500 1,81 15,96 1,53 15,19 1,25 14,45 0.88 13.56

  7 1,000 2.84 15.60 2.53 14.88 2.24 14.19 1.85 13.36

  8 0.850 3.42 15.33 3.41 14.62 2.80 13.94 2.39 13.08

  (R, ANGLE) = 2,000 -2,469 1,500 -3,480 1,000 -5,910 0,850 -7,500

2 5 POS R rs r rs r rs

  1 0.000 -0.490 -0.460 -0.399 -0, 367

  2 10,000 -0.483 -0.452 -0.392 -0, 360

  3 5,000 -0,475 -0,444 -0,385 -0, 354

  4 3,000 -0.463 -0.434 -0.376 -0, 345

  3 0 5 2,000 -0,448 0,000 -0,420 -0,363 -0,333

  6 1,500 -0,433 -0,406 0,000 -0,350 -0, 321

  7 1,000 -0,399 -0,373 -0,320 0,000 -0,293

  8 0.850 -0.378 -0.353 -0.303 -0.277 0, 000

POS R bf f bf t bf f bf f

  I 0.000 -1.21 12.83 -1.60 12.07 -2.36 9.64 -2.75 8.49

  2 10,000 -0.98 12.74 -1.38 12.04 -2.15 9.59 -2.54 8.45

  3 5,000 -0.74 12.65 -1.15 12.03 -1.93 9.53 -2.34 8.40

  4 3,000 -0.42 12.57 -0.83 12.07 -1.63 9.45 -2.05 8.33

  2,000 0.00 0.00 -0.42 12.25 -1.25 9.32 -1.68 8.22

  4 0 6 1,500 0.44 12.84 0.00 0.00 -0.85 9.12 -1.29 9.09

  7 1,000 1.37 12.38 0.91 11.05 0.00 0.00 -0.47 7.89

  8 0.850 1.90 12.08 1.42 10.83 0.48 8.82 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.78, KaR / YaR = 1.32

Table 17

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the telephoto end (103.0 mm) of the first example f = 103.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,437 5,000 -0,900 3,000 -1,560

POS R rs r rs r rs

  1 0.000 -2.491 0.000 -2.285 -2.101 -1, 896

  2 10,000 -2,478 -2,263 0,000 -2,078 -1, 876

  3 5,000 -2,453 -2,237 -2,056 0.000 -1, 857

  4 3,000 -2,423 -2,209 -2,031 -1,829 0,000

2,000 -2,382 -2,168 -1,990 -1,789

  6 1,500 -2,337 -2,124 -1,946 -1, 746

  7 1,000 -2,228 -2,017 -1,842 -1, 647

  8 0.850 -2.157 -1.949 -1.777 -1, 585

POS R bf f bf t bf t bf t

  1 0,000 0.00 0.00 -1.00 101.35 -1.89 86.26 -2.96 80.46

  2 10,000 1.08 206.65 0.00 0.00 -0.96 90.85 -2.11 82.73

  3 5,000 2.21 143.35 1.04 89.82 0.00 0.00 -1.23 81.46

  4 3,000 3.78 137.85 2.48 103.95 1.34 108.77 0.00 0.00

  5 2,000 5.88 133.72 4.40 105.55 3.12 97.61 1.62 73.49

  6 1,500 8,12 130.66 6,46 105.05 5.02 94.01 3.35 74.10

  7 1,000 13.17 124.34 11.04 101.71 9.23 88.89 7.17 72.08

  8 0.850 16.18 120.56 13.77 99.20 11.73 86.25 9.41 70.47

  (R, ANGLE) = 2,000 -2,466 1,500 -3,477 1,000 -5,911 0,850 -7,500

POS R rs r rs r rs

  1 0.000 -1.681 -1.498 -1.196 -1.059

  2 10,000 -1.662 -1.480 -1.180 -1, 044

  3 5,000 -1,643 -1,462 -1,164 -1, 030

  4 3,000 -1,616 -1,436 -1,141 -1, 009

  5 2,000 -1,578 0,000 -1,402 -1.111 - 0.981

  6 1,500 -1,539 -1,366 0,000 -1,078 - 0,950

  7 1,000 -1,446 -1,277 -1,001 0,000 -0,981

  8 0.850 -1.388 -1.223 -0.957 -0.840 0, 000

POS R bf bf a bf t bf t

  I 0.000 -4.15 63.20 -5.21 53.84 -7.07 36.24 -7.94 30.52

  2 10,000 -3.37 63.13 -4.50 53.84 -6.46 36.01 -7.38 30.37

  3 5,000 -2.57 62.02 -3.77 53.52 -5.83 35.70 -6.80 30.17

  4 3,000 -1.46 60.78 -2.75 53.47 -4.96 35.29 -5.99 29.91

  2,000 0.00 0.00 -1.42 54.02 -3.83 34.64 -4.94 29.56

  6 1,500 1.56 63.61 0.00 0.00 -2.62 33.79 -3.82 29.20

  7 1,000 4.98 59.61 3.11 47.73 0.00 0.00 -1.40 28.64

  8 0.850 6.98 58.01 4.92 47.04 1.52 35.10 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.87, KaR / 'YaR = 1.26 As indicated in Tables 15, 16 and 17 above, when a change in the conversion coefficient Ka (rs) (c') that is to say in the fourth column of the first part) for a given disposition of the lenses (for example at infinity) is envisaged, the rate of variation becomes small compared to the Ka change (Tables 6, 7 and 8). ) of the embodiment of Japanese Patent Application Laid-Open No. 5-142475

previously considered.

  More precisely, if one defines the conversion coefficient Ka in rotation by Ka = ABf / Aa and if the amplitude of the focusing defect ABf is the same as in the embodiment of the Japanese patent application laid down 5-142475 for the same lens arrangement, the rotation amplitude Aa for focusing from the first embodiment on the object side to infinity becomes relatively smaller than that on the side of the object. closer to Japanese Patent Application No. 5-142475. In fact, when the ratio of the amplitude of rotation for focusing to the smallest distance (R = 0.85 m) and the focus rotation amplitude to the distance of the object (R = 5.0 m) is calculated from Tables 1 and 10, resulting in 3, 379 / 10.0 = 0.338 in the embodiment of Japanese Patent Application Laid-open No. 5-142475 and -0.9 / -7.5 = 0.120 is obtained in the first embodiment. As described above, when the focusing cam made according to the invention is used, as the rotation amplitude Aa for focusing becomes smaller on the object side at infinity, the conversion coefficient Ka becomes relatively large. side of the object to infinity so that the change of the conversion coefficient Ka in rotation can be reduced compared to

classic system.

  The results of the calculation of the rate of variation of Ka with respect to Ya for the set focused at infinity and the set focused at the nearest point at the wide-angle end (F = 36.0 mm), in the median position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the example of Japanese Patent Application Laid-open No. 5-142475 and in the first example of the invention are as follows. Japanese Patent Application Laid-Open No. 5-142475 At Infinity KaO / YaO Closest KaR / YaR Wide Angle (F = 36.0) 2.75 0.44 Median Position (F = 50.0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 First example Infinity Kao / yao Nearest KaR / YaR Wide-angle (F = 36.0) 0 , 77 1.34 Median position (F = 50.0) 0.78 1.32 Telephoto (F = 103.0) 0.87 1.26 As previously described, according to the invention, as the speed of variation of Ka Compared to Ya is small in comparison to the classical system and as the contribution of the correction term (ABf / g) in Ka = Ya (1 - ABf / L) can be reduced, the value of the correction coefficient y can be set to a significant value with respect to the amplitude of the focusing defect ABf and, simultaneously, the change

  the correction coefficient y can be reduced.

  Consequently, even when a single pair of values of the conversion coefficient Ya and the correction coefficient y is established for a given disposition of the lenses, an error on the conversion coefficient Ka calculated using Ya and y or on the actual driving amplitude Aa of lenses for focusing can

to be eliminated.

  Next, in the example of Japanese Patent Application Laid-open No. 5-142475 and in the first example of the invention, when the lens drive amplitudes during focusing of the focused disposition to the infinity to the object at the smallest distance and when focusing the focused whole at the smallest distance to the object at infinity at the wide-angle end (F = 36.0 mm) ), in the middle position (F = 52.0 mm) and at the telephoto end (F = 103.0 mm) are calculated from Aa = ABf / ya (1 to Bf / g) and when the errors with respect to the actual magnitudes of lens displacement are calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing from the set focused at infinity to the object at the smallest distance takes the value of the object distance (POS-5), and the value of the correction coefficient y when focusing the focused disposition at the nearest point on the object to infinity

  takes the value of the object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% First example Infinity focused state most Nearest near state Focused at infinity Wide-angle (F = 36, 0) -1.4% -0.2% Median position (F = 50.0) -1.4% -0.5% Telephoto -1.5% -0 , 4%

(F = 103.0)

  As previously described, even when a single pair of values of the conversion coefficient γ and the correction coefficient γ is set for a given range of lens arrangement, an error between the conversion coefficient Ka is calculated from Ya and y. and the lens driving amplitude Aa for focusing becomes small compared to the conventional system, and the focusing

  can be performed with greater precision.

  By way of reference, when errors in the drive magnitudes of the focus lenses of the infinity-focused disposition at the distance of the object (R = 10.0 m) and the focus of the focused disposition the closer to the distance of the object (R = 1.0 m) are calculated and compared, the following results are obtained. As the following tables indicate, focus accuracy can be relatively

* Increased regardless of the distance of the object.

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused State to Nearest Condition 10 Lm Focused at 1m Wide Angle (F = 36.0) -6.7% 1.5% Position median (F = 50.0) 3.2% 2.5% Telephoto (F = 103.0) 5.1% 2.4% First example Infinity focused state to Nearest to state lm focused to 1 m Large angle (F = 36.0) -0.7% 1.7% Median position (F = 50.0) 0.3% 1.0% Telephoto (F = 103.0) 0.0% 0.2% Then, we examine if not only a precise automatic focusing but also a so-called "manual" focusing can be realized with the zoom lens of this

first example.

  Table 18 summarizes the amplitude (ANGLE DA) of rotation for focusing during manual focusing using the focusing cam (middle portion of Table 10) of the first example, the amplitude DX (mm). ) of displacement in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the amplitude Bf (mm) of displacement of the image point when the amplitude (DX) of

  displacement in the direction of the optical axis is given.

  The upper part of Table 18 summarizes the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0, 85 m) for the respective states of variation for the focal lengths (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm), and the middle portion gives the values of the amplitude (ANGLE DA) of rotation for focusing necessary to obtain an optimum focused state for the respective photography distances (R = 5.0, 3.0, 2.0, 1.5, 1, 0 and 0.85 m). It should be noted that the rotational amplitudes selected for focusing have values allowing the removal of any displacement of the image point at the wide-angle end and at the telephoto end. The lower part of the table gives the magnitudes of displacement (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the focusing amplitude (ANGLE DA) for the photography distances (R = 5.0 , 3.0, 2.0, 1.5, 1.0 and 0.85 m) at the respective states of variation for the focal lengths (F = 36, 0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm). In the lower part of the table, (F) designates the focal length (in mm) of the whole system, (R) la

  distance of photography (m), and (DX) the range of motion

  cement (mm) in the direction of the optical axis of each of the first, second, third and fourth sets of lenses, progressively from the right. It should be noted that the amplitude of displacement in the direction of the optical axis towards the side of the object is represented by a

positive value.

Table 18

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the first example 0.85 m 1.00 m 1.50 m 2.00 m 3.00 m 5.00 m 36.000 Bf 0.000 0, 000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,000 0.001 0.001 0.001 0.001, 000 Bf 0.000 0.001 0, 002 0.002 0.002 0.001, 000 Bf 0.000 0.000 0.000 -0.002 -0.004 -0.002, 000 Bf 0.000 0.000 -0.005 -0, 003 -0,001 -0,001 103,000 Bf 0,000 0,000 0, 000 0,000 0,000 0,000

  ANGLE DA -7,500 -5,911 -3,477 -2,466 -1,560 -0,900

  F 36,000 DX 0,000 1,037 0,000 0,000 R 0,85 m F 50,000 DX 0,000 1,483 0,000 0,000 R 0,85 m F 60,000 DX 0,000 1,872 0,000 0,000 R 0.85 m F 70,000 DX 0,000 2,311 0,000 0,000 R 0.85 m F 85,000 DX 0.000 3,049 0,000 0,000 R 0,85 m F 103,000 DX 0,000 4,080 0,000 0,000 R 0,85 m F 36,000 DX 0,000 0,875 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,261 0,000 0,000 R 1,00 m F 60,000 DX 0,000 1,600 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,990 0,000 0,000 R 1,00 m F 85,000 DX 0,000 2,656 0,000 0,000 R 1,00 m F 103,000 DX 0,000 3,609 0,000 0,000 R 1,00 m F 36,000 DX 0,000 0,576 0,000 0.000 R 1.50 m F 50.000 DX 0.000 0.841 0.000 0.000 R 1.50 m F 60.000 DX 0.000 1.081 0.000 0.000 R 1.50 m F 70.000 DX 0.000 1.365 0.000 0.000 R 1.50 m F 85.000 DX 0.000 1.871 0.000 0.000 R 1.50 m F 103,000 DX 0,000 2,636 0,000 0,000 R 1,50 m F 36,000 DX 0,000 0,429 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,631 0,000 0,000 R 2,00 m F 60,000 DX 0,000 0,817 0,000 0,000 R 2 00 m F 70,000 DX 0,000 1,042 0,000 0,000 R 2,00 m F 85,00 0 DX 0,000 1,449 0,000 0,000 R 2,00 m F 103,000 DX 0,000 2,090 0,000 0,000 R 2,00 m F 36,000 DX 0,000 0,285 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,422 0,000 0,000 R 3,00 m F 60,000 DX 0.000 0.549 0.000 0.000 R 3.00 m F 70.000 DX 0.000 0.708 0.000 0.000 R 3.00 m F 85.000 DX 0.000 1.001 0.000 0.000 R 3.00 m F 103.000 DX 0.000 1.488 0.000 0.000 R 3.00 m F 36.000 DX 0.000 0.170 0,000 0,000 R 5,00 m F 50,000 DX 0, 000 0,253 0,000 0,000 R 5,00 m F 60,000 DX 0,000 0,332 0, 000 0,000 R 5,00 m F 70,000 DX 0,000 0,432 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,620 0,000 0,000 R 5,00 m F 103,000 DX 0,000 0,951 0,000 0,000 R 5,00 m As shown in Table 18, a so-called "manual" focus can be achieved because the magnitudes of displacement of the image point for the focal lengths respective distances and respective photography distances are very small and enter the depth of field regardless of the state of variation of the focal length

and the distance of photography.

  Second Embodiment The second embodiment or example relates to a zoom lens having a four-array arrangement which are sets of positive, negative, positive, and negative type lenses that provide focus with a second set of lenses. Negative type lenses. In this zoom lens, the ratio of the rotational amplitudes (aF / az) of the focus rotation amplitude of the infinitely focused position to the focused position at the nearest location (R = 0.5 m) and the range of variation in focal length variation from the wide-angle end (F = 29.0 mm) to the telephoto end (F = 102.0 mm)

  is set to a value equal to -0.95.

  Table 19 which follows contains various paraxial data of the optical system and data determining the configuration of a focusing cam in the second

example.

  The upper part of table 19 indicates the focal length and range data of the main points of the respective lens assemblies of the optical system corresponding to the second example for six states of focal length variation (focal lengths F = 29.0, 35, 0, 50.0,

0, 85.0 and 102.0 mm).

  The middle portion of Table 19 shows the spline sampling data when the configuration of a focus cam of the second lens set of the second embodiment, used for focusing, is represented by a spline function associated with the spline function. angle a rotation of a rotary barrel and the amplitude x of displacement in the direction of the optical axis. In addition, the lower part of Table 19 gives a summary of the positions of focus at infinity (positions

  corresponding to infinity) for the focal lengths

  (F = 29.0, 35.0, 50.0, 70.0, 85.0 and 102.0 mm) and the focusing amplitudes (rotation amplitudes for focusing) for focusing at the respective photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) using the focusing cam of the second example or embodiment. In the lower part of Table 19, as the amplitude of rotation for the distance variation

  focal length of the wide-angle end (F = 29.0 mm) at the end

  telephoto range (F = 102.0 mm) is set to a value of 10.0, and the rotation amplitude for focusing the infinity focus position to the focused position at the nearest R = 0.5 m) is set at -9.5, the rotational amplitude ratio (aF / az) of the rotation amplitude for the focus to the rotation amplitude for the focal length variation in the second mode of

achievement is equal to -0.95.

Table 19

  Second example f = 29.0 to 102.0 (ratio of amplitudes of rotation: aF / az = -0.95) Focal distances and intervals of the principal points of the objectives of the second example

  F 29,0000 35,0000 50,0000 70,0000 85,0000 102,0000

  F1 85.5479 D1 6.4919 11.0833 19.2490 26.4661 30.4661 34.1273

  F2 -17.6992 D2 31.4311 28.0686 22.5272 18.0704 15.7280 13.6136

  F3 25.9878 D3 4.6185 -1.8297 4.161 10.3911 14.1536 17.6639

  F4 -251.0549 D4 69.6355 69.6334 69.6324 69.6422 69.6550 69.6692

  Focusing cam shape (split interpolated point) corresponding to the second example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.6220 0.0000 0.0000

  2 -10,0000 0.0000 1.5277 0.0000 0.0000

  3 -9.5000 0.0000 1.4768 0.0000 0.0000

  4 -5.7095 0.0000 1.0205 0.0000 0, 0000

-3,5854 0.0000 0.6980 0.0000 0.0000

  6 -1.6038 0.0000 0.3402 0.0000 0.0000

  7 -1.0337 0.0000 0.2250 0.0000 0.0000

  8 -0.6043 0.0000 0.1391 0.0000 0.0000

  2 0 9 0.0000 0.0000 0.0000 0, 0000 0.0000

0.5000 0.0000 -0.11775 0.0000 0.0000

  1 1 4.2905 0.0000 -1.2397 0.0000 0.0000

  12 6.4146 0.0000 -2.1304 0.0000 0.0000

  13 8.3962 0.0000 -3.2517 0.0000 0.0000

  2 5 14 8.9663 0.0000 -3.6627 0, 0000 0.0000

9,3957 0.0000 -4.0013 0.0000 0.0000

  16 10.0000 0.0000 -4.5381 0.0000 0.0000

  17 11.0000 0.0000 -5.5850 0.0000 0.0000

  Rotation amplitude for focal length change and focus rotation amplitude of the second example (ratio of rotation amplitudes aF / az = -0.95) Focal length Positon corresponding Distance of amplitude of rotation to infinity photography for focus 29.0 mm 0.0000 5.00 m -0.604, 0 mm 1.6924 3.00 m -1.034 50.0 mm 4.7321 2.00 m -1.604, 0 mm 7.3904 1.00 m - 3.585, 0 mm 8.7927 0.70 m -5.710 102.0 mm 10.00.00 0.50 m -9.500 Table 20 indicates in the following the data representing the numerical values of the cams of the set of focusing lenses of the second example, the data being calculated by interpolation using the spline function from the sample data of the cam of

  focusing shown in the middle part of Table 19.

  It should be noted that the meanings of the respective symbols

  of Table 20 are the same as in the first example.

Table 20

  Cam numerical values for focusing objective of the second example Focus cam digital values Focal distance dimming compensation digital cam values

ANGLE (2) F ANGLE (2) F

-9.5000 1.4768 0.0000

-9.0000 1.4238 0.0000

-8.5000 1.3688 0.0000

-8.0000 1.3118 0.0000

-7.5000 1.2526 0.0000

-7.0000 1.1900 0.0000

-6,5000 1,1270 0,0000

-6.0000 1.0604 0.0000

-5,5000 0.9911 0.0000

-5.0000 0.9190 0.0000

-4.5000 0.8438 0.0000

4.0000 0.7654 0.0000

-3.5000 0.6838 0.0000

-3.0000 0.5986 0.0000

-2,5000 0,5097 0,0000

-2.0000 0.4168 0.0000

-1.5000 0.3197 0.0000

-1.0000 0.2179 0.0000

-0.5000 0.115 0.0000

  0.0000 0.0000 29.0000 0.0000 0.0000 29.0000

  0.5000 -0.1175 30.6387 0.5000 -0.1124 30.6387

  1.0000 -0.2407 32.3858 1.0000 -0.1690 32.3858

  1,5000 -0,3702 34,2491 1,5000 -0,1691 34,2491

  2.0000 -0.5066 36.2424 2.0000 -0.1121 36.2424

  2.5000 -0.6507 38.3792 2.5000 0.0028 38, 3792

  3,0000 -0,8031 40,6724 3,0000 0,1767 40,6724

  3,5000 -0,9645 43,1349 3,5000 0,4104 43,1349

  4.0000 -1.1356 45.7783 4.0000 0.7043 45.7783

  4.5000 -1.3171 48.6138 4.5000 1.0581 48.6138

  5,0000 -1,5100 51,6599 5,0000 1,4719 51,6599

  , 5000 -1.7158 54.9436 5.5000 1.9466 54.9436

  6.0000 -1.9359 58.4921 6.0000 2.4825 58.4921

  6,5000 -2,1719 62,3292 6,5000 3,0791 62,3292

  7.0000 -2.4256 66.4882 7.0000 3.7364 66.4882

  7.5000 -2.7004 71.0327 7.5000 4.4575 71.0327

  8.0000 -2.9999 76.0245 8.0000 5.2441 76.0245

  8.5000 -3.3276 81.5206 8.5000 6.0952 81.5206

  9.0000 -3.6881 87.5991 9.0000 7.0101 87.5991

  9.5000 -4.0885 94.3772 9.5000 7.9903 94.3772

  10,0000 4,5381 102,000 10,0000 9,0367 102, 0000

  The left side of table 20 gives the numerical values of the focus cam of the second example and the right part those of the zoom compensation cam of this example. A value obtained by synthesis of the amplitudes (2) of displacement in the direction of the optical axis of the numerical values of the focusing cam and the zoom compensation cam, in the range between the amplitude of rotation (ANGLE = 0,0) and the amplitude of rotation (ANGLE = 10,0), coincides with the place of displacement of the second set of lenses calculated with the

  Paraxial data from the top of Table 19.

  The following tables 21, 22 and 23 give the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Px of the respective sets of images. lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  Ya conversion associated with rotation at the far end

  angle (F = 29.0 mm), at the middle position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the second example. The provisions of the respective tables and the meanings of the symbols are the same as in the

first example.

Table 21

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (29.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) 0.067 3) 0.000 4) 0.000

  R 5,000 ANG -0,604 1) 0,000 2) 0,134 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 0,225 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 0,340 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 0,698 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) 1.021 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 1.477 3) 0.000 4) 0.000

  Nk image magnification of lenses at the wide-angle end (29.0 mm) of the second example

  R 0,000 ANG 0.000 1) 0.000 2) -0.288 3) -0.920 4) 1, 277

  R 10,000 ANG -0,296 1) -0,009 2) -0,285 3) -0,920 4) 1, 277

  R 5,000 ANG -0.604 1) -0.018 2) -0.281 3) -0.920 4) 1, 277

  R 3,000 ANG -1,034 1) -0,030 2) -0,276 3) -0,920 4) 1, 277

  R 2,000 ANG -1,604 1) -0,047 2) -0,269 3) -0,920 4) 1, 277

  R 1,000 ANG -3,585 1) -0,105 2) -0,249 3) -0,920 4) 1, 277

  R 0.700 ANG -5.709 1) -0.167 2) -0.231 3) -0.920 4) 1, 277

  R 0.500 ANG -9.500 1) -0.275 2) -0.205 3) -0.920 4) 1, 277

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (29.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 1,266 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 1,269 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 1,272 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 1,276 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 1,295 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) 1.307 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 1.323 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide-angle end (29.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,229 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) -0,222 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) -0,216 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) -0,207 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,197 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,166 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) -0.139 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.104 3) 0.000 4) 0.000

  Coefficient of conversion Ya associated with the direction of rotation at the wide-angle end (29.0 mm) of the

second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,290 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.282 3) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -0.274 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -0,265 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,252 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,214 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) -0.182 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.138 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / YxO = 1.04, YaR / yao = 0.48

Table 22

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 0,112 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 0,224 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) 0,373 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) 0,561 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) 1,126 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) 1.618 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 2.290 3) 0.000 4) 0.000

  Objective image magnification Pk at the median position (50.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,364 3) -1,256 4) 1,277

  R 10,000 ANG -0,296 1) -0,009 2) -0,358 3) -1,256 4) 1,277

  R 5,000 ANG -0,604 1) -0,018 2) -0,352 3) -1,256 4) 1,277

  R 3,000 ANG -1,032 1) -0,031 2) -0,343 3) -1,256 4) 1,277

  R 2,000 ANG -1,601 1) -0,048 2) -0,333 3) -1,256 4) 1,277

  R 1,000 ANG -3,581 1) -0,107 2) -0,301 3) -1,256 4) 1,277

  R 0.700 ANG -5.707 1) -0.171 2) -0.273 3) -1.256 4) 1.277

  R 0.500 ANG -9.500 1) -0.286 2) -0.235 3) -1.256 4) 1.277

  Coefficient of conversion Yx associated with the direction of the optical axis at the median position (50.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 2,234 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 2,246 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 2,257 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) 2,272 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) 2,291 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) 2,343 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) 2.384 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 2.434 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,385 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) -0,371 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) -0,358 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) -0,340 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) -0,318 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) -0,256 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) -0.209 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.150 3) 0.000 4) 0.000

  Coefficient of conversion Ya associated with the direction of rotation at the middle position (50.0 mm) of the

second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,860 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.833 3) 0.000 4) 0.000

  R 5,000 ANG -0,604 1) 0,000 2) -0,808 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) -0,773 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) -0,729 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) -0,601 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) -0.497 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.365 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / YxO = 1.09, YaR / yao = 0.42

Table 23

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (102.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 0,273 3) 0,000 4) 0,000

  R 5,000 ANG -0.604 1) 0.000 2) 0.537 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 2,408 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) 3.298 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 4.421 3) 0.000 4) 0.000

  Nk image magnification of lenses at the telephoto end (102.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,525 3) -1,778 4) 1, 278

  R 10,000 ANG -0,296 1) -0,009 2) -0,509 3) -1,778 4) 1, 278

  R 5,000 ANG -0.604 1) -0.018 2) -0.495 3) -1.778 4) 1, 278

  R 3,000 ANG -1,034 1) -0,031 2) -0,475 3) -1,778 4) 1, 278

  R 2,000 ANG -1,604 1) -0,048 2) -0,452 3) -1,778 4) 1, 278

  R 1,000 ANG -3,585 1) -0,110 2) -0,389 3) -1,778 4) 1, 278

  R 0.700 ANG -5.710 1) -0.178 2) -0.339 3) -1.778 4) 1, 278

  R 0.500 ANG -9.500 1) -0.306 2) -0.275 3) -1.778 4) 1, 278

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (102.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) 3,739 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 3,821 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 3,898 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 3,994 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 4,104 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 4,380 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) 4.569 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 4.770 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (102.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -0,959 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.887 3) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -0.826 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -0,753 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,673 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,483 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) -0.365 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.241 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (102.0 mm) of the second example

  R 0,000 ANG 0,000 1) 0,000 2) -3,586 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -3.3913) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -3.219 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -3,009 3) 0,000 4) 0,000

* R 2,000 ANG -1,604 1) 0,000 2) -2,7613) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -2,115 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) -1.666 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -1.148 3) 0.000 4) 0.000

  3 0 Condition corresponding to the values: YxR / YxO = 1.28, YaRlYao = 0, 32 As indicated in Tables 21, 22 and 23, for each focal length, the conversion coefficient yx associated with the direction of the axis optical increases but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. Consequently, as can be noted from these tables, the conversion coefficient Ya associated with the rotation, this coefficient being the product of the conversion coefficient yx by the slope (dx / da) of the focusing cam, decreases when the distance of photography approaches the smallest distance under the action of the slope (dx / da) of the focusing cam. In Tables 21, 22 and 23, the rate of variation, from the position focussed at infinity to the position focused at the nearest location, of the conversion coefficient Ya associated with the rotation is x0.48. wide-angle end (F = 29.0 mm), x0.42 at the middle position (F = 50.0 mm) and x0.32 at the telephoto end (F = 102.0 mm). When the number of divisions of the focusing range upon a change in the conversion coefficient Ya of the second example is calculated with the formula (a) and is compared with the example of the Japanese patent application laid out to the public inspection 5-142475, the division numbers Nw, NM and NT at the wide-angle end, in the median position and at the telephoto end respectively have the following values: example of the Japanese patent application placed under inspection Public No. 5-142475

NW> 9.3 NM> 10.1 NT> 8.1

second example

  Nw> 4.1 NM> 4.7 NT> 6.2 Therefore, as indicated in the above comparison, although this example gives a greater focal length variation ratio than the example of the patent application submitted to Public Inspection No. 5-142475, the

  The values of the division numbers are small.

  As previously described, in the second example also, since the speed of variation of the conversion coefficient associated with the rotation is lower than that of the conventional system, the value of the number N of divisions is small, the number of data of the conversion coefficient ya and the correction coefficient y can be reduced, and the

  storage capacity can also be deleted.

  Tables 24, 25 and 26 give the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 29.0 mm), in the median position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the second example. The provisions of the tables and the symbols are the same as in the first example. The position of the focusing lenses of the first pair in both parts

  of each of Tables 24, 25 and 26, that is,

  say in the third and fourth column is (R, ANGLE) = (0,0; 0,0), and indicates that this position corresponds to infinity. Similarly, the position in the fourth pair of the two lower portions of each of Tables 24, 25 and 26, i.e. in the ninth and tenth columns, is (R, ANGLE) = (0.5; -9.5) and indicates that the position corresponds to the focus at the lowest

distance (R = 0.5 m).

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  Z & L Ln O Ei ~ - <nc, 1O00C (z zo CDC) Ci) <(U 8 C - oooooooooooooooooooooooooooo The results of the calculation of the rate of variation of Ka as a function of Ya for the set focused at infinity and at the most convenient location. near the wide-angle end, in the middle position and at the telephoto end of the example of Japanese Patent Application Laid-open No. 5-142475 and in the second example

of the invention are as follows.

  Example of Japanese Patent Application Laid-Open No. 5142475 At Infinity Ka / yao Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43

Second example

  At infinity Kao / Yao Nearest KaR / YaR Wide-angle (F = 29.0) 0.75 1.36 Median position (F = 50.0) 0.78 1.33 Telephoto (F = 102, 0) 0.94 1.23 As previously described, in the second example also, as the rate of variation of Ka with respect to ya is small compared to the conventional system and the contribution of the correction term (ABf / g) in Ka = Ya (1 - ABf / g) can be reduced, the error of the conversion coefficient Ka calculated with Ya and y or the actual displacement amplitude Aa for focusing can be eliminated when a single pair of the values of the coefficient of Ya conversion and correction coefficient is fixed for a given range of lens arrangement (by

  example the beach focused to infinity).

  Next, in the example of Japanese Patent Application Laid-Open No. 5-142475 and the second example of the invention, when the lens driving amplitudes during focusing of the focused assembly to the infinity to the object at the smallest distance and when focusing the focused assembly at the smallest distance to the object at infinity at the wide-angle end, in the middle position and at the telephoto end are calculated from Aa = ABf / Ya (1 - ABf / g), and the errors derived from the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the set focused at infinity to the focused object at the shortest distance takes the value at the object distance (POS-5), and the value the correction coefficient y when focusing for the focused set at the smallest distance to the object at infinity

  takes the value at object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6%

Second example

  Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 29.0) -1.3% -0.2% Midpoint (F = 50.0) -3.4% -0 , 1% Telephoto (F = 102.0) -1.2% -0.3% As previously described, in the second embodiment also, even when only a pair of values of the conversion coefficient Ya and the coefficient of correction is established for a given range of the set, an error between the conversion coefficient Ka calculated from Ya and y and the driving amplitude Aa of the lens for focusing becomes low compared to that of the system. conventional, and focusing can be performed with higher precision. Table 27 indicates the amplitude of rotation (ANGLE DA) for the manual focusing with the aid of the focusing cam (middle of the table of FIG. 19) of the second example, the amplitude DX (mm) of displacement in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point for a given value of the displacement amplitude (DX) in the direction of the optical axis.

  It should be noted that the table layout and the symbols are the same as in the first example. The upper portion of Table 27 indicates the range of motion (Bf) of the image point corresponding to the photography distances (A = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m ) to the respective states of variation for the focal lengths (F = 29.0, 35.0, 50.0, 70.0, 85.0 and 102.0 mm), and the middle portion indicates the amplitude values of focusing (ANGLE DA) necessary to obtain an optimal state focused for the respective distances of photography. The lower part gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the focusing amplitude (ANGLE DA) with the

  focal lengths and respective photographing distances.

  Table 27 Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the second example 0,50m 0,70 m 1,00 m 2,00 m 3,00 m 5,00 m 29,000 Bf 0,000 0,000 0,000 0,000 0,000 0,000 35,000 Bf 0,000 -0,001 -0,003 -0,002 -0,001 -0,001,000 Bf 0,000 -0,003 0.001 0.005 0.004 0.002, 000 Bf 0.000 -0.003 0.003 0.000 -0.001 -0.001 102.000 Bf 0.000 0.000 0.000 0, 000 0.000 0.000

  ANGLE DA -9,500 -5,710 -3,585 -1,604 -1,034 -0,604

  F 29,000 DX 0,000 1,477 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,711 0,000 0,000 R 0,50 m F 50,000 DX 0,000 2,290 0,000 0,000 R 0,50 m F 70,000 DX 0,000 3,076 0,000 0,000 R 0 50 m F 85,000 DX 0, 000 3,690 0,000 0,000 R 0,50 m F 102,000 DX 0,000 4, 421 0,000 0,000 R 0,50 m F 29,000 DX 0,000 1,021 0,000 0,000 R 0,70 m F 35,000 DX 0,000 1,190 0,000 0,000 R 0.70 m F 50,000 DX 0,000 1,618 0,000 0,000 R 0,70 m F 70,000 DX 0,000 2,219 0,000 0,000 R 0,70 m F 85,000 DX 0,000 2,705 0,000 0,000 R 0, 70 m F 102,000 DX 0,000 3,298 0,000 0,000 R 0, 70 m F 29,000 DX 0,000 0,698 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,818 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,127 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,571 0,000 0,000 R 1 00 m F 85,000 DX 0,000 1,941 0,000 0,000 R 1,00 m F 102,000 DX 0,000 2,408 0,000 0,000 R 1,00 m F 29,000 DX 0,000 0,340 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,401 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,562 0,000 0,000 R 2,00 m F 70,000 DX 0,000 0,798 0,000 0,000 R 2,00 m F 85,000 DX 0,000 1,007 0,000 0,000 R 2,00 m F 102,000 DX 0,000 1,281 0,000 0,000 R 2,00 m F 29,000 DX 0,000 0,225 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,266 0,000 0,000 R 3,00 m F 50,000 DX 0.000 0.374 0.000 0.000 R 3.00 m F 70.000 DX 0.000 0.536 0.000 0.000 R 3.00 m F 85.000 DX 0.000 0.682 0.000 0.000 R 3.00 m F 102.000 DX 0.000 0.875 0.000 0.000 R 3.00 m F 29,000 DX 0.000 0,134 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,159 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,224 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,324 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,414 0,000 0.000 R 5.00 m F 102.000 DX 0.000 0.537 0.000 0.000 R 5.00 m As shown in Table 27, in the zoom lens of the second embodiment, the so-called "manual" focusing can be achieved because the amplitudes of displacement of the image point at the respective focal distances and photograph distances are very small and enter the depth of field regardless of the state of variation

  focal length and photography distance.

  Third Embodiment A zoom lens according to the third embodiment or third example is an objective that comprises a group of four sets, i.e. positive, negative, positive and negative lens sets, with focus. performed by a second group of negative type lenses, as in the second example. In this zoom lens, the ratio (aF / az) of the focusing rotation amplitudes of the position focused at infinity to the position focused at the smallest distance (R = 0.5 m) and the rotation amplitude focal length variation of the wide-angle end (F = 29.0 mm) at the end of

  telephoto (F = 102.0 mm) is set to -0.75.

  Table 28 shows various paraxial data of the optical system and data allowing the delineation of the configuration of a focusing cam according to the

third example.

  The upper portion of Table 28 indicates the focal lengths and interval data of the major points of the respective lens assemblies of the optical system of the third example. As a result, these results are the same as various paraxial data (part

  table 19) of the second example.

  The middle portion of Table 28 shows the spline sampling data when the configuration of a focus cam of the second lens set of the third example is represented as a spline function associated with the rotation angle α. a rotary barrel and amplitude x of displacement in the direction

of the optical axis.

  In addition, the lower part of Table 28 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 29.0, 35.0, 50.0, 70.0, 85.0 and 102.0 mm) and the rotational amplitudes (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) with the focusing cam of the third embodiment. In the lower part of Table 28, as the rotation amplitude of the focal length variation of the wide-angle end (F = 29.0 mm) at the telephoto end (F = 102.0 mm) is equal to 10.0 and the focus rotation amplitude of the position focused at infinity at the position focused at the nearest point (R = 0.5 m) is set to a value of -7.5, the ratio (aF / az) of the focus rotation amplitude to the focal length variation rotation amplitude of the

  third example is -0.75.

Table 28

  Third example f = 29.0 to 102.0 (ratio of amplitudes of rotation: aF / az = -0.75) Focal distances and intervals of the main points of the objectives of the third example

  F 29,0000 35,0000 50,0000 70,0000 85,0000 102,0000

  F1 85.5479 D1 6.4919 11.0833 19.2490 26.4661 30.4661 34.1273

  F2 -17.6992 D2 31.4311 28.0686 22.5272 18.0704 15.7280 13, 6136

  F3 25.9878 D3 4.6185 -1.8297 4.161 10.3911 14.1536 17.6639

  F4 -251.0549 D4 69.6355 69.6334 69.6324 69.6422 69.6550 69, 6692

  Focusing cam shape (spline interpolated point) corresponding to the third example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.9300 0.0000 0.0000

  2 -10.0000 0.0000 1.8106 0.0000 0.0000

  3 -7.5000 0.0000 1.4768 0.0000 0.0000

  4 4.6857 0.0000 1.0205 0.0000 0.0000

-3.0036 0.0000 0.6980 0.0000 0.0000

  6 -1.3690 0.0000 0.3402 0.0000 0.0000

  7 -0.8867 0.0000 0.2250 0.0000 0.0000

  8 -0.5202 0.0000 0.1391 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,5000 0.0000 -0.7468 0.0000 0.0000

  11 5.3143 0.0000 -1.8691 0.0000 0.0000

  12 6.9964 0.0000 -2.7598 0.0000 0.0000

  13 8.6310 0.0000 -3.8865 0.0000 0.0000

  14 9,1133 0.0000 4.2920 0.0000 0.0000

9,4798 0.0000 4.6307 0.0000 0.0000

  16 10.0000 0.0000 -5.1675 0.0000 0.0000

  17 11.0000 0.0000 -6.3900 0.0000 0.0000

  Rotation amplitude for focal length change and rotation amplitude for focussing the third example (ratio of rotation amplitudes: aF / az = -0.75) Focal distance Corresponding position Distance of rotation amplitude at infinity photography for focusing 29.0 mm 0.0000 5.00 m -0.520, 0 mm 1.7766 3.00 m -0.887, 0 mm 4.8854 2.00 m -1.369, 0 mm 7, 5076 1.00 m -3.004, 0 mm 8.8596 0.70 m -4.686 102.0 mm 10.00 0.00 0.50 m -7.500 Table 29 shows the numerical value data of the cams of the focus lens assembly of the third example, the data being calculated by interpolation with a spline function from the focus cam sample data shown in the middle portion of Table 28. It should be noted that the meanings of the respective symbols of the

  Table 29 are the same as in the first example.

Table 29

  Digital Cam Values for Focusing Lens of the Third Example Focusing Cam Numerals Focal Length Compensation Cam Numerical Values

ANGLE (2) F ANGLE (2) F

-7.5000 1.4768 0.0000

-7.0000 1.4025 0.0000

-6.5000 1.3254 0.0000

-6.0000 1.2455 0.0000

-5,5000 1,1625 0,0000

-5.0000 to 1.0763 0.0000

-4.5000 0.9869 0.0000

-4.0000 0.8941 0.0000

-3,5000 0.7976 0.0000

-3.0000 0.6972 0.0000

-2.5000 0.5928 0.0000

-2.0000 0.4840 0.0000

-1.5000 0.3707 0.0000

-1.0000 0.2525 0.0000

-0.5000 0.1290 0.0000

  0.0000 0.0000 29.0000 0.0000 0.0000 29.0000

  0.5000 -0.1351 30.5457 0.5000 -0.0835 30.5457

  1.0000 -0.2767 32.1978 1.0000 -0.11165 32.1978

  1.5000 -0.4256 33.9669 1.5000 -0.0978 33.9669

  2.0000 -0.5821 35.8637 2.0000 -0.0258 35, 8637

  2.5000 -0.7468 37.8978 2.5000 0.1010 37.8978

  3.0000 -0.9204 40.0812 3.0000 0.2839 40.0812

  3.5000 -1.1039 42.4338 3.5000 0.5247 42.4338

  4.0000 -1.2982 44.9759 4.0000 0.8253 44.9759

  4,5000 -1,5046 47,7262 4,5000 1,1877 47, 7262

  , 0000 -1.7240 50.7032 5.0000 1.6131 50.7032

  , 5000 -1.9575 53.9230 5.5000 2.1019 53.9230

  6,0000 -2,2068 57,4129 6,0000 2,6552 57, 4129

  6.5000 -2.4742 61.2163 6.5000 3.2753 61.2163

  7.0000 -2.7619 65.3719 7.0000 3.9637 65, 3719

  7.5000 -3.0729 69.9276 7.5000 4.7214 69.9276

  8,0000 -3,4116 74,9664 8,0000 5,5532 74, 9664

  8,5000 -3,7831 80,5728 8,5000 6,4617 80, 5728

  9.0000 -4.1929 86.8316 9.0000 7.4465 86, 8316

  9,5000 -4,6502 93,9043 9,5000 8,5131 93, 9043

  , 0000 -5,1675 102,0000 10,0000 9,6661 102,0000

  The left-hand portion of Table 29 shows the numerical value data of the focus cam of the third example, and the right-hand portion of Table 29 shows the numerical value data of the zoom compensation cam of this embodiment. A value obtained by synthesis of the magnitudes (2) of displacement in the direction of the optical axis of the data of the focusing cam and the data of the zoom compensation cam, in the range between the amplitude of rotation (ANGLE = 0.0) to the amplitude of rotation (ANGLE = 10.0), coincides with the place of displacement of the second set of lenses calculated using the paraxial data of the upper part of the

table 28.

  Tables 30, 31 and 32 which follow indicate the amplitude DX (mm) of displacement for the focusing, in the direction of the optical axis, of the set of focusing lenses, the magnifications Px of image formation of the images. respective sets of lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end (F = 29.0 mm), at the center position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the third example. As various paraxial data are the same as in the second example, in each of the tables 30, 31 and 32, the displacement amplitude DX (mm) in the direction of the optical axis in the first part, the formation magnitudes Px of images of the respective sets of lenses of the second part and the conversion coefficient yx associated with the direction of the optical axis of the set of focusing lenses of the third part of the table are the same as in the second mode of production. On the other hand, although the values of the slope (dx / da) of the focusing cam in the fourth table are large compared to the second embodiment, their rate of variation becomes small in return. Consequently, although the values of the conversion coefficient Ya associated with the rotation in the fifth part of the table are

  large, the speed of variation becomes low.

Table 30

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (29.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 0,067 3) 0,000 4) 0,000

  R 5,000 ANG -0,520 1) 0,000 2) 0,134 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) 0,225 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) 0,340 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) 0,698 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) 1.021 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) 1.477 3) 0.000 4) 0.000

  3k image magnification of lenses at the wide-angle end (29.0 mm) of the third example

  R 0,000 ANG 0.000 1) 0.000 2) -0.288 3) -0.920 4) 1, 277

  R 10,000 ANG -0,256 1) -0,009 2) -0,285 3) -0,920 4) 1, 277

  R 5,000 ANG -0,520 1) -0,018 2) -0,281 3) -0,920 4) 1, 277

  R 3,000 ANG -0,887 1) -0,030 2) -0,276 3) -0,920 4) 1, 277

  R 2,000 ANG -1,369 1) -0,047 2) -0,269 3) -0,920 4) 1, 277

  R 1,000 ANG -3,004 1) -0,105 2) -0,249 3) -0,920 4) 1, 277

  R 0.700 ANG -4.686 1) -0.167 2) -0.231 3) -0.920 4) 1, 277

  R 0.500 ANG -7.500 1) -0.275 2) -0.205 3) -0.920 4) 1, 277

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (29.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 1,266 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 1,269 3) 0,000 4) 0,000

  R 5,000 ANG -0,520 1) 0,000 2) 1,272 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) 1,276 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) 1,295 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) 1.307 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) 1.323 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide-angle end (29.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -0,264 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,258 3) 0,000 4) 0,000

  R 5,000 ANG -0,520 1) 0,000 2) -0,252 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) -0,244 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) -0,234 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) -0,205 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) -0.180 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) -0.146 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (29.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -0,334 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,327 3) 0,000 4) 0,000

  R 5,000 ANG -0,520 1) 0,000 2) -0,320 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) -0,311 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) -0,300 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) -0,265 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) -0.235 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) -0.193 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.04, YaR / Yao = 0.58

Table 31

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the middle position (50.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,255 1) 0,000 2) 0,112 3) 0,000 4) 0,000

  R 5,000 ANG -0,518 1) 0,000 2) 0,224 3) 0,000 4) 0,000

  R 3,000 ANG -0,883 1) 0,000 2) 0,373 3) 0,000 4) 0,000

  R 2,000 ANG -1,364 1) 0,000 2) 0,561 3) 0,000 4) 0,000

  R 1,000 ANG -2,997 1) 0,000 2) 1,126 3) 0,000 4) 0,000

  R 0.700 ANG -4.681 1) 0.000 2) 1.618 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) 2.290 3) 0.000 4) 0.000

  P3k magnification of objective image at the median position (50.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -0,364 3) -1,256 4) 1,277

  R 10,000 ANG -0.255 1) -0.009 2) -0.358 3) -1.256 4) 1.277

  R 5,000 ANG -0,518 1) -0,018 2) -0,352 3) -1,256 4) 1,277

  R 3,000 ANG -0,883 1) -0,031 2) -0,343 3) -1,256 4) 1,277

  R 2,000 ANG -1,364 1) -0,048 2) -0,333 3) -1,256 4) 1,277

  R 1,000 ANG -2,997 1) -0,107 2) -0,301 3) -1,256 4) 1,277

  R 0.700 ANG -4.681 1) -0.171 2) -0.273 3) -1.256 4) 1.277

  R 0.500 ANG -7.500 1) -0.286 2) -0.235 3) -1.256 4) 1.277

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 2,234 3) 0,000 4) 0,000

  R 10,000 ANG -0,255 1) 0,000 2) 2,246 3) 0,000 4) 0,000

  R 5,000 ANG -0,518 1) 0,000 2) 2,257 3) 0,000 4) 0,000

  R 3,000 ANG -0,883 1) 0,000 2) 2,272 3) 0,000 4) 0,000

  R 2,000 ANG -1,364 1) 0,000 2) 2,291 3) 0,000 4) 0,000

  R 1,000 ANG -2,997 1) 0,000 2) 2,343 3) 0,000 4) 0,000

  R 0.700 ANG -4.681 1) 0.000 2) 2.384 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) 2.434 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the center position (50.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -0,446 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.432 3) 0.000 4) 0.000

  R 5,000 ANG -0,518 1) 0,000 2) -0,419 3) 0,000 4) 0,000

  R 3,000 ANG -0.883 1) 0.000 2) -0.400 3) 0.000 4) 0.000

  R 2,000 ANG -1,364 1) 0,000 2) -0,378 3) 0,000 4) 0,000

  R 1,000 ANG -2,997 1) 0,000 2) -0,317 3) 0,000 4) 0,000

  R 0.700 ANG -4.681 1) 0.000 2) -0.269 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) -0.211 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (50.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -0,997 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.971 3) 0.000 4) 0.000

  R 5,000 ANG -0,518 1) 0,000 2) -0,945 3) 0,000 4) 0,000

  R 3,000 ANG -0.883 1) 0.000 2) -0.910 3) 0.000 4) 0.000

  R 2,000 ANG -1,364 1) 0,000 2) -0,867 3) 0,000 4) 0,000

  R 1,000 ANG -2,997 1) 0,000 2) -0,744 3) 0,000 4) 0,000

  R 0.700 ANG -4.681 1) 0.000 2) -0.641 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) -0.514 3) 0.000 4) 0.000

* 2 0 Condition corresponding to the values: YxR / Yxo = 1,09, YaR / yao = 0, 52

Table 32

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (102.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) 0.273 3) 0.000 4) 0.000

  R 5,000 ANG -0,520 1) 0,000 2) 0,537 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) 2,408 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) 3.298 3) 0.000 4) 0.000

  R 0.500 ANG -7.500 1) 0.000 2) 4.421 3) 0.000 4) 0.000

  Lens magnification 3k at the telephoto end (102, 0 mm) of the third

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,525 3) -1,778 4) 1, 278

  R 10,000 ANG -0.255 1) -0.009 2) -0.509 3) -1.778 4) 1, 278

  R 5,000 ANG -0,520 1) -0,018 2) -0,495 3) -1,778 4) 1, 278

  R 3,000 ANG -0.887 1) -0.031 2) -0.475 3) -1.778 4) 1, 278

  R 2,000 ANG -1,369 1) -0,048 2) -0,452 3) -1,778 4) 1, 278

  R 1,000 ANG -3,004 1) -0,110 2) -0,389 3) -1,778 4) 1, 278

  R 0.700 ANG -4.686 1) -0.178 2) -0.339 3) -1.778 4) 1, 278

  R 0.500 ANG -7.500 1) -0.306 2) -0.275 3) -1.778 4) 1, 278

  Conversion coefficient yx associated with the direction of the optical axis at the telephoto end (102.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) 3,739 3) 0,000 4) 0,000

  R 10,000 ANG -0,255 1) 0,000 2) 3,821 3) 0,000 4) 0,000

  R 5,000 ANG -0,520 1) 0,000 2) 3,898 3) 0,000 4) 0,000

  R 3,000 ANG -0,887 1) 0,000 2) 3,994 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) 4,104 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) 4,380 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) 4.569 3) 0.000 4) 0.000

  R 0.500 ANG -7.5001) 0.000 2) 4,770 3) 0,000 4) 0,000

  Slope dx / da focusing cam at the telephoto end (102.0 mm) of the third

example

  R 0,000 ANG 0,000 1) 0,000 2) -1,110 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -1.031 3) 0.000 4) 0.000

  R 5,000 ANG -0.5201) 0.000 2) -0.964 3) 0.000 4) 0.000

  R 3,000 ANG -0,887 1) 0,000 2) -0,886 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) -0,799 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) -0,597 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) -0.471 3) 0.000 4) 0.000

  R 0.500 ANG -7.5001) 0.000 2) -0.338 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (102.0 mm) of the third example

  R 0,000 ANG 0,000 1) 0,000 2) -4,149 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -3.938 3) 0.000 4) 0.000

  R 5,000 ANG -0.5201) 0.000 2) -3.757 3) 0.000 4) 0.000

  R 3,000 ANG -0,887 1) 0,000 2) -3,538 3) 0,000 4) 0,000

  R 2,000 ANG -1,369 1) 0,000 2) -3,280 3) 0,000 4) 0,000

  R 1,000 ANG -3,004 1) 0,000 2) -2,615 3) 0,000 4) 0,000

  R 0.700 ANG -4.686 1) 0.000 2) -2.151 3) 0.000 4) 0.000

  R 0.500 ANG -7.5001) 0.000 2) -1.613 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.28, YaR / YaO = 0.39 As indicated in Tables 30, 31 and 32, for each focal length, the conversion coefficient yx, associated with the direction of the Optical axis increases, but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is closer to the weakest distance because of the slope (dx / da) of the focusing cam. According to Tables 30, 31 and 32, the rate of variation, from the position focused at infinity to the position focused at the smallest distance, of the conversion coefficient Ya associated with the rotation is x 0.58 to 1. wide-angle end (F = 29.0 mm), x0.52 at the middle position (F = 50.0 mm) and x0.39 at the telephoto end (F = 102.0 mm). When the number of divisions of the focusing range during a change of the conversion coefficient Ya of the third example is calculated with the formula (a) and is compared with the second example, the numbers Nw, NM and NT of divisions at the wide-angle end, mid-position and telephoto end respectively have the following values: second example (rotation angle ratio -0.95)

NW> 4.1 NM> 4.7 NT> 6.2

  third example (rotation angle ratio -0.75) Nw> 3.0O NM> 3.6 NT> 5.2 As indicated in the above comparison, such as the ratio of rotation amplitudes for distance variation focal and for focusing in the third example

  (-0.75) is closer to the upper limit of the

  (2) that in the second example (-0.95), the values of the numbers N of divisions are lower than in the second

example.

  As previously described, when the data

  are the same, if the ratio (aF / az) of the ampli-

  study of rotation from variation of focal length to ampli-

  focus rotation approximates the upper limit of condition (2), the rate of change of the conversion coefficient Ya associated with the rotation becomes

  the number N of divisions in the focus range

  can be reduced. However, as indicated by the comparison with the second example, when the rate of change of the conversion coefficient is. associated with the rotation decreases, the value itself of the conversion coefficient Ya associated with the rotation increases. Consequently, when the rate of variation (YaR / YaO) of the conversion coefficient γ exceeds the upper limit of the condition (3), the sensitivity criterion (dBf / da) associated with the rotational displacement becomes stricter and a change of the image point due to a small error factor in rotation becomes large and disrupts the precise auto focus. Tables 33, 34 and 35 show the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 29.0 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the third example. The provisions and symbols of the tables are the same as

  in the second example. The position of the focal lenses

  the first pair of the two upper parts of each of Tables 33, 34 and 35, ie in the third and fourth columns, is (R, ANGLE) = (0,0; 0,0) and indicates that this position corresponds to infinity. Similarly, the position in the fourth pair in the two lower parts of each of Tables 33, 34 and 35, ie the ninth and tenth columns, is

  (R, ANGLE) = (0.5; -7.5) indicating that this position corresponds to

  focus at the nearest location

(R = 0.5 m).

Table 33

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and coefficient of correctness p: (i) at the wide-angle end (29.0 mm) of the third example f = 29.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.256 5,000 -0.520 3,000 - 0.887

POS R rs r rs r rs

  1 0,000 -0.334 0.000 -0.329 -0.325 -0, 319

  2 10,000 -0.332 -0.327 0.000 -0.323 -0, 317

  3 5,000 -0,329 -0,325 -0,320 0,000 -0,314

  4 3,000 -0.326 -0.322 -0.317 -0.311 0, 000

2,000 -0,322 -0,318 -0,313 -0,307

  6 1,000 -0,309 -0,305 -0,300 -0, 294

  7 0.700 -0.296 -0.292 -0.288 -0, 282

  8 0.500 -0.276 -0.272 -0.268 -0, 263

POS R bf f bf t bf t bf s

  1 0,000 0.00 0.00 -0.08 12.09 -0.17 12.15 -0.28 11, 80

  2 10,000 0.08 12.50 0.00 0.00 -0.09 12.36 -0.20 11, 78

  3 5,000 0.17 12.37 0.09 12.36 0.00 0.00 -0.12 11, 58

  4 3,000 0.29 12.43 0.20 12.38 0.12 12.17 0.00 0.00

  5 2,000 0.44 12.38 0.35 12.25 0.27 11.97 0.15 11.60

  6 1,000 0.93 12.27 0.84 12.09 0.75 11.86 0.62 11, 58

  7 0.700 1.39 12.12 1.29 11.93 1.20 11.71 1.07 11, 43

  8 0.500 2.07 11.85 1.97 11.65 1.87 11.43 1.74 11, 15

  (R, ANGLE) = 2,000 -1,369 1,000 -3,004 0,700 -4,686 0,500 -7,500

  2 5 POS R rs r rs r rs r rs i 0,000 -0,311 -0,287 -0,266 -0,237

  2 10,000 -0.309 -0.285 -0.264 -0, 235

  3 5,000 -0,307 -0,283 -0,262 -0, 234

  4 3,000 -0.304 -0.280 -0.260 -0, 231

  3 0 5 2,000 -0,300 0,000 -0,277 -0,257 -0,228

  6 1,000 -0,287 -0,265 0,000 -0,246 -0, 218

  7 0.700 -0.275 -0.254 -0.235 0.000 -0, 208

  8 0.500 -0.256 -0.236 -0.218 -0.193.0.000

POS R bf s bf t bf s bf

  1 0.000 -0.43 11.45 -0.86 10.34 -1.25 9.35 -1.78 7, 78

  2 10,000 -0.34 11.43 -0.78 10.32 -1.17 9.33 -1.71 7, 76

  3 5,000 -0.26 11.39 -0.70 10.30 -1.09 9.31 -1.63 7, 74

  4 3,000 -0.15 11.44 -0.59 10.27 -0.99 9.28 -1.53 7, 71

  2,000 0.00 0.00 -0.45 10.22 -0.85 9.25 -1.40 7.66

  6 1,000 0.47 11.25 0.00 0.00 -0.41 9.14 -0.98 7, 51

  7 0.700 0.91 11.08 0.43 9.94 0.00 0.00 -0.59 7, 31 8 0.500 1.57 10.80 1.06 9.69 0.61 8.65 0.00 0, 00

  Condition corresponding to the values: Kao / Yao = 0.83, KaR / YaR = 1.23

Table 34

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (50.0 mm) of the third example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,255 5,000 -0,518 3,000 - 0,883

POS R rs r rs r rs

  1 0.000 -0.997 0.000 -0.976 -0.956 -0, 929

  2 10,000 -0.992 -0.971 0.000 -0.950 -0, 923

  3 5,000 -0,986 -0,965 -0,945 0,000 -0,918

  4 3,000 -0.978 -0.957 -0.937 -0.910 0, 000

2,000 -0,967 -0,947 -0,927 -0,900

  6 1,000 -0,932 -0,912 -0,893 -0, 867

  7 0.700 -0.898 -0.879 -0.859 -0.834

  8 0.500 -0.844 -0.826 -0.808 -0.784

POS R bf t bf i bf t bf f

  1 0.000 0.00 0.00 -0.25 45.16 -0.50 42.56 -0.82 39, 91

  2 10,000 0.25 48.32 0.00 0.00 -0.25 41.94 -0.58 39, 40

  3 5,000 0.51 46.88 0.25 44.53 0.00 0.00 -0.34 38, 81

  4 3,000 0.86 45.77 0.60 43.36 0.34 41.76 0.00 0.00

  2 0 5 2,000 1.32 44.73 1.05 42.52 0.78 40.79 0.43 38.87

  6 1,000 2.79 43.24 2.50 41.51 2.21 40.08 1.83 38, 47

  7 0.700 4.20 42.45 3.89 40.92 3.58 39.61 3.17 38.07

  8 0.500 6.33 41.43 5.98 40.06 5.64 38.83 5.18 37.34

  (R, ANGLE) = 2,000 -1,364 1,000 -2,997 0,700 -4,681 0,500 -7,500

POS R rs r rs r rs

  1 0.000 -0.895 -0.798 -0.719 -0, 617

  2 10,000 -0.890 -0.793 -0.714 -0, 613

  3 5,000 -0.884 -0.788 -0.710 -0, 609

  4 3,000 -0.877 -0.781 -0.703 -0, 603

  3 0 5 2,000 -0,867 0,000 -0,772 -0,695 -0,596

  6 1,000 -0,835 -0,744 0,000 -0,668 -0,572

  7 0.700 -0.803 -0.714 -0.641 0.000 -0.549

  8 0.500 -0.754 -0.670 -0.601 -0.514 0, 000

POS R bf t bf t bf f bf i

  1 0.000 -1.22 37.39 -2.39 32.63 -3.36 27.76 -4.63 23, 02

  2 10,000 -0.99 37.07 -2.18 32.57 -3.16 27.68 -4.44 22, 98

  3 5,000 -0.75 36.79 -1.95 32.55 -2.95 27.61 -4.25 22, 94

  4 3,000 -0.42 36.48 -1.65 32.56 -2.67 27.51-3.99 22, 89

  2,000 0.00 0.00 -1.26 32.62 -2.31 27.37 -3.66 22.83

  6 1,000 1.36 36.87 0.00 0.00 -1.13 26.65 -2.58 22.63

  7 0.700 2.66 36.38 1.20 30.61 0.00 0.00 -1.55 22, 53

  8 0.500 4.63 35.63 3.02 30.34 1.69 27.01 0.00 0.00

  Condition corresponding to the values: KaO / yao = 0.85, KaR / YaR = 1.20

Table 35

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the end of telephoto (102.0 mm) of the third example f = 102.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,255 5,000 -0,520 3,000 -0,887

POS R rs r rs r rs

  1 0.000 -4.149 0.000 -3.943 -3.757 - 3.536

  2 10,000 -4,145 -3,938 0,000 -3,753 - 3,534

  3 5,000 -4,144 -3,940 -3,757 0,000 - 3,537

  4 3,000 -4,152 -3,948 -3,765 -3,538 0,000

2,000 -4,162 -3,955 -3,768 -3, 537

  6 1,000 -4,193 -3,976 -3,778 - 3,537

  7 0.700 -4.221-3.992-3.774 - 3.532

  8 0.500 -4.255 -4.006 -3.782 - 3.513

POS R bf t bf t bf I bf f

  1 0.000 0.00 0.00 -1.01 778.65 -1.95 -9999.99 -3.14 - 4568.68

  2 10,000 1.06 1095.80 0.00 0.00 -0.99 -964.37 -2.23 - 1995.84

  3 5,000 2.16 1950.99 1.04 -2492.06 0.00 0.00 -1.30 - 4185.41

  4 3,000 3.68 -4502.09 2.49 -958.21 1.38 -689.32 0.00 0.00

  5 2,000 5.70 -1804.76 4.40 -996.03 3.20 -1136.48 1.71 6562.23

  6 1,000 12.60 -1169.10 10.93 -1130.00 9.38 -1702.90 7.49 25172.14

  7 0.700 19.78 -1133.19 17.69 -1291.69 15.76 -2245.64 13.42 7863, 16

  8 0.500 31.91 -1245.31 29.02 -1679.28 26.39 -4091.86 23.23 3267, 49

  (R, ANGLE) = 2,000 -1,369 1,000 -3,004 0,700 -4,686 0,500 -7,500

2 5 POS R rs r rs r rs

  1 0.000 -3.286 -2.669 -2.251 - 1.794

  2 10,000 -3.284 -2.665 -2.246 - 1.788

  3 5,000 -3,284 -2,661 -2,240 - 1,782

  4 3,000 -3,281 -2,655 -2,233 - 1,774

  3 0 5 2,000 -3,280 0,000 -2,647 -2,223 -1,763

  6 1,000 -3,269 -2,615 0,000 -2,187 - 1,725

  7 0.700 -3.253 -2.586 -2.151 0.000 - 1.685

  8 0.500 -3.218 -2.526 -2.081 -1.612 0.000

POS R bf t bf i bf I bf i

  1 0,000 -4.50 2705.80 -8.02 386.79 -10.55 227.24 -13.45 119.58

  2 10,000 -3.66 3719.80 -7.32 384.79 -9.95 226.69 -12.95 118.99

  3 5,000 -2.79 2889.10 -6.61 376.50 -9.33 225.18 -12.44 118.25

  4 3,000 -1.58 4983.53 -5.62 368.65 -8.48 223.87 -11.73 117.30

  2,000 0.00 0.00 -4.33 354.26 -7.37 222.07 -10.81 116, 00

  6 1,000 5,34 1478.74 0.00 0.00 -3.68 220.04 -7.76 111.33

  7 0.700 10.79 1307.69 4.35 388.42 0.00 0.00 -4.74 105.33

  8 0.500 19.73 1043.85 11.36 332.21 5.86 180.88 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 1.03, KaR / YTaR = 1.11 The results of the calculation of the rate of variation of Ka as a function of Ya for the infinite-focused set and the set focused on the nearest location at the wide-angle end, at the middle position and at the telephoto end in the second and third

example are as follows.

Second example

  At infinity Ka / ao Nearest KaR / YaR Wide-angle (F = 29.0) 0, 75 1.36 Median position (F = 50.0) 0.78 1.33 Telephoto (F = 102, 0) 0.94 1.23 Third example At infinity <aO / YaO Closest KaR / YaR Wide angle (F = 29.0) 0.83 1.23 Median position (F = 50.0) 0 , 85 1.20 Telephoto (F = 102.0) 1.03 1.11 As previously described, in the third example, since the rate of change of Ka as a function of Ya is small compared to the second example, the contribution of correction term (ABf / p) in Ka = Ya (1 - ABf / I) can

  undergo further reduction.

  Errors in lens drive magnitudes when focusing the infinite focused assembly to the object at the smallest distance and focusing the focused assembly at the smallest distance to the object object at infinity, at the wide-angle end, in the middle position and at the telephoto end in the third example are calculated and compared to the errors of the second example. It should be noted that the values of the correction coefficient y for the sets focused at infinity and at the nearest location respectively have the values of the object distances (POS-5) and (POS-4) as representative values.

Second example

  Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 29.0) -1.3% -0.2% Median Position (F = 50.0) -3.4% - 0.1% Telephoto (F = 102.0) -1.2% -0.3% Third Example Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 29.0) - 0.8% -0.1% Median position (F = 50.0) -1.4% -0.1% Telephoto (F = 102.0) 0.8% -0.2% As previously described, when a given range of lens arrangements is represented only by a pair of values of the conversion coefficient Ya and the correction coefficient A, the setting of the ratio (aF / az) of the amplitude of rotation for the variation of distance focal length and rotation amplitude for focusing to a value near the upper limit of the condition (2) allows the reduction of the error on the lens drive amplitude Aa for the focusing calculated by the pair of values Ya and y and the focalisat ion can be

  performed with greater precision.

  Table 36 shows the focusing amplitude (ANGLE DA) during manual focusing with the focusing cam (middle part of table 28) of the third example, the displacement amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX)

  in the direction of the optical axis is given.

  It should be noted that the arrangement of the table and the symbols are the same as in the second example. The upper part of Table 36 gives the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m ) in the respective focusing states at the focal lengths (F = 29.0, 35, 0, 50.0, 70.0, 85.0 and 102.0 mm) and the middle part gives the values of the amplitude of focusing (ANGLE DA) rotation necessary to obtain an optimal focused state for the respective photography distances. The lower table shows the optical axis direction displacement amplitudes (DX) for the respective sets of lenses corresponding to the rotational amplitude (ANGLE DA) of rotation providing focusing for the focal lengths and distances of the optical axis.

respective photograph.

Table 36

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) displacement for focusing of the third example 0.50 m 0.70 m 1.00 m 2.00 m 3.00 m 5.00 m 29.000 Bf 0.000 0,000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,001 0,000 -0,001 -0,001 0,000, 000 Bf 0,000 -0,003 -0,005 -0,004 -0, 003 -0,002, 000 Bf 0,000 -0,005 -0,002 0.003 0.003 0.003 85,000 Bf 0.000 -0.003 0.004 0.003 0.002 0.002 102, 000 Bf 0,000 0,000 0,000 0,000 0,000 0,000

  ANGLE DA -7,500 -4,686 -3,004 -1,369 -0,887 -0,520

  F 29,000 DX 0,000 1,477 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,711 0,000 0,000 R 0,50 m F 50,000 DX 0,000 2,290 0,000 0,000 R 0,50 m F 70,000 DX 0,000 3,076 0,000 0,000 R 0 50m F 85,000 DX 0,000 3, 690 0,000 0,000 R 0,50 m F 102,000 DX 0,000 4,421 0,000 0,000 R 0,50 m F 29,000 DX 0,000 1,021 0,000 0,000 R 0,70 m F 35,000 DX 0,000 1,190 0,000 0.000 R 0.70 m F 50.000 DX 0.000 1.619 0.000 0.000 R 0, 70 m F 70.000 DX 0.000 2.220 0.000 0.000 R 0.70 m F 85,000 DX 0.000 2,705 0,000 0,000 R 0,70 m F 102,000 DX 0,000 3,298 0,000 0,000 R 0.70 m F 29,000 DX 0,000 0,698 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,818 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,128 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,572 0,000 0,000 R 1,00 m F 85,000 DX 0,000 1,940 0,000 0,000 R 1,00 m F 102,000 DX 0,000 2,408 0,000 0,000 R 1,00 m F 29,000 DX 0,000 0,340 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,402 0,000 0,000 R 2 00 m F 50,000 DX 0,000 0,562 0, 000 0,000 R 2,00 m F 70,000 DX 0,000 0,799 0,000 0,000 R 2,00 m F 85,000 DX 0,000 1,007 0,000 0,000 R 2,00 m F 102,000 DX 0,000 1,281 0,000 0,000 R 2,00 m F 29,000 DX 0,000 0,225 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,266 0,000 0,000 R 3,00 m F 50,000 DX 0, 000 0.375 0.000 0.000 R 3.00 m F 70,000 DX 0.000 0, 536 0.000 0.000 R 3.00 m F 85,000 DX 0.000 0.681 0.000 0.000 R 3.00 m F 102,000 DX 0.000 0.875 0.000 0.000 R 3.00 m F 29,000 DX 0,000 0,134 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,159 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,225 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,000 0,000 0,000 R 5 00 m F 85,000 DX 0,000 0, 414 0,000 0,000 R 5,00 m F 102,000 DX 0,000 0,537 0,000 0,000 R 5,00 m As shown in Table 36, so-called "manual" focusing can be achieved because the displacement amplitudes of the image point for the respective focal distances and photographing distances are very small even when the ratio of the rotational amplitudes (aF / az) for the focal length variation and the focus is changed. Fourth Embodiment The fourth embodiment or example relates to a zoom lens having a four-set arrangement, i.e. positive, negative, positive and positive lens sets, and giving focus to

  using a second set of negative type lenses.

  In this zoom lens, the ratio (az / az) of the rotational amplitudes for the focusing of the position focused at infinity to the position focused at the nearest location (R = 0.5 m) and the Focal length variation rotation amplitude of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 82.5 mm)

is set to -0.9.

  Table 37 shows various paraxial data of an optical system and the data allowing the definition of the configuration of a focusing cam in the

fourth example.

  The upper part of table 37 indicates the focal lengths and intervals of the main points of the respective lens assemblies of the optical system corresponding to the fourth example with six focusing control states (focal lengths F = 28.8, 35.0, 50.0 ,

0, 70.0 and 82.5 mm).

  The middle part of Table 37 shows the spline sampling data when the focus cam configuration of the second lens set of the fourth example, used for focusing, is represented by a spline function associated with the angle a of rotation of a rotating barrel and at the amplitude x of

  displacement in the direction of the optical axis.

  In addition, the lower part of Table 37 indicates the infinite focus positions (positions corresponding to infinity) for the respective focal lengths (F = 28.0, 35.0, 50.0, 60.0, 70.0 and 82.5 mm) and the rotational amplitudes (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) using the focusing cam of the fourth example. In the lower part of Table 37, as the amplitude of rotation for the focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 82.5 mm) is equal to 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 0.5 m) is -9.0, the ratio (aF / az) focusing and variation amplitudes of

  Focal length of the fourth example is -0.90.

Table 37

  Fourth example f = 28.8 to 82.5 (ratio of amplitudes of rotation: aF / az = -0.9) Focal distances and intervals of the main points of the objectives of the fourth example

  F 28.8000 35.0000 50.0000 60.0000 70.0000 82.5000

  F1 74.0345 D1 9.2069 13.4025 20.8711 24.7305 27.9387 31.2269

  F2 -14.6500 D2 19.6762 17.1764 13.3033 11.5956 10.2135 8.7449

  F3 38.9970 D3 18.6590 17.9190 16.7790 16.3000 15.9999 15.7889

  F4 51.0000 D4 51.6857 55.8574 63.7033 67.4419 70.3975 73.3520

  Focusing cam shape (spline interpolated point) corresponding to the fourth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.2800 0.0000 0.0000

  2 -10.0000 0.0000 1.2062 0.0000 0.0000

  3 -9.0000 0.0000 1.1246 0.0000 0.0000

  4 -5.4641 0.0000 0.7797 0.0000 0, 0000

-3,4495 0.0000 0.5344 0.0000 0.0000

  6 -1.5517 0.0000 0.2611 0.0000 0.0000

  7 -1.0015 0.0000 0.1727 0.0000 0.0000

  8 -0.5861 0.0000 0.1030 0.0000 0.0000

  2 0 9 0.0000 0.0000 0.0000 0, 0000 0.0000

1.0000 0.0000 -0.1894 0.0000 0.0000

  1 1 4.5359 0.0000 -1.0442 0.0000 0.0000

  12 6.5505 0.0000 -1.7196 0.0000 0.0000

  13 8.4483 0.0000 -2.5669 0.0000 0.0000

  2 5 14 8.9985 0.0000 -2.8691 0, 0000 0.0000

9,4139 0,0000 -3,1200 0.0000 0.0000

  16 10.0000 0.0000 -3.5146 0.0000 0.0000

  17 11.0000 0.0000 -4.2900 0.0000 0.0000

* Rotational amplitude for focal length change and focus rotation amplitude of the fourth example (ratio of rotation amplitudes: aF / az = -0.9) Focal distance Corresponding position Distance of amplitude of rotation to infinity photograph for focusing 28.8 mm 0.0000 5.00 m -0.586, 0 mm 1.9432 3.00 m -1.002 50.0 mm 5.4278 2.00 m -1.552, 0 mm 7.2013 1.00 m -3.449, 0 mm 8.6217 0.70 m -5.464 82.5 mm 10.0000 0, 50 m -9.000 The following table 38 gives the numerical values data of the cams of the set of focusing lenses of the fourth example, the data being calculated by interpolation with a spline function, from the sample data of the focusing cam indicated in the middle part of table 37. It should be noted that the meanings of the symbols and references of the

  Table 38 are the same as in the first example.

Table 38

  Digital cam values for focusing objective of the fourth example Focusing cam digital values Focal distance dimming compensation digital cam values

ANGLE (2) F ANGLE (2) F

-9.0000 1.1246 0.0000

-8.5000 1.0813 0.0000

-8.0000 1.0363 0.0000

-7.5000 0.9896 0.0000

-7.0000 0.9412 0.0000

-6.5000 0.8908 0.0000

-6.0000 0.8383 0.0000

-5.5000 0.7837 0.0000

-5.0000 0.7268 0.0000

-4.5000 0.6675 0.0000

-4.0000 0.6056 0.0000

-3,5000 0,5411 0,0000

-3.0000 0.4737 0.0000

-2.5000 0.4034 0.0000

-2.0000 0.3298 0.0000

-1.5000 0.2529 0.0000

-1.0000 0.1725 0.0000

-0.5000 0.0883 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.0924 30.2861 0.5000 0.3088 30.2861

  1.0000 -0.1894 31.8415 1.0000 0.6313 31.8415

  1,5000 -0,2912 33,4752 1,5000 0,9786 33,4752

  2.0000 -0.3984 35.2011 2.0000 1.3639 35.2011

  2,5000 -0,5115 37,0318 2,5000 1,7986 37,0318

  3 0 3,0000 -0,6310 38,9731 3,0000 2,2818 38,9731

  3.5000 -0.7575 41.0275 3.5000 2.8083 41.0275

  4.0000 -0.8916 43.1956 4.0000 3.3705 43.1956

  4.5000 -1.0337 45.4747 4.5000 3.9590 45.4747

  , 0000 -1.1845 47.8633 5.0000 4.5632 47.8633

  5,5000 -1,3451 50,3698 5,5000 5,1742 50,3698

  6,0000 -1,5166 53,0072 6,0000 5,7872 53,0072

  6.5000 -1.7003 55.7941 6.5000 6.4064 55.7941

  7.0000 -1.8976 58.7520 7.0000 7.0380 58.7520

  7.5000 -2.1106 61.9210 7.5000 7.6908 61.9210

  8.0000 -2.3419 65.3422 8.0000 8.3695 65.3422

  8.5000 -2.5939 69.0503 8.5000 9.0736 69.0503

  9.0000 -2.8699 73.0903 9.0000 9.8041 73.0903

  9,5000 -3,1747 77,5414 9,5000 10,5690 77,5414

  , 0000 -3,5146 82,5000 10,0000 11,3794 82,5000

  The left side of table 38 shows the numerical values of the focus cam of the fourth example, and the right part those of the zoom compensation cam. A value obtained by synthesizing the displacement amplitudes (2) in the direction of the optical axis of the digital values of the focusing cam and the zoom compensation cam in the range between the rotation amplitude (ANGLE = 0 , 0) to the amplitude of rotation (ANGLE = 10,0) coincides with the displacement location of the second set of lenses calculated from the data

  from the top of Table 37.

  Tables 39, 40 and 41 which follow indicate the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Px of the respective sets of images. lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  of converting your partner to the rotation at the far end

  angle (F = 28.8 mm), medial position (F = 50.0 mm) and telephoto end (F = 82.5 mm) in the fourth example. The provisions of the respective tables and the meanings of the symbols are the same as in the

first example.

Table 39

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 0.051 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) 0,103 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 0,173 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 0,261 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 0,534 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 0.780 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.125 3) 0.000 4) 0.000

  Objective image magnification at the wide-angle end (28.8 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,292 3) 99,097 4) -0,013

  R 10,000 ANG -0.288 1) -0.008 2) -0.288 3) 99.097 4) -0.013

  R 5,000 ANG -0,586 1) -0,015 2) -0,285 3) 99,097 4) -0,013

  R 3,000 ANG -1,002 1) -0,026 2) -0,280 3) 99,097 4) -0,013

  R 2,000 ANG -1,552 1) -0,041 2) -0,274 3) 99,097 4) -0,013

  R 1,000 ANG -3,449 1) -0,090 2) -0,255 3) 99,097 4) -0,013

  R 0.700 ANG -5.464 1) -0.141 2) -0.239 3) 99.097 4) -0.013

  R 0.500 ANG -9.000 1) -0.227 2) -0.215 3) 99.097 4) -0.013

  Conversion coefficient Yx associated with the direction of the optical axis at the wide-angle end (28.8 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,624 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 1.628 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) 1,631 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 1,636 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 1,642 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 1,659 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 1.674 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.693 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide-angle end (28.8 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,181 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.176 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) -0,171 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) -0,165 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -0,157 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,132 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.112 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.085 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.8 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,293 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.286 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) -0.279 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) -0,269 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -0,257 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,220 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.187 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.144 3) 0.000 4) 0.000

  Condition corresponding to the values: yxR / yxo = 1.04, yaR / yao = 0.49

Table 40

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the middle position (50.0 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) 0.093 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) 0,185 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) 0.309 3) 0.000 4) 0.000

  R 2,000 ANG -1,549 1) 0,000 2) 0,463 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) 0,927 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) 1.328 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.872 3) 0.000 4) 0.000

  13k image magnification of lenses at the median position (50.0 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,380 3) 7,128 4) - 0,249

  R 10,000 ANG -0,287 1) -0,008 2) -0,374 3) 7,128 4) - 0,249

  R 5,000 ANG -0,585 1) -0,015 2) -0,368 3) 7,128 4) - 0,249

  R 3,000 ANG -1,000 1) -0,026 2) -0,359 3) 7,128 4) - 0,249

  R 2,000 ANG -1,549 1) -0,041 2) -0,349 3) 7,128 4) - 0,249

  R 1,000 ANG -3,446 1) -0,091 2) -0,317 3) 7,128 4) - 0,249

  R 0.700 ANG -5.465 1) -0.145 2) -0.290 3) 7.128 4) - 0.249

  R 0.500 ANG -9.000 1) -0.238 2) -0.253 3) 7.128 4) - 0.249

  Coefficient of conversion rx associated with the direction of the optical axis at the median position (50.0 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,696 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) 2.711 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) 2,726 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) 2,745 3) 0,000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) 2,769 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) 2,835 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) 2.888 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 2.951 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,329 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) -0.317 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) -0,305 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) -0,290 3) 0,000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) -0,272 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) -0,220 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) -0.180 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.131 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the median position (50.0 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,886 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) -0.858 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) -0,831 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) -0,797 3) 0,000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) -0,753 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) -0,623 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) -0.520 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.387 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / Yxo = 1.09, YaR / Yao = 0.44

Table 41

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (82.5 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 0.200 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) 0.395 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) 0,646 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 0,948 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 1,795 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 2.470 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 3.325 3) 0.000 4) 0.000

  Nk image magnification of lenses at the telephoto end (82.5 mm) of the fourth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,520 3) 4,887 4) -0,438

  R 10,000 ANG -0.288 1) -0.008 2) -0.507 3) 4.887 4) - 0.438

  R 5,000 ANG -0,586 1) -0,015 2) -0,493 3) 4,887 4) -0,438

  R 3,000 ANG -1,002 1) -0,026 2) -0,476 3) 4,887 4) -0,438

  R 2,000 ANG -1,552 1) -0,041 2) -0,456 3) 4,887 4) -0,438

  R 1,000 ANG -3,449 1) -0,093 2) -0,398 3) 4,887 4) -0,438

  R 0.700 ANG -5.464 1) -0.149 2) -0.352 3) 4.887 4) - 0.438

  R 0.500 ANG -9.000 1) -0.249 2) -0.293 3) 4,887 4) -0,438

  Conversion coefficient Yx associated with the direction of the optical axis at the telephoto end (82.5 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) 3,346 3) 0,000 4) 0,000

  R 10,000 ANG -0,288 1) 0,000 2) 3,410 3) 0,000 4) 0,000

  R 5,000 ANG -0,586 1) 0,000 2) 3,471 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 3,547 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 3,635 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 3,861 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 4.020 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 4.193 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (82.5 mm) of the fourth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,721 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.673 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) -0,630 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) -0,579 3) 0,000 4) 0,000 R 2,000 ANG -1,552 1) 0,000 2) -0,522 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,383 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.294 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.199 3) 0.000 4) 0.000

  Coefficient of conversion associated with the direction of rotation at the telephoto end (82.5 mm) of the fourth example

  R 0,000 ANG 0,000 1) 0,000 2) -2,412 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -2.295 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) -2.187 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) -2,053 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -1,897 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -1,479 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -1.181 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.833 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / yxo = 1.25, YaR / YaO = 0.35 As indicated in tables 39, 40 and 41, for each focal length, the conversion coefficient yx associated with the direction of the axis optical increases, but the slope (dx / da) of the focusing cam decreases as the photographic distance approaches the shortest distance. As a result, as indicated in these tables, the conversion coefficient associated with the rotation, defined as the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance due to the influence of the slope (dx / da) of the focusing cam. In tables 39, 40 and 41, the rate of variation, from the position focused at infinity to the position focused at the nearest location, of the conversion coefficient associated with the rotation is xO, 49 to wide-angle end (F = 28.0 mm), xO, 44 in the middle position (F = 50.0 mm) and x0.35 at the telephoto end (F = 82.5 mm). When the number N of divisions of the focusing range, upon a change of the conversion coefficient Ya of the fourth example, is calculated with the formula (a) and is compared with the value of the example of the Japanese patent application laid down to the public inspection No. 5- 142475, the numbers Nw, NM and NT of divisions at the wide-angle end, in the median position and at the telephoto end respectively have the following values: example of the patent application submitted to the public inspection No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 fourth example Nw> 3.9 NM> 4.5 NT> 5.8 As indicated previously, in the fourth For example, since the speed of variation of the conversion coefficient δ associated with the rotation is smaller than that of the conventional system, the values of the division numbers N become small. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y can be reduced, and the capacity of

  memorisation can be deleted.

  Tables 42, 43 and 44 show the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 28.8 mm), in the median position (F = 52.0 mm) and at the telephoto end (F = 82.5 mm) in the fourth example. The provisions and symbols of the tables are the same as in the first example. The position of the lenses, in the first pair of the two upper parts of each of the tables 42, 43 and 44, i.e. in the third and fourth columns, is (R, ANGLE) = (O, O; O, O) and indicates that this position corresponds to infinity. Similarly, the position of the lenses in the fourth pair of the two parts

  of each of Tables 42, 43 and 44, that is,

  say in the ninth and tenth columns, is (R, ANGLE) = (O, 5; -9, O) and indicates that this position corresponds to the focused position at the most

close (R = 0.5 m).

Table 42

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (1) at the wide-angle end (28.8 mm) of the fourth example f = 28.8 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,288 5,000 -0,586 3,000 -1,002

POS R rs r rs r rs

  1 0.000 -0.293 0.000 -0.289 -0.284 -0, 278

  2 10,000 -0.291 -0.286 0.000 -0.282 -0, 276

  3 5,000 -0,288 -0,284 -0,279 0,000 -0, 273

  4 3,000 -0,284 -0,280 -0,275 -0,269 0,000

2,000 -0,279 -0,275 -0,271 -0,265

  6 1,000 -0,263 -0,259 -0,255 -0, 249

  7 0.700 -0.247 -0.243 -0.239 -0, 234

  8 0.500 -0.223 -0.219 -0.215 -0, 210

  POS R bf t bf i bf t bf i 0.000 0.00 0.00 -0.08 9.15 -0.17 8.80 -0.28 8.47

  2 10,000 0.08 9.51 0.00 0.00 -0.08 8.68 -0.20 8, 41

  3 5,000 0.17 9.35 0.08 9.00 0.00 0.00 -0.11 8, 37

  4 3,000 0.28 9.21 0.20 8.88 0.11 8.63 0.00 0.00

  5 2,000 0.43 9.09 0.35 8.81 0.26 8.59 0.15 8.35

  6 1,000 0.91 8.84 0.82 8.60 0.73 8.40 0.61 8.14

  7 0.700 1.35 8.63 1.26 8.41 1.17 8.22 1.04 7.96

  8 0.500 2.01 8.34 1.91 8.14 1.81 7.96 1.68 7.71

  (R, ANGLE) = 2,000 -1,552 1,000 -3,449 0,700 -5,464 0,500 -9,000

2 5 POS R rs r rs r rs

  1 0.000 -0.270 -0.246 -0.224 -0, 194

  2 10,000 -0.268 -0.244 -0.222 -0, 192

  3 5,000 -0,265 -0,241 -0,220 -0, 190

  4 3,000 -0.262 -2.238 -0.217 - 0.187

  5 2,000 -0,257 0,000 -0,234 -0,213 - 0,184

  6 1,000 -0,242 -0,220 0,000 -0,200 -0, 172

  7 0.700 -0.227 -0.206 -0.187 0.000 -0, 161

  8 0.500 -0.204 -0.185 -0.168 -0.144 0.000

POS R bf b bf bf bf

  1 0.000 -0.42 8.13 -0.85 7.08 -1.23 6.16 -1.74 5.09

  2 10,000 -0.34 8.09 -0.77 7.05 -1.15 6.14 -1.67 5.07

  3 5,000 -0.26 6.06 -0.69 7.03 -1.07 6.12 -1.60 5.06

  4 3,000 -0.14 8.01 -0.58 6.99 -0.97 6.09 -1.50 5.04

  2,000 0.00 0.00 -0.44 6.95 -0.83 6.05 -1.37 5.02

  4 0 6 1,000 0.46 7.80 0.00 0.00 -0.40 5.92 -0.95 4.97

  7 0.700 0.89 7.64 0.42 6.67 0.00 0.00 -0.57 4.95

  8 0.500 1.52 7.40 1.03 6.48 0.59 5.73 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.76, KaR / YaR = 1.34

Table 43

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (50.0 mm) of the fourth example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,287 5,000 -0,585 3,000 - 1,000

POS R rs r rs r rs

  1 0,000 -0.886 0.000 -0.865 -0.845 -0.819

  2 10,000 -0.879 -0.858 0.000 -0.838 -0, 812

* 3 5,000 -0.871 -0.851 -0.831 0.000 -0, 806

  4 3,000 -0.861 -0.841 -0.822 -0.797 0, 000

2,000 -0,849 -0,829 -0,810 -0,785

  6 1,000 -0.805 -0.786 -0.767 -0, 742

  7 0.700 -0.760 -0.742 -0.724 -0, 701

  8 0.500 -0.691 -0.675 -0.658 -0.636

POS R bf t bf! bf t bf t

  1 0.000 0.00 0.00 -0.25 29.47 -0.49 29.29 -0.82 29, 15

  2 10,000 0.25 31.02 0.00 0.00 -0.25 29.14 -0.58 29, 34

  3 5,000 0.51 31.03 0.25 30.84 0.00 0.00 -0.33 29, 63

  4 3,000 0.86 31.18 0.60 30.80 0.34 30.69 0.00 0.00

  5 2,000 1.31 31.32 1.05 30.84 0.78 30.37 0.43 28.79

  6 1,000 2.77 30.24 2.48 29.39 2.19 28.44 1.82 26, 75

  7 0.700 4.15 29.31 3.84 28.41 3.53 27.46 3.13 25.98

  8 0.500 6.22 28.35 5.88 27.48 5.54 26.58 5.09 25.30

  (R, ANGLE) = 2,000 -1,549 1,000 -3,446 0,700 -5,465 0,500 -9,000

POS R rs r rs r rs

  1 0.000 -0.787 -0.692 -0.613 -0.511

  2 10,000 -0.780 -0.686 -0.608 -0, 507

  3 5,000 -0,774 -0,680 -0,602 -0, 502

  4 3,000 -0.765 -0.672 -0.594 -0, 495

  3 0 5 2,000 -0,753 0,000 -0,661 -0,584 -0,486

  6 1,000 -0,712 -0,623 0,000 -0,551 -0,458

  7 0.700 -0.672 -0.587 -0.520 0.00 -0.431

  8 0.500 -0.610 -0.532 -0.469 -0.387 0, 000

POS R bf t bf t bf f bf t

  1 0.000 -1.22 27.36 -2.38 21.42 -3.35 18.67 -4.60 14, 28

  2 10,000 -0.98 27.31 -2.17 21.28 -3.15 18.61 -4.41 14, 24

  3 5,000 -0.75 27.16 -1.95 21.11 -2.94 18.55 -4.22 14, 19

  4 3,000 -0.42 26.62 -1.64 20.87 -2.65 18.49 -3.96 14, 13

  2,000 0.00 0.00 -1.25 20.60 -2.29 18.44 -3.62 14.05

  6 1,000 1.35 24.66 0.00 0.00 -1.11 18.64 -2.54 13, 79

  7 0.700 2.63 24.24 1.19 20.85 0.00 0.00 -1.52 13, 38

  8 0.500 4.54 23.79 2.96 20.35 1.66 17.10 0.00 0.00

  Condition corresponding to the values: Kao / YaO = 0.78, KaR / raR = 1.32

Table 44

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: () at the telephoto end (82.5 mm) of the fourth example f = 82.5 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,288 5,000 -0,586 3,000 -1,002

POS R rs r rs r rs

  1 0.000 -2.412 0.000 -2.309 -2.213 -2.095

  2 10,000 -2,397 -2,294 0,000 -2,199 -2, 082

  3 5,000 -2,383 -2,281 -2,187 0,000 -2,071

  4 3,000 -2,365 -2,265 -2,171 -2,053 0, 000

2,000 -2,342 -2,241 -2,148 -2,031

  6 1,000 -2,260 -2,161 -2,068 -1, 952

  7 0.700 -2.174 -2.076 -1.984 -1, 871

  8 0.500 -2.028 -1.933 -1.844 -1.735

POS R bf bf i bf t bf I

  1 0.000 0.00 0.00 -0.66 104.19 -1.30 110.19 -2.10 103.72

  2 10,000 0.69 116.11 0.00 0.00 -0.66 116.02 -1.49 104.84

  3 5,000 1.40 118.30 0.68 120.80 0.00 0.00 -0.86 102.04

  4 3,000 2.37 123.78 1.62 124.87 0.90 121.43 0.00 0.00

  5 2,000 3.63 125.80 2.83 123.14 2.07 115.24 1.12 101.24

  6 1,000 7.80 124.25 6.83 117.48 5.92 108.64 4.78 97.17

  7 0.700 11.88 120.59 10.75 112.93 9.68 104.43 8.35 93.95

  8 0.500 18.25 114.66 16.84 106.84 15.52 98.97 13.88 89.49

  (R, ANGLE) = 2,000 -1,552 1,000 -3,449 0,700 -5,464 0,500 -9,000

2 5 POS R rs r rs r rs

  1 0.000 -1.959 -1.608 -1.357 -1, 069

  2 10,000 -1.947 -1.597 -1.347 -1, 061

  3 5,000 -1,935 -1,586 -1,337 -1, 052

  4 3,000 -1,918 -1,570 -1,323 -1,040

  3 0 5 2,000 -1,897 0,000 -1,550 -1,304 -1,024

  6 1,000 1,820 -1,479 0,000 -1,242 -0,972

  7 0.700 1.741 -1.411 -1.181 0.000 -0.919

  8 0.500 -1.610 -1.297 -1.079 -0.833 0.000

POS R bf t bf i bf f bf i

  1 0.000 -3.04 93.12 -5.55 63.97 -7.41 49.97 -9.62 33.87

  2 10,000 -2.46 93.42 -5.05 63.62 -6.97 49.80 -9.24 33.74

  3 5,000 -1.87 92.87 -4.54 63.14 -6.52 49.61 -8.85 33.59

  4 3,000 -1.06 93.77 -3.84 62.52 -5.90 49.36 -8.32 33.40

  2,000 0.00 0.00 -2.94 61.62 -5.10 49.08 -7.63 33.15

  6 1,000 3.45 84.94 0.00 0.00 -2.50 48.54 -5.39 32.28

  7 0.700 6.81 82.87 2.84 61.63 0.00 0.00 -3.25 31.19

  8 0.500 11.99 79.43 7.20 58.36 3.82 44.10 0.00 0.00

  Condition corresponding to the values: KaO / yaO = 0.84, KaR / YaR = 1.28 The results of the calculation of the rate of variation of Ka as a function of Ya for the set focused at infinity and the set focused at the nearest location at the wide-angle end, in the middle position and at the telephoto end in the example of Japanese Patent Application Laid-open No. 5-142475 and in the fourth example according to the invention are as follows. Japanese Patent Application Laid-open No. 5-142475 At infinity Ka0 / YaOLe nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50 , 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Fourth Example At infinity KaO / YaOLe nearest KaRITaR Wide-angle (F = 28.8) 0.76 1, 34 Median position (F = 50.0) 0.78 1.32 Telephoto (F = 82.5) 0.84 1.28 As previously described, in the first example, as the rate of variation of Ka as a function of Ya is weak compared to the classical system, the contribution of the correction term (ABf / M) in Ka = Ya (1 ABf / i) can be reduced. For this reason, an error of the conversion coefficient Ka calculated from Ya and y or an error of the actual driving amplitude Aa of lenses obtained when using a single pair of values of the conversion coefficient Ya and the correction coefficient

y can be reduced.

  In the embodiment of Japanese Laid-open Patent Application No. 5-142475 and in the fourth example of the invention, when the lens driving amplitudes during focusing of the focused assembly to the infinity towards the nearest object and when focusing the focused assembly on the nearest object towards the object at infinity, at the wide-angle end, in the middle position and at the telephoto end, are calculated from the relation Aa = ABf / Ya (1 - ABf / p) and the errors on the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the set focused at infinity towards the object at the shortest distance takes the value of the object distance (POS-5), and the value of the correction coefficient y when focusing the focused set to the shortest distance to the object at infinity takes the value of

object distance (POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest-Near-Focused-Infinity Wide-angle (F = 36.0) -4.4% -13.0% Midpoint (F = 50.0) -11, 8% -12.0% Telephoto (F = 103.0) -12.6% -14, 6% Fourth example Infinity Focused Most Nearest Focused at infinity Wide-angle (F = 28.8) -2.1% -0.2% Median position (F = 50.0) -2.7% -0.4% Telephoto (F = 82.50) - 1.7% -0.4% As previously described, in the fourth embodiment also, when only a pair of values of the conversion coefficient ya and the correction coefficient y are set for a given range of adjustment of the lenses, an error between the conversion coefficient Ka calculated from Ya and l and the lens driving amplitude Aa for focusing becomes low compared to the conventional system and the focusing can be achieved with

increased accuracy.

  Table 45 gives the rotation amplitude (ANGLE DA) for the focusing during the manual focusing with the focusing cam (middle part of table 37) of the fourth example, the displacement amplitude DX (mm) in the direction of rotation. the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  It should be noted that the layout of the table and its symbols are the same as in the first example. The upper part of Table 45 summarizes the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m ) for the respective focusing states giving the focal lengths (F = 28.8, 35.0, 50.0, 60.0, 70.0 and 82.5 mm), and the middle part indicates the values of the amplitude of rotation (ANGLE DA) of focusing necessary to obtain an optimal state of focus for the respective distances of photography. The lower part gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for the focusing, with the focal lengths and distances of

photography.

Table 45

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the fourth example 0.50 m 0.70 m 1.00 m 2.00 m 3.00 m 5.00 m 28.800 Bf 0.000 0,000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,000 0.001 0.001 0.001 0.001, 000 Bf 0.000 0.000 -0.002 -0.002 -0.001 -0.001, 000 Bf 0.000 -0.002 -0.002 -0.001 0.000 0.000, 000 Bf 0.000 -0.004 - 0.001 -0.003 - 0.003 -0.002 82.500 Bf 0.000 0.000 0, 000 0.000 0.000 0.000

  ANGLE DA -9,000 -5,464 -3,449 -1,552 -1,002 -0,586

  F 28,800 DX 0,000 1,125 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,333 0,000 0,000 R 0,50 m F 50,000 DX 0,000 1,872 0,000 0,000 R 0,50 m F 60,000 DX 0,000 2,281 0,000 0,000 R 0 50m F 70,000 DX 0,000 2,726 0,000 0,000 R 0,50 m F 82,500 DX 0,000 3,325 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,780 0,000 0,000 R 0,70 m F 35,000 DX 0,000 0,930 0,000 0,000 R 0.70 m F 50,000 DX 0,000 1,328 0,000 0,000 R 0,70 m F 60,000 DX 0,000 1,640 0,000 0,000 R 0,70 m F 70,000 DX 0,000 1,989 0,000 0,000 R 0.70 m F 82,500 DX 0,000 2,470 0,000 0,000 R 0 70 m F 28,800 DX 0,000 0,534 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,640 0,000 0,000 R 1,00 m F 50,000 DX 0,000 0,928 0,000 0,000 R 1,00 m F 60,000 DX 0,000 1,157 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,420 0,000 0,000 R 1,00 m F 82,500 DX 0,000 1,795 0,000 0,000 R 1,00 m F 28,800 DX 0,000 0,261 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,314 0,000 0,000 R 2,00 m F 50,000 DX 0.000 0, 464 0.000 0.000 R 2.00 m F 60,000 DX 0.000 0.586 0.000 0.000 R 2.00 m F 70, 000 DX 0.000 0.732 0.000 0.000 R 2.00 m F 82,500 DX 0,000 0,948 0,000 0,000 R 2,00 m F 28,800 DX 0,000 0,173 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,208 0,000 0,000 R 3,00 m F 50,000 DX 0.000 0.309 0.000 0.000 R 3.00 m F 60.000 DX 0.000 0.393 0.000 0.000 R 3.00 m F 70,000 DX 0.000 0.494 0.000 0.000 R 3.00 m F 82,500 DX 0,000 0,646 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,103 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,124 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,185 0,000 0,000 R 5,00 m F 60,000 DX 0,000 0, 237 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0 , 300 0.000 0.000 R 5.00 m F 82.500 DX 0.000 0.395 0.000 0.000 R 5.00 m As shown in Table 45, in the zoom lens of the fourth example, the so-called "manual focus" can be achieved because the image point shift magnitudes for the respective focal distances and photograph distances are very small and enter the depth of field regardless of the state of variation

  focal length and photography distance.

  Fifth Embodiment The fifth embodiment or fifth example relates to a zoom lens having a five-array arrangement, i.e. positive, negative, positive, negative, and positive lens assemblies, with focus on the lens. using a second set of negative type lenses. In this zoom lens, the ratio (aF / az) of the focusing rotation amplitude of the position focused at infinity to the position focused at the nearest location (R = 0.8 mm) and the Focal length variation rotation amplitude of the wide-angle end (F = 28.7 mm) at the telephoto end (F = 131.0 mm)

is set to -0.85.

  Table 46 gives various paraxial data of the optical system and data allowing the definition of the configuration of a focusing cam in the

fifth example.

  The upper part of Table 46 shows the focal lengths and intervals of the main points of the respective sets of lenses of the optical system of the fifth example for six states of variation of focal lengths (focal lengths F = 28.7, 35.0, 50.0 , 70.0, 105.0

and 131.0 mm).

  The middle portion of Table 46 shows spline sample data when the focus cam configuration of the second lens set of the fifth example, used for focusing, is expressed by a spline function associated with the angle α of rotation of a rotating barrel and the amplitude x of displacement in the

direction of the optical axis.

  In addition, the lower part of Table 46 indicates

  focus positions at infinity (positions corresponding to

  infinitely spanning) for the respective focal lengths (focal lengths F = 28.7, 35.0, 50.0, 70.0, 105.0 and 131.0 mm), and the amplitudes of rotation (amplitudes of focusing rotation) when focusing at respective photographing distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.8 m) using focus of the fifth example. In the lower portion of Table 46, as the zoom range of focal length variation from the wide-angle end (F = 28.7) to the telephoto end (F = 131.0) is set to 10. , 0 and the focus rotation amplitude of the position focused at infinity at the position focused at the nearest location (R = 0.8 m) is set at -8.5, the ratio (aF / az) focusing and variation amplitudes of

  The focal length of the fifth example is -0.85.

Table 46

  Fifth example f = 28.7 to 131.0 (ratio of rotation amplitudes: aF / az = -0.85) Focal distances and intervals of the main points of the objectives of the fifth example

  F 28,7000 35,0000 50,0000 70,0000 105,0000 131,0000

  F1 91,3108 D1 11,1134 16,1861 27,1959 34,7239 38,1201 39,1199

  F2 -16.5244 D2 36.8414 32.9701 27.9348 23.5294 18.1537 15, 9002

  F3 25.11621 D3 10.7552 12.6122 15.6328 17.5434 21.3827 23.4271

  F4 -35.4049 D4 12.9390 11.0820 8.0614 6.1508 2.3115 0.2671

  F5 55.8741 D5 52.1460 53.3605 54.4244 59.3670 71.3442 81.2252

  Focusing cam shape (spline interpolated point) corresponding to the fifth example

ANGLE (1) (2) (3) (4) (5)

  1 -11.0000 0.0000 0.9660 0.0000 0.0000 0.0000

  2 -10,0000 0.0000 0,9113 0.0000 0.0000 0.0000

  3 -8.5000 0.0000 0.8210 0.0000 0.0000 0.0000

  4 -6,0559 0.0000 0.6448 0.0000 0.0000 0.0000

  -3,5451 0.0000 0.4198 0.0000 0.0000 0.0000

  6 -2.5111 0.0000 0.3112 0.0000 0.0000 0.0000

  7 -1.5854 0.0000 0.2051 0.0000 0.0000 0.0000

  8 -0.9143 0.0000 0.1220 0.0000 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

  1,5000 0.0000 -0.2326 0.0000 0.0000 0.0000

  11 3.9441 0.0000 -0.7068 0.0000 0.0000 0.0000

  12 6.4549 0.0000 -1.3595 0.0000 0.0000 0.0000

  13 7.4889 0.0000 -1.6972 0.0000 0.0000 0.0000

  14 8.4146 0.0000 -2.0445 0.0000 0.0000 0.0000

  9,0857 0.0000 -2.3304 0.0000 0.0000 0.0000

  16 10.0000 0.0000 -2.7753 0.0000 0.0000 0.0000

  17 11.0000 0.0000 -3.3400 0.0000 0.0000 0.0000

  Magnitude of rotation for focal length change and rotation amplitude for focusing of the fifth example (ratio of rotation amplitudes: aF / az = -0.85) Focal length Corresponding position Distance of amplitude of rotation to infinity photography for focusing 28.7 mm 0.0000 5.00 m -0.914, 0 mm 1.6419 3.00 m -1.585, 0 mm 5.4298 2.00 m -2.511, 0 mm 8, 2173 1.50 m-3.545, 0 mm 9,5602 1,00 m -6,056 131,0 mm 10,0000 0, 80 m -8,500 Table 47 which follows gives the numerical data of the cams of the set of focusing lenses of the fifth example, the data being Calculated by interpolation with a spline function from the focus cam sample data shown in the middle portion of Table 46. It should be noted that the meanings of the symbols in Table 47 are the same as

  in the first embodiment.

Table 47

  Digital Cam Values for Focusing Lens of the Fifth Example Focusing Cam Numerals Focal Length Compensation Cam Numerical Values

ANGLE (2) F ANGLE (2) F

-8.5000 0.8210 0.0000

-8.0000 0.7880 0.0000

-7.5000 0.7535 0.0000

-7.0000 0.7174 0.0000

1 0 -6.5000 0.6797 0.0000

-6.0000 0.6403 0.0000

-5,5000 0.5992 0.0000

-5.0000 0.5563 0.0000

-4.5000 0.5114 0.0000

4.0000 0.4644 0.0000

-3,5000 0.4152 0.0000

-3.0000 0.3638 0.0000

-2.5000 0.3100 0.0000

-2.0000 0.2538 0.0000

-1.5000 0.14949 0.0000

-1.0000 0.139 0.0000

-0.5000 0.0682 0.0000

  0.0000 0.0000 28.7000 0.0000 0.0000 28.7000

  0.5000 -0.0728 30.4901 0.5000 -0.7869 30.4901

  1.0000 -0.1504 32.4166 1.0000 -1.5295 32, 4166

  1.5000 -0.2326 34.4256 1.5000 -2.2134 34.4256

  2.0000 -0.3194 36.4414 2.0000 -2.8320 36.4414

  2,5000 -0,4111 38,4264 2,5000 -3,3908 38,4264

  3,0000 -0,5081 40,3764 3,0000 -3,8961 40,3764

  3 0 3.5000 -0.6107 42.2979 3.5000 -4.3504 42.2979

  4.0000 -0.7193 44.2091 4.0000 -4.7526 44.2091

  4,5000 -0,8342 46,1429 4,5000 -5,0984 46,1429

  , 0000 -0,954 48,1532 5,0000 -5,3792 48,1532

  , 5000 -1.0864 50.3168 5.5000 -5.5782 50.3168

  3 5 6.0000 -1.2251 52.7342 6.0000 -5.6706 52.7342

  6,5000 -1,3732 55,4963 6,5000 -5,6363 55,4963

  7.0000 -1.5316 58.7165 7.0000 -5.4517 58.7165

  7.5000 -1.7011 62.5804 7.5000 -5.0846 62.5804

  8.0000 -1.8828 67.4339 8.0000 -4.4806 67.4339

  8,5000 -2,0792 73,9375 8,5000 -3,5284 73,9375

  9.0000 -2.2921 83.5071 9.0000 -1.8748 83.5071

  9,5000 -2,5230 101,5990 9,5000 2,1702 101,5990

  , 0000 -2.7753 131.0000 10.00 10.00 10.9268 131.0000

  The left-hand side of Table 47 shows the numerical value data of the focus cam of the fifth example, and the right-hand portion of Table 47 shows the values for the zoom compensation cam. A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis taken from the numerical values of the focusing cam and the zoom compensation cam, in the angle of rotation range (ANGLE = 0 , 0) to the amplitude of rotation (ANGLE = 10.0), coincides with the displacement location of the second set of lenses calculated with the paraxial data of the upper part of the

table 46.

  Tables 48, 49 and 50 which follow indicate the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Px of the respective sets of images. lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end (F = 28.7 mm), in the middle position (F = 70.0 mm) and at the telephoto end (F = 131.0 mm) in the fifth example. The layout of the respective tables and the meaning of their symbols are the same as in the

first example.

Table 48

  Amplitude DX (rrm) of focus shift in the direction of the optic axis at the wide-angle end (28.7 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) 0.061 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 0,122 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 0,205 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 0,311 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 0,420 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 0,645 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 0.821 3) 0.000 4) 0.000 5) 0.000

  Lens image grandissernent at the wide-angle end (28.7 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,260 3) -0,774 4) 23,411 5) 0.067

  R 10,000 ANG -0.443 1) -0.009 2) -0.256 3) -0.774 4) 23.411 5) 0.067

  R 5,000 ANG -0,914 1) -0,019 2) -0,252 3) -0,774 4) 23,411 5) 0,067

  R 3,000 ANG -1,585 1) -0,033 2) -0,247 3) -0,774 4) 23,411 5) 0,067

  R 2,000 ANG -2,511 1) -0,051 2) -0,241 3) -0,774 4) 23,411 5) 0.067

  R 1,500 ANG -3,545 1) -0,071 2) -0,234 3) -0,774 4) 23,411 5) 0.067

  R 1,000 ANG -6,056 1) -0,116 2) -0,221 3) -0,774 4) 23,411 6) 0,067

  R 0.800 ANG -8.500 1) -0.156 2) -0.210 3) -0.774 4) 23.411 5) 0.067

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (28.7 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,368 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) 1.371 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 1,374 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 1,377 3) 0,000 4) 0,000 5) 0,000 R 2,000 ANG -2,511 1) 0,000 2) 1,382 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 1,386 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 1,396 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) 1.402 3) 0.000 4) 0.000 5) 0.000

  2 dxlda focusing cam at the wide-angle end (28.7 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,141 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,443 1) 0,000 2) -0,133 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,914 1) 0,000 2) -0,128 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,120 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,110 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -0,100 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,080 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.064 3) 0.000 4) 0.000 5) 0.000

  Coefficient of conversion Ya associated with the direction of rotation at the wide-angle end (28.7 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,193 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) -0.183 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -0,175 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,165 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,152 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -0,139 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,112 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.090 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / YxO = 1.03, TaR / YaO = 0.47

Table 49

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (70.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) 0.170 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) 0,337 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) 0,558 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) 0,829 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) 1,096 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) 1,619 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 2.005 3) 0.000 4) 0.000 5) 0.000

  Objective image magnification Pk at the median position (70.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,412 3) -1,159 4) -25,649 5) -0,063

  R 10,000 ANG -0.450 1) -0.009 2) -0.402 3) -1.159 4) -25.649 5) -0.063

  R 5,000 ANG -0,926 1) -0,019 2) -0,392 3) -1,159 4) -25,649 5) -0,063

  R 3,000 ANG -1,603 1) -0,033 2) -0,379 3) -1,159 4) -25,649 5) -0,063

  R 2,000 ANG -2,530 1) -0,052 2) -0,362 3) -1,159 4) -25,649 5) -0,063

  R 1,500 ANG -3,566 1) -0,072 2) -0,346 3) -1,159 4) -25,649 5) -0,063

  R 1,000 ANG -6,065 1) -0,119 2) -0,314 3) -1,159 4) -25,649 5) -0,063

* R 0,800 ANG -8,500 1) -0,161 2) -0,291 3) -1,159 4) -25,649 5) -0,063

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (70.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,867 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) 2.896 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) 2,923 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) 2,959 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) 3,001 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) 3,041 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) 3,113 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8,500 1) 0,000 2) 3,162 3) 0,000 4) 0,000 5) 0,000

  Slope dx / da focus cam at the center position (70.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,390 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) -0.364 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) -0,341 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) -0,311 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) -0,275 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) -0,241 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) -0,181 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) -0.136 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (70.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,119 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) -1.055 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) -0,996 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) -0,920 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) -0,826 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) -0,733 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) -0,565 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.429 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / 'YxO = 1.10, YaR / Yao = 0.38

Table 50

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (131.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) 0.225 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 0,445 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 0,731 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 1,078 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 1,416 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 2,063 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) 2.543 3) 0.000 4) 0.000 5) 0.000

  Lens magnification Ok at the telephoto end (131, 0 mm) of the fifth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,463 3) -1,686 4) -4,049 5) -0,454

  R 10,000 ANG -0.444 1) -0.009 2) -0.450 3) -1.686 4) -4.049 5) -0.454

  R 5,000 ANG -0,914 1) -0,019 2) -0,436 3) -1,686 4) -4,049 5) -0,454

  R 3,000 ANG -1,585 1) -0,033 2) -0,419 3) -1,686 4) -4,049 5) -0,454

  R 2,000 ANG -2,511 1) -0,052 2) -0,398 3) -1,686 4) -4,049 5) -0,454

  R 1,500 ANG -3,545 1) -0,073 2) -0,378 3) -1,686 4) -4,049 5) -0,454

  R 1,000 ANG -6,056 1) -0,122 2) -0,338 3) -1,686 4) -4,049 5) -0,454

  R 0.800 ANG-8.500 1) -0.166 2) -0.309 3) -1.686 4) -4.049 5) -0.454

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (131.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) 7,531 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) 7.650 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 7,763 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 7,905 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 8,070 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 8,222 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 8,493 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 8.671 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focusing cam at the telephoto end (131.0 mm) of the fifth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,529 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) -0.486 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -0,449 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,403 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,350 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -0,304 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,222 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.169 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (131.0 mm) of the fifth example

  R 0,000 ANG 0,000 1) 0,000 2) -3,987 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) -3.721 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -3,487 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -3,187 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -2,825 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -2,503 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -1,885 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -1.465 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: yxR / YxO = 1.15, YaR / Yao = 0.37 As shown in tables 48, 49 and 50, for each focal length, the conversion coefficient yx associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance due to the influence of the slope (dx / da) of the focusing cam. According to Tables 48, 49 and 50, the rate of variation, from the position focused at infinity to the position focused at the nearest location, of the conversion coefficient Ya associated with the rotation is xO, 47 for the wide-angle end (F = 28.7 mm), xO, 38 for the middle position (F = 70.0 mm) and x0.37 for the telephoto end (F = 131, 0 mm). When the number N of divisions of the focusing range during a change of the conversion coefficient Ya of the fifth example is calculated with the formula (a) and is compared with that of the example of the Japanese patent application 5-142475, the numbers Nw, NM and NT of divisions at the wide-angle end, in the median position and at the telephoto end respectively have the following values: example of the Japanese patent application inspection n 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 fifth example

NW> 4.2 NM> 5.3 NT> 5.5

  Accordingly, although the zoom lens of this embodiment has a greater focal length variation ratio than the example of Japanese Patent Application Laid-open No. 5,14,275, the

  values of the numbers N of divisions decrease.

  As previously described, in the fifth example, since the rate of change of the conversion coefficient Ya associated with the rotation is smaller than that of the conventional system, the values of the division numbers N become small. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient I can be reduced, and the storage capacity can

also be deleted.

  Tables 51, 52 and 53 show the results of the calculation of the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 28.7 mm), in the median position (F = 70.0 mm) and at the telephoto end (F = 131.0 mm) in the fifth example. The provisions and symbols of the tables are the same as in the first example. The position of the focusing lenses of the first pair of the two parts

  of each of Tables 51, 52 and 53, that is,

  say the third and fourth columns, is (R, ANGLE) = (0,0; 0,0) and indicates that this position corresponds to infinity. Similarly, the position of the lenses of the fourth pair for the two lower parts of each of the tables 51, 52 and 53, ie the ninth and tenth columns, is (R, ANGLE) = (0, 8; -8,5), and indicates that the position corresponds to the focused position

  at the shortest distance (R = 0.8 m).

Table 51

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (}) at the wide-angle end (28.7 mm) of the fifth example f = 28.7 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,443 5,000 -0,914 3,000 - 1,585

POS R rs r rs r rs

  1 0.000 -0.193 0.000 -0.187 -0.182 -0.176

  2 10,000 -0.188 -0.183 0.000 -0.178 -0, 173

  3 5,000 -0,184 -0,179 -0,175 0,000 -0,170

  4 3,000 -0,179 -0,175 -0,171 -0,165 0,000

2,000 -0,173 -0,169 -0,165 -0,159

  6 1,500 -0,166 -0,162 -0,158 -0,153

  7 1,000 -0,152 -0,148 -0,144 -0,139

  8 0.800 -0.139 -0.136 -0.132 -0.127

POS R bf f bf f bf bf

  1 0,000 0.00 0.00 -0.08 3.59 -0.17 4.33 -0.28 4, 30

  2 10,000 0.08 3.44 0.00 0.00 -0.08 4.87 -0.20 4, 37

  3 5,000 0.17 3.74 0.08 4.39 0.00 0.00 -0.11 4, 13

  4 3,000 0.28 4.12 0.20 4.75 0.11 4.95 0.00 0.00

  5 2,000 0.43 4.25 0.35 4.58 0.26 4.43 0.15 3, 85

  6 1,500 0.59 4.32 0.50 4.52 0.42 4.36 0.30 4. 02

  7 1,000 0.92 4.32 1.83 4.37 0.74 4.21 0.62 3.95

  8 0.800 1.18 4.26 1.09 4.25 1.00 4.09 0.88 3.85

  (R, ANGLE) = 2,000 -2,511 1,500 -3,545 1,000 -6,056 0,800 -8,500

POS R rs r rs r rs

  I 0.000 -0.168 -0.160 -0.134 -0, 129

  2 10,000 -0.165 -0.157 -0.140 -0, 126

  3 5,000 -0,162 -0,154 -0,137 -0,124

  4 3,000 -0.157 -0.150 -0.134 -0, 120

  5 2,000 -0,152 0,000 -0,145 -0,129 -0,116

  6 1,500 -0,146 -0,139 0,000 -0,123 -0,111

  7 1,000 -0,133 -0,126 -0,112 0,000 -0, 100

  8 0.800 -0.121 -0.115 -0.102 -.090 0.000

POS R bf f bf f bf t bf!

  1 0.000 -0.42 3.93 -0.57 3.75 -0.86 3.11 -1.10 2, 57

  2 10,000 -0.34 3.93 -0.49 3.75 -0.79 3.10 -1.02 2.55

  3 5,000 -0.26 3.86 -0.41 3.72 -0.71 3.07 -0.94 2, 53

  4 3,000 -0.15 3.93 -0.29 3.74 -0.60 3.05 -0.83 2, 51

  2,000 0.00 0.00 -0.15 3.67 -0.46 3.01 -0.69 2.47

  6 1,500 0.15 4.08 0.00 0.00 -0.31 2.98 -0.55 2.42

  7 1,000 0.47 3.77 0.32 3.39 0.00 0.00 -0.24 2, 28

  8 0.800 0.73 3.64 0.57 3.32 0.25 2.76 0.00 0.00

  Condition corresponding to the values: Ka0dYa0 = 0.72, KaR / YaR = 1.43

Table 52

  Coefficients of conversion Ka: (rs), ya (r) associated with direction of rotation and correction coefficient IJp: () at the median position (70.0 mm) of the fifth example f = 70.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.450 5,000 -0.926 3,000 -1, 603

POS R rs r rs r rs

  1 0.000 -1.119 0.000 -1.072 -1.028 -0, 972

  2 10,000 -1,100 -1,054 0,000 -1,012 -0, 957

  3 5,000 -1,082 -1,038 -0,996 0,000 -0,942

  4 3,000 -1,058 -1,015 -0,974 -0,920 0, 000

2,000 -1,026 -0,984 -0,943 -0,890

  6 1,500 -0,990 -0,949 -0,909 -0,857

  7 1,000 -0,910 -0.871 -0.834 -0, 785

  8 0.800 -0.838 -0.801 -0.766 -0, 721

POS R bf i bf t bf t bf i

  1 0.000 0.00 0.00 -0.48 28.69 -0.95 29.67 -1.56 27, 46

  2 10,000 0.50 29.37 0.00 0.00 -0.48 30.46 -1.10 27, 41

  3 5,000 1.00 30.48 0.49 31.49 0.00 0.00 -0.64 26, 87

  4 3,000 1.70 31.28 1.17 31.44 0.66 29.58 0.00 0, 00

  5 2,000 2.60 31.19 2.05 30.52 1.51 28.41 0.82 25.31

  6 1,500 3,53 30.62 2.96 29.52 2.40 27.43 1.68 24, 59

  7 1,000 5.52 29.52 4.89 28.14 4.28 26.27 3.50 23, 89

  8 0.800 7.12 28.34 6.45 26.89 5.80 25.15 4.97 22.94

  (R, ANGLE) = 2,000 -2,530 1,500 -3,566 1,000 -6,065 0,800 -8,500

2 5 POS R rs r rs r rs

  1 0.000 -0.905 -0.838 -0.712 -0.619

  2 10,000 -0.890 -0.825 -0.700 -0, 608

  3 5,000 -0.875 -0.810 -0.687 -0, 596

  4 3,000 -0.854 -0.790 -0.669 -0, 580

  3 0 5 2,000 -0,825 0,000 -0,763 -0,645 -0,558

  6 1,500 -0.794 -0.733 0.000 -0.620 -0.535

  7 1,000 -0,727 -0,671 -0,565 0,000 -0,483

  8 0.800 -0.666 -0.613 -0.512 -0.429 0, 000

POS R bf i bf t bf bf t

  3 5 1 0.000 -2.29 23.87 -2.99 20.88 -4.32 16.56 -5.26 11.91

  2 10,000 -1.85 23.60 -2.57 20.65 -3.93 16.44 -4.89 11, 77

  3 5,000 -1.40 23.18 -2.14 20.37 -3.53 16.31 -4.51 11, 62

  4 3,000 -0.79 22.62 -1.55 20.02 -2.99 16.15 -4.00 11, 40

  2,000 0.00 0.00 -0.79 19.72 -2.28 15.99 -3.33 11.09

  6 1,500 0.82 21.68 0.00 0.00 -1.55 15.76 -2.64 10.68

  7 1,000 2.57 21.49 1.68 19.69 0.00 0.00 -1.18 9, 34

  8 0.800 3.98 20.57 3.03 18.48 1.25 13.30 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.75, KaR / 7aR = 1.44

Table 53

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the telephoto end (131.0 mm) of the fifth example f = 131.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,444 5,000 -0,914 3,000 -1,585

POS R rs r rs r rs

  1 0.000 -3.987 0.000 -3.747 -3.528 - 3.244

  2 10,000 -3.960 -3.721 0.000 -3.505 - 3.222

  3 5,000 -3,937 -3,700 -3,486 0,000 - 3,223

  4 3,000 -3,912 -3,676 -3,460 -3,187 0,000

2,000 -3,867 -3,628 -3,408 -3,133

  6 1,500 -3,820 -3,579 -3,358 - 3,084

  7 1,000 -3,694 -3,449 -3,225 - 2,951

  8 0.800 -3.559 -3.314 -3.089 -2.817

POS R bf t bf t bf! bf t

  1 0.000 0.00 0.00 -1.66 238.31 -3.23 269.89 -5.17 214.29

  2 10,000 1.76 265.93 0.00 0.00 -1.65 312.86 -3.70 212.69

  3 5,000 3.60 291.17 1.74 306.89 0.00 0.00 -2.16 190.70

  4 3,000 6.20 330.11 4.20 341.66 2.32 309.47 0.00 0.00

  5 2,000 9.71 324.29 7.50 300.51 5.44 242.93 2.90 170.05

  6 1,500 13.54 324.29 11.10 291.16 8.83 239.30 6.04 186.38

  7 1,000 22.37 304.43 19.36 264.93 16.58 221.31 13.19 178.19

  8 0.800 30.25 282.38 26.70 243.82 23.44 205.79 19.48 167.68

  (R, ANGLE) = 2,000 -2,511 1,500 -3,545 1,000 -6,056 0,800 -8,500

2 5 POS R rs r rs r rs

  1 0,000 -2,956 -2,677 -2,179 - 1,843

  2 10,000 -2,933 -2,655 -2,157 - 1,822

  3 5,000 -2,910 -2,632 -2,134 - 1,801

  4 3,000 -2,872 -2,596 -2,101 - 1,770

  5 2,000 -2,825 0,000 -2,552 -2,057 - 1,728

  6 1,500 -2,779 -2,503 0,000 -2,007 - 1,681

  7 1,000 -2,645 -2,368 -1,885 0,000 - 1,570

  8 0.800 -2.513 -2.242 -1.772 -1.465 0, 000

POS R bf f bf t bf f bf a

  1 0.000 -7.42 160.41 -9.49 136.07 -13.19 84.53 -15.67 60.76

  2 10,000 -6.06 158.48 -8.23 135.46 -12.11 83.74 -14.68 60.22

  3 5,000 -4.65 154.27 -6.92 134.36 -10.97 82.79 -13.66 59.63

  4 3,000 -2.66 159.56 -5.09 135.99 -9.39 81.71 -12.24 58.86

  2,000 0.00 0.00 -2.64 132.76 -7.29 79.55 -10.35 57.65

  6 1,500 2,877 174.97 0.00 0.00 -5.04 77.61 -8.33 56.46

  7 1,000 9.37 146.92 5.95 110.57 0.00 0.00 -3.84 53.43

  8 0.800 15.05 136.47 11.11 106.51 4.33 72.66 0.00 0.00

  Condition corresponding to the values: KaO / YaO = 0.89, KaR / YaR = 1.26 The results of the calculation of the rate of variation of Ka as a function of Ya for the set focused at infinity and the set focused at the shortest distance at the wide-angle end, in the middle position and at the telephoto end of the example of Japanese Patent Application Laid-open No. 5-142475 and the fifth telephoto end

  example of the invention are as follows.

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity KaoIYao Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50.0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Fifth example At infinity Kao / yao Nearest KaR / YaR Wide angle (F = 28.7) 0.72 1, 43 Median position (F = 70, 0) 0.75 1.44 Telephoto (F = 131.0) 0.89 1.26 As previously described, in the fifth example, as the rate of variation of Ka with respect to ya is weak compared to the classical system, the contribution of the correction term (ABf /) in the relation Ka = Ya (1 - ABf / p) can be reduced. For this reason, the error of the conversion coefficient Ka calculated as a function of Ya and y or the error on the actual driving amplitude Aa of lenses obtained with a single pair of values of the conversion coefficient Ya and the coefficient of correction

M can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and the fifth example of the invention, when the driving amplitudes of the lenses during focusing of the set focused to infinity to the object at the smallest distance and when focusing the focused assembly at the smallest distance to the object at infinity at the wide-angle end, the middle position and at the telephoto end are calculated from Aa = ABf / Ya (1 ABf / 9) and the errors on the actual driving amplitudes of the lenses are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the set focused at infinity on the object at the smallest distance has the value of the object distance (POS-5) and the value of the correction coefficient y when focusing the focused set to the smallest distance to the object at infinity takes the

  value corresponding to the object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Fifth example Infinity focused state most Nearest near-state Focused at infinity Wide-angle (F = 28.7) -0.4% -0.0% Median position (F = 70.0) -3.0% -1.3% Telephoto (F = 131.0) -1.6% -0.6% As previously described, in the fifth example, even when only a pair of values of the conversion coefficient γ and the correction coefficient γ are set for a given range of the set of lenses , an error existing between the conversion coefficient Ka calculated from ta and y and the lens driving amplitude Aa for focusing becomes low compared to the conventional system and the focusing can be achieved with

increased accuracy.

  Table 54 indicates the manually focusing amplitude (ANGLE DA) with the focusing cam (middle part of table 46) of the fifth example, the displacement amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses corresponding to the focusing amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the direction of the axis

optical is determined.

  It should be noted that the layout and the symbols of the table are the same as in the first example. The upper part of table 54 indicates the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.8 m ) for the respective states of variation of the focal lengths (F = 28.7, 35.0, 50.0, 70.0, 105.0 and 131.0 mm), and the middle part indicates the values of the amplitude of rotation (ANGLE DA) for focusing necessary to obtain the optimum state of focus for the respective distances of photography. The lower part indicates the magnitudes of displacement (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the focusing amplitude (ANGLE DA) with the focal lengths and photographing distances.

Table 54

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the fifth example 0.80 m 1.00 m 1.50 m 2.00 m 3.00 m 5.00 m 28.700 Bf 0.000 0,000 0,000 0,000 0, 000 0,000, 000 Bf 0,000 -0,001 -0,004 -0,006 -0,008 -0,006 50,000 Bf 0,000 -0,011 -0,013 -0,009 -0,004 -0,003, 000 Bf 0,000 0.005 0.015 0.015 0.016 0.012, 000 Bf 0.000 0.020 0.031 0.032 0.028 0.017 131,000 Bf 0,000 0,000 0,000 0, 000 0,000 0,000

  ANGLE DA -8,500 -6,056 -3,545 -2,511 -1,585 -0,914

  F 28,700 DX 0,000 0,821 0,000 0,000 0,000 R 0,80 m F 35,000 DX 0,000 0,964 0,000 0,000 0,000 R 0,80 m F 50,000 DX 0,000 1,439 0,000 0,000 0,000 R 0.80 m F 70,000 DX 0,000 2,005 0,000 0,000 0,000 R 0.80 m F 105,000 DX 0.000 2,392 0,000 0,000 0,000 R 0,80 m F 131,000 DX 0,000 2,543 0,000 0,000 0,000 R 0,80 m F 28,700 DX 0,000 0,645 0,000 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,760 0,000 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,152 0,000 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,618 0,000 0,000 0,000 R 1,00 m F 105,000 DX 0,000 1,940 0,000 0,000 0,000 R 1.00 m F 131,000 DX 0,000 2,068 0,000 0,000 0,000 R 1,00 m F 28,700 DX 0,000 0,420 0,000 0,000 0,000 R 1,50 m F 35,000 DX 0,000 0,499 0,000 0,000 0,000 R 1,50 m F 50,000 DX 0,000 0,769 0,000 0.000 0.000 R 1.50 m F 70.000 DX 0.000 1.091 0.000 0.000 0.000 R 1.50 m F 105.000 DX 0.000 1.323 0.000 0.000 0.000 R 1.50 m F 131.000 DX 0.000 1.416 0.000 0.000 0.000 R 1.50 m F DX 0.000 0.311 0.000 0.000 0.000 R 2.00 m F 28.700 DX 0.000 0.373 0, 000 0.000 0.000 R 2.00 m F 35,000 DX 0.000 0.576 0.000 0.000 0.000 R 2.00 m F 50, 000 DX 0.000 0.824 0.000 0.000 0.000 R 2.00 m F 70, 000 DX 0.000 1.004 0.000 0.000 0.000 R 2.00 m F 105, 000 DX 0.000 1.078 0.000 0.000 0.000 R 2.00 m

131,000

  F 28,700 DX 0,000 0,205 0,000 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,249 0,000 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,383 0,000 0,000 0,000 R 3,00 m F 70, 000 DX 0,000 0,552 0,000 0,000 0,000 R 3.00 m F 105, 000 DX 0.000 0.679 0.000 0.000 0.000 R 3.00 m F 131.000 DX 0.000 0.731 0.000 0.000 0.000 R 3.00 m F 28, 700 DX 0.000 0.122 0.000 0.000 0.000 R 5.00 m F 35, 000 DX 0.000 0.149 0.000 0.000 0.000 R 5.00 m F 50, 000 DX 0.000 0.230 0.000 0.000 0.000 R 5.00 m F 70, 000 DX 0.000 0.333 0.000 0.000 0.000 R 5.00 m F 105.000 DX 0.000 0.413 0.000 0.000 0.000 R 5.00 m F 131.000 DX 0.000 0.445 0.000 0.000 0.000 R 5.00 m As shown in Table 54, in the zoom lens of the fifth example, the so-called "manual" focusing can be achieved since the movement amplitudes of the image point at the respective focal distances and photography distances are very small and enter the depth of field regardless of the focus state and the

distance of photography.

  Sixth Embodiment The sixth embodiment or sixth example relates to a zoom lens having a four-set arrangement, i.e. positive, negative, positive and positive lens assemblies, with focus to

  using a second set of negative type lenses.

  For this purpose, the ratio (aF / az) of the focusing rotation amplitudes of the position focused at infinity to the nearest position (R = 0.5 mm) and the amplitude of rotation of distance variation focal length of the wide-angle end (F = 28.8 mm) at the telephoto end

(F = 103.0 mm) is set at -0.80.

  The following table 55 indicates various paraxial data of the optical system and data allowing the definition of the configuration of a focusing cam.

in the sixth example.

  The upper part of table 55 gives the focal lengths and intervals of the main points of the respective sets of lenses of the optical system of the sixth example with six focusing states (focal lengths

  F = 28.8, 35.0, 50.0, 70.0, 85.0 and 103.0 mm).

  The middle part of Table 55 shows the spline sampling data when the focus cam configuration of the second lens set of the sixth example, used for focusing, is represented by a spline function associated with the angle a of rotation of a rotating barrel and at the amplitude x of

  displacement in the direction of the optical axis.

  In addition, the lower part of table 55 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85 , 0 and 103.0 mm) and the rotational amplitudes (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0 , 7 and 0.5 m) using the focusing cam of the sixth example. In the lower part of Table 55, as the amplitude of rotation for the focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 103.0 mm) is set at 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 0.5 mm) is -8.0, the ratio (aF / az) focusing and variation amplitudes of

* focal length of the sixth example is equal to -0.80.

Table 55

  Sixth example f = 28.8 to 103.0 (ratio of amplitudes of rotation: aF / az = -0.8) Focal distances and intervals of the main points of the objectives of the sixth example

  F 28,8000 35,0000 50,0000 70,0000 85,0000 103,0000

  F1 74,0000 D1 9,3999 13,5341 20,7443 27,2220 30,8921 34,4309

  F2 -14,6500 D2 19,7436 17,2131 13,2504 10,0511 8,3204 6,5915

  F3 39,0000 D3 18,6578 18,1057 17.0929 16.2060 15.8259 15.5510

  F4 51.0000 D4 51.5373 55.7437 63.9000 71.6679 75.7659 79.3156

  Focusing cam shape (spline interpolated point) corresponding to the sixth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.3850 0.0000 0.0000

  2 -10.0000 0.0000 1.3095 0.0000 0.0000

  3 -8,0000 0.0000 1,1334 0.0000 0.0000

  4 -4.8586 0.0000 0.7860 0.0000 0.0000

-3,0690 0.0000 0.5389 0.0000 0.0000

  6 -1.3807 0.0000 0.2633 0.0000 0.0000

  7 -0.8909 0.0000 0.1743 0.0000 0.0000

  8 -0.5213 0.0000 0.1040 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,0000 0.0000 -0.4569 0.0000 0.0000

  11 5,1414 0.0000 -1.4493 0.0000 0.0000

  12 6.9310 0.0000 -2.2575 0.0000 0.0000

  13 8.6193 0.0000 -3.3154 0.0000 0.0000

  14 9,1091 0.0000 -3,7092 0.0000 0.0000

9,4787 0.0000 -4.0447 0.0000 0.0000

  16 10.0000 0.0000 -4.5918 0.0000 0.0000

  17 11.0000 0.0000 -5.8900 0.0000 0.0000

  Rotation amplitude for focal length change and rotation amplitude for focus of the sixth example (ratio of rotation amplitudes: aF / az = -0.8) Focal length Corresponding position Distance of amplitude of rotation at infinity photography for focusing 28.8 mm 0.0000 5.00 m -0.521, 0 mm 1.7158 3.00 m -0.891, 0 mm 4.7378 2.00 m -1.381, 0 mm 7, 3846 1.00 m -3.069, 0 mm 8.7811 0.70 m -4.859 103.0 mm 10.0000 0.50 m -8.000 The following table 56 gives the numerical value data of the cams of the focus lens assembly of the sixth example. data being calculated by interpolation using a spline function using the sampling data of the cam of

  focus in the middle part of Table 55.

  It should be noted that the meaning of the symbols in the table

  56 is the same as the first example.

Table 56

  Digital Cam Values for Focusing Lens of the Sixth Example Focusing Cam Digital Values Focal Length Variation Compensation Cam Numerals

ANGLE (2) F ANGLE (2) F

-8.0000 1.1334 0.0000

-7.5000 1.0842 0.0000

-7.0000 1.0329 0.0000

-6.5000 0.9794 0.0000

-6.0000 0.9235 0.0000

-5.5000 0.8650 0.0000

-5.0000 0.8039 0.0000

4.5000 0.7398 0.0000

-4.0000 0.6727 0.0000

-3.5000 0.6023 0.0000

-3.0000 0.5285 0.0000

-2.5000 0.4511 0.0000

-2.0000 0.3698 0.0000

-1.5000 0.2844 0.0000

2 0 -1.0000 0.1945 0.0000

-0.5000 0.0998 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.1051 30.4738 0.5000 0.3770 30.4738

  1.0000 -0.2159 32.2530 1.0000 0.8059 32.2530

  1,5000 -0,3329 34,1462 1,5000 1,2864 34,1462

  2.0000 -0.4569 36.1602 2.0000 1.8172 36.1602

  2,5000 -0,5884 38,3049 2,5000 2,3973 38,3049

  3.0000 -0.7284 40.5988 3.0000 3.0271 40.5988

  3,5000 -0,8780 43,0618 3,5000 3,7070 43,0618

  3 4.0000 -1.0382 45.7122 4.0000 4.4367 45.7122

  4.5000 -1.2101 48.5665 4.5000 5.2146 48.5665

  , 0000 -1,3946 51,6399 5,0000 6,0380 51,6399

  , 5000 -1.5930 54.9443 5.5000 6.9027 54.9443

  6,0000 -1,8073 58,5082 6,0000 7,8072 58,5082

  3 5 6,5000 -2,0401 62,3662 6,500 8,7495 62,3662

  7.0000 -2.2938 66.5452 7.0000 9.7240 66.5452

  7.5000 -2.5720 71.0842 7.5000 10.7252 71.0842

  8.0000 -2.8809 76.0754 8.0000 11.7551 76.0754

  8.5000 -3.2267 81.6155 8.5000 12.8115 81.6155

  9.0000 -3.6169 87.7918 9.0000 13.8860 87.7918

  9.5000 -4.0652 94.8156 9.5000 14.9837 94.8156

  , 0000 -4,5918 103,0000 10,0000 16,1112 103,0000

  The left part of Table 56 shows the numerical values of the focusing cam of the sixth example and

  the right part that of the zoom compensation cam.

  A value obtained by synthesizing the amplitudes of

  (2) in the direction of the optical axis from the numerical values of the focusing cam and the zoom compensation cam, in the range from rotation amplitude (ANGLE = 0.0), to amplitude of rotation (ANGLE = 10,0) coincides with the place of displacement of the second set of lenses calculated with the data

  of the upper part of Table 55.

  The following tables 57, 58 and 59 indicate the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Ax of the respective sets of lenses, the coefficient of Yx conversion associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end (F = 28.8 mm) , in the middle position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the sixth example. The provisions and meaning of the symbols in the tables are

  the same as in the first example.

Table 57

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 0,052 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 0,104 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 0,174 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 0,263 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 0,539 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 0.786 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.133 3) 0.000 4) 0.000

  P3k magnification of lenses at the wide-angle end (28.8 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,293 3) 125,947 4) -0,011

  R 10,000 ANG -0,256 1) -0,008 2) -0,290 3) 125,947 4) -0,011

  R 5,000 ANG -0.521 1) -0.015 2) -0.286 3) 125.947 4) - 0.011

  R 3,000 ANG -0,891 1) -0,026 2) -0,281 3) 125,947 4) -0,011

  R 2,000 ANG -1,381 1) -0,041 2) -0,275 3) 125,947 4) -0,011

  R 1,000 ANG -3,069 1) -0,090 2) -0,257 3) 125,947 4) -0,011

  R 0.700 ANG -4.859 1) -0.141 2) -0.240 3) 125.947 4) -0.011

  R 0.500 ANG -8.000 1) -0.227 2) -0.216 3) 125.947 4) - 0.011

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (28.8 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,609 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 1,613 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 1,617 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 1,621 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 1,627 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 1,645 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 1.660 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.679 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the wide-angle end (28.8 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,205 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,200 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,194 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -0,187 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -0,177 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,150 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.127 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.096 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.8 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,330 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,322 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,314 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -0,302 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -0,289 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,247 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.211 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.162 3) 0.000 4) 0.000

  Condition corresponding to the values: YXR / Yxo = 1.04, YaR / Yao = 0.49

Table 58

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the middle position (50.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) 0.092 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) 0,184 3) 0,000 4) 0,000

  R 3,000 ANG -0.886 1) 0.000 2) 0.307 3) 0.000 4) 0.000

  R 2,000 ANG -1,375 1) 0,000 2) 0,460 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) 0,922 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) 1.321 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.864 3) 0.000 4) 0.000

  13k image magnification of lenses at the median position (50.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,379 3) 7,039 4) -0,253

  R 10,000 ANG -0.255 1) -0.008 2) -0.373 3) 7.039 4) - 0.253

  R 5,000 ANG -0,519 1) -0,015 2) -0,367 3) 7,039 4) -0,253

  R 3,000 ANG -0,886 1) -0,026 2) -0,359 3) 7,039 4) -0,253

  R 2,000 ANG -1,375 1) -0,041 2) -0,348 3) 7,039 4) -0,253

  R 1,000 ANG -3,068 1) -0,091 2) -0,317 3) 7,039 4) -0,253

  R 0.700 ANG -4.862 1) -0.145 2) -0.289 3) 7.039 4) - 0.253

  R 0.500 ANG -8.000 1) -0.238 2) -0.252 3) 7.039 4) -0.253

  Coefficient of conversion Yx associated with the direction of the optical axis at the median position (50.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,714 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) 2.729 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) 2,744 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) 2,763 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) 2,786 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) 2,853 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) 2.905 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 2.969 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,368 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.355 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) -0,342 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) -0,325 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) -0,304 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) -0,246 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) -0.202 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.147 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (50.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.969 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) -0,939 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) -0,897 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) -0,846 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) -0,701 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) -0.588 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.438 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / YxO = 1.09, YaR / YaO = 0.44

Table 59

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (103.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 0,281 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 0,547 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 0,883 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 1,276 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 2,334 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 3.143 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 4.135 3) 0.000 4) 0.000

  Ek image magnification of lenses at the telephoto end (103, 0 mm) of the sixth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,588 3) 4,264 4) -0,555

  R 10,000 ANG -0,256 1) -0,008 2) -0,569 3) 4,264 4) - 0,555

  R 5,000 ANG -0,521 1) -0,015 2) -0,551 3) 4,264 4) -0,555

  R 3,000 ANG -0,891 1) -0,027 2) -0,528 3) 4,264 4) -0,555

  R 2,000 ANG -1,381 1) -0,041 2) -0,501 3) 4,264 4) -0,555

  R 1,000 ANG -3,069 1) -0,094 2) -0,429 3) 4,264 4) -0,555

  R 0.700 ANG -4.859 1) -0.151 2) -0.373 3) 4.244 4) - 0.555

  R 0.500 ANG -8.000 1) -0.255 2) -0.306 3) 4.244 4) -0.555

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (103.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) 3,668 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 3,792 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 3,906 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 4,045 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 4,200 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 4,576 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 4.824 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 5.082 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (103.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,152 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -1,048 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,960 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -0,859 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -0,754 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,524 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.390 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.255 3) 0.000 4) 0.000

  2 0 Conversion coefficient Ya associated with the direction of rotation at the telephoto end (103.0 mm) of the sixth example

  R 0,000 ANG 0,000 1) 0,000 2) -4,225 3) 0,000 4) 0,000

  R 10,000 ANG -0.256 1) 0.000 2) -3.975 3) 0.000 4) 0.000

  R 5,000 ANG -0,521 1) 0,000 2) -3,749 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -3,474 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -3,168 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -2,396 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -1.883 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -1.297 3) 0.000 4) 0.000

  3 0 Condition corresponding to the values: yxR / Yxo = 1.39, YaR / Yao = 0, 31 As indicated in tables 57, 58 and 59, for each focal length, the conversion coefficient yx associated with the direction of the The optical axis increases, but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya of rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the photographing distance becomes smaller. closer to the smaller distance due to the slope (dx / da) of the focusing cam. In tables 57, 58 and 59, the rate of change, from the position focused at infinity to the position focused at the nearest location, of the conversion coefficient Ya associated with the rotation is xO, 49 to wide-angle end (F = 28.8 mm), xO, 44 at the center position (F = 50.0 mm), and x0.31 at the telephoto end (F = 103.0 mm). When the number N of divisions of the focusing range, upon a change of the conversion coefficient Ya in the sixth example, is calculated with the formula (a) and compared with the example of the Japanese patent application 5-142475, the numbers Nw, NM and NT of divisions at the wide-angle end, in the median position and at the telephoto end respectively have the following values: example of the Japanese patent application inspection n 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 sixth example Nw> 3.9 NM> 4.5 NT> 6.5 Therefore, as indicated by the comparison which precedes, although the zoom lens of this example has a greater focal length variation ratio than that of the example of Japanese Patent Application Laid-open No. 5-142475, the values of the numbers N

  On the contrary, divisions are reduced.

  As described above, in the sixth example, since the rate of change of the conversion coefficient Ya associated with the rotation is lower than that of the conventional system, the values of the numbers N of the divisions become small. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y can be reduced, and the capacity of

  memorisation can also be deleted.

  Tables 60, 61 and 62 show the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 28.8 mm), in the median position (F = 50, 0 mm) and at the telephoto end (F = 103.0 mm) in the sixth example. The layout of the tables and the symbols of them are the same as in the first example. The position of the lenses of the first pair of the two upper parts of each of the tables 60, 61 and 62, i.e. the third and fourth columns, is (R, ANGLE) = (0.0; 0,0) and indicates that this position corresponds to infinity. Similarly, the position of the lenses in the fourth pair of the two lower parts of each of the tables 60, 61 and 62, ie in the ninth and tenth columns, is (R, ANGLE) = (0, 5; -0, 8) and indicates that the position corresponds

  at the closest focusing position (R = 0.5 m).

Table 60

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient pJ: (i) at the wide-angle end (28.8 mm) of the sixth example f = 28.8 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,256 5,000 -0,521 3,000 -0,891

POS R rs r rs r rs

  1 0,000 -0.330 0.000 -0.325 -0.320 -0, 313

  2 10,000 -0.327 -0.322 0.000 -0.317 -0, 310

  3 5,000 -0,324 -0,319 -0,314 0,000 -0,307

  4 3,000 -0.320 -0.314 -0.309 -0.302 0, 000

2,000 -0,314 -0,309 -0,304 -0,297

  6 1,000 -0,296 -0,291 -0,286 -0, 280

  7 0.700 -0.278 -0.274 -0.269 -0, 263

  8 0.500 -0.251 -0.246 -0.242 -0, 237

POS R bf t bf i bf i bf t

  1 0,000 0.00 0.00 -0.08 9.38 -0.17 8.77 -0.28 8.30

  2 10,000 0.08 9.79 0.00 0.00 -0.08 8.47 -0.20 8, 17

  3 5,000 0.17 9.59 0.08 9.00 0.00 0.00 -0.11 8, 13

  4 3,000 0.28 9.28 0.20 8.75 0.11 8.37 0.00 0.00

  5 2,000 0.43 9.08 0.35 8.65 0.26 8.36 0.15 8, 21

* 6 1,000 0.91 8.83 0.82 8.54 0.73 8.34 0.61 8, 16

  7 0.700 1.35 8.65 1.26 8.40 1.17 8.21 1.04 8.00

  8 0.500 2.00 8.35 1.91 8.14 1.81 7.96 1.68 7, 74

  (R, ANGLE) = 2,000 -1,381 1,000 -3,069 0,700 -4,859 0.500 -8,000

  2 5 POS R rs r rs r rs r rs i 0,000 -0,304 -0,276 -0,252 -0,218

  2 10,000 -0.301 -0.274 -0.250 -0, 216

  3 5,000 -0,298 -0,271 -0,247 -0, 213

  4 3,000 -0.294 -0.267 -0.244 -0, 210

  3 0 5 2,000 -0,289 0,000 -0,263 -0,239 -0,206

  6 1,000 -0,272 -0,247 0,000 -0,225 -0, 193

  7 0.700 -0.255 -0.232 -0.211 0.000 -0, 181

  8 0.500 -0.230 -0.208 -0.189 -0.162.0, 000

POS R bf f bf f bf e bf e

  3 5 1 0.000 -0.42 8.03 -0.85 7.12 -1.22 6.20 -1.74 5.05

  2 10,000 -0.34 7.99 -0.77 7.10 -1.15 6.18 -1.67 5, 04

  3 5,000 -0.26 8.00 -0.69 7.08 -1.07 6.16 -1.60 5, 03

  4 3,000 -0.14 8.03 -0.58 7.06 -0.97 6.13 -1.49 5, 01

  2,000 0.00 0.00 -0.44 7.02 -0.83 6.09 -1.37 4.98

  6 1,000 0.46 7.88 0.00 0.00 -0.40 5.95 -0.95 4, 91

  7 0.700 0.89 7.70 0.41 6.72 0.00 0.00 -0.57 4.87

  8 0.500 1.52 7.44 1.03 6.49 0.59 5.68 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 0.76, KaR / YaR = 1.34

Table 61

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (50.0 mm) of the sixth example f = 50.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.255 5,000 -0.519 3,000 - 0.886

POS R rs r rs r rs

  1 0,000 -1,000 0,000 -0,977 -0,955 -0,925

  2 10,000 -0.992 -0.969 0.000 -0.947 -0, 917

  3 5,000 -0,984 -0,961 -0,939 0,000 -0,909

  4 3,000 -0.972 -0.950 -0.927 -0.897 0, 000

2,000 -0,956 -0,934 -0,912 -0,882

  6 1,000 -0,904 -0,883 -0,861 -0,833

  7 0.700 -0.855 -0.835 -0.814 -0.788

  8 0.500 -0.779 -0.760 -0.741 -0.717

  POS R bf i bf f bf I bf I i 0.000 0.00 0.00 -0.25 30.70 -0.49 29.17 -0.82 27.13

  2 10,000 0.25 32.48 0.00 0.00 -0.25 28.77 -0.58 26, 77

  3 5,000 0.51 31.82 0.25 30.33 0.00 0.00 -0.33 26, 42

  4 3,000 0.86 31.10 0.60 29.50 0.34 27.98 0.00 0.00

  2 0 5 2,000 1.31 30.35 1.05 28.84 0.78 27.43 0.43 25.89

  6 1,000 2.77 29.02 2.28 27.80 2.20 26.69 1.82 25, 43

  7 0.700 4.16 28.74 3.85 27.69 3.54 26.73 3.13 25.64

  8 0.500 6.23 28.16 5.88 27.22 5.54 26.35 5.10 25.31

  (R, ANGLE) = 2,000 -1,375 1,000 -3,068 0,700 -4,862 0,500 -8,000

2 5 POS R rs r rs r rs

  1 0.000 -0.887 -0.778 -0.690 -0, 577

  2 10,000 -0.880 -0.772 -0.684 -0, 571

  3 5,000 -0.872 -0.764 -0.678 -0, 566

  4 3,000 -0.861 -0.754 -0.669 -0, 558

  3 0 5 2,000 -0,846 0,000 -0,741 -0,658 -0,549

  6 1,000 -0,799 -0,701 0,000 -0,621 -0,517

  7 0.700 -0.755 -0.662 -0.588 0.000 -0.487

  8 0.500 -0.687 -0.601 -0.530 -0.437 0, 000

POS R bf f bf t bf t bf

  1 0.000 -1.22 25.05 -2.39 21.48 -3.36 19.17 -4.61 14, 50

  2 10,000 -0.99 24.78 -2.17 21.44 -3.15 15.16 -4.43 14, 47

  3 5,000 -0.75 24.54 -1.95 21.42 -2.94 19.17 -4.23 14, 43

  4 3,000 -0.42 24.22 -1.65 21.44 -2.66 19.20 -3.97 14, 38

  2,000 0.00 0.00 -1.25 21.56 -2.29 19.26 -3.63 14.31

  6 1,000 1.35 24.18 0.00 0.00 -1.11 19.40 -2.55 13.98

  7 0.700 2.63 24.52 1.19 21.75 0.00 0.00 -1.53 13.56

  8 0.500 4.55 24.15 2.96 20.82 1.66 17.09 0.00 0.00

  Condition corresponding to the values: KaO / yaO = 0.78, KaR / YaR = 1.32

Table 62

  Coefficients of conversion Ka: (rs), ya: (r) associated with direction of rotation and correction coefficient p: (i) at the telephoto end (103.0 mm) of the sixth example f = 103.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,256 5,000 -0,521 3,000 -0,891

POS R rs r rs r rs

  I 0.000 -4.224 0.000 -3.988 -3.772 -3, 516

  2 10,000 -4,215 -3,975 0,000 -3,759 -3, 504

  3 5,000 -4,203 -3,963 -3,748 0,000 -3, 492

  4 3,000 -4,190 -3,949 -3,734 -3,474 0, 000

2,000 -4,171 -3,929 -3,711 -3,450

  6 1,000 -4,105 -3,857 -3,634 -3, 370

  7 0.700 -4.028 -3.774 -3.548 -3, 280

  8 0.500 -3.876 -3.615 -3.385 -3, 115

POS R bf f bf t bf f bf t

  1 0.000 0.00 0.00 -1.02 312.42 -1.97 301.80 -3.13 255.83

  2 10,000 1.08 500.78 0.00 0.00 -1.00 329.94 -2.23 258.19

  3 5,000 2.19 442.39 1.05 361.69 0.00 0.00 -1.29 242.76

  4 3,000 3.73 460.62 2.51 392.96 1.38 368.87 0.00 0.00

  2 0 5 2,000 5.76 458.69 4.42 381.87 3.19 325.33 1.69 249.97

  6 1,000 12.60 446.74 10.85 364.97 9.26 305.35 7.34 245.42

  7 0.700 19.57 421.02 17.37 343.62 15.39 287.87 13.01 233.41

  8 0.500 31.01 376.35 28.00 309.72 25.32 261.52 22.15 214.52

  (R, ANGLE) = 2,000 -1,381 1,000 -3,069 0,700 -4,859 0.500 -8,000

2 5 POS R rs r rs r rs

  1 0.000 -3.233 -2.555 -2.106 -1, 621

  2 10,000 -3.220 -2.542 -2.094 -1, 610

  3 5,000 -3,207 -2,529 -2,081 -1, 598

  4 3,000 -3.188 -2.510 -2.064 -1, 583

  5 2,000 -3,167 0,000 -2,486 -2,041 - 1,562

  6 1,000 -3,081 -2,396 0,000 -1,962 -1, 493

  7 0.700 -2.989 -2.313 -1.883 0.000 -1, 422

  8 0.500 -2.825 -2.159 -1.740 -1.297 0.000

POS R bf I bf i bf i bf f

  1 0.000 -4.46 216.27 -7.84 118.59 -10.23 86.34 -12.96 51.92

  2 10,000 -3.62 218.89 -7.15 117.79 -9.64 86.06 -12.47 51.66

  3 5,000 -2.76 219.81 -6.44 116.67 -9.03 85.72 -11.95 51.39

  4 3,000 -1.56 235.61 -5.47 115.12 -8.19 85.31 -11.25 51.01

  2,000 0.00 0.00 -4.20 112.21 7.10 84.74 -10.34 50.50

  6 1,000 5.20 191.32 0.00 0.00 -3.51 83.88 -7.36 48.64

  7 0.700 10.40 185.26 4.14 119.18 0.00 0.00 -4.47 46.29

  8 0.500 18.70 172.83 10.65 107.57 5.47 72.05 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.92, KaR / YaR = 1.25 The calculated results of rate of variation of Ka as a function of ya for the set focused at infinity and at the nearest location , at the wide-angle end, in the middle position and at the telephoto end, in the example of Japanese Patent Application Laid-open No. 5-142475 and in the sixth example

of the invention are as follows.

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Kao / Yao Nearest KaRIYaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50.0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0, 43 Sixth example At infinity Kao / yao Nearest KaR / YaR Wide-angle (F = 28.8) 0.76 1, 34 Median position (F = 50.0) 0.78 1.32 Telephoto (F = 103.0) 0.92 1.25 As previously described, in the sixth example, as the rate of variation of Ka with respect to Ya is weak compared to the classical system, the contribution of the correction term (ABf / g) in the relation Ka = Ya (l - ABf /.) can be reduced. For this reason, the error of the conversion coefficient Ka calculated as a function of Ya and i or the error with respect to the actual driving amplitude Aa of lenses obtained with a single pair of values of the conversion coefficient γ and the coefficient

  correction, can be reduced.

  In the embodiment of Japanese Patent Application Laid-open No. 5-142475 and the sixth example of the invention, when the driving amplitudes of the lenses during focusing of the focused assembly to the infinity towards the object at the smallest distance and when focusing with the focused set at the smallest distance to the object at infinity at the wide-angle end, in the middle position and at the end of telephoto, are calculated from the relation Aa = ABf / Ya (1 - ABf / g), the errors with respect to the actual lens drive amplitudes are then calculated and give the following values. It should be noted that the value of the correction coefficient y during the focusing by the set focused to infinity on the object at the smallest distance takes the value of the object distance (POS-5) while the value of the correction coefficient g when focusing with the focused set at the shortest distance on the object at infinity

  takes the value of the object distance (POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Positon median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Sixth example Infinity Focused Most Nearest Near Focused at infinity Wide-angle (F = 28.8) -2.8% -0.3% Median position (F = 50.0) -2.0% -0.1% Telephoto (F = 103.0) - 1.6% -0.4% As previously described, in the sixth example, even when only a pair of values of the conversion coefficient ya and the correction coefficient g are set for a given range of lens arrangements, an error between the conversion coefficient Ka calculated from Ya and y and the lens driving amplitude Aa for focusing becomes low compared to that of the conventional system and the focusing can be achieved with

greater precision.

  Table 63 shows the focusing amplitude (ANGLE DA) during manual focusing with the focusing cam (middle part of table 55) of the sixth example, the displacement amplitude DX (mm) in the direction of the the optical axis of the set of focusing lenses corresponding to the focusing rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  It should be noted that the layout and the symbols of the table are the same as in the first example. The upper part of Table 63 shows the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2n0, 1.0, 0.7 and 0.5 m) at respective focusing states for the focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85.0 and 103.0 mm), and the middle portion indicating the values of the rotation amplitude (ANGLE DA) focusing necessary to obtain an optimal focused state at the respective photography distances. The lower part of the table gives the amplitudes (DX) of displacement in the direction of the optical axis of the respective lens assemblies corresponding to the rotation amplitude (ANGLE DA) for the focusing with the focal lengths and distances of photography.

respectively.

Table 63

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the sixth example 0.50m 0.70m 1.00m 2.00m 3.00m 5.00m 28.800 Bf 0.000 0.000 0.000 0, 000 0,000 0,000, 000 Bf 0,000 0.001 0.001 0.002 0.002 0, 001, 000 Bf 0.000 0.002 -0.001 -0.005 -0.004 -0.003, 000 Bf 0, 000 -0.009 -0.009 -.001 0.001 0.001, 000 Bf 0.000 -0.012 - 0, 005 -0,005 -0,005 -0,002 103,000 Bf 0,000 0,000 0,000 0,000 0,000 0,000

  ANGLE DA -8,000 4,859 -3,069 -1,381 -0,891 -0,521

  F 28,800 DX 0,000 1,133 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,341 0,000 0,000 R 0,50m F 50,000 DX 0,000 1,864 0,000 0,000 R 0,50 m F 70,000 DX 0,000 2,627 0,000 0,000 R 0,50 m F 85,000 DX 0,000 3,273 0,000 0,000 R 0,50 m F 103,000 DX 0,000 4,135 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,786 0,000 0,000 R 0,70 m F 35,000 DX 0,000 0,936 0,000 0,000 R 0,70 m F 50,000 DX 0,000 1,321 0,000 0,000 R 0,70 m F 70,000 DX 0,000 1,910 0,000 0,000 R 0, 70 m F 85,000 DX 0,000 2,427 0,000 0,000 R 0,70 m F 103,000 DX 0,000 3,143 0,000 0,000 R 0,70 m F 28,800 DX 0,000 0.539 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,644 0,000 0,000 R 1,00 m F 50,000 DX 0,000 0,922 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,360 0,000 0,000 R 1,00 m F 85,000 DX 0,000 1,758 0,000 0,000 R 1.00 m F 103,000 DX 0.000 2,334 0,000 0,000 R 1,00 m F 28,800 DX 0,000 0,263 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,316 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,462 0,000 0,000 R 2 , 00 m F 70,000 DX 0,000 0,696 0,000 0,000 R 2,00 m F 85, 000 DX 0,000 0,926 0,000 0,000 R 2,00 m F 103,000 DX 0,000 1,276 0,000 0,000 R 2,00 m F 28,800 DX 0,000 0,174 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,209 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,308 0,000 0,000 R 3,00 m F 70,000 DX 0,000 0,468 0,000 0,000 R 3,00 m F 85,000 DX 0,000 0,630 0,000 0,000 R 3,00 m F 103,000 DX 0,000 0,883 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,104 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,125 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,185 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,283 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,384 0.000 0.000 R 5.00 m F 103, 000 DX 0.000 0.547 0.000 0.000 R 5.00 m As shown in Table 63, in the zoom lens of the sixth example, the so-called "manual" focusing can be achieved because the amplitudes of the image point at the respective focal distances and photography distances are very small and enter the depth of field regardless of the focus state and

distance of photography.

  Seventh Embodiment The seventh embodiment or seventh example relates to a zoom lens having a five-array arrangement, i.e. positive, negative, positive, negative and positive lens sets, and provides focus. using a second set of negative type lenses. For this purpose, the ratio (aF / az) of the focus rotation amplitude of the focused position to infinity and to the position focused at the nearest location (R = 0.5 m) and the Focal length variation rotation amplitude of the wide-angle end (F = 28.8 mm) at the telephoto end

(F = 102.0 mm) is set at -0.72.

  Table 64 which follows indicates various paraxial data of the optical system and data intended to define the configuration of a focusing cam in the

seventh example.

  The upper part of table 64 indicates the focal lengths and intervals of the main points of the respective sets of lenses of the optical system corresponding to the seventh example with six focusing states (focal length F = 28.8, 35.0, 50.0, 70 , 0,

, 0 and 102.0 mm).

  The middle portion of table 64 indicates the spline sample data when the focus cam configuration of the second lens set of the seventh embodiment, used for focusing, is represented by a spline function associated with the angle. has rotation of a rotating barrel and amplitude x of

  displacement in the direction of the optical axis.

  In addition, the lower part of table 64 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85.0 and 102.0 mm) and the rotational amplitudes (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) when using the focusing cam of the seventh example. In the lower part of Table 64, as the amplitude of rotation for the focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 102.0 mm) is equal to 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 0.5 mm) is equal to -7.2, the ratio (aF / az) magnitudes of focus rotation and focal length variation in the seventh example is

equal to -0.72.

Table 64

  Seventh example f = 28.8 to 102.0 (ratio of rotation amplitudes: aFlaz = -0.72) Focal distances and intervals of the main points of the objectives of the seventh example

  F 28.8000 35.0000 50.0000 70.0000 85.0000 102.0000

  F1 79.2449 D1 10.3882 14.8655 22.7700 30.1777 34.3149 38.0039

  F2 -15.4624 D2 25.2941 22.6661 18.5824 15.3362 13.5483 11, 8188

  F3 22.0957 D3 6.6017 7.6595 9.5884 11.0937 11.7828 12.3244

  F4 -35.5101 D4 5.9639 4.9061 2.9772 1.4719 0.7828 0.2412

  F5 46.4677 D5 18.3315 50.3856 54.3234 57.9012 59.7291 61.2142

  Focusing cam shape (spline interpolaion sampled point) corresponding to the seventh example

ANGLE (1) (2) (3) (4) (5)

  1 -11.0000 0.0000 1.6620 0.0000 0.0000 0.0000

  2 -10,0000 0.0000 1.5641 0.0000 0.0000 0.0000

  3 -7.2000 0.0000 1.2474 0.0000 0.0000 0.0000

  4 4.5026 0.0000 0.8685 0.0000 0.0000 0.0000

  -2.8872 0.0000 0.5972 0.0000 0.0000 0.0000

  6 -1.3163 0.0000 0.2928 0.0000 0.0000 0.0000

  7 -0.8525 0.0000 0.1940 0.0000 0.0000 0.0000

  8 -0.5001 0.0000 0.1158 0.0000 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

  2,8000 0.0000 -0.7734 0.0000 0.0000 0.0000

  11 5,4974 0.0000 -1.8290 0.0000 0.0000 0.0000

  12 7,1128 0.0000 -2.7118 0.0000 0.0000 0.0000

  13 8.6837 0.0000 -3.9029 0.0000 0.0000 0.0000

  14 9,1475 0.0000 4.3583 0.0000 0.0000 0.0000

  9,4999 0.0000 4,7525 0.0000 0.0000 0.0000

  16 10.0000 0.0000 -5.4099 0.0000 0.0000 0.0000

  17 11.0000 0.0000 -7.0970 0.0000 0.0000 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focusing of the seventh example (ratio of amplitudes of rotation: aF / az = -0.72) Focal length Corresponding position Distance of amplitude of rotation to infinity photography for focusing 28.8 mm 0.0000 5.00 m -0.500, 0 mm 1.7943 3.00 m -0.852, 0 mm 4.8878 2.00 m -1.316, 0 mm 7, 5822 1.00 m -2.887, 0 mm 8.9328 0.70 m -4.503 102.0 mm 10.0000 0.50 m -7.200 The following table 65 gives the numerical value data of the cams of the focusing lens assembly of the seventh example, the data calculated by interpolation with a spline function using the focus cam sample data shown in the middle portion of table 64. It should be noted that the meanings of the symbols in table 65 are

  the same as in the first example.

Table 65

  Cam numerical values for focusing objective of the seventh example Focus cam digital values Focal distance dimming compensation digital cam values

ANGLE (2) F ANGLE (2) F

-7.2000 1.2474 0.0000

-7.0000 1.2220 0.0000

-6,5000 1,1568 0,0000

-6.0000 1.0890 0.0000

-5,5000 1,0184 0,0000

-5.0000 0.9448 0.0000

-4.5000 0.8681 0.0000

-4.0000 0.7881 0.0000

-3,5000 0.7046 0.0000

-3.0000 0.6174 0.0000

-2.5000 0.5262 0.0000

-2.0000 0.4307 0.0000

-1.5000 0.3307 0.0000

-1.0000 0.2259 0.0000

-0.5000 0.1158 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.1215 30.3871 0.5000 -0.0782 30.3871

  1,0000 -0,2493 32,0759 1,0000 -0,1189 32,0759

  1,5000 -0,3842 33,8798 1,5000 -0,1222 33,8798

  2.0000 -0.5269 35.8098 2.0000 -0.0881 35, 8098

  2,5000 -0,6782 37,8759 2,5000 -0,0164 37,8759

  3,0000 -0,8388 40,0860 3,0000 0.0928 40.0860

  3.5000 -1.0100 42.4533 3.5000 0.2389 42.4533

  4.0000 -1.11931 44.9978 4.0000 0.4216 44.9978

  4.5000 -1.3899 47.7360 4.5000 0.6400 47, 7360

  , 0000 -1.6017 50.6785 5.0000 0.8925 50.6785

  , 5000 -1.8303 53.8326 5.5000 1.1760 53.8326

  6.0000 -2.0774 57.2175 6.0000 1.4874 57.2175

  6.5000 -2.3466 60.8803 6.5000 1.8248 60.8803

  7.0000 -2.6414 64.8675 7.0000 2.162 64.8675

  7.5000 -2.9660 69.2369 7.5000 2.5694 69.2369

  8,0000 -3,3284 74,1111 8,0000 2,9753 74,1111

  8.5000 -3.7384 79.6222 8.5000 3.4040 79.6222

  9.0000 -4.2064 85.8958 9.0000 3.8529 85.8958

  9,5000 -4,7527 93,2084 9,5000 4,3235 93,2084

  , 0000 -5,4099 102,0000 10,0000 4,8173 102,0000

  The left side of table 65 shows the numerical values of the focus cam of the seventh example, and the right side that of the zoom compensation cam. A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis derived from the numerical values of the focusing cam and the zoom compensation cam, in the range of the rotation amplitudes (ANGLE = 0, 0) and (ANGLE = 10.0), coincides with the locus of displacement of the second set of lenses calculated with the paraxial data of the upper part of the

table 64.

  The following tables 66, 67 and 68 give the focusing amplitude DX (mm) in the direction of the optical axis of the focusing lens assembly, the magnification magnifications Px of the respective sets of lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  Ya conversion associated with rotation at the far end

  angle (F = 28.8 mm), medial position (F = 50.0 mm), and at the telephoto end (F = 102.0 mm) in the seventh example. The layout and meaning of the symbols in the respective tables are the same as in the

first example.

Table 66

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 0.058 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 0,116 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 0,194 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 0,293 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 0,597 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 0.869 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 1.247 3) 0.000 4) 0.000 5) 0.000

  Objective image magnification at the wide-angle end (28.8 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,290 3) -0,955 4) -32,766 5) -0,40

  R 10,000 ANG -0.246 1) -0.008 2) -0.286 3) -0.955 4) -32.766 5) -0.40

  R 5,000 ANG -0,500 1) -0,016 2) -0,282 3) -0,955 4) -32,766 5) -0,40

  R 3,000 ANG -0.852 1) -0.028 2) -0.277 3) -0.955 4) -32.766 5) -0.40

  R 2,000 ANG -1,316 1) -0,043 2) -0,271 3) -0,955 4) -32,766 5) -0,40

  R 1,000 ANG -2,887 1) -0,096 2) -0,251 3) -0,955 4) -32,766 5) -0,40

  R 0.700 ANG -4.503 1) -0.151 2) -0.233 3) -0.955 4) -32.766 5) -0.40

  R 0.500 ANG -7.200 1) -0.244 2) -0.209 3) -0.955 4) -32.766 5) -0.40

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (28.8 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 1,443 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,246 1) 0,000 2) 1,446 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,500 1) 0,000 2) 1,450 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 1,454 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 1,460 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 1,476 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 1.489 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 1.506 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focusing cam at the wide-angle end (28.8 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,237 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -0.232 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -0,226 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -0,218 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,208 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,180 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.157 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.126 3) 0.000 4) 0.000 5) 0.000

* Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.8 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,342 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -0.335 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -0,327 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -0,317 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,304 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,266 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.233 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.190 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / YxO = 1.04, YaR / yao = 0.55

Table 67

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) 0.104 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) 0,207 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) 0,345 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) 0,516 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) 1,025 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) 1.461 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 2.044 3) 0.000 4) 0.000 5) 0.000

  Bk image magnification of lenses at the median position (50.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,377 3) -1,243 4) -7,965 5) -0,169

  R 10,000 ANG -0.245 1) -0.008 2) -0.370 3) -1.243 4) -7.965 5) -0, 169

  R 5,000 ANG -0,497 1) -0,016 2) -0,364 3) -1,243 4) -7,965 5) -0,169

  R 3,000 ANG -0.849 1) -0.028 2) -0.355 3) -1.243 4) -7.965 5) -0, 169

  R 2,000 ANG -1,312 1) -0,044 2) -0,344 3) -1,243 4) -7,965 5) -0,169

  R 1,000 ANG -2,886 1) -0,098 2) -0,311 3) -1,243 4) -7,965 5) -0,169

  R 0.700 ANG -4.507 1) -0.155 2) -0.283 3) -1.243 4) -7.965 5) -0.169

  R 0.500 ANG -7.200 1) -0.254 2) -0.245 3) -1.243 4) -7.965 5) -0.169

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 2,403 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) 2.417 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) 2,430 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) 2,448 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) 2,470 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) 2,530 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) 2.577 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 2.633 3) 0.000 4) 0.000 5) 0.000

  Slope dxlda of focusing cam at the median position (50.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,432 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) -0.417 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) -0,401 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) -0,382 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) -0,357 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) -0,294 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) -0.246 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.190 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (50.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -1,039 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) -1.007 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) -0,976 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) -0,934 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) -0,883 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) -0,743 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) -0.634 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.500 3) 0.000 4) 0.000 5) 0.000

  2 0 Condition corresponding to the values: YxR / Yxo = 1, 1 0, YaR / Yao = 0.48

Table 68

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (102.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 0.340 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 0,657 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 1,052 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 1,507 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 2,698 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 3.581 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 4.636 3) 0.000 4) 0.000 5) 0.000

  Objective image magnification Pk at the telephoto end (102.0 mm) of the seventh

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,600 3) -1,528 4) -4,425 5) -0,317

  R 10,000 ANG -0.246 1) -0.008 2) -0.578 3) -1.528 4) -4.425 5) -0.317

  R 5,000 ANG -0,500 1) -0,017 2) -0,557 3) -1,528 4) -4,425 5) -0,317

  R 3,000 ANG -0,852 1) -0,028 2) -0,532 3) -1,528 4) -4,425 5) -0,317

  R 2,000 ANG -1,316 1) -0,044 2) -0,502 3) -1,528 4) -4,425 5) -0,317

  R 1,000 ANG -2,887 1) -0,099 2) -0,425 3) -1,528 4) -4,425 5) -0,317

  R 0.700 ANG -4.503 1) -0.159 2) -0.368 3) -1.528 4) -4.425 5) -0.317

  R 0.500 ANG -7.200 1) -0.267 2) -0.300 3) -1.528 4) -4.425 5) -0.317

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (102.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) 2,948 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 3.067 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 3,175 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 3,303 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 3,443 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 3,772 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 3.981 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 4.191 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focusing cam at the telephoto end (102.0 mm) of the seventh

example

  R 0,000 ANG 0,000 1) 0,000 2) -1,462 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -1.311 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -1,188 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -1,054 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,917 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,631 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.475 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.423 3) 0.000 4) 0.000 5) 0.000

  Coefficient of conversion associated with the direction of rotation at the telephoto end (102.0 mm) of the seventh example

  R 0,000 ANG 0,000 1) 0,000 2) -4,310 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,246 1) 0,000 2) -4,022 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,500 1) 0,000 2) -3,772 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -3,481 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -3,159 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -2,381 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -1.889 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -1.355 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.42, YaR / YaO = 0.31 As shown in tables 66, 67 and 68, for each focal length, the conversion coefficient yx associated with the direction of the axis optical increases but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance given the influence of the slope (dx / da) of the focusing cam. In tables 66, 67 and 68, the rate of change from the infinite focus position to the shortest distance focus position of the conversion coefficient associated with the rotation is x0.55 at the large end. -angle (F = 28.0 mm), x0.48 at the middle position (F = 50.0 mm) and x0.31 at the telephoto end (F = 102.0 mm). When the number N of divisions of the focusing range, following a change in the conversion coefficient Ya of the seventh example, is calculated using the formula (a) and is compared with that of the example of Japanese Patent Application Laid-Open No. 5,224,775, the division numbers Nw, NM and NT at the wide-angle end, in the median position and at the telephoto end respectively have the following values: of Japanese Patent Application Laid-Open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 Seventh Example Nw> 3.2 NM> 4.0 NT> 6.3 As a result , although the zoom lens of this example has a greater focal length variation ratio than the example of Patent Application Laid-open No. 5- 142475, the values of the numbers N of divisions

are reduced.

  As previously described, in the seventh example, since the rate of change of the conversion coefficient Ya associated with the rotation is smaller than that of the conventional system, the values of the numbers N of divisions are small. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y can be reduced, and the storage capacity can

also be reduced.

  Tables 69, 70 and 71 show the results of calculating the conversion coefficient Ka and correction coefficient I at the wide-angle end (F = 28.8 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the seventh embodiment. The provisions of the tables and symbols are the same as in the first example. The position of the focusing lenses of the first pair of the two upper parts of each of the tables 69, 70 and 71, that is to say of the third and fourth columns, is (R, ANGLE) = (0, 0; 0,0) and indicates that this position corresponds to infinity. Similarly, the position of the focusing lenses of the fourth pair of the two lower parts of each table 69, 70 and 71, that is to say in the ninth and tenth columns, is (R, ANGLE) = (0, 5; -7,2) and indicates that the position corresponds to the focus at the nearest location

(R = 0.5 m).

Table 69

  Conversion coefficients Ka: (rs), ya: (r) associated with direction of rotation and correction coefficient p: (t) at the wide-angle end (28.8 mm) of the seventh example f = 28.8 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.246 5,000 -0.500 3,000 - 0.852

POS R rs r rs r rs

  1 0.000 -0.342 0.000 -0.337 -0.333 -0, 326

  2 10,000 -0.340 -0.335 0.000 -0.330 -0, 323

  3 5,000 -0,337 -0,332 -0,327 0,000 -0,321

  4 3,000 -0.334 -0.329 -0.324 -0.317 0, 000

2,000 -0,329 -0,324 -0,319 -0,312

  6 1,000 -0,313 -0,309 -0,304 -0, 298

  7 0.700 -0.299 -0.294 -0.290 -0, 284

  8 0.500 -0.276 -0.272 -0.268 -0, 262

POS R bf i bf t bf i bf t

  1 0.000 0.00 0.00 -0.08 11.45 -0.17 10.55 -0.28 9, 93

  2 10,000 0.08 12.26 0.00 0.00 -0.08 10.26 -0.20 9, 79

  3 5,000 0.17 11.70 0.08 10.84 0.00 0.00 -0.11 9, 75 4 3,000 0.28 11.22 0.20 10.45 0.19 9.94 0.00 0, 00

  5 2,000 0.43 10.94 0.35 10.34 0.26 10.01 0.14 9.95

  6 1,000 0.90 10.68 0.81 10.32 0.73 10.11 0.61 9, 97

  7 0.700 1.34 10.52 1.25 10.23 1.16 10.03 1.03 9.84

  8 0.500 1.99 10.30 1.89 10.05 1.79 9.86 1.66 9, 65

  (R, ANGLE) = 2,000 -1,316 1,000 -2,887 0,700 -4,503 0,500 -7,200

2 5 POS R rs r rs r rs

  1 0.000 -0.317 -0.291 -0.269 -0, 238

  2 10,000 -0.315 -0.289 -0.267 -0, 236

  3 5,000 -0,312 -0,287 -0,264 -0, 234

  4 3,000 -0.308 -0.283 -0.261 -0, 231

  3 0 5 2,000 -0,304 0,000 -0,279 -0,258 -0,228

  6 1,000 -0,290 -0,266 0,000 -0,245 -0, 216

  7 0.700 -0.276 -0.253 -0.233 0.000 -0, 206

  8 0.500 -0.255 -0.234 -0.215 -0.190 0.000

POS R bf i bf t bf I bf

  3 5 1 0.000 -0.42 9.72 -0.84 8.82 -1.21 7.94 -1.71 6.77

  2 10,000 -0.34 9.69 -0.76 8.80 -1.13 7.93 -1.64 6, 75

  3 5,000 -0.25 9.72 -0.68 8.79 -1.06 7.91 -1.57 6, 74

  4 3,000 -0.14 9.81 -0.58 8.77 -0.95 7.89 -1.47 6, 72

  2,000 0.00 0.00 -0.44 8.73 -0.82 7.86 -1.34 6.70

  4 0 6 1,000 0.46 9.68 0.00 0.00 -0.40 7.78 -0.93 6.63

  7 0.700 0.88 9.53 0.41 8.51 0.00 0.00 -0.56 6, 56

  8 0.500 1.50 9.34 1.01 8.36 0.58 7.52 0.00 0.00

  Condition corresponding to the values: Ka / Yao = 0.81, KaR / YaR = 1.25

Table 70

  Conversion coefficients Ka (rs), Ya: (r) associated with direction of rotation and correction coefficient IJp: (>) at the median position (50.0 mm) of the seventh example f = 50.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.245 5,000 -0.497 3,000 - 0.849

POS R rs r rs r rs

  1 0.000 -1.039 0.000 -1.015 -0.990 -0, 959

  2 10,000 -1,032 -1,007 0,000 -0,983 -0, 952

  3 5,000 -1,024 -1,000 -0,976 0,000 -0,944

  4 3,000 -1,014 -0,989 -0,965 -0,934 0, 000

2,000 -1,000 -0,976 -0,952 -0,921

  6 1,000 -0,956 -0,932 -0,910 -0,880

  7 0.700 -0.915 -0.892 -0.870 -0.842

  8 0.500 -0.854 -0.833 -0.313 -0.786

POS R bf f bf i bf f bf

  1 0.000 0.00 0.00 -0.25 34.57 -0.49 32.89 -0.81 30.93

  2 10,000 0.25 36.71 0.00 0.00 -0.25 32.19 -0.57 30.59

  3 5,000 0.51 36.07 0.25 34.00 0.00 0.00 -0.33 30.26

  4 3,000 0.86 35.39 0.60 33.54 0.34 32.07 0.00 0.00

  2 0 5 2,000 1.31 34.75 1.04 33.07 0.78 31.69 0.43 30.20

  6 1,000 2.76 34.38 2.46 33.10 2.17 32.05 1.79 30.98

  7 0.700 4.12 34.46 3.80 33.32 3.49 32.35 3.08 31.29

  8 0.500 6.15 34.61 5.80 33.55 5.45 32.62 4.99 31.53

  (R, ANGLE) = 2,000 -1,312 1,000 -2,886 0,700 -4,507 0,500 -7,200

  POS R rs r rs r rs r rs i 0,000 -0,920 -0,810 -0,723 -0,615

  2 10,000 -0.913 -0.804 -0.717 -0, 611

  3 5,000 -0,906 -0,797 -0,712 -0, 606

  4 3,000 -0.896 -0.789 -0.704 -0, 599

  3 0 5 2,000 -0,883 0,000 -0,778 -0,694 -0,591

  6 1,000 -0,844 -0,743 0,000 -0,663 - 0,564

  7 0.700 -0.808 -0.711 -0.634 0.000 -0.539

  8 0.500 -0.754 -0.663 -0.591 -0.500 0.000

POS R bf t bf f bf t bf

  1 0.000 -1.21 28.99 -2.34 26.21 -3.26 23.30 -4.43 19.18

  2 10,000 -0.97 28.79 -2.12 26.24 -3.06 23.32 -4.25 19.17

  3 5,000 -0.74 28.64 -1.90 26.31 -2.85 23.36 -4.06 19.16

  4 3,000 -0.41 28.49 -1.61 26.44 -2.58 23.41 -3.81 19.15

  2,000 0.00 0.00 -1.22 26.61 -2.22 23.46 -3.48 19.12

  6 1,000 1.33 30.20 0.00 0.00 -1.07 23.62 -2.43 18.93

  7 0.700 2.58 30.26 1.15 26.11 0.00 0.00 -1.45 18.48

  8 0.500 4.44 30.35 2.86 26.36 1.59 23.34 0.00 0.00

  Condition corresponding to the values: Kao / Tyao = 0.82, KaR / YaR = 1.23 @N Os a (NJcQQ) LUrcs4NCD <00) ODorCO <0 <00NeuaMrsn n <E2 Sacv) cvn- "Os <<c 5 < ## STR5 ## ## EQU1 ## where ## STR2 ## is 0, ## STR2 ## where ## STR2 ## ## EQU1 ## where ## EQU1 ## ## STR5 ## wherein Y is a compound of the formula ## STR2 ## wherein Y is a compound of the formula ## STR2 ## #################################################################### ## STR5 ## (NI O has aeqa0 io & 5W f.im -: LnN '-Ccn Lnrcd u M0 aM LO ----.--- <') CoP ON ce) IlI (çI 11 <910M u) c :) ODCYCN ## STR1 ## ## STR1 ## ## STR1 ## ## STR2 ## a4 ac (OC Cwm O0LflICv) CccCDOcD G> l Mc: 4 OCDCN) CD) C CDcCcr (NNC 6OL6OCiCD c 0 a> O0000Cr00 00 (OCD <OrNDCoNI4 Cv) Na) v'C CC CDCD C) 0-cnC) CD N CN00r-00 CDCDN C'A0 oo o% o CD Mlemic xo 4-> Lr-0.-.- D00a -Mw (OCv) nC <vLCD.JeO) - ON 'oeaC-t

O Z,

  U) ZL000ooil 00qoa0000 <nU 'o 0D (Dw Coo

  0 M 'q tD CD - CD 0 VY M e W) O r' - - m Ci) cn 0mtreO -

CL O 0O10O1

  Ln 0Hr CD. The results of the calculation of the rate of change of Ka as a function of Ya for the set focused at infinity and focused at the nearest point at the wide-angle end, in the median position and at the the telephoto end of the example of Japanese Patent Application Laid-Open No. 5-142475 and Seventh Example

  according to the invention are the following.

  Example of Japanese Patent Application Laid-open No. 5142475 To Infinity KaO / YaO Closest KaR / YaR Wide Angle (F = 36.0) 2.75 0.44 Median Position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Seventh example At infinity K7aoYaO Closest KaR / YaR Wide angle (F = 28.8) 0.81 1, 25 Median position (F = 50, 0) 0.82 1.23 Telephoto (F = 102.0) 1.00 1.18 As previously described, in the seventh example, as the rate of change of Ka as a function of Ya is weak compared to the classical system, the contribution of the correction term (ABf / g) of the relation Ka = Ya (1 - ABf / l) can be reduced. For this reason, an error of the conversion coefficient Ka calculated from Ya and y or an error from the actual lens driving amplitude Aa obtained when only a pair of values of the conversion coefficient Δa and the coefficient of correction

is established, can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the seventh example of the invention, when the lens driving amplitudes during focusing for the focused assembly to the infinity to the object at the smallest distance and during focusing for the whole focused at the smallest distance on the object at infinity, at the wide-angle end, in the middle position and at the telephoto end, are calculated from Aa = ABf / Ya (1 - ABf / g) and the errors on the actual driving amplitudes of the lenses are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient M during focusing with the set focused to infinity up to the object at the shortest distance has the value of the object distance (POS-5) and the value of the correction coefficient y when focusing for the set focused at the smallest distance on the object to infinity takes the value of the

object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Seventh example Focused Infinity Nearest Focused Near-Focused at infinity Wide-angle (F = 28.8) -1.2% -0.4% Median position (F = 50.0) -0.1% -0.1% Telephoto (F = 102.0) 0 , 3% -0.2% As previously described, in the seventh embodiment, even when only a pair of values of the conversion coefficient Ya and the correction coefficient y are established for a given range of lens arrangements, a error between the conversion coefficient Ka calculated from ya and y and the driving amplitude of lenses Aa for focusing becomes low compared to that of the conventional system, and the focusing can be

  performed with greater precision.

  Table 72 indicates the rotation amplitude (ANGLE DA) for the manual focusing with the aid of the focusing cam (middle part of table 64) of the seventh example, the displacement amplitude DX (mm) in the direction of rotation. the optical axis of the set of focusing lenses corresponding to the rotation amplitude for the focusing, and the displacement amplitude Bf (mm) of the point

  image formation when the amplitude or quantity of

  placement (DX) in the direction of the optical axis is given.

  It should be noted that the layout and reference symbols of the table are the same as in the first example. The upper part of Table 72 indicates the range of motion (Bf) of the imaging point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) in the respective states of variation of focal lengths (F = 28.8,, 0, 50.0, 70.0, 85.0 and 102.0 mm), and the middle portion indicates the values of the amplitude of rotation (ANGLE DA) for the focusing, necessary to obtain an optimal focused state for the respective photography distances. The lower part gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for the focusing,

  with focal lengths and photography distances.

Table 72

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) displacement for focusing of the seventh example 0.50 m 0.70 m 1.00 m 2.00 m 3.00 m 5.00 m 28.800 Bf 0.000 0.000 0.000 0, 000 0.000 0.000, 000 Bf 0.000 0.001 0.002 0.002 0.002 0, 001, 000 Bf 0.000 0.003 -0.001 -0.004 -0.004 -0.003, 000 Bf 0, 000 -0.010 -0.010 -0.002 0.000 0.001, 000 Bf 0.000 - 0.010 -0, 004 -0.006 -0.005 -0.001 102.000 Bf 0.000 0.000 0.000 0.000 0.000 0.000

  ANGLE DA -7,200 4,503 -2,887 -1,316 -0,852 -0,500

  F 28,800 DX 0,000 1,247 0,000 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,472 0,000 0,000 0,000 R 0,50 m F 50,000 DX 0,000 2,044 0,000 0,000 0,000 R 0.50 m F 70,000 DX 0,000 2,930 0,000 0,000 0,000 R 0.50 m F 85, 000 DX 0.000 3,690 0,000 0,000 0,000 R 0,50 m F 102, 000 DX 0,000 4,636 0,000 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,869 0,000 0,000 0,000 R 0,70 m F 35,000 DX 0.000 1.032 0.000 0.000 0.000 R 0.70 m F 50.000 DX 0.000 1.460 0.000 0.000 0.000 R 0.70 m F 70.000 DX 0.000 2.157 0.000 0.000 0.000 R 0.70 m F 85.000 DX 0.000 2.778 0.000 0.000 0.000 R 0.70 m F 102,000 DX 0, 000 3,581 0,000 0,000 0,000 R 0,70 m F 28,800 DX 0,000 0,597 0,000 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0, 713 0,000 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,026 0,000 0,000 0,000 R 1.00 m F 70,000 DX 0,000 1, 552 0,000 0,000 0,000 R 1,00 m F 85,000 DX 0,000 2,039 0,000 0,000 0,000 R 1,00 m F 102,000 DX 0,000 2,698 0, 000 0,000 0,000 R 1,00 m F 28,800 DX 0.000 0.293 0.000 0.000 0.000 R 2.00 m F 35,000 DX 0.000 0.3 51 0,000 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,517 0,000 0,000 0,000 R 2,00 m F 70,000 DX 0,000 0,805 0,000 0,000 0,000 R 2,00 m F 85,000 DX 0,000 1,093 0,000 0,000 0,000 R 2 00 m F 102,000 DX 0,000 1,507 0,000 0,000 0,000 R 2.00 m F 28,800 DX 0,000 0,194 0,000 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,233 0,000 0,000 0,000 R 3.00 m F 50,000 DX 0,000 0,346 0,000 0,000 0,000 R 3,00 m F 70,000 DX 0,000 0,544 0,000 0,000 0,000 R 3,00 m F 85,000 DX 0,000 0,749 0,000 0,000 0,000 R 3,00 m F 102,000 DX 0,000 1,052 0,000 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,116 0,000 0,000 0,000 R 5,0000 F 35,000 DX 0,000 0,139 0,000 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,208 0,000 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,330 0,000 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,459 0,000 0,000 0,000 R 5,00 m F 102,000 DX 0,000 0,657 0,000 0,000 0,000 R 5,00 m As shown in Table 72, in the zoom lens of the seventh embodiment, the so-called "manual" focus can be obtained because q that the magnitudes of displacement of the image point, for the respective focal lengths and photographing distances, are very small and enter the depth of field regardless of the focusing adjustment state and the photographing distance. Eighth Embodiment The eighth embodiment or eighth example relates to a zoom lens having a four-array arrangement, i.e., positive, negative, positive and negative lens sets, and providing focus to the lens. using a third set of positive type lenses. For this purpose, the ratio (aF / az) of the amplitude of rotation for the focusing of the position focused at infinity to the position focused at the smallest distance (R = 1.2 m) and the amplitude rotation

  for the variation of the focal length of the

  angle (F = 72.0 mm) at the telephoto end

  (F = 200.0 mm) is set to -0.75.

  Table 73 shows various paraxial data of an optical system and data for defining the configuration of a focus cam of the eighth

example.

  The upper part of table 73 indicates the focal lengths and intervals of the main points of the respective lens assemblies of the optical system corresponding to the eighth example with five focusing range setting states (focal lengths F = 72.0,

, 0, 135.0, 150.0 and 200.0 mm).

  The middle part of Table 73 shows the spline sample data when the focus cam configuration of the third lens set of the eighth example, used for focusing, is expressed by a spline function associated with the angle a of rotation of a rotating barrel and to the amplitude of displacement x in

the direction of the optical axis.

  In addition, the lower part of Table 73 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 72.0, 105.0, 135.0, 150.0 and 200.0 mm) and the magnitudes of rotation (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 4.0, 3.0, 2.0, 1.5 and 1.2 m) using the focusing cam of the eighth example. In the lower part of Table 73, as the amplitude of rotation used for the focal length variation of the wide-angle end (F = 72.0 mm) at the telephoto end (F = 200.0 mm) is set to 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 1.2 m) is set at -7.5, the ratio (aF / az) of the focal rotation and focal length variation amplitudes of the eighth example is equal

at -0.75.

  Table 73 Eighth example f = 72.0 to 200.0 (ratio of amplitudes of rotation: aF / az = -0.75) Focal distances and intervals of the main points of the objectives of the eighth example

  F 72.0000 105.0000 135.0000 150.0000 200.0000

  F1 104.6018 D1 3.988 20.2900 31.6591 36.5381 50.0257

  F2 -79.6837 D2 55.9381 47.4314 41.7208 39.4416 34.0263

  F3 41.6144 D3 24.2323 16.4388 10.7803 8.1805 0.1081

  F4 -51.6678 D4 37.5317 53.8320 65.2011 70.0800 83.5677

  Focusing cam shape (spline interpolated point) corresponding to the eighth example

ANGLE (1) (2) (3) (4)

  I -11.0000 0.0000 0.0000 2.0100 0.0000

  2 -10,0000 0.0000 0.0000 1,9133 0.0000

  3 -7.5000 0.0000 0.0000 1.6182 0.0000

  4 -5.2371 0.0000 0.0000 1.2678 0.0000

* 5 -3.5101 0.0000 0.0000 0.9317 0.0000

  6 -2.1243 0.0000 0.0000 0.6090 0.0000

  7 -1.5249 0.0000 0.0000 0.4523 0.0000

  8 -1.1898 0.0000 0.0000 0.3598 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

  10 2.5000 0.0000 0.0000 -0.9336 0.0000

  11 4.7629 0.0000 0.0000 -2.0535 0.0000

  12 6,4899 0.0000 0.0000 -3.1437 0.0000

  13 7.8757 0.0000 0.0000 -4.2099 0.0000

  14 8.4751 0.0000 0.0000 4.7357 0.0000

  15 8.8102 0.0000 0.0000 -5.0491 0.0000

  16 10.0000 0.0000 0.0000 -6.2905 0.0000

  17 11.0000 0.0000 0.0000 -7.4900 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focusing of the eighth example (ratio of amplitudes of rotation: aF / az = -0.75) Focal distance Corresponding position Distance of amplitude of rotation to infinity photography for focusing 72.0 mm 0.0000 5.00 m -1.190, 0 mm 3.5209 4.00 m -1.525, 0 mm 5.9912 3.00 m -2.124, 0 mm 7, 0528 2.00 m-3.510, 0 mm 10.0000 1.50 m -5.237 1.20 m -7.500 Table 74 which follows indicates the data of the numerical values of the cams of the set of focusing lenses of the eighth example, the data being calculated by interpolation with a spline function from the focus cam sample data of the middle portion of table 73. It should be noted that the meanings of the symbols in table 74 are the same as

  in the first embodiment.

Table 74

  Digital Cam Values for Eighth-Focus Focusing Lens Digital Focus Cam Values Focal Length Variation Compensation Cam Digital Values

ANGLE (3) F ANGLE (3) F

-7.5000 1.6182 0.0000

-7.0000 1.5483 0.0000

-6.5000 1.4744 0.0000

-6.0000 1.3962 0.0000

-5.5000 1.3133 0.0000

-5.0000 1.2255 0.0000

4.5000 1.1325 0.0000

4.0000 1.0339 0.0000

-3.5000 0.9295 0.0000

-3.0000 0.8189 0.0000

-2.5000 0.7017 0.0000

-2.0000 0.5774 0.0000

-1.5000 0.4456 0.0000

-1.0000 0.3057 0.0000

-0.5000 0.1572 0.0000

  0.0000 0.0000 72.0000 0.0000 0.0000 72.0000

  0.5000 -0.1660 76.1236 0.5000 1.3748 76.1236

  1.0000 -0.3416 80.4107 1.0000 2.7619 80.4107

  1.5000 -0.5276 84.8761 1.5000 4.1606 84.8761

  2.0000 -0.7246 89.5329 2.0000 5.5699 89.5329

  2.5000 -0.9336 94.3931 2.5000 6.9884 94.3931

  3,0000 -1,1554 99,4683 3,0000 8,4147 99,4683

  3.5000 -1.3909 104.7727 3.5000 9.8477 104.7727

  4.0000 -1.6411 110.3201 4.0000 11.2862 110.3201

  4,5000 -1,9071 116,1211 4,5000 12,7281 116,1211

  , 0000 -2,1897 122,1805 5,0000 14,1701 122,1805

  , 5000 -2,4902 128,5085 5,5000 15,6102 128,5085

  6,0000 -2,8101 135,1192 6,0000 17,0469 135,1192

  6,5000 -3,1508 142,0209 6,5000 18,4779 142,0209

  7.0000 -3.5139 149.2214 7.0000 19.9005 149.2214

  7.5000 -3.9014 156.7540 7.5000 21.3156 156.7540

  8.0000 -4.3155 164.6446 8.0000 22.7226 164.6446

  8,5000 -4,7585 172,9045 8,5000 24,1180 172,9045

  9.0000 -5.2331 181.5381 9.0000 25.4980 181.5381

  9,5000 -5,7420 190,5503 9,5000 26,8586 190,5503

  , 0000 -6,2905 200,0000 10,0000 28,2022 200,0000

  The left-hand portion of table 74 gives the numerical values of the focus cam of the eighth example and the right-hand portion of the zoom compensation cam of this example. A value obtained by synthesis of the displacement amplitudes (3) in the direction of the optical axis, with the numerical values of the focusing cam and the zoom compensation cam, in the range between the rotation amplitudes (ANGLE = 0.0) and (ANGLE = 10.0), coincides with the displacement location of the third set of lenses calculated using the paraxial data of the upper part of the

table 73.

  The following tables 75, 76 and 77 indicate the displacement amplitude DX (mm) for the focusing, in the direction of the optical axis, of the set of focusing lenses, the magnifications Px of the images given by the sets. of the lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end ( F = 72.0 mm), at the middle position (F = 135.0), and at the telephoto end (F = 200.0 mm) in the eighth example. The layout and meaning of the symbols in the respective tables are the same as in

the first example.

Table 75

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (72.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) 0.178 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 0,360 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 0,452 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 0,609 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 0,932 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 1,268 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 1,618 4) 0,000

  Lens magnification Ok at the wide-angle end (72.0 mm) of the eighth example

  R 0,000 ANG 0.000 1) 0.000 2) -3.807 3) -0.105 4) 1, 726

  R 10,000 ANG -0.568 1) -0.011 2) -3.614 3) -0.109 4) 1, 726

  R 5,000 ANG -1,190 1) -0,022 2) -3,432 3) -0,113 4) 1,72

  R 4,000 ANG -1,525 1) -0,028 2) -3,344 3) -0,116 4) 1,72

  R 3,000 ANG -2,124 1) -0,038 2) -3,204 3) -0,119 4) 1,72

  R 2,000 ANG -3,510 1) -0,059 2) -2,941 3) -0,127 4) 1,72

  R 1.500 ANG -5.237 1) -0.082 2) -2.699 3) -0.135 4) 1, 726

  R 1,200 ANG -7,500 1) -0,107 2) -2,477 3) -0,144 4) 1,72

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (72.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 2,948 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) 2.945 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 2,942 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 2,941 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 2,938 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 2,932 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 2,926 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 2,919 4) 0,000

  Slope dx / da focus cam at the wide-angle end (72.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,323 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) -0.303 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -0,282 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,271 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,252 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,215 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,176 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,136 4) 0,000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (72.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,952 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) -0.893 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -0,829 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,796 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,741 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,629 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,514 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,397 4) 0,000

  Condition corresponding to the values: YxR / Yxo = 0.99, YaR / Yao = 0.42

Table 76

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (135.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) 0.360 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) 0,728 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) 0,915 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3 1,230 4) 0,000

  R 2,000 ANG-3.509 1) 0.000 2) 0.000 3) 1.879 4) 0.000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) 2,552 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3 3,252 4) 0,000

  Magnification, target image k at the median position (135.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 11,821 3) 0,048 4) 2,262

  R 10,000 ANG -0,566 1) -0,011 2) 14,182 3) 0,040 4) 2,262

  R 5,000 ANG -1,188 1) -0,022 2) 17,964 3) 0,031 4) 2,262

  R 4,000 ANG -1,523 1) -0,028 2) 20,858 3) 0,026 4) 2,262

  R 3,000 ANG -2,122 1) -0,038 2) 28,907 3) 0,019 4) 2,262

  R 2,000 ANG -3,509 1) -0,060 2) 167,907 3) 0.003 4) 2,262

  R 1,500 ANG -5,241 1) -0,084 2) -39,060 3) -0,013 4) 2,262

  R 1,200 ANG -7,500 1) -0,111 2) -16,516 3) -0,030 4) 2,262

  Coefficient of conversion Yx associated with the direction of the optical axis at the median position (135.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 5,104 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) 5.108 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) 5,111 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) 5,113 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) 5,115 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) 5,116 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) 5,115 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 5,112 4) 0,000

  Slope dx / da focus cam at the center position (135.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,659 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) -0.614 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) -0,569 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) -0,546 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) -0,508 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) -0,430 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) -0,351 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,271 4) 0,000

  Conversion coefficient Ya associated with the direction of rotation at the median position (135.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -3,366 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) -3.137 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) -2,907 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) -2,792 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) -2,596 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) -2,198 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) -1,796 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -1,386 4) 0,000

  Condition corresponding to the values: YxR / YxO = 1.00, YaRlyao = 0.41

Table 77

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (200.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) 0.618 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 1,241 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 1,555 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 2,081 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 3,147 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 4,237 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 5,357 4) 0,000

  Lens magnification Pk at the telephoto end (200, 0 mm) of the eighth

example

  R 0,000 ANG 0,000 1) 0,000 2) 3,174 3) 0,230 4) 2,617

  R 10,000 ANG -0.567 1) -0.011 2) 3.323 3) 0.215 4) 2, 617

  R 5,000 ANG -1,190 1) -0,022 2) 3,496 3) 0,200 4) 2,617

  R 4,000 ANG -1,525 1) -0,028 2) 3,594 3) 0,193 4) 2,617

  R 3,000 ANG -2,124 1) -0,038 2) 3,777 3) 0,180 4) 2,617

  R 2,000 ANG -3,510 1) -0,061 2) 4,244 3) 0,155 4) 2,617

  R 1,500 ANG -5,237 1) -0,085 2) 4,920 3) 0,128 4) 2,617 R 1,200 ANG -7,500 1) -0,113 2) 5,985 3) 0,101 4) 2,617

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (200.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 6,488 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) 6.533 4) 0.000

  R 5,000 ANG -1,1901) 0,000 2) 0,000 3) 6,576 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 6,596 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 6,628 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 6,687 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 6,738 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 6,780 4) 0,000

  Slope dx / da focus cam at the telephoto end (200.0 mm) of the eighth

example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -1,140 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) -1.045 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -0,957 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,914 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,842 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,702 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,566 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,4304) 0,000

  Coefficient of conversion associated with the direction of rotation at the telephoto end (200.0 mm) of the eighth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -7,395 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) -6.828 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -6,2914) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -6,028 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -5,581 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -4,696 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -3,814 4) 0,000

  R 1200 ANG -7.500 1) 0.000 2) 0.000 3) -2.9194) 0.000

  Condition corresponding to the values: YxR / YxO = 1.05, YaR / Yao = 0.39 As shown in Tables 75, 76 and 77, the conversion coefficient yx associated with the direction of the optical axis undergoes almost no change at the wide-angle end and at the middle position but increases to

  the telephoto end when the distance of photo-

  graphy approaches the shortest distance, and the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance for the respective focal lengths. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance because of the slope (dx / da) of the focusing cam. In Tables 75, 76, and 77, the rate of change from the infinite focus position to the focused position at the nearest location of the conversion coefficient Ya associated with the rotation is x0.42 to wide-angle end (F = 72.0 mm), x0.41 at the middle position (F = 135.0 mm) and x0.39 at the telephoto end (F = 200.0 mm). When the number N of divisions of the focusing range, following a change of the conversion coefficient Ya of the eighth example, is calculated with the formula (a) and is compared with the value of the example of the demand for Japanese Patent Laid-open No. 5-142475, the Nw, NM and NT numbers of divisions at the wide-angle end, in the middle position and at the telephoto end respectively have the following values: example of the demand Japanese Patent Application Laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8, 1 eighth example Nw> 4.8 NM> 4.9 NT> 5.1 As previously described, in the eighth example, as the speed of variation of the conversion coefficient Ya associated with the rotation is lower than that of the conventional system, the values of the numbers N of divisions become weak. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y can be reduced and the storage capacity can also be reduced.

to be reduced.

  Tables 78, 79 and 80 show the results of calculating the conversion coefficient Ka and the correction coefficient A at the wide-angle end (F = 72.0 mm), in the median position (F = 135.0 mm) and at the telephoto end (F = 200.0 mm) in the eighth example. The layout and symbols of the tables are the same as in the first example. The position of the focusing lenses in the first pair of the two parts

  of each of Tables 78, 79 and 80, that is to say

  say in the third and fourth columns, is (R, ANGLE) = (0,0; 0, 0) and indicates that this position corresponds to infinity. Similarly, the position of the focusing lenses in the fourth pair, in both parts

  of each of Tables 78, 79 and 80, that is to say

  say in the ninth and tenth columns, is (R, ANGLE) = (1.0; -7.5) and indicates that the position corresponds to the focused position at the shortest distance

(R = 1.2 m).

Table 78

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the wide-angle end (72.0 mm) of the eighth example f = 72.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,568 5,000 -1,190 4,000 -1,525

POS R rs r rs r rs

  I 0.000 -0.952 0.000 -0.918 -0.881 -0, 861

  2 10,000 -0.928 -0.893 0.000 -0.856 -0.837

  3 5,000 -0,900 -0,866 -0,829 0,000 -0,810

  4,000 -0.885 -0.851 -0.815 -0.796 0.000

3,000 -0.859 -0.826 -0.790 -0.772

  6 2,000 -0.803 -0.770 -0.737 -0.719

  7 1,500 -0,739 -0,708 -0,677 -0,660

  8 1,200 -0,665 -0,637 -0,607 -0,592

  POS R bf i bf t bf t bf! i 0.000 0.00 0.00 -0.52 18.91 -1.05 16.75 -1.31 15, 95

  2 10,000 0.53 20.46 0.00 0.00 -0.53 16.16 -0.80 15.52

  3 5,000 1.07 19.62 0.54 17.61 0.00 0.00 -0.27 15.37

  4 4,000 1.35 19.22 0.81 17.27 0.27 15.67 0.00 0.00

  5 3,000 1.83 18.73 1.28 16.98 0.74 15.68 0.46 15.33

  6 2,000 2.82 17.97 2.27 16.50 1.71 15.35 1.43 14.87

  7 1,500 3.87 17.29 3.31 15.99 2.74 14.90 2.45 14.41

  8 1,200 4.99 16.54 4.41 15.36 3.83 14.32 3.54 13.82

  (R, ANGLE) = 3,000 -2,124 2,000 -3,510 1,500 -5,237 1,200 -7,500

2 5 POS R rs r rs r rs

  1 0.000 -0.828 -0.759 -0.685 -0, 604

  2 10,000 -0.804 -0.736 -0.664 - 0.584

  3 5,000 -0.778 -0.712 -0.641 -0, 563

  4,000 -0.765 -0.699 -0.629 - 0.553

  3 0 5 3,000 -0,741 0,000 -0,677 -0,609 -0,534

  6 2,000 -0,690 -0,629 0,000 -0,564 - 0,493

  7 1,500 -0,633 -0,576 -0,514 0,000 - 0,448

  8 1,200 -0,567 -0,514 -0,457 -0,397 0, 000

POS R bf I bf a bf t bf r

  1 0.000 -1.76 14.96 -2.66 12.93 -3.59 10.83 -4.53 8.68

  2 10,000 -1.25 14.70 -2.17 12.76 -3.10 10.69 -4.05 8.57

  3 5,000 -0.73 14.56 -1.65 12.62 -2.59 10.55 -3.55 8.47

* 4 4,000 -0.46 14.47 -1.39 12.53 -2.34 10.48 -3.30 8.41

  3,000 0.00 0.00 -0.94 12.40 -1.89 10.35 -2.87 8.31

  4 0 6 2,000 0.96 13.92 0.00 0.00 -0.97 10.04 -1.97 8.08

  7 1,500 1.97 13.50 0.99 11.67 0.00 0.00 -1.01 7.86

  8 1,200 3,05 12,95 2,05 11,16 1,03 9,31 0,00 0,00

  Condition corresponding to the values: KaO / YaO = 0.70, KaR / 'YaR = 1.52

Table 79

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the median position (135.0 mm) of the eighth example f = 135.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,566 5,000 -1,188 4,000 - 1,523

POS R rs r rs r rs

  1 0.000 -3.366 0.000 -3.198 -3.031 -2, 948

  2 10,000 -3.304 -3.137 0.000 -2.972 -2, 889

  3 5,000 -3,235 -3,071 -2,907 0,000 -2, 826

  4,000 -3,199 -3,035 -2,873 -2,792,0,000

3,000 -3.134 -2.972 -2.812 -2.731

  6 2,000 -2,984 -2,827 -2,670 -2, 592

  7 1.500 -2.804 -2.652 -2.501 -2, 426

  8 1,200 -2,584 -2,441 -2,298 -2, 227

POS R bf I bf t bf I bf t

  1 0.000 0.00 0.00 -1.81 92.30 -3.60 84.53 -4.49 80, 44

  2 10,000 1.87 101.28 0.00 0.00 -1.85 83.54 -2.76 79, 36

  3 5,000 3.84 99.01 1.91 90.81 0.00 0.00 -0.95 78, 02

  4,000 4.87 98.09 2.90 89.82 0.96 81.84 0.00 0.00

  5 3,000 6.65 96.41 4.62 88.11 2.63 79.72 1.64 75.17

  6 2,000 10.47 92.34 8.32 84.17 6.20 75.99 5.15 71, 84

  7 1,500 14.69 87.99 12.40 80.23 10.14 72.60 9.02 68, 83

  8 1,200 19.38 83.48 16.92 76.24 14.50 69.20 13.31 65, 76

  (R, ANGLE) = 3,000 -2,122 2,000 -3,509 1,500 -5,241 1,200 -7,500

2 5 POS R rs r rs r rs

  1 0.000 -2.808 -2.525 -2.236 -1, 938

  2 10,000 -2,751 -2,471 -2.185 -1, 891

  3 5,000 -2,689 -2,412 -2,130 -1,841

  4,000 -2,656 -2,380 -2,101 -1,814

  3 0 5 3,000 -2,596 0,000 -2,324 -2,049 -1,767

  6 2,000 -2,461 -2,198 0,000 -1,932 -1, 661

  7 1,500 -2,300 -2,049 -1,796 0.000 -1, 539

  8 1,200 -2,108 -1,872 -1,635 -1,386 0, 000

POS R bf f bf I bf t bf I

  1 0.000 -5.96 73.06 -8.86 59.45 -11.72 47.84 -14.54 36, 50

  2 10,000 -4.28 71.85 -7.27 58.46 -10.21 47.15 -13.11 35.98

  3 5,000 -2.51 70.31 -5.60 57.37 -8.63 46.41 -11.62 35, 42

  4 4,000 -1.59 69.40 -4.73 56.81 -7.81 46.05 -10.84 35, 12

  3,000 0.00 0.00 -3.22 55.92 -6.39 45.44 -9.50 34.61

  4 0 6 2,000 3.41 65.41 0.00 0.00 -3.35 44.20 -6.63 33.39

  7 1,500 7.17 62.95 3.55 52.48 0.00 0.00 -3.48 31, 47

  8 1,200 11.34 60.34 7.47 50.47 3.69 41.34 0.00 0, 00

  Condition corresponding to the values: KaO0yao = 0.77, KaR / YaR = 1.40

Table 80

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the telephoto end (200.0 mm) of the eighth example f = 200, Omm

  (R, ANGLE) = 0,000 0,000 10,000 -0,567 5,000 -1,190 4,000 -1,525

POS R rs r rs r rs

  1 0.000 -7.394 0.000 -6.878 -6.391 -6, 158

  2 10,000 -7,349 -6,828 0,000 -6,341 -6, 109

  3 5,000 -7,299 -6,778 -6,291 0,000 -6,058

  1 0 4 4,000 -7,275 -6,752 -6,264 -6,027 0,000

3,000 -7,226 -6,700 -6,207 -5,967

  6 2,000 -7,097 -6,563 -6,061 -5,820

  7 1,500 -6,908 -6,367 -5,861 -5,618

  8 1,200 -6,620 -6,077 -5,571 -5, 330

POS R bf t bf i bf i bf

  1 0.000 0.00 0.00 -3.90 536.53 -7.60 481.38 -9.39 429.63

  2 10,000 4.16 677.88 0.00 0.00 -3.95 502.26 -5.85 429.82

  3 5,000 8.68 679.26 4.22 568.84 0.00 0.00 -2.03 390.50

  4,000 11.09 688.18 6.47 580.29 2.10 490.77 0.00 0.00

  5 3,000 15.35 677.43 10.44 556.71 5.80 431.35 3.58 363.92

  6 2,000 24.91 620.40 19.32 496.79 14.06 384.73 11.55 336.66

  7 1,500 36.18 550.24 29.74 440.07 23.72 346.70 20.86 307.91

  8 1,200 49.65 474.13 42.13 382.69 35.15 307.02 31.85 275.46

  (R, ANGLE) = 3,000 -2,124 2,000 -3,510 1,500 -5,237 1,200 -7,500

2 5 POS R rs r rs r rs

  1 0,000 -5,781 -5,058 -4,367 -3, 691

  2 10,000 -5,730 -5,004 -4,312 -3, 637

  3 5,000 -5,674 -4,944 -4,250 -3,576

  4,000 -5,642 -4,910 -4,216 -3, 543

  3 0 5 3,000 -5,580 0,000 -4,847 -4,154 -3,482

  6 2,000 -5,431 -4,696 0,000 -4,006 -3, 340

  7 1,500 -5,229 -4,498 -3,814 0,000 -3,158

  8 1,200 -4,944 -4,224 -3,555 -2,919 0, 000

POS R bf i bf t bf i bf I

  1 0.000 -12.28 341.22 -17.75 230.41 -22.87 157.75 -27.68 104.61

  2 10,000 -8.92 332.54 -14.73 224.58 -20.14 154.25 -25.21 102, 51

  3 5,000 -5.30 313.45 -11.47 217.19 -17.20 150.28 -22.57 100, 21

  4 4,000 -3.38 305.95 -9.75 213.89 -15.65 148.33 -21.17 99.03

  3,000 0.00 0.00 -6.72 208.26 -12.93 144.95 -18.72 96.97

  6 2,000 7.53 281.46 0.00 0.00 -6.92 137.39 -13.33 92.37

  7 1,500 16.28 258.81 7.77 184.07 0.00 0.00 -7.15 87.04

  8 1,200 26.58 233.22 16.85 167.57 8.04 118.49 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 0.90, KaR / YaR = 1.26 The results of the computation of the rate of variation of Ka as a function of ya for the set focused at infinity and the set focused at the shortest distance at the wide-angle end, in the middle position and at the telephoto end of the example of Japanese Patent Application Laid-Open No. 5-142475 in the eighth

  example of the invention are as follows.

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Kao / Yao Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0, 43 Eighth example At infinity Kao / YaO Nearest KaR / YaR Wide-angle (F = 72.0) 0.70 1.52 Median position 0.77 1.40

(F = 135.0)

  Telephoto (F = 200.0) 0.90 1.26 As previously described, in the eighth example, since the rate of variation of Ka with respect to ya is small compared to the conventional system, the contribution of the correction term (ABf / g) in the relation Ka = Ya (1 - ABf / 9) can be reduced. For this reason, the error of the conversion coefficient Ka calculated from ya and y or the error of the actual driving amplitude Aa of lenses obtained when a single pair of values of the conversion coefficient Δa and the coefficient correction

  is established, can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and the eighth example according to the invention when the driving amplitudes of the lenses during focusing for the set focused to infinity on the object at the shortest distance and during the focusing of the focused assembly at the shortest distance on an object at infinity at the wide-angle end, in the middle position and at the telephoto end are calculated from the relation Aa = ABf / Ya (1 - ABf /) and the errors of the actual driving amplitudes of the lenses are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing with the infinite focusing set on the object at the shortest distance takes the value of the object distance (POS-5), and that the value of the correction coefficient y when focusing with the set focused at the shortest distance on the object at infinity takes the value of the

object distance (POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest-Near-Focused-Infinity Wide-angle (F = 36.0) -4.4% -13.0% Midpoint (F = 50.0) -11, 8% -12.0% Telephoto (F = 103.0) -12.6% -14, 6% Eighth example Infinity Focused Most Nearest Focused at infinity Wide-angle (F = 72.0) -4.7% -1.2% Median position (F = 135.0) -3.9% -1.1% Telephoto (F = 200.0) - 3.4% -1.2% As described previously, in the eighth example, even when only one pair of the conversion coefficient γ and the correction coefficient i is set for a given range of the lens assembly, an error between the conversion coefficient Ka calculated from Ya and y and the lens driving amplitude Aa for focusing becomes low compared to the conventional system and the focusing can be performed with greater precision. Table 81 indicates the manually focusing amplitude (ANGLE DA) with the focus cam (middle part of table 73) of the eighth example, the displacement amplitude DX (mm) in the direction of the optical axis of the focusing lens assembly corresponding to the rotation amplitude for focusing, and the displacement amplitude Bf (mm) of the image forming point when the displacement amplitude (DX)

  in the direction of the optical axis is given.

  It should be noted that the layout and symbols of the

  table are the same as in the first mode of

  tion. The upper part of Table 81 shows the

  displacement study (Bf) of the imaging point corresponding to the photography distances (R = 5.0, 4.0, 3.0, 2.0, 1.5 and 1.2 m) in the respective states focal length variation (F = 72.0, 105.0, 135.0,, 0 and 200.0 mm), and the median portion indicates the focus values (ANGLE DA) required for obtaining an optimum focused state for the respective photography distances. The lower part of the table indicates the magnitudes of displacement (DX), in the direction of the optical axis, of the respective sets of lenses corresponding to the amplitude of rotation (ANGLE DA) for the focusing, with the distances

  focal lengths and distances of photography.

Table 81

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the eighth example 1,20m 1,50m 2,00 m 3,00 m 4,00 m 5,00 m 72,000 Bf 0,000 0, 000 0.000 0.000 0.000 0.000, 000 Bf 0.000 0.000 0.010 0.011 0.008 0.007, 000 Bf 0.000 0.007 -0, 001 -0.005 -0.004 -0.004, 000 Bf 0.000 -0.005 -0.014 -0.013 -0.011 -0.009, 000 Bf 0.000 0.000 0.000 0 , 000 0,000 0,000

  ANGLE DA -7,500 -5,237 -3,510 -2,214 -1,525 -1,190

  F 72,000 DX 0,000 0,000 1,618 0,000 R 1,20 m F 105,000 DX 0,000 0,000 2,431 0,000 R 1,20 m F 135,000 DX 0,000 0,000 3,252 0,000 R 1,20 m F 150,000 DX 0,000 0,000 3,695 0,000 R 1,20 m F 200,000 DX 0,000 0,000 5,357 0,000 R 1,20 m F 72,000 DX 0,000 0,000 1,268 0,000 R 1,50 m F 105,000 DX 0,000 0,000 1,905 0,000 R 1,50 m F 135,000 DX 0,000 0,000 2,550 0,000 R 1,50 m F 150,000 DX 0,000 0,000 2,903 0,000 R 1,50 m F 200,000 DX 0,000 0,000 4,237 0,000 R 1,50 m F 72,000 DX 0,000 0,000 0,932 0,000 R 2,00 m F 105,000 DX 0,000 0,000 1,398 0,000 R 2,00 m F 135,000 DX 0,000 0,000 1,879 0,000 R 2,00 m F 150,000 DX 0,000 0,000 2,142 0,000 R 2,00 m F 200,000 DX 0,000 0,000 3,147 0,000 R 2,00 m F 72,000 DX 0,000 0,000 0,609 0,000 R 3,00 m F 105,000 DX 0,000 0,000 0,913 0,000 R 3.00 m F 135,000 DX 0,000 0,000 1,231 0,000 R 3,00 m F 150,000 DX 0,000 0,000 1,405 0,000 R 3,00 m F 200,000 DX 0,000 0,000 2,081 0,000 R 3.00 m F 72,000 DX 0,000 0,000 0,452 0,000 R 4 00 m F 105,000 DX 0,000 0,000 0,678 0,000 R 4.00 m F 135,000 DX 0,000 0,000 0,916 0,000 R 4,00 m F 150,000 DX 0,000 0,000 1,046 0,000 R 4,00 m F 200,000 DX 0,000 0,000 1,555 0,000 R 4,00 m F 72,000 DX 0,000 0,000 0,360 0,000 R 5, 00 m F 105,000 DX 0,000 0,000 0,539 0,000 R 5,00 m F 135,000 DX 0,000 0,000 0,729 0,000 R 5,00 m F 150,000 DX 0,000 0,000 0,833 0,000 R 5,00 m F 200,000 DX 0,000 0,000 1,241 0,000 R 5,00 m As shown in Table 81, in the zoom lens of the eighth example, so-called "manual" focusing can be achieved because the magnitudes of displacement of the imaging point at the respective focal distances and photograph distances are very small. and enter the depth of field regardless of the setting status

  focus and distance photography.

  In the eighth example, as shown in Tables 75 and 76, the conversion coefficient yx associated with

  the direction of the optical axis decreases slightly at the end

  wide-angle and mid-position when the distance to photography is closer to the shorter distance. Consequently, since the conversion coefficient Ya associated with the rotation is defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, we can consider that the slope (dx / da) of the focusing cam preferably increases when the distance of photography approaches the shortest

  as in the example of the Japanese patent application

  placed in public inspection no. 5-142475. However, as the yx conversion coefficient associated with the direction

  of the optical axis increases greatly at the far end of

  lens in relation to the wide-angle end and to the

  median position, the slope (dx / da) of the focus cam

  sation preferably decreases when the photographing distance approaches the smallest distance according to the invention taking into account the speed of variation of the

  conversion coefficient is associated with the direction of rota-

tion as a whole.

  Ninth Embodiment A zoom lens of the ninth embodiment or ninth example is a lens comprising a four-set arrangement, i.e. positive, negative, positive and positive lens sets, and provides focusing with a second set of negative type lenses, as in the example of Japanese Patent Application Laid-Open No. 5,144,575, described in detail above with reference to the prior art. For this purpose, the ratio (aF / az) of the focus rotation amplitude of the infinitely focused position to the focused position at the nearest location (R = 0, 85 m) and the Focal length variation rotation amplitude of the wide-angle end (F = 36.0 mm) at the telephoto end (F = 103.0 mm) is set to

-0.75.

  Table 82 shows various paraxial data of an optical system and data determining the configuration

  of the focusing cam of the ninth example.

  The upper portion of table 82 indicates the focal length and key point interval data of the respective sets of lenses in the

  optical system of the ninth example.

  In this table, F1, F2, F3 and F4 respectively designate

  the focal lengths of the first, second, third and fourth sets of lenses and D1, D2, D3 and D4 are respectively the intervals between the main points between the first and the second set of lenses, between the second and third sets of lenses. between the third and fourth sets of lenses and between the

  fourth set of lenses and a predefined

  completed for six states of focal length variation

  (F = 36.0, 50.0, 60.0, 70.0, 85.00 and 103.0 mm). As a result

  therefore, these data are the same as the various paraxial data (upper part of Table 1) of the example of the Japanese patent application laid open to the public.

No. 5-142475.

  The middle part of table 82 indicates the spline sample data when the configuration (curve g2F of FIG. 3B) of the focusing cam of the second lens group of the ninth example, used for focusing, is represented by the aforementioned function of spline associated with the angle of rotation of a rotating barrel and the amplitude x of displacement in the direction

of the optical axis.

  In addition, the lower part of table 82 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm), and the magnitudes of rotation (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.5 , 1.0 and 0.85 m) using the focusing cam of the ninth example. In the lower part of Table 82, as the amplitude of rotation at the focal length variation of the wide-angle end (F = 36.0 mm) at the telephoto end (F = 103.0 mm) is set to 0, and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 0.85 m) is set to -7.5, the ratio (aF / az) of the focusing and focal length variation amplitudes of the ninth example is

equal to -0.75.

Table 82

  Ninth example f = 36.0 to 103.0 (ratio of rotation amplitudes: aF / az = -0.75) Focal distances and intervals of the main points of the objectives of the ninth example

1-POS 2-POS 3-POS 4-POS 5-POS 6-POS

  F 36,0000 50,0000 60.0000 70.0000 85.0000 103.0000

  F1 71.3528 D1 10.0000 16.9506 20.8432 24.0040 27.6859 31.0684

  F2 -16,8076 D2 18,0119 13.8825 11.8221 10,1086 7,9077 5,6236

  F3 37.3219 D3 13.2200 12.3744 11.9702 11.6986 11.3811 11.3103

  F4 61.7098 D4 53.2211 59.4228 62.5744 65.172 68.2854 71.2371

  Focusing cam shape (spline interpolated point) corresponding to the ninth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.3230 0.0000 0.0000

  2 -10,0000 0.0000 1.2489 0.0000 0.0000

  3 -7.5000 0.0000 1.0365 0.0000 0.0000

  4 -5.9106 0.0000 0.8749 0.0000 0.0000

-3,4773 0.0000 0.5760 0.0000 0.0000

  6 -2.4665 0.0000 0.4295 0.0000 0.0000

  7 -1.5604 0.0000 0.2847 0.0000 0.0000

  8 -0.8999 0.0000 0.171 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,5000 0.0000 -0.5740 0.0000 0.0000

  1 1 4.0894 0.0000 -1.0445 0.0000 0.0000

  12 6.5227 0.0000 -2.0183 0.0000 0.0000

  13 7.5335 0.0000 -2.5636 0.0000 0.0000

  14 8.4396 0.0000-3.156 0.0000 0.0000

9,1001 0.0000 -3,7034 0.0000 0.0000

  16 10.0000 0.0000 -4.6540 0.0000 0.0000

  17 11.0000 0.0000 -6.0900 0.0000 0.0000

  Amplitude of rotation for focal length change and amplitude of rotation for focusing of the ninth example (ratio of amplitudes of rotation: aF / az = -0.75) Focal length Position corresponding to Distance of Amplitude of rotation infinity photography for focusing 36.0 mm 0.0000 5.00 m -0.900 3 5 50.0 mm 3.3747 3.00 m -1.560, 0 mm 5.3126 2.00 m -2.466, 0 mm 6.8602 1.50 m -3,477, 0 mm 8,5875 1,00 m - 5,911 103,0 mm 10,0000 0,85 m -7, 500 Condition Matching Value (6) 1,59 Condition Matching Value (7) 3,94 Condition corresponding to value (8) -0.75 Condition corresponding to value (12) 0.50 (wide-angle) 0.34 (telephoto) Condition corresponding to value (13) 0.77 (wide-angle) 0.87 (teleobjective ) Condition corresponding to value (14) 1.34 (wide-angle) 1.26 (telephoto) Table 83 below shows the numerical value data of the cams of the focus lens assembly of the ninth example, the data being calcu interpolated using a spline function and using data from the samples of the

  focus cam of the middle part of table 82.

  In this table (ANGLE) designates the rotation angle of the rotary barrel, (2) the amplitude (mm) of displacement in the direction of the optical axis of the second set of lenses and (F) the focal length (mm) from the entire system to the infinite focused state corresponding to

the amplitude of rotation (ANGLE).

Table 83

  Numeric Cam Values for the Focusing Lens of the Ninth Example Focusing Cam Numerals Focal Length Compensation Cam Numerical Values

ANGLE (2) F ANGLE (2) F

-7.5000 1.0365 0.0000

-7.0000 0.9882 0.0000

-6.5000 0.9376 0.0000

-6.0000 0.8846 0.0000

-5.5000 0.8292 0.0000

-5.0000 0.7711 0.0000

-4.5000 0.7102 0.0000

-4.0000 0.6463 0.0000

-3,5000 0.5792 0.0000

-3.0000 0.5087 0.0000

-2.5000 0.4346 0.0000

-2.0000 0.3567 0.0000

-1.5000 0.2746 0.0000

-1.0000 0.1880 0.0000

2 0 -0.5000 0.0965 0.0000

  0.0000 0.0000 36.0000 0.0000 0.0000 36.0000

  0.5000 -0.1018 37.8527 0.5000 0.2874 37.8527

  1.0000 -0.2095 39.7739 1.0000 0.5787 39.7739

  1.5000 -0.3236 41.7710 1.5000 0.8752 41.7710

  2.0000 -0.4449 43.8494 2.0000 1.1779 43.8494

  2.5000 -0.5740 46.0113 2.5000 1.4874 46.0113

  3,0000 -0,7115 48,2581 3,0000 1,8042 48,2581

  3,5000 -0,8583 50,5936 3,5000 2,1295 50,5936

  4.0000 -1.0153 53.0235 4.0000 2.4641 53.0235

  3 0 4,5000 -1,1834 55,5614 4,5000 2,8089 55,5614, 0000 -1,3645 58,2390 5,0000 3,1669 58,2390

  , 5000 -1,5607 61,0923 5,5000 3,5411 61,0923

  6,0000 -1,7743 64,1537 6,0000 3,9342 64,1537

  6,5000 -2,0072 67,4546 6,5000 4,3478 67,4546

  7,0000 -2,2622 71,0314 7,0000 4,7845 71,0314

  7.5000 -2.5437 74.9521 7.5000 5.2500 74.9521

  8.0000 -2.8572 79.2786 8.0000 5.7510 79.2786

  8,5000 -3,2109 84,0989 8,5000 6,2975 84,0989

  9.0000 -3.6152 89.5118 9.0000 6.9013 89.5118

  4 0 9.5000 -4.0860 95.6899 9.5000 7.5804 95.6899

  , 0000 -4,6540 103,0000 10,0000 8,3719 103,0000

  The left side of table 83 gives the numerical values of the focus cam of the ninth example and the right part gives those of the focus compensation cam. A value obtained by synthesis of the amplitudes (2) of displacement in the direction of the optical axis of the numerical value of the focusing cam and the zoom compensation cam, in the range of the amplitude of rotation (ANGLE = 0.0) to the amplitude of rotation (ANGLE = 10.0), coincides with the place of displacement (curve g2 in FIG. 3A) of the second set of lenses calculated using the paraxial data of the upper part of

table 82.

  As a result, the zoom compensation cam (curve g2H of FIG. 3B) is determined by subtracting the focus cam (curve g2 of FIG. 3B) from the displacement location (curve g2 of FIG. 3A) during the variation. of the focal length of the second set of lenses determined by the paraxial data of the part

Table 82.

  3A is briefly described below and

3B and Figure 4.

  FIG. 3A shows the paraxial arrangement and the places of displacement during the zooming of the zoom lens of the ninth example, and FIG. 3B shows the configurations of the focusing cam and the zoom compensation cam of the second set of lenses of this example. In FIGS. 3A and 3B, Gl, G2, G3 and G4 respectively represent the first, second, third and fourth sets of lenses, and gl, g2, g3 and g4 respectively represent the places of displacement during the variation of focal lengths in the first, second, third and fourth sets of lenses. In

  In addition, g2F and g2H represent respectively the configu-

  feeding of the focusing cam and the zoom compensation cam of the second set of lenses. As described previously, a configuration obtained by synthesis

  of the focus cam g2F and the compensation cam g2H

  zooming of the second set of lenses coincides with

  the place of displacement g2 of the second set of lenses.

  FIG. 4 is a view allowing the description of

  the configuration of the focusing cam g2F of the ninth embodiment. In Figure 4, (f = 36, R = one) and (f = 36, R = 0.85) represent respectively the positions focused at infinity and at the shortest distance (R = 0.85 m) at the wide-angle end, and the positions of

  coordinates (x; a) on the focusing cam are respectively

  (x; a) = (0; O) and (x; a) = (1.037; -7.5). On the other hand,

  (f = 103, R = one) and (f = 103, R = 0.85) represent respectively

  the positions focused at infinity and at the shortest distance (R = 0.85 m) at the telephoto end, and the positions of the coordinates (x; a) on the focusing cam are respectively (x; a) ) = (-4.654; 10) and

(x; a) = (-0.574; 2.5).

  When varying the focal length from the wide-angle end to the telephoto end, the second set of lenses moves on the focusing cam g2F from the coordinate position (0; 0) to the coordinate position ( -4.654; 10) for an object at infinity, and the coordinate position (1.37; -7.5) at the coordinate position (-0.574; 2.5) for the object at the lowest distance. As a result, the second set of lenses moves 10.0 in rotation (direction of the axis a) in both cases. On the other hand, when focusing the infinite disposition to the object at the shortest distance, the second set of lenses moves on the focusing cam g2F from the coordinate position (0; 0) to the

  coordinate position (1,035; -7,5) at the large end

  angle, and coordinate position (-4.654; 10) at the coordinate position (-0.574; 2.5) at the telephoto end. As a result, the second set of lenses moves -7.5 in rotation (direction of the axis a) at these ends. In contrast, in the direction of the optical axis (x-axis direction), the second set of lenses moves from 1.037 to the wide-angle end and

  from 4.08 to the telephoto end.

  Since the configuration of the focusing cam g2F is determined by interpolation of the coordinates (f = 36, R = 0.85), (f = 36, R = one), (f = 103, R = 0.85) and ( f = 103; R = a) by the spline function, the slope variation (dx / da) of the focusing cam g2F becomes larger when the absolute value of the coordinate x2 (f = 0.36; R = 0 , 85) is smaller or when the absolute value of the x2 coordinate (f = 103; R = one) is larger. More precisely, when the ratio (AxTR / AxwR) between the amplitudes AXTR and AxwR of displacement in the direction of the optical axis of the set of focusing lenses necessary for the focusing of the infinite to the

  shorter distance at the wide-angle end and the

  Telephoto mite is larger, slope variation

  (dx / da) of the focusing cam becomes larger.

  The following tables 84, 85 and 86 indicate the focusing amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses, the magnifications Px of image formations of the respective sets of lenses. lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  Ya conversion associated with rotation at the far end

  angle (F = 36.0 mm), medial position (F = 50.0 mm) and telephoto end (F = 104.0 mm) in the ninth example. In these tables, (R) on the left indicates the photography distance (m), (ANG) the rotation amplitude of the focusing cam during focusing at the respective photography distances, and 1), 2), 3) and 4) on the right represent the first, second, third and fourth sets of lenses, respectively. In addition, in these tables, the first part gives the displacement amplitude DX (mm) for focusing in the direction of the optical axis when focusing at the respective photography distances (T = 10.0, 5.0 , 3.0, 2.0, 1.5, 1.0 and 0.85 m) (note that moving to the side of the object is positive). The second part gives the image-forming magnifications PK of the respective sets of lenses in the focused state at the respective photographing distances (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m). The third part gives the conversion coefficient Yx, associated with the direction of the optical axis of the set of focusing lenses in the focused state at the respective photography distances (R = 10.0, 5.0, 3, 0, 2.0, 1.5, 1.0 and 0.85 m). In addition, the fourth part gives the slope (dx / da) of the focusing cam at the positions on this cam which correspond to the focused state at the respective photographing distances (R = 10.0, 5.0, 3). , 0, 2,0, 1,5, 1,0 and 0,85 m), and the fifth part gives the conversion coefficient Ya associated with the rotation of the set of focusing lenses in the focused state at distances respective

  photograph (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m).

Table 84

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (36.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 0.085 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 0,170 3) 0,000 4) 0,000

* R 3,000 ANG -1,560 1) 0,000 2) 0,285 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 0,430 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 0,576 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.037 3) 0.000 4) 0.000

  Lens magnification P3k at the wide-angle end (36.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,377 3) -9,721 4) 0,138

  R 10,000 ANG -0.438 1) -0.007 2) -0.372 3) -9.721 4) 0.138

  R 5,000 ANG -0,900 1) -0,015 2) -0,367 3) -9,721 4) 0,138

  R 3,000 ANG -1,560 1) -0,025 2) -0,360 3) -9,721 4) 0,138

  R 2,000 ANG -2,466 1) -0,039 2) -0,352 3) -9,721 4) 0,138

  R 1,500 ANG -3,477 1) -0,054 2) -0,343 3) -9,721 4) 0,138

  R 1,000 ANG -5,911 1) -0,088 2) -0,325 3) -9,721 4) 0,138

  R 0.850 ANG -7.500 1) -0.107 2) -0.316 3) -9.721 4) 0.138

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (36.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,533 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 1.540 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 1,547 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 1,556 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 1,567 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 1,578 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 1,599 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.610 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide-angle end (36.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,198 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.189 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,180 3) 0,000 4) 0, 000

  R 3,000 ANG -1,560 1) 0,000 2) -0,167 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,152 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,138 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,109 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.095 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the wide-angle end (36.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,304 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.291 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,278 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -0,261 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,239 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,217 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,175 3) 0,000 4) 0,000

  R 0.850 ANG -7,500 1) 0,000 2) -0,152 3) 0,000 4) 0,000

  3 0 Condition corresponding to the values: YxR / 7xO = 1.05, yaR / YaO = 0, 50

Table 85

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 0.127 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) 0,254 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) 0,422 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) 0,632 3) 0,000 4) 0,000

  R 1.500 ANG -3.480 1) 0.000 2) 0.841 3) 0.000 4) 0.000

  R 1,000 ANG -5,910 1) 0,000 2) 1,261 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 1.483 3) 0.000 4) 0.000

  Nk image magnification of lenses at the median position (50.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,447 3) -42,292 4) 0,037

  R 10,000 ANG -0.438 1) -0.007 2) -0.440 3) -42.292 4) 0, 037

  R 5,000 ANG -0,901 1) -0,015 2) -0,432 3) -42,292 4) 0, 037

  R 3,000 ANG -1,562 1) -0,025 2) -0,422 3) -42,292 4) 0,037

  R 2,000 ANG -2,469 1) -0,040 2) -0,409 3) -42,292 4) 0,037

  R 1,500 ANG -3,480 1) -0,055 2) -0,397 3) -42,292 4) 0,037

  R 1,000 ANG -5,910 1) -0,089 2) -0,372 3) -42,292 4) 0,037

  R 0.850 ANG -7.500 1) -0.109 2) -0.359 3) -42.292 4) 0.037

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,966 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) 1.982 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) 1,998 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) 2,019 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) 2,045 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) 2,069 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) 2,117 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 2.140 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,298 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.282 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) -0,265 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) -0,244 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) -0,219 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) -0,196 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) -0,151 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.129 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the median position (50.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,587 3) 0,000 4) 0,000

  R 10,000 ANG -0.438 1) 0.000 2) -0.558 3) 0.000 4) 0.000

  R 5,000 ANG -0,901 1) 0,000 2) -0,530 3) 0,000 4) 0,000

  R 3,000 ANG -1,562 1) 0,000 2) -0,494 3) 0,000 4) 0,000

  R 2,000 ANG -2,469 1) 0,000 2) -0,448 3) 0,000 4) 0,000

  R 1,500 ANG -3,480 1) 0,000 2) -0,406 3) 0,000 4) 0,000

  R 1,000 ANG -5,910 1) 0,000 2) -0,320 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.277 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / YxO = 1.09, YaR / 'Yao = 0.47

Table 86

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (103.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) 0.502 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 0,951 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 1,488 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 2,090 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 2,636 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 3,609 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) 4.080 3) 0.000 4) 0.000

  Lens magnification Ok at the telephoto end (103, 0 mm) of the ninth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,716 3) 13,060 4) -0,154

  R 10,000 ANG -0.437 1) -0.007 2) -0.686 3) 13.060 4) -0, 154

  R 5,000 ANG -0,900 1) -0,015 2) -0,659 3) 13,060 4) -0,154

  R 3,000 ANG -1,560 1) -0,026 2) -0,627 3) 13,060 4) -0,154

  R 2,000 ANG -2,466 1) -0,040 2) -0,592 3) 13,060 4) -0,154

  R 1,500 ANG -3,477 1) -0,055 2) -0,559 3) 13,060 4) -0,154

  R 1,000 ANG -5,911 1) -0,090 2) -0,501 3) 13,060 4) -0,154

  R 0.850 ANG -7.500 1) -0.112 2) -0.473 3) 13.060 4) -0.154

  Coefficient of conversion Yx associated with the direction of the optical axis at the telephoto end (103.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,982 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) 2.152 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) 2,298 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) 2,465 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) 2,643 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) 2,795 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) 3,044 3) 0,000 4) 0,000

  R 0.850 ANG -7,500 1) 0,000 2) 3,155 3) 0,000 4) 0,000

  Slope dx / da focus cam at the telephoto end (103.0 mm) of the ninth

example

  R 0,000 ANG 0,000 1) 0,000 2) -1,257 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) -1.052 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -0,895 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -0,742 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -0,597 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -0,489 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -0,329 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.266 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (103.0 mm) of the ninth example

  R 0,000 ANG 0,000 1) 0,000 2) -2,492 3) 0,000 4) 0,000

  R 10,000 ANG -0.437 1) 0.000 2) -2.263 3) 0.000 4) 0.000

  R 5,000 ANG -0,900 1) 0,000 2) -2,056 3) 0,000 4) 0,000

  R 3,000 ANG -1,560 1) 0,000 2) -1,829 3) 0,000 4) 0,000

  R 2,000 ANG -2,466 1) 0,000 2) -1,578 3) 0,000 4) 0,000

  R 1,500 ANG -3,477 1) 0,000 2) -1,366 3) 0,000 4) 0,000

  R 1,000 ANG -5,911 1) 0,000 2) -1,001 3) 0,000 4) 0,000

  R 0.850 ANG -7.500 1) 0.000 2) -0.840 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / YxO = 1.59, YaRYao = 034 As shown in Tables 84, 85 and 86, for

  each focal length, the associated conversion coefficient

  The direction of the optical axis increases, but the slope (dx / da) of the focusing cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is closer to the lower value because of the slope (dx / da) of the focusing cam, contrary to the example of the request for

  Japanese Patent Laid-Open No. 5-142475.

  As described previously, when the ratio (AxTR / AxwR) between the axial displacement amplitudes AxTR and AxWR, in the direction of the optical axis, of the set of focusing lenses necessary for the focusing of the position to infinity to the position at the shortest distance, at the wide-angle end and at the telephoto end, is great, the degree of slope reduction

  (dx / da) of the focusing cam becomes as important.

  For this reason, the conversion coefficient Ya associated with the rotation decreases further under the influence of the slope (dx / da) of the focusing cam when the distance of

  photography is getting closer to the shorter distance.

  In tables 84, 85 and 86, the rate of change, from the position focused at infinity to the position focused at the shortest distance, of the conversion coefficient Ya associated with the rotation is xO, 50 at the end. wide-angle (F = 36.0 mm), xO, 47 at the center position (F = 50.0 mm), and xO, 34 at the telephoto end (F = 103.0 mm). When the number N of divisions of the focusing range upon a change of the conversion coefficient Ya of the ninth example is calculated with the formula (a) and is compared with the example of the Japanese patent application being inspected 5-142475, the numbers Nw, NM and NT of divisions at the wide-angle end, in the median position and at the end of the telephoto end, respectively have the following values: Example of the Japanese Patent Application Laid-Open inspection n 5-142475 Nw> 9.3 NM> 10.1 NT> 8, 1 ninth example

NW> 3.8 NM> 4.1 NT> 5.9

  Accordingly, as indicated by the comparison with the previously calculated values for the example of Japanese Patent Application Laid-Open No. 5-142475, the values of the ninth example become remarkably low. As previously described, in the zoom lens of the ninth embodiment, as the rate of change, from the infinitely focused position to the closest focused position, the conversion coefficient Ya associated with the rotation becomes much smaller that in the example of Japanese Patent Application Laid-open No. 5-142475, the number of data of the conversion coefficient Ya and the correction coefficient I can be

  reduced, and the storage capacity can be reduced.

  Tables 87, 88 and 89 show the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 36.0 mm), in the median position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the ninth example. In these tables, (R) denotes the object distance (m), (ANG) designates the amplitude of rotation for the focusing of the

  position corresponding to infinity on the focus cam

  sation, (r) is the conversion coefficient Ya in rotation, (rs) is the conversion coefficient Ka, (bf) denotes the focusing defect amplitude (mm), and (Q) denotes the correction coefficient u. Each table has a matrix structure and eight lines 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 0.85 m) and four pairs (R, ANGLE) in a horizontal direction represent the

  lenses of the set of focusing lenses.

  Specifically, the position of the focus lenses of the first pair in both parts

  of each of Tables 87, 88 and 89, that is,

  say in the third and fourth column, is

  (R, ANGLE) = (0,0; 0,0) and indicates that this position corresponds to

  pond to infinity. Consequently, the third column (r) of the first part represents the value of the conversion coefficient Ya in rotation when the set of focusing lenses is focused on the object at infinity, and the fourth column (rs) represents the value of the coefficient

  when the focus lens set

  sation is moved from a focused state on an object to infinity to a focused state at the distance of the given object in the second column. Further, the third column (bf) of the second portion represents the focus defocus amplitude ABf with respect to a predetermined image position when the position of the focus lens assembly is infinite, and a object is at the distance of the object (or distance from the object) from the region, and the fourth column (t) represents the value of the correction coefficient y when the focus lens assembly is moved from the a state focused on an object at infinity to a state focused at the distance from the object given in the

  second column (called in the following distance).

  Similarly, the position of the focusing lens of the fourth pair of the two lower parts of each of the tables 87, 88 and 89, i.e. in the ninth and tenth columns, is (R, ANGLE) = (0, 85; -7.5) and indicates that the position corresponds to the nearest position (R = 85 m). As a result, the ninth column (r) of the third part represents the value of the conversion coefficient ta in rotation when the set of focusing lenses is focused at the smallest distance (R = 0.85 m) and the tenth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is shifted from a focused state to the shortest distance (R = 0.85 m) to the focused state at the distance of the object given in the second column. Further, the ninth column (bf) of the fourth portion represents the focus defocus amplitude ABf from a predetermined image position when the position of the focus lens assembly is the shortest distance, and the object is at the distance indicated in the second column, and the tenth column (Q) represents the value of the correction coefficient y when the set of focusing lenses is shifted from a focused state to the shortest distance (R = 0.85 m) in the focused state at

  the distance given in the second column.

  As previously described, as the conversion coefficient in rotation is calculated by the relation

  Ka = ABf / Aa (Ka being the amplitude of rotation of

  sation), and the correction coefficient y is calculated by the relation y = ABf / (1 - Ka / Ta), the value of the conversion coefficient Ka (eighth row, fourth column of the first part -0.233) when the set of focusing lenses is shifted from the focused state on the object to infinity in the focused state on the object at the shortest distance (R = 0.85 m) in Table 87 is calculated in the form Ka = 1.75 / -7.5 = -0.233 with ABf = 1.75 and Aa = 7.5. On the other hand, the value of the correction coefficient y (eighth row and fourth column of the second table 7.46) is calculated as y = 7.46 using

  ABf = 1.75, Ka = -0.233 and Ya = -0.304.

Table 87

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the wide-angle end (36.0 mm) of the ninth example f = 36.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,438 5,000 -0,900 3,000 - 1,560

POS R rs r rs r rs

  1 0.000 -0.304 0.000 -0.296 -0.288 -0, 277

  2 10,000 -0.299 -0.291 0.000 -0.283 -0, 272

  3 5,000 -0,294 -0,286 -0,278 0,000 -0, 267

  4 3,000 -0,287 -0,279 -0,271 -0,261 0, 000

2,000 -0,278 -0,270 -0,262 -0,252

  6 1,500 -0,268 -0,260 -0,253 -0, 243

  7 1,000 -0,246 -0,239 -0,232 -0, 222

  8 0.850 -0.233 -0.226 -0.219 -0, 211

POS R bf bf f bf f bf

  1 0.000 0.00 0.00 -0.13 8.13 -0.26 7.46 -0.43 6.94

  2 10,000 0.13 8.61 0.00 0.00 -0.13 7.23 -0.31 6, 85

  3 5,000 0.26 8.37 0.13 7.72 0.00 0.00 -0.18 6, 84

  4 3,000 0.45 8.09 0.31 7.52 0.18 7.10 0.00 0.00

  5 2,000 0.68 7.91 0.55 7.44 0.41 7.12 0.23 6, 85

  6 1,500 0.93 7.80 0.79 7.39 0.65 7.09 0.47 6, 79

  7 1,000 1.45 7.58 1.31 7.23 1.16 6.96 0.97 6, 62

  8 0.850 1.75 7.46 1.60 7.13 1.45 6.86 1.25 6, 52

  (R, ANGLE) = 2,000 -2,466 1,500 -3,477 1,000 -5,911 0,850 -7,500

2 5 POS R rs r rs r rs

  1 0.000 -0.263 -0.248 -0.219 -0, 204

  2 10,000 -0.258 -0.244 -0.216 -0, 200

  3 5,000 -0,254 -0,240 -0,212 -0,196

  4 3,000 -0.247 -2.234 -0.206 -0, 191

  3 0 5 2,000 -0,239 0,000 -0,226 -0,199 -0,184

  6 1,500 -0,230 -0,217 0,000 -0,191 -0,177

  7 1,000 -0,211 -0,199 -0,175 0,000 -0,161

  8,850 -0,119 -0,188 -0,165 -0,152,0,000

POS R bf t bf g bf i bf f

  3 5 1 0.000 -0.65 6.51 -0.86 6.05 -1.30 5.05 -1.53 4.52

  2 10,000 -0.52 6.47 -0.74 6.03 -1.18 5.02 -1.41 4, 50

  3 5,000 -0.40 6,46 -0.62 6.01 -1.06 5.00 -1.30 4, 48

  4 3,000 -0.22 6.43 -0.45 5.98 -0.90 4.96 -1.14 4, 44

  2,000 0.00 0.00 -0.23 5.92 -0.69 4.91 -0.93 4.40

  6 1,500 0.23 6.35 0.00 0.00 -0.47 4.85 -0.71 4, 35

  7 1,000 0.73 6.17 0.48 5.68 0.00 0.00 -0.26 4, 23

  8 0.850 1.00 6.06 0.76 5.59 0.26 4.68 0.00 0.00

  Condition corresponding to the values: KaO / yao = 0.77, KaR / YaR = 1.34

Table 88

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the median position (50.0 mm) of the ninth example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,438 5,000 -0,901 3,000 - 1,562

POS R rs r rs r rs r rs 1 0,000 -0,587 0,000 -0,567 -0,548 -0, 522

  2 10,000 -0,578 -0,558 0,000 -0,539 -0,514

  3 5,000 -0,569 -0,549 -0,530 0,000 -0,505

  4 3,000 -0,556 -0,537 -0,518 -0,493 0, 000

2,000 -0,538 -0,520 -0,502 -0,478

  6 1,500 -0,520 -0,502 -0,485 -0,461

  7 1,000 -0,480 -0,463 -0,447 -0,425

  8 0.850 -0.456 -0.440 -0.424 -0, 403

POS R bf b bf f bf bf

  I 0.000 0.00 0.00 -0.25 15.94 -0.49 15.15 -0.82 14.06

  2 10,000 0.25 16.72 0.00 0.00 -0.25 15.02 -0.58 13.94

  3 5,000 0.51 16.57 0.25 15.74 0.00 0.00 -0.33 13.77

  4 3,000 0.87 16.40 0.60 15.59 0.34 14.82 0.00 0.00

  5 2,000 1.33 16.14 1.06 15.33 0.79 14.55 0.43 13.53

  6 1,500 1,81 15,96 1,53 15,19 1,25 14,45 0.88 13.56

  7 1,000 2.84 15.60 2.53 14.88 2.24 14.19 1.85 13.36

  8 0.850 3.42 15.33 3.41 14.62 2.80 13.94 2.39 13.08

  (R. ANGLE) = 2,000 -2,469 1,500 -3,480 1,000 -5,910 0,850 -7,500

POS R rs r rs r rs

  1 0.000 -0.490 -0.460 -0.399 -0, 367

  2 10,000 -0.483 -0.452 -0.392 -0, 360

  3 5,000 -0,475 -0,444 -0,385 -0, 354

  4 3,000 -0.463 -0.434 -0.376 -0, 345

  3 0 5 2,000 -0,448 0,000 -0,420 -0,363 -0,333

  6 1,500 -0,433 -0,406 0,000 -0,350 -0, 321

  7 1,000 -0,399 -0,373 -0,320 0,000 -0,293

  8 0.850 -0.378 -0.353 -0.303 -0.277 0, 000

POS R bf w bf I bf t bf i

  3 5 1 0.000 -1.21 12.83 -1.60 12.07 -2.36 9.64 -2.75 8.49

  2 10,000 -0.98 12.74 -1.38 12.04 -2.15 9.59 -2.54 8.45

  3 5,000 -0.74 12.65 -1.15 12.03 -1.93 9.53 -2.34 8.40

  4 3,000 -0.42 12.57 -0.83 12.07 -1.63 9.45 -2.05 8.33

  2,000 0.00 0.00 -0.42 12.25 -1.25 9.32 -1.68 8.22

* 6 1,500 0.44 12.84 0.00 0.00 -0.85 9.12 -1.29 8.09

  7 1,000 1.37 12.38 0.91 11.05 0.00 0.00 -0.47 7.89

  8 0.850 1.90 12.08 1.42 10.83 0.48 8.82 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 0.78, KaR / YaR = 1.32

Table 89

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the telephoto end (103.0 mm) of the ninth example f = 103.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,437 5,000 -0,900 3,000 -1,560

POS R rs r rs r rs

  1 0.000 -2.491 0.000 -2.285 -2.101 -1, 896

  2 10,000 -2,478 -2,263 0,000 -2,078 -1, 876

  3 5,000 -2,453 -2,237 -2,056 0.000 -1, 857

  4 3,000 -2,423 -2,209 -2,031 -1,829 0,000

2,000 -2,382 -2,168 -1,990 -1,789

  6 1,500 -2,337 -2,124 -1,946 -1, 746

  7 1,000 -2,228 -2,017 -1,842 -1, 647

  8 0.850 -2.157 -1.949 -1.777 -1, 585

POS R bf I bf i bf f bf i

  1 0,000 0.00 0.00 -1.00 101.35 -1.89 86.26 -2.96 80.46

  2 10,000 1.08 206.65 0.00 0.00 -0.96 90.85 -2.11 82.73

  3 5,000 2.21 143.35 1.04 89.82 0.00 0.00 -1.23 81.46

  4 3,000 3.78 137.85 2.48 103.95 1.34 108.77 0.00 0.00

  5 2,000 5.88 133.72 4.40 105.55 3.12 97.61 1.62 73.49

  6 1,500 8,12 130.66 6,46 105.05 5.02 94.01 3.35 74.10

  7 1,000 13.17 124.34 11.04 101.71 9.23 88.89 7.17 72.08

  8 0.850 16.18 120.56 13.77 99.20 11.73 86.25 9.41 70.47

  (R, ANGLE) = 2,000 -2,466 1,500 -3,477 1,000 -5,911 0,850 -7,500

POS R rs r rs r rs

  I 0.000 -1.681 -1.498 -1.196 -1.059

  2 10,000 -1.662 -1.480 -1.180 -1, 044

  3 5,000 -1,643 -1,462 -1,164 -1, 030

  4 3,000 -1,616 -1,436 -1,141 - 1,009

  5 2,000 -1,578 0,000 -1,402 -1.111 - 0.981

  6 1,500 -1,539 -1,366 0,000 -1,078 - 0,950

  7 1,000 -1,446 -1,277 -1,001 0,000 -0,981

  8 0.850 -1.388 -1.223 -0.957 -0.840 0, 000

POS R bf t bf i bf i bf t

  3 5 1 0.000 -4.15 63.20 -5.21 53.84 -7.07 36.24 -7.94 30.52

  2 10,000 -3.37 63.13 -4.50 53.84 -6.46 36.01 -7.38 30.37

  3 5,000 -2.57 62.02 -3.77 53.52 -5.83 35.70 -6.80 30.17

  4 3,000 -1.46 60.78 -2.75 53.47 -4.96 35.29 -5.99 29.91

  2,000 0.00 0.00 -1.42 54.02 -3.83 34.64 -4.94 29.56

  6 1,500 1.56 63.61 0.00 0.00 -2.62 33.79 -3.82 29.20

  7 1,000 4.98 59.61 3.11 47.73 0.00 0.00 -1.40 28.64

  8 0.850 6.98 58.01 4.92 47.04 1.52 35.10 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.87, KaR / YaR = 1.26 As indicated in Tables 87, 88 and 89 above, when considering a change in the conversion coefficient Ka (rs) (by example in the fourth column of the first part of the tables) for a given arrangement of the lenses (for example the infinite focusing arrangement), the rate of variation becomes small compared to the variation of Ka (Tables 6, 7 and 8). ) of the example of the Japanese patent application

  Public Inspection No. 5-142475, discussed previously.

  More precisely, when we consider that the coefficient

  The conversion factor Ka in rotation is defined by Ka = ABf / Aa and the defocusing amplitude ABf are the same as in the example of Japanese Patent Application Laid-open No. 5-142475 for the same disposition

  lenses, the amplitude Aa of rotation for focusing

  of the ninth example on the object side at infinity becomes relatively weaker than on the object side at the shortest distance, compared to the example of demand

  Japanese Patent Laid-Open No. 5-142475.

  In fact, when the ratio of the focusing rotation amplitude to the shortest distance (R = 0.85 m) and the rotation amplitude for focusing at the distance from the object (R = 5, 0 m) is calculated in Tables 1 and 82, we obtain 3,379 / 10,0 = 0,338 for the example of the Japanese patent application laid out to the public inspection

  No. 5-142475 and -0.9 / -7.5 = 0.120 in the ninth example.

  As indicated above, when the focus cam of the arrangement according to the invention is used, as the rotation amplitude Aa for the focusing is smaller on the object side at infinity, the conversion coefficient Ka becomes relatively large on the object side to infinity, so that the variation of the conversion coefficient Ka in rotation can be reduced compared to

classic system.

  The results of the calculation of the rate of variation of the Ka coefficient with respect to ya in the infinite focusing arrangement and focusing at the shortest distance at the wide-angle end (F = 36.0 mm), in the median position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the example of Japanese Patent Application Laid-open No. 5-142475 and in the ninth example of the present invention. invention are as follows. Example of Japanese Patent Application Laid-open No. 5-142475 Infinity KaoIyao Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Ninth example At infinity K1aOyao Nearest KaR / YaR Wide-angle (F = 36.0) 0, 77 1, 34 Median position (F = 50.0) 0.78 1.32 Telephoto (F = 103.0) 0.87 1.26 As previously described, according to the invention, as the speed of variation of Ka with respect to Ya is weak compared to the conventional system and since the contribution of the correction term (ABf / g) in the relation Ka = Ya (1 - ABf / 9) can be reduced, the value of the correction coefficient i can be adjusted to a large extent. value with respect to the focusing defect amplitude ABf and, simultaneously, the variation of the coefficient of

correction can be reduced.

  Accordingly, even when a single pair of values of the conversion coefficient γ and the correction coefficient γ is set for a given range of lens arrangement, an error of the conversion coefficient Ka calculated with Ya and y or on the amplitude actual Aa lens drive when focusing can

to be eliminated.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and the ninth example of the invention, when the lens driving amplitudes for focusing the infinity focused arrangement to the object at the shortest distance and for focusing the focused disposition at the shortest distance on the object at infinity at the wide-angle end (F = 36.0 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) are calculated at

  from Aa = ABf / ya (1 - ABf / g) and the errors of the amplifiers

  The actual driving training of the lenses is then calculated and the following values are obtained. It should be noted that the value of the correction coefficient i when focusing the set focused to infinity on the object at the shortest distance has the value of the object distance (POS-5) and that the value of the correction coefficient y when focusing the focused assembly at the shortest distance to the object at infinity at the corresponding value

at object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Ninth example Infinity focused state most Nearest near-state Focused at infinity Wide-angle (F = 36.0) -1.4% -0.2% Median position (F = 50.0) -1.4% -0.5% Telephoto (F = 103.0) -1.5% -0.4% As previously described, even when only a pair of values of the conversion coefficient ya and the correction coefficient M are set for a given range, an error between the conversion coefficient Ka calculated at from the and y and the lens driving amplitude Aa for focusing becomes low compared to the conventional system, and focusing can be achieved

with greater precision.

  As a reference, when the errors on the driving amplitudes of the lenses during the focusing of the set focused at infinity towards the distance of the object (R = 10.0 m) and during the focusing of the set focused at the shortest distance to the distance of the object (R = 1.0 m) are calculated and compared, the following results are obtained. It can be noted from these tables that the focusing accuracy can be relatively improved regardless of the distance of the object. Example of Japanese Patent Application Laid-Open No. 5-142475 Infinity Focused State to Nearest Condition 10 Lm Focused at 1m Wide Angle (F = 36.0) - 6.7% 1.5 % Median Positon (F = 50.0) 3.2% 2.5% Telephoto (F = 103.0) 5.1% 2.4% Ninth example Infinity focused state to Nearest to state lm focused to 1 m Wide-angle (F = 36.0) - 0.7% 1.7% Median position (F = 50.0) 0.3% 1.0% Telephoto (F = 103.0) 0.0% 0, 2% We now determine if we can obtain not only a precise automatic focusing, but also a so-called "manual" focusing with the zoom lens of

ninth example.

  Table 90 shows the rotation amplitude (ANGLE DA) for manual focusing using the focusing cam (middle part of table 82) of the ninth

  for example, the displacement amplitude DX (mm) in the direc-

  of the optical axis of the set of focal lenses

  corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  The upper part of table 90 indicates the displacement amplitude (Bf) of an image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.85 m) to the respective states of variation of the focal lengths (F = 36.0, 50.0, 60.0, 70, 0, 85.0 and 103.0 mm), and the middle portion indicates the values of the amplitude of rotation (ANGLE DA) for focusing, necessary to obtain an optimal focused state at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0 , 85 m). It should be noted that the focusing rotation amplitudes, which have values enabling the elimination of a possible displacement of the image point at the end

  wide-angle and at the telephoto end, are selec-

  tioned. The lower part of the table gives the ampli-

  displacement studies (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the focusing amplitude (ANGLE DA) with the photography distances (R = 5.0, 3.0, 2, 0, 1.5, 1.0 and 0.85 m) in the respective states of variation of focal lengths (F = 36.0, 50.0, 60.0, 70.0, 85.0 and 103.0 mm). At the bottom, (F) designates the focal length (mm) of the whole system, (R) the distance of photography (m) and (DX) the displacement amplitude (mm) in the direction of the optical axis for each of the first, second, third and fourth sets of lenses, in turn from the right. It should be noted that the amplitude of displacement in the direction of the optical axis towards the side of the object is

  represented by a positive value.

Table 90

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) displacement for focusing of the ninth example 0.85m 1.00 m 1, 50 m 2.00 m 3.00 m 5.00 m 36.000 Bf 0.000 0 , 000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,000 0.001 0.001 0.001 0.001, 000 Bf 0.000 0.001 0.002 0.002 0.001, 000 Bf 0.000 0.000 0.000 -0.002 -0.004 -0.002, 000 Bf 0.000 0.000 -0.005 -0.005 - 0.002, 000 Bf 0.001 -0.001 103.000 Bf 0.000 0.000 0.000 0, 000 0.000 0.000

  ANGLE DA -7,500 -5,911 -3,477 -2,466 -1,560 -0,900

  F 36,000 DX 0,000 1,037 0,000 0,000 R 0,85 m F 50,000 DX 0,000 1,483 0,000 0,000 R 0,85 m F 60,000 DX 0,000 1,872 0,000 0,000 R 0.85 m F 70,000 DX 0,000 2,311 0,000 0,000 R 0.85 m F 85,000 DX 0.000 3,049 0,000 0,000 R 0,85 m F 103,000 DX 0,000 4,080 0,000 0,000 R 0,85 m F 36,000 DX 0,000 0,875 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,261 0,000 0,000 R 1,00 m F 60,000 DX 0,000 1,600 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,990 0,000 0,000 R 1,00 m F 85,000 DX 0,000 2,656 0,000 0,000 R 1,00 m F 103,000 DX 0,000 3,609 0,000 0,000 R 1,00 m F 36,000 DX 0,000 0,576 0,000 0.000 R 1.50 m F 50.000 DX 0.000 0.841 0.000 0.000 R 1.50 m F 60.000 DX 0.000 1.081 0.000 0.000 R 1.50 m F 70.000 DX 0.000 1.365 0.000 0.000 R 1.50 m F 85.000 DX 0.000 1.871 0.000 0.000 R 1.50 m F 103,000 DX 0,000 2,636 0,000 0,000 R 1,50 m F 36,000 DX 0,000 0,429 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,631 0,000 0,000 R 2,00 m F 60,000 DX 0,000 0,817 0,000 0,000 R 2 00 m F 70,000 DX 0,000 1,042 0,000 0,000 R 2,00 m F 85,00 0 DX 0,000 1,449 0,000 0,000 R 2,00 m F 103,000 DX 0,000 2,090 0,000 0,000 R 2,00 m F 36,000 DX 0,000 0,285 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,422 0,000 0,000 R 3,00 m F 60,000 DX 0.000 0.549 0.000 0.000 R 3.00 m F 70.000 DX 0.000 0.708 0.000 0.000 R 3.00 m F 85.000 DX 0.000 1.001 0.000 0.000 R 3.00 m F 103.000 DX 0.000 1.488 0.000 0.000 R 3.00 m F 36.000 DX 0.000 0.170 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,253 0,000 0,000 R 5,00 m F 60,000 DX 0,000 0,332 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,432 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,620 0,000 0,000 R 5.00 m F 103,000 DX 0.000 0.951 0.000 0.000 R 5.00 m As Table 90 shows, so-called focus

  "manual" can be obtained because the amplitudes of

  of the image point at respective focal lengths and respective photography distances are very small and enter the depth of field regardless of the

  of focal length and distance

  graphy. Tenth Embodiment The tenth example relates to a zoom lens having a four-set arrangement, i.e. sets of positive, negative, positive and positive type lenses, and provides focus with a second set of negative type lenses. For this purpose, the ratio (aF / az) of the focusing rotation amplitude of the position focused at infinity to the position focused at the shortest distance (R = 0.5 m) and the amplitude Focal length variation rotation of the wide-angle end (F = 28.8 mm) at the telephoto end

  (F = 103.0 mm) is set at -0.80.

  Table 91 gives various paraxial data of the optical system and data for determining the configuration of the focusing cam in the tenth

example.

  The upper part of table 91 gives the focal lengths and intervals of the main points of the respective sets of lenses of the optical system of the tenth example for six focusing states (focal lengths

  F = 28.8, 35.0, 50.0, 70.0, 85.0 and 103.0 mm).

  The middle portion of Table 91 shows spline sampling data when the focus cam configuration of the second lens set of the tenth example used for focusing is represented by a spline function associated with the rotation angle α. a rotating barrel and the amplitude x of displacement in

the direction of the optical axis.

  In addition, the lower part of table 91 gives the infinite focusing positions (positions corresponding to infinity) at the respective focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85 , 0 and 103.0 mm), and the rotational amplitudes (rotation amplitudes for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) using the focusing cam of the tenth example. In this table, as the zoom range of focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 103.0 mm) is set to an equal value at 10.0 and since the focus rotation amplitude of the infinitely focused position at the position focused at the nearest location (R = 0.5) is -0.0, the ratio ( aF / az) of the rotational amplitudes used for the focusing and for the variation of the focus in the tenth example is

equal to -0.80.

Table 91

  Tenth example f = 28.8 to 103.0 (ratio of amplitudes of rotation: aF / az = -0.8) Focal distances and intervals of the main points of the objectives of the tenth example

1-POS 2-POS 3-POS 4-POS 5-POS 6-POS

  F 28,8000 35,0000 50,0000 70,0000 85,0000 103,0000

  F1 74,0000 D1 9,3999 13,5341 20,7443 27,2220 30,8921 34,4309

  F2 -14,6500 D2 19,7436 17,2131 13,2504 10,0511 8,3204 6,5915

  F3 39,0000 D3 18,6578 18,1057 17.0929 16.2060 15.8259 15.5510

  F4 51.0000 D4 51.5373 55.7437 63.9000 71.6679 75.7659 79.3156

  Focusing cam shape (spline interpolated point) corresponding to the tenth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.3850 0.0000 0.0000

  2 -10.0000 0.0000 1.3095 0.0000 0.0000

  3 8.0000 0.0000 1.1334 0.0000 0.0000

  4 -4.8586 0.0000 0.7860 0.0000 0.0000

-3,0690 0.0000 0.5389 0.0000 0.0000

  6 -1.3807 0.0000 0.2633 0.0000 0.0000

  7 -0.8909 0.0000 0.1743 0.0000 0.0000

  8 -0.5213 0.0000 0.1040 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,0000 0.0000 -0.4569 0.0000 0.0000

  1 1 5,1414 0.0000 -1.4493 0.0000 0.0000

  12 6.9310 0.0000 -2.2575 0.0000 0.0000

  13 8.6193 0.0000 -3.3154 0.0000 0.0000

  14 9,1091 0.0000 -3,7092 0.0000 0.0000

9,4787 0.0000 -4.0447 0.0000 0.0000

  16 10.0000 0.0000 -4.5918 0.0000 0.0000

  17 11.0000 0.0000 -5.8900 0.0000 0.0000

  Rotation amplitude for focal length change and rotation amplitude for focusing of the tenth example (ratio of rotation amplitudes: aF / az = -0.8) Focal length Position corresponding to Distance of amplitude of rotation infinity photography for focusing 28.8 mm 0.0000 5.00 m -0.521 35.0 mm 1.7158 3.00 m -0.891, 0 mm 4.7378 2.00 m -1.381, 0 mm 7.3846 1.00 m -3.069 , 0 mm 8,7811 0,70 m - 4,859 103,0 mm 10,0000 0,50 m -8,000 Condition corresponding to value (6) 1,39 Condition corresponding to value (7) 3,65 Condition corresponding to value (8) -0.80 Condition corresponding to value (12) 0.49 (wide-angle) 0.31 (telephoto) Condition corresponding to value (13) 0.76 (wide-angle) 0.92 (telephoto corresponding condition value (14) 1.34 (wide-angle) 1.25 (telephoto) The following table 92 gives the numerical values of the cams of the focus lens assembly of the tenth example, the data being calculated by interpolation. n with a spline function and taken from the sampling data of the focusing cam of the middle part of table 91. It should be noted that the meanings of the symbols of table 92 are the same as in the

ninth example.

Table 92

  Digital Cam Values for Focusing Objective of Tenth Example Focusing Cam Numerals Focal Length Compensation Cam Numerical Values

ANGLE (2) F ANGLE (2) F

-8.0000 1.1334 0.0000

-7.5000 1.0842 0.0000

-7.0000 1.0329 0.0000

-6.5000 0.9794 0.0000

-6.0000 0.9235 0.0000

-5.5000 0.8650 0.0000

-5.0000 0.8039 0.0000

4.5000 0.7398 0.0000

-4.0000 0.6727 0.0000

1 5 -3.5000 0.6023 0.0000

-3.0000 0.5285 0.0000

-2.5000 0.4511 0.0000

-2.0000 0.3698 0.0000

-1.5000 0.2844 0.0000

-1.0000 0.1945 0.0000

-0.5000 0.0998 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.1051 30.4738 0.5000 0.3770 30.4738

  1.0000 -0.2159 32.2530 1.0000 0.8059 32.2530

  1,5000 -0,3329 34,1462 1,5000 1,2864 34,1462

  2.0000 -0.4569 36.1602 2.0000 1.81.72 36.1602

  2,5000 -0,5884 38,3049 2,5000 2,3973 38,3049

  3.0000 -0.7284 40.5988 3.0000 3.0271 40.5988

  3,5000 -0,8780 43,0618 3,5000 3,7070 43,0618

  4.0000 -1.0382 45.7122 4.0000 4.4367 45.7122

  4.5000 -1.2101 48.5665 4.5000 5.2146 48.5665

  , 0000 -1,3946 51,6399 5,0000 6,0380 51,6399

  , 5000 -1.5930 54.9443 5.5000 6.9027 54.9443

  6,0000 -1,8073 58,5082 6,0000 7,8072 58,5082

  3 5 6,5000 -2,0401 62,3662 6,500 8,7495 62,3662

  7.0000 -2.2938 66.5452 7.0000 9.7240 66.5452

  7.5000 -2.5720 71.0842 7.5000 10.7252 71.0842

  8.0000 -2.8809 76.0754 8.0000 11.7551 76.0754

  8.5000 -3.2267 81.6155 8.5000 12.8115 81.6155

  9.0000 -3.6169 87.7918 9.0000 13.8860 87.7918

  9.5000 -4.0652 94.8156 9.5000 14.9837 94.8156

  , 0000 -4,5918 103,0000 10,0000 16,1112 103,0000

  The left part of table 92 gives the numerical values of the focusing cam of the tenth example and

  the right part those of the zoom compensation cam.

  A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis derived from the numerical values of the focusing cam and the zoom compensation cam, in the range of the rotation amplitudes (ANGLE = 0, 0) to (ANGLE = 10.0), coincides with the displacement location of the second set of lenses calculated using the paraxial data of the upper part of the

table 91.

  The following tables 93, 94 and 95 give the focusing amplitude DX (mm), in the direction of the optical axis, of the set of focusing lenses, the magnifications ix of image formation of the sets. of the lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  Ya conversion associated with rotation at the far end

  angle (F = 28.8 mm), medial position (F = 50.0 mm) and at the telephoto end (F = 103.0 mm) in the tenth example. The provisions of the tables and the meanings of their symbols are the same as in the ninth

example.

Table 93

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 0,052 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 0,104 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 0,174 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 0,263 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 0,539 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 0.786 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.133 3) 0.000 4) 0.000

  Nk image magnification of lenses at the wide-angle end (28.8 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,293 3) 125,947 4) -0,011

  R 10,000 ANG -0,256 1) -0,008 2) -0,290 3) 125,947 4) -0,011

  R 5,000 ANG -0,521 1) -0,015 2) -0,286 3) 125,947 4) -0,011

  R 3,000 ANG -0,891 1) -0,026 2) -0,281 3) 125,947 4) -0,011

  R 2,000 ANG -1,381 1) -0,041 2) -0,275 3) 125,947 4) -0,011

  R 1,000 ANG -3,069 1) -0,090 2) -0,257 3) 125,947 4) -0,011

  R 0.700 ANG -4.859 1) -0.141 2) -0.240 3) 125.947 4) -0.011

  R 0.500 ANG -8.000 1) -0.227 2) -0.216 3) 125.947 4) -0.011

  Conversion coefficient yx associated with the direction of the optical axis at the wide-angle end (28.8mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,609 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 1,613 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 1,617 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 1,621 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 1,627 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 1,645 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 1.660 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.679 3) 0.000 4) 0.000

  Slope dxlda focusing cam at the wide-angle end (28.8mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,205 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,200 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,194 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -0,187 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -0,177 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,150 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.127 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.096 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.8 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,330 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -0,322 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,314 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) -0,302 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -0,289 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,247 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.211 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.162 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / yxo = 1.04, YaR / yao = 0.49

Table 94

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) 0.092 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) 0,184 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) 0,307 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) 0,460 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) 0,922 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) 1.321 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 1.864 3) 0.000 4) 0.000

  Nk image magnification of lenses at the median position (50.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,379 3) 7,039 4) - 0,253 R 10,000 ANG -0,255 1) -0,008 2) -0,373 3) 7,039 4) - 0,253

  R 5,000 ANG -0,519 1) -0,015 2) -0,367 3) 7,039 4) - 0,253

  R 3,000 ANG -0,886 1) -0,026 2) -0,359 3) 7,039 4) - 0,253

  R 2,000 ANG -1,375 1) -0,041 2) -0,348 3) 7,039 4) - 0,253

  R 1,000 ANG -3,068 1) -0,091 2) -0,317 3) 7,039 4) - 0,253

  R 0.700 ANG -4.862 1) -0.145 2) -0.289 3) 7.039 4) - 0.253

  R 0.500 ANG -8.000 1) -0.238 2) -0.252 3) 7.039 4) - 0.253

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,714 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) 2.729 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) 2,744 3) 0,000 4) 0,000

* R 3,000 ANG -0,886 1) 0,000 2) 2,763 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) 2,786 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) 2,853 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) 2.905 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 2.969 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,368 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.355 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) -0,342 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) -0,325 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) -0,304 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) -0,246 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) -0.202 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.147 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (50.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.255 1) 0.000 2) -0.969 3) 0.000 4) 0.000

  R 5,000 ANG -0,519 1) 0,000 2) -0,939 3) 0,000 4) 0,000

  R 3,000 ANG -0,886 1) 0,000 2) -0,897 3) 0,000 4) 0,000

  R 2,000 ANG -1,375 1) 0,000 2) -0,846 3) 0,000 4) 0,000

  R 1,000 ANG -3,068 1) 0,000 2) -0,701 3) 0,000 4) 0,000

  R 0.700 ANG -4.862 1) 0.000 2) -0.588 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.438 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxRlyxo = 1.09, YaR / Yao = 0.44

Table 95

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (103.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 0,281 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 0,547 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 0,883 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 1,276 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 2,334 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 3.143 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) 4.135 3) 0.000 4) 0.000

  Uk image magnification of lenses at the telephoto end (103, 0 mm) of the tenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,588 3) 4,264 4) -0,555

  R 10,000 ANG -0,256 1) -0,008 2) -0,569 3) 4,264 4) - 0,555

  R 5,000 ANG -0,521 1) -0,015 2) -0,551 3) 4,264 4) -0,555

  R 3,000 ANG -0,891 1) -0,027 2) -0,528 3) 4,264 4) -0,555

  R 2,000 ANG -1,381 1) -0,041 2) -0,501 3) 4,264 4) -0,555

  R 1,000 ANG -3,069 1) -0,094 2) -0,429 3) 4,264 4) -0,555

  R 0.700 ANG -4.859 1) -0.151 2) -0.373 3) 4.244 4) - 0.555

  R 0.500 ANG -8.000 1) -0.255 2) -0.306 3) 4.244 4) -0.555

  Conversion coefficient Yx associated with the direction of the optical axis at the telephoto end (103.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) 3,668 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) 3,792 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) 3,906 3) 0,000 4) 0,000

  R 3,000 ANG -0,891 1) 0,000 2) 4,045 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) 4,200 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) 4,576 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) 4.824 3) 0.000 4) 0.000

  R 0.500 ANG -8.0001) 0.000 2) 5.082 3) 0.000 4) 0.000

  Slope dx / da focusing cam at the telephoto end (103.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,152 3) 0,000 4) 0,000

  R 10,000 ANG -0,256 1) 0,000 2) -1,048 3) 0,000 4) 0,000

  R 5,000 ANG -0,521 1) 0,000 2) -0,960 3) 0,000 4) 0,000

  R 3,000 ANG -0.8911) 0.000 2) -0.859 3) 0.000 4) 0.000

  R 2,000 ANG -1,381 1) 0,000 2) -0,754 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -0,524 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -0.390 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -0.255 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (103.0 mm) of the tenth example

  R 0,000 ANG 0,000 1) 0,000 2) -4,225 3) 0,000 4) 0,000

  R 10,000 ANG -0.256 1) 0.000 2) -3.975 3) 0.000 4) 0.000

  R 5,000 ANG -0,521 1) 0,000 2) -3,749 3) 0,000 4) 0,000

  R 3,000 ANG -0,8911) 0,000 2) -3,474 3) 0,000 4) 0,000

  R 2,000 ANG -1,381 1) 0,000 2) -3,168 3) 0,000 4) 0,000

  R 1,000 ANG -3,069 1) 0,000 2) -2,396 3) 0,000 4) 0,000

  R 0.700 ANG -4.859 1) 0.000 2) -1.883 3) 0.000 4) 0.000

  R 0.500 ANG -8.000 1) 0.000 2) -1.297 3) 0.000 4) 0.000

  3 0 Condition corresponding to the values: YxR / Yxo = 1.39, YaRlyao = 0, 31 As indicated in tables 93, 94 and 95, at each focal length, the conversion coefficient yx associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance due to the influence of the slope (dx / da) of the focusing cam. In tables 93, 94 and 95, the rate of change, from the position focused at infinity to the focused position at the nearest point, of the conversion coefficient Ya associated with the rotation is x0.49 at the large end. -angle (F = 28.8 mm), x0.44 at the middle position (F = 50.0 mm), and x0.31 at the telephoto end (F = 103.0 mm). When the number N of divisions of the focusing range, for a change of the conversion coefficient Ya of the tenth example, is calculated using the formula (a) and is compared with the number given by the example of the request for Japanese Patent Laid-open No. 5-142475, the division numbers Nw, NM and NT at the wide-angle end, in the middle position and at the telephoto end respectively, have the following values: Example of the Japanese Patent Application Laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 tenth example Nw> 3.9 NM> 4.5 NT> 6.5 As a result, as the above comparison, although the zoom lens of this embodiment has a greater focal length variation ratio than

  the example of the Japanese patent application being inspected

  5-142475, the values of the numbers N of

divisions are reduced.

  As described previously, in the tenth example, since the rate of change of the conversion coefficient Ya associated with the rotation is smaller than that of the conventional system, the values of the numbers N of divisions are

  low. For this reason, the number of data of the coeffi-

  the conversion factor Ya and the correction coefficient y can be reduced and the storage capacity can be

deleted.

  Tables 96, 97 and 98 give the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 28.8 mm), in

  median position (F = 50.0 mm) and at the end of

  objective (F = 103.0 mm) in the tenth embodiment.

  The provisions of the tables and the reference symbols are the same as in the ninth example. The position of the focusing lens in the first pair of the two upper portions of each of the tables 96, 97 and 98, i.e. the third and fourth columns, is (R, ANGLE) = (0 , 0; 0,0) and indicates that the position corresponds to infinity. Similarly, the position of the focus lens of the fourth pair, in both parts

  of each of the tables 96, 97 and 98, that is,

  say in the ninth and tenth column, is

  (R, ANGLE) = (0.5; -8.0), and indicates that the position corresponds to

  pond at the focused position at the shortest distance

(R = 0.5 m).

Table 96

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the wide-angle end (28.8mm) of the tenth example f = 28.8 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,256 5,000 -0,521 3,000 - 0,891

POS R rs r rs r rs

  1 0,000 -0.330 0.000 -0.325 -0.320 -0, 313

  2 10,000 -0.327 -0.322 0.000 -0.317 -0, 310

  3 5,000 -0,324 -0,319 -0,314 0,000 -0,307

  4 3,000 -0.320 -0.314 -0.309 -0.302 0, 000

2,000 -0,314 -0,309 -0,304 -0,297

  6 1,000 -0,296 -0,291 -0,286 -0, 280

  7 0.700 -0.278 -0.274 -0.269 -0, 263

  8 0.500 -0.251 -0.246 -0.242 -0, 237

  POS R bf t bf t bf i bf i 0.000 0.00 0.00 -0.08 9.38 -0.17 8.77 -0.28 8.30

  2 10,000 0.08 9.79 0.00 0.00 -0.08 8.47 -0.20 8, 17

  3 5,000 0.17 9.59 0.08 9.00 0.00 0.00 -0.11 8, 13

  4 3,000 0.28 9.28 0.20 8.75 0.11 8.37 0.00 0.00

  5 2,000 0.43 9.08 0.35 8.65 0.26 8.36 0.15 8.21

  6 1,000 0.91 8.83 0.82 8.54 0.73 8.34 0.61 8, 16

  7 0.700 1.35 8.65 1.26 8.40 1.17 8.21 1.04 8.00

  8 0.500 2.00 8.35 1.91 8.14 1.81 7.96 1.68 7, 74

  (R, ANGLE) = 2,000 -1,381 1,000 -3,069 0,700 -4,859 0.500 -8,000

2 5 POS R rs r rs r rs

  1 0.000 -0.304 -0.276 -0.252 -0, 218

  2 10,000 -0.301 -0.274 -0.250 -0, 216

  3 5,000 -0,298 -0,271 -0,247 -0, 213

  4 3,000 -0.294 -0.267 -0.244 -0, 210

  3 0 5 2,000 -0,289 0,000 -0,263 -0,239 -0,206

  6 1,000 -0,272 -0,247 0,000 -0,225 -0, 193

  7 0.700 -0.255 -0.232 -0.211 0.000 -0, 181

  8 0.500 -0.230 -0.208 -0.189 -0.162.0, 000

POS R bf i bf t bf f bf

  1 0.000 -0.42 8.03 -0.85 7.12 -1.22 6.20 -1.74 5.05

  2 10,000 -0.34 7.99 -0.77 7.10 -1.15 6.18 -1.67 5, 04

  3 5,000 -0.26 8.00 -0.69 7.08 -1.07 6.16 -1.60 5, 03

  4 3,000 -0.14 8.03 -0.58 7.06 0.97 6.13 -1.49 5, 01

  2,000 0.00 0.00 -0.44 7.02 -0.83 6.09 -1.37 4.98

  6 1,000 -0.46 7.88 0.00 0.00 -0.40 5.95 -0.95 4, 91

  7 0.700 -0.89 7.70 8.41 6.72 0.00 0.00 -0.57 4.87

  8 0.500 -1.52 7.44 1.03 6.49 0.59 5.68 0.00 0.00

  Condition corresponding to the values: Ka0 / yao = 0.76, KaR / YaR = 1.34

Table 97

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient ,: (t) at the median position (50.0 mm) of the tenth example f = 50.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.255 5,000 -0.519 3,000 - 0.886

POS R rs r rs r rs

  1 0,000 -1,000 0,000 -0,977 -0,955 -0,925

  2 10,000 -0.992 -0.969 0.000 -0.947 -0, 917

  3 5,000 -0,984 -0,961 -0,939 0,000 -0,909

  4 3,000 -0.972 -0.950 -0.927 -0.897 0, 000

2,000 -0,956 -0,934 -0,912 -0,882

  6 1,000 -0,904 -0,883 -0,861 -0,833

  7 0.700 -0.855 -0.835 -0.814 -0.788

  8 0.500 -0.779 -0.760 -0.741 -0.717

POS R bf t bf t bf t bf

  1 0.000 0.00 0.00 -0.25 30.70 -0.49 29.17 -0.82 27, 13

  2 10,000 0.25 32.48 0.00 0.00 -0.25 28.77 -0.58 26, 77

  3 5,000 0.51 31.82 0.25 30.33 0.00 0.00 -0.33 26, 42

  4 3,000 0.86 31.10 0.60 29.50 0.34 27.98 0.00 0.00

  5 2,000 1.31 30.35 1.05 28.84 0.78 27.43 0.43 25.89

  6 1,000 2.77 29.02 2.28 27.80 2.20 26.69 1.82 25, 43

  7 0.700 4.16 28.74 3.85 27.69 3.54 26.73 3.13 25.64

  8 0.500 6.23 28.16 5.88 27.22 5.54 26.35 5.10 25.31

  (R, ANGLE) = 2,000 -1,375 1,000 -3,068 0,700 -4,862 0,500 -8,000

POS R rs r rs r rs

  1 0.000 -0.887 -0.778 -0.690 -0, 577

  2 10,000 -0.880 -0.772 -0.684 -0, 571

  3 5,000 -0.872 -0.764 -0.678 -0, 566

  4 3,000 -0.861 -0.754 -0.669 -0, 558

  3 0 5 2,000 -0,846 0,000 -0,741 -0,658 -0,549

  6 1,000 -0,799 -0,701 0,000 -0,621 -0,517

  7 0.700 -0.755 -0.662 -0.588 0.000 -0.487

  8 0.500 -0.687 -0.601 -0.530 -0.437 0, 000

POS R bf t bf I bf f bf a

  1 0.000 -1.22 25.05 -2.39 21.48 -3.36 19.17 -4.61 14, 50

  2 10,000 -0.99 24.78 -2.17 21.44 -3.15 15.16 -4.43 14, 47

  3 5,000 -0.75 24.54 -1.95 21.42 -2.94 19.17 -4.23 14, 43

  4 3,000 -0.42 24.22 -1.65 21.44 -2.66 19.20 -3.97 14, 38

  2,000 0.00 0.00 -1.25 21.56 -2.29 19.26 -3.63 14.31

  6 1,000 1.35 24.18 0.00 0.00 -1.11 19.40 -2.55 13, 98

  7 0.700 2.63 24.52 1.19 21.75 0.00 0.00 -1.53 13.56

  8 0.500 4.55 24.15 2.96 20.82 1.66 17.09 0.00 0.00

  Condition corresponding to the values: Ka0dyao = 0.78, KaR / YaR = 1.32

Table 98

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (,) at the telephoto end (103.0 mm) of the tenth example f = 103.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,256 5,000 -0,521 3,000 -0,891

POS R rs r rs r rs

  1 0.000 -4.224 0.000 -3.988 -3.772 -3, 516

  2 10,000 -4,215 -3,975 0,000 -3,759 -3, 504

  3 5,000 -4,203 -3,963 -3,748 0,000 -3, 492

  4 3,000 -4,190 -3,949 -3,734 -3,474 0, 000

2,000 -4,171 -3,929 -3,711 -3,450

  6 1,000 -4,105 -3,857 -3,634 -3, 370

  7 0.700 -4.028 -3.774 -3.548 -3, 280

  8 0.500 -3.876 -3.615 -3.385 -3, 115

  POS R bf t bf i bf t bf i 0.000 0.00 0.00 -1.02 312.42 -1.97 301.80 -3.13 255, 83

  2 10,000 1.08 500.78 0.00 0.00 -1.00 329.94 -2.23 258.19

  3 5,000 2.19 442.39 1.05 361.69 0.00 0.00 -1.29 242.76

  4 3,000 3.73 460.62 2.51 392.96 1.38 368.87 0.00 0.00

  5 2,000 5.76 458.69 4.42 381.87 3.19 325.33 1.69 249.97

  6 1,000 12.60 446.74 10.85 364.97 9.26 305.35 7.34 245.42

  7 0.700 19.57 421.02 17.37 343.62 15.39 287.87 13.01 233.41

  8 0.500 31.01 376.35 28.00 309.72 25.32 261.52 22.15 214.52

  (R, ANGLE) = 2,000 -1,381 1,000 -3,069 0,700 -4,859 0.500 -8,000

2 5 POS R rs r rs r rs

  1 0.000 -3.233 -2.555 -2.106 -1, 621

  2 10,000 -3.220 -2.542 -2.094 -1, 610

  3 5,000 -3,207 -2,529 -2,081 -1, 598

  4 3,000 -3,188 -2,510 -2,064 - 1,583

  5 2,000 -3,167 0,000 -2,486 -2,041 - 1,562

  6 1,000 -3,081 -2,396 0,000 -1,962 -1, 493

  7 0.700 -2.989 -2.313 -1.883 0.000 -1, 422

  8 0.500 -2.825 -2.159 -1.740 -1.297 0.000

POS R bf i bf t bf i bf

  1 0.000 -4.46 216.27 -7.84 118.59 -10.23 86.34 -12.96 51.92

  2 10,000 -3.62 218.89 -7.15 117.79 -9.64 86.06 -12.47 51.66

  3 5,000 -2.76 219.81 -6.44 116.67 -9.03 85.72 -11.95 51.39

  4 3,000 -1.56 235.61 -5.47 115.12 -8.19 85.31 -11.25 51.01

  2,000 0.00 0.00 -4.20 112.21 -7.10 84.74 -10.34 50.50

  6 1,000 5.20 191.32 0.00 0.00 -3.51 83.88 -7.36 48.64

  7 0.700 10.40 185.26 4.14 119.18 0.00 0.00 -4.47 46.29

  8 0.500 18.70 172.83 10.65 107.57 5.47 72.05 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.92, KaR / YaR = 1.25 The results of the calculation of the rate of variation of Ka as a function of Ya for the set focused at infinity and

  focused at the shortest distance at the far end

  angle, at the middle position and at the telephoto end in the example of Japanese Patent Application Laid-open No. 5-142475 and in the tenth

  example of the invention are as follows.

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Kao / yao Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Tenth Example At infinity KaO / Tao The nearest KaR / YaR Grandangle (F = 28.8) 0.76 1, 34 Median position (F = 50, 0) 0.78 1.32 Telephoto (F = 103.0) 0.92 1.25 As previously described, in the tenth example, as the rate of change of Ka as a function of Ya is weak compared to the classical system, the contribution of the correction term (ABf / g) in the relation Ka = ya (1 - ABf / I) can be reduced. For this reason, an error on the conversion coefficient Ka calculated from

  of ta and y or an error on the actual amplitude of

  Aa obtained when a single pair of values of the conversion coefficient ya and the coefficient of

  correction is established, can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the tenth

  example of the invention, when the training amplitudes

  lens when focusing the infinite focused assembly toward the object at the shortest distance and when focusing the focus arrangement at the shortest distance to the object at infinity, the wide-angle end, in the middle position and at the telephoto end, are calculated from the relation Aa = ABf / ya (1 ABf / g) and when the errors of the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the infinite focused set on the object at the shortest distance has the value of the object distance (POS-5), and that the value of the correction coefficient y when focusing the focused disposition at the shortest distance to the object at infinity takes the value

  corresponding to the object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Tenth example Focused Infinity Infinest closest to Near Focused at infinity Wide-angle (F = 28.8) -2.8% -0.3% Median position (F = 50.0) -2.0% -0.1% Telephoto (F = 103.0) -1.6% -0.4% As described previously, in the tenth example, even when a single pair of values of the conversion coefficient Ya and the correction coefficient y is established for a given range, an error between the coefficient of conversion Ka calculated from Ya and y and the driving amplitude Aa of focusing lenses becomes low compared to the conventional system, and the focusing

  can be performed with greater precision.

  Table 99 gives the amplitude (ANGLE DA) of rotation for the focusing during the manual focusing with the focusing cam (middle part of table 91) of the tenth example, the displacement amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  It should be noted that the arrangement of the table and the symbols used are the same as in the ninth example. The upper part of Table 99 shows the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m ) in the respective focusing states of the focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85.0 and 103.0 mm), and the middle portion gives the values of the amplitude (ANGLE DA) rotation for focusing necessary to obtain an optimal focused state for the respective photography distances. The lower part of the table gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for the focusing, with the distances

  focal lengths and distances of photography.

Table 99

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the tenth example 0,50m 0,70m 1,00 m 2,00 m 3,00 m 5,00 m 28,800 Bf 0,000 0,000 0,000 0.000 0.000 0.000, 000 Bf 0.000 0.001 0.001 0.002 0.002 0.001 50.000 Bf 0.000 0.002 -0.001 -0.005 -0.004 -0.003, 000 Bf 0, 000 -0.009 -0.009 -.001 0.001 0.001, 000 Bf 0.000 -0.012 -0, 005 -0.005 -0.005 -0.002 103.000 Bf 0.000 0.000 0.000 0.000 0, 000 0.000

  ANGLE DA -8,000 4,859 -3,069 -1,381 -0,891 -0,521

  F 28,800 DX 0,000 1,133 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,341 0,000 0,000 R 0,50 m F 50,000 DX 0,000 1,864 0,000 0,000 R 0,50 m F 70,000 DX 0,000 0,627 0,000 0,000 R 0 50m F 85,000 DX 0,000 3,273 0,000 0,000 R 0,50 m F 103,000 DX 0,000 4,135 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,786 0,000 0,000 R 0,70 m F 35,000 DX 0,000 0,936 0,000 0,000 R 0.70 m F 50,000 DX 0,000 1,321 0,000 0,000 R 0,70 m F 70,000 DX 0,000 1,910 0,000 0,000 R 0,70 m F 85,000 DX 0,000 2,427 0,000 0,000 R 0.70 m F 103,000 DX 0,000 3,143 0,000 0,000 R 0 70 m F 28,800 DX 0,000 0,539 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,644 0,000 0,000 R 1,00 m F 50,000 DX 0,000 0,922 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,360 0,000 0,000 R 1 00 m F 85,000 DX 0,000 1,758 0,000 0,000 R 1,00 m F 103,000 DX 0,000 2,334 0,000 0,000 R 1,00 m F 28,800 DX 0,000 0,263 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,316 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0, 462 0,000 0,000 R 2,00 m F 70,000 DX 0,000 0,696 0,000 0,000 R 2,00 m F 85,000 DX 0,000 0,926 0,000 0,000 R 2,00 m F 103,000 DX 0,000 1,276 0,000 0,000 R 2.00 m F 28,800 DX 0,000 0,174 0,000 0,000 R 3.00 m F 35,000 DX 0,000 0.209 0,000 0,000 R 3.00 m F 50,000 DX 0,000 0,308 0,000 0,000 R 3,00 m F 70,000 DX 0,000 0,468 0,000 0,000 R 3,00 m F 85,000 DX 0,000 0,630 0,000 0,000 R 3,00 m F 103,000 DX 0,000 0,883 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,104 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,125 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,185 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,283 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,384 0,000 0,000 R 5,00 m F 103,000 DX 0,000 0,647 0,000 0,000 R 5,00 m As shown in Table 99, in the zoom lens of the tenth example, a so-called "manual" focus can be realized because the magnitudes of displacement of the point image

  at the respective focal lengths and photo distances

  respective graphs are very small and enter the depth of field regardless of the state of variation of

  the focal length and the distance of photography.

  Eleventh Embodiment The eleventh embodiment or eleventh example relates to a zoom lens having a five-set arrangement, that is to say sets of positive, negative, positive, negative and positive type lenses, with focus on the lens. using the second set of negative type lenses. In this object, the ratio (aF / az) of the focusing rotation amplitudes of the position focused at infinity to the position focused at the nearest location (R = 0.5 m) and of focal length variation from the wide-angle end (F = 28.8 mm) to

  the telephoto end (F = 102.0 mm) is set at -0.72.

  The following table 100 indicates various paraxial data of an optical system and data defining the configuration of a focusing cam in the

eleventh example.

  The upper part of table 100 gives the focal lengths and principal point intervals of the respective lens assemblies of the optical system of the eleventh example with six focusing states (focal lengths

  F = 28.8, 35.0, 50.0, 70.0, 85.0 and 102.0 mm).

  The middle part of the table shows the spline sample data when the focus cam configuration of the second lens set of the eleventh example, used for focusing, is represented by a spline function associated with the rotation angle α of the rotary barrel and the amplitude x of displacement in the

direction of the optical axis.

* In addition, the lower part of the table gives the

  focusing positions at infinity (corresponding positions).

  infinitely) for the respective focal lengths (F = 28.8, 35.0, 50.0, 70.0, 85.0 and 102.0 mm) and the rotational amplitudes (for focusing) focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) using the focusing cam of the eleventh example. In the table, as the zoom range of focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 109.0 mm) is equal to 10.0 and the focus rotation amplitude of the position focused at infinity at the position focused at the shortest distance (R = 0.5 m) is equal to -7.2, the ratio (aF / az) of magnitudes of focus rotation and variation of

  The focal length of the eleventh example is -0.72.

  Table 100 Eleventh example f = 28.8 to 102.0 (ratio of amplitudes of rotation: aF / az = -0.72) Focal distances and intervals of the main points of the objectives of the eleventh example

1-POS 2-POS 3-POS 4-POS 5-POS 6-POS

  F 28.8000 35.0000 50.0000 70.0000 85.0000 102.0000

  F1 79.2449 D1 10.3882 14.8655 22.7700 30.1777 34.3149 38.0039

  F2 -15.4624 D2 25.2941 22.6661 18.5824 15.3362 13.5483 11.8188

  F3 22.0957 D3 6.6017 7.6595 9.5884 11.0937 11.7828 12.3244

  F4 -35.5101 D4 5.9639 4.9061 2.9772 1.4719 0.7828 0.2412

  F5 46.4677 D5 48.3315 50.3856 54.3234 57.9012 59.7291 61.2142

  Focusing cam shape (spline interpolated point) corresponding to the eleventh example

ANGLE (1) (2) (3) (4) (5)

  I -11.0000 0.0000 1.6620 0.0000 0.0000 0.0000

  2 -10,0000 0.0000 1.5641 0.0000 0.0000 0.0000

  3 -7.2000 0.0000 1.2474 0.0000 0.0000 0.0000

  4.5026 0.0000 0.8685 0.0000 0.0000 0.0000

  -2.8872 0.0000 0.5972 0.0000 0.0000 0.0000

  6 -1.3163 0.0000 0.2928 0.0000 0.0000 0.0000

  7 -0.8525 0.0000 0.1940 0.0000 0.0000 0.0000

  8 -0.5001 0.0000 0.1158 0.0000 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

  2,8000 0.0000 -0.7734 0.0000 0.0000 0.0000

  11 5,4974 0.0000 -1.8290 0.0000 0.0000 0.0000

  12 7,1128 0.0000 -2.7118 0.0000 0.0000 0.0000

  13 8.6837 0.0000 -3.9029 0.0000 0.0000 0.0000

  14 9,1475 0.0000 -4.3583 0.0000 0.0000 0.0000

  9,4999 0.0000 -4.7525 0.0000 0.0000 0.0000

  16 10.0000 0.0000 -5.4099 0.0000 0.0000 0.0000

  17 11.0000 0.0000 -7.0970 0.0000 0.0000 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focusing of the eleventh example (ratio of rotation amplitudes aF / az = -0.72) Focal length Position corresponding to Distance of amplitude of rotation infinity photography for focusing 28 , 8 mm 0.0000 5.00 m -0.500, 0 mm 1.7943 3.00 m -0, 852, 0 mm 4.8878 2.00 m -1.316, 0 mm 7.5822 1.00 m -2.887 , 0 mm 8, 9328 0.70 m -4.503 102.0 mm 10.0000 0.50 m -7.200 Condition corresponding to value (6) 1.42 Condition corresponding to value (7) 3.72 Condition corresponding to value ( 8) -0.72 Condition corresponding to value (12) 0.55 (wide-angle) 0.31 (telephoto) Condition corresponding to value (13) 0, 81 (wide-angle) 1.00 (telephoto) Corresponding Condition value (14) 1.25 (wide-angle) 1.18 (telephoto) Table 101 shows numerical values of the cams of the focus lens assembly of the eleventh example, the data being calculated by interpolation with a spline function by using the sampling data of the focusing cam of the middle part of table 100. It should be noted that the meanings of the symbols of table 101 are the same as in the

ninth example.

Table 101

  Digital Cam Values for Focusing Lens in Example Eleven Focusing Cam Digital Values Focal Length Variation Compensation Cam Numerals

ANGLE (2) F ANGLE (2) F

-7.2000 1.2474 0.0000

-7.0000 1.2220 0.0000

-6,5000 1,1568 0,0000

-6.0000 1.0890 0.0000

-5,5000 1,0184 0,0000

-5.0000 0.9448 0.0000

-4.5000 0.8681 0.0000

-4.0000 0.7881 0.0000

-3,5000 0.7046 0.0000

-3.0000 0.6174 0.0000

-2.5000 0.5262 0.0000

-2.0000 0.4307 0.0000

-1.5000 0.3307 0.0000

-1.0000 0.2259 0.0000

-0.5000 0.1158 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.1215 30.3871 0.5000 -0.0782 30.3871

  1,0000 -0,2493 32,0759 1,0000 -0,1189 32,0759

  1,5000 -0,3842 33,8798 1,5000 -0,1222 33,8798

  2.0000 -0.5269 35.8098 2.0000 -0.0881 35.8098

  2,5000 -0,6782 37,8759 2,5000 -0,0164 37,8759

  3,0000 -0,8388 40,0860 3,0000 0.0928 40.0860

  3.5000 -1.0100 42.4533 3.5000 0.2389 42.4533

  4.0000 -0.1931 44.9978 4.0000 0.4216 44.9978

  4.5000 -1.3899 47.7360 4.5000 0.6400 47.7360

  , 0000 -1.6017 50.6785 5.0000 0.8925 50.6785

  , 5000 -1.8303 53.8326 5.5000 1.1760 53.8326

  6.0000 -2.0774 57.2175 6.0000 1.4874 57.2175

  6.5000 -2.3466 60.8803 6.5000 1.8248 60.8803

  7.0000 -2.6414 64.8675 7.0000 2.162 64.8675

  7.5000 -2.9660 69.2369 7.5000 2.5694 69.2369

  8,0000 -3,3284 74,1111 8,0000 2,9753 74,1111

  8.5000 -3.7384 79.6222 8.5000 3.4040 79.6222

  9.0000 -4.2064 85.8958 9.0000 3.8529 85.8958

  9,5000 -4,7527 93,2084 9,5000 4,3235 93,2084

  , 0000 -5,4099 102,0000 10,0000 4,8173 102,0000

  The left-hand side of table 101 shows the numerical values of the focus cam of the eleventh example, and the right-hand side shows those of the zoom compensation cam of this example. A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis obtained with the numerical values of the focusing cam and the zoom compensation cam in the range between the rotation amplitudes (ANGLE = 0,0) and (ANGLE = 10,0) s coincides with the displacement location of the second set of lenses calculated using paraxial data from the top of the table

100.

  Tables 102, 103 and 104 give the displacement amplitude DX (mm) for focusing in the direction of the optical axis of the set of focusing lenses, the imaging magnifications Px of the respective sets of lenses. , the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end (F = 28 , 8 mm), in the middle position (F = 50.0 mm), and at the telephoto end (F = 102.0 mm) in the eleventh example. The provisions and meanings of the symbols in the tables are the same as in the ninth

example.

Table 102

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 0.058 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 0,116 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 0,194 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 0,293 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 0,597 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 0.869 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 1.247 3) 0.000 4) 0.000 5) 0.000

  3k image magnification of lenses at the wide-angle end (28.8 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,290 3) -0,955 4) -32,766 5) -0,040

  R 10,000 ANG -0.246 1) -0.008 2) -0.286 3) -0.955 4) -32.766 5) -0.040

  R 5,000 ANG -0,500 1) -0,016 2) -0,282 3) -0,955 4) -32,766 5) -0,040

  R 3,000 ANG -0,852 1) -0,028 2) -0,277 3) -0,955 4) -32,766 5) -0,040

  R 2,000 ANG -1,316 1) -0,043 2) -0,271 3) -0,955 4) -32,766 5) -0,040

  R 1,000 ANG -2,887 1) -0,096 2) -0,251 3) -0,955 4) -32,766 5) -0,040

  R 0.700 ANG -4.503 1) -0.151 2) -0.233 3) -0.955 4) -32.766 5) -0.040

  R 0.500 ANG -7.200 1) -0.244 2) -0.209 3) -0.955 4) -32.766 5) -0.040

  Conversion coefficient Yx associated with the direction of the optical axis at the wide-angle end (28.8mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 1,443 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,246 1) 0,000 2) 1,446 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,500 1) 0,000 2) 1,450 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 1,454 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 1,460 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 1,476 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 1.489 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 1.506 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focus cam at the wide-angle end (28.8mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,237 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -0.232 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -0,226 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -0,218 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,208 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,180 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.157 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.126 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.8 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,342 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -0.335 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -0,327 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -0,317 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,304 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,266 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.233 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.190 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.04, YaR / Yao = 0.55

Table 103

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) 0.104 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) 0,207 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) 0,345 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) 0,516 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) 1,025 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) 1.461 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 2.044 3) 0.000 4) 0.000 5) 0.000

  Objective image magnification Ok at the middle position (50.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,377 3) -1,243 4) -7,965 5) -0,169

  R 10,000 ANG -0.245 1) -0.008 2) -0.370 3) -1.243 4) -7.965 5) -0.169

  R 5,000 ANG -0,497 1) -0,016 2) -0,364 3) -1,243 4) -7,965 5) -0,169

  R 3,000 ANG -0.849 1) -0.028 2) -0.355 3) -1.243 4) -7.965 5) -0.169

  R 2,000 ANG -1,312 1) -0,044 2) -0,344 3) -1,243 4) -7,965 5) -0,169

  R 1,000 ANG -2,886 1) -0,098 2) -0,311 3) -1,243 4) -7,965 5) -0,169

  R 0.700 ANG -4.507 1) -0.155 2) -0.283 3) -1.243 4) -7.965 5) -0.169

  R 0.500 ANG -7.200 1) -0.254 2) -0.245 3) -1.243 4) -7.965 5) -0.169

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 2,403 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) 2.417 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) 2,430 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) 2,448 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) 2,470 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) 2,530 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) 2.577 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 2.633 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -0,432 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) -0.417 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) -0,401 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) -0,382 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) -0,357 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) -0,294 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) -0.246 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.190 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the median position (50.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -1,039 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.245 1) 0.000 2) -1.007 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,497 1) 0,000 2) -0,976 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,849 1) 0,000 2) -0,934 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,312 1) 0,000 2) -0,883 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,886 1) 0,000 2) -0,743 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.507 1) 0.000 2) -0.634 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.500 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / Yxo = 1.10, YaR / 'Yao = 0.48

Table 104

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (102.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 0.340 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 0,657 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 1,052 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 1,507 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 2,698 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 3.581 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 4.636 3) 0.000 4) 0.000 5) 0.000

  13k Lens Magnification at the Telephoto End (102, 0 mm) of the Eleventh

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,600 3) -1,528 4) -4,425 5) -0,317

  R 10,000 ANG -0.246 1) -0.008 2) -0.578 3) -1.528 4) -4.425 5) -0.317

  R 5,000 ANG -0,500 1) -0,017 2) -0,557 3) -1,528 4) -4,425 5) -0,317

  R 3,000 ANG -0,852 1) -0,028 2) -0,532 3) -1,528 4) -4,425 5) -0,317

  R 2,000 ANG -1,316 1) -0,044 2) -0,502 3) -1,528 4) -4,425 5) -0,317

  R 1,000 ANG -2,887 1) -0,099 2) -0,425 3) -1,528 4) -4,425 5) -0,317

  R 0.700 ANG -4.503 1) -0.159 2) -0.368 3) -1.528 4) -4.425 5) -0.317

  R 0.500 ANG -7.200 1) -0.267 2) -0.300 3) -1.528 4) -4.425 5) -0.317

  Coefficient of conversion Yx associated with the direction of the optical axis at the telephoto end (102.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) 2,948 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) 3.067 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) 3,175 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) 3,303 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) 3,443 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) 3,772 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) 3.981 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) 4.191 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da of focus cam at telephoto end (102.0 mm) of eleventh

example

  R 0,000 ANG 0,000 1) 0,000 2) -1,462 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.246 1) 0.000 2) -1.311 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,500 1) 0,000 2) -1,188 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -1,054 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -0,917 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -0,631 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -0.475 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -0.323 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient associated with the direction of rotation at the telephoto end (102.0 mm) of the eleventh example

  R 0,000 ANG 0,000 1) 0,000 2) -4,310 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,246 1) 0,000 2) -4,022 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,500 1) 0,000 2) -3,772 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -0,852 1) 0,000 2) -3,481 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -1,316 1) 0,000 2) -3,159 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -2,887 1) 0,000 2) -2,381 3) 0,000 4) 0,000 5) 0,000

  R 0.700 ANG -4.503 1) 0.000 2) -1.889 3) 0.000 4) 0.000 5) 0.000

  R 0.500 ANG -7.200 1) 0.000 2) -1.355 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: yxR / Yxo = 1.42, YaR / Yao = 0.31 As indicated in tables 102, 103 and 104, at each focal length, the conversion coefficient x associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in the tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of The photograph is closer to the shorter distance, because of the influence of the slope (dx / da) of the focusing cam. In tables 102, 103 and 104, the rate of variation, from the infinitely-focused position to the position focused at the nearest location, of the conversion coefficient Ya associated with the rotation is x 0.55 to wide-angle end (F = 28.8 mm), x0.48 at the position

  median (F = 50.0 mm), and x0.31 at the telegraph end

  objective (F = 102.0 mm). When the number N of divisions of

  range of focus, when the coefficient of

  The conversion example of the eleventh example is calculated with the formula (a) and is compared with the value of the example of the Japanese patent application placed under public inspection.

  5-142475, the numbers Nw, NM and NT of divisions at the

  the wide-angle, mid-position and telephoto end respectively have the following values: example of Japanese Patent Application Laid-open No. 5-142475

NW> 9.3 NM> 10.1 NT> 8.1

  Example 11 Nw> 3.2 NM> 4.0 NT> 6.3 As a result, although the zoom lens of this embodiment has a greater focal length variation ratio than in the embodiment of the demand Japanese Patent Application Laid-open No. 5-142475, the values of the numbers N of divisions are reduced. As previously described, in the eleventh example, since the rate of change of the conversion coefficient Ya associated with the rotation is smaller than the value of the conventional system, the values of the division numbers N are small. For this reason, the number of data of the conversion coefficient Ya and the correction coefficient y can be reduced, and the storage capacity can be

deleted.

  Tables 105, 106 and 107 show the results of calculating the conversion coefficient Ka and the correction coefficient p at the wide-angle end (F = 28.8 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 102.0 mm) in the eleventh example. The arrangement of the tables and the reference symbols are the same as in the ninth example. The focus lens position of the first pair of the two upper portions of each of Tables 105, 106 and 107, i.e. in the third and fourth columns, is (R, ANGLE) = (0.0 ; 0,0) and indicates that the position corresponds to infinity. Similarly, the position of the focus lens of the fourth pair in both parts

  of each of Tables 105, 106 and 107, that is,

  say in the ninth and tenth columns, is (R, ANGLE) = (0.5; -7, 2), and indicates that the position

  corresponds to the nearest position (R = 0.5 m).

Table 105

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the wide-angle end (28.8mm) of the eleventh example f = 28.8 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.246 5,000 -0.500 3,000 - 0.852

POS R rs r rs r rs

  1 0.000 -0.342 0.000 -0.337 -0.333 -0, 326

  2 10,000 -0.340 -0.335 0.000 -0.330 -0, 323

  3 5,000 -0,337 -0,332 -0,327 0,000 -0,321

  4 3,000 -0.334 -0.329 -0.324 -0.317 0, 000

2,000 -0,329 -0,324 -0,319 -0,312

  6 1,000 -0,313 -0,309 -0,304 -0, 298

  7 0.700 -0.299 -0.294 -0.290 -0, 284

  8 0.500 -0.276 -0.272 -0.268 -0, 262

* POS R bf f bf t bf f bf

  1 0.000 0.00 0.00 -0.08 11.45 -0.17 10.55 -0.28 9, 93

  2 10,000 0.08 12.26 0.00 0.00 -0.08 10.26 -0.20 9, 79

  3 5,000 0.17 11.70 0.08 10.84 0.00 0.00 -0.11 9, 75

  4 3,000 0.28 11.22 0.20 10.45 0.11 9.94 0.00 0.00

  5 2,000 0.43 10.94 0.35 10.34 0.26 10.01 0.14 9.95

  6 1,000 0.90 10.68 0.81 10.32 0.73 10.11 0.61 9, 97

  7 0.700 1.34 10.52 1.25 10.23 1.16 10.03 1.03 9.84

  8 0.500 1.99 10.30 1.89 10.05 1.79 9.86 1.66 9, 65

  (R, ANGLE) = 2,000 -1,316 1,000 -2,887 0,700 -4,503 0,500 -7,200

2 5 POS R rs r rs r rs

  1 0.000 -0.317 -0.291 -0.269 -0, 238

  2 10,000 -0.315 -0.289 -0.267 -0, 236

  3 5,000 -0,312 -0,287 -0,264 -0, 234

  4 3,000 -0.308 -0.283 -0.261 -0, 231

  3 0 5 2,000 -0,304 0,000 -0,279 -0,258 -0,228

  6 1,000 -0,290 -0,266 0,000 -0,245 -0, 216

  7 0.700 -0.276 -0.253 -0.233 0.000 -0, 206

  8 0.500 -0.255 -0.234 -0.215 -0.190 0.000

POS R bf a bf t bf t bf t

  3 5 1 0.000 -0.42 9.72 -0.84 8.82 -1.21 7.94 -1.71 6.77

  2 10,000 -0.34 9.69 -0.76 8.80 -1.13 7.93 -1.64 6, 75

  3 5,000 -0.25 9.72 -0.68 8.79 -1.06 7.91 -1.57 6, 74

  4 3,000 -0.14 9.81 -0.58 8.77 -0.95 7.89 -1.47 6, 72

  2,000 0.00 0.00 -0.44 8.73 -0.82 7.86 -1.34 6.70

  4 0 6 1,000 0.46 9.68 0.00 0.00 -0.40 7.78 -0.93 6.63

  7 0.700 0.88 9.53 8.41 8.51 0.00 0.00 -0.56 6, 56

  8 0.500 1.50 9.34 1.01 8.36 0.58 7.52 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 0.81, KaR / YaR = 1.25

Table 106

  Coefficients of conversion K .: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (50.0 mm) of the eleventh example f = 50.0 mm

  (R, ANGLE) = 0.000 0.000 10,000 -0.245 5,000 -0.497 3,000 - 0.849

POS R rs r rs r rs

  1 0.000 -1.039 0.000 -1.015 -0.990 -0, 959

  2 10,000 -1,032 -1,007 0,000 -0,983 -0, 952

  3 5,000 -1,024 -1,000 -0,976 0,000 -0,944

  4 3,000 -1,014 -0,989 -0,965 -0,934 0, 000

2,000 -1,000 -0,976 -0,952 -0,921

  6 1,000 -0,956 -0,932 -0,910 -0,880

  7 0.700 -0.915 -0.892 -0.870 -0.842

  8 0.500 -0.854 -0.833 -0.813 -0.786

POS R bf e bf! bf t bf

  I 0.000 0.00 0.00 -0.25 34.57 -0.49 32.89 -0.81 30, 93

  2 10,000 0.25 36.71 0.00 0.00 -0.25 32.19 -0.57 30, 59

  3 5,000 0.51 36.07 0.25 34.00 0.00 0.00 -0.33 30, 26

  4 3,000 0.86 35.39 0.60 33.54 0.34 32.07 0.00 0.00

  2 0 5 2,000 1.31 34.75 1.04 33.07 0.78 31.69 0.43 30.20

  6 1,000 2.76 34.38 2.46 33.10 2.17 32.05 1.79 30, 98

  7 0.700 4.12 34.46 3.80 33.32 3.49 32.35 3.08 31.29

  8 0.500 6.15 34.61 5.80 33.55 5.45 32.62 4.99 31.53

  (R, ANGLE) = 2,000 -1,312 1,000 -2,886 0,700 -4,507 0,500 -7,200

POS R rs r rs r rs

  I 0.000 -0.920 -0.810 -0.723 -0.615

  2 10,000 -0.913 -0.804 -0.717 -0, 611

  3 5,000 -0,906 -0,797 -0,712 -0, 606

  4 3,000 -0.896 -0.789 -0.704 -0, 599

  3 0 5 2,000 -0,883 0,000 -0,778 -0,694 -0,591

  6 1,000 -0,844 -0,743 0,000 -0,663 -0,564

  7 0.700 -0.808 -0.711 -0.634 0.000 -0.539

  8 0.500 -0.754 -0.663 -0.591 -0.500 0.000

POS R bf f bf t bf! bf f

  1 0.000 -1.21 28.99 -2.34 26.21 -3.26 23.30 -4.43 19, 18

  2 10,000 -0.97 28.79 -2.12 26.24 -3.06 23.32 -4.25 19, 17

  3 5,000 -0.74 28.64 -1.90 26.31 -2.85 23.36 -4.06 19, 16

  4 3,000 -0.41 28.49 -1.61 26.44 -2.58 23.41 -3.81 19, 15

  2,000 0.00 0.00 -1.22 26.61 -2.22 23.46 -3.48 19.12

  4 0 6 1,000 1.33 30.20 0.00 0.00 -1.07 23.62 -2.43 18.93

  7 0.700 2.58 30.26 1.15 26.11 0.00 0.00 -1.45 18, 48

  8 0.500 4.44 30.35 2.86 26.36 1.59 23.34 0.00 0.00

  Condition corresponding to the values: Kao / ao = 0.82, KaR / YaR = 1.23 n N 0) ON cO gmm ODN oO N 8 o1aO) LCa M Ln 0 sm 0 oCD a: "o and 0 _ O m ON ## EQU1 ## where ## STR5 ## N- (N) N-10 N0) Nt)> 1 (0, n _ _ * E 8 v <8 s v5r- - oCDCD CDII II (ct) Lt CtI ILn (a) III 9 I (a) M CD) Ln ## STR2 ##

  ## STR1 ## _ _o s N ..

  ## STR5 ## wherein R 1 is OCD-Co (O-O-O-NNNNO) ## EQU1 ## where: ## STR1 ## ## STR1 ## THIS!. ## EQU1 ##

  E CD Lt v- <O -CD 0 DD DC toDN M8-O 0 V-e Cle0Oe -

  ## STR2 ## uD -NC14 N rd) 0DsCNeZtUDs0 0 -OtUD1 r-wO II (O Li n

C (N) a> N ...

  ## EQU1 ## CD ## EQU1 ## CD ## EQU1 ## CD ## STR2 ## ) C4 CJ c iiC) 4I-0C C (CD) aII II CD aIIcci-- Co CM)

0 E W

  CO a) oo-1o-1o-1N-eNo oo 0o O) o -9c-i c)) O E 00000 00000IlW q ckQ o aCD nNc ON CD o

(v 0CD <nU (-J m Ln -

  0 0 = 0 -.Ii-1CNC '-Ni-0 ONC r. Oi-NcI-0 ONCD O M- 'i-0CND O o8_aCL-o-aci Ln O) Ln) O Ln CD Ln) O Hi-4 <N <S ic The results of calculations of the speed of variation of Ka relative to Ya for the infinite focus assembly and the focus assembly at the shortest distance at the wide-angle end, in the middle position and at the telephoto end in the example of the patent application Japanese put to public inspection No. 5-142475 and in the eleventh

  example of the invention are as follows.

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity KOyaO | Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50.0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0, 43 Eleventh example To infinity Ka / Y The nearest KaR / YaR Grandangle (F = 28.8) 0.81 1.25 Median position (F = 50, 0) 0.82 1.23 Telephoto (F = 102 , 0) 1,00 1,18 As described previously, in the eleventh example, since the rate of variation of Ka with respect to Ya is small compared to the conventional system, the contribution of the correction term (ABf / i) in the Ka = Ya relationship (1 - ABf / p) can be reduced. For this reason, the error of the conversion coefficient Ka calculated from ya and y and the error on the actual driving amplitude of lenses Aa obtained when using a single pair of values of the coefficient of Ya conversion and coefficient

  correction can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the eleventh example of the invention, when the lens driving amplitudes during focusing of the focused disposition to infinity to focus on the object at the shortest distance and when focusing with the focused assembly at the shortest distance on the object at infinity at the wide-angle end, in the middle position and at the telephoto end, are calculated from the relation Aa = ABf / ya (1 - ABf / g) and the errors on the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the set focused at infinity to the object at the shortest distance corresponds to that of the object distance (POS-5), and that the value of the correction coefficient y when focusing with the focused set to the shortest distance on the object to infinity takes a value

  corresponding to the object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Eleventh example Infinity focused state most closest to near-focused at infinity Wide-angle (F = 28.8)) -1.2% -0.4% Median position (F = 50.0) -0.1% -0.1% Telephoto (F = 102.0) 0.3% -0.2% As described previously, in the eleventh example, even when only a pair of values of the conversion coefficient Ya and the correction coefficient y are set for a given range of lens arrangement, an error between the conversion coefficient KA calculated from Ya and y and the focusing lens Aa drive amplitude becomes small compared to the conventional system, and the focusing can be performed with a

greater precision.

  Table 108 indicates the focusing amplitude (ANGLE DA) during manual focusing with the focusing cam (middle part of table 100) of the eleventh example, the displacement amplitude DX (mm) in the direction of the the optical axis of the set of focusing lenses corresponding to the focusing rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  Note that the table layout and reference symbols are the same as in the ninth

  example. The upper part of Table 108 gives the ampli-

  displacement study (Bf) of the image point corresponding to the photographic distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) to the respective states of variation of the focal lengths (F = 28.8, 35.0, 50.0, 70, 0, 85.0 and 102.0 mm), and the median portion gives the values of the amplitude of

  rotation (ANGLE DA) of focusing necessary to obtain

  an optimal focused state at the respective photography distances. The lower part gives the displacement amplitudes (DX) in the direction of the optical axis of the

  respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for focussing, with the

  focal distances and photography distances.

  Table 108 Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the eleventh example 0.50 m 0.70 m 1.00 m 2.00 m 3.00 m 5.00 m 28.800 Bf 0,000 0,000 0,000 0,000 0,000 0,000 35,000 Bf 0,000 0.001 0.002 0.002 0.002 0.001, 000 Bf 0.000 0.003 -0.001 -0.004 -0.004 -0.003, 000 Bf 0.000 -0.010 -0.010 -0.002 0.000 0.001, 000 Bf 0.000 -0.010 -0.004 -0.006 -0.005 -0.001 102.000 Bf 0.000 0.000 0.000 0, 000 0.000 0.000

  ANGLE DA -7,200 4,503 -2,887 -1,316 -0,852 -0,500

  F 28,800 DX 0,000 1,247 0,000 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,472 0,000 0,000 0,000 R 0,50 m F 50,000 DX 0,000 2,044 0,000 0,000 0,000 R 0.50 m F 70,000 DX 0,000 2,930 0,000 0,000 0,000 R 0.50 m F 85, 000 DX 0.000 3,690 0,000 0,000 0,000 R 0,50 m F 102, 000 DX 0,000 4,636 0,000 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,869 0,000 0,000 0,000 R 0,70 m F 35,000 DX 0.000 1.032 0.000 0.000 0.000 R 0.70 m F 50.000 DX 0.000 1.460 0.000 0.000 0.000 R 0.70 m F 70.000 DX 0.000 2.157 0.000 0.000 0.000 R 0.70 m F 85.000 DX 0.000 2.778 0.000 0.000 0.000 R 0.70 m F 102,000 DX 0, 000 3,581 0,000 0,000 0,000 R 0,70 m F 28,800 DX 0,000 0,597 0,000 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0, 713 0,000 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,026 0,000 0,000 0,000 R 1.00 m F 70,000 DX 0,000 1, 552 0,000 0,000 0,000 R 1,00 m F 85,000 DX 0,000 2,039 0,000 0,000 0,000 R 1,00 m F 102,000 DX 0,000 2,698 0, 000 0,000 0,000 R 1,00 m F 28,800 DX 0.000 0.293 0.000 0.000 0.000 R 2.00 m F 35,000 DX 0.000 0.3 51 0,000 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,517 0,000 0,000 0,000 R 2,00 m F 70,000 DX 0,000 0,805 0,000 0,000 0,000 R 2,00 m F 85,000 DX 0,000 1,093 0,000 0,000 0,000 R 2 00 m F 102,000 DX 0,000 1,507 0,000 0,000 0,000 R 2.00 m F 28,800 DX 0,000 0,194 0,000 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,233 0,000 0,000 0,000 R 3.00 m F 50,000 DX 0,000 0,346 0,000 0,000 0,000 R 3,00 m F 70,000 DX 0,000 0,544 0,000 0,000 0,000 R 3,00 m F 85,000 DX 0,000 0,749 0,000 0,000 0,000 R 3,00 m F 102,000 DX 0,000 1,052 0,000 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,116 0,000 0,000 0,000 R 5,0000 F 35,000 DX 0,000 0,139 0,000 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,208 0,000 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,330 0,000 0,000 0,000 R 5,00 m F 85,000 DX 0,000 0,459 0,000 0,000 0,000 R 5,00 m F 102,000 DX 0,000 0,657 0,000 0,000 0,000 R 5,00 m As shown in Table 108, in the zoom lens of the eleventh example, a so-called "manual" focus can be realized because the amplitudes of the image point at the respective focal distances and photograph distances are very small and enter the depth of field regardless of the focus state and

distance of photography.

  Twelfth Embodiment The twelfth embodiment or twelfth example relates to a zoom lens having a four-set arrangement, i.e. lens sets of types

  positive, negative, positive and negative, and ensures the

  using a third set of positive type lenses. For this purpose, the ratio (aF / az) of the amplitude of rotation for the focusing of the position focused at infinity to the position focused at the shortest distance (R = 1.2 m) and the amplitude of rotation for the focal length variation of the wide-angle end (F = 72.0 mm) at the telephoto end (F = 200.0 mm) is equal to

-0.75.

  Table 109 which follows shows various paraxial data of an optical system and data for determining the configuration of a focusing cam.

in the twelfth example.

  The upper part of table 109 gives the focal lengths and intervals of the main points of the respective lens assemblies of the optical system corresponding to the twelfth example with five focusing states (distances

  focal length F = 72.0, 105.0, 135.0, 150.0 and 200.0 mm).

  The middle portion of table 109 shows spline sample data obtained when the focus cam configuration of the third lens set of the twelfth example, used for focusing, is represented by a spline function associated with the angle α. rotation of a rotating barrel and amplitude

  x of displacement in the direction of the optical axis.

  In addition, the lower part of table 109 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 72.0, 105.0, 135.0, 150.0 and 200.0 mm) and the rotational (focus) amplitudes when focusing at the respective photographing distances (R = 5.0, 4.0, 3.0, 2.0, 1.5 and 1.2 m ) using the focusing cam of the twelfth example. In this table, as the focal length variation rotation amplitude of the wide-angle end (F = 72.0 mm) at the telephoto end (F = 200.0 mm) is equal to 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 1.2 m) is equal to -7.5, the ratio (aF / az) zoom magnitudes of focus and variation of

  focal length of the twelfth example is equal to -0.75.

Table 109

  Twelfth example f = 72.0 to 200.0 (ratio of amplitudes of rotation: aF / az = -0.75) Focal distances and intervals of the principal points of the objectives of the twelfth example

  F 72.0000 105.0000 135.0000 150.0000 200.0000

  F1 104.6018 D1 3.988 20.2900 31.6591 36.5381 50.0257

  F2 -79.6837 D2 55.9381 47.4314 41.7208 39.4416 34.0263

  F3 41.6144 D3 24.2323 16.4388 10.7803 8.1805 0.1081

  F4 -51.6678 D4 37.5317 53.8320 65.2011 70.0800 83.5677

  Focusing cam shape (spline interpolated point) corresponding to the twelfth example

ANGLE (1) (2) (3) (4)

  I -11.0000 0.0000 0.0000 2.0100 0.0000

  2 -10,0000 0.0000 0.0000 1,9133 0.0000

  3 -7.5000 0.0000 0.0000 1.6182 0.0000

  4 -5.2371 0.0000 0.0000 1.2678 0.0000

-3,5101 0.0000 0.0000 0.9317 0.0000

  6 -2.1243 0.0000 0.0000 0.6090 0.0000

  7 -1.5249 0.0000 0.0000 0.4523 0.0000

  8 -1.1898 0.0000 0.0000 0.3598 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000

2,5000 0.0000 0.0000 -0.9336 0.0000

  1 1 4,7629 0.0000 0.0000 -2.0535 0.0000

  12 6,4899 0.0000 0.0000 -3.1437 0.0000

  13 7.8757 0.0000 0.0000 -4.2099 0.0000

  14 8.4751 0.0000 0.0000 -4.7357 0.0000

8,8102 0.0000 0.0000 -5.0491 0.0000

  16 10.0000 0.0000 0.0000 -6.2905 0.0000

  17 11.0000 0.0000 0.0000 -7.4900 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focusing of the twelfth example (ratio of rotation amplitudes aF / az = -0.75) Focal length Corresponding position Distance of amplitude of rotation to infinity photography for focusing 72 , 0 mm 0.0000 5.00 m -1.190, 0 mm 3.5209 4.00 m -1.525, 0 mm 5.9912 3.00 m -2.124, 0 mm 7.0528 2.00 m -3.510, 0 mm 10,0000 1,50 m -5,237 1,20 m -7,500 Condition corresponding to value (6) 1,05 Condition corresponding to value (7) 3,31 Condition corresponding to value (8) -0,75 Condition corresponding to value (12) 0.42 (wide-angle) 0.39 (telephoto) Condition corresponding to value (13) 0.70 (wide-angle) 0.90 (telephoto) Condition corresponding to value (14) 1.52 ( wide-angle) 1.26 (telephoto) Table 110 below shows the numerical values of the cams in the focus lens assembly of the

  twelfth example, the data being calculated by interpolating

  using the spline function and with the focus cam sample data contained in the middle portion of table 109. It should be noted that the meanings of the symbols in table 110 are the same.

  only in the ninth embodiment.

Table 110

  Digital Cam Values for Twelfth Example Focusing Lens Digital Focus Cam Values Digital Focal Length Compensation Cam Values

ANGLE (3) F ANGLE (3) F

-7.5000 1.6182 0.0000

-7.0000 1.5483 0.0000

-6.5000 1.4744 0.0000

-6.0000 1.3962 0.0000

-5.5000 1.3133 0.0000

-5.0000 1.2255 0.0000

-4,5000 1,1325 0,0000

4.0000 1.0339 0.0000

-3.5000 0.9295 0.0000

-3.0000 0.8189 0.0000

-2.5000 0.7017 0.0000

-2.0000 0.5774 0.0000

-1.5000 0.4456 0.0000

-1.0000 0.3057 0.0000

2 0 -0.5000 0.1572 0.0000

  0.0000 0.0000 72.0000 0.0000 0.0000 72.0000

  0.5000 -0.1660 76.1236 0.5000 1.3748 76.1236

  1.0000 -0.3416 80.4107 1.0000 2.7619 80.4107

  1.5000 -0.5276 84.8761 1.5000 4.1606 84.8761

  2 5 2.0000 -0.7246 89.5329 2.0000 5.5699 89.5329

  2.5000 -0.9336 94.3931 2.5000 6.9884 94.3931

  3,0000 -1,1554 99,4683 3,0000 8,4147 99,4683

  3.5000 -1.3909 104.7727 3.5000 9.8477 104.7727

  4.0000 -1.6411 110.3201 4.0000 11.2862 110.3201

  4,5000 -1,9071 116,1211 4,5000 12,7281 116,1211

  , 0000 -2,1897 122,1805 5,0000 14,1701 122,1805

  , 5000 -2,4902 128,5085 5,5000 15,6102 128,5085

  6,0000 -2,8101 135,1192 6,0000 17,0469 135,1192

  6,5000 -3,1508 142,0209 6,5000 18,4779 142,0209

  7.0000 -3.5139 149.2214 7.0000 19.9005 149.2214

  7.5000 -3.9014 156.7540 7.5000 21.3156 156.7540

  8.0000 -4.3155 164.6446 8.0000 22.7226 164.6446

  8,5000 -4,7585 172,9045 8,5000 24,1180 172,9045

  9.0000 -5.2331 181.5381 9.0000 25.4980 181.5381

  9,5000 -5,7420 190,5503 9,5000 26,8586 190,5503

  , 0000 -6,2905 200,0000 10,0000 28,2022 200,0000

  The left side of table 110 gives the numerical values of the focusing cam of the twelfth example and the right part those of the zoom compensation cam

  of this example. A value obtained by synthesis of

  displacement studies (3) in the direction of the optical axis taken from the numerical values of the focusing cam and the zoom compensating cam, in the range of the rotational amplitudes (ANGLE = 0.0) to (ANGLE = 10,0), coincides with the locus of displacement of the third set of lenses, calculated using the paraxial data of the

top of table 109.

  The following tables 111, 112 and 113 give the focusing amplitude DX (mm), in the direction of the optical axis, of the set of focusing lenses, the magnifications Px of image formation of the images.

  respective sets of lenses, the conversion coefficient

  yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the conversion coefficient Ya associated with the rotation at the wide-angle end (F = 72.0 mm) in the middle position (F 135.0 mm) and at the telephoto end (F = 200.0 mm) in the twelfth embodiment. The provisions and meanings of the symbols in the respective tables are the same as in the

ninth example.

Table 111

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (72.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) 0.178 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 0,360 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 0,452 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 0,609 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 0,932 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 1,268 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 1,618 4) 0,000

  Objective image magnification at the wide-angle end (72.0 mm) of the twelfth example

  R 0,000 ANG 0.000 1) 0.000 2) -3.807 3) -0.105 4) 1, 726

  R 10,000 ANG -0.568 1) -0.011 2) -3.614 3) -0.109 4) 1, 726

  R 5,000 ANG -1,190 1) -0,022 2) -3,432 3) -0,113 4) 1,72

  R 4,000 ANG -1,525 1) -0,028 2) -3,344 3) -0,116 4) 1,72

  R 3,000 ANG -2,124 1) -0,038 2) -3,204 3) -0,119 4) 1,72

  R 2,000 ANG -3,510 1) -0,059 2) -2,941 3) -0,127 4) 1,72

  R 1.500 ANG -5.237 1) -0.082 2) -2.699 3) -0.135 4) 1, 726

  R 1,200 ANG -7,500 1) -0,107 2) -2,477 3) -0,144 4) 1,72

  Conversion coefficient Yx associated with the direction of the optical axis at the wide-angle end (72.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 2,948 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) 2.945 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 2,942 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 2,941 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 2,938 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 2,932 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 2,926 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 2,919 4) 0,000

  Slope dx / da focus cam at the wide-angle end (72.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,323 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) -0.303 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -0,282 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,271 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,252 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,215 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,176 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,136 4) 0,000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (72.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,952 4) 0,000

  R 10,000 ANG -0.568 1) 0.000 2) 0.000 3) -0.893 4) 0, 000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) -0,829 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,796 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,741 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,629 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,514 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,397 4) 0,000

  Condition corresponding to the values: YxR / Yxo = 0.99, yaR / YaO = 0.42

Table 112

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (135.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) 0.360 4) 0.000

* R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) 0,728 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) 0,915 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3 1,230 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) 1,879 4) 0,000

  R 1.500 ANG -5.241 1) 0.000 2) 0.000 3) 2.552 4) 0.000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 3,252 4) 0,000

  Ik image magnification of lenses at the median position (135.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 11,821 3) 0,048 4) 2, 262

  R 10,000 ANG -0.566 1) -0.011 2) 14.182 3) 0.040 4) 2, 262

  R 5,000 ANG -1,188 1) -0,022 2) 17,964 3) 0,031 4) 2, 262

  R 4,000 ANG -1,523 1) -0,028 2) 20,858 3) 0,026 4) 2, 262

  R 3,000 ANG -2,122 1) -0,038 2) 28,907 3) 0,019 4) 2, 262

  R 2,000 ANG -3,509 1) -0,060 2) 167,907 3) 0.003 4) 2, 262

  R 1,500 ANG -5,241 1) -0,084 2) -39,060 3) -0,013 4) 2, 262

  R 1,200 ANG -7,500 1) -0,111 2) -16,516 3) -0,030 4) 2, 262

  Coefficient of conversion Yx associated with the direction of the optical axis at the median position (135.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 5,104 4) 0,000

  R 10,000 ANG -0,566 1) 0,000 2) 0,000 3) 5,108 4) 0,000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) 5,111 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) 5,113 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) 5,115 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) 5,116 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) 5,115 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 5,112 4) 0,000

  Slope dx / da focus cam at the center position (135.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -0,659 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) -0.614 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) -0,569 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) -0,546 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) -0,508 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) -0,430 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) -0,351 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -0,271 4) 0,000

  Conversion coefficient Ya associated with the direction of rotation at the median position (135.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -3,366 4) 0,000

  R 10,000 ANG -0.566 1) 0.000 2) 0.000 3) -3.137 4) 0.000

  R 5,000 ANG -1,188 1) 0,000 2) 0,000 3) -2,907 4) 0,000

  R 4,000 ANG -1,523 1) 0,000 2) 0,000 3) -2,792 4) 0,000

  R 3,000 ANG -2,122 1) 0,000 2) 0,000 3) -2,596 4) 0,000

  R 2,000 ANG -3,509 1) 0,000 2) 0,000 3) -2,198 4) 0,000

  R 1,500 ANG -5,241 1) 0,000 2) 0,000 3) -1,796 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) -1,386 4) 0,000

  2 0 Condition corresponding to the values: yxR / yxo = 1.00, YaR / YaO = 0, 41

Table 113

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (200.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) 0.618 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 1,241 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 1,555 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 2,081 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 3,147 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 4,237 4) 0,000

  R 1,200 ANG -7,500 1) 0,000 2) 0,000 3) 5,357 4) 0,000

  13k Lens magnification at the telephoto end (200, 0 mm) of the twelfth

example

  R 0,000 ANG 0,000 1) 0,000 2) 3,174 3) 0,230 4) 2,617

  R 10,000 ANG -0.567 1) -0.011 2) 3.323 3) 0.215 4) 2, 617

  R 5,000 ANG -1,190 1) -0,022 2) 3,496 3) 0,200 4) 2,617

  R 4,000 ANG -1,525 1) -0,028 2) 3,594 3) 0,193 4) 2,617

  R 3,000 ANG -2,124 1) -0,038 2) 3,777 3) 0,180 4) 2,617

  R 2,000 ANG -3,510 1) -0,061 2) 4,244 3) 0,155 4) 2,617

  R 1.500 ANG -5.237 1) -0.085 2) 4.920 3) 0.128 4) 2, 617

  R 1,200 ANG -7,500 1) -0,113 2) 5,985 3) 0,101 4) 2,617

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (200.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 6,488 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) 6.533 4) 0.000

  R 5,000 ANG -1,190 1) 0,000 2) 0,000 3) 6,576 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) 6,596 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) 6,628 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) 6,687 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) 6,738 4) 0,000

  R 1200 ANG -7.5001) 0.000 2) 0.000 3) 6.780 4) 0.000

  Slope dx / da focus cam at the telephoto end (200.0 mm) of the twelfth

example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -1,140 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) -1.045 4) 0.000

  R 5,000 ANG -1,1901) 0,000 2) 0,000 3) -0,957 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -0,914 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -0,842 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -0,702 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -0,566 4) 0,000

  R 1200 ANG -7.5001) 0.000 2) 0.000 3) -0.430 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (200.0 mm) of the twelfth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) -7,395 4) 0,000

  R 10,000 ANG -0.567 1) 0.000 2) 0.000 3) -6.828 4) 0.000

  R 5,000 ANG -1,1901) 0,000 2) 0,000 3) -6,291 4) 0,000

  R 4,000 ANG -1,525 1) 0,000 2) 0,000 3) -6,028 4) 0,000

  R 3,000 ANG -2,124 1) 0,000 2) 0,000 3) -5,581 4) 0,000

  R 2,000 ANG -3,510 1) 0,000 2) 0,000 3) -4,696 4) 0,000

  R 1,500 ANG -5,237 1) 0,000 2) 0,000 3) -3,814 4) 0,000

  R 1200 ANG -7.5001) 0.000 2) 0.000 3) -2.919 4) 0.000

  Condition corresponding to the values: YxR / yxo = 1.05, yaR / YaO = 0.39 As indicated in Tables 111, 112 and 113, the conversion coefficient yx associated with the direction of the axis

  optical system shows virtually no change at the

  wide-angle and mid-position, but increases at the telephoto end when the distance of photography approaches the shortest distance, and the slope (dx / da) of the focusing cam decreases when the distance of photography gets closer to the shorter distance at the respective focal lengths. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of The photograph is close to the shortest distance, because of the slope (dx / da) of the focusing cam. In tables 111, 112 and 113, the rate of change, from the position focused at infinity to the position focused at the nearest point, of the conversion coefficient associated with the rotation is xO, 42 at the large end. - angle (F = 72.0), x0.41 at the middle position (F = 135.0 mm), and x0.39 at the telephoto end (F = 200.0 mm). When the number N of divisions of the focusing range during a change in the conversion coefficient is twelfth example is calculated using the formula (a) and is compared with the example of the Japanese patent application put In Public Inspection No. 5-142475, the division numbers Nw, NM and NT at the wide-angle end, in the middle position and at the telephoto end respectively, have the following values: example of the patent application Japanese laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8.1 Twelfth Example Nw> 4.8 NM> 4.9 NT> 5.1 As previously described, in the twelfth For example, since the rate of change of the conversion coefficient Ya associated with the rotation is smaller than that of the conventional system, the values of the numbers N of divisions are

  low. For this reason, the number of data of the coeffi-

  The conversion factor γ and the correction coefficient γ can be reduced, and the storage capacity can also be suppressed. Tables 114, 115 and 116 give the results of calculating the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 72.0 mm), in the median position (F = 135.0 mm) , and at the telephoto end (F = 200.0 mm) in the twelfth example. The provisions of the tables and their symbols are the same as in the ninth example. The position of the focusing lens of the first pair of the two upper parts of each of the tables 114, 115 and 116, ie the third and fourth columns, is

  (R, ANGLE) = (0,0; 0,0), and indicates that this position corresponds to

  pond to infinity. Similarly, the position of the focusing lens in the fourth pair in both parts

  of each of Tables 114, 115 and 116, that is,

  say in the ninth and tenth column, is

  (R, ANGLE) = (1.0, -7.5) and indicates that this position corresponds to

  pond at the focus position at the most location

close (R = 1.2 m).

Table 114

  Conversion coefficients Ka: (rs), ya: (r) associated with direction of rotation and correction coefficient p: (t) at the wide-angle end (72.0 mm) of the twelfth example f = 72.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,568 5,000 -1,190 4,000 - 1,525

POS R rs r rs r rs

  I 0.000 -0.952 0.000 -0.918 -0.881 -0, 861

  2 10,000 -0.928 -0.893 0.000 -0.856 -0.837

  3 5,000 -0,900 -0,866 -0,829 0,000 -0,810

  4,000 -0.885 -0.851 -0.815 -0.796 0.000

3,000 -0.859 -0.826 -0.790 -0.772

  6 2,000 -0.803 -0.770 -0.737 -0.719

  7 1,500 -0,739 -0,708 -0,677 -0,660

  8 1,200 -0,665 -0,637 -0,607 -0,592

POS R bf f bf t bf t bf t

  1 0,000 0.00 0.00 -0.52 18.91 -1.05 16.75 -1.31 15.95

  2 10,000 0.53 20.46 0.00 0.00 -0.53 16.16 -0.80 15.52

  3 5,000 1.07 19.62 0.54 17.61 0.00 0.00 -0.27 15.37

  4 4,000 1.35 19.22 0.81 17.27 0.27 15.67 0.00 0.00

  5 3,000 1.83 18.73 1.28 16.98 0.74 15.68 0.46 15.33

  6 2,000 2.82 17.97 2.27 16.50 1.71 15.35 1.43 14.87

  7 1,500 3.87 17.29 3.31 15.99 2.74 14.90 2.45 14.41

  8 1,200 4.99 16.54 4.41 15.36 3.83 14.32 3.54 13.82

  (R, ANGLE) = 3,000 -2,124 2,000 -3,510 1,500 -5,237 1,200 -7,500

2 5 POS R rs r rs r rs

  I 0.000 -0.828 -0.759 -0.685 -0, 604

  2 10,000 -0.804 -0.736 -0.664 -0, 584

  3 5,000 -0.778 -0.712 -0.641 -0, 563

  4,000 -0,765 -0,699 -0,629 -0,553

  3 0 5 3,000 -0,741 0,000 -0,677 -0,609 -0,534

  6 2,000 -0,690 -0,629 0,000 -0,564 -0, 493

  7 1,500 -0,633 -0,576 -0,514 0,000 -0,448

  8 1,200 -0,567 -0,514 -0,457 -0,397 0, 000

POS R bf fbf t bf i bf e

  1 0.000 -1.76 14.96 -2.66 12.93 -3.59 10.83 -4.53 8.68

  2 10,000 -1.25 14.70 -2.17 12.76 -3.10 10.69 -4.05 8.57

  3 5,000 -0.73 14.56 -1.65 12.62 -2.59 10.55 -3.55 8.47

  4 4,000 -0.46 14.47 -1.39 12.53 -2.34 10.48 -3.30 8.41

  3,000 0.00 0.00 -0.94 12.40 -1.89 10.35 -2.87 8.31

  6 2,000 0.96 13.92 0.00 0.00 -0.97 10.04 -1.97 8.08

  7 1,500 1.97 13.50 0.99 11.67 0.00 0.00 -1.01 7.86

  8 1,200 3,05 12,95 2,05 11,16 1,03 9,31 0,00 0,00

  Condition corresponding to the values: Kao / yao0 = 0.70, KaR / YaR = 1.52

Table 115

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (135.0 mm) of the twelfth example f = 135.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,566 5,000 -1,188 4,000 - 1,523

POS R rs r rs r rs

  1 0.000 -3.366 0.000 -3.198 -3.031 -2, 948

  2 10,000 -3.304 -3.137 0.000 -2.972 -2, 889

  3 5,000 -3,235 -3,071 -2,907 0,000 -2, 826

  4,000 -3,199 -3,035 -2,873 -2,792,0,000

3,000 -3.134 -2.972 -2.812 -2.731

  6 2,000 -2,984 -2,827 -2,670 -2, 592

  7 1.500 -2.804 -2.652 -2.501 -2, 426

  8 1,200 -2,584 -2,441 -2,298 -2, 227

POS R bf I bf t bf f bf t

  1 0.000 0.00 0.00 -1.81 92.30 -3.60 84.53 -4.49 80, 44

  2 10,000 1.87 101.28 0.00 0.00 -1.85 83.54 -2.76 79, 36

  3 5,000 3.84 99.01 1.91 90.81 0.00 0.00 -0.95 78, 02

  4,000 4.87 98.09 2.90 89.82 0.96 81.84 0.00 0.00

  5 3,000 6.65 96.41 4.62 88.11 2.63 79.72 1.64 75.17

  6 2,000 10.47 92.34 8.32 84.17 6.20 75.99 5.15 71, 84

  7 1,500 14.69 87.99 12.40 80.23 10.14 72.60 9.02 68, 83

  8 1,200 19.38 83.48 16.92 76.24 14.50 69.20 13.31 65, 76

  (R, ANGLE) = 3,000 -2,122 2,000 -3,509 1,500 -5,241 1,200 -7,500

POS R rs r rs r rs

  1 0.000 -2.808 -2.525 -2.236 -1, 938

  2 10,000 -2,751 -2,471 -2.185 -1, 891

  3 5,000 -2,689 -2,412 -2,130 -1,841

  4,000 -2,656 -2,380 -2,101 -1,814

  3 0 5 3,000 -2,596 0,000 -2,324 -2,049 -1,767

  6 2,000 -2,461 -2,198 0,000 -1,932 -1, 661

  7 1,500 -2,300 -2,049 -1,796 0.000 -1, 539

  8 1,200 -2,108 -1,872 -1,635 -1,386 0, 000

POS R bf a bf a bf a bf f

  I 0.000 -5.96 73.06 -8.86 59.45 -11.72 47.84 -14.54 36, 50 2 10,000 -4.28 71.85 -7.27 58.46 -10.21 47.15 -13.11 35.98

  3 5,000 -2.51 70.31 -5.60 57.37 -8.63 46.41 -11.62 35, 42

  4 4,000 -1.59 69.40 -4.73 56.81 -7.81 46.05 -10.84 35, 12

  3,000 0.00 0.00 -3.22 55.92 -6.39 45.44 -9.50 34.61

  6 2,000 3.41 65.41 0.00 0.00 -3.35 44.20 -6.63 33.39

  7 1,500 7.17 62.95 3.55 52.48 0.00 0.00 -3.48 31, 47

  8 1,200 11.34 60.34 7.47 50.47 3.69 41.34 0.00 0, 00

  Condition corresponding to the values: Kao / ao = 0.77, KaR / YaR = 1.40

Table 116

  Conversion coefficients Ia: (rs), ya: (r) associated with direction of rotation and correction coefficient pI: (t) at the end of telephoto (200, 0 mm) of the twelfth example f = 200, Omm

  (R, ANGLE) = 0,000 0,000 10,000 -0,567 5,000 -1,190 4,000 -1,525

POS R rs r rs r rs

  1 0.000 -7.394 0.000 -6.878 -6.391 -6, 158

  2 10,000 -7,349 -6,828 0,000 -6,341 -6, 109

  3 5,000 -7,299 -6,778 -6,291 0,000 -6,058

  4,000 -7,275 -6,752 -6,264 -6,027 0, 000

3,000 -7,226 -6,700 -6,207 -5,967

  6 2,000 -7,097 -6,563 -6,061 -5,820

  7 1,500 -6,908 -6,367 -5,861 -5,618

  8 1,200 -6,620 -6,077 -5,571 -5, 330

POS R bf t bf t bf t bf f

  1 0.000 0.00 0.00 -3.90 536.53 -7.60 481.38 -9.39 429.63

  2 10,000 4.16 677.88 0.00 0.00 -3.95 502.26 -5.85 429.82

  3 5,000 8.68 679.26 4.22 568.84 0.00 0.00 -2.03 390.50

  4,000 11.09 688.18 6.47 580.29 2.10 490.77 0.00 0.00

  5 3,000 15.35 677.43 10.44 556.71 5.80 431.35 3.58 363.92

  6 2,000 24.91 620.40 19.32 496.79 14.06 384.73 11.55 336.66

  7 1,500 36.18 550.24 29.74 440.07 23.72 346.70 20.86 307.91

  8 1,200 49.65 474.13 42.13 382.69 35.15 307.02 31.85 275.46

  (R, ANGLE) = 3,000 -2,124 2,000 -3,510 1,500 -5,237 1,200 -7,500

POS R rs r rs r rs

  1 0,000 -5,781 -5,058 -4,367 -3, 691

  2 10,000 -5,730 -5,004 -4,312 -3, 637

  3 5,000 -5,674 -4,944 -4,250 -3,576

  4,000 -5,642 -4,910 -4,216 -3, 543

  5 3,000 -5,580 0,000 -4,847 -4,154 - 3,482

  6 2,000 -5,431 -4,696 0,000 -4,006 -3, 340

  7 1,500 -5,229 -4,498 -3,814 0,000 -3,158

  8 1,200 -4,944 -4,224 -3,555 -2,919 0, 000

POS R bf t bf f bf t bf t

  1 0.000 -12.28 341.22 -17.75 230.41 -22.87 157.75 -27.68 104.61

  2 10,000 -8.92 332.54 -14.73 224.58 -20.14 154.25 -25.21 102, 51

  3 5,000 -5.30 313.45 -11.47 217.19 -17.20 150.28 -22.57 100, 21

  4 4,000 -3.38 305.95 -9.75 213.89 -15.65 148.33 -21.17 99.03

  3,000 0.00 0.00 -6.72 208.26 -12.93 144.95 -18.72 96.97

  6 2,000 7.53 281.46 0.00 0.00 -6.92 137.39 -13.33 92.37

  7 1,500 16.28 258.81 7.77 184.07 0.00 0.00 -7.15 87.04

  8 1,200 26.58 233.22 16.85 167.57 8.04 118.49 0.00 0.00

  Condition corresponding to the values: KaO / yaO = 0.90, KaR / YaR = 1.26 The results of the calculation of the rate of variation of Ka as a function of Ya for the set focused at infinity and the set focused at the nearest location at the wide-angle end, in the middle position and at the telephoto end of the example of Japanese Patent Application Laid-open No. 5-142475 and

  of the twelfth example of the invention are the following.

  Example of Japanese Patent Application Laid-open No. 5142475 At Infinity Ka / yaO Nearest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Twelfth example At infinity Ka0o / YaO Nearest KaR / YaR Wide angle (F = 72.0) 0.70 1.52 Median position 0.77 1.40

(F = 135.0)

  Telephoto (F = 200.0) 0.90 1.26 As previously described in the twelfth example, since the rate of change of Ka in function Ya is small, compared with the conventional system, the contribution of the correction term (ABf / g) of the relation Ka = ya (1 - ABf / M) can be reduced. For this reason, the error of the conversion coefficient Ka calculated as a function of Ya and y or the error on the actual driving amplitude of lenses Aa obtained when using a single pair of the values of the coefficient of Ya conversion and

  correction coefficient y can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the twelfth

  example of the invention, when the training amplitudes

  lens during focusing with a set focused to infinity to the object at the shortest distance and during focusing with a focused set at the shortest distance to the object at infinity at infinity. wide-angle end, in the middle position and at the telephoto end are calculated from the

  Aa = ABf / ya (1 - ABf / i), and the errors of the amplifiers

  The actual driving training of the lenses is then calculated and the following values are obtained. It should be noted that the value of the correction coefficient y when focusing with the set focused to infinity until the object at the shortest distance has the value corresponding to the object distance (POS-5), and that the value of the correction coefficient A when focusing with the set focused at the shortest distance on an object to infinity

  takes the value corresponding to the object distance (POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest-Near-Focused-Infinity Wide-angle (F = 36.0) -4.4% -13.0% Midpoint (F = 50.0) -11, 8% -12.0% Telephoto (F = 103.0) -12.6% -14, 6% Twelfth example Infinity Focused Most Focus Near Focused at infinity Wide-angle (F = 72.0) -4.7% -1.2% Median position (F = 135.0) -3.9% -1.1% Telephoto (F = 200.0) - 3.4% -1.2% As described previously, in the twelfth example, when a single pair of values of the conversion coefficient Ya and the correction coefficient y is fixed for a given range of the objective, an error between the conversion coefficient Ka calculated from Ya and y and the lens driving amplitude Aa for focusing becomes low compared to the conventional system and the focusing can be performed with increased accuracy. Table 117 gives the amplitude of rotation (ANGLE DA) for the manual focusing with the aid of the focusing cam (middle part of table 109) of the twelfth example, the displacement amplitude DX (mm) in the direction of rotation. the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  It should be noted that the table layout and reference symbols are the same as in the ninth example. The upper part of table 117 indicates the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 4.0, 3.0, 2.0, 1.5 and 1.2 m ) for the respective states of variation of the focal lengths (F = 72.0, 105.0, 135.0, 150.0 and, 0 mm), and the middle part gives the values of the amplitude of rotation (ANGLE DA ) focusing necessary to obtain an optimal focused state at the respective photography distances. The lower part of the table gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for focusing with the focal lengths and distances

of photography.

Table 117

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the twelfth example 1,20m 1,50m 2,00 m 3,00 m 4,00 m 5,00m 72,000 Bf 0,000 0,000 0,000 0 , 000 0.000 0.000, 000 Bf 0.000 0.000 0.010 0.011 0.008 0, 007, 000 Bf 0.000 0.007 -0.001 -0.005 -0.004 -0.004, 000 Bf 0, 000 -0.005 -0.014 -0.013 -0.011 -0.009, 000 Bf 0.000 0.000 0 , 000 0,000 0,000 0,000

  ANGLE DA -7,500 -5,237 -3,510 -2,214 -1,525 -1,190

* F 72,000 DX 0,000 0,000 1,618 0,000 R 1,20 m F 105,000 DX 0,000 0,000 2,431 0,000 R 1,20 m F 135,000 DX 0,000 0,000 3,252 0,000 R 1,20 m F 150,000 DX 0,000 0,000 3,695 0,000 R 1,20 m F 200,000 DX 0,000 0, 000 5,357 0,000 R 1,20 m F 72,000 DX 0,000 0,000 1,268 0,000 R 1,50 m F 105,000 DX 0,000 0,000 1,905 0,000 R 1,50 m F 135,000 DX 0,000 0,000 2,550 0,000 R 1.50 m F 150,000 DX 0,000 0,000 2,903 0,000 R 1,50 m F 200,000 DX 0,000 0,000 4,237 0,000 R 1,50 m F 72,000 DX 0,000 0,000 0,932 0,000 R 2,00 m F 105,000 DX 0,000 0,000 1,398 0,000 R 2 , 00 m F 135,000 DX 0,000 0,000 1,879 0,000 R 2,00 m F 150,000 DX 0,000 0,000 2,142 0,000 R 2,00 m F 200,000 DX 0,000 0,000 3,147 0,000 R 2,00 m F 72,000 DX 0,000 0,000 0,609 0,000 R 3.00 m F 105,000 DX 0,000 0,000 0,913 0,000 R 3,00 m F 135,000 DX 0,000 0,000 1,231 0,000 R 3,00 m F 150,000 DX 0,000 0,000 1,405 0,000 R 3.00 m F 200,000 DX 0,000 0,000 2,081 0,000 R 3 , 00 m F 72,000 DX 0,000 0,000 0,452 0,000 R 4,00 m F 105,000 DX 0,000 0,000 0,67 8 0.000 R 4.00 m F 135,000 DX 0.000 0.000 0.916 0.000 R 4.00 m F 150.000 DX 0.000 0.000 1, 046 0.000 R 4.00 m F 200.000 DX 0.000 0.000 1, 555 0.000 R 4.00 m F 72,000 DX 0,000 0,000 0,360 0,000 R 5,00 m F 105,000 DX 0,000 0,000 0,539 0,000 R 5,00 m F 135,000 DX 0,000 0,000 0,729 0,000 R 5,00 m F 150,000 DX 0,000 0,000 0,833 0,000 R 5,00 m F 200,000 DX 0,000 0,000 1,241 0,000 R 5,00 m As shown in Table 117, in the zoom lens of the twelfth example, a "manual" focus can be achieved because the magnitudes of the image point displacement for the focal lengths and distances respective photographs are very small and enter the depth of field regardless of the state of variation of distance

  focal length and photography distance.

  In the twelfth example, as indicated in Tables 111 and 112, the conversion coefficient Ya associated with the direction of the optical axis decreases slightly at the wide-angle end and in the median position when the photographing distance approaches the shortest distance. Consequently, since the conversion coefficient associated with the rotation is defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, we can consider that the slope (dx / da) of the focusing cam preferably increases when the distance of photography approaches the shortest distance, as in the example of the request for

  Japanese Patent Laid-Open No. 5-142475.

  However, since the conversion coefficient yx associated with the direction of the optical axis increases much at the telephoto end with respect to the wide-angle end and at the middle position, the slope (dx / da) of the cam Preferably, the focusing distance decreases when the photographing distance approaches the shortest distance according to the invention, taking into account the speed of variation of the conversion coefficient Ya associated with the rotation as a whole. Thirteenth Embodiment The thirteenth embodiment or thirteenth example relates to a zoom lens having a five-set arrangement, that is to say sets of positive, negative, positive, negative and positive type lenses, and provides focusing. using a second set of negative type lenses. For this purpose, the ratio (aF / az) of the focusing rotation amplitude of the position focused at infinity to the position focused at the shortest distance (R = 0.8 m) and the amplitude of Focal length variation rotation from wide-angle end (F 28.7 mm) to end / telephoto end (F = 131.0 mm)

is adjusted to -0.85.

  Table 118 below shows various paraxial data of an optical system and data for determining the configuration of a focusing cam.

in the thirteenth example.

  The upper part of table 118 indicates the focal lengths and intervals of the main points of the respective lens assemblies of the optical system corresponding to the thirteenth example with six focusing states (focal lengths F = 28.7, 35.0, 50.0, 70 , 0,

, 0 and 131.0 mm).

  In this table, F1, F2, F3, F4 and F5 respectively denote the focal lengths of the first, second, third, fourth and fifth sets of lenses, and D1, D2, D3, D4 and D5 are the intervals of the main points between respectively the first and the second set of lenses, the second and the third set of lenses, the third and fourth set of lenses, the fourth and the fifth set of lenses, and the fifth set of lenses and a predetermined image plane for the six focusing conditions (focal lengths F = 28.7, 35.0, 50.0, 70.0, 105.0 and

131.0 mm).

  The middle portion of Table 118 shows the spline sample data when the configuration of the focusing cam (curve g2F of FIG. 5B) of the second set of lenses of the thirteenth example, used for focusing, is represented by the function of aforementioned spline associated with the rotational barrel rotation angle a and the displacement amplitude x in the direction

of the optical axis.

  In addition, the lower portion of table 118 indicates the infinite focus positions (positions corresponding to infinity) for the respective focal lengths (F = 28.5, 35.0, 50.0, 70.0, 105.0 and 131.0 mm), and the magnitudes of rotation (for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.5, 1, 0 and 0.8 mm) with the focusing cam of the thirteenth example. In this table, as the amplitude of rotation for the focal length variation from the wide-angle end (F = 28.7 mm) to the telephoto end (F = 131.0 mm) is set to 10.0 and the focus rotation amplitude of the position focused at infinity at the position focused at the nearest location (R = 0.8 mm) is -8.5, the ratio (aF / az) the focal rotation and focal length variation amplitudes of the thirteenth example is equal

at -0.85.

Table 118

  Thirteenth example f = 28.7 to 131.0 (ratio of amplitudes of rotation: aF / az = -0.85) Focal distances and intervals of the main points of the objectives of the thirteenth example

  F 28,7000 35,0000 50,0000 70,0000 105,0000 131,0000

  F1 91,3108 D1 11,1134 16,1861 27,1959 34,7239 38,1201 39,1199

  F2 -16.5244 D2 36.8414 32.9701 27.9348 23.5294 18.1537 15.9002

  F3 25.11621 D3 10.7552 12.6122 15.6328 17.5434 21.3827 23.4271

  F4 -35,4049 D4 12,9390 11,0820 8,0614 6,1508 2,3115 0, 2671

  F5 55.8741 D5 52.1460 53.3605 54.4244 59.3670 71.3442 81, 2252

  Focusing cam shape (spline interpolated point) corresponding to the thirteenth example

ANGLE (1) (2) (3) (4) (5)

  1 -11.0000 0.0000 0.9660 0.0000 0.0000 0.0000

  2 -10,0000 0.0000 0,9113 0.0000 0.0000 0.0000

  3 -8.5000 0.0000 0.8210 0.0000 0.0000 0.0000

  4 -6,0559 0.0000 0.6448 0.0000 0.0000 0.0000

  -3,5451 0.0000 0.4198 0.0000 0.0000 0.0000

  6 -2.5111 0.0000 0.3112 0.0000 0.0000 0.0000

  7 -1.5854 0.0000 0.2051 0.0000 0.0000 0.0000

  8 -0.9143 0.0000 0.1220 0.0000 0.0000 0.0000

  9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

  1,5000 0.0000 -0.2326 0.0000 0.0000 0.0000

  1 1 3,9441 0.0000 -0.7068 0.0000 0.0000 0.0000

  12 6.4549 0.0000 -1.3595 0.0000 0.0000 0.0000

  13 7.4889 0.0000 -1.6972 0.0000 0.0000 0.0000

  14 8.4146 0.0000 -2.0445 0.0000 0.0000 0.0000

  9,0857 0.0000 -2.3304 0.0000 0.0000 0.0000

  16 10.0000 0.0000 -2.7753 0.0000 0.0000 0.0000

  17 11.0000 0.0000 -3.3400 0.0000 0.0000 0.0000

  Rotation amplitude for focal length change and rotation amplitude for focusing of the thirteenth example (ratio of rotation amplitudes: aF / az = -0.85) Focal length Corresponding position Distance of amplitude of rotation to infinity photography for focusing 28.7 mm 0.0000 5.00 m -0.914, 0 mm 1.6419 3.00 m -1, 585, 0 mm 5.4298 2.00 m -2.511, 0 mm 8.2173 1.50 m - 3,545, 0 mm 9, 5602 1,00 m -6,056 131,0 mm 10, 0000 0,80 m -8,500 Condition corresponding to value (9) 1,15 Condition corresponding to value (10) 3,10 Condition corresponding to value (11) -0.85 Condition corresponding to value (12) 0.47 (wide-angle) 0.37 (telephoto) Condition corresponding to value (13) 0.72 (wide-angle) 0.89 (telephoto) Condition corresponding to value (14) 1.43 (large angle) 1.26 (telephoto) Table 119 which follows shows the numerical values of the cams of the focus lens assembly of the thirteenth example, the values being calculated by integer with a spline function using the focus cam sample data shown in the middle portion of Table 118. In this table, (ANGLE) refers to the rotation angle of the rotating barrel, (2) the amplitude displacement (mm) in the direction of the optical axis of the second set of lenses, and (F) the focal length (mm) of the entire system in the focused state at infinity, corresponding to the amplitude of

rotation (ANGLE).

Table 119

  Digital Cam Values for the Focusing Lens of the Thirteenth Example Focusing Cam Numerals Focal Length Compensation Cam Numerical Values

ANGLE (2) F ANGLE (2) F

-8.5000 0.8210 0.0000

-8.0000 0.7880 0.0000

-7.5000 0.7535 0.0000

-7.0000 0.7174 0.0000

-6.5000 0.6797 0.0000

-6.0000 0.6403 0.0000

-5,5000 0.5992 0.0000

-5.0000 0.5563 0.0000

4.5000 0.5114 0.0000

-4.0000 0.4644 0.0000

-3,5000 0.4152 0.0000

-3.0000 0.3638 0.0000

-2.5000 0.3100 0.0000

-2.0000 0.2538 0.0000

-1.5000 0.14949 0.0000

-1.0000 0.139 0.0000

-0.5000 0.0682 0.0000

  0.0000 0.0000 28.7000 0.0000 0.0000 28.7000

  0.5000 -0.0728 30.4901 0.5000 -0.7869 30.4901

  1.0000 -0.1504 32.4166 1.0000 -1.5295 32, 4166

  1.5000 -0.2326 34.4256 1.5000 -2.2134 34.4256

  2.0000 -0.3194 36.4414 2.0000 -2.8320 36.4414

  2,5000 -0,4111 38,4264 2,5000 -3,3908 38,4264

  3,0000 -0,5081 40,3764 3,0000 -3,8961 40,3764

  3 0 3.5000 -0.6107 42.2979 3.5000 -4.3504 42.2979

  4.0000 -0.7193 44.2091 4.0000 -4.7526 44.2091

  4,5000 -0,8342 46,1429 4,5000 -5,0984 46,1429

  , 0000 -0,954 48,1532 5,0000 -5,3792 48,1532

  , 5000 -1.0864 50.3168 5.5000 -5.5782 50.3168

  3 5 6.0000 -1.2251 52.7342 6.0000 -5.6706 52.7342

  6,5000 -1,3732 55,4963 6,5000 -5,6363 55,4963

  7.0000 -1.5316 58.7165 7.0000 -5.4517 58.7165

  7.5000 -1.7011 62.5804 7.5000 -5.0846 62.5804

  8.0000 -1.8828 67.4339 8.0000 -4.4806 67.4339

  4 0 8,5000 -2,0792 73,9375 8,5000 -3,5284 73,9375

  9.0000 -2.2921 83.5071 9.0000 -1.8748 83.5071

  9,5000 -2,5230 101,5990 9,5000 2,1702 101,5990

  , 0000 -2.7753 131.0000 10.00 10.00 10.9268 131.0000

  The left-hand side of table 119 shows the numerical values of the focus cam of the thirteenth example, and the right-hand side those of the zoom compensation cam of this example. A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis derived from the numerical values of the focusing cam and the zoom compensation cam, in the range of rotation amplitudes (ANGLE = 0 , 0) to (ANGLE = 10.0), coincides with the place of displacement (curve g2 of FIG. 5A) of the second set of lenses calculated with the paraxial data of the upper part of the

table 118.

  As a result, the zoom compensation cam (curve g2H of FIG. 5B) is determined by subtracting the focus cam (curve g2F of FIG. 5B) from the moving place (curve g2 of FIG. 5A) during the variation. focal length of the second set of lenses determined by the paraxial data of the upper part of the

table 118.

  5A, 5B and 6 are briefly described in the following. FIG. 5A represents the paraxial arrangement and the places of displacement during the variation of the focal length of the zoom lens of the thirteenth example, and FIG. 5B shows the configurations of FIG. the focusing cam and the zoom compensating cam of the second set of lenses of this embodiment. In FIGS. 5A and B, G1, G2, G3, G4 and G5 respectively represent the first, second, third, fourth and fifth sets of lenses, and g1, g2, g3, g4 and g5, respectively, represent the places of displacement during the focal length variation for the first, second, third, fourth and fifth sets of lenses. Further, g2F and g2H respectively represent the configurations of the focusing cam and the zoom compensation cam of the second lens. As previously described, the configuration obtained by synthesis of the focusing cam g2F and the zoom compensation cam g2H of the second set of lenses coincides with the location of

  displacement g2 of the second set of lenses.

  FIG. 6 is a view allowing the description of

  the configuration of the focusing cam g2F in the thirteenth example. Referring to Figure 6; (f = 28.7, R = one) and f = 28.7, R = 0, 80) respectively represent the positions focused at infinity and at the smallest distance (R = 0.80 m) at wide-angle end, and the coordinate positions (x; a) of the focusing cam are respectively (x; a) = (0; 0) and (x; a) = (0,821; -8,5). On the other hand, (f = 131, R = one) and (f = 131, R = 0.80) represent respectively the positions focused at infinity and at the smallest distance (R = 0.80 m) at the telephoto end, and the coordinate positions (x; a) on the focusing cam are

  respectively (x; a) = (-2.775; 10) and (x; a) = (-0.233; 1.5).

  When varying the focal length from the wide-angle end to the telephoto end, the second set of lenses moves on the focusing cam g2F from the coordinate position (0; 0) to the coordinate position ( -2.775; 10) for an object at infinity, and the coordinate position (0.821; -8.5) at the coordinate position (-0.233; 1.5) for the object at the shortest distance. As a result, the second set of lenses moves 10.0 in rotation (direction of the axis a) in both cases. On the other hand, when focusing the infinite focused assembly on the object at the shortest distance, the second set of lenses moves on the focus cam g2F of the coordinate position (0; ) at the coordinate position (0.821; -0.5) at the wide-angle end, and the coordinate position (-2.775; 10) at the coordinate position (-0.233; 1.5) at the telephoto end. As a result, the second set of lenses moves -8.5 in rotation (direction of the axis a) at these ends. In contrast, in the direction of the optical axis (x-axis direction), the second set of lenses moves from 0.821 to the wide-angle end and

  from 2,543 to the telephoto end.

  Since the configuration of the focusing cam g2F is determined by interpolation of the coordinates (f = 28.7, R = 0.80), (f = 28.7, R = one), (f = 131; R = 0, 80) and (F = 131; R = one) thanks to the spline function, the slope variation (dx / da) of the focusing cam g2F

  becomes larger when the absolute value of the coordinate

  born x of (f = 28.7, R = 0.80) is smaller or when the absolute value of the coordinate (f = 131; R = one) is larger. More precisely, when the ratio (AxTR / AxWR) between the displacement amplitudes AxTR and AxwR, in the direction of the optical axis, of the set of focusing lenses necessary for the focusing of the position to

  infinity to the nearest position at the far end

  angle or at the telephoto end is larger, the slope variation (dx / da) of the focusing cam

becomes bigger.

  The following tables 120, 121 and 122 give the focusing amplitude DX (mm), in the direction of the optical axis, of the set of focusing lenses, the magnifications Pk of image formation of the sets. of the lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam and the coefficient

  Ya conversion associated with rotation, at the far end

  angle (F = 28.7 mm), medial position (F = 70.0 mm) and at the telephoto end (F = 131.0 mm) in the thirteenth example. In these tables, (R) on the left indicates the distance of photography (m), (ANG) designates the amplitude of rotation on the focusing cam when focusing at the respective distances of photography, and 1), 2), 3 ), 4) and) to the right respectively represent the first, second, third, fourth and fifth sets of lenses. In addition, in these tables, the first part gives the displacement amplitude DX (mm) for focusing in the direction of the optical axis when focusing at the respective photography distances (R = 10.0, 5.0 , 3.0, 2.0, 1.5, 1.0 and 0.80 m) (note that moving to the side of the object is positive). The second part gives the imaging magnitudes 1K of the respective sets of lenses in the focused 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 part gives the conversion coefficient yx associated with the direction of the optical axis of the set of focusing lenses in the focused state at the respective distances of

  photograph (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0.80 m).

  In addition, the fourth part gives the slope (dx / da) of the focusing cam at the positions on the focusing cam, which correspond to the focused 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 part gives the conversion coefficient Ya associated with the rotation of the focus lens assembly in the focused state at the respective photography distances (R = 10.0, 5.0,

3.0, 2.0, 1.5, 1.0 and 0.80 m).

Table 120

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.7 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) 0.061 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 0,122 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 0,205 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 0,311 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 0,420 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 0,645 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 0.821 3) 0.000 4) 0.000 5) 0.000

  Magnification N of lens images at the wide-angle end (28.7 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,260 3) -0,774 4) 23,411 5) 0.067

  R 10,000 ANG -0.443 1) -0.009 2) -0.256 3) -0.774 4) 23.411 5) 0.067

  R 5,000 ANG -0,914 1) -0,019 2) -0,252 3) -0,774 4) 23,411 5) 0,067

  R 3,000 ANG -1,585 1) -0,033 2) -0,247 3) -0,774 4) 23,411 5) 0,067

  R 2,000 ANG -2,511 1) -0,051 2) -0,241 3) -0,774 4) 23,411 5) 0.067

  R 1,500 ANG -3,545 1) -0,071 2) -0,234 3) -0,774 4) 23,411 5) 0.067

  R 1,000 ANG -6,056 1) -0,116 2) -0,221 3) -0,774 4) 23,411 6) 0,067

  R 0,800 ANG -8,500 1) -0,156 2) -0,210 3) -0,774 4) 23,411 5) 0,067 Coefficient of conversion yx associated with the direction of the optical axis at

  the wide-angle end (28.7 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,368 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) 1.371 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 1,374 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 1,377 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 1,382 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 1,386 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 1,396 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) 1.402 3) 0.000 4) 0.000 5) 0.000

  Focusing cam dxlda slope at the wide-angle end (28.7 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,141 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,443 1) 0,000 2) -0,133 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,914 1) 0,000 2) -0,128 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,120 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,110 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -0,100 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,080 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.064 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (28.7 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,193 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.443 1) 0.000 2) -0.183 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -0,175 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,165 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,152 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -0,139 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,112 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.090 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / YxO = 1.03, YaR / Yao = 0.47

Table 121

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (70.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) 0.170 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) 0,337 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) 0,558 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) 0,829 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) 1,096 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) 1,619 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 2.005 3) 0.000 4) 0.000 5) 0.000

  Objective image magnification P3k at the median position (70.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,412 3) -1,159 4) -25,649 5) -0,063

  R 10,000 ANG -0.450 1) -0.009 2) -0.402 3) -1.159 4) -25.649 5) -0.063

  R 5,000 ANG -0,926 1) -0,019 2) -0,392 3) -1,159 4) -25,649 5) -0,063

  R 3,000 ANG -1,603 1) -0,033 2) -0,379 3) -1,159 4) -25,649 5) -0,063

  R 2,000 ANG -2,530 1) -0,052 2) -0,362 3) -1,159 4) -25,649 5) -0,063

  R 1,500 ANG -3,566 1) -0,072 2) -0,346 3) -1,159 4) -25,649 5) -0,063

  R 1,000 ANG -6,065 1) -0,119 2) -0,314 3) -1,159 4) -25,649 5) -0,063

  R 0.800 ANG -8.500 1) -0.161 2) -0.291 3) -1.159 4) -25.649 5) -0.063

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (70.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,867 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) 2.896 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) 2,923 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) 2,959 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) 3,001 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) 3,041 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) 3,113 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8,500 1) 0,000 2) 3,162 3) 0,000 4) 0,000 5) 0,000

  Slope dx / da focus cam at the center position (70.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,390 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) -0.364 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) -0,341 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) -0,311 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) -0,275 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) -0,241 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) -0,181 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) -0.136 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient associated with the direction of rotation at the middle position (70.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -1,119 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.450 1) 0.000 2) -1.055 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,926 1) 0,000 2) -0,996 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,603 1) 0,000 2) -0,920 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,530 1) 0,000 2) -0,826 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,566 1) 0,000 2) -0,733 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,065 1) 0,000 2) -0,565 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.429 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / YxO = 1.10, YaR / Yao = 0.38

Table 122

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (131.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) 0.225 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) 0,445 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 0,731 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 1,078 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 1,416 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 2,068 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG-8.500 1) 0.000 2) 2.543 3) 0.000 4) 0.000 5) 0.000

  Lens magnification k at the telephoto end (131.0 mm) of the thirteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,463 3) -1,686 4) -4,049 5) -0,454

  R 10,000 ANG -0.444 1) -0.009 2) -0.450 3) -1.686 4) -4.049 5) -0.454

  R 5,000 ANG -0,914 1) -0,019 2) -0,436 3) -1,686 4) -4,049 5) -0,454

  R 3,000 ANG -1,585 1) -0,033 2) -0,419 3) -1,686 4) -4,049 5) -0,454

  R 2,000 ANG -2,511 1) -0,052 2) -0,398 3) -1,686 4) -4,049 5) -0,454

  R 1,500 ANG -3,545 1) -0,073 2) -0,378 3) -1,686 4) -4,049 5) -0,454

  R 1,000 ANG -6,056 1) -0,122 2) -0,338 3) -1,686 4) -4,049 5) -0,454

  R 0.800 ANG-8.500 1) -0.166 2) -0.309 3) -1.686 4) -4.049 5) -0.454

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (131.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 7,531 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0,444 1) 0,000 2) 7,650 3) 0,000 4) 0,000 5) 0,000

  R 5,000 ANG -0,914 1) 0,000 2) 7,763 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) 7,905 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) 8,070 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) 8,222 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) 8,493 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) 8.671 3) 0.000 4) 0.000 5) 0.000

  Slope dx / da focus cam at the telephoto end (131.0 mm) of the thirteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,529 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) -0.486 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -0,449 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -0,403 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -0,350 3) 0,000 4) 0,000 5) 0,000

* R 1,500 ANG -3,545 1) 0,000 2) -0,304 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -0,222 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -0.169 3) 0.000 4) 0.000 5) 0.000

  Conversion coefficient associated with the direction of rotation at the telephoto end (131.0 mm) of the thirteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -3,984 3) 0,000 4) 0,000 5) 0,000

  R 10,000 ANG -0.444 1) 0.000 2) -3.721 3) 0.000 4) 0.000 5) 0.000

  R 5,000 ANG -0,914 1) 0,000 2) -3,487 3) 0,000 4) 0,000 5) 0,000

  R 3,000 ANG -1,585 1) 0,000 2) -3,187 3) 0,000 4) 0,000 5) 0,000

  R 2,000 ANG -2,511 1) 0,000 2) -2,825 3) 0,000 4) 0,000 5) 0,000

  R 1,500 ANG -3,545 1) 0,000 2) -2,503 3) 0,000 4) 0,000 5) 0,000

  R 1,000 ANG -6,056 1) 0,000 2) -1,885 3) 0,000 4) 0,000 5) 0,000

  R 0.800 ANG -8.500 1) 0.000 2) -1.465 3) 0.000 4) 0.000 5) 0.000

  Condition corresponding to the values: YxR / yxo = 1.15, aR / yao = 0.37 As indicated in tables 120, 121 and 122, for each focal length, the conversion coefficient yx associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as the product of the conversion coefficient yx, by the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance because of the slope (dx / da) of the focusing cam, contrary to the example of the application of

  Japanese Patent Laid-Open No. 5-142475.

  As indicated previously, when the ratio (AxTR / AxwR) of the AxTR and AxwR amplitudes of displacement in the direction of the optical axis of the set of focusing lenses necessary to focus the position at infinity at the position to the shorter distance at the wide-angle end and the telephoto end is large, the degree of slope reduction (dx / da) of the focusing cam becomes as large. For this reason, the conversion coefficient associated with the rotation decreases further under the action of the slope (dx / da) of the focusing cam when the distance of photography is

  closer to the shortest distance.

  In tables 120, 121 and 122, the rate of change from the infinite focus position to the shortest distance focused position of the conversion coefficient Ya associated with the rotation is x0.47 at the large end. -angle (F = 28.7 mm), x0.38 at the middle position (F = 70.0 mm), and x0.37 at the telephoto end (F = 131.0 mm). When the number N of divisions of the focusing range during a change of the coefficient of

  conversion of the thirteenth example is calculated with

  mule (a) and is compared with that of the example of Japanese Patent Application Laid-open No. 5-142475,

  the numbers Nw, NM and NT of divisions at the extreme

  angle, in the middle position and at the telephoto end respectively, have the following values: example of Japanese Patent Application Laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8, 1 Thirteenth Example Nw> 4.2 NM> 5.3 NT> 55 Accordingly, as indicated by the comparison of the calculated values of the example of Japanese Patent Application Laid-open No. 5-142475, although that the zoom lens of this example has a greater focal length variation ratio than the example of Japanese Patent Application Laid-Open No. 5-142475, the values of the division numbers N are reduced. As described above, in the zoom lens of the thirteenth example, as the rate of change, from the position focused at infinity to the position focused at the nearest location, the conversion coefficient Ya associated with the rotation becomes more as in the embodiment of the example of Japanese Patent Application Laid-Open No. 5-142475, the number of data of the conversion coefficient Ya and the correction coefficient i can be reduced, and the capacity of memorization can

also be deleted.

  Tables 123, 124 and 125 show the results of calculating the conversion coefficient Ka and the correction coefficient i at the end at the wide-angle end (F = 28.7 mm), in the middle position (F = 70 , 0 mm) and at the telephoto end (F = 131.0 mm) in the thirteenth example. In these tables (R) denotes the object distance (m), (ANG) the focus rotation amplitude of the

  position corresponding to infinity on the focus cam

  sation, (r) the conversion coefficient Ya in rotation, (rs) the conversion coefficient Ka, (bf) the amplitude of defect

  focus (mm), and (I) the correction coefficient y.

  Each array has a matrix structure and eight vertical lines indicated by (POS) represent the object positions (R = 10.0, 5.0, 3.0, 2.0, 1.5, 1.0 and 0, 80 m) and four pairs (R, ANGLE) in the horizontal direction represent the lens arrangements of the set of

focusing lenses.

  More precisely, the position of the focusing lens in the first pair of the two parts

  of each of Tables 123, 124 and 125, that is,

  say in the third and fourth columns, is (R, ANGLE) = (0,0; 0, 0), and indicates that the position is infinite. Consequently, the third column (r) of the first part represents the value of the conversion coefficient Ya in rotation when the set of focusing lenses is focused on an object at infinity, and the fourth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is shifted from the focused state to an object at infinity in the focused state on the object at the distance indicated in the second column. In addition, the third column (bf) of the second portion represents the focus defect amplitude ABf with respect to a predetermined image-forming position when the position of the focus lens assembly corresponds to the position at which infinity, and the object is at the object distance of the second column, and the fourth column (9) represents the value of the correction coefficient y when the set of focusing lenses is shifted from a focused state to a object to infinity to a state focused on

  an object at the object distance given by the second column.

  Similarly, the position of the focusing lens in the fourth pair of the two lower portions of each of the tables 123, 124 and 125, i.e. in the ninth and tenth columns, is (R, ANGLE) = ( 0.8; -8.5) and indicates that this position corresponds to the focusing position at the shortest distance (R = 0.80 m). Consequently, the ninth column (r) of the third part represents the value of the conversion coefficient ya in rotation when the set of focusing lenses is focused on an object at the shortest distance (R = 0.80 m), and the tenth column (rs) represents the value of the conversion coefficient Ka when the set of focusing lenses is shifted from a focused state to the shortest distance (R = 0.80 m) to a distance focused state. of the object indicated in the second column. Of

  Moreover, the ninth column (bf) of Part Four represents

  senses the focus defocus amplitude ABf with respect to a predetermined image position when the position of the focus lens assembly corresponds to the nearest position, and the object is at the given distance in the second column, and the tenth column (P) represents the value of the correction coefficient M when the set of focusing lenses is shifted from the focused state to the shortest distance (R = 0.80 m) to the focused state at the distance of the given object in the

second column.

  As indicated previously, as the conversion coefficient in rotation is calculated by the relation Ka = ABf / Aa (Aa being the rotation amplitude for the focusing), and as the correction coefficient y is calculated by the relation y = ABf / (1 - Ka / Ya), the value of the conversion coefficient Ka (eighth line, fourth column of the first part -0,139) when the focusing assembly is moved from the focused state to the object at infinity to the object-focused state at distance (R = 0.80 m) in Table 23 is calculated as

  Ka = 1.18 / -8.5 = -0.139 using ABf = 1.18 and Aa = -0.5.

  On the other hand, the value of the correction coefficient y (eighth row, fourth column of the second part 4,26) is calculated as y = 4,26 with ABf = 1,18,

Ka = -0.139 and Ya = -0.193.

Table 123

  Coefficients of conversion Ka: (rs), a: (r) associated with direction of rotation and correction coefficient p: (0) at the wide-angle end (28.7 mm) of the thirteenth example f = 28.7 mm

  (R. ANGLE) = 0,000 0,000 10,000 -0,443 5,000 -0,914 3,000 - 1,585

POS R rs r rs r rs

  I 0.000 -0.193 0.000 -0.187 -0.182 -0.176

  2 10,000 -0.188 -0.183 0.000 -0.178 -0, 173

  3 5,000 -0,184 -0,179 -0,175 0,000 -0,170

  4 3,000 -0,179 -0,175 -0,171 -0,165 0,000

2,000 -0,173 -0,169 -0,165 -0,159

  6 1,500 -0,166 -0,162 -0,158 -0,153

  7 1,000 -0,152 -0,148 -0,144 -0,139

  8 0.800 -0.139 -0.136 -0.132 -0.127

POS R bf I bf t bf i bf t

  1 0,000 0.00 0.00 -0.08 3.59 -0.17 4.33 -0.28 4, 30

  2 10,000 0.08 3.44 0.00 0.00 -0.08 4.87 -0.20 4, 37

  3 5,000 0.17 3.74 0.08 4.39 0.00 0.00 -0.11 4, 13

  4 3,000 0.28 4.12 0.20 4.75 0.11 4.95 0.00 0.00

  5 2,000 0.43 4.25 0.35 4.58 0.26 4.43 0.15 3.85

  6 1,500 0.59 4.32 0.50 4.52 0.42 4.36 0.30 4.02

  7 1,000 0.92 4.32 1.83 4.37 0.74 4.21 0.62 3.95

  8 0.800 1.18 4.26 1.09 4.25 1.00 4.09 0.88 3.85

  (R, ANGLE) = 2,000 -2,511 1,500 -3,545 1,000 -6,056 0,800 -8,500

2 5 POS R rs r rs r rs

  1 0.000 -0.168 -0.160 -0.143 -0, 129

  2 10,000 -0.165 -0.157 -0.140 -0, 126

  3 5,000 -0,162 -0,154 -0,137 -0,124

  4 3,000 -0.157 -0.150 -0.134 -0, 120

  5 2,000 -0,152 0,000 -0,145 -0,129 - 0,116

  6 1,500 -0,146 -0,139 0,000 -0,123 -0,111

  7 1,000 -0,133 -0,126 -0,112 0,000 -0, 100

  8 0.800 -0.121 -0.115 -0.102 -.090 0.000

POS R bf! bf b bf bf f

  I 0.000 -0.42 3.93 -0.57 3.75 -0.86 3.11 -1.10 2.57

  2 10,000 -0.34 3.93 -0.49 3.75 -0.79 3.10 -1.02 2.55

  3 5,000 -0.26 3.86 -0.41 3.72 -0.71 3.07 -0.94 2.53

  4 3,000 -0.15 3.93 -0.29 3.74 -0.60 3.05 -0.83 2.51

  2,000 0.00 0.00 -0.15 3.67 -0.46 3.01 -0.69 2.47

  6 1,500 0.15 4.08 0.00 0.00 -0.31 2.98 -0.55 2.42

  7 1,000 0.47 3.77 0.32 3.39 0.00 0.00 -0.24 2.28

  8 0.800 0.73 3.64 0.57 3.32 0.25 2.76 0.00 0.00

  Condition corresponding to the values: Kao / Yao = 0.72, KRyaR / a 1.43

Table 124

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the median position (70.0 mm) of the thirteenth example f = 70.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,450 5,000 -0,926 3,000 - 1,603

POS R rs r rs r rs

  1 0.000 -1.119 0.000 -1.072 -1.028 -0, 972

  2 10,000 -1,100 -1,054 0,000 -1,012 -0, 957

  3 5,000 -1,082 -1,038 -0,996 0,000 -0,942

  4 3,000 -1,058 -1,015 -0,974 -0,920 0,000

2,000 -1,026 -0,984 -0,943 -0,890

  6 1,500 -0,990 -0,949 -0,909 -0,857

  7 1,000 -0,910 -0.871 -0.834 -0, 785

  8 0.800 -0.838 -0.801 -0.766 -0, 721

POS R bf t bf f bf r bf t

  1 0.000 0.00 0.00 -0.48 28.69 -0.95 29.67 -1.56 27, 46

  2 10,000 0.50 29.37 0.00 0.00 -0.48 30.46 -1.10 27.41

  3 5,000 1.00 30.48 0.49 31.49 0.00 0.00 -0.64 26.87

  4 3,000 1.70 31.28 1.17 31.44 0.66 29.58 0.00 0.00

  5 2,000 2.60 31.19 2.05 30.52 1.51 28.41 0.82 25.31

  6 1,500 3,53 30.62 2.96 29.52 2.40 27.43 1.68 24.59

  7 1,000 5.52 29.52 4.89 28.14 4.28 26.27 3.50 23.89

  8 0.800 7.12 28.34 6.45 26.89 5.80 25.15 4.97 22.94

  (R, ANGLE) = 2,000 -2,530 1,500 -3,566 1,000 -6,065 0,800 -8,500

2 5 POS R rs r rs r rs

  1 0.000 -0.905 -0.838 -0.712 -0.619

  2 10,000 -0.890 -0.825 -0.700 -0, 608

  3 5,000 -0.875 -0.810 -0.687 -0, 596

  4 3,000 -0.854 -0.790 -0.669 -0, 580

  3 0 5 2,000 -0,825 0,000 -0,763 -0,645 -0,558

  6 1,500 -0.794 -0.733 0.000 -0.620 -0.535

  7 1,000 -0,727 -0,671 -0,565 0,000 -0,483

  8 0.800 -0.666 -0.613 -0.512 -0.429 0, 000

POS R bf t bf t bf f bf t

  I 0.000 -2.29 23.87 -2.99 20.88 -4.32 16.56 -5.26 11.91

  2 10,000 -1.85 23.60 -2.57 20.65 -3.93 16.44 -4.89 11.77

  3 5,000 -1.40 23.18 -2.14 20.37 -3.53 16.31 -4.51 11.62

  4 3,000 -0.79 22.62 -1.55 20.02 -2.99 16.15 -4.00 11.40

  2,000 0.00 0.00 -0.79 19.72 -2.28 15.99 -3.33 11.09

  6 1,500 0.82 21.68 0.00 0.00 -1.55 15.76 -2.64 10.68

  7 1,000 2.57 21.49 1.68 19.69 0.00 0.00 -1.18 9.34

  8 0.800 3.98 20.57 3.03 18.48 1.25 13.30 0.00 0.00

  Condition corresponding to the values: KaO / yao = 0.75, KaR / YaR = 1.44

Table 125

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the telephoto end (131.0 mm) of the thirteenth example f = 131.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,444 5,000 -0,914 3,000 - 1,585

POS R rs r rs r rs

  1 0.000 -3.987 0.000 -3.747 -3.528 -3, 264

  2 10,000 -3.960 -3.721 0.000 -3.505 - 3.222

  3 5,000 -3,937 -3,700 -3,486 0,000 - 3,223

  4 3,000 -3,912 -3,676 -3,460 -3,187 0,000

2,000 -3,867 -3,628 -3,408 -3,133

  6 1,500 -3,820 -3,579 -3,358 - 3,084

  7 1,000 -3,694 -3,449 -3,225 - 2,951

  8 0.800 -3.559 -3.314 -3.089 -2.817

POS R bf t bf t bf I bf I

  1 0.000 0.00 0.00 -1.66 238.31 -3.23 269.89 -5.17 214.29

  2 10,000 1.76 265.93 0.00 0.00 -1.65 312.86 -3.70 212.69

  3 5,000 3.60 291.17 1.74 306.89 0.00 0.00 -2.16 190.70

  4 3,000 6.20 330.11 4.20 341.66 2.32 309.47 0.00 0.00

  5 2,000 9.71 324.29 7.50 300.51 5.44 242.93 2.90 170.05

  6 1,500 13.54 324.29 11.10 291.16 8.83 239.30 6.04 186.38

  7 1,000 22.37 304.43 19.36 264.93 16.58 221.31 13.19 178.19

  8 0.800 30.25 282.38 26.70 243.82 23.44 205.79 19.48 167.68

  (R, ANGLE) = 2,000 -2,511 1,500 -3,545 1,000 -6,056 0,800 -8,500

2 5 POS R rs r rs r rs

  1 0,000 -2,956 -2,677 -2,179 - 1,843

  2 10,000 -2,933 -2,655 -2,157 - 1,822

  3 5,000 -2,910 -2,632 -2,134 - 1,801

  4 3,000 -2,872 -2,596 -2,101 - 1,770

  5 2,000 -2,825 0,000 -2,552 -2,057 - 1,728

  6 1,500 -2,779 -2,503 0,000 -2,007 - 1,681

  7 1,000 -2,645 -2,368 -1,885 0,000 - 1,570

  8 0.800 -2.513 -2.242 -1.772 -1.465 0, 000

POS R bf! bf f bf! bf t

  1 0.000 -7.42 160.41 -9.49 136.07 -13.19 84.53 -15.67 60.76

  2 10,000 -6.06 158.48 -8.23 135.46 -12.11 83.74 -14.68 60.22

  3 5,000 -4.65 154.27 -6.92 134.36 -10.97 82.79 -13.66 59.63

  4 3,000 -2.66 159.56 -5.09 135.99 -9.39 81.71 -12.24 58.86

  2,000 0.00 0.00 -2.64 132.76 -7.29 79.55 -10.35 57.65

  6 1,500 2,877 174.97 0.00 0.00 -5.04 77.61 -8.33 56.46

  7 1,000 9.37 146.92 5.95 110.57 0.00 0.00 -3.84 53.43

  8 0.800 15.05 136.47 11.11 106.51 4.33 72.66 0.00 0.00

  Condition corresponding to the values: Kao / TaO = 0.89, KaR / YaR = 1.26 As indicated in Tables 123, 124 and 125 above, when a change in the conversion coefficient Ka (rs) (this is ie the fourth column of the first part of the table) for a given lens arrangement (i.e. for the infinite focusing set) is taken into consideration, the rate of change becomes low by relative to the Ka variation (Tables 6, 7 and 8) of the example of the Japanese patent application

  Public Inspection No. 5-142475, previously considered.

  More specifically, the focus rotation amplitude Aa in the ninth example on the object side at infinity becomes relatively smaller than the nearest object side with respect to the Japanese patent application. Public Inspection No. 5-142475. In fact, when the ratio of the focus rotation amplitude during the focus to the shortest distance and the focus rotation amplitude when focusing to the distance from the object (R = 5.0 m) is calculated in Tables 1 and 118, there is 3,779 / 10,0 = 0,338 in the example of Japanese Patent Application Laid-Open No. 5-142475 and -0.914 / -0.5 = 0.108 in the thirteenth example. As described above, when the focusing cam having the arrangement according to the invention is used, as the focusing amplitude Aa becomes relatively smaller on the object side at infinity, the conversion coefficient Ka becomes relatively large on the object side to infinity and, consequently, the variation of the conversion coefficient Ka in

  the rotation diectian can be written by rpxt to the classical system.

  The results of the computation of the rate of variation of Ka with respect to Ya for the set focused at infinity and the set focused at the nearest point at the end

  wide angle, in the middle position and at the end of

  objective, in the example of Japanese Patent Application Laid-Open No. 5-142475 and in the Thirteenth

  example of the invention are as follows.

  Japanese Patent Application Laid-open No. 5142475 To infinity KaO / yyO Closest KaR / YaR Wide-angle (F = 36.0) 2.75 0.44 Median position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Thirteenth example At infinity Kao0IaO Nearest KaR / YaR Wide-angle (F = 28.7) 0.72 1, 43 Median Positon (F = 70.0) 0.75 1.44 Telephoto (F = 131.0) 0.89 1.26 As previously described, according to the invention, as the rate of variation of Ka with respect to Ya is weak compared to the classical system and the contribution of the correction term (ABf / j) of the relation Ka = Ya (1 - ABf / p) can be reduced, the value of the correction coefficient y can be set to a high value in relation to amplitude

  focusing defect ABf and, at the same time, the varia-

  the correction coefficient i can be reduced.

  As a result, even when a single pair of values

  the conversion coefficient ya and the coefficient of

  is established for a given range of lens arrangements, an error on the conversion coefficient Ka calculated from Ya and y or on the actual driving amplitude of lenses Aa during focusing may

to be eliminated.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the thirteenth

  example of the invention, when the training amplitudes

  lens when focusing the infinite focused assembly on the object at the shortest distance and when focusing the focused assembly at the shortest distance to the object at infinity, the wide-angle end, in the middle position and at the telephoto end, are calculated from the relation Aa = ABf / ya (1-ABf / I) and the errors with respect to the actual drive amplitudes of the lenses are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the set focused to infinity to the object at the shortest distance takes the value corresponding to the object distance (POS-5) and that the value of the correction coefficient y when focusing with the set focused at the closest distance to the object at infinity takes the value corresponding to the object distance

(POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% -13.0% Positon median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Thirteenth example Infinity focused state most Nearest near-state Focused at infinity Wide-angle (F = 28.7) -0.4% -0.0% Median position (F = 70.0) - 3.0% -1.3% Telephoto (F = 131.0) -1.6% -0.6% As previously described, even when a single pair of values of the conversion coefficient γ and the correction coefficient γ is established for a given range of the lens set, an error between the conversion coefficient Ka calculated from Ya and i and the focus Aa lens driving amplitude becomes small compared to the conventional system and focusing

  can be performed with increased accuracy.

  For reference, when errors in drive amplitudes when focusing the infinite focus set at the object distance (R = 10.0 m) and when focusing the focused set at nearest point at the object distance (R = 1.0 m) are calculated and compared, the following results are obtained. As these tables indicate, focus accuracy can be improved independently

of the object distance.

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused to Nearest in Om-Focused State at 1m Wide-angle (F = 36.0) -6.7% 1, 5% Median Position (F = 50.0) 3.2% 2.5% Telephoto (F = 103.0) 5.1% 2.4% Thirteenth example Infinity focused state to Nearest to state 10 m focused to 1 m Large -angle (F = 28.7) - 4.6% -0.4% Median position (F = 70.0) 0.9% 2.4% Telephoto (F = 131.0) -0.0% 0 , 7% We now examine whether not only the precise automatic focusing but also the so-called "manual" focusing can be achieved with the zoom lens of

thirteenth example.

  Table 126 indicates the manually focusing amplitude (ANGLE DA) with the focusing cam (middle part of table 118) of the thirteenth example, the displacement amplitude DX (mm) in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

  direction of the optical axis is given.

  The upper part of Table 126 indicates the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.80 m ) for the respective states of focal length variation (F = 28.7, 35.0, 50.0, 70.0, 105.0 and 131.0 mm) and the middle part gives the values of the amplitude of the focus rotation (ANGLE DA) necessary to obtain the optimum focused state for the respective photographing distances (R = 5.0, 3.0, 2.0, 1.5, 1.0 and 0.80 m). It should be noted that the selected focus rotation magnitudes have values permitting the elimination of any displacement of the image point at the wide-angle end and at the telephoto end. The lower part gives the displacement amplitudes (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the focusing amplitude (ANGLE DA) with the photography distances (R = 5.0, 3). , 0, 2.0, 1.5, 1.0 and 0.80 m) for the respective states of focal length variation (F = 28.7, 35.0, 50.0, 70.0,, 0 and 131.0 mm). In the lower part, (F) designates the focal length (mm) of the whole system, (R) the photography distance (m) and (DX) the displacement amplitude (mm) in the direction of the optical axis of each of the first, second, third, fourth and fifth sets of lenses in turn from the right. It should be noted that the amplitude of displacement in the direction of the optical axis towards the side of the object is

  represented by a positive value.

Table 126

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) displacement for focusing of the thirteenth example 0.80m 1.00m 1.50m 2.00m 3.00m 5.00m 28.700 Bf 0.000 0.000 0.000 0, 000 0,000 0,000, 000 Bf 0,000 -0,001 -0,004 -0,006 -0,008 -0, 006,000 Bf 0,000 -0,011 -0,013 -0,009 -0,004 -0,003, 000 Bf 0, 000 0.005 0.015 0.015 0.016 0.012, 000 Bf 0.000 0.020 0, 031 0.032 0.028 0.017 131,000 Bf 0,000 0,000 0,000 0,000 0,000 0,000

  ANGLE DA -8,500 4-6,056 -3,545 -2,511 -1,585 -0,914

  F 28,700 DX 0,000 0,821 0,000 0,000 0,000 R 0,80 m F 35,000 DX 0,000 0,964 0,000 0,000 0,000 R 0,80 m F 50,000 DX 0,000 1,439 0,000 0,000 0,000 R 0.80 m F 70,000 DX 0,000 2,005 0,000 0,000 0,000 R 0.80 m F 105, 000 DX 0.000 2,392 0,000 0,000 0,000 R 0,80 m F 131, 000 DX 0,000 2,543 0,000 0,000 0,000 R 0,80 m F 28,700 DX 0,000 0,645 0,000 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,760 0,000 0,000 0,000 R 1,00 m F 50,000 DX 0,000 1,152 0,000 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,618 0,000 0,000 0,000 R 1,00 m F 105,000 DX 0,000 1,940 0,000 0,000 0,000 R 1,00 m F 131,000 DX 0, 000 2,068 0,000 0,000 0,000 R 1,00 m F 28,700 DX 0,000 0,420 0,000 0,000 0,000 R 1,50 m F 35,000 DX 0,000 0, 499 0,000 0,000 0,000 R 1,50 m F 50,000 DX 0,000 0,769 0,000 0,000 0,000 R 1.50 m F 70,000 DX 0,000 1, 091 0,000 0,000 0,000 R 1,50 m F 105,000 DX 0,000 1,323 0,000 0,000 0,000 R 1,50m F 131,000 DX 0,000 1,416 0, 000 0,000 0,000 R 1,50m F DX 0,000 0,311 0.000 0.000 0.000 R 2.00 m F 28.700 DX 0.000 0.373 0, 000 0.000 0.000 R 2.00 m F 35,000 DX 0.000 0.576 0.000 0.000 0.000 R 2.00 m F 50,000 DX 0.000 0.824 0.000 0.000 0.000 R 2.00 m F 70.000 DX 0.000 1.004 0.000 0.000 0.000 R 2.00 m F 105,000 DX 0,000 1,078 0,000 0,000 0, 000 R 2.00 m

131,000

  F 28,700 DX 0,000 0,205 0,000 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,249 0,000 0,000 0,000 R 3,00 m F 50,000 DX 0,000 0,383 0,000 0,000 0,000 R 3,00 m F 70,000 DX 0,000 0,552 0,000 0,000 0,000 R 3,00 m F 105,000 DX 0,000 0,679 0,000 0,000 0,000 R 3,00 m F 131,000 DX 0,000 0,731 0,000 0,000 0,000 R 3,00 m F 28,700 DX 0,000 0,122 0,000 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,149 0,000 0,000 0,000 R 5,00 m F 50,000 DX 0, 000 0,230 0,000 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0,333 0,000 0,000 0,000 R 5,00 m F 105,000 DX 0, 000 0,413 0,000 0,000 0,000 R 5,00 m F 131,000 DX 0,000 0,445 0,000 0,000 0,000 R 5,00 m As shown in Table 126, so-called "manual" focusing can be achieved because the magnitudes of displacement of the image point at the respective focal distances and photograph distances are very small, and enter the depth of field regardless of the state of variation of the focal length and the photographing distance. Fourteenth Embodiment The fourteenth or fourteenth embodiment relates to a zoom lens having an arrangement of four sets, i.e. positive, negative, positive and negative lens assemblies, providing focus by a second lens. set of negative type lenses. In this zoom lens, the ratio (aF / az) of the focusing rotation amplitude of the position focused at infinity to the position focused at the nearest location (R = 0.5 m) and the Focal length variation rotation amplitude of the wide-angle end (F = 29.0 mm) at the telephoto end (F = 102.0 mm)

is equal to -0.95.

  The following table 127 gives various paraxial data of an optical system and data for determining the configuration of a focusing cam in

the fourteenth example.

  The upper part of Table 127 shows the focal lengths and intervals of the main points of

  respective sets of lenses of the optical system corresponding to

  in the fourteenth example, for six states of

  sation (focal lengths F = 29.0, 35.0, 50.0, 70.0, 85.0

and 102.0 mm).

  The middle part of Table 127 shows the spline sample data when the configuration of a cam

  of focus of the second set of lenses of the four

  example, used for focusing, is represented

  sensed by a spline function associated with the rotation angle a of a rotating barrel and the amplitude x of

  displacement in the direction of the optical axis.

  In addition, the lower part of table 127 indicates the infinite focusing positions (positions corresponding to infinity) for the respective focal lengths (F = 29.0, 35.0, 50, 70.0, 85, 0 and 102.0 mm) and the magnitudes of rotation (for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0 , 5 m) with the focusing cam of the fourteenth example. In this table, as the amplitude of rotation for the focal length variation of the wide-angle end (F = 29.0 mm) at the telephoto end (F = 102.0 mm) is equal to 10, 0, and the rotation amplitude for focusing from the infinitely focused position to the focused position at the nearest location (R = 0.5 m) is -9.5, the ratio (aF / az) magnitudes of focus rotation and focal length variation in the fourteenth example equals

-0.95.

Table 127

  Fourteenth example f = 29.0 to 102.0 (ratio of amplitudes of rotation: aF / az = -0.95) Focal distances and intervals of the main points of the objectives of the fourteenth example

  F 29,0000 35,0000 50,0000 70,0000 85,0000 102,0000

  F1 85.5479 D1 6.4919 11.0833 19.2490 26.4661 30.4661 34.1273

  F2 -17.6992 D2 31.4311 28.0686 22.5272 18.0704 15.7280 13.6136

  F3 25.9878 D3 -4.6185 -1.8297 4.161 10.3911 14.1536 17.6639

  F4 -251.0549 D4 69.6355 69.6334 69.6324 69.6422 69.6550 69.6692

  Focusing cam shape (spline interpolated point) corresponding to the fourteenth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.6220 0.0000 0.0000

  2 -10,0000 0.0000 1.5277 0.0000 0.0000

  3 -9.5000 0.0000 1.4768 0.0000 0.0000

  1 5 4 -5.7095 0.0000 1.0205 0, 0000 0.0000

-3,5854 0.0000 0.6980 0.0000 0.0000

  6 -1.6038 0.0000 0.3402 0.0000 0.0000

  7 -1.0337 0.0000 0.2250 0.0000 0.0000

  8 -0.6043 0.0000 0.1391 0.0000 0.0000

  2 0 9 0.0000 0.0000 0.0000 0, 0000 0.0000

0.5000 0.0000 -0.11775 0.0000 0.0000

  11 4.2905 0.0000 -1.2397 0.0000 0.0000

  12 6.4146 0.0000 -2.1304 0.0000 0.0000

  13 8.3962 0.0000 -3.2517 0.0000 0.0000

  14 8.9663 0.0000 -3.6627 0.0000 0, 0000

9,3957 0.0000 -4.0013 0.0000 0.0000

  16 10.0000 0.0000 -4.5381 0.0000 0.0000

* 17 11.0000 0.0000 -5.5850 0.0000 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focus of the fourteenth example (ratio of rotation amplitudes: aF / az = -0.95) Focal distance Corresponding position Distance of rotation amplitude at infinity for focusing 29.0 mm 0.0000 5.00 m -0.604, 0 mm 1.6924 3.00 m -1.034 50.0 mm 4.7321 2.00 m -1.604, 0 mm 7.3904 1.00 m -3,585, 0 mm 8,7927 0,70 m -5,710 102,0 mm 10,0000 0,50 m -9,500 Condition corresponding to value (9) 1,28 Condition corresponding to value (10) 2,99 Condition corresponding to value (11) -0.95 Condition corresponding to value (12) 0.48 (wide-angle) 0.32 (teleobjective) Condition corresponding to value (13) 0.75 (wide-angle) 0.94 (telephoto) Condition corresponding to value (14) 1.36 (wide-angle) 1.23 (telephoto) Table 128 which follows shows the numerical values of the cams of the focus lens assembly of the fourteenth example, the data being calculated by interpolation with a spline function from the sample data of the focusing cam of the middle part of table 127. It should be noted that the meanings of the respective symbols of table 128 are

  the same as in the thirteenth example.

Table 128

  Cam numerical values for focusing objective of the fourteenth example Focusing cam digital values Focal compensation dimming cam digital values

ANGLE (2) F ANGLE (2) F

-9.5000 1.4768 0.0000

-9.0000 1.4238 0.0000

-8.5000 1.3688 0.0000

-8.0000 1.3118 0.0000

-7.5000 1.2526 0.0000

-7.0000 1.1900 0.0000

-6,5000 1,1270 0,0000

-6.0000 1.0604 0.0000

-5,5000 0.9911 0.0000

-5.0000 0.9190 0.0000

-4.5000 0.8438 0.0000

-4.0000 0.7654 0.0000

-3.5000 0.6838 0.0000

-3.0000 0.5986 0.0000

-2,5000 0,5097 0,0000

-2.0000 0.4168 0.0000

-1.5000 0.3197 0.0000

-1.0000 0.2179 0.0000

-0.5000 0.115 0.0000

  0.0000 0.0000 29.0000 0.0000 0.0000 29.0000

  0.5000 -0.1175 30.6387 0.5000 -0.1124 30.6387

  1.0000 -0.2407 32.3858 1.0000 -0.1690 32.3858

  1,5000 -0,3702 34,2491 1,5000 -0,1691 34,2491

  2.0000 -0.5066 36.2424 2.0000 -0.1121 36.2424

  2.5000 -0.6507 38.3792 2.5000 0.0028 38.3792

  3,0000 -0,8031 40,6724 3,0000 0,1767 40,6724

  3,5000 -0,9645 43,1349 3,5000 0,4104 43,1349

  4.0000 -1.1356 45.7783 4.0000 0.7043 45.7783

  4.5000 -1.3171 48.6138 4.5000 1.0581 48.6138

  5,0000 -1,5100 51,6599 5,0000 1,4719 51,6599

  , 5000 -1.7158 54.9436 5.5000 1.9466 54.9436

  6.0000 -1.9359 58.4921 6.0000 2.4825 58.4921

  6,5000 -2,1719 62,3292 6,5000 3,0791 62,3292

  7.0000 -2.4256 66.4882 7.0000 3.7364 66.4882

  7.5000 -2.7004 71.0327 7.5000 4.4575 71.0327

  8.0000 -2.9999 76.0245 8.0000 5.2441 76.0245

  8.5000 -3.3276 81.5206 8.5000 6.0952 81.5206

  9.0000 -3.6881 87.5991 9.0000 7.0101 87.5991

  9.5000 -4.0885 94.3772 9.5000 7.9903 94.3772

  10,0000 -4,5381 102,000 10,0000 9,0367 102,0000

  The left side of table 128 indicates numerical values of the focus cam, and the right side of the zoom compensation cam in this fourteenth example. A value obtained by synthesizing the displacement amplitudes (2) in the direction of the optical axis from the numerical values of the focusing cam and the zoom compensation cam, in the range between (ANGLE = 0.0 ) and (ANGLE = 10.0), coincides with the displacement location of the second set of lenses calculated using paraxial data from the top of Table 127. The following tables 129, 130 and 131 indicate the amplitude in the direction of the optical axis of the focusing lens assembly, the magnification Px (mm) of the respective sets of lenses, the conversion coefficient yx associated with the direction of rotation, the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  of conversion there associated with the rotation at the far end-

  angle (F = 29.0 mm), middle position (F = 50.0 mm) and telephoto end (F = 102.0 mm) respectively in the fourteenth example. The provisions of the tables and the meaning of the symbols are the same as in the

thirteenth example.

Table 129

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (29.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) 0.067 3) 0.000 4) 0.000

  R 5,000 ANG -0,604 1) 0,000 2) 0,134 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 0,225 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 0,340 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 0,698 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) 1.021 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 1.477 3) 0.000 4) 0.000

  Nk image magnification of lenses at the wide-angle end (29.0 mm) of the fourteenth

example

  R 0,000 ANG 0.000 1) 0.000 2) -0.288 3) -0.920 4) 1, 277

  R 10,000 ANG -0,296 1) -0,009 2) -0,285 3) -0,920 4) 1, 277

  R 5,000 ANG -0.604 1) -0.018 2) -0.281 3) -0.920 4) 1, 277

  R 3,000 ANG -1,034 1) -0,030 2) -0,276 3) -0,920 4) 1, 277

  R 2,000 ANG -1,604 1) -0,047 2) -0,269 3) -0,920 4) 1, 277

  R 1,000 ANG -3,585 1) -0,105 2) -0,249 3) -0,920 4) 1, 277

  R 0.700 ANG -5.709 1) -0.167 2) -0.231 3) -0.920 4) 1, 277

  R 0.500 ANG -9.500 1) -0.275 2) -0.205 3) -0.920 4) 1, 277

  Coefficient of conversion yx associated with the direction of the optical axis at the wide-angle end (29.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,266 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 1,269 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 1,272 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 1,276 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 1,295 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) 1.307 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 1.323 3) 0.000 4) 0.000

  Slope dx / da focus cam at the wide end (29.0 mm) of the fourteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,229 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) -0,222 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) -0,216 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) -0,207 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,197 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,166 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) -0.139 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.104 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the wide-angle end (29.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,290 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.282 3) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -0.274 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -0,265 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,252 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,214 3) 0,000 4) 0,000

  R 0.700 ANG -5.709 1) 0.000 2) -0.182 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.138 3) 0.000 4) 0.000

  Condition corresponding to the values: yXR / yXO = 1.04, YaR / yao = 0.48

Table 130

  Amplitude DX (mm) of focus shift in the direction of the optical axis at the center position (50.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 0,112 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 0,224 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) 0,373 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) 0,561 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) 1,126 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) 1.618 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 2.290 3) 0.000 4) 0.000

  Objective image magnification Pk at the median position (50.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,364 3) -1,256 4) 1,277

  R 10,000 ANG -0,296 1) -0,009 2) -0,358 3) -1,256 4) 1,277

  R 5,000 ANG -0,604 1) -0,018 2) -0,352 3) -1,256 4) 1,277

  R 3,000 ANG -1,032 1) -0,031 2) -0,343 3) -1,256 4) 1,277

  R 2,000 ANG -1,601 1) -0,048 2) -0,333 3) -1,256 4) 1,277

  R 1,000 ANG -3,581 1) -0,107 2) -0,301 3) -1,256 4) 1,277

  R 0.700 ANG -5.707 1) -0.171 2) -0.273 3) -1.256 4) 1.277

  R 0.500 ANG -9.500 1) -0.286 2) -0.235 3) -1.256 4) 1.277

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,234 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 2,246 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 2,257 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) 2,272 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) 2,291 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) 2,343 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) 2.384 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 2.434 3) 0.000 4) 0.000

  Slope dx / da focus cam at the center position (50.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,385 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) -0,371 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) -0,358 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) -0,340 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) -0,318 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) -0,256 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) -0.209 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.150 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the middle position (50.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,860 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.833 3) 0.000 4) 0.000

  R 5,000 ANG -0,604 1) 0,000 2) -0,808 3) 0,000 4) 0,000

  R 3,000 ANG -1,032 1) 0,000 2) -0,773 3) 0,000 4) 0,000

  R 2,000 ANG -1,601 1) 0,000 2) -0,729 3) 0,000 4) 0,000

  R 1,000 ANG -3,581 1) 0,000 2) -0,601 3) 0,000 4) 0,000

  R 0.700 ANG -5.707 1) 0.000 2) -0.497 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.365 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / YxO = 1.09, yaR / yao = 0, 42

Table 131

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (102.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 0,273 3) 0,000 4) 0,000

  R 5,000 ANG -0.604 1) 0.000 2) 0.537 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) 0,875 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 1,281 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 2,408 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) 3.298 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 4.421 3) 0.000 4) 0.000

  Lens magnification Pk at the telephoto end (102, 0 mm) of the fourteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,525 3) -1,778 4) 1, 278

  R 10,000 ANG -0,296 1) -0,009 2) -0,509 3) -1,778 4) 1, 278

  R 5,000 ANG -0.604 1) -0.018 2) -0.495 3) -1.778 4) 1, 278

  R 3,000 ANG -1,034 1) -0,031 2) -0,475 3) -1,778 4) 1, 278

  R 2,000 ANG -1,604 1) -0,048 2) -0,452 3) -1,778 4) 1, 278

  R 1,000 ANG -3,585 1) -0,110 2) -0,389 3) -1,778 4) 1, 278

  R 0.700 ANG -5.710 1) -0.178 2) -0.339 3) -1.778 4) 1, 278

  R 0.500 ANG -9.500 1) -0.306 2) -0.275 3) -1.778 4) 1, 278

  Coefficient of conversion yx associated with the direction of the optical axis at the telephoto end (102.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 3,739 3) 0,000 4) 0,000

  R 10,000 ANG -0,296 1) 0,000 2) 3,821 3) 0,000 4) 0,000

  R 5,000 ANG -0,604 1) 0,000 2) 3,898 3) 0,000 4) 0,000

  R 3,000 ANG -1,034 1) 0,000 2) 3,994 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) 4,104 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) 4,380 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) 4.569 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) 4.770 3) 0.000 4) 0.000

  Slope dx / da focus cam at the telephoto end (102.0 mm) of the fourteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,959 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -0.887 3) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -0.826 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -0,753 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -0,673 3) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -0,483 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) -0.365 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -0.241 3) 0.000 4) 0.000

  Coefficient of conversion associated with the direction of rotation at the telephoto end (102.0 mm) of the fourteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -3,586 3) 0,000 4) 0,000

  R 10,000 ANG -0.296 1) 0.000 2) -3.3913) 0.000 4) 0.000

  R 5,000 ANG -0.604 1) 0.000 2) -3.219 3) 0.000 4) 0.000

  R 3,000 ANG -1,034 1) 0,000 2) -3,009 3) 0,000 4) 0,000

  R 2,000 ANG -1,604 1) 0,000 2) -2,7613) 0,000 4) 0,000

  R 1,000 ANG -3,585 1) 0,000 2) -2,115 3) 0,000 4) 0,000

  R 0.700 ANG -5.710 1) 0.000 2) -1.666 3) 0.000 4) 0.000

  R 0.500 ANG -9.500 1) 0.000 2) -1.148 3) 0.000 4) 0.000

  Condition corresponding to the values: yxR / yxo = 1.28, YaR / Yao = 0.32 As shown in tables 129, 130 and 131, for each focal length, the conversion coefficient Yx associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photograph is approaching the shortest distance given the influence of the slope (dx / da) of the focusing cam. In tables 129, 130 and 131, the rate of variation, from infinite focus to focus at the nearest location, of the conversion coefficient Ya associated with the rotation is xO, 48 at the large end. -angle (F = 29.0 mm), x0.42 in position

  median (F = 50.0 mm), and xO, 32 at the telegraph end.

  objective (F = 102.0 mm). When the number N of divisions of

  range of focus, when the coefficient of

  The fourteenth embodiment of the conversion code Ya is calculated with the formula (a) and is compared with that of the example of Japanese Patent Application Laid-open No. 5-142475, the numbers Nw, NM and NT. at the wide-angle end, in the median position and at the telephoto end, respectively, are the following values: example of Japanese Patent Application Laid-Open No. 5-142475 Nw> 9.3 NM > 10.1 NT> 8, 14th example Nw> 4.1 NM> 4.7 NT> 6.2 As indicated in the above comparison,

  although this embodiment gives a focal point

  than the example of Japanese Patent Application Laid-Open No. 5-142475, the

  values of division numbers become low.

  As described previously, in the fourteenth example, since the rate of change of the conversion coefficient Ya associated with the rotation is lower than that given by the conventional system, the value of the number N of divisions is small, the number of data of the coefficient of Ya conversion and the correction coefficient y can be reduced, and the

  storage capacity can be deleted.

  Tables 132, 133 and 134 show the results of the calculation of the conversion coefficients Ka and the correction coefficient y at the wide-angle end (F = 29.0 mm), in the median position (F = 50, 0 mm). and at the telephoto end (F = 102.0 mm) in the fourteenth example. The provisions of the tables and the symbols are the same as in the thirteenth example. The position of the focusing lens of the first pair of the two parts

  of each of Tables 132, 133 and 134, that is,

  say the third and the fourth column, is (R, ANGLE) = (0,0; 0,0) and indicates that the position corresponds to infinity. Similarly, the position of the focus lens of the fourth pair of the two parts

  of each of Tables 132, 133 and 135, that is,

  say the ninth and tenth columns, is (R, ANGLE) = (0.5; -9.5), and indicates that the position corresponds to the focus at the shortest distance

(R = 0.5 m).

Table 132

  Coefficients of conversion Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the wide-angle end (29.0 mm) of the fourteenth example f = 29.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,296 5,000 -0,604 3,000 - 1,034

POS R rs r rs r rs

  I 0.000 -0.290 0.000 -0.285 -0.280 -0, 273

  2 10,000 -0.287 -0.282 0.000 -0.277 -0, 271

  3 5,000 -0,284 -0,279 -0,274 0,000 -0, 268

  4 3,000 -0.280 -0.275 -0.271 -0.265 0, 000

2,000 -0,275 -0,271 -0,266 -0,260

  6 1,000 -0,259 -0,254 -0,250 -0, 244

  7 0.700 -0.243 -0.239 -0.235 -0, 229

  8 0.500 -0.218 -0.214 -0.210 -0.205

  POS R bf t bf i bf! bf i 0.000 0.00 0.00 -0.08 7.87 -0.17 8.61 -0.28 8.67

  2 10,000 0.08 7.68 0.00 0.00 -0.09 8.98 -0.20 8, 78

  3 5,000 0.17 8.09 0.09 8.77 0.00 0.00 -0.12 8, 64

  4 3,000 0.29 8.51 0.20 9.11 0.12 9.31 0.00 0.00

  5 2,000 0.44 8.68 0.35 9.01 0.27 8.90 0.15 8.25

  6 1,000 0.93 8.66 0.84 8.68 0.75 8.48 0.62 8.08

  7 0.700 1.39 8.56 1.29 8.50 1.20 8.30 1.07 7, 97

  8 0.500 2.07 8.32 1.97 8.21 1.87 8.02 1.74 7, 73

  (R, ANGLE) = 2,000 -1,604 1,000 -3,585 0,700 -5,709 0,850 -9,500

2 5 POS R rs r rs r rs

  I 0.000 -0.265 -0.241 -0.219 -0, 187

  2 10,000 -0.263 -0.238 -0.216 -0, 185

  3 5,000 -0,260 -0,236 -0,214 -0, 183

  4 3,000 -0,257 -2,233 -0,211 -0, 181

  5 2,000 -0,252 0,000 -0,228 -0,207 - 0,177

  6 1,000 -0,237 -0,214 0,000 -0,194 -0,166

  7 0.700 -0.222 -0.201 -0.182 0.000 -0, 155

  8 0.500 -0.199 -0.179 -0.162 -0.138 0.000

POS R bf t bf g bf! bf f

  3 5 1 0.000 -0.43 8.14 -0.86 6.18 -1.25 6.18 -1.78 4.97

  2 10,000 -0.34 8.13 -0.78 7.06 -1.17 6.17 -1.71 4, 96

* 3 5,000 -0.26 6,03 -0.70 7.03 -1.09 6.14 -1.63 4, 95

  4 3,000 -0.15 7.92 -0.59 7.00 -0.99 6.12 -1.53 4, 93

  2,000 0.00 0.00 -0.45 6.99 -0.85 6.09 -1.40 4.91

  6 1,000 0.47 7.76 0.00 0.00 -0.41 5.96 -0.98 4.83

  7 0.700 0.91 7.67 0.43 6.76 0.00 0.00 -0.59 4.78

  8 0.500 1.57 7.43 1.06 6.50 0.61 5.64 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.75, KaR / YaR = 1.36

Table 133

  Coefficients of conversion Ka: (rs), a: (r) associated with direction of rotation and correction coefficient p: (0) at the median position (50.0 mm) of the fourteenth example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,296 5,000 -0,604 3,000 - 1,032

POS R rs r rs r rs

  I 0.000 -0.860 0.000 -0.840 -0.820 -0, 795

  2 10,000 -0.853 -0.833 0.000 -0.814 -0, 788

  3 5,000 -0,846 -0,827 -0,808 0,000 -0,782

  4 3,000 -0.837 -0.818 -0.798 -0.773 0.000

2,000 -0.824 -0.805 -0.786 -0.761

  6 1,000 -0,780 -0,762 -0,743 -0,719

  7 0.700 -0.736 -0.719 -0.701 -0, 678

  8 0.500 -0.667 -0.650 -0.634 -0.612

POS R bf t bf a bf t bf!

  I 0.000 0.00 0.00 -0.25 31.18 -0.50 31.08 -0.82 29, 10

  2 10,000 0.25 32.52 0.00 0.00 -0.25 31.37 -0.58 28.87

  3 5,000 0.51 32.49 0.25 32.63 0.00 0.00 -0.34 28.40

  4 3,000 0.86 32.42 0.60 31.86 0.34 30.19 0.00 0.00

  5 2,000 1.32 31.93 1.05 31.01 0.78 29.37 0.43 27.35

  6 1,000 2.79 30.18 2.50 29.07 2.27 27.70 1.83 26.05

  7 0.700 4.20 29.30 3.89 28.25 3.58 27.09 3.17 25.67

  8 0.500 6.33 28.18 5.98 27.22 5.64 26.20 5.18 24.94

  (R, ANGLE) = 2,000 -1,601 1,000 -3,581 0,700 -0,707 0,500 -9,500

2 5 POS R rs r rs r rs

  1 0.000 -0.763 -0.668 -0.590 -0, 487

  2 10,000 -0.757 -0.662 -0.584 -0, 483

  3 5,000 -0,750 -0,656 -0,579 -0, 478

  4 3,000 -0.741 -0.648 -0.571 -0, 472

  3 0 5 2,000 -0,729 0,000 -0,637 -0,561 -0,463

  6 1,000 -0,688 -0,601 0,000 -0,529 -0,435

  7 0.700 -0.649 -0.566 -0.497 0.000 -0.408

  8 0.500 -0.586 -0.510 -0.447 -0.365 0, 000

POS R bf t bf f bf 9 bf

  1 0.000 -1.22 26.55 -2.39 21.33 -3.36 18.14 -4.63 13.88

  2 10,000 -0.99 26.27 -2.18 21.20 -3.16 18.08 -4.44 13.84

  3 5,000 -0.75 25.91 -1.95 21.08 -2.95 18.02 -4.25 13.80

  4 3,000 -0.42 25.43 -1.65 20.96 -2.67 17.95 -3.99 13.74

  2,000 0.00 0.00 -1.26 20.88 -2.31 17.88 -3.66 13.68

  6 1,000 1.36 24.29 0.00 0.00 -1.13 17.57 -2.58 13.44

  7 0.700 2.66 24.16 1.20 20.72 0.00 0.00 -1.55 13.20

  8 0.500 4.63 23.54 3.02 19.89 1.69 16.66 0.00 0.00

  Condition corresponding to the values: KaO / ya0 = 0.78, KaR / YaR = 1.33

Table 134

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (t) at the telephoto end (102.0 mm) of the fourteenth example f = 102.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,296 5,000 -0,604 3,000 -1,034

POS R rs r rs r rs

  1 0.000 -3.586 0.000 -3.402 -3.234 -3, 033

  2 10,000 -3,575 -3,391 0,000 -3,225 -3,025

  3 5,000 -3,567 -3,384 -3,218 0,000 -3,019

  4 3,000 -3,561 -3,379 -3,213 -3,009 0, 000

2,000 -3,553 -3,368 -3,200 -2,993

  6 1,000 -3,513 -3,322 -3,147 -2, 935

  7 0.700 -3.464 -3.267 -3.087 -2, 870

  8 0.500 -3.359 -3.153 -2.967 -2, 744

POS R bf t bf f bf! bf t

  I 0.000 0.00 0.00 -1.01 303.86 -1.95 408.75 -3.14 391.00

  2 10,000 1.06 348.12 0.00 0.00 -0.99 522.97 -2.23 420.91

  3 5,000 2.16 409.36 1.04 514.78 0.00 0.00 -1.30 383.82

  4 3,000 3.68 536.00 2.49 705.99 1.38 821.77 0.00 0.00

  5 2,000 5.70 610.30 4.40 667.05 3.20 556.67 1.71 327.46

  6 1,000 12.60 617.85 10.93 539.46 9.38 424.49 7.49 303.81

  7 0.700 19.78 581.95 17.68 484.63 15.76 386.56 13.42 290.78

  8 0.500 31.91 504.47 29.02 414.47 26.39 337.96 23.23 264.25

  (R, ANGLE) = 2,000 -1,604 1,000 -3,585 0,700 -5,710 0,500 -9,500

2 5 POS R rs r rs r rs

  1 0.000 -2.805 -2.236 -1.847 -1, 416

  2 10,000 -2,796 -2,227 -1,838 -1, 407

  3 5,000 -2,789 -2,217 -1,828 -1, 398

  4 3,000 -2,777 -2,203 -1,814 - 1,386

  5 2,000 -2,761 0,000 -2,184 -1,795 - 1,369

  6 1,000 -2,696 -2,115 0,000 -1,732 - 1,311

  7 0.700 -2.628 -2.048 -1.666 0.000 -1, 251

  8 0.500 -2.499 -1.920 -1.545 -1.148 0.000

POS R bf t bf a bf f bf t

  1 0,000 -4.50 280.72 -8.02 139.24 -10.55 96.95 -13.45 57.63

  2 10,000 -3.66 283.07 -7.32 138.17 -9.95 96.57 -12.95 57.38

  3 5,000 -2.79 274.34 -6.61 136.50 -9.33 96.07 -12.44 57.10

  4 3,000 -1.58 275.20 -5.62 134.70 -8.48 95.55 -11.73 56.75

  2,000 0.00 0.00 -4.33 132.44 -7.37 94.97 -10.81 56.28

  4 0 6 1,000 5,34 228.96 0.00 0.00 -3.68 93.07 -7.76 54.62

  7 0.700 10.79 224.80 4.35 137.82 0.00 0.00 -4.74 52.91

  8 0.500 19.73 208.14 11.36 123.56 5.86 80.88 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.94, KaR / YaR = 1.23 The results of the computation of the rate of variation of Ka with respect to Ya for the set focused at infinity and the set focused at the nearest location, at the wide-angle end, in the middle position and at the telephoto end in the example of Japanese Patent Application Laid-open No. 5-142475 and in the fourteenth example of the invention are as follows. Example of Japanese Patent Application Laid-open No. 5-142475 At Infinity Ka0yaoLe Closest KaR / YaR Wide-angle (F = 36.0) 2.75 0, 44 Median position (F = 50.0 ) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Fourteenth example At infinity Ka0 / yaOf closest KaR / YaR Wide-angle (F = 29.0) 0.75 1, 36 Median position (F = 50.0) 0, 78 1.33 Telephoto (F = 102.0) 0.94 1.23 As previously described, in the fourteenth example, as the rate of variation of Ka with respect to Ya is weak compared to the classical system and as the contribution of the correction term (ABf / g) of the relation Ka = Ya (1 - ABf / p) can be reduced, an error on the conversion coefficient Ka calculated with Ya and y Or on

  the actual driving amplitude of the focal lens Aa

  can be eliminated when only a pair of values of the conversion coefficient Ya and the correction coefficient y are used for a given range of

  lens arrangement (for example, the range of

infinity).

  Next, in the example of Japanese Laid-open Patent Application No. 5-142475 and in the fourteenth example of the invention, when the lens drive amplitudes during focusing of the focused disposition to the infinity towards the object at the shortest distance and when focusing the focused disposition at the shortest distance to the object at infinity at the wide-angle end, in the middle position and at the end of telephoto, are calculated from the relation Aa = ABf / ya (1 - ABf / p) and the errors on the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the infinity focused disposition on the object at the shortest distance corresponds to the object distance value (POS-5), and that the value the correction coefficient y when focusing the focused disposition to the nearest distance on the object to

  infinity is the value at object distance (POS-4).

  Example of Japanese Patent Application Laid-open No. 5142475 Infinity Focused Most Nearest Focused Near Infinity Wide-angle (F = 36.0) -4.4% - 13.0% Position median (F = 50.0) -11.8% -12.0% Telephoto (F = 103.0) -12.6% -14.6% Fourteenth example Infinity focused state most Nearest near state Focused at infinity Wide-angle (F = 29.0) -1.3% -0.2% Median position (F = 50.0) -3.4% -0.1% Telephoto (F = 102.0) -1.2% -0.3% As described previously, in the fourteenth example, even when only a pair of values of the conversion coefficient Ya and the correction coefficient y are established for a given range of lens arrangement, a error between the conversion coefficient Ka calculated for ya and y and the focusing lens Aa drive amplitude becomes low compared to the conventional system and the focusing can be performed with precision

higher.

  Table 135 shows the focusing amplitude (ANGLE DA) during manual focusing using the focusing cam (middle part of

  Table 127) of the fourteenth example, the range of

  cement DX (mm) in the direction of the optical axis of the set of focusing lenses corresponding to the focus rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the direction of the optical axis is given. It should be noted that the arrangement of the table and the symbols are the same as in the thirteenth example. The upper part of table 135 indicates the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2, 0, 1.0, 0.7 and 0.5 m ) in the respective focusing states (F = 29, 0, 35.0, 50.0,, 0, 85.0 and 102.0 mm), and the middle part indicates the values of the rotation amplitude (ANGLE DA) necessary to obtain the focused state optimally at the respective photography distances. The lower part of the table shows the displacement amplitudes (DX) in the direction of the optical axis of the

  respective sets of lenses corresponding to the amplifier

  rotation study (ANGLE DA) for focusing at the respective focal lengths and respective distances

of photography.

Table 135

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the fourteenth example 0,50m 0,70 m 1,00 m 2,00 m 3,00 m 5,00 m 29,000 Bf 0,000 0,000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,000 0,000 0,000 0,000 0,000, 000 Bf 0,000 -0,001 -0, 003 -0,002 -0,001 -0,001, 000 Bf 0,000 -0,003 0.001 0.005 0.004 0.002, 000 Bf 0.000 -0.003 0.003 0, 000 - 0.001 -0.001 102.000 Bf 0.000 0.000 0.000 0.000 0.000 0.000

  ANGLE DA -9,500 -5,710 -3,585 -1,604 -1,034 -0,604

  F 29,000 DX 0,000 1,477 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,711 0,000 0,000 R 0,50 m F 50,000 DX 0,000 2,290 0,000 0,000 R 0,50 m F 70,000 DX 0,000 3,076 0,000 0,000 R 0,50 m F 85,000 DX 0,000 3,690 0,000 0,000 R 0,50 m F 102,000 DX 0,000 4,421 0,000 0,000 R 0,50 m F 29,000 DX 0,000 1,021 0,000 0,000 R 0.70 m F 35,000 DX 0,000 1,190 0,000 0,000 R 0.70 m F 50,000 DX 0,000 1,618 0,000 0,000 R 0,70 m F 70,000 DX 0,000 2,219 0,000 0,000 R 0,70 m F 85,000 DX 0,000 2,705 0,000 0,000 R 0,70 m F 102,000 DX 0,000 3,298 0,000 0,000 R 0.70 m F 29,000 DX 0,000 0,698 0,000 0.000 R 1.00 m F 35.000 DX 0.000 0.818 0.000 0.000 R 1.00 m F 50.000 DX 0.000 1.127 0.000 0.000 R 1.00 m F 70.000 DX 0.000 1.571 0.000 0.000 R 1.00 m F 85,000 DX 0.000 1,941 0,000 0,000 R 1,00 m F 102,000 DX 0,000 2,408 0,000 0,000 R 1,00 m 3 0 F 29,000 DX 0,000 0,340 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,401 0,000 0,000 R 2,00 m F 50,000 DX 0,000 0,562 0,000 0,000 R 2,00 m F 70,000 DX 0,000 0,798 0,000 0,000 R 2,00 m F 8 5,000 DX 0,000 1,007 0,000 0,000 R 2,00 m F 102,000 DX 0,000 1,281 0,000 0,000 R 2,00 m F 29,000 DX 0,000 0,225 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,266 0,000 0,000 R 3,00 m F 50,000 DX 0.000 0.374 0.000 0.000 R 3.00 m F 70.000 DX 0.000 0.536 0.000 0.000 R 3.00 m F 85.000 DX 0.000 0.682 0.000 0.000 R 3.00 m F 102.000 DX 0.000 0.875 0.000 0.000 R 3.00 m F 29,000 DX 0.000 0.134 0,000 0,000 R 5,00 m F 35,000 DX 0, 000 0,159 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,224 0, 000 0,000 R 5,00 m F 70,000 DX 0,000 0,324 0,000 0,000 R 5,00 m F 85,000 DX 0.000 0.414 0.000 0.000 R 5.00 m F 102.000 DX 0.000 0.537 0.000 0.000 R 5.00 m As shown in Table 135, in the zoom lens of the fourteenth example, a so-called "manual" focusing can be achieved because the amplitudes of displacement of the image point at respective focal distances and respective photography distances are very small and enter the depth of field regardless of the state of

  focus and distance photography.

  Fifteenth Embodiment The fifteenth embodiment or fifteenth example relates to a zoom lens having a four-array arrangement, i.e. positive, negative, positive and positive lens assemblies, with focus using second set of negative type lenses. In this zoom lens, the ratio (aF / az) of the focusing rotation amplitude of the position focused at infinity to the position focused at the closest distance (R = 0.5 m) and from the amplitude of rotation of focal length variation of the wide-angle end (F = 28.8 mm) to

  the telephoto end (F = 82.5 mm) is equal to -0.9.

  Table 136 shows various paraxial data of an optical system and data for determining the configuration of a focusing cam of the fifteenth example. The upper part of table 136 gives the focal lengths and intervals of the main points of the respective lens assemblies of the optical system of the fifteenth example, for six focusing states (distances

  focal length F = 28.8, 35.0, 50.0, 60.0, 70.0 and 82.5 mm).

  The middle portion of table 136 shows spline sample data when the focus cam configuration of the second lens set of the fifteenth example, used for focusing, is expressed by a spline function associated with the angle a of rotation of a rotating barrel and the amplitude x of displacement in the

direction of the optical axis.

  In addition, the lower part of table 136 indicates the infinite focusing positions (positions corresponding to infinity) at the respective focal lengths (F = 28.8, 35.0, 50.0, 60.0, 70 , 0 and 82.5 mm) and the magnitudes of rotation (for focusing) when focusing at the respective photographing distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m) using the focusing cam of the fifteenth example. In this table, as the zoom range of focal length variation of the wide-angle end (F = 28.8 mm) at the telephoto end (F = 82.5 mm) is equal to 10.0 and the focus rotation amplitude of the infinitely focused position at the focused position at the nearest location (R = 0.5 m) is -9.0, the ratio (aF / az) zoom magnitudes of focus and variation of

  focal lengths of the fifteenth example is equal to -0.90.

Table 136

  Fifteenth example f = 28.8 to 82.5 (ratio of amplitudes of rotation: aF / az = -0.9) Focal distances and intervals of the main points of the objectives of the fifteenth example

  F 28.8000 35.0000 50.0000 60.0000 70.0000 82.5000

  F1 74.0345 D1 9.2069 13.4025 20.8711 24.7305 27.9387 31.2269

  F2 -14.6500 D2 19.6762 17.1764 13.3033 11.5956 10.2135 8.7449

  F3 38.9970 D3 18.6590 17.9190 16.7790 16.3000 15.9999 15.7889

  F4 51.0000 D4 51.6857 55.8574 63.7033 67.4419 70.3975 73.3520

  Focusing cam shape (spline interpolated point) corresponding to the fifteenth example

ANGLE (1) (2) (3) (4)

  1 -11.0000 0.0000 1.2800 0.0000 0.0000

  2 -10.0000 0.0000 1.2062 0.0000 0.0000

  3 -9.0000 0.0000 1.1246 0.0000 0.0000

  4 -5.4641 0.0000 0.7797 0.0000 0, 0000

-3,4495 0.0000 0.5344 0.0000 0.0000

  6 -1.5517 0.0000 0.2611 0.0000 0.0000

  7 -1.0015 0.0000 0.1727 0.0000 0.0000

  8 -0.5861 0.0000 0.1030 0.0000 0.0000

  2 0 9 0.0000 0.0000 0.0000 0, 0000 0.0000

1.0000 0.0000 -0.1894 0.0000 0.0000

  1 1 4.5359 0.0000 -1.0442 0.0000 0.0000

  12 6.5505 0.0000 -1.7196 0.0000 0.0000

  13 8.4483 0.0000 -2.5669 0.0000 0.0000

  2 5 14 8.9985 0.0000 -2.8691 0, 0000 0.0000

9,4139 0,0000 -3,1200 0.0000 0.0000

  16 10.0000 0.0000 -3.5146 0.0000 0.0000

  17 11.0000 0.0000 -4.2900 0.0000 0.0000

  Amplitude of rotation for focal length change and rotation amplitude for focussing the fifteenth example (ratio of rotation amplitudes: aF / az = -0.9) Focal length Corresponding position Distance from rotation amplitude to infinity for focusing 28.8 mm 0.0000 5.00 m -0.586, 0 mm 1.9432 3.00 m -1.002 3 5 50.0 mm 5.4278 2.00 m -1.552, 0 mm 7.2013 1, 00 m -3,449, 0 mm 8,6217 0,70 m -5,464 82,5 mm 10,0000 0,50 m -9,000 Condition corresponding to value (9) 1,25 Condition corresponding to value (10) 2,96 Condition corresponding to value (11) -0.90 Condition corresponding to value (12) 0.49 (wide-angle) 0.35 (telephoto) Condition corresponding to value (13) 0.76 (wide-angle) 0.84 ( telephoto) Condition corresponding to value (14) 1.34 (wide-angle) 1.28 (telephoto) Table 137 which follows shows numerical values of the cams of the focus lens assembly of the fifteenth example, the data being calculatedby interpolation with a spline function by using the sample data of the focusing cam of the middle part of table 136. It should be noted that the meanings of the symbols of table 137 are the same

than in the thirteenth example.

Table 137

  Digital Cam Values for the Focusing Lens of the Fifteenth Example Focusing Cam Digital Values Focal Length Variation Compensation Cam Numerals

ANGLE (2) F ANGLE (2) F

-9.0000 1.1246 0.0000

-8.5000 1.0813 0.0000

-8.0000 1.0363 0.0000

-7.5000 0.9896 0.0000

-7.0000 0.9412 0.0000

-6.5000 0.8908 0.0000

-6.0000 0.8383 0.0000

-5.5000 0.7837 0.0000

-5.0000 0.7268 0.0000

-4.5000 0.6675 0.0000

-4.0000 0.6056 0.0000

-3,5000 0,5411 0,0000

-3.0000 0.4737 0.0000

-2.5000 0.4034 0.0000

-2.0000 0.3298 0.0000

-1.5000 0.2529 0.0000

-1.0000 0.1725 0.0000

-0.5000 0.0883 0.0000

  0.0000 0.0000 28.8000 0.0000 0.0000 28.8000

  0.5000 -0.0924 30.2861 0.5000 0.3088 30.2861

  1.0000 -0.1894 31.8415 1.0000 0.6313 31.8415

  1,5000 -0,2912 33,4752 1,5000 0,9786 33,4752

  2.0000 -0.3984 35.2011 2.0000 1.3639 35.2011

  2,5000 -0,5115 37,0318 2,5000 1,7986 37,0318

  3 0 3,0000 -0,6310 38,9731 3,0000 2,2818 38,9731

  3.5000 -0.7575 41.0275 3.5000 2.8083 41.0275

  4.0000 -0.8916 43.1956 4.0000 3.3705 43.1956

  4.5000 -1.0337 45.4747 4.5000 3.9590 45.4747

  , 0000 -1.1845 47.8633 5.0000 4.5632 47.8633

  5,5000 -1,3451 50,3698 5,5000 5,1742 50,3698

  6,0000 -1,5166 53,0072 6,0000 5,7872 53,0072

  6.5000 -1.7003 55.7941 6.5000 6.4064 55.7941

  7.0000 -1.8976 58.7520 7.0000 7.0380 58.7520

  7.5000 -2.1106 61.9210 7.5000 7.6908 61.9210

  8.0000 -2.3419 65.3422 8.0000 8.3695 65.3422

  8.5000 -2.5939 69.0503 8.5000 9.0736 69.0503

  9.0000 -2.8699 73.0903 9.0000 9.8041 73.0903

  9,5000 -3,1747 77,5414 9,5000 10,5690 77,5414

  , 0000 -3,5146 82,5000 10,0000 11,3794 82,5000

  The left side of table 137 indicates the numerical values of the focusing cam and the right part those of the zoom compensation cam in this fifteenth example. A value obtained by synthesis of the displacement amplitudes (2) in the direction of the optical axis, taken from the numerical values of the focusing cam and the compensating cam, in the rotation range (ANGLE = 0,0) and (ANGLE = 10.0), coincides with the displacement location of the second set of lenses calculated using paraxial data from the upper portion of Table 136. Tables 138, 139 and 140 that follow indicate the range of motion DX (mm) of focusing, in the direction of the optical axis, of the set of focusing lenses, the magnifications Px of imaging the respective sets of lenses, the conversion coefficient yx associated with the direction of the optical axis, the slope (dx / da) of the focusing cam, and the coefficient

  of conversion there associated with the rotation at the far end-

  angle (F = 28.8 mm), in the middle position (F = 50.0 mm) and at the telephoto end (F = 82.5 mm) in the fifteenth example. The provisions of the respective tables and the meanings of the symbols are the same as in the

thirteenth example.

Table 138

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the wide-angle end (28.8 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 0.051 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) 0,103 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 0,173 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 0,261 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 0,534 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 0.780 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.125 3) 0.000 4) 0.000

  Objective image magnification Pk at the wide-angle end (28.8 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,292 3) 99,097 4) -0,013

  R 10,000 ANG -0.288 1) -0.008 2) -0.288 3) 99.097 4) -0.013

  R 5,000 ANG -0,586 1) -0,015 2) -0,285 3) 99,097 4) -0,013

  R 3,000 ANG -1,002 1) -0,026 2) -0,280 3) 99,097 4) -0,013

  R 2,000 ANG -1,552 1) -0,041 2) -0,274 3) 99,097 4) -0,013

  R 1,000 ANG -3,449 1) -0,090 2) -0,255 3) 99,097 4) -0,013

  R 0.700 ANG -5.464 1) -0.141 2) -0.239 3) 99.097 4) -0.013

  R 0.500 ANG -9.000 1) -0.227 2) -0.215 3) 99.097 4) -0.013

  Coefficient of conversion yx associated with the direction of the optical axis at the wide-angle end (28.8 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 1,624 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 1.628 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) 1,631 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 1,636 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 1,642 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 1,659 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 1.674 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.693 3) 0.000 4) 0.000

  Slope dxlda focusing cam at the wide-angle end (28.8 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,181 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.176 3) 0.000 4) 0.000

  R 5,000 ANG -0,586 1) 0,000 2) -0,171 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) -0,165 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -0,157 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,132 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.112 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.085 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the wide-angle end (28.8 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,293 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.286 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) -0.279 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) -0,269 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -0,257 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,220 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.187 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.144 3) 0.000 4) 0.000

  Condition corresponding to the values: yxR / yxO = 1.04, yaR / yao = 0.49

Table 139

* Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the median position (50.0 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) 0.093 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) 0,185 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) 0.309 3) 0.000 4) 0.000

  R 2,000 ANG -1,549 1) 0,000 2) 0,463 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) 0,927 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) 1.328 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 1.872 3) 0.000 4) 0.000

  Objective image magnification Pk at the median position (50.0 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,380 3) 7,128 4) -0,249

  R 10,000 ANG -0,287 1) -0,008 2) -0,374 3) 7,128 4) - 0,249

  R 5,000 ANG -0,585 1) -0,015 2) -0,368 3) 7,128 4) -0,249

  R 3,000 ANG -1,000 1) -0,026 2) -0,359 3) 7,128 4) -0,249

  R 2,000 ANG -1,549 1) -0,041 2) -0,349 3) 7,128 4) -0,249

  R 1,000 ANG -3,446 1) -0,091 2) -0,317 3) 7,128 4) -0, 249

  R 0.700 ANG -5.465 1) -0.145 2) -0.290 3) 7.128 4) - 0.249

  R 0.500 ANG -9.000 1) -0.238 2) -0.253 3) 7.128 4) -0.249

  Coefficient of conversion yx associated with the direction of the optical axis at the median position (50.0 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 2,696 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) 2.711 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) 2,726 3) 0,000 4) 0, 000 R 3,000 ANG -1,000 1) 0,000 2) 2,745 3) 0,000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) 2,769 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) 2,835 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) 2.888 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 2.951 3) 0.000 4) 0.000

  Slope dx / da of focus cam at the middle position (50.0 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,329 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) -0.317 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) -0,305 3) 0,000 4) 0,000

  R 3,000 ANG -1,000 1) 0,000 2) -0,290 3) 0,000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) -0,272 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) -0,220 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) -0.180 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.131 3) 0.000 4) 0.000

  Conversion coefficient associated with the direction of rotation at the middle position (50.0 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -0,886 3) 0,000 4) 0,000

  R 10,000 ANG -0.287 1) 0.000 2) -0.858 3) 0.000 4) 0.000

  R 5,000 ANG -0,585 1) 0,000 2) -0,831 3) 0,000 4) 0,000

  1'5 R 3,000 ANG -1,000 1) 0,000 2) -0,797 3) 0, 000 4) 0,000

  R 2,000 ANG -1,549 1) 0,000 2) -0,753 3) 0,000 4) 0,000

  R 1,000 ANG -3,446 1) 0,000 2) -0,623 3) 0,000 4) 0,000

  R 0.700 ANG -5.465 1) 0.000 2) -0.520 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) -0.387 3) 0.000 4) 0.000

  2 0 Condition corresponding to the values: YxR / yxo = 1.09, yaR / Yao = 0.44

Table 140

  Amplitude DX (mm) of focusing displacement in the direction of the optical axis at the telephoto end (82.5 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 0,000 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) 0.200 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) 0.395 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) 0,646 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 0,948 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 1,795 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 2.470 3) 0.000 4) 0.000

  R 0.500 ANG -9.000 1) 0.000 2) 3.325 3) 0.000 4) 0.000

  Lens magnification 1k at the telephoto end (82.5 mm) of the fifteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,520 3) 4,887 4) -0,438

  R 10,000 ANG -0.288 1) -0.008 2) -0.507 3) 4.887 4) - 0.438

  R 5,000 ANG -0,586 1) -0,015 2) -0,493 3) 4,887 4) -0,438

  R 3,000 ANG -1,002 1) -0,026 2) -0,476 3) 4,887 4) -0,438

  R 2,000 ANG -1,552 1) -0,041 2) -0,456 3) 4,887 4) -0,438

  R 1,000 ANG -3,449 1) -0,093 2) -0,398 3) 4,887 4) -0,438

  R 0.700 ANG -5.464 1) -0.149 2) -0.352 3) 4.887 4) - 0.438

  R 0.500 ANG -9.000 1) -0.249 2) -0.293 3) 4,887 4) -0,438

  Conversion coefficient Yx associated with the direction of the optical axis at the telephoto end (82.5 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) 3,346 3) 0,000 4) 0,000

  R 10,000 ANG -0,288 1) 0,000 2) 3,410 3) 0,000 4) 0,000

  R 5,000 ANG -0,586 1) 0,000 2) 3,471 3) 0,000 4) 0,000

  R 3,000 ANG -1,002 1) 0,000 2) 3,547 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) 3,635 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) 3,861 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) 4.020 3) 0.000 4) 0.000

  R 0.500 ANG -9.0001) 0.000 2) 4.193 3) 0.000 4) 0.000

  Slope dx / da focus cam at telephoto end (82.5 mm) of fifteenth

example

  R 0,000 ANG 0,000 1) 0,000 2) -0,721 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -0.673 3) 0.000 4) 0.000

  R 5,000 ANG -0.5861) 0.000 2) -0.630 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) -0,579 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -0,522 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -0,383 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -0.294 3) 0.000 4) 0.000

  R 0.500 ANG -9.0001) 0.000 2) -0.199 3) 0.000 4) 0.000

  Conversion coefficient Ya associated with the direction of rotation at the telephoto end (82.5 mm) of the fifteenth example

  R 0,000 ANG 0,000 1) 0,000 2) -2,412 3) 0,000 4) 0,000

  R 10,000 ANG -0.288 1) 0.000 2) -2.295 3) 0.000 4) 0.000

  R 5,000 ANG -0.586 1) 0.000 2) -2.187 3) 0.000 4) 0.000

  R 3,000 ANG -1,002 1) 0,000 2) -2,053 3) 0,000 4) 0,000

  R 2,000 ANG -1,552 1) 0,000 2) -1,897 3) 0,000 4) 0,000

  R 1,000 ANG -3,449 1) 0,000 2) -1,479 3) 0,000 4) 0,000

  R 0.700 ANG -5.464 1) 0.000 2) -1.181 3) 0.000 4) 0.000

  R 0.500 ANG -9.0001) 0.000 2) -0.833 3) 0.000 4) 0.000

  Condition corresponding to the values: YxR / YxO = 1.25, yaR / YaO = 0.35 As indicated in tables 138, 139 and 140, for each focal length, the conversion coefficient yx associated with the direction of the axis Optics increases, but the slope (dx / da) of the focus cam decreases as the distance of photography approaches the shortest distance. Consequently, as indicated in these tables, the conversion coefficient Ya associated with the rotation, defined as being the product of the conversion coefficient yx and the slope (dx / da) of the focusing cam, decreases when the distance of photography is approaching the shortest distance because of the slope (dx / da) of the focusing cam. In tables 138, 139, and 140, the rate of change from the infinite focus position to the shortest distance focus position of the conversion coefficient Ya associated with the rotation is x0.49 for the large end. angle (F = 28.8 mm), x0.44 for the middle position (F = 50.0 mm), and x0.35 at the telephoto end (F = 82.5 mm). When the number N of divisions

  the focus range when changing the coeffi-

  Ya conversion example of the fifteenth example is calculated with the formula (a) and is compared with that of the example of the Japanese patent application laid to public inspection

  5-142475, the numbers Nw, NM and NT of divisions at the

  wide-angle, mid-position and telephoto end have the following values: example of Japanese Patent Application Laid-open No. 5-142475 Nw> 9.3 NM> 10.1 NT> 8 Example 15, Nw> 3.9 NM> 4.5 NT> 5.8 As described previously, in the fifteenth example, as the rate of change of the conversion coefficient Ya associated with the rotation is lower than that of the conventional system, the values of the numbers M of divisions are small. For this reason, the number of data of the conversion coefficient γ and the correction coefficient γ can be reduced and the storage capacity can be suppressed. Tables 141, 142 and 143 give the results of the calculation of the conversion coefficient Ka and the correction coefficient y at the wide-angle end (F = 28.8 mm), in

  median position (F = 50.0 mm) and at the end of

  objective (F = 82.5 mm) in the fifteenth example. The provisions of the tables and the reference symbols are the same as for the thirteenth example. The position of the focusing lens in the first pair of parts

  of each of Tables 141, 142 and 143, that is,

  say in the third and fourth column, is (R, ANGLE) = (O, O; O, O) and indicates that the position corresponds

  to infinity. Similarly, the position of the focal lens

  the fourth pair of the two lower parts of each of Tables 141, 142, and 143, that is, in the ninth and tenth columns, is (R, ANGLE) = (O, 5; -9, O ), and indicates that this position corresponds to the position of

  focusing at the shortest distance (R = 0.5 m).

Table 141

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (0) at the wide-angle end (28.8 mm) of the fifteenth example f = 28.8 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,288 5,000 -0,586 3,000 - 1,002

POS R rs r rs r rs

  1 0.000 -0.293 0.000 -0.289 -0.284 -0, 278

  2 10,000 -0.291 -0.286 0.000 -0.282 -0, 276

  3 5,000 -0,288 -0,284 -0,279 0,000 -0, 273

  4 3,000 -0.284 -0.280 -0.275 -0.269 0, 000

2,000 -0,279 -0,275 -0,271 -0,265

  6 1,000 -0,263 -0,259 -0,255 -0, 249

  7 0.700 -0.247 -0.243 -0.239 -0, 234

  8 0.500 -0.223 -0.219 -0.215 -0, 210

POS R bf i bf I bf t bf i

  1 0,000 0.00 0.00 -0.08 9.15 -0.17 8.80 -0.28 8, 47

  2 10,000 0.08 9.51 0.00 0.00 -0.08 8.68 -0.20 8, 41

  3 5,000 0.17 9.35 0.08 9.00 0.00 0.00 -0.11 8, 37

  4 3,000 0.28 9.21 0.20 8.88 0.11 8.63 0.00 0.00

  5 2,000 0.43 9.09 0.35 8.81 0.26 8.59 0.15 8.35

  6 1,000 0.91 8.84 0.82 8.60 0.73 8.40 0.61 8, 14

  7 0.700 1.35 8.63 1.26 8.41 1.17 8.22 1.04 7.96

  8 0.500 2.01 8.34 1.91 8.14 1.81 7.96 1.68 7, 71

  (R, ANGLE) = 2,000 -1,552 1,000 -3,449 0,700 -5,464 0,500 -9,000

2 5 POS R rs r rs r rs

  1 0.000 -0.270 -0.246 -0.224 -0, 194

  2 10,000 -0.268 -0.244 -0.222 -0, 192

  3 5,000 -0,265 -0,241 -0,220 -0, 190

  4 3,000 -0.262 -2.238 -0.217 -0, 187

  5 2,000 -0,257 0,000 -0,234 -0,213 -0,184

  6 1,000 -0,242 -0,220 0,000 -0,200 -0, 172

  7 0.700 -0.227 -0.206 -0.187 0.000 -0, 161

  8 0.500 -0.204 -0.185 -0.168 -0.144 0.000

POS R bf t bf t bf f bf I

  1 0.000 -0.42 8.13 -0.85 7.08 -1.23 6.16 -1.74 5, 09

  2 10,000 -0.34 8.09 -0.77 7.05 -1.15 6.14 -1.67 5.07

  3 5,000 -0.26 6.06 -0.69 7.03 -1.07 6.12 -1.60 5, 06

  4 3,000 -0.14 8.01 -0.58 6.99 -0.97 6.09 -1.50 5, 04

  2,000 0.00 0.00 -0.44 6.95 -0.83 6.05 -1.37 5.02

  6 1,000 0.46 7.80 0.00 0.00 -0.40 5.92 -0.95 4, 97

  7 0.700 0.89 7.64 0.42 6.67 0.00 0.00 -0.57 4, 95

  8 0.500 1.52 7.40 1.03 6.48 0.59 5.73 0.00 0.00

  Condition corresponding to the values: KaO / yao = 0.76, KaR / YaR 1.34

Table 142

  Coefficients of conversion Ka: (rs), a: (r) associated with direction of rotation and coefficient of correctness p: (i) at the median position (50.0 mm) of the fifteenth example f = 50.0 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,287 5,000 -0,585 3,000 - 1,000

POS R rs r rs r rs

  I 0.000 -0.886 0.000 -0.865 -0.845 -0.819

  2 10,000 -0.879 -0.858 0.000 -0.838 -0, 812

  3 5,000 -0.871 -0.851 -0.831 0.000 -0, 806

  4 3,000 -0.861 -0.841 -0.822 -0.797 0, 000

2,000 -0,849 -0,829 -0,810 -0,785

  6 1,000 -0.805 -0.786 -0.767 -0, 742

  7 0.700 -0.760 -0.742 -0.724 -0, 701

  8 0.500 -0.691 -0.675 -0.658 -0.636

POS R bf i bf f bf! bf

  1 0.000 0.00 0.00 -0.25 29.47 -0.49 29.29 -0.82 29, 15

  2 10,000 0.25 31.02 0.00 0.00 -0.25 29.14 -0.58 29, 34

  3 5,000 0.51 31.03 0.25 30.84 0.00 0.00 -0.33 29, 63

  4 3,000 0.86 31.18 0.60 30.80 0.34 30.69 0.00 0.00

  2 0 5 2,000 1.31 31.32 1.05 30.84 0.78 30.37 0.43 28.79

  6 1,000 2.77 30.24 2.48 29.39 2.19 28.44 1.82 26, 75

  7 0.700 4.15 29.31 3.84 28.41 3.53 27.46 3.13 25.98

  8 0.500 6.22 28.35 5.88 27.48 5.54 26.58 5.09 25.30

  (R, ANGLE) = 2,000 -1,549 1,000 -3,446 0,700 -5,465 0,500 -9,000

POS R rs r rs r rs

  1 0.000 -0.787 -0.692 -0.613 -0.511

  2 10,000 -0.780 -0.686 -0.608 -0, 507

  3 5,000 -0,774 -0,680 -0,602 -0, 502

  4 3,000 -0.765 -0.672 -0.594 -0, 495

  3 0 5 2,000 -0,753 0,000 -0,661 -0,584 -0,486

  6 1,000 -0,712 -0,623 0,000 -0,551 -0,458

  7 0.700 -0.672 -0.587 -0.520 0.00 -0.431

  8 0.500 -0.610 -0.532 -0.469 -0.387 0, 000

POS R bf f bf f bf f bf I

  1 0.000 -1.22 27.36 -2.38 21.42 -3.35 18.67 -4.60 14, 28

  2 10,000 -0.98 27.31 -2.17 21.28 -3.15 18.61 -4.41 14, 24

  3 5,000 -0.75 27.16 -1.95 21.11 -2.94 18.55 -4.22 14, 19

  4 3,000 -0.42 26.62 -1.64 20.87 -2.65 18.49 -3.96 14, 13

  2,000 0.00 0.00 -1.25 20.60 -2.29 18.44 -3.62 14.05

  6 1,000 1.35 24.66 0.00 0.00 -1.11 18.64 -2.54 13, 79

  7 0.700 2.63 24.24 1.19 20.85 0.00 0.00 -1.52 13, 38

  8 0.500 4.54 23.79 2.96 20.35 1.66 17.10 0.00 0.00

  Condition corresponding to the values: Kao / yao = 0.78, KaR / 7aR = 1.32

Table 143

  Conversion coefficients Ka: (rs), Ya: (r) associated with direction of rotation and correction coefficient p: (i) at the telephoto end (82.5 mm) of the fifteenth example f = 82.5 mm

  (R, ANGLE) = 0,000 0,000 10,000 -0,288 5,000 -0,586 3,000 -1,002

POS R rs r rs r rs

  1 0.000 -2.412 0.000 -2.309 -2.213 -2.095

  2 10,000 -2,397 -2,294 0,000 -2,199 -2, 082

  3 5,000 -2,383 -2,281 -2,187 0,000 -2,071

  4 3,000 -2,365 -2,265 -2,171 -2,053 0, 000

2,000 -2,342 -2,241 -2,148 -2,031

  6 1,000 -2,260 -2,161 -2,068 -1, 952

  7 0.700 -2.174 -2.076 -1.984 -1, 871

  8 0.500 -2.028 -1.933 -1.844 -1.735

  POS R bf t bf t bf t bf t i 0.000 0.00 0.00 -0.66 104.19 -1.30 110.19 -2.10 103.72

  2 10,000 0.69 116.11 0.00 0.00 -0.66 116.02 -1.49 104.84

  3 5,000 1.40 118.30 0.68 120.80 0.00 0.00 -0.86 102.04

  4 3,000 2.37 123.78 1.62 124.87 0.90 121.43 0.00 0.00

  5 2,000 3.63 125.80 2.83 123.14 2.07 115.24 1.12 101.24

  6 1,000 7.80 124.25 6.83 117.48 5.92 108.64 4.78 97.17

  7 0.700 11.88 120.59 10.75 112.93 9.68 104.43 8.35 93.95

  8 0.500 18.25 114.66 16.84 106.84 15.52 98.97 13.88 89.49

  (R, ANGLE) = 2,000 -1,552 1,000 -3,449 0,700 -5,464 0,500 -9,000

2 5 POS R rs r rs r rs

  1 0.000 -1.959 -1.608 -1.357 -1, 069

  2 10,000 -1.947 -1.597 -1.347 -1, 061

  3 5,000 -1,935 -1,586 -1,337 -1, 052

  4 3,000 -1,918 -1,570 -1,323 -1,040

  3 0 5 2,000 -1,897 0,000 -1,550 -1,304 -1,024

  6 1,000 1,820 -1,479 0,000 -1,242 -0,972

  7 0.700 1.741 -1.411 -1.181 0.000 -0.919

  8 0.500 -1.610 -1.297 -1.079 -0.833 0.000

POS R bf t bf t bf f bf

  1 0.000 -3.04 93.12 -5.55 63.97 -7.41 49.97 -9.62 33.87

  2 10,000 -2.46 93.42 -5.05 63.62 -6.97 49.80 -9.24 33.74

  3 5,000 -1.87 92.87 -4.54 63.14 -6.52 49.61 -8.85 33.59

  4 3,000 -1.06 93.77 -3.84 62.52 -5.90 49.36 -8.32 33.40

  2,000 0.00 0.00 -2.94 61.62 -5.10 49.08 -7.63 33.15

  4 0 6 1,000 3.45 84.94 0.00 0.00 -2.50 48.54 -5.39 32.28

  7 0.700 6.81 82.87 2.84 61.63 0.00 0.00 -3.25 31.19

  8 0.500 11.99 79.43 7.20 58.36 3.82 44.10 0.00 0.00

  Condition corresponding to the values: Kao / Tao = 0.84, KaR / YaR = 1.28 The results of the calculations of the speed of variation of Ka with respect to Ya for the set focused at infinity and

  the whole focused at the shortest distance to the extreme

  at the wide-angle, in the middle position and at the telephoto end in the example of Japanese Patent Application Laid-open No. 5-142475 and in the fifteenth

  Examples of the present invention are as follows.

  Example of Japanese Patent Application Laid-Open No. 5142475 At Infinity KaO / yaO Closest KaR / YaR Wide Angle (F = 36.0) 2.75 0.44 Median Position (F = 50, 0) 3.36 0.43 Telephoto (F = 103.0) 3.80 0.43 Fifteenth example At infinity Ka / yaO Nearest KaR / YaR Wide angle (F = 28.8) 0.76 1.34 Median position (F = 50, 0) 0.78 1.32 Telephoto (F = 82.5) 0.84 1.28 As previously described, in the fifteenth example, as the rate of change of Ka over at Ya is weak compared to the classical system, the contribution of the correction term (ABf / g) in the relation Ka = ya (1 - ABf /) can be reduced. For this reason, an error of the conversion coefficient Ka calculated as a function of Ya and y or an error with respect to the actual driving amplitude of lenses Aa obtained when using a single pair of values of the coefficient of Ya conversion

  and the correction coefficient y can be reduced.

  In the example of Japanese Patent Application Laid-open No. 5-142475 and in the fifteenth

  example of the invention, when the amplitudes of

  lens when focusing the infinity focused disposition on the object at the shortest distance and when focusing the focused disposition at the shortest distance on the object at infinity, at the wide-angle end, in the middle position and at the telephoto end, are calculated from the relation Aa = ABf / ya (1-ABf / u) and the errors with respect to the actual lens drive amplitudes are then calculated, the following values are obtained. It should be noted that the value of the correction coefficient y when focusing the disposition focused to infinity on

  the object at the shortest distance takes on a corresponding value.

  spawning at the object distance (POS-5), and that the value of the correction coefficient y when focusing with the focused disposition at the shortest distance on the object at infinity takes the value corresponding to the object distance

(POS-4).

  Example of Japanese Patent Application Laid-Open No. 5142475 Infinity Focused Most Nearest-Near-Focused-Infinity Wide-angle (F = 36.0) -4.4% -13.0% Midpoint (F = 50.0) -11, 8% -12.0% Telephoto (F = 103.0) -12.6% -14, 6% Fifteenth example Infinity Focused Most Nearest Focused at infinity Wide-angle (F = 28.8) -2.1% -0.2% Median position (F = 50.0) -2.7% -0.4% Telephoto (F = 82.50) - 1.7% -0.4% As described previously, in the fifteenth example, even when only a pair of values of the conversion coefficient Ya and the correction coefficient are given for a given range of the arrangement of the lenses, a error between the conversion coefficient Ka calculated from Ya and y and the driving amplitude of the lenses Aa for the focusing becomes small compared with the conventional assembly and the focusing can be realized

with increased precision.

  Table 144 shows the rotation amplitude (ANGLE DA) of "manual" focusing with the focusing cam (middle portion of table 136) of the fifteenth

  for example, the displacement amplitude DX (mm) in the direc-

  of the optical axis of the set of focusing lenses corresponding to the focusing rotation amplitude, and the displacement amplitude Bf (mm) of the image point when the displacement amplitude (DX) in the

* Direction of the optical axis is given.

  It should be noted that the arrangement of the table and the reference symbols are the same as in the thirteenth example. The upper portion of Table 144 indicates the range of motion (Bf) of the image point corresponding to the photography distances (R = 5.0, 3.0, 2.0, 1.0, 0.7 and 0.5 m ) in the respective states of variation of the focal lengths (F = 28.8, 35.0, 50.0, 60.0, 70.0 and 82.5 mm), and the middle part indicates the values of the amplitude of rotation (ANGLE DA) for the focusing necessary to obtain the optimal focused state at the respective photography distances. The lower part indicates the magnitudes of displacement (DX) in the direction of the optical axis of the respective sets of lenses corresponding to the rotation amplitude (ANGLE DA) for the focusing with the focal lengths and distances of

photograph that are indicated.

Table 144

  Displacement amplitude Bf (mm) of image point and amplitude DX (mm) of displacement for focusing of the fifteenth example 0.50 m 0.70 m 1.00 m 2.00 m 3.00 m 5.00 m 28.800 Bf 0.000 0,000 0,000 0,000 0,000 0,000, 000 Bf 0,000 0,000 0.001 0.001 0.001 0.001, 000 Bf 0.000 0.000 -0.002 -0.002 -0.001 -0.001, 000 Bf 0.000 -0.002 -0.002 -0.001 0.000 0.000, 000 Bf 0.000 -0.004 - 0.001 -0.003 - 0.003 -0.002 82.500 Bf 0.000 0.000 0, 000 0.000 0.000 0.000

  ANGLE DA -9,000 -5,464 -3,449 -1,552 -1,002 -0,586

  F 28,800 DX 0,000 1,125 0,000 0,000 R 0,50 m F 35,000 DX 0,000 1,333 0,000 0,000 R 0,50 m F 50,000 DX 0,000 1,872 0,000 0,000 R 0,50 m F 60,000 DX 0,000 2,281 0,000 0,000 R 0 50m F 70,000 DX 0,000 2,726 0,000 0,000 R 0,50 m F 82,500 DX 0,000 3,325 0,000 0,000 R 0,50 m F 28,800 DX 0,000 0,780 0,000 0,000 R 0,70 m F 35,000 DX 0,000 0,930 0,000 0,000 R 0.70 m F 50,000 DX 0,000 1,328 0,000 0,000 R 0,70 m F 60,000 DX 0,000 1,640 0,000 0,000 R 0,70 m F 70,000 DX 0,000 1,989 0,000 0,000 R 0.70 m F 82,500 DX 0,000 2,470 0,000 0,000 R 0 70 m F 28,800 DX 0,000 0,534 0,000 0,000 R 1,00 m F 35,000 DX 0,000 0,640 0,000 0,000 R 1,00 m F 50,000 DX 0,000 0,928 0,000 0,000 R 1,00 m F 60,000 DX 0,000 1,157 0,000 0,000 R 1,00 m F 70,000 DX 0,000 1,420 0,000 0,000 R 1,00 m F 82,500 DX 0,000 1,795 0,000 0,000 R 1,00 m F 28,800 DX 0,000 0,261 0,000 0,000 R 2,00 m F 35,000 DX 0,000 0,314 0,000 0,000 R 2,00 m F 50,000 DX 0.000 0, 464 0.000 0.000 R 2.00 m F 60,000 DX 0.000 0.586 0.000 0.000 R 2.00 m F 70, 000 DX 0.000 0.732 0.000 0.000 R 2.00 m F 82,500 DX 0,000 0,948 0,000 0,000 R 2,00 m F 28,800 DX 0,000 0,173 0,000 0,000 R 3,00 m F 35,000 DX 0,000 0,208 0,000 0,000 R 3,00 m F 50,000 DX 0.000 0.309 0.000 0.000 R 3.00 m F 60.000 DX 0.000 0.393 0.000 0.000 R 3.00 m F 70,000 DX 0.000 0.494 0.000 0.000 R 3.00 m F 82,500 DX 0,000 0,646 0,000 0,000 R 3,00 m F 28,800 DX 0,000 0,103 0,000 0,000 R 5,00 m F 35,000 DX 0,000 0,124 0,000 0,000 R 5,00 m F 50,000 DX 0,000 0,185 0,000 0,000 R 5,00 m F 60,000 DX 0,000 0, 237 0,000 0,000 R 5,00 m F 70,000 DX 0,000 0 , 300 0.000 0.000 R 5.00 m F 82.500 DX 0.000 0.395 0.000 0.000 R 5.00 m As shown in Table 144, in the zoom lens of the fifteenth example, the so-called "manual" focusing can be achieved since the amplitudes of moving the image point for the respective focal lengths and the respective photography distances are very small and enter the depth of field regardless of the state

  focusing and photography distance.

  As described previously in the examples, the invention can be applied to zoom lenses having various arrangements of lens assemblies or various

  sets of focusing lenses.

  As described above, according to the invention, in a zoom lens of the internal focusing type which is mounted for example on a focusing camera

  automatic device having a focus detection device

  a storage device, a computing device and the like, the number of data of the particular coefficients (for example the conversion coefficient Ya and

  the correction coefficient y) necessary for the

  Automatic calibration can be reduced compared to the conventional system. Furthermore, an error in calculating the lens driving amplitude of the focusing lens assembly obtained with the particular stored coefficients corresponding to the detected focus defect amplitude can be reduced compared to the conventional system. In other words, when the arrangement according to the invention is adopted, as the speed of variation of the conversion coefficient Ya is reduced compared with the conventional system, the number of data of the conversion coefficient Ya, the correction coefficient y and which are stored for calculating the lens driving amplitude for focusing can be reduced, and a cost reduction can be realized on the ability to

storage.

  In addition, as the variation in the conversion coefficient

  Ka as a function of the conversion coefficient ya becomes low, the contribution of the correction term (ABf / g) in

  the relation Ka = Ya (1 - ABf / g) can be reduced.

  As a result, the error in the conversion coefficient

  Ka calculated from Ya and g or the error on the actual lens driving amplitude Aa obtained when using a single pair of values of the conversion coefficient Ya and the correction coefficient y, for a certain range of lens arrangements, can be reduced. According to the invention, the conversion coefficient Ya at the focusing point and the correction coefficient i which is defined by the formula Ka = Ya (1 - ABf / 1) are determined as specific coefficients. In a variant,

  a correction coefficient defined by a different formula

  annuity of the preceding formula can be established. In addition, the conversion coefficient Ya is not always set to a value that corresponds to the sensitivity (dBf / da) associated with the rotation at a focused point. As long as the focus accuracy can be increased, the sensitivity at a point other than the focused point and the corresponding correction coefficient can be set to values of

specific coefficients.

  It should be noted that the present invention may apply

  to various other zoom lens systems employing lens array arrangements and focusing lens assemblies other than those

previous examples.

359 2724023

Claims (8)

  A zoom lens system, wherein a moving location of a focus lens assembly is defined by synthesizing a focus cam and a zoom compensation cam by expressing a predetermined moving location.   for the variation of the focal length by an ampli-   displacement study, in a direction of an optimum axis   of lens assemblies (G1, G2, G3, G4, G5), and by an angle of rotation of a rotary lens barrel, characterized in that when a gear   (dBf / dx) of infinite displacement amplitude dBf   simal of an image plane and the amplitude dx of   infinitesimal in the direction of the optical axis   focusing lens set and a report   port (dBf / da) of the amplitude dBf of   of the image plane and an amplitude da of   infinitesimal placement in rotation of the set of focusing lenses on the focusing cam are respectively represented by Y., and Y0 for a   focus point to infinity and are represented   yxR and haR for the closest focused point, said zoom lenses fill the   next condition at least at the teleob-   jective; 1.0 <s / o and, when a ratio of an amplitude aF of rotation of the set of focusing lenses on the focusing cam, this amplitude corresponding to the focusing of a state focused to infinity to a state   focused at the closest distance, and an ampli-   az study of rotation corresponding to the change in focal length from a wide-angle end to a telephoto end is determined so that it corresponds to the relationship; -1.0 <aF / az <-0.7   then, said zoom lenses fulfill the   following edition at least at the wide-angle end and at the telephoto end: 0.3 <aR / YaO <0.7   2. The system of claim 1, wherein   in that, when conversion coefficients   Ka, which are expressed by the relation Ka = Bf / 4a a and are obtained when the set of lenses of   focus is placed with provisions of   which correspond to the state focused at infinity and the focused state at the shortest distance, are respectively represented by Kao and Kar, said lenses fulfilling the following conditions at least at the wide-angle end and at the telephoto end: 0.6 <Kao / yao <1.2 0.8 <KaR / yaR <1.7   Bf being the amplitude of defocusing between a position of the image of an object in arbitrary position   milking and a predetermined position of the image point, and da being the angle of rotation of the set of focusing lenses on the focusing cam necessary to obtain the focused state on the object. 3. A zoom lens system, wherein a locus of movement of a focus lens assembly is defined by synthesis of a focus cam and a zoom compensation cam.   to obtain a focused state with a substantially constant rotation amplitude for an identical distance from the object regardless of the focus state, by expression of a predetermined location.   of displacement for the variation of focal length   by a range of motion, in a direction   an optical axis, sets of lenses (G1,   G2, G3, G4, G5) and by a rotation angle of a   rotary rillet of lenses, characterized in that   ratios (dBf / dx) of a dBf amplitude of a movement   infinitesimal relationship of an image plane to an amplitude dx of infinitesimal motion, in the direction of   the optical axis, of the set of lenses of   focusing at the infinite point and at the location   the closest are respectively represented by Yxo and YxR, displacement amplitudes, in the   direction of the optical axis, of the lens assembly   the focus needed to focus   from an infinite position to the most   at the wide-angle end and at the telephoto end are respectively represented by   AxwR and AxTR, and an amplitude of rotation of the   seems to focus lenses on the focusing cam corresponding to the focal length variation of the wide-angle end at the end of   telephoto lens and a corresponding amplitude of rotation   when focusing from an infinitely focused state to a focused state at the nearest distance are respectively represented by az and aEF, said zoom lenses fulfill the following conditions at least at the telephoto end; 1.00 <xR / YxO <1.80 3.20 <xR / xR <4.50 -0.90 c aE / az <-0.70   4. System according to claim 3, characterized   rised in that, when the ratios (dBf / da) of the   dBf of infinitesimal displacement of the image plane   to the amplitude da of infinitesimal displacement, in   tation, of the lens set focusing on 362 2724023   the focusing cam at the point focused at infinity and at the nearest location are respectively   represented by Yao and aR, the said lenses   the following condition, at least at the   wide-angle tee and at the telephoto end: 0.25 <aR / ao <0.70   5. The system of claim 3, characterized   in that, when conversion coefficients   Ka, which are expressed by the relation K = 4Bf / 4a and are obtained when the set of focusing lenses has a disposition corresponding to the state   focused to infinity and the focused state at the location   the nearest, respectively, are shown   by KaO and KaR, said lenses fulfill the   following edition, at least at the wide-angle end and at the telephoto end: 0.60 <Kao / yao <1.20 0.80 <KaR / YaR <1.70 & Bf being the default amplitude of focusing between an image position of an object in an arbitrary position and a predetermined position of the image point, and ta being the angle of rotation of the focusing lens assembly on the focusing cam required   to obtain the focused state on the object.   6. System of zoom lenses, in which   when a place of displacement of a set of lenses   the focusing is defined by synthesis of a focusing cam and a zoom compensation cam to obtain a focused state with a magnitude   practically constant rotation for the same disc   object direction regardless of the focal length variation state, by expression of a predetermined displacement location for the focal length variation by an amplitude of displacement, in a direction of an optical axis, of the lens groups (G1, G2, G3, G4, G5) and by a rotation angle of a barrel 363 2724023   rotary lens system, characterized in that when   the ratios (dBf / dx) of a dBf amplitude of a displacement   infinitesimal cementation of an image plane at an amplitude dx of an infinitesimal displacement in the direction of the optical axis of the set of focal lenses at the point focused at infinity and at the nearest point are respectively represented by   Yxo and oxR, displacement amplitudes, in the direc-   optical axis, the set of focusing lenses necessary for focusing from infinity to a position at the smallest distance at the wide-angle end and at the telephoto end are respectively represented by AxVR and AxTR, and rotation amplitude of the assembly   of focusing lenses on the focusing cam   corresponding to the change in focal length   from the wide-angle end to the telephoto end   tif and an amplitude of rotation corresponding to the focusing of a state focused at infinity to a state   focused at the nearest location are respectively   represented by az and aF, said lenses   fulfill the following conditions at least in the ex-   telephoto end: 1.00 <YxR / Yxo <1.80 2.00 <AxTR / AxWR <3.20 -1.00 <aF / az <-0.80   7. The system of claim 6, characterized   in that, when the ratios (dBf / da) of the amplitude dBf of the infinitesimal displacement of the image plane to the amplitude da of infinitesimal displacement,   in rotation, of the set of focusing lenses   on the focusing cam at the focused point at   infinity and at the nearest location are   respectively represented by aO and ya, said lenses fulfill the following condition, at least   at the wide-angle end and at the tele-end target: 0.25 <aR / Yao <0.70   8. The system of claim 6, characterized   characterized in that, when Ka conversion coefficients, which are expressed by the relation Ka = 4Bf / 4a and are obtained when the set of focusing lenses has a disposition corresponding to the state   focused to infinity and the focused state at the location   the nearest, respectively, are shown   by Kao and KaR, said lenses fulfill the   at least at the wide-angle end and at the telephoto end: 0.60 <Kao / yao <1.20 0.80 <KaR / yaR <1.70 ABf being the magnitude of the focus defect between an image position of an object in an arbitrary position and a predetermined position of the image point, and a being the angle of rotation of the lens assembly   focusing on the focusing cam necessary to obtain the focused state on the object.